rx022[1]

Research Laboratoriesof the

Portland Cement Association

BULLETIN 22

Studies of the Physical Proper-ties of Hardened Portland

Cement Paste

BY

T. C. POWERS and T. L.

MARCH, 1948

CHICAGO

Authorizedreprint from copyrighted

.JOURNALOF THE &dERtCAN CONCREITE INSTITUTE

New Center Bldg., Detroit 2, MichiganOct. 1946-ApriI19=47,Proceedi?W8, Vol.43, 1947

Bulletins Published by theResearch Department

Research and Development Divisionof the


Bulletin I—’’Estimation of Phase Composition of Clinker in the System 3Ca0.SiOa-2Ca0. SiOz-3Ca0 ~Al, Og-4Ca0. AIzO,~FezO, at Clinkering Temper-atures,” by L. A. DAHL, May, 1939.

Reprinted from Rock Products, 41, No. 9, 48; No. 10, 48; No. 11, 42; No. 12, 44(1938) ; 42, No. 1, 68; No. 2, 46; No. 4, 50 (1939).

Bulletin 2—’’The Bleeding of Portland Cement Paste, Mortar and Concrete Treatedas a Special Case of Sedimentation, ” by ‘I’. C. POWERS; with an appendixby L. A. DAIIL; JLIly, 1939.

Bulletin 3—’’Rate of Sedimentation: I. Nonflocculated Suspensions of UniformSpheres; II. Suspensions of Uniform-Size Angular Particles III.Concentrated Flocculated Suspensions of Powders”; by HAROLTrH.STEINOUR,October, 1944.

Reprinted from Indwrtr{al and Engineering CJ,emidrv, 36, 018, 840, 901 (1944).

Bulletin 4—’’Further Studies of the Bleeding of Portland Cement Paste,” by HAROLDH. STEINOUR,December, 1945.

Bulletin 5—”A Working Hypothesis for Further Studies of Frost Resistance ofConcrete?” by ‘F. C. POWERS, February, 1945.

Reprinted from .Journal d the -4ma’ican6’oncrefe~nafihde(Felmmry, 1945);Pro-ceedings, 41, 245 (1945).

Bulletin 5A—Supplement to Bulletin 5; Discussion of the paper “A Working Hy-pothesis for Further Studies of Frost Resistance of Concrete, ” byT. C. POWERS; discussion by: RUTH D. TERZAGHJ,DOUGLASMCHENRY andH, W. BREWER, A. R. COLLINS, and Author; March, 1946.

Reprinted fro? .loumal of the American Concrete Institute Supplement (November,1945);Proccedwr.v, 41, 272-1 (1!245).

Bulletin 6—” Dynamic Testing of Pavements, ” by GERALD PrCKETT, April, 1945.Reprinted from Journal of the AmericanConcr;te Institute (April, 1945); Proceedinoa,41, 473 (1945).

Bulletin 7—’’Equations for Computing Elastic Constants from Flexural and Tor-sional Resonant Frequencies of Vibration of Prisms and Cylinders,”by GERALn PICKE~T, September, 1945.

Reprinted from I%oceedinfls,Am.rican Societv for Testinu Mat.riat., 45, 846 (1945);discumion, S64.

Bulletin 8—’’Flexural Vibration of Unrestrained Cylinders and Disks,” by GERALDPICKETT,December, 1945,

Reprinted from Journal ./ Applied Phv.,ica, 16, s20 (1945).

Bulletin 9—” Should Portland Cement Be Dispersed ?“ by T. C. POWERS, February,1946.

Reprinted from Journal of the American Concve[e Indilllle (November,1!143):Pro-ceedings, 42, 117 (1946).

Bulletin 10—”Interpretation of Phase Diagrams of Ternary Systems, ” bY L. A. l)ARL,March, 1946.

Reprintedfrom Journal of Phueicut Chemis&rr, 50, (I6 (1046).

—Continued on Inside Back Cover

Research Laboratories

of the


BULLETIN 22

Studies of the Physical Proper-ties of Hardened Portland

Cement Paste

BY

T. C. POWERS and T. L. BROWNYARD

MARCH, 1948

CHICAGO

Authorized reprint from copyrighted

JOURNAL OF THE AMERICAN CONCRETE INSTITUTE

New Center Bklg., Detroit 2, MichiganOct. 1946-April 1947, Procwdinos, Vol. 43, 1947

Authorized reprint from the copyrightedJOURNALOFTHEAMERICANCONCRETEINSTITUTE

New Center Building, Detroit 2, MichiganOct. 1946-April 1941’,Proceedin@, Vol. 43, 1947

Studies of the Physical PropetItiesof Hardened PortlandCement Paste

By T. C, POWERS*Member American Concrete Institute

and T. L, BROWNYARD?

Part 1.

Part %

Part 3.

Part 4.

Part 5.

Part 6.

Part 7.

Part 8.

Part 9.

IN NINE PARTS

A Review of Methods That Have Been Used for Studying the Physical Propertiesof Hardened Portland Cement Paste

Studies of Water FixationAppendix to Part 9

Theoretical Interpretation of Adsorption Data

The Thermodynamics of AdsorptionAppendix to Parts 3 and 4

Studies of the Hardened Paste by Means of Specific-Volume Measurements

Relation of Physical Characteristics of the Paste ta Compressive Strength

Permeability and Absorptivity

The Freezing of Water in Hardened Portland Cement Paste

General Summary of Findings on the Properties of Hardened Portland CementPaste

SYNOPSIS

This paper deals mainly with data on water fixation in hardened port-land cement paate, the properties of evaporable water, the density ofthe solid substance, and the porosity of the paete se a whole. Thestudies of the evaporable water include water-vapor-adsorptionchar-acteristicsand the thermodynamicsof adsorption. The discussionsin-cludethe followingtopics:

1, Theoreticalinterpretation of adsorptiondata2, The specificsurfaceof hardenedportland cementpaste3. Minimumporosityof hardenedpaste4. Relativeamounts of gel-waterand capillarywater5. The thermodynamicsof adsorption6. The energyof bindingof water in hardenedpads7. Swellingpressure

*Manager of Basic Rasearch, Portland Cement &an. Research Laboratory, Chicago 10, 111.tNavy Dept., Washington, D. C., formerly Research Chemist, Portland Cement tin. Research Labora-

tory, Chicago 10, Ill.

(101)

10s? JOURNAL OF THE AMERICAN CONCRETE INSTITUTE October 1946

8. Mechanismof shrinkingand swelling9. Capillary-flowand moisturediffusion

10. Estimation of absolute volumeof solidphase in hardenedpaste11. Specificvolumesof evaporableand non-evaporablewater12. Computationof volumeof solid phasein hardenedpaste13. Limit of hydration of portland cement14. Relation of physical characteristics of paste to compressive

strength15. Permeabilityand absorptivity16. Freezingof water in hardenedportland cementpaste

FOREWORD

This paper deals with the properties of hardened portland cementpaste. The purpose of the experimental work on which it is based was tobring to light as much information as is possible by the methods of colloidchemistry and physics, Owing to the war, the original program, whichincluded only a part of the field to be explored, was not completed. More-over, the interpretation of the data is incomplete, partly because of theinability of the authors to comprehend their meaning, and partly be-cause of the need of data from experiments yet to be made.

Although the work is incomplete, it represents a considerable amountof time and effort, Experimental work began in a small way in 1934and continued until January 1943. Some additional work was done in1945 during the preparation of this paper. The first three years was aperiod of intermittent work in which little of permanent value wasaccomplished beyond the development of apparatus and procedures.This phase of the work presented many problems, some of which havenever been solved to our complete satisfaction.

The interpretation of the results of experiments also presented manydifficulties. During the course of our experiments, important newdevelopments in colloid science were coming to light through a series ofpapers from other laboratories. It was necessary to study these papersas they appeared and to seek their applications to our problems. Theresult is that the theory on which much of our present interpretation isbased is one that did not exist when our work began and is one that isstill in the process of development. The reader may note that many ofthe papers referred to in Part 3 were not published until 1940 or later.

The theory referred to is that of multimolecular adsorption by Bru-nauer, Emmett, and Teller as first given in 1938 and as amplified inthe paper by Brunauer, Deming, Deming, and Teller in 1940. In justifi-cation for the use of such a recent and unfinished development, we maynote in the first place that a remarkable number of papers by variousauthors have appeared since 1940 strongly supporting the kind of usethat we have made of the theory, particularly the estimation of surfacearea. In the second place, the basic conclusions reached through the

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE 103

use of the theory might have been reached from a strictly empiricalanalysis of the data. However, it is difficult to imagine how a picture ofthe hardened paste as detailed as the one presented in this paper couldhave been drawn without adopting theoretically justified assumptions.

The paper is composed of nine parts. Part 1 contains a review ofprevious work done in this field and discusses various experimentalmethods. Part 2 elaborates on the principal method used in the presentstudy, namely, the measurement of water-fixation, It also pre~cnts theempirical aspects of the data ,s0 that the reader may become familiarwith facts to be dealt with.

Part 3 presents the theories upon which an interpretation of the datain Part 2 can be based. It gives also a partial analysis of most of theexperimental data given in Part 2 in the light of the adopted basis ofinterpretation, Part 4 is a discussion of the thermodynamics of moisture-content changes in hardened paste and the phenomena accompanyingthose changes, It is thus an extension of the earlier discussion of theory.

In Part 5 data are presented pertaining to the volumes of differentphases in the paste. The interpretation of these data involves the use offactors developed in the preceding parts of the paper. The final resultis a group of diagrams illustrating five clifferent phases, the relativeproportions of each, and how those relative proportions change ashydration progresses,

The relationship between the physical characteristics of the hard-ened cement paste and compressive strength of mortars is discussed inPart 6. A similar discussion of permeability and absorptivity is givenin Part 7,

A study of the freezing of water in hardened paste is presented inPart. 8. The conditions under which ice can exist in the paste are de-scribed and empirical equations are given for the amounts of water thatare freezable under designated conditions.

The properties of portland cement paste as they appear in the lightof these studies are described in Part 9, This part amounts to a summaryof the outcome of the study, at its present incomplete stage, withoutdetails of ~perimental procedures, or theoretical background.

As mentioned in the first paragraph, a particular point of view asto the meaning of the data has been adopted. Specifically, we haveassumed, on the basis of evidence given in the paper, that the variousphenomena discussed are predomi~antly of physical rather than chemicalnature. The result of the study therefore constitutes a hypothesis, orseries of hypotheses, rather than a rigorous presentation of establishedfacts. Considering the present state of our knowledge, we believe thispolicy to be more fruitful than one of trying to maintain a strictly un-

104 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE October 1946

biased view as to the meaning of the data. As written, the paper repre-sents the thinking of one group of workers (influenced, of course, bymany others), and it implicitly invites independent investigations of thesame field by any who may have good reason to adopt a different pointof view. To this end, we have appended tabulations of the originaldata.

Though we thus concede the possibility of other interpretations, wenevertheless feel confident that a large part of the present interpre-tation will withstand logical criticism. However, it seems very likelythat corrections and changes of emphasis will develop as experimentalwork continues, and as further advances are made in fundamental colloidscience.

The paper is directed primarily toward all who are engaged in researchon portland cement and concrete. However, it may be of considerableinterest to many who seek only to understand concrete as they workwith it in the field. Studied in connection with earlier papers on thecharacteristics of paste in the plastic state, * this paper affords a com-prehensive, though incomplete, picture of the physical nature of portlandcement paste, It, therefore, pertains to any phase of concrete technologythat involves the physical properties of the cement paste. This meansthat the paper should find application to most phases of concretetechnology.

For the most part, the reader will find few items of data that beardirectly on specific questions or problems. Successful application ofthis study to research or practical technology requires some degree ofcomprehension of the work in its entirety. Consequently, it is notlikely that a single, casual reading will reveal much that is of value toone not already familiar with the methods and background of this typeof investigation.

ACKNOWLEDGMENTS

We are deeply indebted to Mark L, Dannis and Harold Tarkow,not only for their long and painstaking labor with the various experi-ments, but also for their contributions to an understanding of the results.Mark Dannis made most of the adsorption and specific-volume measure-ments and Harold Tarkow performed the freezing experiments reportedin Part 8.

We are grateful to Gerald Pickett, whose constructive criticism was ofgreat value throughout most of the period of study.

*BuIL 2, “The Bleeding of Portland Cement Paste, Mortar and Concrete,” by T. C. Powers, P.C.A.Rmearch Laboratory (1939); Bull, 3, “Rate of Sedimentation, ” by Harold H. Steinour, P.C.A. ReeearchLaboratory (1944), reprinted from Ind. Etwr. Chem. S6, 618; 840; 901 (1944); Bull. 4, “Further Studim oftbe Bleeding of Portland Cement Paste, ” by Harold H. Steinour, P.C.A.Reeearch Laboratory (1945).


We are especially indebted to Harold H, Steinour, who took timefrom his own work to carry on the final volumenometer work describedin Part 6, Also, he helped prepare the discussion of thermodynamics inPart 4 and gave much valuable oriticism of various other parts of thepaper,

To Virginia Atherton, who made many of the hundreds of computa-tional typed the manuscript, and correoted printer’s proof we express ourkindest thanks,

Part 1, A ROVIOWof Methods That Havo Boon Used for Studying thoPhysical Propartios of Hardonod Portland Comont

CONTENTS

Methodnfor studyingthe physiod propertiesof the hardenedpaetaIvIiorosoopioexaminations!Ii!o!o!!t!t 1!!!,!,!.,,, !,, ,,, ,

Thelight-miorosoope,,,,,,,,,,,,,,,,,,,,,,,, ,,,.,,,,,The eleotronmiorosoope!,, ,,, ,, !,,, ,,, ,,, ,,, ,,, ,,, ,,,

X-ray exiuninatione,,.,,, ,,, ,,, ,,, ,,, , ,,, ,,, ,,, ,,, ,,, ,,,Water fixation,,, !,,,,,,, , !,,,,,,,,, ,,, ,,, ,,, ,, ,,, ,,, ,,

Isothermsandisobars,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,Bindingofwater in hydroxides,,,,,,,, ,,, ,,, ,,, ,,, ,,, ,Water boundbyoovalent bonds,,,,,,,,, ,,,, ,,, ,,, ,,, ,Water bound byhydroge,nbonds,,,,,,,, ,,, ,,, ,,, ,,,, ,[email protected]!!.,!,,! !,, ,!, ..!,, , !!!.!,!,!, ,,, ,,,Lattioe water,.,,,,,,,,,,,,,,,,,,,, !!!!!!.!!.. ,,, ,,,Adsorbedwater0...4!!!, t,, ,!, ,,, , ,,, ,,, ,,, , ,,, ,,4, ,

Interpretation of isobars, ,,, ,,, ,, .,, ,,, ,,, ,,, ,,, ,,, ,,, ,,Influenceofeurface adsorption, ,,, ,,, ,,. ,,, ,,, ,,, ,,,, ,

Interpretation ofisotherrne, ,,, ,,, ,,, ,, .,, ,,, ,,, ,,, ,,, ,,,Iaother~ of hydrates,,,,,,,,,,,,,,., ,,, , .,,,,,,,,,,,Isothermsof gels, ,,,,, . !.,,!,,,,, ,,, ,,, ,,, ,. ,,, ,, .,,,

Water contentve,temperaturecurvee(isobars)fromhardenedportland cementpaete, ,,, ,,, ,,, ,,, ,,, ,,, ,,, ,,, ,,, .,,,Retiewof publisheddata,,,,,,..,.,.,.,., ,,, ,,,,.. .,,Discussionofisobare,. ,,, , .,..,,,,,, .,, ,,, , .,,,..,,,.

Water contmt vs. vapor pressureourvesat constant tempera-ture (isotherms)..,.,,,.,,,,,.,,,,.,,. , .,..,.,,,.,,,..Relationshipbetweenisothermsand isobars,, . ., . . . . ., .,Significanceofisotherme,,.. t..,.,,,, . .,.,,,,....,.,,,

Studiesof water fixationby meansof freezingtests, . . . . .Summaryof Part l,..,, ,, . .,, .,,..,... . . . . . . . . . . . . . . . . . . . . . .References,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

106106106108109110110110110110111111112112112116116116

118118122

124127127128128131

Starting as a suspension of cement particles in water, portland cementpaste becomes a solid as the result of chemical and physical reactionsbetween the constituents of the cement and water, A solidified paste oftypical characteristics is capable of giving up or absorbing a volume ofwater equal to as much as 50 per cent of the apparent volume of the


paste. These facts engender the idea that whatever the chemical con-stitution of the new material produced by chemical reaction, the newmaterial is laid down in such a way as to enclose water-filled, inter-connected spaces. That is, the hydration product appears to be not acontinuous, homogeneous solid, but rather it appears to be composedof a large number of primary units bound together to form a porousstructure. It seems self-evident that the manner in which the primaryunits are united, that is, the physical structure of the paste, is closelyrelated to the quality of the paste and is therefore something aboutwhich we should be well informed.

FreyssinetfQ* discerned the need for knowledge of paste structureand devised a hypothesis about the setting and hardening process andabout the structure of the hardened paste. Giertz-Hedstroq (2)an activecontributor to this subject, has given an excellent review of publicationson this subject. This review, together with Bogue’s@j earlier one of aslightly different aspect of the subject, obviates the necessity of an ex-tensive historical review at this time.

A program of studies of the properties of the hardened paste wasbegun in this laboratory in 1934. It has consisted mainly of studiesof the fixation of water, but has also included measurements of the heat-effects accompanying the regain of water by the previously dried paste,measurements of the freezing of the water in the saturated paste, andvarious other related matters.

This work has yielded a considerable amount of information on thephysical aspects of hardened paste. It contributes to the knowledgeof the chemical constitution of the hydration products only in a negativeway; that is, it shows that some of the current information on the con-stitution of the hydration products must be incorrect. Later parts ofthis paper will give an account of these studies.

METHODS FOR STUDYING THE P~lY}:~L PROPERTIES OF THE HARDENED

The question of structure can be broken down into three parts: first,the question as to the chemical constitution of the hydration products,which includes the question of structure of the ultimate parts; second,the question of the structure of the smallest primary aggregations of theultimate parts; third, the question of how the primary aggregationsare assembled and how they are held together. A review of some of thework done by earlier investigators follows.

Microscopic examinations

The lirjht-microscope. The effectiveness of the microscope as a meansof studying the structure of the hardened paste is limited because the

*See references end of Part 1.Wee also the review hy Giertz-Hedstrdm (Ref. 3).


units of the essential part of the structure are too small to be seen.The results obtained by Brown and Carlson@j are typical, They, likeothers, observed that the hardened paste is predominantly ‘‘amor-phous)” so far as the microscope can reveal. Embedded in this amor-phous mass are the remnants of unhydrated clinker grains, crystals ofcalcium hydroxide, and sometimes crystals of other compounds.

Kuhlt5) reported that thin sections of hardened cement paste showed((. . . a residue of undecomposed cement particles, separated by agray and only slightly differentiated mass which gives a feebly diffusedluminescence in polarized light. Even under the highest magnificationindividual particles cannot be distinguished in this material, which isobviously almost entirely ultramicroscopic in structure. ” However,on examining the same specimens 20 years later he found that ‘(. . . thepassage of years had resulted in fundamental changes. No longer (wasthe material) uniform and only slightly differentiated under polarizedlight as was the case a few months after their preparation. They nowshowed a definitely increased (polarized-light) transmission and, mostnoteworthy of all, their properties were markedly different according tothe percentages of water with which they had been gaged, The speci-mens gaged with the greatest amount of water showed the greatestchanges while those mixed with the least water had undergone consid-erably less modification. ” The changes mentioned were such as tosuggest that the originally colloidal material had gradually changedtoward the microcrystalline state, the change being greater the higherthe original water content.

Useful information has been obtained by microscopic observationsof the hydration of cement in the presence of relatively large quantitiesof water. But it is unlikely that the structure developed under theseconditions is the same as that developed in pastes; hence, conclusionsabout the normal structure dra]vn from observations of this kind areopen to quesiion, @) For example, Le Chatelier(7J observed that when alarge quantity of water was used, needlelike crystals of microscopicdimensions soon developed. He concluded from this that similar,though submicroscopic, crystals developed under all conditions.

Brownmiller(8J described the results of microscopic examinations ofhardened paste by means of reflected light. The method is a modifica-tion of that described by Tavasci(g) and Insley[l”) for studying the con-stitution of clinker. In addition to the use of etchants to bring differentphases into contrast, Brownmiller treated the surface with a dye whichwas taken up by the so-called amorphous material and the microcrystal-line phases. Although Brownmiller’s primary object was to developthe experimental technique, some of his conclusions concerning thenature of hardened paste and the hydration process are of considerable


interest, He found that there was “, , , no microscopic evidence ofchanneling of water into the interior of cement particles to selectivelyhydrate any single major constituent, Hydration seems to proceed bythe gradual reduction in the size of the particles as a function of thesurface exposed, ” This conclusion seemed to be based on the appear-ance of the coarser particles that remained unhydrated after the firstday,

Brownmiller found that a Type III* cement having Rspecific surface of2600 appeared to be almost completely hydrated after one day in asealed vial and six days in water, A Type I cement having t-t specificsurface of 1800 showed an unhydrated residue of about 16 per cent afterone day in a sealed vial and 28 days in water, The water-cement ratioof the original paste was 0.4 by weight in both cases,

The only microcrystalline hydrate mentioned by Brownmiller was ‘calcium hydroxide, This was found as clusters of fine crystals em-bedded in what Brownmiller called the hydrogel.

Brownmiller found that the etched surface of the 7-day-old pastemade of Type I cement showed “an extremely complicated but interest-ing structure. A close examination , , , shows that the cement hydrogelis not a formless mass but has an intricate structure. ”

The electron microscope. Eiteltll) used the ele@ron microscope forphotographing the hydration products of some of the constituents ofportland cement. The article consulted gives almost no details concern-ing the method of preparing the samples that were photographed. Itappears that the samples were taken from dilute suspensions of thehydrated material, Presumably, samples of Ca(OH)Z were taken fromsaturated or supersaturated ‘{milk of lime” and hydration products of(7v9and CW4from saturated solutions of water in isobutyl alcohol, Theisobutyl alcohol was used to dilute the water and thus make possible arelatively high concentration of the solid with respect to water and atthe same time a dilute suspension. Since the isokutyl alcohol wassaturated with water, the chemical acti wity of the water was unaffectedby the presence of the isobutyl alcohol.

Several photographs of these preparations (magnifications rangingfrom 7200 to 36000) were published. The Ca(OH)2 taken from milk oflime as well as that formed from the hydrolysis of C& appeared ashemispheres ranging in size from about 0.1 to 0,5 micron. The calciumsilicate hydrate appeared as thin crystalline needles about one-half

*SeeA.S.T.M.Designation C150-44 where five types of portland cement are defined as follows:Type I —For uae in eneral conorete construction when the special properties specified for Types II,

tIII, IV, an V are not required.Type II —For use in general concrete construction exposed to moderate eulfate action, or where moderate

heat of hydration is required,Type III—For use when hiuh early strength is required.Type IV —For use when a low heat of hydration is required.Type V —For use when high sulfate resistance is required.


micron long. The C3A appeared mainly as rounded particles (“roses”)about 0.1 micron in diameter. Referring to these and apparently toother observations, Eitel concluded that although the hydration prod-ucts of portland cement are predominantly colloidal, they appear crys-talline—not amorphous—to the electron microscope.

Sliepcevich, Gildart, and Katz,f’2j reported the results of attempts tophotograph the hydration products of portland cement and the majorconstituents hydrated separately. Most of the photographs publishedwere of samples prepared as follows: 0,5 to 0.75 g of portland cement ora cement constituent was mixed with about 10 cc of purified water andallowed to stand. At the desired age the specimen for photographingwas obtained by taking a drop of the supernatant liquid $nd allowingit to evaporate on a callodion film previously prepared. The materialon this film was thus whatever dissolved or suspended material the dropcontained.

In some respects the results were like those found by Eitel. Photo-graphs of calcium hydroxide appeared like those of Eltel but whereasEitel concluded that the particles were hemispheres, Sliepcevich, Gildart,and Katz concluded that they were spheres. From each material thelatter investigators usually found material of several geometric forms.Some of the material appeared amorphous and some crystalline, Asdid Eitel, those investigators found the majority of crystals to be in thecolloidal size range,

The significance of these results is open to question until it is knowndefinitely just what relation the samples obtained in the manner de-scribed have to the hydration products making up the mass of a hard-ened cement paste.

X.ray examinations

The results of X-ray examinations were summarized by Giertz-Hedstr5m(18J as follows: “X-ray examinations of hardened cementhave so far given little beyond a confirmation of what has been shownby the microscope, The presence of clinker remains and crystallizedcalcium hydroxide is thus confirmed by Brandenberger. ~1’j The struc-ture of the main mass, the “cement gel,” is, however, such as to give,at least for the present, no clear guidance in the X-ray diagrams. Thismay be due to its lacking a crystalline structure or other regular finestructure or to the crystals being so small or deformed (for example bentneedles) that no definite interferences are obtained. ”

Bogue and LerchQs) mention the use of X-ray analysis in connectionwith microscopic examination, The X-ray confirms the microscopicindication that unaltered beta or gamma dicalcium silicate remained inpastes after 2 years of curing. X-ray diffraction patterns from both


hydrated tricalcium silicate and hydrated dicalcium silicate showed atthe end of 2 years no evidence of the development of a new crystallinestructure such as would be expected if the hydrates were to change fromthe theoretically unstable gel state to the stable microcrystalline state.As mentioned above, evidence of the beginning of such a change within aperiod of 20 years was reported by Kuhl.

Water fixation

Because direct observation fails to answer many questions concerningthe structure, properties, and behavior of hardened portland cementpaste, indirect methods of study have been used. The principal oneis that of studying the manner in which water is held in the hardenedpaste.

Isotherms and isobars. The fixation of water by water-containingsolids is usually measured in terms of the amounts of water held atvarious vapor pressures with temperature constant, or in terms of theamounts held at various temperatures with pressure constant. Thecurves obtained by the first method are called isotherms. Those ob-tained by the second method are called isobars. Both of these methodshave been used in the study of hardened portland cement paste. Thenature of the hydration or dehydration curve depends on the manner inwhich the water is combined and on other factors to be diecussed.

Binding o.f watw in hydroxides. In metallic hydroxides, which repre-sent one class of compounds that may be included among hydrates,the elements of water are present as OH-groups that are strongly boundby the metallic ions. This is usually recognized in writing the formulasof metallic hydroxides; thus, calcium hydroxide is usually given theformula Ca (OH)9 rather than CaO.HjO.

Water bound by covalent bonds. In many hydrates, the water moleculeretains its identity to a large degree, i.e., H.20 is a unit in the structure.An example is MgC12.6Hs0. In this hydrate the six molecules of waterare bound to the magnesium ion by covalent bonds and are arrangedaround the magnesium ion in an octahedral grouping. To indicate this,the formula should be written Mg(H20)&’12, for this more nearly repre-sents the structure.

Water bound by hydrogen bonds. There is another type of compoundin which the water molecule remains intact and is bound to the com-pound by one or both of its hydrogen atoms. The molecules so held aresaid to be bound by hydrogen bonds. CUS04..5HZOand NiSO~.7H@ arehydrates in which one of the water molecules is bound in this way.

Water held in a compound by any of the types of bond describedabove is properly regarded as being chemically bound. The removal of


water from such hydrates necessarily gives rise to a new solid phase andhence the isotherms and isobars of these hydrates should show wellmarked steps in accordance with the phase rule. Fig. la gives, forexample, the relationship between water content and vapor pressure forthe hydrates of copper sulfate.

(a)0

2

4

5‘3!3o 2s 5C14W

Water VaporPressure

(b) (c)

,6

E13?+%--1,

,2

9 9

6

3 3

0 03 50 100 lso~c O ?5 159 2Z5$C

Te!nperature Temperature

Fig. 1- Univariant and bivariantdehydration curves

[J{sobarlaT-xcurveforCr*(S04)j,18H*0a so)hermal p-n curve for CUS04.5H20

The (fIst 15H20 come off along a uni.variant curve, the remaining 3H20being zeolltic

(c) Zeolitic dehydration of greenCrZ(SO,),.15H20

(Curves and caption from Emele.s &Anderson)

Zeolz’ticwater. One type of microcrystalline hydrate, which com-prises the zeolites and’ several basic salts and hydroxides of bivalentmetals, gives smooth isotherms or isobars. Fig. lC is an example of anisobar frOm Cr2(~~i)3, 15H@. Water held in this type of compound iscalled zeolitic water.

According to Emeleus and Andersonf@ zeolitic water is regardedas being packed between the layers of the crystal or in the interstices ofthe structure. A distinguishing characteristic of zeolitic water is thatit may be removed without giving rise to a new solid phase. Its removalmay, however, change the spacing between successive layers of thecrystal.

Water held in such a way as to exhibit the behavior described above issometimes referred to as being in a state of zeolitic solution or solidsolution. @7)

Lattice water. Emeleus and Andersonf’8) distinguish a type of hydratein which there is water of crystallization “that cannot be supposed to beassociated chemically with the principal constituents of the crystallattice.” As an example, they cite potassium alum, 2041(S04)2. 12HZ0.There is little question that six of the twelve molecules of water arelinked to the aluminum ion by covalent bonds. The remaining six mole-cules are known to be arranged octahedrally around the potassium ionbut at such a large distance from it as to suggest to Emeleus and An-derson that the interaction is very weak and hence that the water is notchemically bound to the potassium ion. This perhaps represents aborderline case between chemically bound water and zeolitic water,which is supposed not to be chemically bound. The fact that exactlysix molecules of water are associated with the potassium ion is accountedfor by the geometry of the crystal lattice. The removal of these sixmolecules of water presumably gives rise to a new crystalline phase,

11s! JOURNAL QF THE AMERICAN CONCRETE INSTITUTE October 1946

however, and hence the isobars and isotherms should be stepped. Whenmore information on this type of hydrate becomes available, perhapsmany of the examples cited wdl have to be placed in one of the classifica-tions listed above.

Adsorbed water. In addition to any water held by the chemical forcesmentioned above, a small amount per unit of surface is held by surfaceforces, These forces, physical rather than chemical, are known collec-tively as van der Waal’s forces, (18) If the specific surface of the solidphase is small, the amount so held is usually undetectable. But if thespecific surface is very !arge, as it is for colloidal material, then physicallyadsorbed water can be a large fraction of the total held under given con-ditions; indeed, anhydrous solids such as quartz powder can hold rela-tively large amounts of water by surface adsorption if the powder isextremely fine. Zcolitic water can be regarded as adsorbed water, the“surfaces” in thk case being certain planes in the crystal, as describedabove. The subject of adsorption will be treated much more fully inlater sections of this paper.

Intorpretatlonof isobars

Influence of surface adsorption. From what was said above it mightappear that by means of isobaric or isothermal dehydration data waterheld in microcrystalline hydrates could readily be distinguished fromthat held as zeolite water, in solid solution, or by adsorption, It will bedeveloped below that such a distinction can be drawn under somecircumstances but not under others. The complication can best beillustrated by describing the work of Hagiwara. @) Theoretically, thevapor pressure of the water in a very small crystal of a hydrate shouldbe greater than that of a lc,rger crystal of the same substance at thesame temperature. Consequently, a mixture containing various sizedcrystals should exhibit a range in vapor pressures according to the rangein particle size. Practically, the effect is not noticeable unless theparticle size range extends into the range of colloidal dimensions. Theo-retically, very small natural crystals or very small fragments of largecrystals should behave similarly, though not necessarily identically.Consequently, the results of experiments with preparations made bypulverizing macrocrystals should be indicative of the general effects ofchanging particle size and particle-size range.

Hagiwara pulverized crystalline hydrates and obtained the isobarfor each preparation, In one series of experiments, he used Al@~,3H@prepared by the method of Bonsdorff, t20J The original crystals were ofmicroscopic size. The preparation was dried to constant weight in adesiccator over concentrated Hv5’Odto establish the initial water content,which was determined by igniting a portion of the material, Samplesthus dried were then heated in im electric oven at 100C for 30 minutes


after which they were cooled in a desiccator and weighed. Firudly, theamount of residual water was found by ignition, This was repeatedon other samples at temperatures ranging from 90 to 220C as indioatedin Fig, 2, Heating at 170C and at higher temperatures was oontinueduntil further heating caused no more change in the dry weight. Thetotal heating period at these higher temperatures was not less than 5hours and at 21OC was 20 hours,

Although the corncnw are somewhat rounded, there is a well definedstep in the isobar* at approximately 20SC, where the water contentdecreases from 3 molecules to one molecule. This is in good agreementwith the result obtained by Weiser and Milligan. [z’) The roundedcorner is the usual result in such experiments; very sharply definedcorners are the exception.

4

Microcr sfoll!ne$(Al, ,.3HZC

3 - --—. ------ .- 0000 )

c,

Om

:2 -+

0

0

:

L Fig,2:0i..,~043

‘6* Microcrystofline

-:3 -——— A

<Alz 0> .3H2 Oc,0

000z 1b

,

2

/“-

Finelg Ground

I AIzOS3HZ0 0

(Some moterwl os that o

gw,ng upper curve)

Fig. 30(! 40 60 120 160 ‘zoo 140

Temperature - “C

Fig. 9 & 3- isobars forAl,O,.3H@

Dafa from T. HagiwaraAlexander: Colloid Chemistry

Vol. 1, PP. 647.658The Chemical Catalog Co.

Inc. (N, Y,) 1996

*Mthough the curves in Fig. 2 and 3 are called isobars and tbe text inclioates that isobaric condi~ions wereintended, it seems p~~b~b;e~hat isobaric conditions were not actually maintained., If the heatm~ of thesample was done in an oven m tb,e prese]lce of room am, the act,ual vapor pressure m the oven would varywith tbe humidity of the room am and would be d!fferent nt different temperatures. However, over thetemperature range used l!) the experq~lent the vanatlons i! pressure were probably small. At any rateit is not likely that had strictly Lsobrmc oondltlons been mamtamed the outcome would have been signifi-cantly d}fferent.

114 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE Ocfober 1946

Hagiwara then ground a portion of the dried preparation in an agatemortar for 1YZhours, using fine quartz powder as a grinding aid, thusgreatly reducing the particle size. The experiments were repeated withthis finely ground material with the results shown in Fig. 3, where theresults shown in Fig. 2 are reproduced for comparison. A comparisonof the curves in Fig. 3 shows three significant effects of reducing thesize of the crystals:

(1) All semblance of a step is absent in the curve for the finely groundsample.

(2) The initial water content of the finely ground material is higherby 0.25 mole than that of the unground material. This additional watermust have come from the atmosphere during the grinding. (The initialwater content is that of the sample after it is dried to constant weightin a desiccator over cone. H2S04.)

(3) The water is lost from the finely ground sample at a much lowertemperature than from the unground material.

Hagiwara made a similar series of experiments with Fe~03.H20 with theresults shown in Fig, 4. The curve for the unground microcrystallinematerial shows a well defined step. The curve for “Grind A,” theshorter period of grinding, still shows a step though the corners aresomewhat more rounded than for the unground hydrate and the stepoccurs at a lower temperature. When the grinding was more pro-longed, “Grind B,” the step disappeared and the initial water contentincreased to 1.54 molecules. Grinding had little effect on the tempera-ture at which the final water content was reached.

It appears from Hagiwara’s results that a hydrate in which the wateris bound by chemical bonds may still yield a smooth isobar if the sampleis made up of a mixture of particles of various sizes, the smallest particlesbeing very small. This has a significant bearing on the interpretationof isobars in general. When a solid that has water for one of its con-

Fig. 4-- Effect of pro-Ion ed grindin on the

t8iso ors of Fez J.HzOHagiwara, Colloid Chemistry

Alexander Ed., Vol. 1,pp. 647-58 (1926)

0.0

Grind .4 represeotf 3 hc

Grin d B of grmdtng by bond m on

L

Nofum/ Geoih , k F.-, 0, H2O

0 40 lw 120 \60 200 240 280 320Tenlperature “C


Fig. 5- isobar for pyrophylliteData from Kelley, Jenny and Brown

Soil Sci. v. 41, P Q60 (1936)

Temperature “C

stituents yields a stepped isobar, it can usually* be concluded that thesolid is a well crystallized hydrate. When, however, the isobar is asmooth curve without steps, it may represent a sample of the hydratecomprising particles of various sizes or it may represent a material inwhich the water is not bound by chemical bonds in the usual sense ofthis term. It appears also that a lack of steps in an isobar is not sufficientevidence that the hydrate has a zeolitic structure, for neither of thehydrates with which Hagiwara experimented was of that nature.

The other effeet of fine grinding, namely, the increase in the initialwater content brought about by grinding, is fully as significant as theone just mentioned. It must be assumed that the water in excess ofthat required by the formula is held by forces of a kind different fromthose that hold the hydrate water, The effect is clearly a surface effect,for the initial water content is much higher after the longer period ofgrinding than after the shorter period. (Compare “Grind B“ with“Grind A“ in Fig, 4.) It seems reasonable to suppose that this excesswater is held by adsorption forces, i.e., forces which reside in the sur-face of the crystal and which came into prominence after the specificsurface of the hydrate had been greatly increased by grinding,

This aspect of the effect of fine grinding is further emphasized by theresults of experiments made by Kelley, Jenny, and Brown. @2) Theseauthors studied the effect of grinding on the isobars of clay minerals.See Fig. 5. The isobar for the 100-mesh sample shows a well markedstep near 500C and thus gives unmistakable evidence that the mineralis a microcrystalline hydrate. Comparing this with the isobar for thefinely ground pyrophyllite, we see that the isobars are very nearly——

*13ut not always. See remarks below on silica gel.

116 JOURNALOF THE AMERICANCONCRETE INSTITUTE October 1946

identical above 400C. Each exhibits a well marked step; the stepsoccur at very nearly the same temperature; however, the height of thestep is slightly less for the finely ground sample. Below 260C} thefinely ground sample shows a larger water content than the 100-meshsample. That is) just as with the materials Hagiwara used, after grind-ing there is initially a large amount of water in the finely ground samplein excess of the hydrate water represented by the nearly vertical portionof the isobar, This additional water must have been acquired from theatmosphere during grinding and must be held by some mechanismother than that which holds the hydrate water, It seems most unlikelythat the excess water is zeolitic water, since fine grinding could hardlyincrease the total interplanar area of zeolite crystals.

Interpretationof Isotherms

Isotherm~ of hydrates. The usual behavior of a hydrate when thewater-vapor pressure around it is varied at constant temperature isillustrated in Fig. 6. This isotherm shows well defined steps with thecorners slightly rounded) as indicated by the dotted lines. What theeffect of pulverizing such material on the shape of the isotherm mightbe is not known directly from experiment, for apparently no experimentsof this kind have been published. Presumably, a sufficient amount ofgrinding would produce a smooth isotherm, by virtue of the change inparticle size and particle-size range. It might also be presumed that in asaturated condition the minute crystals would retain more water thancorresponds to the highest hydrate, These presumptions follow from

considerations given above in connection with the isobars.Isotherms of gels. The appearance of a well defined step in the isotherm

of a solid is not always positive proof of the existence of a hydrate ofdefinite chemical composition. Fig. 7 illustrates this point, (23) As thearrow indicates, the isotherm was obtained by progressively loweringthe water vapor pressure. Just below a pressure of 4 mm Hg, the iso-therm becomes very steep, a fact which might be takefi to indicate theexistence of hydrates having the formulas SiOs. 1Y~H@ and Si02.H20.Fig. 8 shows the same isotherm as well as that obtained by progressivelyincreasing the vapor pressure, the “dehydration isotherm” as it is some-times called. Note that the latter gives no evidence of a hydrate. Weiser,Nlilligan, and Holmes investigated this matter fully by preparing silicagel from the same materials at various temperatures ranging from O to100C and from other materials at various temperatures and undervarious conditions. Not all preparations exhibited the vertical sectionin the dehydration isotherm, Gels prepared at low temperatures ex-hibited a step at a higher water content than gels prepared at a hightemperature. The samples prepared at 100C and aged at this tem-perature for a few hours, and hence under conditions favoring crystal


cuso,,51i*03Y“

Temperature 25°C

CUSO*.3HzO, ,v

WS04.h“0,v

0.2 0.4 0.6 0.8Relative Vapor pressure, p/p~

2.5

0.0

13*C IsotAerm7

1

[

024681012Water vapor Pressure, mm.Hg

Fig. 6- Water content vs.vapor pressure curve of

CUS04Collins ❑nd Menzies, J. Phys.

Chem. v. 40, PP, 379-97 (1936)

water Vapor Pressure, mm. H9

Fig, 7—(left) Dehydration isotherm for silica gel prepared from water glass at !?5CWeiser, Millioan and Holmes, J. Phys. Chem. v. 46, P. 586 (1949)

Fig, 8 (right)—Dehydration and dehydration isotherms for silica gel prepared from waterglass at !?5C

Weiser, Milligan and Holmes, J. Phys. Chem. V. 46, P. 586 (1949)

118 JOURNAL OF THE AMERICAN CONCRETF INSTITUTE October 1946

growth, gave no evidence of a step, No evidence of a step appeared

in the dehydration isotherm of any preparation. No preparation gaveevidence of crystallinity when examined by the electron diffractionmethod. These authors concluded that the step that occurs in thedehydration isotherm of some of the preparations is not evidence of theexistence of a hydrate but is rather the result of a peculiarity of thephysical structure of these gels. It follows from this conclusion that thestructure of the gels prepared at low temperatures differs from that ofthe gels prepared at high temperatures, and there is evidence that,thischange in structure accompanying the increase in temperature of prep-aration is progressive,

Fig. 8 illustrates also the phenomenon called “sorption hysteresis.”This will be discussed in another part of this paper.

*****

The foregoing review shows that the interpretation of isobars andisotherms is not always a simple matter. Particularly, when the iso-therm is smooth throughout, alternative interpretations must be con-sidered carefully in the light of other pertinent information.

Watercontent vs. temperature curves (isobars) hamhardened portland cement paste

Review oj published data. In this laboratory Wilson and Martinf24Jobtained a group of isobars from hardened portland cement paste. Thehardened paste was ground to pass the 28-mesh sieve and then was driedto constant weight at a constant temperature in a stream of air main-tained at a low, constant water vapor pressure by bubbling the airthrough concentrated sulfuric acid. * The dry sample was then ignitedat 1000C and the loss on ignition was taken as the water retained at thetemperature of drying. Various drying temperatures were used, rangingfrom 50 to about 600C. t The resulting isobars are given in Fig. 9. Leaand Jones@5j obtained the isobars shown in Fig. 10. These authorsplotted the loss in water rather than the amount retained.

In general those curves are not like those obtained from crystallinehydrates having definite amounts of water of crystallization. The nearlyvertical rise in the curves between 400 and 450C, seen clearly in thecurves of Lea and Jones, is attributed to the decomposition of Ca(OH)z.

Krauss and Jorns@8) obtained isobars for the hardened paste at aconstant vapor pressure of 7 mm Hg by using the instrument shown inFig. 11, The sample is placed in A, which can be detached from therest of the apparatus and which serves as a weighing bottle in followingthe changes in weight of the sample. With A in place as shown, the—.

*The air was freed of CCh by suitable means. to Prevent. carbonation.tThe procedure used does not maintain strmtly isobaric conditions, for the pressure would vary with

temperature. However, the pressure is so small under all conditions that variations can usually be neglected.


24 1 I

+Cement .4, 60% Mixing Wafer

c

; ~.u

k

i

‘glb3n

;; 12

u

:,-gl~8c!.al !

z34

00 100 200 300 400 500 600

Temperature, “C

Fig. 9- Effect of drying temperature on water retained, temperature range 50Wilson and Martin, J. Am. Concrete Inst. v. 31, p. 979 (1935)

to 600C

Fig. 10—Loss-on-heating curves for hardenedneat cement, w/c = 0.%2

Lea & Jones, J. SO.. Chem, Ind., v. 54, P. 63, 1935

1S?o JOURNAL OF THE AMERICAN CONCRETE INSTITUTE October 1946

Manometer

To Vat. Pump

Fig, 11- Krauss & Jorns’ Apparatus

system is evacuated, thus removing water vapor as well as air, Periodi-cally, the removal of water is interrupted by closing the stopcock andthe water vapor pressure is observed, If the equilibrium pressure ex-ceeds 7 mm Hg, the value chosen by Krauss and Jorns, the stopcockis opened and more water is removed by pumping, This process is re-peated until at room temperature the equilibrium vapor pressure of thesample is less than,7 mm Hg, The temperature of the sample is thenslowly raised until the pressure is exactly 7 mm, The loss of water to

*

\

Pressure = 7m m. Hg

\

-—+..

II

Ioc 200 300 400 s

Temperature -“C

Fig, 1 Q - Isobar forhardened 3Ca0.Si0, **Probabl o mixture ot CA

dand Ca( H)i (See texf)) Data from Krauss and Jorns

Zement v, 90, p, 317 (1931j

PHYSICAL PROPERTIESOF HARDENED PORTLAND

2? I I0

Por+lono’ Cement Posfe”t

20 ~-— — CUPL79 :28 Gk7ys0 tn No/st Air0a

18 !0z :,g)

16 )0; :n 0n 14 c: I

t;

4J :

: 1’2 -:

&‘“l

: 10

j‘f~0“j

58. -.--—.-,...—-.....—..

0 0 % .Q& 0 0$6 .2.?= o0000

4 :O*0000 0

z0

“8000 00~

o0 100 200 300 400 500 6;0 700

Temperature -“C

this point is determined by weighing A. Beyond

CEMENT PASTE 1S21

Fig, 13 - Isobar forportland comont past.obtalnod by I(raw andJorns.Zom*nt v, 20, p. 343 (1931

this point, water isremoved in small amounts by evacuation and after each decrement thetemperature of the sample is raised until the pressure is exactly 7 mmHg. Thus, the isobar is obtained. The results obtained by Krauss andJorns are given in Fig. 12, 13, and 14.

Fig, 12 represents a sample described as tricalcium silicate (C&*mixed with enough water to correspond with the formula 3Ca0. Si0z.-2HZ0. The mixture was cured in saturated air 24 hours before themeasurements were started. There is a suggestion of a step in the isobar

*Throughou$ ,this discussion the compositions of portland ramente will be described in terms of the com-~~ ~OmPOs,tlon comp”tedbytl]em,th~d~ of I,, A. Dnhl, Rock Proclucts v. 32 (23) p. 50, (192!3) and R.H.

e, Iw.L ,97?0. Ckem. (Anal. Ed.) v. 1 (4) p. 192, (1929) or PCAF Paper No. 21 (1929). The followingabbreviations will be used.

CWS = 3Ca0.Si02 C,A = 3Ca0.AlzO~C2S = 2Ca0.SiOg C,AF = 4Ca0. AlzOs.FezO,

On this basis the composition is computed on the assumption that the iron and alumina compunds areC{AF and CaA. Swayze, Am. J, Sci, v, 244, pp. 1-30, 65-94, (1946) bas recently shown that the iron oxideOII1Ofl.A.F(,-c) (in which x may vary from O to 2) which includes

. ..!.. .V,w.. y....,. =“. ”.-... .- ma!ie allowance for this finding, discussions in lateri recastmz In dlff erent terms. It seems unlikely, however, that any of the argu-

oocurs in a phase having the general form --- -..,-.. .. .C~A F as a, special case, J <+-. ;+ 1,..,,,,,.. n,w., hln t,nparts of thm paper may needmcmti or deductions would be greatlj altered.

1$!9 JOURNAL OF THF AMERICAN CONCRETE INSTITUTE October 1946

near 100C and a prominent step near 350C. The latter probably repre-sents the decomposition of calcium hydroxide. A compound that mightbe represented by the break at 100C is not identified. Owing to themanner of its preparation (from a melt), the material thought to betricalcium silicate was probably a mixture of ciicalcium silicate andcalcium hydroxide.

Fig. 13 represents a paste cured 28 days in moist air. There appearto be numerous closely spaced steps in this isobar. Krauss and Jornsbelieved that these steps were sufficiently distinct to indicate the presenceof several hydrates having definite chemical formulas.

Fig. 14 represents a paste that had. been cured several hours in boilingwater* and then stored in the air of the laboratory for several years.As can be seen, the isobar has several well defined steps.

Endell@Tj determined isobars for hardened paste, but he arbitrarilylimited the heating period at any one temperature to one hour. There isevidence in his results that this was not always sufficient for the attain-ment of equilibrium. The isobars he obtained do not exhibit any featuresnot exhibited by those reproduced in this paper.

Meyers@’) published isobars for hardened pastes and for hydratedsamples of the pure compounds CsSj CSS, CSA~C~AF, and CaO hydratedseparately (Figi 15). The samples were heated in a vacuum in which the,},ater vapor pressure was maintained at about 0.1 micron. Under these

conditions the dissociation temperature of calcium hydroxide was foundto be about 380-400F (193-204C). Neat hydrated cement heated underthe same conditions showed a step at about 430F; presumably the stepwas due to the decomposition of calcium hydroxide. The conditionsdescribed for the experiments were such as to suggest that the differencebetween the dissociation temperature of the sample of Ca(OH), and thatof the CCZ(OH)Zin the hydrated cement, was probably due to a differencein vapor pressure, the pressure being higher under the conditions thatprevailed when the hydrated cement was tested,

The isobars for hydrated CWSand CY$’show steps near 400F that mayalso be attributed to calcium hydroxide. The isobars for hydrate CSAand CIAF show a large step near 240F.

Discussion of isobars. The data of Krauss and Jorns seem to indicatethat hydrated cement contains a series of hydrates besides Ca(OH),.However, the other curves, including those published recently by Meyers,indicate that the curves are smooth, except for one step in the neigh-borhood of 400F that is apparently due to microcrystalline Ca(OH)2.

since the structure of the hardened paste is predominantly of sub.microscopic texture, a smooth isobar is to be expected whether the

*The specimen was a part ll$ed in the G-~n st~nd~rd T-t fOr SOundn@s.


16 -!! \

000 Port/and Cement paste0 Soundness Pato

2 14 { curing: /d. moistg-l % 27din H20

6g in air$ ,2 0‘;.

%Dm &+ “oe; 10 8v z. cwQ8 o+ “ocal ‘8 .aQ

6-E .0~o2 1.L

4-$ . ,

2,

%~

20

0c o~

.0 ~.o-0 I00 200 300, 400 500 600 -700

Temperature -“C

24

20

z$ 16

k

alz

zo‘8Lu

!!4

o100 200 300 400 500

Fig. 14 - Isobar forportland cement pasteobtained by Krduss andJorns.Zement v. S!0, p. 343 (1931)

100 200 300 ~o Soo

Tern perature -“F

Fig. 15- Isobars obtained by S. L. MeyersPit and Quarry (JuIY ,1949)

7Q4 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE October 1946

hydratkm products am crystalline or not, As will be shown later, thespecific surface of the hydrated material is so high that if the structureis of granular nature the granules must be of colloidal dimensions, Ifthe particde~ were all of exactly the same si~e and constitution, a step inthe isobar might be expected, despite the smallness of the particles,Without any a priori reason for assuming such uniformity in particlesize, there is no basis for expecting anything but a smooth isobar exceptfor the effect of calcium hydroxide already noted,

In general the isobars do not tell much about the hydration products,However, when the isobars are considered together with the informationobtained with the microscope and X-ray, they may be considered toshow that the hydration products are, for the most part, not in themicrocrystalline state, *

Meyers’ data on the four compounds C@, (2,S, (7w4, and C4AF hy-drated separately are of special interest, Note that both of the alumina-bearing compounds lost large amounts of water at about 250F, Sincethese two compounds usually constitute 20 per cent or more of thecement, a step on the curve for portland cement, or at least a sharpincrease in slope, should oucur at about 24013’ (116(2) if those compoundsare present in the hydrated cement, The fact that no such indicationhas been found can be taken as evidence that the hydration products ofcement are not a simple mixture of the same hydration products thatform when the compounds are hydrated separately; at least, they differradically with respect to physical state, whether they do with respectto constitution or not,

Water cantont VS. vapor prossuro curvot atconstant tomporaturo (bothorms)

Jesser(aO) was apparently the first to study the relationship betweenwater content and vapor pressure for hardened paste at constant tem-perature, He used the method of van Bemmelen,(sl) i.e., he left thespecimens in a closed container over a solution of a salt or of H@04 atconstant temperature, until they reached equilibrium with the vaporpressure of the solution, Starting with the saturated condition, heprogressively subjected the samples to lower and lower humidities, fi-nally drying them over concentrated H2iS04. He then subjected themto progressively higher humidities, finally storing them over a solutionhaving a relative vapor pressure of 0,98. After this he determined asecond drying curve. His results are given in Fig. 16.

*Throughout this discussion a distinction will be made between the colloidal and microcrystalline stktea,Tbe Jerm ‘:ccdloid” refers to an y material, cry~talline or not, having a specific eurface of a higher order thanparticles vm!ble with the light microscope. A colloidal material may exist as diaorete part~clea or ae gele,tbe latter being regarded ae aggregations of once discrete colloidal partwlea. Tbe term ‘‘mnmocryetalhne”re~ere to ordered aggregatlone of molecules, atome, or Ions, at least large enough to be eeen with a lightmicroscope. The adjective “amorphous” is not aced as the eynon m of “colloidal” for euch ueage tande

/’”to obscure the fact that colloidal particl~ may tbemselvea be crvsta hne, that ia, of ordered structure. Thepossibilityof crystallinecolloid,q has long been recognized by oofloid chemists, The actual exid,e.nce of suchcolloids has been demonstrated by means of the electron microscope,~

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE 1$25

Jesser used prisms about 1%x1%x4 in. made of neat paste having awater-cement ratio of 0,25 by weight. On the average, he left eachprism at a given humidity about six weeks and assumed that this wassufficient time for equilibrium to be attained. Experiments in thislaboratory, in which prisms of smaller cross section (1x1 in.) having ahigher water-cement ratio (and consequently, a higher drying rate) weredried over dilute H&Od by much the same procedure, showed that 6weeks was insufficient for the attainment of constant weight. More-over, in specimens as large as those used by Jesser, hydration of thecement continues at an appreciable rate at the higher relative vaporpressures, especially in specimens cured only three days. These factsmake the interpretation of his results difficult. The results are of in-terest none the less because they were the first to indicate the similaritybetween the behavior of the hardened paste and that of typically colloidalsubstances such as silica gel.

One striking fact in Jesser’s results is that the first drying curve is notreversible. Work done in this laboratory confirms this.

30 t 1 1 ! 1

0 Isf dry]ng

A Is f we ffing

26 - ❑ 2nd drying

o 2nd wkftlng /st drying

W/C = O 2S9Curing 3 cloys in Woter

~ 22

1!

t

18zalLJ .------ w-

~.

l~t wett!ng

z 1 ,a

I I

zO 28 - 0 Ist dryingLJ b Isf wetfingL_al o 2nd drying

% w/c = 0.?5 /s~drying,3 24 - Curing .?8 doy$ in woter

versus relative vapor

1600.2

pressure,084 0.6 Oa 1<0 Leopold Jesser Zemerd

Reletive Vapor Pressure, p/~ v,76, P.747 (19$?7)


.———__-. ——___ _

cement pasteZement v. 90, P. 67$? (1931)

Fig. 17 - Diagram for apparatus used by Giertz- \Bc CrEF

Hedstrom for determining isotherms far hardened

L-

iioa - old specimen -age not givenL.alQ+.60

M

w/c =046 ,j Cured inc moi~f air

G 40

:

; 2(I

o0 0.25 0.50 0.75 Loo

b-Age variable

c - Gypsum-free cement d-cement containing 10’%gypsumRelative Vapor pressure p/p~

Fig: 18- Isotherms for hydrated cementGiertz-Hedstrom, Zement v. $?0, p, 734 (1941)

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE 7$?7

Giertz-Hedstrom(32J published a number of isotherms for hardenedpaste. His procedure can be explained with the aid of Fig. 17. A pump,A, circulated air through a copper coil, B, a flow-meter, C, a wash bottle,D, and the sample-holder, F. The wash bottle, D, contained diluteHzSO* and was partly filled with glass beads. The manometer, G,measured the pressure drop across D and F. The apparatus, except forthe pump, was kept at a constant temperature in an air thermostat, Al-g sample of pulverized, saturated paste was placed in F, which was de-tachable and served as a weighing bottle. Air was passed through thesample until periodic weighing showed that it had reached constantweight. When this point was reached, the HJ$Od-solution first used inD, which was made very dilute to give a high relative vapor pressure,was replaced by a more concentrated solution and the sample was driedto constant weight at the lower relative vapor pressure. This procedurewas repeated with progressively more concentrated HJ104-solutions, andended with concentrated H2S04, so that several points were obtainedalong the isotherm. Giertz-Hedstrom’s results are given in Fig. 18.

Berchem(33J has published isotherms for hardened cement and forhardened specimens of, three of the principal compounds of portlandcement, His method was essentially the method of Giertz-Hedstrom.As shown in Fig. 19 he obtained no experimental points at vapor pressuresabove p = 0.63 p,.

So far as the authors know, Jesser, Giertz-Hedstrom, and Berchemare the only investigators who have published isotherms for hardenedportland cement pastes. *

Relationship between isotherms and isobars. In general, isotherms andisobars give information about the fixation of different portions of thewater in the hardened paste. The isotherms give information about thefixation of that part of the water that is evaporable at a constant tem-perature, usually near room temperature; the isobars, on the other hand,give information about the fixation of the water that is not evaporableat room temperature. An exception is the work of Krauss and Jorns who,instead of determining isobars at a very low water vapor pressure as iscommonly done, determined isobars at a vapor pressure of 7 mm Hg.This corresponds to a relative vapor pressure of approximately 0.3 at25C. Thus, the range of their isobars overlaps the lower part of theisotherms given above as well as those determined in this laboratory.

A’ignij%ance of isotherms. The isotherms, like the isobars, indicatethat the hydration products are predominantly colloidal. They can beinterpreted so as to give information about the volume and surface

*Gessner w has also studied the relationship between water content and relative vapor pressure ofcement pastes. However, ins~ead of determining a complete isotherm for a single sample, a differentsample was wed at each relntlve vapor pressure. Moreover, the procedure was such that the extent ofchemical reaction and the water-cement ratio were diflerent for each. Thus, many variables are involvedand it is difficult to interpret the ourv=.

1S!8 JOURNAL OF THF AMERICAN CONCRETE INSTITUTE October 1946

gtJ I M I I

16~o 0.2 0.4 0.6 0.8

Fig. 19 - Water content vs.vapor pressure relationship

Berchem, Diw Eid . Techn,RHochschule, Z.ric (1936)

o

Relative Vapor Pressure, p/p$

area of the solid phase and other significant features of the propertiesand behavior of hardened paste. The presentation of such data and theirinterpretation are the main purpose of this paper,

Studies of water fixation by means of freezing teds

Studies of water fixation by means of freezing tests in various materialssuch as soils and plants have been reported by several investigators.Similar studies of hardened portland cement paste were reported byGiertz-Hedstrom@5j and by von Gronow(ao), With respect to this methodGiertz-Hedstromt8TJ says: “In all these tests the treatment is compar-able with a reduction in water vapor pressure, that is to say, a form ofdrying out but with the addition of a different complication for eachmethod. ” *

In a later paper the work done in this laboratory on the freezing ofwater in hardened portland cement pastes will be described,

SUMMARY OF PART 1

The material presented in Part 1 attempts to review the most signifi-cant information obtained by other investigators on the physical prop-erties of hardened portland cement paste, It describes the experimentalprocedures and presents the test data of several important investigations.

*See a!ao F, M, Lea, Cement and Cement Manufacture, v, 5, p. 395 (1932).

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE 1i29

From reported microscopic studies it can be conoluded that hardenedcement paste is predominantly of submicroscopic texture, The onlymicrocrystalline hydrate consistently reported is calcium hydroxide.13rownmiller found this to occur in clusters of very small crystals in the“cement gel, ” Although the gel state is theoretically unstable, 130gueand Lerch found no evidence of change toward the microcrystalline stateover a period of 2 years, However, Ktihl found evidence of such a changein pastes about 20 years old,

X-ray analyses do no more than confirm results of the microscopicmethod,

The relatively few reported observations made with the electronmicroscope indicate that the hydration products of portland cement maybe colloidal but not amorphous, That is, they, may be made up ofsubmicroscopic crystals.

Several studies of physical properties of paste have been made bystudying the fixation of water in hardened portland cement paste, Suchstudies are based on the fact that the characteristics of hydration ordehydration cmrves depend on both the physical and chemical character-istics of the materials involved, In hydroxides the water loses its chemicalidentity and appears in the structure as OH-groups, In many compoundsit is bound molecularly by covalent bonds, In a third type of compoundsome of the water is bound by hydrogen bonds, In all the types of bind-ing just mentioned the amount of water combined c,an usually be repre-sented in a definite chemical formula and when the particles are ofmicroscopic size or larger, such hydrates are stable through definiteranges of temperature and pressure,

In bodies of the zeolite type the water molecules are believed to bepacked in the interstices of the solid structure and they are relativelyloosely bound to the solid,

Any solid is capable of holding a small amount of water or othersubstance on its exposed surface by adsorption, The quantity held inthis manner can be large when the specific surface of the solid is veryhigh,

The amount of zeolitic water or adsorbed water held by a solid de-pends on the temperature and pressure of the water vapor surroundingthe solid and the ~mount varies continuously with changes in eitherpressure or temperature.

A graph of the relationship between water content and temperatureat constant vapor pressure is called an ‘iisobar, ” The shape of theisobar of a hydrous solid depends on the specific surface of the solid andupon the nature of the combination between the solid and the water.Microcrystalline hydrates give stepped isobars having one or more steps,


The same hydrates reduced to submicroscopic particles of various sizesproduce smooth isobars, showing more water in combination at the lowertemperatures and less water at the higher temperatures than does thesame material in the microcrystalline state. The isobar for zeolitic orfor adsorbed water is a smooth curve under all conditions.

A graph of the relationship between water content and water vaporpressure at constant temperature is called an “isotherm.” For micro-crystalline hydrates the isotherm, like the isobar, is stepped. Thematerial retains more water at low vapor pressures and less at high vaporpressures than does the same material in the microcrystalline state.This conclusion is based partly on experimental data and partly oninference from the isobaric relationships.

Under certain conditions isotherms from silica gel show a step similarto that of a microcrystalline hydrate. The resemblance is superficial,however, as other information shows that no definite hydrate existsover any given pressure range.

Isobars from portland cement paste have been obtained by severalinvestigators, The findings of different investigators vary in some de-tails. In general they show that the isobar is a smooth curve except forone step that is attributed to the decomposition of calcium hydroxide.

Isobars from the four principal compounds of portland cement, hy-drated separately, show that the hydrates of C3S and CMSresemble thatfrom portland cement, whereas the hydrates of CSA and C4AF showmainly the characteristics of microcrystalline hydrates, a step occurringat about 240F when vapor pressure is about 0.1 micron. The fact thatMeyers found no step on the isobars fcsr portland cement at 240F isevidence that the hydrates of C,A and CA F that occur in portlandcement are not the same, at least with respect to physical state, as thosewhich form’ when these compounds are hydrated separately.

Isotherms from portland cement pastes have been obtained by a fewinvestigators. The isotherms give information about the fixation of thatpart of the water that is evaporable at a constant temperature, usuallynear room temperature, whereas the isobars give the information aboutthe fixation of that part of the water that is not evaporable at roomtemperature. The isotherms that have been obtained agree with theisobars in indicating that the water in hardened paste is not held as it isin microcrystalline compounds, Instead, the manner of binding issimilar to that between water and silica gel.

Some studies of water fixation by a freezing-out procedure have beenreported. The method is fundamentally similar to the drying-out pro-cedure and the results obtained have about the same significance.


The data on the isothermal relationship between water content andvapor pressure obtained before the present investigation are too few tothrow much light on the question of paste structure. Several of theearlier investigations were conducted under what are now known to befaulty test conditions.

,;

REFERENCES

(1) E. Freyssinet,Scienceet Industrie, Jan., 1933.(2) S. Glertz-Hedetrom,“Proc. Symposiumon the Chemistry of Cements,” p. 505

(Stockholm1938).(3) R. H, Bogue, “A Digest of the Literature on the Nature of the Setting and Hard-

ening Processes in Portland Cement, ” Portland Cement Association Fellowship PaperNo, 17 (O& 1928).

(4) L. S. Brown and R. W, Carleon, Proc. A.S.T.31. v. 36, Pt. II, 332 (1936).(5) Hans Kuhl, “Cement Chemistry and Theory and Practice,” p. 34, Concrete Pub-

lications Ltd., London.(6) Ref. 5, p, 36.(7) Henri Le Chatelier, Cornpt. rend. v. 94, p. 13 (1882) “The Constitution of Hy-

draulic Mortars,” (1887). Translated by J, L. Mack, McGraw-Hill, New York (1905).(8) L, T, Brownmiller, ACI JOURNAL, Jan. 1943; F%-oceedings v: 39, p. 193 (1943).

(9) B, Tavasci, Richerche sulla Constituzione del Clinker di Cemento Portland, Giorn.them. id appla’ca/a,p. 583 (Nov. 1934).

(10) H. Insley, J, Res. Natl, Bur. Stds. v, 17, p, 353 (1936).(11) W. Eitel, Angewandte Chemie, v. 54, p. 185-193 (1941).(12) C. M. Sliepcevich, L. Gildart and D. L. Katz, Ind. Eng. Chem v. 35, p. 1178

(1943).(13) Stockholm Symposium, p. 513. (See Ref. 2)

(14) E. Brandenberger, Schweizer Archiv, p. 45,1937.(15) R. H. Bogue and Wm. Lerch, Ind. Eng. Chem. v. 26, p. 837 (1934), or Paper

No. 27, Portland Cement Association Fellowship, National Bureau of Standards, Wash-ington, D. C.

(16) H. J. Emeleue and J. S. Anderson, “Modern .4spects of Inorganic Chemistry, ” D.van Nostrand, Inc., p. 163, New York, 1942.

(17) R. M. Barrer, Trans. Faraday SOC.v. 40, p. 374 (1944).(18) Stephen Brunauer, “The Adsorption of Gases and Vapors,” Vol. I, Chapter 7,

Princeton University Press, 1943.(19) T. Hagiwara. In “Colloid Chemistry” by J. Alexander, Chapter 38, The

Chemical Catalog Co., 1926.(20) P. A. Bonsdorff, Pogg. Ann. v. 27, p. 275 (1833).(21) H. B. Weiser and W. O. Milligan, J. Phy.s. Chem. v. 38, p. 1175 (1934).(22) W. P. Kelley, Hans Jenny, and S, M. Brown, Soil Sci. v. 41, p. 260 (1936).(23) H. B. Weiser, W, O. Milligan and J. Holmes, J. Phys. Chem. v. 46, p. 586 (1942).(24) R. Wilson and F. Martin, ACI JOURNAL, Jan. -Feb., 1935; l%oceedirtgs v. 31, p.

272.

(25) F. M. Lea and F. E. Jones, J. Sot. Chem. Id v. 54, p. 63 (1935).(26) F. Krauss and G. Jorns, Zement v. 20, pp. 314, 341 (1931); also ibid v. 19, p.

1054 (1930).(27) K. Endell, Zement, v. 15, p. 823 (1926).(28) S. L. Meyers, Pit and Quarry, v. 35 p. 97, July, 1942.(29) Thomas F. Anderson, “The Study of Colloids with the Electron Microscope,”

from “Ilecent Advances in Colloid Science,” Interscience Pub. Co., New York, (1942).

13$? JOURNAL OF THE AMERICAN CONCRETE INSTITUTE October 1946

(30) L, Jesser, Zemeru!v. 16, p. 741 (1927); v.,,18, p. 161 (1929). Earlier reports in“Protokoll der Generalversamrnlungen des Veremes der Osterr.” Zementjabrikanten,1912, 1913, and 1914.

(31) J, M, van Bemmelen,“Die Absorption,”Dresden, 1910.(32) S.Giertz-Hedstrbm,Zernentv. 20,pp. 672,734(1941).(33) Hans Berchem,Dissertation,Eidg. Tech, Hochschule,Ztirich,1936.(34) H, Gessner,KolloidZeitschrijt v, 46 (3) (1928); v. 47 (l-2) (1929).(35) S. Giertz-Hedstrom, Zement v. 20, p. 672 (1931).(36) H. E. von Gronow, Zement v. 25 (1936).(37) Stockholm Symposium, p, 517. (See Ref. 2)

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE $?49

Part 2. Studies of Water Fixation

CONTENTS

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...250Porosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...251

Classification of water in hardened paste. . . . . . . . . . . . . . . . . . . . . .252

Materials and experimental procedures. . . . . . . . . . . . . . . . . . . . . ..253

preparation of specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...253

Neat cement cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...253Mortar specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...253

Truncated cones. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...255

Testing of mortar specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...255

Preparation of samples for studies of hardened paste. . . . . . . . ...255

Mortar specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...255

Neat cement cylinders and mortar cones. . . . . . . . . . . . . . . . . ...255

Neat cement slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...256

Drying of samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...256Reproducibility of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...256

Determination of non-evaporable water. . . . . . . . . . . . . . . . . . . . . . .257

Degree of desiccation of dried samples. . . . . . . . . . ~. . . . . . . . ...258Stability of hydrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...260

Determinationof total evaporablewater. . . . . . . . . . . . . . . . . . . . . .263

Discussionof granular samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . ...265Neat cement-effect of granulationon porosity. . . . . . . . . . . ...266Neat cement-effect of dryingon porosityof granules. . . . . ...266Mortar specimens-effect of granulation on porosity of paste. .266

Methods of studying the evaporable water. . . . . . . . . . . . . . . . . ...267

The apparatus for sorption measurements. . . . . . . . . . . . . . . . . . . . .269High-vacuum apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...269

Air-stream apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...271

Reproducibility ofremdts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...274

Useof ordinary desiccators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...275

$?50 JOURNAL OF THE AMERICAN CONCRETE .INSTITUTE November 1946

Results of sorption measurements-Empirical aspects of the data, 275

General features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...275

Comparisonofthe results obtained with high-vacuum and air-stream apparatus . . . . . . . . . . . . . . .,....,....,............,.282

Effect of extent of hydration on the position of the adsorptioncurve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .289Influence of original w/con the shape of the adsorption curve. .,290

Empirical relationship between the amount of adsorption atlow pressures and the non-evaporable water content. . . . . . . . . . .293

General results from various cements. , . . . . . . . . . . ., ., . . . . ...294Effect ofsteam curing....,.,...,,, ... .,. .,. ... ,, . . . . . . . ..3oo

Sunlmary of Part 2 . . . . . . . . . . . . . . . . . . . .,...........,......,.300

References . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . ...302

INTRODUCTION

In the preceding part of this paper some of the methods of studyinghydrated portland cement paste were reviewed and the principal resultsobtained by previous investigators were presented. In this part of thepaper the studies of water fixation carried out in this laboratory will bedescribed. *

As shown in the first section, water fixation has claimed the interest ofseveral investigators. The reason for such interest is not hard to find.Some of the water associated with hardened cement paste is obviouslya constituent of the new solids produced by chemical reactions. Ifall such water is driven from the paste, the cohesion of the paste is de-stroyed, Another part of the water, amounting in saturated paste to asmuch as 50 percent of the volume of the paste, or even more, is free toleave the hardened paste without destroying the cementing value of thematerial. It does, however, have important effects on the hardenedpaste: the paste shrinks as water is lost and swells as it is gained; thestrength and hardness of the hardened paste vary with its degree ofsaturation; some of this water is freezable and is thus a source of dis-ruptive pressures that tend to disintegrate concrete exposed to weather.Furthermore, the amount of water that is free to come and go in responseto changes in ambient conditions is an index to the degree of porosity ofthe hardened paste. The porosity is obviously an important propertyof the material related directly to its quality.

One incentive for studying the fixation of water in hardened pastewas the possibility that suitable measurements of the manner in which thewater is associated with the solids would provide the means of estimatingthe nature and size of the pores in the paste. It was hoped that such

*The characteristms of the cements mentioned in thu part may be found in the Appendix to Part 2.


knowledge would simplify the problem of relating the chemical andphysical characteristics of the cement to its quality. This hope aroserather directly from the hypothesis of Freyssinet(l) * which had a majorinfluence on our choice of experimental procedure. The chosen procedurewas intended to yield information on the porosity and pore-size dktribu-tion of the hardened paste and other information that might bear on thequestions of volume change, durability, plastic flow, etc.

Porosity. To speak, as above, of the porosity of hardened paste islikely to be misleading unless the term is properly qualified. The word“porosity” can be interpreted differently according to past experienceor to the chosen criterion as to what constitutes porosity. Certainly,the term is misleading here if it calls to mind such materials as felt orsponge.

Whether or not a material is considered to be porous depends in parton the means employed for detecting its porosity. If a material werejudged by its perviousness alone, the decision would rest primarily on thechoice of medium used for testing its perviousness. For example, vul-canized rubber would be found impervious, and hence, non-porous, iftested with mercury, but if tested with hydrogen it would be found highlyporous. The perviousness of hardened cement paste to water and otherfluids is direct evidence of the porosity of the paste.

Regardless of the size of the pore, a substance near enough to theboundary of the pore is attracted toward the boundary by one or moretypes of force known collectively as forces of adsorption. These forcesare sufficiently intense to compress a fluid that comes within their range.If the fluid is a vapor, the degree of compression may be very great;the vapor may be liquefied or solidified; if the fluid is already a liquid, itmay undergo further densification on making contact with the solidsurface, Since the range of the forces causing such effects is very small—a few hundredths or thousandths of a micron—only a negligible part ofthe enclosed space in pores of microscopic or macroscopic dimensions iswithin the range of surface forces. However, when the pores are of thesame order of magnitude as the range of surface-forces, it follows that alarge portion, or all, of the enclosed space is within the range of surfaceforces. For this reason, substances containing a large volume of sub-microscopic pores exhibit properties and behavior not noticeable inordinary porous bodies, For example, porous bodies of submicroscopic(colloidal) texture shrink and swell markedly on changing the liquidcontent of the pores, the magnitude of the effect being controlled bythe intensity of attraction between the solid and the liquid. Moreover,changes in liquid content alter such properties as strength, elasticity,

●Seereferences,end of Part 2.

!259 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

heat content, and other properties that in non-colloidal solids are vir-tually constant at a given temperature. Some of these effects will bethe subject of discussion farther on.

CLASSIFICATION OF WATER IN HARDENED PASTE

The present discussion aims to elucidate those features of a hardenedpaste that are revealed by the relative proportions of the total watercontent that fall in three different categories, as follows:

(1) Water of constitution,

As used here, this term refers to water of crystallization orwater otherwise chemically combined; it refers to water that is apart of the solid matter in a hardened paste.

($2) Water bound by surface-forces-adsorbed water.

(S) Capillary water.

This is that water which occupies space beyond the range ofthe surface-forces of the solid phase.

The above classification is of little practical use, for as yet no way hasbeen devised for actually separating the total water content into suchdivisions. Or, drying, water of category (2) and of category (3) are lostsimultaneously. Furthermore, not all the water in these two categoriescan be removed without removing also some of the water of constitution(category (1) ). Nevertheless, since evaporation or condensation is themost feasible means of manipulating it, the total water must be studiedfirst with r~spect to the relative volatilities exhibited by different portionsof it. From such data, means of estimating the amounts of water in thethree categories given above have been developed, as will be shown.

The water in a saturated, hardened paste is classified in this paperaccording to its volatility as follows: The water that is retained bya sample of cement paste after it has been dried at 23 C to constantweight in an evacuated desiccator over the system Mg (C10&0X120 +Mg(C10J2.4H20 as a desiccant* is regarded, in this discussion, as “fixed” or“combined” water, To avoid any unintentional commitments as to thestate of combination of this part of the water, it is called non-evaporablewater. The rest of the water in a saturated specimen is called the evapor-able water. The non-evaporable water probably includes most of thewater of constitution, but not all of it, for at least one of the hydrates,calcium sulfoaluminate, is partially decomposed when the evaporablewater is removed. On the other hand, it is not certain that all the non-evaporable water is water of constitution, for it is possible that some of

*Thematerialinpurchasedas ‘‘Dehydrite’’-Mg(fOJzJz. The two molecules of water are added at thetime of use. See Drving of Samples.


it can be removed (by slightly raising the temperature) without decom-posing any compound present. (See Part 1, Isobars from PortlandCement Paste.) In this connection, a reading of Lea’s paper “Water inSet Cement” is recommended,2

MATERIALS AND EXPERIMENTAL PROCEDURES

The materials used for these studies were hardened neat cement pastes,pastes of cement and pulverized silica, or cement-sand mortars madewith a wide variety of commercial and laboratory-prepared cements.The experimental procedures differed somewhat from time to time andwith the type of specimen employed. The general features of the pro-cedures will be described here, and certain other details will be given atappropriate points in other sections of this paper. A detailed descriptionof the materials and methods of the various projects will be found in theAppendix to Part 2.

PREPARATION OF SPECIMENS

Neat cement cylinders

(Series 254-K4B and 254-MRB). Neat cement specimens were pre-pared, usually at a water-cement ratio of 0.5 by weight, by molding themixed paste in cylindrical wax-impregnated paper molds ~-in. by 6-in.long, In some investigations cylindrical molds of other types were used.The molds were stoppered and laid in water horizontally as soon as theywere filled, and the stoppers were removed after about 24 hours so thatthe curing water might have ready access to the cement paste.

In mixing the pastes, 200 g of cement was mixed with the desiredamount of water in a kitchen-type mixer. The mixer was operated attop speed for two minutes and then the paste was allowed to rest forthree minutes, and finally mixed again for two minutes. This procedurewas followed to avoid the effects of certain types of premature stiffening,whether or not the cements showed any such tendency.

Mortar specimens

The majority of the mortar specimens were made from the mixesshown in Table 1.

TABLE I–MIXES FOR MORTAR SPECIMENS

(Series 254-S-9-10-11)

Mix

—..

ABc

I Proportion by weight I Batch quantities in grams

Cement Pu~&ed Stannd

1.00 1.640<3 2.30

;:: 0.71 3.65

Cement Pulverized Standardsilica sand

1400 23001000 GO 2300750 530 2300

s254 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

A~ indicated in the Table 1, the aggregate consisted of standardOttawa sand (20-30 mesh) and pulverized silica, the latter being of aboutthe same specific surface as ttie cement. The quantity of silica wassuch as to give all the mixes about the same total (absolute) volume ofcement + silica + water.

The water-cement ratios were adjusted to give a 1~-2-in. slump(6-inch cone) and varied through a small range with the different cementsused. The values (after bleeding) were about 0.33, 0.45, and 0,58 formixes A, B, and C, respectively.

The batches were mixed in a small power-driven, open-tub mixer.Each batch was first mixed 30 seconds dry and then for 2 minutes afterthe water was added, Two operators working simultaneously then madeduplicate slump tests and returned the slump samples to the mixing tub.After remixing the material for 30 seconds, 2x2-in. cubes and 2x2x9 ~-in.prisms were cast in watertight, three-gang molds which had beenpreviously weighed,

Measurements were made from which the air contents and the loss ofwater due to bleeding could be computed. This procedure was as follows:Before each cube mold was filled, its outside surface was carefully cleanedand, after filling, the mold and contents were weighed, Then the moldwas placed in saturated air. After two hours, water that had accumu-lated at the top through settlement was carefully removed with absorbentpaper and the mold again was weighed. The molds were then im-mersed in water at 70 F where they remained for at least 12 hours. Theywere then removed from the water, dried with paper and again weighed.Following thk the specimens were removed from the molds, weighed inair surface-dry, and then in water so as to obtain the weight and volumeof the material, The cubes were then stored in a fresh supply of waterat 70 F where they remained until test or until they were 28 days old.Those that were scheduled for tests beyond 28 days were then stored in thefog room at 70 F.

During the water storage the water was changed periodically to preventthe building up of high alkali concentration.

At the scheduled time of test the cubes were again weighed in thesurface-dry condition and under water, Those that had had a period ofstorage in moist air were placed in water one day before the scheduledtest date to allow them to absorb water if they could.

The data obtained in this manner made it possible to ascertain theaverage amount of original unhydrated cement, silica, sand, water, andair in each group of companion hardened specimens,

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE !255

The prisms were treated in the same way as the cubes except that themeasurements of settlement (bleeding) were not made.

Truncated cones

In one of the earlier investigations (Series 254-7) mortar specimenswere cast in watertight, truncated cones of 4-in. base, 2-in. top diameter,and 6-in. height. Measurements similar to those made on the cubeswere made on these cones before and after removing the molds. Thisgave accurate data on the settlement and the final proportions of theingredients of the mixtures.

TESTING OF MORTAR SPECIMENS

At the scheduled test ages, which usually ranged from 7 days to 6months, two cubes of a kind were tested for compressive strength.Throughout these procedures the cubes were carefully kept wet and,after being tested, cubes of a kind were placed immediately in airtightcontainers,

PREPARATION OF SAMPLES FOR STUDIES

OF HARDENED PASTE

Mortar specimens

The tested mortar cubes in airtight containers, mentioned above, weretaken from the containers as soon after the strength test as possible andpassed quickly through a small jaw crusher. The crushed material wasimmediately transferred to a nest of sieves (No. 4-8-14-28-35-100-150)al~ead y cleaned, assembled, and sealed at the joints with \vide rubberbands, The sieves were shaken on a sieving machine for 5 or 10 minutesand then, to prevent losses of water by evaporation, the nest of sieveswas opened in the moist room and the material caught between the 35-and 100-mesh or, in some series, between the 48- and 100-mesh sieves,was transferred to a screw-top sample bottle. This material, whichconsisted of granules of hardened cement paste or hardened paste andpulverized silica, was used for the studies to be described.

Neat cement cylinders and mortar cones

The neat cement cylinders and mortar cones were weighed in air and inwater by procedures somewhat like that described for the mortar cubes.Then, since no physical tests were made on these specimens, they wereimmediately passed through the jaw crusher and a granular sample wasoht ~ined by the procechlrc described above. In some of the earliest tests

956 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

the crushing was done with mortar and pestle, but this procedure per-mitted too much drying and carbonation of the material,

Neat cement slabs

For the most recent project of this study (Series 254-18) the testsamples were very thin, neat-cement slabs. These were prepared fromcylinders by sawing off slices and then grinding the slices on a glass platewith Carborundum dust and water, By this method the slabs werereduced to an average thickness of about 0.3 mm. When saturated,they were translucent.

DRYING OF SAMPLES

The granular samples described above, in quantities not exceeding15 g, were placed in wide-mouthed weighing bottles and stored invacuum desiccators with anhydrous magnesium perchlorate (Dehydrite),(The desiccators were exhausted with a Cenco Hyvac pump,) When anexcess of the anhydrous desiccant was used, the effective drying agentwas a mixture of Mg(CZO& and Mg(CZOi)Z.2H@, With the thought ofavoiding the dehydration of the calcium hydroxide, we used a quantityof anhydrous magnesium perchlorate in each desiccator such that whenthe original compound had combined with all the water given up by thesamples the desiccant had become a mixture of Mg(C10&,2Hz0 andMg(CIOJz.4H20; that is, this was the mixture that determined the finalwater vapor pressure in the desiccator. (Although this was the inten-tion, there is some evidence in the data that the desired result was notalways realized. In some cases the final desiccant was probably themixture Mg(CIO& + Mg(CIOJz.2Hz0. Some of these cases are mentionedin later discussions, but it was impossible to identify all cases withcertainty.)

In some of the earlier projects other desiccants were used, namely,Pz06, H2~04j and CaO. In some the drying was done in desiccators con-taining air instead of in vacuum desiccators. However, most of the datareported here were obtained by the procedure described above.

Reproducibility of results

To test the reproducibility of results obtained by the drying procedureused for the greater part of this investigation, four sets of samples,each comprising 11 companion portions, were prepared from a single neatpaste specimen 3% months old. The results are given in Table 2.

The differences among the figures in any one column indicate thedegree of variation among the samples in a given desiccator. The figuresfor the average loss for the different sets indicate the variations, if any,between conditions in different desiccators. The average losses for setsA and B are slightly higher than for sets C and D. Sets A and B were


TABLE 2–REPR0DUC1BILIT% OF DRYING LOSSES

Cement: Laboratory blend of 4 commercial brands, Lot 13495Nominal W/C = 0.50 by wt.CUfina: 3M months in ~a~r

SaNmople

Average

A

19.8120,0619.9319.9920,0620.0919,9820.0020.1320.0019,72

19,98

Loss of water-% by wt.

B

20.1420.0120.1020.1320,1020.0720.0420.0920.0320.0420,20

20.09

c— D

19.7519.8419.8519,6619.6719.8619.9319.6319.8419.7419.58

19.76

19,8719.8019.9619.8919.8219.8419.8719.8719.8419,7919.90

19.86I

dried immediately after they were prepared. Sets C and D were storedin screw-top sample bottles-for about one week before they were dried.It seems, therefore, that the smaller loss from sets C and D was probablydue to the additional hydration of these two sets during the one-weekwaitihg period.

DETERMINATION OF NON-EVAPORABLE WATER

One-gram portions of the samples dried as described above were heatedat about 1000 C for about 15 minutes. The samples were cooled andweighed and then given a 5-minute reheat to check the completeness ofignition. The amount of loss minus the ignition loss of the originalcement is called the non-evaporable water content of the sample.

The computation involves the assumption that the weight of the non-evaporable water is exactly equal to the increase in ignition loss. Suchan assumption introduces some error. In the first, place the originalcement was not pre-dried as were the hydrated samples before determin-ing loss on ignition. Hence, the ignition loss as reported for the originalcement might be slightly above the value correct for this computation,A second, more serious, source of error arises from ignoring the increasein the amount of combined carbon dioxide. Although precautions againstexposure of the granular samples of hardened paste to carbon dioxidewere taken, some carbonation did occur. Tests made on 15 differentsamples showed that in 60 percent of the cases carbonation amounted toless than 0.5 percent of the weight of the original cement. However,carbonation as high as 1.9 percent was found. When carbonation hasoccurred, the loss on ignition of the carbonated sample will be greater

$?58 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

than the non-evaporable water content before carbonation occurred.The increase is about 0.59 times the weight of CO~ combined. Forexample, if the loss on ignition is 0,2 g per g of cement greater than theoriginal loss on ignition, and if the C02 content has increased by 0,005g per g of cement, the non-evaporable water would be 0.2 minus thequantity (0,005 x 0.59) = 0.197. Thus, in this example, the assumptionthat the increase in loss on ignition is equal to the non-evaporable waterresults in an error of about 1,5 percent, At earlier stages of hydration,when the loss on ignition is smaller, the relative error would be consider-ably greater for the same amount of carbonation.

Since the necessary data are available on only a few of the samplesand since also there is some question as to the accuracy of the figuresfor amount of carbonation, no attempt to correct loss on ignition for COZwas made in preparing the data for this report. Variations in the amountof carbonation among the various samples undoubtedly contribute tothe random variations that will be noted,

Degree of desiccation of dried samples

The degree of desiccation obtained by the drying procedure describedabove is indicated by the data given in Table 3, which gives also theresults obtained with other desiccants, For brevity, only one of the twocomponents of the desiccating mixture is given. The samples testedwere neat cement pastes (original w/c (by wt. ) = 0,5), that had beencured 1 year in water. Each paste was made with a different cement,the group representing a wide range in chemical composition.

It will be noted that with any given desiccant, the percentages of non-evaporable water for the di ll~:rcnt pastes cliffer over a considerablerange. However, it is significant that all the results obtained with onedesiccant bear a virtually constant ratio to the results obtained withanother. This is shown in Table 4, where the results are expressed as

TABLE 3

(Data from Series 254-K4B)

Water retained at equilibrium with the desiccantindicated, ~. by wt. of cement in specimen

—P$ts P*OS Mg(CIO,)z Mg(CIOJ,.2H,0 H,S04

cone.——

4s 18.3 21.4 22.8 22.35s 17.4 20,6 22,0 22,7

;921.4 25,4 26,6 27,121.1 25.2 26,5 27.1

7s 20.6 24.6 25,9 26,511s 17.6 20.9 22.2 22.5


PasteNo.

4s5s7Q7P

1!:

TABLE 4

Amount of water retained relative to thatretained by Mg(CIOJa.2Ha0

P,O.!

0.800.790.800.800.790.79

Mg(c204)2

0.950.94

Mg(CIO,)z.2H,0

1.001.001.001.001,001.00

:.;;*

1:021.021,021,02

*Thievaluei probablyin-er’ror-toolow. In another group of testi, the ratio for cono. H2S04 w= foundto be 1.08. . Po ibly the sulfuric acid used in this second group had a slightly higher water vapor pressurethan the acid represented in the table.

ratios to the quantity retained over a mixture of magnesium perchloratedihydrate and magnesium perchlorate tetrahydrate.

The published information on the actual water vapor pressures main-tained by these desiccants is not entirely satisfactory. The values givenin Table 5, below, are the most reliable that can be found. Note thatthese values are upper limits; the actual water vapor pressures may be

P206

Mg(CIO&(anhyd.)

Hx.S’04

CaO

TABLE 5

Residual water at 25 C

<2.5x1W

<3 x 10-3

<3 x 103

<3 x 10-~

Relative vaporpressure,

P/Pa*

<lxlo~

< 130x 10-0

< 130x 10-e

<130 x lW

Reference

(1)

(3)

(2)

(3)

*P = .ex~tin.g water vapor premure. P* - wa~r vapOr pr~ure over ~ plane surfa~ Of pure watir-the“saturation pressure”at a given temperature.

(1) Morley, J. Am. Chem. Sm. v. 26, 1171 (1904).?(2) Morley, Am. J. Sci. v. 30, P. 141 1S85).

(3) Bower, Bureau Stale. J. Research v. 12, p.246 (1934).

The data for CaO are open to question. Evidence to bee presentedin Part 4 indicates that the equilibrium relative vapor pressure of waterover CaO may be much less than the value given.

The data for Pz06 and HZ804 are the result of very painstakingmeasurements and are probably close to the correct ones. The resultsin Table 4 bear this out. The amount of water retained by pastes driedo~,er PZ05 is less than that retained over any other desiccant; that re-


tained over Hz804, cone., is more. With respect to i14g(C10&(anhyd.),the water vapor pressure maintained by this desiccant is certainly farless than the upper limit given in Table 5, The data in Table 4, togetherwith the data given on page 286, indicate that the relative vapor pres-sure is well below 24 x 10-6, the vapor pressure of water at dry icetemperature (-78 C) relative to “saturation pressure” at 25 C.

Data on the vapor pressure over Mg(C104)z.2Hz0 are not availablein the literature. However, the data on page 286, indicate that it isabout 24 millionths of the “saturation pressure. ”

A method of drying more commonly used than the isothermal pro-cedures just discussed is that of oven-drying at a temperature at orslightly above the normal boiling point of water. To compare the degreeof desiccation obtained from such oven-drying with that obtained iso-thermally over flfg(CIO~)~.2H~0 +My(C10~),.4Hz0, four samples that hadpreviously been dried by the latter procedure were placed in an ovenat 105 C and allowed to come to constant weight, The results areshown in Table 6.*

TABLE 6

ILoss in weight in oven—~. of non-

evaporable water content asNO. found by isothermal drying overof Mg(CIO,),.2H,0 +

Sample Mg(CIOJ,.4H,0—————..-—————.—— ———c

16213 101621416198 ;:15669 13

Stability of hydrates

The figures given in the foregoing paragraphs indicate the “degreeof dryness” produced by the method adopted for this investigation interms of the amount of water retained by the paste and the relativevapor pressure of this residual waterl called non-evaporable water. Anattempt will now be made to indicate the amount of water retained bythe hydrated compounds of portland cement when dried by this pro-cedure.

The microscope reveals that both microcrystalline and colloidal ma-terials occur in hardened paste, the colloidal material appearing as anamorphous mass enclosing microcrystalline Ca(OH)z and unhydratedresidum of the original cement grains. Any such microcr~%talline hy--..

l!, t his t c-t !),, :$tlernpt was mnde to control tl]e water vapor pressure in the oven. This i~ the incorrectIU*>,ml,,] e tl, ut I):i: fre<jue]ktly been used in studies of this kind.

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE S!61

drate will remain unaltered during the process of drying if its dissocia-tion pressure is lower than the vapor pressure maintained by the dryingagent. If the dissociation pressure of the hydrate is higher than the vaporpressure maintained by the drying agent, dehydration is possible butnot certain; only direct trial will tell whether it will occur under the con-ditions of the experiment, Under suitable experimental conditions, thehydrate will lose one or more gram-molecular weights of water per moleof hydrate without appreciable change in vapor pressure, the amountlost being determined by the nature of the hydrate,

As was shown in Part 1, the water content of colloidal hydrates bearsno small-whole-number, molar ratio to the anhydrous material (exceptperhaps by chance) and none of it can be removed without a corre-sponding change in the equilibrium water vapor pressure. That is, thewater content of a colloidal hydrate varies continuously with changesin ambient conditions. The colloidal material in hardened cement pastespredominates over non-colloidal constituents to such a degree that thedehydration process shows only the characteristics associated withcolloidal material and therefore the dehydration curves do not indicatedirectly the extent to which the microcrystalline material becomesdecomposed.

The extent to which the hydrates of the major compounds of portlandcement are dehydrated under the drying conditions described can beestimated from the data given in Table 7. The data pertain to productsobtained by hydrating the compounds separately. The first seven linesof data show the amounts of water retained by CSS (under the dryingconditions described) after various periods of hydration. They showthat the amount is greater the longer the period of hydration, However,a maximum would be expected, though it is not clearly indicated bythese data.

As brought out in Part 1j the figures given in Table 7 should be re-garded as single points on smooth isobars and therefore have no uniquesignificance. Had the temperature of drying been higher, the amount ofwater retained at any given age would have been Iessj and vice versa.On the other hand, if the hydration products were microcrystalline hy-drates, each hydrate would probably be stable over a considerabletemperature range, with pressure constant, or over a pressure range withtemperature constant.

The alumina-bearing compounds that occur in portland cementclinker, when hydrated separately, produce microcrystalline hydrateshaving definite amounts of water of crystallization. A list of severalcompounds is given in Table 8, together with information as to theirstability in the presence of Mg(C10&2H@, CaO, or PQ.

s?69 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

TABLE 7—FIXED WATER IN HYDRATED C,S AND c,s AS REPORTEDBY SEVERAL INVESTIGATORS

Com-pound

Cw!i’”

cd’Cis’

C$NlfI(1(

(7,s’:C,@

C2S’

C/csd

‘1

11

Nominalw/obywt.

0.350,400.780.330.450.601,000.30

: ?$0.330<450.601.00

3 days

0,103

0.198————

0.;130!019

—————

“Fixed water” at age indicated,grams per gram of

original anhydrous material

7 days

——

07030.1020.1040.110

—.

0 ;200.0200.0160.017

28 days

0.146—

0743

0.1470.1500.1610,0340,043

0<360.0320.0250.026

6 mo.

0.150—

o ;070.2240,2380.2540,108

—

o T340.1420,1200,130

1 year

0,1900.213

————

07220,138

—————

3 years

—

OX-————

0;9————

— —a — R. H, Bo,guc and Wn.. Lerch, PC} Paper, No. 27.

The specimens were cured in vials ith excess water present. Material ground to Pass 100 mesh, 90percent to p-s 200. “Fixed watedried in an oven at 105 C tiith no

‘ is the loss on heating at 1000 C from samples pulverized andntrol of the water vapor pressure in the oven.

b — R. H, Bo@e,Effects of Phase Composition on the Volume Stability of Portland Cement, I’CAF (1940)(mimeographed)The specimens w,ere cured in vials with no extra water.22~0 cm8/gm.

The material was “ground to approximately‘‘ ‘“Fixed water” as in a.

c — This laboratoryThe specimens were molded and cured in extrfiction-thi mhles surrounded with water. The si Iirateswere each ground to give S5 percent passing the No. ’200 sieve, but the trisilicate, was nevertheless:~oin&. P/P. at,equdlbrlum was &bout 0.5 x 10-8. The amount of water was determmed by heating nt

d — F. P. ~asseter, Chemical I?eactions in the Setting of Portland Cement—Dissertation, ColumbiaUniversity, l!W).The epecimem were cured in vin!s with extra wuter present. Samples of -100 mesh material were dried3 hr. at 105 C in “dry C02-free air. ”

The first compound listed, the high-sulfate form of calcium sulfoalu-minate, may occur in hardened paste to the extent that gypsum ispresent for its formation (assuming an excess of CSA). The data inclicwtethat all but 9 of the 32 molecules of water of crystallization may be lost.In an average cement containing 1.7 percent SOS, all of which reactedto form the calcium sulfoaluminate, the amount of hydrated sulfoalu-minate per gram of cement would be about 0.09 g, About 0,03 g ofthis would be lost on drying.

The second item in Table 8 refers to the low sulfate form of calciumsulfoalurninate, a compound which probably does not form under theconditions prevailing in the hardening of the pastes used here. If itdid occur, the data indicate that 2 of the 12 molecules of water of crys-tallization might be lost on drying over flfg(ClO&.2H@.

The hexahydratc of C3A evidently would not be dehydrated byMg(clo4),.21f20. The 12-hydrate of C~A is reduced to abo@ the 8-hydratc on drying over Mg(CID&.2Hz0. C1.4.12Hz0 is not dehydratedlJY the conditions used for this study.


TABLE 8

Number of molecules of water retainedin the presence of the desiccant indicated

Compounda!fg(cto,)2.2H20 C’aO P20S

CsA.3Cai30e.32Ht0 9(”) $J(b) 7.5(”1d)f&ft,fh804.12H20 10(’) 8 (c)d)

C3A.6H20 (cubic) — 6;)Cd. 12H*0 (hex) — 8(’) —Cd. 12H20 — — 12(0

a — This laboratory.b — Jon@: S mposium onthe Chemistry of Cements (Stockholm, 193S), P. 237.c–Forsen: ~mentv.19, PP.l130,1255 (1930); v.22, PP.73,87,100 (l933).d—Myliu: Acta Acad, Aboen8i8v, 7,p.3(1933); seeb.e —Thorvaklson, Grace &Vigfumon: Can: J. I&9. V. 1, P. 201 (1929).~ — Assarmon: Symposium onthe Chemlatry of Umenti(StockhOlm, 193B), p.2l3.

It thus appears that of the various microcrystalline hydrates thatcan be formed from the constituents of portland cement only the calciumsulfoaluminate would be decomposed to an appreciable extent; it wouldlose 72 percent of its water of crystallization. After a long period ofhydration, the water held by the hydration products of CV5’and C’,Samounts to 20 to 30 percent and 10 to 14 percent of the weight of theoriginal material, respectively.

Before this subject is closed it should be said that the occurrence ofthe microcrystalline hydrates of C8A in hardened paste, particular CBA.-6~20, is very doubtful. Several observations indicate this. One is thefact that drying-shrinkage is greater for cements of high C8A content.This cannot be explained on the basis that CBAcombines with water toform the hexahydrate CSA.6H20, since that crystal does not lose waterunder the conditions of ordinary’ shrinkage tests.

DETERMINATION OF TOTAL EVAPORABLE WATER

The water that a sample is capable of holding in addition to the non-evaporable water is called the euaporahle water, as defined before. Theprocedure for determining the evaporable water content of granulatedsamples is as follows: About 5 grams of the sample to be saturated isplaced in a 50-ml Erlenmeyer flask fitted with a special stopper thatpermi 1A either the introduction of water from a burette or a stream ofdried air free from C02. At the start, water is slowly dropped onto thesample from the burette until the sample, upon being shaken, gathersinto a lump and clings to the flask, Dry air is then passed over thesample while it is vigorously shaken by hand. After 2 minutes of thistreatment, the flow of air is stopped and the shaking of the flask iscontinued. If the sample persists in gathering into a lump, the dryingis continued for 2 more minutes. This procedure is continued until theparticles just fail to cling to each other and to the flask. The total water

$264 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

TABLE 9—DATA ON TOTAL WATER CONTENT OF SATURATED SAMPLES

Series 254-MRB

CementNo.

.1

—.

14900149011490214903149041490514906149071490814909149101491114912149131491414915

.kverage

Age

t:;t,days

2——

126126133133162162173173200200204204212212222222

w.—c

3

0.450.390.390,420.420,410.480,410.390.480.460,460,490,410.420.44

Total water at test, wi/c

Original~pecimer

4

0.5260.4980.5150,5270,4890,4930.5510.4640,4870,5620.5210.5360.5510.4780.4950.518

0.513

——SSD 1

——5

0.5080,4910.5010,5110.4900,4900.5500,4610.4790.5480,5130.5260,5470.4770,4870.520

0,506

Granules

&SD .2

6

0,5150.4930,4950,5160.4810,4820.5410,4580.4750,5460.5100.5210.5410.4760.4990.517

0.504

SSDO

7

0.5270.5030.5110.5260.4990.5020,5670.4740.4920.5720.5350.5460,5680.493

0 ;30.—0.523

w“—c

8

0,2270.2230.2270,2270.2280.2300,2360.2190.2250.2260.2280,2290.2250.2210,2250.224——0.226

SSD = Saturated, surface-dry.SSDf = Gr~nula@d saw!e ( 100-4S mesh) dried in vacuo over WOCKX ~2H20 and then resaturated in

the presence of aLrSSD2 = Granulated sample dried i,n the earne WaY as, SSDl, and resaturated in a,~acuum.SSDO = Granulated s~w!e Of OruvnW undried material brOught tO the SSD condlt]on by adding water in

the presence of a]rw./c = ISo,n:evaporable water, g per a of cement.Wolc = CMgmal water-cement r,at]o by wt., corrected for bleedingWI/c = Total water-cement ratio at time of test

held by the sample in this condition, minus the non-evaporable water,is the total evaporable water as defined above.

Data from 40 such determinations showed that the average differencein the values obtained in duplicate determinations by a given operatorwas 0,36 percent of the dry weight. In three cases out of 40, the differencein values was more than 1 percent. Other experiments showed that theresults obtained by two operators working independently did not differmore than did duplicate determinations made by a given operator.

The procedure just described permits water to enter previously driedgranules from all sides simultaneously. Since the dried grains are knownto contain a considerable amount of adsorbed air, the question arisesas to how completely the air is displaced by the water. To answer thisquestion, some dried samples were evacuated, so as to remove most ofthe adsorbed air, and then the water for saturation was introduced in theabsence of air. Companion samples were treated in the presence of air inthe usual manner.


TABLE f O-DATA ON TOTAL WATER CONTENT OF SATURATED SAMPLESSer;es 254-K4B

Ref.No.

1

1-s1-P1-Q

4-s4-P4-Q

5-s5-P5-Q

6-S6-Q

7-P7-Q

11-P11-Q

15-s15-Q

16-P16-Q

20-s20-P20-Q

Average

Ageat

test,days

2

180180180

144138138

150146150

196191

164171

164172

202202

223223

170167176

w.—c

3

0.4700.4730.425

0.4630.4600.450

0.4270.4530.456

0.4710.447

0.4730.480

0.4450.440

0.4850.445

0.4640.456

0.4720.4620.436

0.455

Total water at test, wt/c

Originalspecimen

4

0.5560.5770.521

0.5220,5480.518

0.5020.5420.533

0.5290,532

0.5700.548

0.5210.515

0.5580,565

0.5400,516

0.5490.5510.520

0.537

Granules

IS’A’D—.

5

0,5430,5590.502

0.5100.5120.495

0.4980,5090.514

0,5080,512

0,5560.549

0.5160.509

0.5360.529

0,5250.502

0.5430,5420.508

0.520

—.—S’SDO

6

0.5570.5760.515

0.5250.5350.515

0.5100.5190.527

0.5300,536

0.5750.564

0.5320.516

0,5610.544

0.5410.520

0.5540,5550.519

0.540

w.—

c

7

~. 223—0.2330.229

0.1790.1770.177

0,1650.1590.165

0.2150.222

0.2400.239

0.1860.190

0.2170.220

0.2260.225

0.2310.2330.226

0.208

‘s” =;::::::;:4? “SiSDO = Granulated samp}e o oru%mal, undried material brought to the S’SB condition by adding water.in

w+ = N&~evaporable water, g per g of cementw./c = Original water-cement ~atlo by wt., corrected for bleedingwl/c = Total water-cement ratio at time of teat

Results are given in columns 5 and 6 of Table 9. (Table 9 gives alsoother data confirming those in Table 10. The averages 0.506 and 0.504for the ordinary and vacuum procedures, respectively, show that theair has no appreciable influence on the results.

DISCUSSION OF GRANULAR SAMPLES

Since most of the experiments to be described were made with granularsamples of the original specimens, it is necessary to consider the extentto which the granules differ from the original material.


Neat cement—effect of granulation on porosity

Table 10 gives water content data for a group of neat cement specimensand the granular samples prepared from them. The original specimenswere lx7-in. neat cement cylinders that had been stored under waterfor the periods shown in column 2, During the curing period, they

gained in weight, the average gain being 0.082 gram per gram of cement(0.537-0.455).

From each specimen one granular sample (100-48 mesh) was preparedand then saturated by adding excess water to the granules. The excesswas evaporated until the saturated surface-dry condition was reached,The results are given in column 6. A comparison of columns 4 and 6 willshow that if the difference shown is significant, we may conclude thatthe saturated granules held slightly more water than the original speci-men did at time of test. This indication is somewhat more definite inTable 9. Compare columns 4 and 7. This proves that in specimens ofthis kind the small granules have very nearly the same porosity as theoriginal specimen, and it indicates that even though the original speci-mens were stored continuously under water, they did not remain fullysaturated. This indication was supported by the dry appearance of thefreshly crushed cylinders.

Neat cement-effect of drying on porosity of granules

Other samples of each specimen were dried over Mg(CIO&.2Hz0 andthen brought to the, saturated surfhce-dry condition. The results, givenin column 5 of Table 9, should be compared with those in column 6,Also in Table 9 compare columns 5 and 6 with column 7. The averagewater content of the dried and resaturated granules is about 96 percentof that of the saturated granule that had not been dried.

This shows that the drying of the granules produceci a permanentshrinkage that reduced the porosity of the granules below that of thepaste in the original specimen. In samples of this kind (moderately loww/c, well cured) the effect is small. In specimens of higher w/c andlesser degree of hydration, the effect should be larger.Mortar specimens—effect of granulation on porosity of paste

The mortar specimens used in these studies were made with non-absorptive, quartz sand, Consequently, all water originally in thespecimen (after bleeding) as well as that absorbed during curing is heldin the paste, and data showing differences between the total water con-tents of the original specimens and that of the granular samples representdifferences in the degree of saturation, or in the porosity, of the hardenedpaste, just as they do with neat specimens.

Data of this kind were obtained from mortar cubes for specimensof different ages and different water-cement ratios, Typical results aregiven in Fig. 2-1, A and B.

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE $267

The cement represented in A is a slow hardening type; that in B isnormal.

In each diagram the circled dots represent the total water content ofthe original specimen; the crosses, the total water content of the dried-and-resaturated granules; and the triangles, the granules that weresaturated without preliminary drying.

It is apparent that for specimens cured 28 days or more, the relation-ships are about as were found for the neat pastes described above. How-ever, at earlier ages, especially for the slow hardening cement, thegranules show less porosity than the pastes of the original specimens,the difference being greater, the higher the original water-cement ratio.

These results seem to indicate that during the early stages of hydra-tion the paste contains voids nearly as large as the granules of the samplesand that as hydration proceeds, these larger voids’ disappear.

On the whole, these results show that the porosity of a granular sampleis about the same as that of the pastes in the original specimen except forspecimens having pastes of very high porosity. A granular sample thathas been dried has a smaller total pore(volume than the original paste.From other data it is known that this effect, in well cured specimens,diminishes with decreas; in the original water-cement ratio and probablybecomes negligible at about we/c = 0.3 by weight.

METHODS OF STUDYING THE EVAPORABLE WATER

AS shown by the earlier work reviewed in Part 1, when a specimen

of hardened paste at room temperature is exposed to water vapor or to

air containing water vapor, its water content spontaneously changesuntil equilibrium between the water held in the specinien and the out-side water vapor is established. The establishment of equilibrium in-

volves a change in moisture content of the sample, for the nature of thehardened paste is such that at a given temperature the relationship be-

tween vapor pressure of the water in the hardened specimen and thewater content is represented by a smooth curve. Moreover, the natureof the paste is such that a specimen can remain saturated only when itis in contact with saturated water vapor or with liquid water.

Much of the work to be reported here consisted in determining the

relationships between the evaporable water content and the vaporpressure for various satiples of hardened cement paste. The taking upof moisture from the atmosphere will be referred to as adsorption, andthe reverse will be called resorption, even though other processes mightbe involved. The plotted results will be called adsorption and resorptionisotherms, respectively. When speaking of both processes collectivelyor of the processes in general without specifying the direction of moisturechange, the term sorption will be used,


iin

.7

A A

<>

.6 -

~ef *54 .9.3 ‘%-0573~ . A

.5 1 A

,’~A

.3’

.7.

Dried-ond-

,1 -x Pesafurafed Granules

0 Original Cubes

@

A JO furo ted Gron ules.

Cem:nf 1493,0 J1,,

not previously drieci

+“ 7c /?ef 2.5-’? -9 -/s w% = 0.587w

F o: .6

jA

; ,cj

.4b o 254- 9;13 ‘- ‘%’0.319

~x

x

(t.3 ~: 254-9 ?5A_wVc ‘0,244. cx

{

.2

.t

@ Cement 153650 1 [

L 2hrx. ?.0 40 60 60 100 120 140 160 180Age in Days

Fig. !2-1-Comparison of water content of intact cubes with that of granular samples fromfrom the same cubes


THE APPARATUS FOR SORPTION MEASUREMENTS

‘h-o types of apparatus were used for sorption measurements. Inone the samples were exposed to water vapor only and in the other thesamples were exposed to COq-free air containing controlled amounts ofwater vapor. The first is referred to as the high-oacuum apparatus andthe se~ond as the air-stream apparatus.

High-vacuum apparatus

The high-vacuum apparatus used for these studies is illustratedschematically in Fig. 2-2, As shown, two samples may be kept undertest simultaneously. The samples may be either small granules or thinTvafcrs, If granules, they are contained in small buckets made of plat-inum foil which are suspended on helical springs made of quartz in thetwo chambers marked C. If the samples are wafers, they are suspendedfrom the springs by platinum hooks.

After the air has been pumped out, water vapor of known pressureis admitted to chamber C. The pressure of the vapor is indicated di-rectly by the oil in manometer D. The arrangement is such that duringthe adsorption process the sample is never subjected to a higher vaporpressure than that with which it will finally be in equilibrium. Thisis an important feature of the method, for experience has shown that ifthe ambient vapor pressure is allowed to change as the samples approachequilibrium, the equilibrium-weight is different from what it wouldhave been had the vapor pressure been maintained constant. This isdue to the phenomenon of hysteresis, discussed later on.

The changes in weight of the sample are observed by measuring thechanges in length of the quartz springs by means of a cathetometer.The spring-cathetometer combination has a sensitivity of about 0.2 mg,With a live load of about 400 mg this gives adequate accuracy.

The water vapor pressure is generated by the water (or ice) in bulb Aor bulb B, Bulb B is used for the lowest pressure of the range employedwhich is that of water at the temperature of dry ice wetted with alcohol,-78 C. For all higher vapor pressures cock 2 is closed and 1 is open, thusutilizing bulb A. The temperature of the water (or ice) in A is con-trolled by a cryostat, which is maintained at any desired temperaturedown to -25 C within about * 0.05 C.

For the highest pressure used, a small amount of water is distilledfrom A into the bottom of C and stopcock 1 is then closed. By main-taining the temperature of the tube outside the 25 C air-bath above 25 C,the water vapor pressure in C is, theoretically, maintained at 23.756 mmof Hg, the saturation pressure of water at 25 C. Accurate measurementsat this vapor pressure, or at any vapor pressure above about 95 percentof the saturation pressure, cannot be obtained by this method because ofcondensation on the springs.


r

/’

Q_prJ.j..,,

Fig. %9-High vacuum sorption apparatus

Fig, %3-General view of apparatus

Between cocks 3 and 4 a Pirani-type vacuum gage is attached so asto indicate the pressure on the ‘(zero” side of the manometer, This is tomake certain that the readings on the manometer are not vitiated by slowleaks on the zero side,

To check against leaks on the other “pressure” side of stopcock 3,the temperature of the bath surrounding A is measured by means of aneight-junction thermocouple and a type-K potentiometer, The vaporpressure of the ice or water in bulb A can then be ascertained from

handbook data. Any discrepancies between the pressure shown at I)and the pressure indicated by the temperature at A that are greater


than the inaccuracy of measurement would be indicative of pressurefrom gas other than water vapor.

A general view of the apparatus is given in Fig. 2-3. The cabinetin the foreground contains the controlled bath for bulb A. The largecabinet in the middle background is the 25 C air-bath, This cabinet isthe same as that used for the air-stream apparatus to be described below,It can be used for both methods simultaneously, although that has notbeen done as yet.

The cabinet in the foreground is the cryostat. It contains a cylindricalvessel of about 10-gallon capacity filled with alcohol. This is cooled bythe refrigeration unit mounted under the cabinet, A one-gallon containeris mounted, submerged to its upper rim, in this alcohol bath, The con-tainer is a double-walled glass vessel with air between the walls. Itcontains the alcohol in which bulb A, Fig. 2-2, is immersed. By meansof an electrical heater and thermoregulator, the temperature of this one-gallon bath is maintained at whatever level is desired. The thermoregu-Iator is a laboratory-made, toluene-mercury type. It operates throughan electronic switch and Mercoid relay.

The air in the large -cabinet is kept in rapid circulation by means oftwo electric fans and two air-driven windshield fans. The cabinet iscooled by continuously circulating cold alcohol through a copper coilinside the cabinet. The circulated alcohol is cooled by means of anothercoil dipping into the outer alcohol bath of the cryostat described in theforegoing paragraph. * The cabinet is heated by an electric heater (about200 watts). The input to the electric heater is controlled by a laboratory-made, toluene-mercury thermoregulator that operates through an elec-tronic switch and Mercoid relay. The sensitivity of the regulator isabout 0.005 C. The variation in temperature at any given point doesnot exceed 0.01 C, and the average temperatures at different points donot differ more than 0.02 C.

Air-stream apparatus

The air-stream apparatus is built in and around the large cabinet justdescribed. It was designed to deliver 11 streams of air simultaneously,each stream having a different water content and hence different watervapor Wessure. The following description pertaining to one of the airstreams is applicable also to the rest.

The air to be conditioned is taken from the compressed air supplyof the laboratory, The air pressure is reduced to 3 lb. per sq. in. bymeans of two diaphragm-type pressure-reduction valves connected inseries, The low-pressure air is then delivered to a train of one-gallonbottles such as is illustrated in the lower part of Fig. 2-4. The first bottle

*This arrangement is used at present. For most of the period covered by this paper cold tap water fromthe building supply was used, but this often failed its purpose during the summer.

97$? JOURNAL OF THE AMERICAN

Fig, 2-4—Schematic diagram of one ofthe air conditioning trains for adsorptiontests

CONCRETE INSTITUTE November 1946

h ~n !.C.pp,,,h.g

Co”,?o”fwnperd”rC.b;n,t ---

)

A;, S/,CO~--

H,o 30% 30% Safetg Cone. DllUteN80H NaOH B.af+leH,SO, H,S04

contains water, and the next two sodium hydroxide solutions. Thewater bottle at the head of the train prevents the formation of sodiumcarbonate in the inlet tube of the caustic-soda bottles. Next in line isan empty bottle for safety and this is followed by a bottle of concen-trated sulfuric acid (specific gravity 1.84) to dry the air. The dry air isthen delivered to a tower of Ascarite to remove any traces of carbondioxide that might have escaped the caustic-soda solutions. The airstream then passes through a 3-gallon bottle containing dilute sulfuricacid. The output of this bottle is divided into two streams, one of whichis shown in Fig, 2-4. The strength of the acid in the large bottle justmentioned is so regulated that it gives the air passing through it a watercontent somewhat below that desired for either of the two streams takenfrom the bottle. This slightly-too-dry air then is piped into the constanttemperature cabinet where it circulates, first through a length of coppertubing to permit the temperature to reach 25 C and then through twotowers of sulfuric acid connected in series as shown in the upper part ofFig. 2-4. The second stream taken from the bottle is led similarly toanother pair of acid-towers, regulated to give a different vapor pressure.The strength of the acid in the towers is carefully regulated to haveexactly the vapor pressure desired in the outgoing stream of air. Toinsure equilibrium between the stream of air and the acid the air isdispersed as fine bubbles by means of porous plugs fastened to the endsof the inlet tubes. (These porous plugs were made in the laboratory bysintering granulated glass in a crucible. ) To remove entrained dropletsof acid, each tower is equipped with a glass-wool filter as shown.

The outgoing stream of air is led through rubber connections to anErlenmeyer flask containing the sample under test. As the air passesthe dry granules, they absorb some of the ]vater vapor. This continuesuntil the vapor pressure of the water in the sample becomes equal tothat of the water vapor in the air stream.

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE S?73

Two samples are run sirnultaneously by connecting sample-flasksin tandem as shown. The outgoing stream of air from the second flaskbubbles through a mineral oil contained in a 6-02. bottle and then escapesto the interior of the cabinet. The mineral-oil trap prevents back-diffusion of moisture and carbon dioxide from the air in the cabinet tothe sample.

Eleven such pairs of sample-bottles in the cabinet make it possible toobtain simultaneously 11 points on the adsorption curves for each oftwo materials.

Because the air delivered to the acid towers inside the cabinet is ineach case slightly drier than the output from the towers, the level ofthe acid in the towers gradually subsides during the continuous flow ofthe air streams. About once a month it is necessary to replenish thetowers by adding distilled water. This is done by means of glass tubes(not shown in sketch) leading from the stoppers in the tops of the acidtowers through the top of the cabinet. Similarly, the acid in the largebottles outside (under) the cabinet and the caustic-soda solutions arerenewed about once a month,

During the development period, the water content of each air streamwas measured by passing a measured volume of the air through weigh-ing tubes filled with P@6, The relative vapor pressure of each streamwas then computed from the law for perfect gases. A number of suchmeasurements showed that the water vapor pressure in the air streamsdiffered from that which could be computed from the strength of theacid by less than 0.025 mm of mercury or a difference in p/p. * of less than0,001, When this was learned, the air streams were considered alwaysto be at equilibrium with the acids in the $owers.

The sample flasks were removed from the cabinet once daily andweighed on a chemical balance, care being taken to minimize the ex-posure of the granules. A typical record of the results of such weighingsis shown in Fig, 2-5. This diagram shows that for those samples exposedto water vapor of relatively low pressure the weights reached a maximumand thereafter declined. At vapor pressures of 0,8 P8or higher the weighteither remained constant after one or two days or else continued to in-crease steadily, though very slightly, with time, this tendency being morepronounced the higher the vapor pressure. The increase in weight justmentioned is believed to be due to hydration of fresh surfaces of clinkerresidues exposed on crushing the originaI sample.

The behavior of the specimens exposed to the drier atmospheres is notunderstood. The phenomenon was not observed when using the high-vacuum apparatus. From this it maybe inferred that the presence of air

*P = vapor pressure of air steamP- = saturation vapor pressure of w8tar

s?74 JOURNAL OF THE AMERICAN

13 P/P. .0.96,

,2 —,.-

E .’”,g!l 0,80w* ,,) ~ ~

,

,, ●,

9 / 0,8/

/’ .,.’” ‘

& / ,’

7,1

6 / . . , 0, SJ,’”-

5 /’

4

, 0, Zq3 : ,,-- ‘-

: ,/’2 -9

0.08,.- — -

, ,., t.

CONCRETE INSTITUTE November 1946

Fig, !2-5-Ty ical relationship between gainJin weight an period of exposure

/0 5

Period’ d E.xpo;ure to A;r.Strea; -Days

may have something to do with the result. However, as will be shown

later, the major aspects of the results obtained in the presence of airare essentially the same as those obtained in the absence of air.

Inasmuch as the decrease in weight shown by the lower curves inFig. 2-5 continued for as long as two weeks, it was decided to use maxi-mum rather than final weights. There was some question as to whetherthe final weight was any more significant than the maximum weight;also, since the decline from the maximum represented but a small per-centage of the total gain, it did not seem justifiable to retard the experi-mental work to the extent necessary to get final weights,

Reproducibilityof results

The reproducibility of the data obtained in the manner just describedis illustrated in Table 11, These are results from two sets of samplesmade from the same specimen, each set being tested independently.The corresponding figures are in very good agreement except at the twohighest pressures, Such differences were commonly observed and wereprobably due to different degrees of proximity to equilibrium.

Comparisons such as those that are given in Table 11 were made atother times during the course of these experiments, with similar results.Nevertheless, there is reason to believe that in some groups of tests thevariability was considerably greater than would be expected from suchdata as those presented above. Possibly such variations are due not somuch to variations in the adsorption measurements themselves as tovariations in auxiliary tests as when the samples contained pulverizedsilica and therefore required a chemical analysis for the estimation ofcement content. The discrepancies that will be noted among the various


TABLE 11—REPRODUCIBILITY OF THE ISOTHERMSCement: 16189Initial w/c: 0.50Curing: 6 weeks in water

Relative vaporpressure

P/Pa. —0.0 (non-e~fi HtO)

0.160.320.390.460,530,600.700.810.880.96

Total water-content of sampleindicated, ~0 by weight of cement

A

15.4717.9818.8720.1020.8221.4422.0222.8224.8227.5230.4335.31

B

15.4218.0318.9420.2820.9821.6522,0922.9024,7627.5329.6934.60

data yet to be presented are often such as would result from errors in thedetermination of the cement content of the sample. The data obtainedfrom samples of neat cement were less erratic.

Use of ordinary desiccators

111 some auxiliary work, neither the air-stream nor high-vacuumapparatus was used, Instead, samples were placed in ordinary air-filleddesiccators in the presence of a suitable desiccating agent. The sampleswere weighed from time to time until the results indicated equilibriumto have been reached.

Theoretically, the results obtained in this way should, in most respects,be the same as those obtained by the methods alrewiy described. Actu-ally, the results from the samples dried in desiccators did not agree verywell with the results obtained by the other two methods. The cause ofthe discrepancy is not known. It was observed, however, that the rateof absorption in an air-filled desiccator is very much less than that invacuum or air stream. This suggests the possibility that the exposure ofsamples was termintited too soon, that is, that they did not approachequilibrium as closely in the air-filled desiccators as they did whentested by either of the other two methods. Another possibility is that,owing to the longer exposure and to the continued presence of air, samplestested in desiccators might have become carbonated sufficiently to in-fluence the final results. At any rate this method is not recommended.

RESULTS OF THE SORPTION MEASUREMENTS-EMPIRICAL ASPECTS

General featuresOF THE DATA

Fig. 2-6 and Tables 12 to 17 record a run made with the high-vacuum

S?76 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

apparatus illustrated in Fig. 2-2, In this case the sample was a verythin wafer of hardened neat cement paste described in Table 12, wo~c =0,5 by weight. In its initial, saturated state it weighed 380.5 mg, asindicated by the uppermost point in Fig. 2-6. After the sample was in-stalled, the air was pumped out of the apparatus. The initial pumpingperiod was made brief to avoid overdrying the sample. The objectwas to remove the air from the chamber without removing water fromthe sample, if possible. To maintain the water vapor pressure as highas possible during the pumping a small amount of water was introducedinto the sample chamber before the pumping began. The desired resultwas not obtained; the pump removed the water vapor so rapidly thatnearly half the evaporable water in the sample was removed during only6 minutes of pumping.

As soon as the initial pumping was finished, the sample was subjectedto a vapor pressure of 0,94 p,, Owing to the losses suffered during theinitial pumping, the sample gained in weight at this pressure until itreached equilibrium at a weight of 374.4 mg. Then the pressure waslowered step by step and the rest of the points appearing on the resorp-tion curve were obtained. At the final weight, 309.8 mg, the samplewas at equilibrium with the vapor pressure of the ice at -78 C, the tem-perature of dry ice.

As soon as the evaporable water had been removed, the vacuum pumpswere operated for many hours so as to remove as much air from thesystem as possible. Then the vapor pressure was increased stepwise,thus establishing the adsorption curve shown.

As shown in Fig. 2-6, the adsorption and resorption curves coincidedonly at pressures below 0,1 p,. (As a matter of fact, it is not certainthat the curves coincided over this range, but it seems probable that they

did so,) Studies of other materials@J show that in the range of pressureswhere the curves form a loop, innumerable curves within the loop canbe produced under suitable experimental conditions. If the process of

adsorption or resorption is reversed at any point short of the horizontalextremes of the loop, the part of the curve that had previously been gen-erated will not be retraced but instead the points will cut across theloop, If at any stage of adsorption in this range the process is reversed,the resulting downward curve will cross over from the adsorption to the

resorption curve. If the resorption curve is reversed, then a new risingcurve will cross over toward the adsorption curve, but instead of joining

the adsorption curve the new curve will rise more or less parallel to theadsorption curve, the loop being closed only at the saturation point.Thus, it is possible to obtain points representing thermodynamic equilib-

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE

380j

370

364

FI 334

:

t ~4~2 /%

k 3300,..03

3Z0Temp. 2S” C‘o/c - ‘0sAge ?~ yeors

310 -

300 -0 0,1 0,2 0.3 0,4 0,5 0,6 0,7 0,8 0,9 LO

Relative Vapor Pressure (P\PJ

Fig. 9-6A upper left)—Data fromiTables 19 an 13

Fig. 2-66 (upper right)-Data fromTables 14 and 15

Fig. $!.6C (lower right) — Data fromTables 16 and 17,

SORPTION ISOTHERMS FOR CE.MENT SLAB MADE FROM CEMENT13495

High vacuum apparatus

3000 0.1 0,2 0.3 0.4 0,3 0,6 0.7 0.8 09 1,Relstlve Vapor Pressure (p/p,)

277

‘“EEl!z730 01 0,2 0.3 0.4 0.5 06 07 08 09 1,0

Relative Vapor Pressure (P/p~)

rium* between the evaporable water in the sample and the ambientwater vapor anywhere between the resorption and adsorption curves.

*Chemists tend to question whether or not these should be called equilibrium points. They feel that, likepoints representing chemical equilibrium, a given point should be attainable from either. side.

However, the requirement that a state of equilibrium must be approachable from eltber side with thesame.result does not properly apply to all physical equilibria. See for example the “ink bottle the or ‘‘ of

Eeorpt~on byst~reem (Brunauer, P. 398). Thi8 thepry shows that ddferent arnpunta ,of wate? could e mequ?hbrmrn w]th the same vapor p~essuw. Thm m not to say that the oondlt]ons pictured m developingthe mk bottle theory actually mnst m hardened paste. It merely refutes the Idea that equdlbrium betweenwater oont ent and vapor pressure requum that only one water content can be associated with a given vaporpreaeure.

A aper by W. O. Smith (Sorption in an Ideal Soil, Soil Sci. V. 41, P. 209. (1936) ) is especially pertinent.%He s owed by geometrical analysis that in an assemblageof sphe~es,holdingwater by capillarycondensa-

tion, ddTerent amounts of water can be m thermodynamic equdlbrmm w]th the same vapor pressure.Such equilibrium ia reversible in the sense that the same surface curu@ure ~bould be established at a givenvapor pressure, regardless of the duectlon of approach. See Part 3, Capdlary Condensation.


TABLE 12—FIRST RESORPTION CURVE FOR SLAB PREPARED FROMCEMENT 13495

High-vacuum apparatusAge 7 years, 116 days

orirnnal w/o = 0.50 by wt.

1.000

0.:420.7800.6630,5090.3510.2600.1930.099O.@Xl

–=,

wt. ofsample,

mg

380.5346.8 (a)374,4369.3363.1355.8346.1336.5333,4328.0309.8

Evaporable waterin the sample

mg ‘Fractionof dr wt.

fof samp e ( = w)

70.737.064.659.553.346,036.326,723.618.200.0

,2485,1194,2085.1921.1720.1485.1139,0862.0762.0587,Oooo

(a) Weightafter 6 minutesof pumping—vaporpressureunknown.

TABLE 13—FIRST ADSORPTION DATA FOR SLAB PREPARED FROMCEMENT 13495

Hi~h-vacuum armaratus

P/P.(p, =23.756mm of 120)

::880.1550.1930.2490.3500.4460.5980.7450.8550,9590.9951.000

wt. ofsample,

mg

309.8326.7329.8330.7332.1335.1338.0343.0351.0356.6366.4369.6

. .


mg

00.016.920.020.922.325.328,233.241.246.856.659.867.0 (est.

Fractionof dry wt.

of sample ( = w)

.0000

.0545

.0646

.0675

.0720

.0817

.0910,1072,1330.1511.1827,1930.2162 (est.)


TABLE 14-SECOND RESORPTION CURVE FOR SLAB PREPARED FROMCEMENT 13495

High-vacuum a~txumtue

0,9950.8480.5940.3970.82*0,3140.1940,1280.0780,0040.000

*Temperaturecontrolsfailed

wt. ofsample,

mg

369.63cr4,1360.7344.0364.3340,6336.7334.2331.7323.4319.6

[d caused uninten(

. .

Evapomble waterin the sample

mg

50.0:;,:

24:444,7::,:

14:612.13.80.0

ml rice in preaeure.

Fractionof dry wt.

of sample ( = w)

,1565.1392,0973.0763,1399,0654,0635.0457.0379.0119,0000

TABLE 15–SECOND ADSORPTION CURVE FOR SLAB PREPARED FROMCEMENT 13495

High-vacuum a~~aratus

P/Pa(p, = 23.756mm of Hg)

O.0000.0420.1120.2200.3640.4500.5960.8061.00 (?)

wt. ofsample,

mg

319.6330.4333.2335.7339.0340.7344.7351.4366.8

. .


w

0.010,813.616,119.421.125.131.847.2

Fractionof dry wt.

>fsample ( = w)

.0000

.0338

.0426

.0504

.0607

.0660

.0785

.0995

.1477


TABLE 16-THIRD RESORPTION OF SLAB PREPARED FROM CEMENT 13495High-vacuum apparatus

P/P8(p, =23.756mm of Hg)

1,00 (?)0.8070.6240.4670.3700.2020.0520.0430,000

wt. ofsample,

mg

366.8360.8352.0348.0345.3340.9335.3334.2321.0


.—.mg Fraction

of dry wt.of sample ( = w)

—. —

45,839.831.027.024.319,914,313.200,0

.1427

.1240;0966.0841.0757,0620.0445:0411,0000

TABLE 17—THIRD PARTIAL ADSORPTION AND PARTIAL RESORPTION DATAFROM SLAB PREPARED FROM CEMENT 13495


P/P8(p, =23.756mm of Hg)

0.0000.0520.0940.1780.3210.4050.3260.1460.049

wt. ofsample,

mg

321.0332.3333.2335.4338.7340.1339.2336.5333,6


mg Fractionof dry wt.

of sample ( =w)

,00001!:: ,035212.2 .038014.4 .044817.7 .055219.1 .059518.2 .056715.5 .048312.6 .0392

The lack of reversibility as described above is shown by materials ofvarious kinds.

Although the phenomenon has not been investigated extensively here,there is little reason to doubt that portland cement pastes all showessentially the behavior described above. This matter of hysteresis issignificant and should be kept in mind in connection with the theoreticaldiscussion that follows later in this paper. It is a principal reason forbelieving that ordinary laws of chemical reaction cannot be applied tothe reactions involving the gain or loss of evaporable water.

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE $281

Besides the effects common to many materials, portland cement pasteexhibits certain irreversible phenomena not found among some othertypes of materials. This is shown in Fig. 2-6B, where the second de-sorption-and-adsorption curves of the sample are given.

A break in the second resorption curve at p = 0.395 p, will be noted.After equilibrium at this pressure had been established, the cryostatwas set to produce a lower pressure, but during the night the tempera-ture controls failed, the pressure rose to p = 0.82 p, and the sample-weight increased, giving the point indicated by the cross. (This pointprobably does not represent an equilibrium value, but is close to it.)When proper operation of the cryostat was restored, the point at p =0,315 p. was obtained.

The light-line curves in Fig, 2-6B are those of Fig. 2-6A, shown forcomparison. The marked difference between the first and second cyclesis believed to be due to two factors: One is the irreversible shrinkage(described in Part 1) that reduces the capacity of the sample for evapor-able water. The other is the additional hydration of the cement in thesample that occurs while the sample is subjected to vapor pressuresabove about 0.8 p,. Although these samples had been stored in water forseveral years they seem to have contained unhydrated clinker that wasexposed when the thin wafers were prepared.

No explanation for one feature of the irreversibility has been found.Note that on the first resorption the minimum weight reached was309.8 mg. On the second resorption the minimum weight was 319.6 mg.Continued hydration has the effect of increasing the minimum weight,but the increase shown here is much too great to be accounted for in thisway. It is possible that the observed minimum weight for the firstdesorption was in error by several milligrams. However, the originaldata offer no clue as to the nature or cause of the error, if there was one.

Fig. 2-6C shows the third resorption and a partial third adsorptioncurve. The third resorption curve differs from both the first and secondresorption curves, but the third adsorption is practically the same as thesecond adsorption. In fact, when the results are expressed as percentageof the minimum weight, the second and third adsorption curves areidentical. Tests on other samples show that after the first cycle of dryingand wetting the adsorption curves are reproducible. But the indicationsof a limited amount of data are that the resorption curves are greatlyinfluenced by small variations in experimental conditions and are diffi-cult to reproduce exactly.

On the third resorption, Fig, 2-6C, after the weight correspondingto 0.4 p. had been established, the pressure was intentionally loweredstepwise with the result indicated by the graph. This illustrates what

98$? JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

was said above about the irreversibility of this process in the range ofpressures where the curves form a loop, Note that the points cut across

the loop and join the resorption curve. This behavior is similar in char-

acter to that obtained with other materialsf3J. It should be noted, how-ever, that the vapor pressure at which the loop closes is much lowerthan that observed with other materials. Moreover, the loop closes at a

much lower pressure than would be predicted from Cohan’s hypothesis(4J.

The size and shape of the hysteresis loop, and the course of the curvewhen the process is reversed within the limits of the loop, are probablycharacteristic of the physical structure of the hardened paste14J). Atany rate the whole phenomenon cannot be understood until these loopscan be adequately interpreted. However, practically all the measure-ments reported in this paper were of adsorption only. Therefore, theinterpretation of the adsorption curve is the only part of the problemthat can be considered here.

Along with the measurements described above, measurements weremade on the sample described in Table 18. This sample was preparedfrom a neat-cement cylinder that had been molded under high pressurewith w/c only 0,12 by weight.

The results are given in Tables 18 to 23 and in Fig. 2-7, all threecycles being shown on the same graph. The features pointed out inFig. 2-6 can be seen here also, and others besides. Note that the effectof the reversal in pressure that occurred during the second resorptionwas somewhat different from that on the other specimen, Note also that thelower parts of the second and third resorption cycles are identical. Theindication is that with a specimen as dense as this, the paste becomes“stabilized” after the first drying so that resorption as well as adsorptioncurves are reproducible, provided that the specimen is always saturatedat the start, The differences among the resorption curves in the upperrange are believed to be due to slight differences in the degree of satura-tion at the beginning of the resorption part of the cycle.

Comparison of the results obtained with high.vacuum and air-stream apparatus

Fig. 2-8 and Tables 24 and 25 give adsorption data for two granu-lated pastes, the data being obtained first with the air-stream apparatusand then, about three years later, with the high-vacuum apparatus.The granules had been sealed in glass ampoules during the three-yearinterval. The later tests were made on samples from the same lot ofgranules as the earlier ones, but not on the same samples as used in thefirst test. Thus, the curves obtained by each method were first-adsorp-tion curves.

The granules had originally been dried by the regular procedure used inconnection with the air-stream method, that is, over Dehydrite in a

PHYSiCAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE 983

TABLE 18—FIRST RESORPTION CURVE ON SLAB PREPARED FROMCEMENT 14675

High-vacuum apparatusAge 4 years 29 days

Original w/c = 0.12 by weightMolded under 24,000 lb/inZ pressure

1.000?

;$%0.7800.6630,5090.3510.2500.1930.0990.000

wt. ofsample,

mg

664.4647.9742.8656.4653,3652.0649,7647,4643.4641.5638.1616.6

Evaporable waterin sample

mg

47.831.3

126.239,836.735.433.130.826.824.921,500.0

Fraction ofdry wt. of

paste ( = w)

0.07750.05080.20460.06450,05950.05740,05370.05000.04350.04040.03490.0000

Initial wt. sat’dWt. rcfter 6 min. pumpingDroplets condensed on sample

TABLE 19—FIRST ADSORPTION CURVE ON SLAB PREPARED FROMCEMENT 14675


P/P3 ( = x)(&=o:~:6

0.0000.0640.1550.1930.2490.3500,4460.5980,7450,8550.9591.000

wt. ofsample,

mg

616.6627.6629.9630.2631.5632.7634.0638.7642,5645.8653.8664.4*


00.011,013,313,614,916.117.422.125.929.237.247.8

—Fracticn ofdry wt. of

paste ( = w)

w%0.02160.02210.02420.02610.02820.03580.04200.04740.06030.0775

*Original weight.

!!84 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

TABLE 90-SECOND RESORPTION CURVE ON SLAB PREPARED FROMCEMENT 14675


1,000(a)0.9570.8480.5940,3970.82 (b)0.3140.1940.1280.0780.0040.000

wt. ofsample,

mg

685.1656.4653.8648.7646.4650.7642.2639.4637.6635,8622.0616.6


68.539.837.232.129.834.125.622.821.019,2

;:;

(.s) Water visible on sample.(b) Temperature controls failed and cawed pressure to rise.


paste ( = w)

0.11110.06’450.06030.05210.04830.05530.04150.03700.03410.03110.00880.0000

TABLE 91 —SECOND ADSORPTION CURVE FOR SLAB PREPARED FROMCEMENT 14675


p/’ps ( = x)(Fhm=o;2~

O.0000.0420.1120.2200.3640.4500.5960.8061.000

wt. ofsample,

mg

616.6626.1629,4631,0633.0634.5638.7644,3662 (est)


oi.5

12.814.416.417.922.127,745.4 (est)


paste ( = zo)

:,01540.02080,02340.02660.02900,03580.04490.0736 (est)


TABLE M-THIRD RESORPTION CURVE FOR SLAB PREPARED FROMCEMENT 14675


P/P* (= x)(~=o:2~

0.8070,6240.4670.3700.2020.0520,0430.000

wt. ofsample,

mg

655.3647.9645.1643.3639.2634.8632.5616.6

Evaporable waterm sample

mg

38,731.328,526.722.618,215.900.0


paste ( = w)

0.06280.05080.04620.04330,03670.02950.02580.0000

TABLE 23—THIRD PARTIAL ADSORPTION AND PARTIAL RESORPTIONCURVES FOR SLAB PREPARED FROM CEMENT 14675

High-vacuum method

P/P8 ( = x)(gm=o~}~

0.00

0.0520.0940.1780,3210.4050.3260.1460.049

wt. ofsample,

mg

616.6627,6628.9631.1633.3634.2633.8631.6628.7

Evaporable waterm sample

w

1!,012.314.516.717,617,215.012,1


paste ( = w)—

o0.01780.01990.02350.02710.02850.02790.02430.0196

QB6 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

Fig. 9.7—Sorption isotherms for neat cement dab made from cement 14675Data hornTabloi 18 to W

vacuum desiccator. In the high-vacuum procedure these granules wereexposed to the vapor pressure generated by ice at the temperature of dryice, the lowest pressure used. After the final exposure to this low pressurein the high-vacuum apparatus, the samples were ignited. The finalweights compared with those obtained after the earlier tests are givenbelow:

Sample No.9-15A-6M K~B.lQ

Loss on ignition as driedoriginally (g/g) . . . . . . . . . . . . . . . . . 0.1428 0.1927

.Losson ignition as dried inhigh-vacuum apparatus (g/g). . . 0.1506 0.1922

Note that the water content of K4B-lQ was the same (within thelimits of probable error) under both drying conditions and that there-fore the sample as received from the sealed ampoule was not changedby the exposure to the lowest vapor pressure used in the high-vacuumapparatus. As mentioned in connection with Table 5, above, this pro-vides data for estimating the vapor pressure of the desiccant used inearlier tests. The vapor pressure over ice at dry ice temperature (-78 C)is given as 0.56 microns of mercury. @J The pressure relative to thesaturation pressure at 25 C is therefore about 24 x 10-6.

The data for the other sample, 9-15A-6M, indicate that the twodrying conditions were not exactly alike, the amount of water removed inthe original drying being somewhat greater than that removed in the

PHYSICAL PROPERTIES OF HARDENED PORTLAND CEMENT PASTE 287

.3 *

.

,3

.2

,2

,1

.1

.1

.0

,0

pl~ at t5° C

Fig. %8 (left)-Adsorption isotherms (25 C) for granular samplesData horntablw 24 and M, Part 9, and tramTablw A-E and A-17 of A~p.ndlx t. Pati 2

Fig. %9 (right)-Adsorption isotherms showing effect of curing (air-stream apparatus)

TABLE 94--FIRST ADSORPTiON CURVE FOR GRANULAR SAMPLE 9-15A-6M

High-vacuum method

PIP.(=x)

0.00

0.0550.0730,1040.1930.2440.3490.4720.7381.000

I Evaporable waterwt. of in the samplesample,

mg I mgI

431.3 0.0441.1442.0 Ii:;443.6 12.3446.3 15.0448.5 17.2450.9 19.6454,7 23.4463.1 31.8

Fraction of dry wt.of sample ( = w)

:0347,0400.0455.0542.0738. 1250*

*O&ervwi value 0,1569, but known to k too high bempe of condensation in sample and epring.0.1250b bemd on the eatuaated watm contant of the eamrdem tbe eaturatad statm.


TABLE 95—ADSORPTION CURVE FOR GRANULAR SAMPLE K4B-I Q

High-vacuum method

I I

P/P.(= x)

0.000.0550.0730.1040.1930.2440.3490.4720.7381.000

wt. ofsample,

mg

542.2562,2563.7566.3571.4574.0579.4586,6608.9


.—

mg Fraction of dry wt.of sample ( = w)

0.0 ,000020.0 .036921,5 .039524.1 ,044229.2 ,054 I31.8 .058737.2 .068644.4 .081966,7

1

,12302295*

‘Original water content aftmr drying and reaaturating.

high-vacuum apparatus. This would indicate that the vapor pressureover the magnesium perchlorate hydrate is somewhat less than thatover ice at -78 C. However, there is some reason to believe, as pointedout before, that the drying agent in the original tests was sometimesinadvertently Mg(CIOJZ + Jfg(CIOJs.2Hs0 instead of J$v(C104)2.2H2O+ Mg(CIOJz.4Hz0. This could he one of those instances,

In regard to the course of the curves over the lower range of vaporpressures, we will show later that theoretically the presence of air shouldreduce the amount of adsorption in the manner shown by the plotteddata for K4B-lQ. That is, the two series of points for this sample differonly as they theoretically should. It will be seen later that in otherimportant respects the two series of points have the same significanceand that the two methods give essentially the same result.

The two series of points for sample 9-15A-6M fall practically on thesame line. Theoretically, the crosses should drop below the circlesin the low-pressure range. The fact that they do not can be accountedfor by the data given above showing that the sample used in the originaltests (air-stream method) was dried to a lower water content than thesample used in the later tests (high-vacuum method). It will be seenlater that the drier the sample jhe higher the “knee” of the adsorptioncurve. It therefore seems that by chance alone the effect of the differ-ence in initial water content exactly offset the effect of the presence ofair.

These data indicate that adsorption in the presence of air is essen-tially the same as that in the absence of air when the small effect of theair itself is taken into account. This is important, for it shows that the

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE s289

interpretations worked out by other investigators for adsorption from

a pure gas phase can be applied with modifications to the adsorption

of water vapor from a mixture of air and water vapor.

It should be noted that practically all the data given in this paperwere obtained by the air-stream method. Unless otherwise stated, it iscorrect to assume that all adsorption data were obtained by the air-streammethod.

Effect of extent of hydratidrr on the position of the adsorption curve

Fig. 2-9 gives a group of adsorption curves for a given kind of paste

at different stages of hydration. The paste was obtained from mortar

prisms that had been cured continuously in water for periods rangingfrom 7days toone year. The results shown are typical except that theyrepresent a Type IV, rather than a Type I, cement. Since the plots ofwater contents are expressed in terms of the weight of the originalcement in the sample, the ordinates at p/p8 = O give the amounts of

non-evaporable water and those at p/p8 = 1* give the total ~~ater ~On-

tents at saturation. The curves illustrate the following general con-clusions that are applicable to all samples tested, regardless of originalwater-cement ratio, age, or type of cement.

(1) The total water held at saturation (p/p, =l) increases as thelength of the curing period increases.

(2) The non-evaporable water content also increases.

(3) Theamount of\vater held atanyintermediate vapor pressure in-creases with the length of the curing period.

(4) Theevaporable ~vatercontent, \vhichis thediffcrence bet\i'een thetotal andthenon-evaporable water, decreases astlie length of the curingperiod increases.

The changes that take place during the period of curing are illustratedin anotherw ayin Fig. 2-10. This, like Fig. 2-9, represents a group ofsamples that were similar except for the extent of hydration at the timeof test; they were prepared from mortar cubes all made from the samemix, Here the bottom curve represents the non-evaporable water andthe top the total water content. The intermediate curves represent thewater content after the originally dry samples had reached equilibriumwith the relative vapor pressures indicated on the curves.

Note that all curves originate at (0,0) except the upper one. Thisone begins at a point representing the original water-cement ratio (cor-rected for bleeding). That is, zero age rcprcscnts the time before anyhydration takes plmm. At that time all the water in the sample will

*The topmost point ha8 been plotted at P/PO= 1 despite the fact that cormideration of the effect ofdissolved alkalies shows that it should be plottad at a lower P/w. This poi,,t k discussed further in connec-tion with the effect of dissolved alkali- in Part 3.

X70 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

have a relative vapor pressure of 1.0* and not any of it would be heldif exposed to an atmosphere having any lesser water vapor pressure. Atany time after hydration begins, only a part of the water can be lost inan atmosphere having an appreciable vapor pressure.

The rise of the top curve is due to absorption of water by the specimen

from the curing tank, The points represent dried-and-resaturatedgranules and therefore are probably slightly below the level representing

the capacity of the paste before drying, as explained before,

The rise of the bottom curve indicates the progress of hydration and,

as will be shown later, is proportional to the increase in volume of thesolid phase of the paste. The heights of the next three curves abovethe bottom curve (p/p, = 0,09; O.19; and 0.36) are believed to depend onthe total surface area of the solid phase and hence to depend primarily onthe quantity of gel present. It will be shown later that the positions ofthese lower curves are independent of the total porosity of the sample.Although this particular plotting does not make it apparent, it is afact that the position of the points representing pressures greater thanabout 0.475 p, depend on the total porosity of the sample as well as onthe extent of hydration, The basis for these interpretations and the usesmade of the information are subjects treated in later parts of this paper.

Fig. 2-11 gives some of the same data that appear in Fig. 2-9 in termsof a unit weight of dry paste rather than weight of original cement asbefore. It therefore shows the evaporable water only. Note that asthe length of the period of wet curing increases, the total evaporablewater decreases and the amount held at low vapor pressures increases.Since the total evaporable water may be taken as a measure of the totalporosity of the hardened paste, this graph shows that the amount ofwater held at vapor pressures near the saturation pressure depends on theporosity of the sample, On the other hand, the amounts of water held atlow pressures appear here to vary inversely with the porosity. However,it will be proved that the amount held at low pressure does not depend onporosity.

Influence of origincrl water-cement ratio (w./c) on the shape of the adsorption curve

Fig, 2-12 to 2-15 prcs.mt adsorption curves for samples having dif-ferent water-cement ratios but the same degree of hydration as measuredby the non-evaporablc water content. ‘The points for these curves wereobtained by interpolations on plots such as that shown in Fig. 2-1o.The four figures represent three different cements, t~vo different degreesof hydration, and three (in one case, four) different water-cement ratios.Considered together, they show that differences in age and original water-cement ratio have no influence on the shape of the lower part of the ad-

*Again neglecting the effect of dissolved alkalies.

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE S?91

o .“

d.,,

..*

60

m “

,24

-ERef ?34.9./ 1 dog, _CrOWnt (4930 J 28 ,, -

; so$! % s 0309 by w,.

-,,0 m~,20

.

% .=

m:

k 40 -/1!.0.96 ~,160. --O*.-. 0.,4 b

%fi 0.:,:; ~

..!?

+.,,,..4 :

‘% .~

i.04

g

3

00.1.23.45678 910

Period of Curing - days~?,

Fig. %1 O (left)--Changes in amounts of water held at any given vapor pressure as in-fluenced by the length of the curing period

Cement 15007J-Ref, 9-5 w./c = 0.433

Fig. 2-11 (right)-Adsorptio~isotherms showing evaporable water only

.54

.Sc

! f. om,

1 1 r t y =M82.

1

f ~

>7J@~Olfl~fNo ‘% $$;—.

. 9-+ 0,316 /80x 9-3 043? 50 $%/.,0432’A 9.6 0,58228.—.—.

Cemenf f5007J

~qc : 0.183

.

‘./, .0326

_—— —v

72

, ,

123.4.5.6.16 .910

P/P<

.50Symbol Ref No. %/= c%;

A 9-4 0.3!620 %//:0.43ZT46 “ 9.5 0432 14 I

w 9-6 0.502 1E cement 15007J~ .42:

z.s 38m

5 ‘% =03’6

% ,34m

&

~ ,30

2

.:

~ 26

jm

= .22

zzt-

,18

.141, 1 I

0 .1 .2 .3 ,4 .; .6 .7 .8 .9 1.0

P/P,

Ffg. %12 (left)-Adsorption isotherms for samples of different w./c but equal nan-evapor-able water

Fig. 2-13 (right)-Adsorption isotherms for samples of different w./c but equal non-evapor-able water

5?99 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

:4*I- I “ 1’””1°’7’1 7 I u E I

II I”HI

cl’j .26 I

I I ./+54 : I

32zt+—+F%—=

2 [ I2 I I I I ‘Vwl : “34

$1 I I L&v z’30%

,“ % /.z 1- ,26t-

18

.22 P

.140~1,0

P/?$ ,123 .4.56.7 8 .9 Lo

P/F$

Fig. 9-14 (left+Adsorption isotherms for samples of different w./c but equal nan-evapor.able water

Fig. %15 (right)-Adsorption isotherms for samples of different WO/C but equalnon-evaporable water

sorption curves apart from the effect on the level of the starting point:

at a given degree of hydration the same curve holds for all ages andwater ratios. In other words, the amount of water taken up in the

lower third of the range of vapor pressures depends only on the extentof hydration and hence only on the increase in quantity of hydration-product in the sample. On the other hand, the total amount of evapor-

able water depends upon the porosity of the solid phase which at a givendegree qf hydration depends upon the original water-cement ratio.

The data just considered show that the lower third of the adsorptioncurve has the same shape for different ages and different porosities ofsamples made from the same cement. Fig. 2-16 and 2-17 are presentedto show that the lower third of the curves have the same shape not onlyfor these conditions but also for different cement compositions. Theseplots are like those of Fig. 2-12 to 2-15 except that the scale of ordinatesis the ratio of the amount of water taken up at a given pressure to the


4.0 - u

JyTIb.,/‘v. ~0/c(Wi) @35 – 0 /7,0 0449 28 dogs - —

x2

23.0 0,449 3 mo.

; Cement No. 1s7.s4

o’ (High Cj5; Med~A)~ 3.0

-uz;~ 2,5

z2

E4 ?,0

~

~

.0

~ 1.5+ 6<

T3

$ 1,0 /

%

,9

l-iu 0.5

00 ,1 ,2 3 .4 .5 .6 .7 .8 .9 Lo

P/P$

Fig. %16 (left)-Adsorption isotherms for which the amount adsorbed is expressed as aratio to the amount adsorbed at p/p, = 0.36

Di(farent degrom of hydration

Fig. %17 (right)-Adsorption isotherms for which the amount adsorbed is expressed qs aratio to the amount adsarbed at p/p, =, 0.36

Differentcementsand diffwan! degreesof h~dratlon

amount taken up at a pressure of 0.36 p,. The coincidence in the lowerrange of pressures proves that the lower part of the curves can be repre-sented by the same form of mathematical expression.

Empirical relationship between the amount af adsorption at low pressuresand the nan-evaporable water content

Fig, 2-18 shows typical relationships between the amount of water heldat low vapor pressure and the non-evaporable water content for samplesprepared from two different cements. Symbols of different shape forthe same cement designate different original water-cement ratios, anddifferent points of the same shape represent a mix of given water ratio atdifferent stages of hydr@ion.

Although these data were among the first obtained in this investiga-tion and as a consequence show the influence of imperfect laboratorytechnique, they illustrate adequately the fact that with any given cement


d-1-—l-.-..u J&

I—. I

,/ o 2.s4- 9./

},49.?OJ

x 2s+.9. ?.0?

: :=::~}’-- –

I I I I,16 .18 .20 .22 .?4

Non- Evapo:able V/ater (W), q

Fig, 9-1 8—Relationship between amount of water held atlow pressure and the non.evaporable water content for two

different cements

the adsorption at low vapor pressure (any pressure below about 0.4 p,)is directly proportional to the extent of hydration as measured by thenon-evaporable water content, A study of this relationship will bepresented in another part of this paper.

General results from various cements

The results of some of the adsorption tests and measurements of non-evaporable water are shown in graphical form for various cements* inFig. 2-19 to 2-23. In Fig. 2-19, for example, the total evaporable wateris represented by the height of the column above the horizontal referenceline and the non-evaporable water by the length of the column extendingdownward. The proportions of evaporable water held between variousrelative vapor pressures are shown by the relative lengths of the blocksmaking up the column. As \vill bc shown later, the length of the first blockabove the zero line (up to line 0,35) is approximately proportional to thesurface area of the cement gel. By assuming that the surface area isproportional to the amount of cement gel, the length of this block mayalso be taken to indicate the relative amount of cement gel in the sample.

The effect of differences in water-cement ratio for specimens of thesame age is shown in Fig. 2-19 and 2-20. The effect of prolonging theperiod of curing for specimens of the same initial water-cerncnt ratiocan best be seen by reference to Fig. 2-21, 2-22, and 2-23. In readingthese diagrams it is helpful to remember that at zero agc tbcrc ~vould be

*For characteristics of the cements, see Appendix to Part 2.

0.50 t

Clin

ker

No.

1C

emen

t15

365

5p.S

urfa

ce16

65cm

Yg

0.5

9

0.2

5L

7O

ay

sIi

my,

.?aD

ays

56

Da

P9

0D

ay

,

Fig

.2-

19—

Eff

ect

of

wat

er-c

emen

tra

tic

on

the

har

den

edp

aste

atth

eag

esin

dic

ated

Cem

ent

1493

0-J

Sp.

Sur

face

2045

an‘/

9

7D

eys

14Da

y.28De

y,36

D.y

s90

Day

s18

.2my,

Fig.

Q-9

0-E

ffec

to

fw

ater

-cem

ent

rati

oo

nth

eh

ard

ened

pas

teat

the

ages

ind

icat

ed

Cl,

nker

No.

1C

emen

t15

365

5p5u

rfac

e16

65cm

’/9

Sh

’.mql

t)

,,3.

-7,4

7,50

s---

%/=

=0.

319

32C

U

wq~

=0.

439

‘~c=

0.58

7—F

ig.

%91

—E

ffec

to

fag

eo

nh

ard

ened

pas

teat

the

wat

er-c

emen

tra

tio

sin

dic

ated

05

0

tC

emen

t14930-J

04

5

I

So

Su

rfac

eZ045cm

2/q

Cu

red

26

day

sm

wat

er,

04

C

0.3

5

1

$“0

?01

‘“/c

=0.

309

ther

eafk

rjn

mo

est

roo

m

‘O/C

=0.

424

IV

Joc

.~57

3

Fig

.2-

29-E

Kec

to

fag

eo

nh

ard

ened

pas

teat

the

wat

er-c

emen

tra

tio

sin

dic

ated

n-i

-i 1? m

5PS

urfd

ceA

ilC

erne

.t.s

=15

00cr

n~a

C“l

tnke

rN

oI

Cem

ent

I575

4

‘?:

,,,’,

0\

,,.(

,2

,,7.

,,,.

28d

‘3kl

1

..

\

..- ,.. ..- ...

~..

Cl

fnke

rN

o.3

‘C

llnkc

rN

02C

linke

rN

05C

l,nk

erN

o.4

Cem

ent

1575

6:

Cem

ent

1575

8;

Cem

ent

1576

1;

Cem

ent

1576

3

7!m

‘-’o

/c=o

.449

‘0/c

=0.

446

~‘~

c=

0.33

4w

~.o

~Ott

i~C

=O

-3H

%,c

=04

m;

w4C

=0.

324

‘~c

=03

28‘+

==

0.31

8c

y==

0.43

7

Fig

.9-

93-E

ffec

to

fag

eon

har

den

ed~#

eso

ffiv

e4f

fere

ntc

emen

h


no non-evaporable water and hence no column extending downwardand the column for evaporable water would have a height equal to theoriginal water-cement ratio, corrected for bleeding, Therefore, the dif-ference between the height of the evaporable water column and theoriginal water ratio indicates the degree of reduction in porosity broughtabout by the curing.

Some of the irregularities shown in these diagrams are believed to bedue to imperfections in experimental technique. It seems probablethat a given group of diagrams representing regular changes in we/c orin age should show a regular pattern of change. In most of the interpre-tations built up in later parts of this paper, these irregularities are ignored.

EFFECT OF STEAM CURING

One test only of steam-cured material was made. The result was sosignificant, however, that it will be given here. The procedure was asfollows: a paste of normal consistency was made, composed of 1 partcement 15756, 0.7”1part pulverized silica (Lot 15918), and 0.43 part water,by weight. This was made into two prisms 1x1x1l% in, The prismswere cured over night in the molds and then were steamed at 420 1?in an autoclave for about 6 hours, after which they were immersed inwater over night. The bars were then crushed and a 48-80 mesh sampletaken for adsorption tests.

Two-inch cubes were made from the same cement-silica mixture,but with slightly higher water-cement ratio-O.50 instead of 0.43. Thesewere cured continuously under water for 28 days. They were thencrushed, granular samples were taken, and adsorption characteristicswere determined in the usual way.

The results of these tests are given in Table 26 and Fig. 2-24. Theyshow that curing at high temperature radically alters the adsorptioncharacteristics. Note particularly that about 90 percent of all theevaporable water was taken up at pressures above 0,8 p,, The sig-nificance of this will be discussed more fully in the succeeding parts ofthe paper,

SUMMARY OF PART !2

The water in saturated hardened cement paste is classified as evapor-able and non-evaporable, This classification is based on the amount ofwater retained by a specimen dried in a vacuum desiccator at 23 c over

the system ilZg(CIO*)z.2Hz0 + lllg(CIO&.4H~0. The pores in a hardenedpaste are defined as those spaces occupied by evaporable water.

This part of the paper deals with measurements of non-evaporablewater and the adsorption isotherms of the evaporable water in varioussamples of hardened cement paste.

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE 301~+057

Fig, 9-94--Effect of steam

,44 curing on adsorption chapacteristics

rOR#kd-t71

“rrvrri,2$~.

P/Ps

TABLE 96-EFFECT OF STEAM CURINGCement 15756

Relative

I73 F for

IA;to&v--d

vapor 28dpressure U&/c = .478 we/c = .43

yJ8* (: ;;;;) (:;:};)

0.16 ,0329 .00170.24 .0390 .00280.32 .0478 .00250.36 .0530 .00260.53 .0689 .00380.70 .0969 .00520.81 .1283 .00810,85 .1408 .00!?00,88 ,1623 ,01310,96 .2230 ,03001.00 ,4367 ,3009

*w. = non-evaporpble water.

A general description of materials and experimental apparatus andprocedures is given, with reference to the Appendix to Part 2 for more

complete information. Data are presented on the stability of the hy-drates of the constituents of portland cement, in the presence of dif-

ferent desiccating agents. Indications are that of the microcrystallinehydrates that might occur in hardened cement paste, only the calcium

sulfoaluminate would be decomposed to an appreciable extent by thedesiccant used in these studies.

The experiments were for the most part made on granular samplesprepared from the original cylinders or cubes.. Data are presented indi-

cating that the granular samples were representative of the origins 1

pastes, except for pastes of comparatively high porosity.

30s! JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

The empirical aspects of the experimental results are described anddiscussed. Adsorption and resorption curves from the same sample pre-sent a so-called hysteresis loop similar to those found for other materials.In addition, the curves show some features of irreversibility not com-monly found among other materials. Most of the study pertainq toadsorption isotherms only.

Adsorption of water vapor from humidified streams of air (air-streamapparatus) was found to be the same as adsorption from water vaporalone (high-vacuum apparatus), except at pressures below about 0.3 p,,where the adsorption in the absence of air was expected to be greaterthan that in the presence of air. The curves obtained by $he two methodsare believed to have the same significance.

Graphs are presented from which the following conclusions are drawn:

(1) The total water held at saturation (p/p, = 1.0) increases as thelength of the curing period increases.

(2) The non-evaporable water content also increases.

(3) The amount of water held at any intermediate vapor pressureincreases with the length of the curing period.

(4) The evaporable water content, which is the difference betweenthe total and the non-evaporable water, decreases as the length of thecwing period increases.

Curves are presented showing that differences in age and originalwater-cement ratio have no influence on the shape of the lower part of theadsorption curves. On the other hand, the position of the upper part of

the curve and the total amount of, evaporable water in a saturatedspecimen depend on both age and original water-cement ratio. Theseconclusions apply to all cements.

For a given cement the amount of evaporable water held at any pressureup to about 0.4 p. is directly proportional to the non-evaporable watercontent. The proportionality constant is different for cements of differenttype.

An adsorption curve for cement paste cured for six hours in the auto-

clave at 420 F is compared with the curve obtained from ti similar pastecured at 73 F for 28 days. Results show that curing at high temperature

and pressure produces adsorption characteristics radically different fromthose observed in specimens cured in the ordinary way.

REFERENCES

1. E. Freyssinet, Science et Zndustrie (Jan. 1933).2. F. M, Lea, Cement k Cement M.fgr. v. 5, p. 395 (1932).3. K. S. Rae, “Hysteresis in Sorption,” J. Phys. Chern. v. 45 (3) pp. 500-531 (1941).4. L. H. Cohan, J. Am. Chem. LSOC.v. 66, p. 98 (1944).5. N. A. Lange, Handbook of Chemistry, 4th Edition, p. 1269.


Appendix to Part 9

CONTENTS

Te#e

Description of Materials and Tabulations of Original Data,,,,,,Characteristics of cements . . <,,....!. . !.,!.!.,!, ,, .!,,!,,,

Series index to cements ., ..!,.,,,, ,,, ,,, ,,, ,, ,,, ,,, ,,, ,, A-1Chemical analyses and computed compound composition, ,, A-2Density, specific volume, and specific eurface,.,, , , ,, , , ,,, , A-3

Series 254-205,...,,,,,,,,,,,,,,,,,,4,4 ,,,, ,,, ,,,., ,,, ,,, ,{

MA-6

Series 254-herb,,,, ,,, . . . . . . . . . . . . . . . . , .,.....,,.,.,,,,, A-7Series 25LK4B . . . . . . . . . . . . . . . . . . . . . . . . . , ...,...,,.,,,,,, A-8Series 254-7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

F&e

308303304305308

311

314

312

Series 254-8. . . . . . . . . . . . ,,, .,,,. ,,, ,, ... ., .,,.., ,, .,,,., , {A-9 316A-10 317

!&ries 2549........,,,.,.......,,,.. . . . . . . . . . . . . . . . . . . . . ~jj~- !j!j~

Series 254-11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Series 254-13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

{A-30- 328-A-33 330

{

A-34 332A-35 332A-36 334

Series 254-16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333Series 254-18.,, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

DESCRIPTIONS OF MATERIALS AND TABULATIONS OF ORIGINAL DATA

Information is given in this appendix concerning the materials used in each series andconcerning the preparation of test specimens and samples. This information supple-ments that given in the text.

Also given are tabulations of the original data. The authors regard such a full pre-sentation desirable because of the uniqueness of the data and because of the speculativenature of the interpretation offered in the text. That is, alternative interpretations mayoccur to other investigators in this field and we consider that they should have accessto the original material.

Characteristics of cements

The cements used in any given series can be readily identified in Table A-1. Theirchemical and physical properties are tabulated in order of lot numbers in Tables A-2and A-3.

Description of specimens made in series 954-965

Mortar Specimens: Truncated cones: Base 4 in.; top 1X in.; altitude 6 in.Cement: Lot 14502 (see Tables A-2 and A-3 for characteristics).Aggregate: A mixture of Elgin sand and Ottawa silica graded as follows:

Weight, per cent of size indicated—

Ottawa Silica Elgin Sand

;~- l~g- 4s- fy lf 8-2s 4

——2.4 4.9 23.6 29.9 16.3 22.9


TABLE A.1—SERIES INDEX TO CEMENTSI

Series

2.54-265 14502

254-MRB 14898-39.4Q14904-45AQ1491O-52AQ

1

254-K4B 13721-1S13733-5s13740-7P13705-15Q13780-20Q

254-7 14675

~4-8 =715014J

2S4-9 I 14930J

254-11 I 1549515761

254-13 1536715923*15930*

——254-16 1.5754

16189

254-18I

13495

148W-40PC14905-46PC14911 -51PC

13722-1P13734-5P13741-7Q13766-16S

15007J

—.15007S

1549715763

=49815924*15932*

15756

14675

Cement Nos.

l’woo-41st14906-47SC14912-53SC

13723-lQ13735-5Q13752-11P13767-16P

15008J

15011J

1566916198

1.562315925*15933*

15758

15365

1490142AQ14907-48AQ14913-54AQ

137304s13736-6S13753-llQ13768-16Q

15011J

15013J

1575416213

1567015926*15934*

15761

13723-lQ

14902-43PC14908-i9PC14914 -55PC

13731-4P13737-6P13763-15S13778-20S

15012J

15365

1575616214

1569915927*15935*

15763

14903-44s(214909-50SC14915-56SC

13732-4Q1373&6Q13764-15P13779-20P

15013J

15758

15921*15929*

16186

*AO oement$ marked * were ground in the laboratory. The rest were ground in commercial plants.

Mixes: Specimens represented the following mortar mixes, by weight: 1:0 (neat);1:1%; 1:1, 1:2, 1:3, 1:5, 1:7.

Mixing: Each batch was mixed 30 sec. dry and 2 rein, wet in a small power-driven,open-tub mixer.

Molding: Cones were cast in watertight molds of known capacity, the mortar beingpuddled with a light tamper,

Measurements: The weight of the filled calibrated mold was measured to 1 g immedi-ately after filling, and again after 20-24 hr. in the fog-room. On stripping, the 6pecimenswere weighed in air and in water.

Curing: In molds in the fog-room for the first 20-24 hr.; in the fog-room thereafter.Temperature: 70 F’.

Druing: The granular samples were dried in air-filled desiccators over concentratedsulfuric acid.

Composition of specimens: See Table A-4.Analysis ofgranular samples: See Table A-5.

Adsorption data: See Table A-6.

TA

BL

EA

-9—

CH

EM

ICA

LA

NA

LY

SE

SA

ND

CO

MP

UT

ED

CO

MP

OU

ND

CO

MP

OS

ITIO

N

All

cmnp

utat

ions

are

base

don

the

wei

ght

ofth

ece

men

tun

less

othe

rwke

indi

cate

d.T

heco

mpu

ted

com

posi

tions

are

base

don

the

oxid

ean

alys

esco

rrec

ted

for

free

lime

but

not

tmot

her

mm

orco

nstit

uent

s.

Min

orC

onst

ituen

~q

.

Fre

eF

eOT

iOZ

P*O

5~

o ;K

,OC

HC

ISC

ao$

kSo

lubl

e—

..

_—

—__

1.11

0.22

0,52

——

—0.

360.

00.

100.

971.

1s0.

00.

310.

101.

581.

490.

300.

101.

11—

——

—_

__

0.29

0.0

0.41

0.10

3.80

1.46

0.37

0.53

020

1.55

1.27

0.37

0.12

—.

——

_—

__—

_0.

040.

00.

270.

1.4

0.32

0.0

0.16

0.3.

50.

460.

410.

00.

370.

42—

——

—,_

__

____

0.00

0.0

0.07

tr.

0.35

0.0

0.26

0.10

0.11

0.45

0.03

0.08

0.08

0.40

0.03

0.33

0.42

0.58

0.53

0.36

0.32

0.38

——

—_

—_

__0.

150.

00.

340.

660.

160.

330.

330.

510.

08—

——

_—

_.—

_0.

110.

00.

2310

.41

1.28

0.0

0.28

0.28

0.86

1.39

0.32

0.20

0.40

——

——

__

_0.

000.

00.

150.

150.

390.

350.

32O

.m,0

.38

0.30

0.57

0.15

0.25

0.32

0.0

0.15

0.42

1.24

0.0

0.45

0.18

0.76

1.38

0.02

0.15

0.4.

5—

——

——

__

__

Maj

orC

onst

ituen

tsL

otX

o.R

ef.

No.

——

—_

1s 1P lQ

—4s 4P 4Q

—— .5

S5P ~Q

-—.

—6s 6P 6Q

—— 7P 7Q 11

PllQ 15

s15

P15

Q

16S

16P

16Q

-20s 20

P20

Q

so,

MgO

3.16

2.91

2.94

2.99

4.12

4.09

4.21

1.52

1.52

1.50

1.38

1.39

1.43

3.31

3.36

0.78

0.79

4.07

4.06

4.06

3.16

3.15

3.16

0.98

0.97

0.9s

——

__

__ 6

’02

(7Z

SC

*SC

*A$

wc

s—

——

—_

_51

2111

102.

8

Lm

s

IYn.

I.w

l

0.79

0.87

0.79

0.90

0.97

0.78

1.20

2.40

1.81

0.92

0.s4

D.8

3

0.80

0.82

0.94

0.86

0.72

,0.

850.

76>

11.8

1~0.

930.

81’

0.6&

0.91

0.73

,

In-

Sol.

Res

.

0.14

0.24

0.23

0.18

0.11

0.37

0.20

0.14

0.13

0.10

0.20

0.17

0.22

0.22

0.20

0.19

0.16

** $*I4

123

** 0.15

**

SiO

r

20.7

9—

—21

.08

20.9

321

.13

1902

19.1

318

.79

23.1

622

.61

22.9

7

21.0

520

.97

20.9

9

20.4

620

.48

——

21.1

821

.57

21.2

321

.21

21.2

3—

—21

.55

21,5

121

.53

——

1’3.

3719

.35

19.3

4

Alj

O,

6.02

6.10

6.18

5.85

4.80

.4.9

25.

08

3.33

3.31

3.27

5.85

5.99

.5.9

0

6.96

6,89

4.70

4.26

.5.5

85.

575.

58

6.10

6.10

6.10

7.35

7.34

7.34

Fez

Oa

3.11

2.15

2.17

2.17

6.85

6.70

7.17

4.15

4.31

4.40

2.97

3.03

3.03

2.31

~~8

4.89

4.48

2.!3

02.

892.

89

2.49

2.49

2.49

3.77

3.77

3.77

~=~1

63.5

7

64.1

063

.48

64.1

8

–iz

.12

61.6

361

.72

64.4

763

.23

63.5

3—

— 6.5.

7765

.’50

6.5.

57

63.2

363

.55

65.1

065

.61

’62.

9062

.59

62.9

2

64.0

063

.SS

63.9

.5

65.3

165

.08

65.2

8

1349

5

1372

1t13

722t

1372

3t

1.65

1.s0

1.80

1.80

1373

0+13

731t

1373

2+

1.s0

1.80

1.80

1373

3t13

734t

1373

5T

1373

6t13

737t

1373

8t

1.80

1.80

1.80

1.80

1.80

1.8o

1.80

1,80

1.s0

1.80

59.0

15.8

10.5

9.0

3.06

56.0

17.8

10.7

9.2

3.06

56.4

17.6

10.5

9.2

3.06

45.0

24.7

14.5

7.0

3,06

46.0

24.0

14.4

7.0

3.06

1374

0t13

741t

1375

2+13

753*

1376

3t13

764t

1376

5t

1.s0

1.80

1.80

1376

6t13

767t

1376

8t

1.80

1.80

1.80

1.80

1.80

1.80

47.0

26.5

12.0

7.63

.06

45.0

27.8

12.0

7.63

.06

45.7

27.3

12.0

7.63

.06

.—

——

__

57.5

12.2

13.1

11.5

3.06

53.0

15.5

13.1

11.5

3.06

33.3

15.3

13.1

11.5

3.06

1377

8t13

779t

1378

0t

(Con

tinue

don

next

page

)

TA

BL

EA

-9--

(CO

NT

INU

ED

)

Lot

No.

1450

214

560

1467

5

1489

8114

899

1490

0\

1490

1114

9021

1490

3t

1490

4$14

905$

1490

6t

1490

7*14

fI08

t14

9091

1491

0t14

911*

1491

2X

1491

3t14

914]

1491

5t

1493

0J15

007J

1500

8J

1501

1J15

012J

1501

3J15

014J

1536

515

367K

1549

515

497

1549

8K

IM

ajor

Con

stitu

ents

IllR

ef.

——

——

No.

Sio,

AlZ

OS

Fe*

O*

~;$

l

——

.

21.0

26.

072.

7563

.49

20.7

8.5

.03

3.98

64.9

920

.76

6.07

2.55

63.8

3

39A

Q20

.72

6.45

3.25

63.8

940

PC20

.80

6.52

3.12

63.6

941

SC20

.78

6.64

3.18

64.1

9—

..

42A

Q20

.68

6.82

3.16

63.7

843

PC20

.72

6.92

3.18

63.6

344

SC20

.78

6.86

3.12

63.7

8

g:~=

3.35

‘:::

48

6.S2

3.12

20:4

06.

983.

1463

.98

48A

Q20

.70

6.95

3.31

63.0

7‘4

:::20

.94

6.79

3.39

63.1

221

.16

6.72

3.38

63.1

4—

..

52A

Q20

.92

6.87

3.47

63.3

051

PC20

.88

7.23

3.51

63.0

953

SC21

.04

7.09

3.41

63.4

0

54A

Q21

.18

7.13

3.39

62.8

955

P(2

21.0

87.

093.

4962

.84

56SC

21.0

66.

593.

3762

.43

25.4

24.

363.

2162

.46

22.7

84.

773.

4664

.92

22.6

94.

874.

1064

.51

23.0

94.

733.

4564

.62

23.6

54.

393.

2564

.53

20.9

86.

852.

4362

.75

21.1

86.

422.

4062

.96

——

—>

0.78

6.42

2.20

63.8

621

.87

6.83

2.23

65.3

0

20.0

45.

.52

2.50

66.4

219

.98

5..5

52.

5966

.55

20,9

25.

822.

5367

.71

—.—

II

ILO

SSIn

-M

gOso

,80

1.F

ree

1:.

Res

.C

.O

2.94

1.76

l.c!a

0.14

0.96

1.35

2.27

0.99

—0.

393.

021.

710.

950.

111.

19

2.6

0.58

0.99

—0.

672.

50.

650.

91—

1.16

2.5

0.52

0.87

—0.

09—

——

——

.2.

70.

581.

04—

0.67

2.4

0.61

0.92

—0.

972.

40.

600.

99—

0.13

.—

..

2.4

0.52

0.81

—0.

582.

60.

571.

02—

0.81

2.7

0.36

0.76

—0.

05

2.7

0.59

0.87

—0.

042.

70.

611,

02—

0.24

2.7

0.52

0.75

—0.

07

2.7

0.52

0.18

—0.

102.

70.

480.

23—

0.04

2.6

0.48

0.30

—0.

06

2.6

0.75

0.28

—0.

960.

760.

37—

0.63

2;0.

780.

35—

0.46

——

—1.

651.

550.

810.

09tr

.1.

321.

300.

840.

070.

621.

271.

260.

780.

090.

08

1,19

1.43

0.67

0,12

0.40

1.09

1.34

0.77

0.15

0.37

3.52

1.71

0.74

0.07

0.64

3.61

1.61

0.70

0.08

0.59

——

—.

.2.

482.

480.

960.

190.

932.

630.

410.

150.

330.

98,_

__

1.28

1.82

1.71

0.26

3.14

1.33

1.82

1.52

0.15

3.14

1.36

0.19

0.85

0.25

2.71

— Fel

— — — . — — — — ).6 ,, — ).0 ., ,, —

2Min

0rC

ons

titue

nt5

1C

ompu

ted

Com

poun

dC

omno

mtio

n

qo g

K4

$k

_.

—0.

290.

6(0.

220.

30.

260.

.5(

_.

—

——

—

_.

—

..

.

—.

—0.

220.

4

0?23

O*5

—.

—b

b0.

220.

4!

0!32

0!4!

).51 .,

0.17 ..

0.1( .,

——

—);

?60;

300.

,4,’

,,,,

——

.—

——

——

—__

6C

HC

bco

,C3

SCa

scd

$m

Solu

ble

6G

-:4

145

2611

813

.060

177

134.

0448

.123

.211

.87.

82.9

0—

——

.49

.422

.211

.69.

9=47

.523

.812

.09.

51.1

149

.222

.512

.29.

70.8

8—

—.

——

46.8

24.0

12.7

9.60

.98

45.2

25.4

12.9

9.71

.03

45.2

25.6

12.9

9.51

.02

——

1—

l—l-

--—

11111148

.422

.912

.210

.20.

8848

.822

.012

.89.

50.9

649

.421

.313

.29.

60.6

0—

-41——.—

42.7

27.2

12.8

lo.

oti

42.0

28.4

12.2

10.3

1.03

41.3

29.6

12.1

10.3

0.88

—.

.—

—42

.528

.012

.310

.60.

8839

.630

.113

.210

.70.

8240

.829

.613

.010

.40.

82

0.02

9d—

—

117-

0.01

40.

6645

.129

.16.

71O

.52.

430.

054

43.0

35.4

6.1

9.92

.28

***

39.0

29.0

14.0

7.03

.00

0.04

141

.729

.313

.07.

32.7

3—

——

—__

0,.,0

390.

3245

.028

.013

.36.

74.2

2“

45.5

28.4

14.3

6.70

.70

---la”

————

0,.,0

050.

1659

.413

.010

.47.

63.1

0“

60.1

11.9

10.3

7.93

.10

,.“

62.5

13.0

11.2

7.70

.32

——

—(C

oncl

uded

onne

xtpa

ge)

1562

3K1.

3669

1567

0K13

699K

0.03

1.82

0.17

o~()

2,36

1.73

1.84

1.82

1.68

0.41

2.36

5.00

0.19

1.85

5.00

0.03

5.00

0.17

5.00

0.20

1.81

5.00

2.45

1.72

1.86

2.27

2.42

1.05

0.73

0.26

0.37

0.25

0.06

0.13

0.16

0.19

0.13

0.17

0.07

0.07

0.33

0.32

0.31

0.73

0.15

0.23

nil

——

0.93

0.49

3.14

nil

0.15

0.98

0.!)

60.

93

——

—.

..

——

—_

..

nil

0.30

0.14

0.09

0.05

0.17

0,00

20.

2247

.630

.94.

s13

.20.

06ql

0.,:1

0.,0

30

.,?9

0.,0

50.

,22

0:+

OQ

9O

.,?6

33.0

54.2

2.3

5.8

3.10

37.4

.51.

92.

45.

70.

27ni

l0.

250.

130.

091.

130.

-44

0.00

60.

1647

.92!

?.0

10.1

7.6

0.34

23.3

027

.57

27.9

322

.72

4..

5s

2.0

92.0

7.5

.38

4.35

1.92

1.87

2.48

65.0

163

.88

65.6

164

.06

63.9

664

.31

66.5

7

<2.

9863

.93

1.44

1.72

1.83

3,43

2..5

01.

461.

25

.— —_—

—

——

.—_

——

._

._).

600.

280

030.

510.

170.

160.

039

0.32

45.(

)27

.713

.46,

7ni

l0.

300.

140,

090.

050.

170.

002

0.22

48.6

27.9

4.7

12.6

).03

0.26

0.08

0.06

0.30

0.40

0.00

50.

1660

.611

.610

.27.

7—

——

—L

nil

0.2.

50.

130.

091.

130.

440.

006

0.16

44.9

29.2

9.8

7.5

nii

0.11

0.03

,009

10.0

.50.

22,

O.(

x)$)

0.26

,33.

5153

.61

2.3

6.0

——

4.0

2.9

3.2

1575

415

756

1575

8

20.8

:22

.50

19.9

8

22.0

027

.52

6.44

4.39

5.50

2.20

4.14

2.55

0.02

1.28

1..5

5

1576

11.

5763

1592

1$15

922$

1592

3$

1592

41.

5925

1592

6!

5.25

2.09

6.83

6.69

6.50

5.S2

5.72

5.53

4.58

4.34

2.07

2.47

1.96

3.4

21.

700.

530.

75

0.15

0.15

0.14

3.1

3.2

(I

\(

——

____

).60

0.28

0.03

0.51

0.17

0.16

0.03

90.

3245

.52

S.41

4.3

6.7

0.7

..,,

..,,

,,.,

,.“

44.6

27.s

14.0

6.6

4.0

,,,,

‘,‘,

‘,,.

.,“

43.3

27.0

13.6

6.4

S.5

21.8

721

.43

20.6

1

2.23

2.19

2.12

2.53

2.49

2.40

65.3

063

.99

62,1

5—

— 67.7

166

.57

64.2

8

2.63

2.58

2..5

0

1.36

1.34

1.2!

3

).<

030.

260.

080.

060.

300.

400,

005

0,16

62.5

13.(

)11

.27.

7lJ

.3,.

.,,,

‘,,,

.,,,

,’!,

‘t,,

,,,,

::61

.412

.811

.07.

63.

159

.312

.310

.67.

38.

5—

——

—.

._

——

——

—ni

l0.

300.

140.

090.

050.

170.

002

0.22

.49.

228

.54.

412

.82.

7.,

.,..

.,,.

,.,,

“46

.627

.04.

212

.18.

5ni

l0.

110.

030.

090.

050.

220.

009

0.26

37.4

51.’

32.

45.

70.

3

20.9

220

.57

19.8

6

2330

22.0

827

.95

0.85

0.64

0.81

0.25

0.25

0.24

2.71

2.66

2..5

7

1592

7~

1392

9~

1593

05

1593

215

933

i15

934

1593

5!

4.35

4.12

1.87

65.0

161

.61

65.6

1

1.44

1.36

1.83

1.05

1.00

0.26

0.25

0.37

0.36

0.35

0.2.

50,

240.

13

0.12

0.16

0.16

0.15

0.73

().6

90.

23

0.22

nil

nil

nil

——

——

——

—,.

,4,,

,’,,

‘,,,

“35

.549

.32.

35.

48.

5ni

l0.

250.

130.

091.

130.

440,

.,006

0.16

47.9

29.0

10.1

7.6

0.3

,,,.

,,,,

,,,.

“!,

,,,,

.,,<

,,:

47.1

28.5

9.9

7.5

3.1

45.5

27.5

9.6

7.2

8.5

).60

0.28

0.03

0.51

0.17

0.16

003

90.

3245

.027

.913

.36.

74.

1ni

l0.

300.

140.

090.

050.

170.

002

0.22

48.7

27.9

4.7

12.6

2.9

nil

0.11

0.03

0.09

0.02

,0.

220.

00!2

0.26

33.4

53.9

2.3

.5.9

3.2

).60

0.28

0.03

0.51

0.17

0.16

0,03

90.

3244

.827

.I

13,4

6,8

3,9

‘,,.

,,.,

,,,,

,,‘<

44.9

27.7

13.3

6.7

4.1

26..5

322

.72

22.3

521

.57

1.96

5.38

.5.2

95.

11

6.42

4.38

2.09

6.48

6.43

i.78

2.48

2.44

2.35

2.20

4.16

1.95

2.21

2.20

62.2

864

.06

63.0

160

.82

63.8

964

.31

63.9

163

.99

63.9

0

1.74

3.43

3.37

3.26

-—16

186

1618

916

198

1621

316

214

21.1

322

..50

27.5

420

.88

20.8

1

2.49

1.46

1.71

2.52

2.49

O.%

1.28

0.74

0.91

0.94

0.19

013

0.07

0.25

0.21

0.93

0.49

0.15

0.!3

30.

93

]The

Se

anal

yses

wer

em

acle

inth

epk

mt.s

furn

ishi

ngth

ecl

inke

r,ex

cept

for

SOJa

mf

free

CaO

whi

chw

ere

dete

rmin

edin

this

labo

rato

ry.

Min

orco

nstit

uent

son

clin

ker

basi

s.T

heva

lues

are

base

don

cbnk

erw

eigh

tsin

stea

dof

cem

ent

wei

ghts

.s

Gm

xmd

inla

bora

tory

.K

Clin

ker

*T

helo

sscm

igni

tion

for

the

clin

ker

was

not

dete

rmin

ed.

The

valu

essh

own

hem

repr

esen

tth

elm

.gcm

igni

tion

from

the

gyps

uman

dth

atfr

omth

ecl

inke

r.**

Fiot

,de

term

ined

.**

*0.

008c

70ta

llow

;0.

005%

Vin

sOl

resi

n.a

Alk

a?j

anal

yses

mad

ecm

1500

8J.

b,,

,,.,

1501

2J.

,,,,

,’:

Tal

low

.“

1501

4J.


TABLE A-3—DENSITY, SPECIFIC VOLUME,

LotNo.

——13495137211372213723

137301373113732

137331373413735

137361373713738

13740137411375213753

137631376413765

137661376713768

137781377913780

14502

14560145601456014560

14675

1489814899

149001490114902

149031490414905

149061490714908

Density and Specific Volume,as Computed from

Displacementin

Kerocene

Densityg/cm8

3.1613.1303.1103.109

3.1633,1523.139

3.1653.1433.104

3.1453.1363.128

3,145

3,1543.1503.1553.156

3.143

3,140

3.1.W

3.167

0.3160.3200.3220.322

0.3160.3170.319

0,3160.3180.322

0.3180.3190.320

0.318

0.3170.3180.3170,317

0.318

0,318

0.318

0,316

Water

Densityg/cm:

3.184:, ;;g

3; 206

3.197

3.225

S:mygl.

0.3140,3160.3140.312

0.313

0.310

SpecificSurface

A%?;(%M.

1868164517451535

173518001705

179017151665

168518151715

1655165517401610

178016301800

184517351745

170517301695

1820

1085154020462560

1866

16201610

162016401590

163015801610

162016601630

laboratory. Tbe rest werea. All those cementi marked a were ground in t;ground in commercial plant-e.

b. Thk }ncludw -t-325 material.c, DensMea of these cements were not determined. The vahm given are for

cements of similar finencca made from tbe same chnker, but no allnwancawac made for dhTerenoca in gypmm content.


AND SPECIFICSURFACE OF CEMENTS

LotNo.

1490914’31014’311

14912149131491414915

14930J15007J15008J

15011J15012J15013J15014J

1536.51549.51549715669

1575415756157581576115763

15921 n15922 a15923 a

15924 a15925 a15926 a

15927 a159z9 ~

15930 a15932 a

15933 a15934015935 a

161861618916198

1621316214

Density and Specific Volume,as Computed from

Displacementin

Kerosene

3.165

3.181

3.144

3.2183,1893,201

3,2043,1913.1623.174

3,1353,1013,1093.215

:, ;;!

3:1073,1553,215

3.135 c!,,,

3, ?,07 c

,,

3.:,76 C

3.215 C,,

3. !,55 c,’

3.1353.1743.215

3.1353.135

0,316

0.314

0.318

0,3110.3140.312

0,3120,3140,3160.315

0.3190.3220.3220.311

0.3100,3150.3220.3170,311

0,:19

t,

0,322

,,

0,315

0,311,,

0.:17

,4

0.3190.3150.311

0,3190.319

Water

3.207

3,228

3.2903,2603,239

3.263

3.247

3,1873,1363,1783,257

3.1743,2093, 1583,2103.252

3.1OOC‘,,,

3.:6c

4,

3,Z20

3,25c‘,

3.21 c

,!

3,1S83,2143.254

3.1793.184

0,312

0,310

0,3040,3070.309

0,306

0,.308

0.3140,3190.3150,307

0,3150.3120.3170.3120.308

0.314‘,!(

0.316

,,

0.:10

0,308,,

0,:12

4.

0.3140,3120,308

0.3150.314

Speci::2~grface,

A,S.T.11

163016101620

1640164016101650

204520151825

1s3.5174018102010

1640144023002290

18001800180018001800

182018902070

181518702020

18002080

17952050

182018552080

1702 b1849 b2014 b

12631528

Per-meability yMethod

-.——

3120278051503810

342o3060357029502760

287033504850

2930336045s0

28604770

26304280

296034s04480

320032003200

24302920


TABLE A-4-UNIT ABSOLUTE VOLUME COMPOSITION OF THE MORTARSUSED IN SERIES 954-965

Unit AbsoluteVolumeComposition Weter-CementiRatioR&

Cement Sand Water Air V;ldy Gsl/Sk,Bwmt&

323 0.5001600

0.4160 0,0102 0,744 0.2360 ,~38

2!060,4040 0,3331 0>0180 0,823

WI0,202 2.05

0.8195 0.3850 0, 2s!!0 0,0129 0,884 0,268 3.17512 0.2221 0,6353616

0.2204 0.0162 1.019 0,323 3,68O,lrlee 0,6022 0,2076 0,0237 1,246 0!306 4,46

618 o,loez 0.6390 0. 22(30 0,0289 2,118 0,070 7,69621 0.0787 0.6698 0!2216 0,0359 2,810 0,893 10,09

TABLE A-5-ANALYSES OF GRANULAR SAMPLES USED FOR ADSORPTIONAND NON.EVAPORABLE WATER MEASUREMENTS IN SERIES S54.265

(1) CO: comes chiefly from oalc~eoue sand (Elqin).[~] pOn-.va~0yable water Obtamedby oorrea~mgl~s pnignition for CO*IC++S.

gnited we]ght taken w cement content since thw M a neat paste.

.137

.1474,1552.1649: }:;;

.1947

.1962

.2013; jl));

.22252M3

.114

.1237

.1310

.1396

.1472

.1526,1634.1649.1703.1776,1868.1887,210

SandcO/&lt

difference)— —801. so:sio: Meth.— —

2::; 17;23,1 26.342,4 37,048!0 42.551,8 48.667.7 55. ti

TABLE A-6-ADSORPTION DATA FOR SERIES 954.965Age: 110 days

Total Water Retained at Relative Vapor PremureIndicated, g/g drY weight

PIP.Ref. Ref. Ref. Ref. Ref. Ref. Ref.323 506 509 512 515 518 521

,.125 .105 .108 ,095

?’11 .1384 .1121 .1141 .10080.20 .1448 .1183 .1199 .10600.36 .1544 .1254 .1274 .112s:,: .1626 ,1331 ,1353 .1206

.1683 .1382 .1400 .12640:75 ,1800 .1491 .1532 .1443O.w .1826 .1510 .1558 .14530.826 , 1s62 .1569 .1636 .15600.888 .1941 .1629 .1731 .16510.93 .2022 .1730 ,1850 ,18650,98 .2053 ; ;:;7 .1888 ,1991SSD .220 .227 .267

W- = non-evaporable water, Pjp, = about 24x1O-$.SSD = Water content of granular sample, saturated, surfao~dry for sample that had been dried and

reeaturated.

Description of specimens made in series 254-MRB

Neat Specimens: Cylinders, 1x7 in.

Cements: See Tables A-1 to A-3. tBurning CoruWons: Lot Nos. 14910, 14911, 14912: hard burned; Lot Nos. 14913,

14914, 14915; soft-burned; others: normal plant burning. Changes in burning conditionwere brought about by changing length of burning zone.


CooliW Condition: The symbol PC signifies cooling-by regular plant method; SCsignifiesslow cooling by storage in an insulated box where temperatures at or above red-heat were maintained for about 24 hours; AQ signifies cooling to temperatures belowdull-redwithin 10 eeconde by use of an air-blast.

Gtindiw: In the laboratory mill with enough added gypsum for 1.8 percent. totalSO*.

Miting: The cement waa placed with water in a kitchen-type mixer and mixed for2 minutes, allowed to rest for 1 minute, and then mixed for 1 minuh w/c = 0.5 by

weight at mixing.

Cad@: The pastes were poured into lx7-in, waxed-paper cylinders,Curing: In the molds under water. Molds stored horizontally.Drying: The granular samples were dried in a vacuum desiccator over M@(CIO,),.-

2H*O.Adsorption Data: See Table A-7.

TABLE A-7-ADSORPTION DATA FOR SERIES 954-MRBWater-cement ratio corrected for bleeding

PIP*

w“. 0ss.20. 3b5,.51.61,69,75.80.84,89,96

WDSSDO

PIP*

w.; ;$3; :f5

.61

.69

.75

. w

.84

. fJ~

.96SSDSA’DO

Key:

Total Water Retaineda

= —l:;:O- Mf#-

w,/c = we/c = W.lc =.382 .3W ,446

kge 120d Age 120d Age 126d

— w.2171 .2274.2615 ;Mi: . 26S4.2737 .2848.2977 ,3034 ,3111.3179 .3209 ,3245. 329S ,3355 .3534.3461 .3511 .3656

,.3610 .3666 .3852.3675 .3724 .3918.37S2 .3813 .4000.3971 .3983 ,4100.431s .4225 ,4459,4604 .4581 . 50S2

— .5267

14flo7-4AQ

Wolc =,406

ige 173d

.2191,2605,2789.3037.3231.3354.3450.3629.3683.3766.4027,4279.4606.4741

SD = V

SSDO -1

AQ=APC= ISc=ew.=?

1

Mjg-

WOJC=.391

~ge 126d

:,:2:;

.2755; :W:

.3332

.3437

.3640,3700.3803.3008.4401,4911.5031

Ielative Vapor Preaaure Indicated,z cement-l;;w2-

UIJC -.393

ke 133d-.2273,2665,2825,3092,32S5,3422357s

,3743,3s073s83

,3{)~1,4475.5013,5108

.2271

.2664

.2823,3091.3277.3448.3602.3797.3842.3926.3996.4401; ;;::

.2284

.2723

.2801

.3143

.3333, 34s5,3578.3749. 3S24.3041.4168.4553.4897.4993

Total Wuter Rctainerl at Relative Vapor Prmaure Indimted,(IE Celrlent

— —,2299 ,2356,2757 ,2794,2024 ,2966,3134 .3271,3393 ,3510,3529 ; :g:;,3631.3811 ,404s,3870 .4107,3082 ,4217,4176 ,443s,4460 .4737;$s: >6406

.6673

— —Mm&- lf&lg9-

W.ic = W.:I;3=.394

ige 200d Age 200c- -

.2250 .2255

.2673 ,2669

.2853 .2846

.310s .3119

.3327 .3346

.3463 .3496

.3.573 .3639

.3764 .3871,3835 . 394t43W0 .4061

.4136 .4333

.4394 .4650,47/71 .5477.4922 .5725

tar content of man)

14910-5AQ

Wolc =.460

me 2C4d

,22s2.2704.2S65.3142.3365.3470.3533.3793. 3X44. 39;2.42S0.4706.6131. 534s

l$m~l.

w./c -.464

ige 204d

.2294

.2723

.2940,3160,3383.3496,3571.3S32,3903,4017.4365,4801.5259.5433

M:&-.

w.fc =,4s9

lge 212d

.2252

.2703

. 2s83

.3167,3416,3558; ;::;

,3956,4048:af.lq

..5473

.5675

14913. M;p8A()

Wolc = W.fc =.410 .423

be 212d Ase 222c

.2206 .2253

.2665 ; ;;:;,2839.3075 ,3101.3275 .3293.3389 ,3443.3514 .3537367X .3736

,3704 .3771.3771 ,3847.4061 .4137.4314 .4347.4767 .4870.4932 —

M;;-

WJC -.437

~ge 222d

.2240

.2667

. 2S30

.3097; ~2;

.3562

.3759

.3787

.3869

.4149

.4327

.5203

.5296

r samnle. saturated. surface-drv for snmde that had baen tiled.nd reaaturated~te~ content of granular sample that waa brought to saturated condition without pre-mmru’y drying.quenched.nt cooled.w Ooolad.n-evaporable water; P/P. = about 24x10-~.

319 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE

Description of specimens made in series 954-K4B

Neat Specimens: Cylinders, 1x734 in.Cernen& See Tables A-1 to A-3.Cooling: Symbol P signifies regulnr plant cooling; S signifies slow

heating clinker; Q signifies quick cooling after reheating clinke~.

November 1946

cooling after re-

grinding: In the laboratory mill with enough added gypsum for 1.8 percent total808.

Miring: The cement was placed with water in a kitchen-type mixer and mixed for2 minutes, allowed to rest for 2 minutes, and then mixed for 2 minutes. w/c = 0.5 byweight at mixing.

Casting: The pastes were poured into lx7~-in. cylindrical molds.Curing: In tbe molds stored horizontally under water for 20-24 hrs.; under water

thereafter. Temperature: 70 F,D@ng: The granular s’amples(48-100 mesh) were dried in a vacuum desiccator over

Mg(CIO,),.2H,0.Adsorption Data: See Table A-8.

Description of specimens made in series !?54-7

Mortar &ecimens: Truncated cones: base, 4 in.; top, 2 in.; altitufle, 6 in.Cement: Lot 14675. See Tables A-2 and A-3 for cha~acteristirs,Batches: The batches were made up as follows:

7-1

7-2

7-3

7-4

7-.5

7-6

7-7

1-0

1-%

1-1

1-2

1-3

1-4

1-5

——-.—Weights,

ottawa Silica

fl:-

—

36

54

77

S6

90

90

1~()-

—

73

110

157

177

1s4

1s4

4s-2s

—

125

187

266

299

311

311

m. per batch

Cow Bay Sand

28-14

—

579

SW

1234

1:189

1447

1447

14-8

—

301

4.33

644

724

654

654

8-4

—

386

57s

~~z

!325

1064

1064

Cement~

4000

3000

2250

1600

1200

93s

750

W3er ,

1010

S30

675

570

545

590

570

Mixing: Each batch was mixed 30 sec. dry and 2 min. wet, in a small power-driven,open-tub mixer.

Molding: From each batch 3 watertight molds of known capacity were filled. Themortar was puddled with a light t~mper.

Measurements: The weight of the filled calibrated mold was measured to 1 g im-mediately after filling, and again after 20-24 hr. in the fog-room. On stripping, theweights of the specimen in air and in water were obtained.

Curing: In molds in the fog-room for the first 20-24 hr.; under water thereafter.Temperature: 70 F. Some of the molds were not stripped until the specimens were48 hr. old, but the specimens were nevertheless immersed after the first 24 hr.

Drying: The granular samples were dried in a vacuum desiccator over Mg(CW,)t..2H,0.

Cement-Silica Specimens: Cylinders cast in test tubes (~ x 6 in.)Cement: Lot 14675. See Tables A-2 and A-3 for characteristics.Silica: Lot 13239. 95 percent passing No. 200-mesh sieve.


Proportions:1

Proportions by Wt. Nominal w/c$:

Cement SHg Water c/sio9 wt.c w

gal/sk

1 0,736 0 0.264 100/o 0.362

4.060,590 0.148 0. 2s!! 80/20 0.444 5.000,483 0.260 0.257 65/35 0.530 5.97

: 0.411 0,336 0.253 55/45 0.6185

6.960,376 0.376 0.248 50/50 0.660 7.43

Mixing: Cement and silica were premixed by tumbling them together in a large glassbottle, The dry material was placed with water in a kitchen-type mixer, and mixed for2 minutes, allowed to rest for 3 minutes, and then mixed for 2 minutes.

Casting: The pastes were poured into ~ x 6 in. test tubes which had previouslybeen calibrated by filling them with water from a burette.

Curing: The level-full test tubes were stored under water until the third day aftercasting, at which time the glass molds were broken off and the specimens were reim-mersed in water where they remained until tested.

Drying.’ The granular samples were dried in a vacuum desiccator Over M,~(Ci04)2.-

2H,0.

Test Results: All test results are given in Part 5.

Description of specimens made in series !?54-8Mortar Specimens: Cubes, 2 in.Cements: See Tables A-1 to A-3.Pulverized Silica: About same fineness, volume basis, as cement.Proportion-s:

-----i

Relative Proportion—. w/0

Mix Cement Pulverized Std. ~~~dWZ3 bySilica weight

(approx.)— ——

A 1 0 1.641

0,330,330 2,30

E 10.46

0.707 3.07 0,611

Mixing: Each batch was mixed 30 sec. dry and 2 min. wet, in a small power-driven,open-tub mixer before making slump test. Slump-sample returned to tub and batchmixed additional 30 sec. before casting.

Slump Test: Made in duplicate on 6-in. cone. Water adjusted to give 1fi-2-in.slump.

Moilding: From each batch 3 cubes were cast in previously weighed, 3-gang, steelmolds.

Measurements: The weight of the filled molds was measured to 1 g immediatelyafter filling, and again 2-2% hr. later after carefully removing any accumulated waterwith a suitable absorbent. The molds were dried and weighed again just prior to strip-ping. After stripping, the cubes were weighed in air and in water.

Curing: In molds in the fog-room for the fist 20-24 hr.; then under water for 27days; thereafter in the fog-room.

Drying: The granular samples were dried in a vacuum desiccator over Mg(ClO&.-2H,0.

Composition of Specimens: The composition of the hardened cubes, derived from themeasurements mentioned above, are given in Table A-9.

TA

BL

EA

-8—

AD

SO

RP

TIO

ND

AT

AF

OR

SE

RIE

SQ

54K

4B

Wat

er-c

emen

tra

tios

corr

ecte

dfo

rbl

eedi

ng

PIP*

u .09

.20

.255 :E .69

.75a

.Sob

.34

.89

& SS

DO

1372

1-1s

w./e

=.4

70A

ge17

4d

.223

1.2

666

.282

0.3

123

.341

0.2

561

.374

6.3

899

.296

2.4

029

:E .543

2.5

572

1372

2–1P

Dol

e=.4

73A

ge18

0d

.233

2.2

769

.293

4.3

208

.347

8.3

595

.376

3.2

394

.399

9.4

079

.445

7.4

727

.559

0.5

755

1372

3-IQ

00/C

=.4

25A

ge18

0d

.229

0.2

709

.28x

33.3

143

.340

5.3

508

.367

3.3

799

.387

8.3

’943

.425

9.4

497

.502

2.5

149

Tot

alW

ater

Ret

aine

dat

Rel

ativ

eV

apor

Pre

ssur

eIn

dica

ted,

E/g

cem

ent

.178

6.2

128

.226

8.2

464

.264

6.2

772

.291

7.2

159

.318

0.3

259

.371

8.4

116

.5W

8.5

249

1373

14P

w./c

=.4

60A

ge12

8d

.177

2.2

072

.217

3.2

363

.251

6.2

647

.278

3.3

056

.312

1.3

215

.369

8.4

056

.512

2.5

249

B73

24Q

w./

c=

.450

Age

138d

.177

3..2

087

.221

1.2

396

.255

4.2

689

.277

7.2

999

.203

7.3

112

-352

8.3

916

.494

9.5

148

1373

3-5s

O./c

=.4

27A

geM

&i

.16

.W.1

994

.213

6.2

227

.250

2.2

608

.277

0.2

975

.299

9.3

091

.348

2.2

839

.497

6.5

102

137%

-5P

we/

c=

.453

Age

146d

.158

9.1

936

.207

1.2

253

.240

4.2

517

.266

7.2

889

.292

2.3

010

.344

6.3

842

.509

3.5

193

1373

5-5Q

W./

c=

.456

Age

150d

.165

0.1

983

.214

0.2

311

.249

1.2

610

.275

6.2

968

.299

6.2

088

.351

3.3

890

.513

9.5

268

1373

6-6S

we/

c=

.471

Age

196d

.214

8.2

568

.272

3.2

978

.326

6.3

397

.357

4.3

675

.376

1.3

824

.409

9.4

318

..508

5.5

295

1373

74P

n./c

=A

ze19

1d~

.229

7.2

729

.290

4.3

181

.348

7.3

634

.381

8.3

940

.402

0.4

095

.433

7.4

554

.518

9.5

462

1373

8-6Q

wQ

/c=

.447

Age

191d

.222

0.2

612

.276

4.3

011

.327

7.3

368

.353

5.3

667

.373

4.3

801

.414

5.4

478

.512

5.5

361

Con

clud

edon

next

page

)

P/P

*

w.

.09

.20

.355

.50C

.61

.69

.747

d.8

02e

.84

.89

.96

SS

DS

SD

O

i-”=

d-“

=e-

”=K

ey:

&

[374

G7P

./.=

.47:

4ge

164d

.239

.5

.20.

51.2

372

.365

3.3

812

.400

3.4

098

.421

5.4

284

.451

8.4

671

.556

4.5

751

1374

1-7Q

1375

2-11

1,./

c=

.480

U,o

/c

=.4

4!A

ge17

1dA

ge16

4d

.239

0.1

864

.281

0.2

988

.2=

86.3

256

.261

1.3

536

.278

2.3

660

.290

4.3

840

.307

4.3

960

.318

8.4

048

.331

6.4

110

.337

8

~%

!j;~

:

.563

9.5

323

6-:,

6-:

and

6-Q

.(,

.,

3753

-1IQ

1376

3-15

S,o

\C=

.440

10/C

=.4

8;hg

e17

2dA

ge20

2d

.189

6.2

267

.240

3.2

651

.282

6.2

944

.312

5.3

240

.334

6.3

401

.377

0.4

148

.508

7.5

158

Tot

alW

ater

Ret

aine

dat

Rel

ativ

eV

apor

Pre

ssur

eIn

dica

ted,

g/g

cem

ent

3764

-15P

1376

5-15

Q‘.

/c=

Wof

c=

.445

,kge

196d

Age

202d

.217

3.2

589

.273

5.3

017

.322

4.3

343

.366

5.3

794

.375

8.3

906

.420

2.4

391

.536

2.5

613

.210

9.2

494

.265

3.2

874

.313

3.3

238

.338

7.3

514

.358

8.3

634

.397

9.4

244

5(X

J8.5

167

—1

.220

1.2

591

.273

5.2

972

.305

0.3

234

.358

3.3

596

.360

4.3

749

.417

4.4

542

.529

0.5

445

I

02G

Rzi

76fo

rR

ef15

-S.

15-P

,an

d15

-Q;

PIP

,=

0.47

for

Ref

s.16

-S,

16-P

,an

d16

-Q.

5fo

r16

-S,

.3-P

,a~

$16

-Q.

n:5.

-..

,*,$

.,

3766

-16S

./c=

kge

322d

.209

6.2

501

.269

5.2

933

.309

4.3

323

.344

1.3

595

.369

33&

4.4

114

.437

6.5

459

.564

1

1376

7-16

P10

/C=

.464

Age

223d

.225

6.2

709

.286

9.3

163

.337

9.3

522

.374

9.3

869

.398

7.4

048

.433

1.4

500

.525

3.5

413

3766

-16Q

‘o/c

=.4

5(kg

e22

2d

.22.

50.2

689

.285

4.3

131

.322

4.3

427

.367

3.3

778

.392

7.3

925

.425

5.4

426

.502

1.5

196

u-

.-.

‘D=

Wat

erco

nten

tof

gra;

ular

sam

ple,

satu

rate

d,su

rfac

e-dr

yfo

rsa

mpl

eth

atha

dbe

endr

ied

and

reaa

tura

ted.

10=

Wat

erco

nten

tof

glan

ukw

sam

ple

that

was

brou

ght

toea

tura

ted

con&

tlon

with

out

prel

imin

ary

dryi

ng.

S=

Slow

cool

edaf

W’

rehe

atin

gcl

inke

r.P

=“P

lant

cool

ed.”

6!=

Qui

ck-c

oole

daf

ter

rehe

atin

gcl

inke

r.U

%=

Non

-eva

pora

ble

wat

er;

p/p.

=ab

out

24x

IOJ.

1377

8-20

SI.

/c=

.47

Age

170d

.230

8.2

736

.291

4.3

183

.344

3.3

597

.376

6.3

888

.397

4.4

035

.430

1.4

499

.542

6.5

5’44

3779

-20F

‘o/c

=.4

6kg

e16

7d

.232

9.2

730

.289

4.3

130

.338

3.3

531

.363

6.3

821

.390

8.3

977

.424

5.4

440

.542

4.5

548

3780

-20Q

.,/C

=.4

36kg

e17

6d

.226

2.2

664

.281

6.3

073

.332

6.3

447

.362

4.3

740

.381

1.3

870

.415

7.4

366

.508

0.5

194


TABLE A-?-UNIT ABSOLUTE VOLUME COMPOSITION OF THE MORTARS

CeNmoent

14930J

15007J

15008J

15011J

15012J

15013J

15D14J

::

8-18-28-3

8-288-298-30

3-328-33

8408411342

844845

8468478-48

8-508-51

USED IN SERIES 954-8

Unit Absolute Volume Compositionat End of the 2nd Hour

.2375; ;:W;

,2363,1698,1288

.1647

.1251

.2407,1730.1298

.1606

.1202

.2345

.1713

.1260

.1566

.1201

Water

.2431

.2466

.2492

.2649

.2567

.2500

,2477.2405

.2508

.2494

.2522

.2419

.2472

.2532

.2520

.2455

,2595.2511

Ak

. of5,032.029

.021

.025

.024

.055

.055

.022,018.015

.077

.068

.040

.025

.046

.079,074

Silica

.4343

.5521

.5953

.4776

.5491

.5978

.5322.5796

.4870

.5598

.6029

.5207

.5636

.4721

.5516

.5825

.5045

.5548

(Wclbt2 ours

,311; :;:

.344

.464

.596

.462

.560

.319,442.595

.461

.624

.332

.453

.599

.510,644

CementContentof P*te

.494

.407

.338

,471.398.340

,399.342

.490

.410

.340

.399

.329

.48 I

.405

.339

.376,324


Aduorpta’onData: See Table A-10,

TABLE A.1 O-ADSORPTION DATA FOR SERIES 954.8Wmter-cernent rntio correotad for blesding

—-

ilelatlve Vapor Preesura Indioated,la oemont

Total W&ter Rete,ined n

l~O~]J-

wo/c -,500

4m 463d—.

,2208,2004,2708,3022,3237.3480.3690382!4

,4084.4278.4461.5208.6763

1:51; J.

‘“:&-Age 478d

P/Pa

—— . — -,2000 ,2101 ,1080

,2016 ,2:)70,Zl .2766 , 2tr38,2S89 , ao48 , 276S,3042 ,3224 ,2018, a20b a444 ,3100,3346 a624 .3170, a4~5 ,3842 ,3240,aozd , 307s , 3a50,37a2 .4082 ,3401,4024 ,4674 , 34nlJ,42a4 ,4909 ,3702, 5a14 ,6802 ,4248,5431 .7060 .6228

-,2323,2700,29a9,318a,3307,3674. a752, ao72.4126.4208,48al,5206.0711.7178

7$;::,47,61.60,7.5,81.84.80,96SSD&SDO

,180s,2100; ;:::

, 20s1.2708.2888.2004, 30!37,ala2,3290,3470, aoa4,4132 —. —

Total Water Retained at Relative Lpor Pre#eure Indicated,

. —15101~J- 15012J-

8-44w./c’ - we/c -

.506 ,461kge 868d Age 464<—. —

l~O~~J-

w./c -.442

,ge 308d

1{O~~J-

uo/c -.624

Lge 464d

.2227,2657. 28a5.3080; ;:;:

.37613S92

.4145

.4320,4540,5205.6978

1WIO~J-

W.ic -.453

4ze 338d

l~W~J-

/woo=

.0094ge 33ac

,2527.20a2,3103. aa4a.3546,3793.3942.4148.42!31.4387,4820,5203.6886

1501$J- l{~~~J-

Wolc = w“/c =.510 ,644

Age 487d Age 487d

P/Pa

-.2185.2567,273729a4

,3076.3163.3333.3424,3468.3514.3673.3826.4245.4461

-,2407,2829.2901,3252.a446.3643.3746.3031.4002.4080.4375.4619.5587

—l———————,2102.2503,2667,2921.3140. 3a45, 346a,3581,3657.3828,4131,433a.5246.5306

,2218 ,2100.2640 ,2619.2817 .2694,3073 ,2022.3329 ,3137. 3S48 .3336.3745 .3504.3031 .3613.4003 a794.4232 .3006,4650 .4066,4975 .4608.6425 .5738.6756 —

run

,09.20.36,47,61.60.75,81

:%,96S8D&SDO

,2472,2885.3079.337a.3587.3834,4050.4190.4350,4436.4656.6116.6355_-, _

Key: SSD = Water content of granular sample, saturated, surfacedry for eample that had been driedand resaturated.

SSDO = Water content of granular sample that was brought to saturated condition without pre-liminary drying.

w. = Non-evapmable water: PIP, = about 24x1O-$,

Description of specimens made in series !254-9

Mortar Specimens: Cubesj 2-in.; Prism, 2x2x9% in.

Cements: See Tables A-1 to A-3.Pulverized Silica: Lot 15282. Specific surface, volume basis, about the same as that

of cement.Batches: The batches were made up as follows:

Weights, gins. per batch

Cement PulverizedNOliind

Std&~:$wa WaterSilica (approx.) Weight

Mix

ABc

1900 31001350

620 0.326z 3100 610

10000.452

730 3100 600 0.600


Mixiw: As in series 2568.~lump l’est: As in ,Series 254-8.Molding: From each batch 12 cubes and 1 prism were cast in previously weighed

steel mold8.Measurerrwnts: Cubes: as in Series 2548. Prism: the prism wae weighed in air

and in water at 28 days.

Cur@: As in Series 2548.Dr@ng: Ask Series 2548.

Test results for series 954-9

composition of Hardened Specimens: The composition of the mortars in the hard-ened cubes, derived as in Series 25LL8,is given in Table A-11.

TABLE A-1 I—UNIT ABSOLUTE VOLUME COMPOSITION OF THE

Ce$ent

14930J

15007J

15011J

15013J

15365

::

9-19-29-3

9-49-59-6

9-7!l-&l9-9

9-1o9-119-12

9-139-149-159-15A

MORTARS USED IN SERIES 954-9

I Unit AbsoluteVolumeCorn mition at$the End of the 2nd our

MixCement

A ,2401B ,1718c ,1268

; ;:4):

c .1292

A .2415,1727

~ ,1288

A .2407Er . 17@dc ,12641

A .2366B .1711c .1295

Neat .5316

Watar

,2437,2397.2360

,2474.2422.2434

.2493

.2445,2394

.2.53!3,2457. 2JO0

. 24(7!

.2453

. 23S0, 42go

Air

,0308.0284.0292

,0312,0289.0211

. 13~45

.0240,0251

.0248,0341.0337

043fl!0313.0224,0487

—

Adsorption Data: See Tables A-12 to A-27.

Chemical Ana@8e8 of Dried (%anukwSample8: See Table A-28,

8ili0a

,4863.6610,6072

.4821

.5568

.6062

.4852

.5593

.6073

,4813.5564.5912

.4752&53ti

.J:~.!

.—

w/0 at2 hm.

(wt. bask)

,309.424,573

.316,433.570

.316

.432

.582

,324.443.611

.319

. 42s587

.244

C’ompremivei%wngfh: cubes were t,eated in compression, two at each age. SeSTables 8-2 to 8-8, Part 6 for results. Samples for adsorption measurements were pre-pared from the broken cubes.

Modulus of Ekwticity: The modulus of elasticity was determined from sonic measure-ment on the prism. See Table A-29 for results.


TABLE A.1 9-ADSORPTION DATA FOR REF. 954=9.1, CEMENT 14930Jw/c (by wt, ): Ori innl 0,316; after bleeding 0.306

fw. - non-avaporabe water: P/PI - about 24x10~WI= total water(w, = evaporablewater can be obtainedfromthe relationnhirrw = w - w.)

P/Pa

Total Water, w, Retainedat Rcand Age Indiorakid, g

2S days S6 daya

ive Vcmor Prce9urecement

90 crawl14 days7 days 180 daye 366 Cf8$Vl

,1704—

,FM.2232

‘&8,089,090,20.356,36,47.S1,61,69,76,30,81.84,89,96S8DSSDO

,0804,09S7—

, iiii8,1097

,0994,1183—

. iz3,1407—

,G3. 1S33.1661,1763,1879

, iiib,2201.2421,3324.3520

,1071 ,1292

, ~8

, ~b

, =3,2024

.ZQ

.2240,2323,2347

, ml, 2(397.2974,3473.3806

,1407

, iii2

, iiii3

, %5.2271

, ~8.2477.2568,2608

,%6,2851.3105,3522.3667

,1620

, Zii

, iiio

,1327

, iii—

,1667,1680

, ~8,189$.4, 2W7,1905

,2336,2482

,=8.2678,2764,2811

, ?iiib.3064.3184. 3S76,3703

,2422,2647

,1185,1247,1341,1477,1547

—, 26S4,2743,2800

xii,2963.3012.3282,3627—

‘d

.1590,1863,2162,3258.3457

,2136,2408,2623,3403,3516

I .—Key: SSD = Water content of granular eample in eaturated, mirfaoedry oondition for ean

bcm dried and reaaturated.SSDO = Water. oontent o! granular sample that wae brought to saturated condition without

prehmmary drying.

TABLE A-1 3-ADSORPTION DATA FOR REF. 254-9-9, CEMENT 14930Jw/c (by wt.):, Original 0,441; after bleeding 0.424w. - non-avaporable woter; P/Pt II= about 24x10~WI - total water(w, = evaporwble water can be obtained from the relationship W, = wt - w“)

Total Water, wt, Retained at Reand Age Indicated, u

ive Vapor Premure

180 daysP 1P*

14 daye

.1029,1227—

.%5

.1487—

,Zl.1551,1722,17971W8

. ~G

.2426.2663.4426.4626

~28 days

.1165

-66 ‘d8Y8 00Cfay,l7 days

.0798,0957

365 dayo

, 19s3—~

,090.20.355.36.47,51.61,69.75.80.81.84.89.96SSDSSDO

.1362

, G7

. Z9

, %9,2194

. ~8,2516,21366,2071

. G5,3238.3684.4738,4864

,1735 ,1853

,~8

.&3

—.1444

, =2

. Ro

.1819

.2093

,iiz4

. G5

.2643

—— .2396

.2569

. ml

.2987

m.3286.3358

.1020,1075— ,2693

.2873—.1160.1214,133.5.1440.1517

.%3

.1879

.2189,3981.3995

—.1892.2076.2142,2051

. E9

.2784,3103.4709,4936

.2751

.2939,3065,3133

. iiio,3496,3797.4X70.5017

.8076

.3184,3205,3347

,3.937.3614.3735.4114,5109

.3520

.3720

.3894,4852.5024

Key: A’SD = Water content of gmnu r mmple in saturated, subeen dried and resatl &ted.

SSDO = Water content ,of grant w sample that wrw brought to saturated condition without pre.hminary drying.

m-dry co] ition for sample that had

3$?0 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

TABLE A-1 4-ADSORPTION DATA FOR REF. 954.9-3, CEMENT 14930JW/C(by wt.): Original 0,600; after bleeding 0.573w. = non-evaporable water; p/pt .= about 24x10-~WI = total wet.er

(w, - evaporable water can be obtained from the relationship w, = WI – w.)-—

Total Water, WI, RetBined at Relative Vapor Pressureand Age Indicated, g/g cementPIP*

——w.,089,20.36,47.61.09.75,80.81,34.89.06SSD&SDO

7 days

,0822.1022,1054,1125.1192.1271; ;~;:

.1653

14 days

,0896,1118.1130.1289.1337.1464.1626; ;;~;

28 days

,1214.1521.1835.1814, 1B48.2086,2173,2371.2354

56 days

,1638.1979,2130.2343,2484,2634.2882.3043.3182

90 days

,1850.2238.2409.2637.2814.3068.3207.3372,3470

180 days 365 &ye~,2008;$;:;

.2341

.3032,3251.3398.3573,3700

.2142

.2625,2342.3125.3327.3508.3700,3838—.4012.4176.4450.5062.6971

,1673.1955.2207,4822.47X3

.2026,2318.2307;fg4f

.2713

.3099,3642.6944,6021

.3380

.3761

.4385

.6314

.6579

.3647

.4114

.4485

.6393

.6562

,3835.4261,4515,5640.6028

Key : SSD ~ Water content of granular SamPIe in *aturated, ,mrfaoe-dry m. ition for sample that hadbeen dried and reaaturated.

SSDO = Water content of granular samde that was brouzht to saturated condition without rme-liminary drying:

TABLE A-1 5-ADSORPTION DATA FOR REF. 954.9-4, CEMENT 15007Jw/c (by wt.): Original 0,338: after bleeding 0.316W. =. non-wmporable water; P/p, = about 24x10-dwt = total water

(w, ==evaporable water can be obtained from the relationship w, = W( - w.)

Total Water, WI, Retained at Relative Vapor Preaeureand Age Indicated, e/g cementPIP.

.—7 daye

.1259

.1603

14 days 28 daye 56 days 90 daye 180 days

,1404,1687

.=6,1962,2111.2243.2378.2440

.1538

.1824.1681.2147

,1729,2105

,1835w.,089,09,20,36,47,61,69.75,80,81.84.89.96SSDSSDO

.2170,2311.2513.2672,2814.2907.2962

“—.1950.2126.2270.2449.2587,2657.2715

X372353

.2496,2651.2752.2810.2856

.=4

.2419

.2574

.2752

.2821

.2891

.2941

.1612

.1759,1848,1949,2082,2185.2215

.=6

.3092,3235.3378.3773.3921

——

.mo

.3146

.3276,3712—

— ..2319.2520.2856.3541.3716

.2584

.2810

.2921

.3643

.2781

.2979

.3131

.3664,3747

.3004,3077.3269.3794.3853—

Key: SS0 = Water content of granular sample in saturated, aurfaw-dry condition for sample that hadbeen dried and raaturatad.

SSDO = Water content of granular sample that waa Lrrougbt to saturated condition without pre-liminary drying.


TABLE A-1 6-ADSORPTION DATA FOR REF. !?54.9-5, CEMENT 15007Jw/c (by wt.): Original 0.467; after bleedhg 0.433w. = non-e vaporable water; p/p. = about 24x10-@WI = total water

(w, = evaporable water can be obtained from the relationship w, = rw – w.)

PIP*

w..089.09.20.36.47.61.69.75,80.81.84.89.96SSDSSDO

7 dnys

.1334

.1585—

.1698

.1843

.1972.2085.2232.2312,2364

.2517

.2774

.3157

.4667

.5000

Total Water, w(, Retained at Relative Vap~r Preccurennd Age Indicated, g/g cement

14 days 28 days 56 days

.1498 ,1714 .1847

.1801 .2026 .2336— — —

.1942 .2169 .2399

.2128 .2357 .2593

.2243 .2522 .2751

.2415 .2763 ,2975

.2570 ,2906 .3128

.2657 ,3020 .3249— .3132 .3302

.%7 ml .3527

.3158 ,3432 .3713

.3254 .3695 .3899

.4764 .4913 .5002

.4971 .5106 ,5156

—.2500.2714.2917.3158,3284.3394.3460

.3607

.3802

.3980

.5092—

180 days

.2018

~6.2555.2778,2979.3152.3315.3411

.&o

.3614

.3994

.4111,5502.5605

Key: SSD = Wnte~content of grenular sample in saturated, eurface-dry condition for sample that hadbeen dried and resaturated.

&SDO = Water content of grmular sample that wca brought to saturated condkion without pre-liminary drying.

TABLE A-1 7—ADSORPTION DATA FOR REF. S!54-9-6, CEMENT 15007J

PIP.

w..089.09.20.36.47.61.69.75.80.81.84.89,96

SSDSSDO

w/c (by wt.): Original 0.6 10; after bleeding 0.570w. = non-eve. porable water; p/p, = about 24x1o.6wt = total water

(w, = evaporable water can be obtained from the relationship ~. = WI - @

Total Water, rut, Retained at Relative Vapor Pressureand Age Indicated, g/x cement

7 days 14 days

,1560 .1634.1824 ,1921— l——,1918 .2066,2078 .2210.2209 ,2342.2423 .2523.2545 .2694.2705 .2864.2816 .2870— —.2998 ,3140.3240 .3409.3597 .3774,5084 .5300.5630 .5846

28 days

,1839.2191

.2341

.2536

.2668

.2943,3136.3297,3347

56 days

,2035—.2398.2561.2781.2975.3240.3405,3524,3585

%6.4132.4456,5900.6347

90 days

.%4,3921.4244.5845.6219

Key: SSD = Water content of granular sample in satur~ ?d, surface-dry condition for sample that hadbeen dried and resaturated.

SSDO = Water content of granular w,mple that wac brought to saturated condition without pre-liminary drying.

.2049

.=8

.2603,2811.3038.3266.3407.3578

%6.3818.4155.4413.6019.6186

180 days

.2132-—

.X8

.3006

.3218,3460,3589,3810

:=8.4151.4430.4780.6676

3$2!2 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

TABLE A-1 8–ADSORPTION DATA FOR REF. !?54-9-7, CEMENT 1501 lJw/c (by wt.): Original 0.353; after bleeding 0.316W. = non-evaporable water, P/PC = about 24x10-8WI = total water

(w, = evaporable water can be obtained from the relationship w. = w, - w“)

Total Water, VA,Ifatained at RelPIP* and Age Indicated, R,

ve Vapor Pressure

~56 days 180 days

,1705.2039

365 daye7 dlm 14 days 28 days-

.1137

.1415.1760.1333

.1534—

.1430

.1785

.G3

.2069

.2193

.2312; ;;;:

.2543

.1557

.1892.G1,2276; ;;;:

.2685

.2764

.2861

—.2035.2211.2295.2401,2535.2627.2684

.2098

.2268

.2410

.2531,2622.2704.2746

.G

.3015

.3138

.3617

.3685

.2191; ;:::

.2632

.2716

.2817

.2873

.1434

.1617

.1703

.1808

.1935

.1942

.2112

.1636,1838.1960.2038.2197.2289.2319

.2931

.3002; ;:::

.3721

—.2767,2905.3140.3591.3713

,2951.3125.3216.3646.3794

.2209

.2480

.2697

.3487

.3587

.2535

.2787

.3059

.3575

.3710

.2738,2955.3130.3619.3696

ace-dry corKey: SSD = WaterOoqtmtof granular sample in eaturated, S1been dried and reaaturated.

SSDO M Wr@~ content of granular sample that was brought to saturat-ed condition without pra-hmmary drying.

ition for sample that had

TABLE A-1 9--ADSORPTION DATA FOR REF. 254-9-8, CEMENT 1501 IJw/c (by wt.): Original 0.459; after bleeding 0.432W. = non-evaporable water; P/PS = about 24xlo-$wt = total water

(w, = evaporable water can be obtained from the rtilationahip $& = wt - wn)

Total Water, WI, Retained at Relative Vapor Pressureand Age Indmated, slg cement

28 daye I 56 days

PIP*

90days

.1913

.2278

180 d8Y67 days

.1228

.1514

14 daya

%&9.20.36.47.61.69.75

R.34.89.96SSDSSDO

,1936.1527.1824

.1654

.2054

.~6

.2300

.2444

.2562

.2764

.2890

.2993

,~8.3251.3778,4843.5045

.1781

.2154G9

.2521

.2751

.2956

.3126

.3250,3364

.izzo,2064.2205,2357.2470.2634.2718

.%5

.3249,3579.4932.5155

.~8

.1762

.1828

.2005,2140.2254

.2444

.2647

.2798

.3023

.3165

.3289

.3380.z?.3587.3827,4108.4975.5119

—.3313.3618.3864.4922.5075

.3591

.3816

.4055

.4952

.5165

.2517,2829.3310.4661—

Key: SSD = Water content of granular mmple in saturated, surface-dry condition for sample that hadbeen dried and resaturatad.

SSDO = Wats: content pf granular sample thut wae brougbt to saturated condition without pra-Imunary dryme.


TABLE A-so-ADSORPTION DATA FOR REF. 9-9, CEMENT 15011 I

P /Pa

~,20.36.47.61.69.7.5,80.81.84.89.96SSDJS8D0

w/c (by wt.): Original 0.610; after bleedhg 0,582 “WII = non-evaporable water; p/p, = abO~t Z4XIOJW = tOtal W8tW

(w, = evaporable watar can be obtained from the relationship w, = WI - w.)

Total Water, w,, Retained at Relative Vapor Preeeureand Age Indimted, g/g cement

.1314

.1573

.2574

.2946,3453.5576

.1567

.1871

.2999

.3381

.3931,5258.5657

28 daye 56 &ye 90 daye

.1756 .1953 .2046

.2176 .2332 .2427

, G4 ,Z4 .G9.3527 .4134 .4291.4233 ,4469 .4588.5793 .6471.6146

.6212.6726 .6306

180 days

.2136

,2523.2693.2914.3139.3364.3526.3664

. fi6,3990.4344.4670.5800.6156

I 1Key: SSD - Water content of granular sample in saturated, surfawdry wndition for sample that had

been dried and reaaturated.&SDO = Water content pf granular sample that w= brought to saturated condition without pre-

liminary drying,

TABLE A-91—ADSORPTION DATA FOR REF. 9-10, CEMENT 1501 3Jw/c (by wt.): Original 0.326; after bleeding 0.324W* = non-evaporable water; p/p, = about 24x10~wt = total water

(w, = evaporable water can be obtained from the relationship w, = wt - w.)

P/Pa

——w..089.09,20.36.47.61.69.75.80.81.84.89.96SSDSSDO

Key: SSD

7 days

.1488

.1748

.1859

.2001

.2110,2287.2330.2500.2541

.%3

.2729

.3019,3745.3745

Total Water, WI, Retained at Relative Vaand he Indicated, g/u oemen

14 days I 28-daY,

,1639 .1711,1909 .2028

,&2 ,G1.2186 .2324.2304 .2472,2465 ,2634.2604 .2761,2705.2680 : :%;

. G3 .Fm

.2997 .3114

.3110 .3228,3831 .3781.3831 ,3914

56 &yS

,1602.2147

.2277

.2452

.2602,2790.2899,2952.2979

.G4,3218.3335.3852.3995

brPreenure

90 daya I 130 day,

.1913 .1877

. iiiio .59

.2409 .2426

.2586 ,2615

.2760 .2763

.2912 ,2907,3015 .2917.3100 .3058

.%5 .G3

.3212 .3151

.3342 .3307

.3417 .3418

.3873 ,3734

.4018 —

. Watercontentofgranularsamplein saturated,eurfwxr-dry condition for sample that badbeen dried and resaturated.

SSDO = Watir content of granular sample that wae brought to eaturated oondition without pm-liminary drying.

3s!4 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

TABLE A-!?2-ADSORPTION DATA FOR REF. 9-11, CEMENT 15013Jw/c (by wt.): Original 0.459; after bleeding 0.443w. = non-evaporable water; P/p, = about 24x10~rut = total water

(w, = evauorable water can be obtained from tbe relationship w, = w, - w.)

PIP*Total Water, w, Retained at Relative Vapor Pressure

and Age Indicated, g/g cement

180 days7 cffum 14 days 28 days 56 days 90 days

~,20,36,47.61.69.75.80.81.34.89.96SSDSSDO

——.1556.1830

.1828

.2143.1770.2131

.2085 ,2152 .2356

.Zio

.2604

.2343

.3017

.3212

.3363,3518

.2530

.2695; ;:;:

.3306,3426.3555

.;9,3763,4034,4265.5643

.2761

.2933

.3179

.3372

.3372; ;;:;

.%2

.2079

.2190

.2369

.2447,2578.2614

.2269

.2434

.2572

.2814

.2911,3026.3051

,2272,2455.2626,2822.2985.3129

.%7

.3690

.3927,4115,5298

.2788,2991.3247.4435.4793

.3228

.3481

.3698

.4831

.5137

.3316,3690.3933.5248.5419 — .—

Key: SSD - Water content of granular sample in saturated, surface-dry condition for sample that hadbeen dried and resaturated.

SSDO = Water content of granular sample that wae brought to saturated condition without pre-liminary drying.

9-1 !?, CEMENT 1501 3JTABLE A-93—ADSORPTION DATA FOR REF.w/c (by wt.): Original 0.635; after bleeding 0.611w. = non-evaporcible water; P/p, = about 24x1 O-6W! = total water

(w. = evaporable water can be obtained from the relationship w. = W, - w,)

Total. Water, w,, Retained at Relative Vapor Pressureand Acre Indicated. gjg cement.PIP*

14 days 28 days 56 days—

90 days——

,2357

180 days

.2447

7 days

.1583

.1841.1828.2129

.2028

.2368220sw.

,089f)g

,20,36,47,61. (jg,75,80,81.84,89.96SSDSSDO

—.2582.2737.2971,3151.3396.3578.3731

.2778

.2937

.3173

.3372

.3579

.3747

.3946

.2856

.3029

.3272,3400; :::;

39W

.1941,2063.2176.234.5,2432.2584

.2238,2395.2532.2747.2848.3003,3034

, G9,3,507.3763,5497,6200

.2502,2663.2850.3075,3232.3395—.—

.3576,3095,4244,5798.6438

—.3796,3974.4296.4563,6136

,4029.4191,4557.4930.7162

,4166.4221.4468.5102.6707

. G2,3018,3244.5148,5743 —

Key: SSD = Water con< i of eranular samvle in saturated, surface-dr.v condition for mmple that hadbeen dri,

SSDO = Water conIiminary

~nd ;esaturated. -t ,of gnmular sample that was brought to saturated condition without pr~ymg.


TABLE A-94-ADSORPTION DATA FOR REF. 9-13, CEMENT 15365w/c (by wt.): Original 0.326; after bleeding 0.319w. = non-e vaporable water; P/P, = about 24x1 O-8w = total water

(w. = evnpomble water can be obtained from the relationehfp W, = wt - w.)

Total Watt wt, Rete, inednd Age Indict

t Relative VaI ‘rPressureid, g/g oemen

56 days7 days 90 da yn14 days 28 days 180 days

%.20.36.47.61,69.75,81,84Ml

.96SSDSSDO

,1326.1596.1681.1809.1925.2052.2134,2244.2319.2391.2682.2906.3570

,1.515. 1s03,1903.2043.2181.2313.2434,2541.2625,2688.2907.3123.3669.3842

.1488,1803.1933.2106,2242.2414,2489,2571.2649.2783,2935,3036.3639

,1789.2133.2269,2460.2591,2734.2824,2926.2973,3026.31s4,3341.3702

.1815

.2168,2311.2495,2608.2740. 2S70,2922.2992.3078.3173,3344.3791—

: Water content of granular sample in saturated, eurface-dry condition for sample that hadbeen dried and resaturated.

SSDO = Water content ,of granular sample that was brought to satumted condition without pre.liminary drying,

Key : SSL

TABLE A-95—ADSORPTION DATA FOR REF. 954.9-14, CEMENT 15365w/c (by wt.): Original 0.459; after bleeding 0.439w. = non-e vnporable water; v/p, - about 24x1OJwt = totalwater

(w, = evaporable we.ter can be obtained from the relationship w, = w - ro.)

Total Water, wt, Retained at Relative Vapor Pressureand Age Indicated, g/g cementP/Pa

.—180 days7 days 14 days 28 d8yS

,1841.2230.2377.2599,2757,2961.3102.32.56,3322.3476,3761.3966,5034

56 days

.2105

.2502,2655.2889.3062,3257.3366.3518.3621.3681.3968,4188,5133.

90 days

,1394.1665.1758.1893.2009,2138,,2237.2343,2419.2512,2828.3098,4182

,1711,2031.2142.2315,2470.2619,2767,2894.3008.3104,3399.3646.4724.4877

w..09,20,36.47.61.69.75.81.84.89.96SSDSSDO

.2224

.2651

.2819,3088,3250.3460.3626.3699.3830,3925.4094.4429.5344—

Key: SSD = Water content of granular sample in saturated, surface-dry condition for sample that badbeen dried and resaturated,

SSDO = Water content ,of granular sample that wae brought to eaturated condition without pre-liminary drying.


TABLE A-96-ADSORPTION DATA FOR REF. 9S499.15, CEMENT 15965w/o(byw%):Oriuinei0.610;sft.a bleeding0,537WII- non.evoorsblowetar;ZI/pJ- about24x1OJ

kWI= total W* r(w, - ovaporabiewatereonbeobtainedfromthe relationebisrw, = WI- w,)

WI,?MalnedAtReietiveVaporPreeeureld Am Indioatad,u/# wment-

!28&Yl

.—.—60 &ye

,aala,86s8,2820,soaa,a240,a434.a641,a767,ases,~8,4800,6400—

90 &ye,2296,2741,2918,a170. aab7, sell, araa,akuo.4074.4177,4461,S104,6614—

7dew 180deye

,2546,2967,alae,2406,a60e,aaal,4056,4176,4247.4456A6al,5218,08a7—

,15S0.1820,1922.206a,2162.2298;:::!

,2678,2716,8060,a489,6167,6707

,2102,!?406,2646,2872,S080.8262,aa82,8541,af3a7.a77a,4197.4687,6272

Wm,Oe

:8Al

,69,76,81

jlD

SSDO

= WOtaroontentof granularmmpleineeturated,mrfaoe-dry oondition for samplethat hedbeendried and reestureted.

&5’DO= Wateroontent of granulwsampletimt weeLrrouht to wtwd.xi oonditionwithoutpr~iimhrwy drying.

Key: Sal

TABLE A-97-ADSORPTION DATA FOR REF. 254-94 5A, CEMENT 15365w/o(by wt.): Oridnai0.246:after bieerfh 0.244w, - non-evBporabio water; P/P. - about !34X1WWI - totai water

(w, - evaporabie wrhr oan be obtained fromthe rektionshipW, - WI- w,)

Totai Water, WI,Retainedat Raiativeand AgeIndioated,if/g oen

hporPreraurelt

Pfv8

14 &ye

,1259

270 dem7 deyn 28 deya

, labs

66 daye

,la96

90 deye

.1462

,K1

180 &ye

,1654

.Re

.FMJ—

,mo,2177

,mJ, 235s

,G9,2469.2489—

,Em.2724,28?4—

-B

.1722

.1918

A

,1691.1910

,x)m

,%3.2111.2159

. Z5—

.=7

. EGJ

. G2

.2634

. G5

.2908—

,1152%1.161.20, 2a8,322.36.47.63.61,69,70;:!

.84

.85

.88

.89

.96S8D88D0

— —,1380

.=6—

.=2,1658

,1501 ,1611 ,1684.1999

,%3.2116.2152

— —,1591—

:%

,1709—

.=0,1933

,1785—

.=1

.2002. G7.2061

.2277.

,E2

— —.176a.1846

,%8.2021.2116

,1918,1993

. Z3

.2146

.2254

.20a4,2116

,%7,2259.2306

.2123!2211

.Zm

.2324

,2182.2240

. me

.2389(2412

,2504—.2583.2619

— —

,K?,2508,3054,3128

— —.2414.2590.2948.3076

,2487.2613.3028

.2426

.2694

.2960

,2509.2698.2969

.2771

.3024— —

Key: SSD - W8tarcontent.of mantir sampiein saturated, surface-dry condition for SamPie thathad been dried and reeaturatid.

ISSDO - Wrpe;contentof mmrdw sample that was brnrwht to saturatad mmdit ion without pr~imunary drying.

A and B refer to aepirafi r~mde.

TA

BL

EA

-98—

AN

AL

YS

ES

OF

GR

AN

UL

AR

SA

MP

LE

SU

SE

DF

OR

AD

SOR

PTIO

NA

ND

NO

N-E

VA

PO

RA

BL

EW

AT

ER

ME

ASU

RE

ME

NT

SIN

SE

RIE

S25

4-9

Com

pmiti

onof

Dry

Sam

plea

at&

eIn

dica

td,

m/c

p8rc

ent

dry

wei

ght

2aZ

r.7

days

14da

ys28

day8

56da

ys90

days

180

dam

(wt.

——

——

——

——

——

——

365

dam

basi

s)C

mt..

ISi

O*

\H

aOC

rnt.

ISi

Ox

IH

aO~S

+fZ

Ocm

t.I

.Sif

AI

Ha

——

Ct.

l=”

Cm

.lSi

Ozl

HzO

~Cm

Ll

SiO

zlH

43

0.30

984

.70.

424

66.1

0.57

346

.5

,—,-

Gm

ent

1492

0J

0.31

676

.314

.10.

433

9.6

74.3

15.3

10.4

74.2

14.4

60.5

31.5

8.1

58.2

33.1

0.57

08.

757

.432

.848

.144

.4,7

.548

.144

.07.

948

.442

.8—

—

——

—.

0.31

679

.012

.19.

071

.718

.90.

432

9.6

75.5

13.7

51.0

42.8

6.3

58.9

32.1

0.58

29.

058

.531

.847

.546

.26.

247

.345

.37.

445

.946

.0

——

—.

0.32

480

.37.

712

.08Q

.2::4

4;62

.727

.59.

859

.446

.146

.67.

347

.7

—,

_,—

,—

6.7

13.1

79.1

7.3

29.8

10.8

25.1

70.5

43.6

8.7

45.4

45.4

cem

ent

1500

iJ

11.4

77.5

9.5

9.8

66.8

27.9

8.9

47.9

42-4

tkm

ent

1501

1J

13.0

11.2 9.7

—t—

—.—

——

70.1

54.4

46.4

43.6

77.6

z119.

013

.475

.810

.313

.960

.627

.711

.747

.942

.59.

747

.542

.310

.232

.660

.57.

0

-d&

&LJ=

aiila

ma!

!rr

10.8

72.8

15.7

11.3

73.7

14.2

12.1

78.6

9.7

58.1

31.5

10.4

61.0

27.3

11.7

57.9

30.6

Cem

ent

1501

3J

13.5

79.1

6.7

4.4

58.1

29.7

9.2

45.0

45.1

Cem

ent

1536

5

——

—.

14.2

78.0

7.1

14.9

12.1

51.0

37.0

11.0

9.9

35.2

56.5

8.3

——

——

62.5

53.4

40.4

0.31

982

.27.

010

.978

.30.

439

9.8

11.9

50.1

42.4

62.2

29.2

‘1?

E?

7?m

>I

-1

7.5

76.8

8.7

60.6

29.0

10.4

51.9

38.6

0.58

745

.447

.69.

660

.027

.412

.658

.628

.612

.856

.131

.312

”57.

048

.542

.59.

044

.845

.89.

446

.643

.010

.346

.542

.910

.747

.740

.2E

z.1

Cem

ent

cont

ent

esti

mat

edfr

omC

aOde

term

inat

iorl

.W

ater

cont

ent

esti

mat

edfr

omig

nitio

nlo

ssco

rrec

ted

for

igni

tion

Ima

ofce

men

t.S

ific

aco

nten

tfo

und

bydi

ffer

ence


TABLE A+29—YCWNG’S MODULUS OF MORTARS USED IN SERIES 954-9

I Young’s Moduluc at Age Indicated*Ce$oent millions of lb/inl

14930J

15007J

15011J

15013J

16365

uyr;t

(wt. be,~is) 7 days

,309 4.47,424 3.67.573 2..57

.316

1

6.18.433 4.65,570 4,23

#316 6.10,432 4.65,582 4.13

.324 5.05,443 4,37,611 3!78

.319 5.30,439 4.64.587 4.40

I

‘Values me for a single pricm,(a) Prmm broken.

14 days

4,98;.;:

5,354,854.50

5,454,854,48

5.174,683497

5.425.274,81

28 days

6,454,854,13

5,686,084,92

5.625.204.83

64304.854,36

5.585.034,96

-56 daye

6,506.144.71

5.545,145.03

5.765;304,89

5.404(FJ5

5,785.185.03

90 days

5.755.364.87

5.485.355,08

5.885,425.00

5(:)7

4.50

5.785.405.03

180 d~ys

:.::5:20

5.735{a~2

6.005,485.00

5,65(a)

4.65

——

TABLE A-30–UNIT ABSOLUTE VOLUhJ4E COMPOSITION OF THEMORTARS USED IN SERIES 954-11

Ce~ent I Ref.No.

15758

15756

15763

15761

15754

162131621416198156691549515497

11-111-2

11-311-4

11-511-6

11-711-8

11-911-10

11-1111-1211-1311-1411-1511-16

(Seepage 317)

AB

AB

t

:

AB

BBBBBB

Unit Absolute Volume Compositionat 2 hours -

Cement

2S95.1721

; ;::;

,2434.1741

Note 1—

,2409.1727

.1775,1766.1745.1725.1764.1731

Silica

,4660,5398

,4828.5604

,4827.5562

——

.4746

.5484

.5592

.5580

.5621

.5579

.5488

.5453

Air

.0437,0382

,0233,0087

,0237,0245

——

.0315

.0271

,0135.0131.0121.0157.0302.0266

Note 1: The epecimens with Cement, 15761, expanded in the molds and hence iae.t~facto~y data for cal$ulatmg the oomposlt] on.

See p. 333 for description of speolmene.

Water

,2526.2506

,2551.2525

,2508.2458

——

.2540

.2526

.2497,2522.2512.2538.2445.2549

me impcmsi

w/c&t2 houre,

wt. basis)

.334,460

,318.446

.324,437

.334

.468

.328

.449

.443,448.443,451.442.464

: to obtain


TABLE A-31—ANALYSES OF GRANULAR SAMPLES USED FOR ADSORPTIONAND NON-EVAPORABLE WATER MEASUREMENTS IN SERIES954-11

15758

15756

15763

15761

15754

1621316214161981566915495 (1:15497 (1:

y;r:t

wt. ba&e

.334

.460

.318,446

,324,437

.334

.468

,328,449

,443,448.443,451,442.464

Cemenfi, Silica-, and NonContent of 35-1OO-M

at. Age Indmated, g

Cement

.783

.598

.788,616

.834

.647

.802

.630

.767

.591

.5834

.5864

.6160,6287.5422.5560

28 days

Silica

.084,264

.115

.302

,089,288

.068

.253

.102

.293

.3082

.3130

.3165,2976.3873,3424

No~-JJ;P.

,134.117

.097

.082

.077

.065

.130

.117

,131.116

, 10s4.1006.0675.0736.0705.1016

:vaporable Water-,h Sampl~dry weight

—

Cement

.773

.607

.776

.617

.788

.169

.798

.611

.760

.588

90 days

Silica

.079

.258

,108,279

,107.289

.059

.260

,091,277

Wm-:eap.

——

,148.135

.116

.104

.105

.092

.144,130

,148,135

TABLE A-3!2-FLEXURAL STRENGTH AND YOUNG’S MODULUS OF ELASTICITY

OF MORTARS MADE WITH SPECIAL CEMENTS FOR THE BASIC-RESEARCH

PROGRAM—SERIES 254-11

CeNmoent

15758

15756

15763

15761

15754

u,/c at2 hrs.

(Wt.bada)

.334,460

,318.446

.324

.437

,334.468

.328,449

28 days

13951090

1170915

1035765

11451015

12751035

ngthat Age%ted~2

130days

1275970

12951010

13451115

980790

1;;:

—Young’s Modulue at Age

Indicatedmillions of lb /inl

28 days

6.05,5

5,85.1

5,44,7

5,65,2

6.05,4

90 days

6.15,4

6.45.6

6,05,5

5.75,3

6,55,7

Flezural stwwlh ie the average of res s for two prisms.Young’s modulus was calculated from ~e resonance frequency of vibration found by the electrodynamiomethod. The values for 28 days are t average of results for 12 prisms; those at 90 days, the av,q~ge for 2

~~%?333 for description of specimens.

33o JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November 1946

332 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE November.1946

TABLE A-34-UNIT ABSOLUTE VOLUME COMPOSITION OF THE

MORTARS USED IN SERIES !254.13

Cl$oker

.15367*

15367**

15623

15699

15498

*First round*+Second ~oul

p:

13-113-213-3134

13-IB13-2B13-3B134B

13-513-613-713-8

13-913-1013-1113-12

13-1313-1413-1513-16

Unit Absolute Volume Com~ositionat 2 hours “

Cement

.2853

.2870

.2909

.2879

.2828

.2628,2822.2849

.2931,2919,2920.2898

.2827

.2824

.2816,2796

,2888.2909.2905.2909

mea8urement8.of measurements.

Silica

.2444

.2458

.2492

.2466

.2422

.2422

.2417

.2441

.2529

.2519

.2520

.2501

.2436

.2433

.2427

.2410

.2444

.2462

.2458

.2462

Air

,0201.0147.0045.0133

.0362,0297.0358.0240

.0053

.0058

.0063

.0073

.0204,0219.0232.0297

. 020+3

.0154

.0114

.0124

Water

.4506

.4528

.4553

.4523

.4400

.4458

.4414

.4476

.4489

.4504

.4497

.4528

.4537

.4530

.4529,4503

,4472.4480.4524.4509

1Io cat2 ours

(wt. basis)

.494

.493,489.491

,486.488.488,492

.470

.474

.473

.480

.498

.499

.499

.498

.488

.487

.493,491

TABLE A-35—ANALYSES OF THE GRANULAR SAMPLES USED FOR ADSORP.

TION AND NON-EVAPORABLE WATER MEASUREMENTS IN SERIES 254.13

Clinoker

15367*

15367**

15623

15699

15498

13-113-213–313-4

13-lB13-2B13-3B134B

13-513-613-713-8

13-913-1013-1113-12

13-1313-1413-1513-16

*Fimt round of mea.mmemente.●*sacO”d ~Omd Of mw”rementi,

1.51.92.43.5

1.51.92.43.5

1,52.02.53.5

1.52.02.53,5

1.52.02.53.5

wfc at2 brs.

(wt. basis)

0.4930.4930,4890.491

0,4860.4880.4880,492

0.4700.4740,4730.480

0,4980.4990,4990.498

0.4880.4870,4930,491

Compcmition of 35-100-MeshSamples, g/g dry weight

Cement Silica

.516 .370

.519 ,371

.520 .372

.524 .374

.519 .371

.518 .370,518 .370.521 .372

,536 .383.536 .383.536 , 3s3.538 .384

.523

.524

.525

.527

.521

.523

.523

.525

.373

.374

.374

.376

.371

.373

.372

.375

water

,111.110.108.102

.110

.112

.112

.106

.081

.081

.081

.078

,104.102.101,097

.108

.104

.105

.W


Description of specimens made in series 954.11

Mortar ~pecimens: Cubes, 2 in.Cements: See Tables A-1 to A-3.Pulverized Silica: Lot 15918. Specific surface (Wagner), 6000 cm2/cm8.Batches: Same as Mixes A and B of Series 254-9.M~xing; Each batch was mixed 30 sec. dry, l% min. wet, allowed to rest 3 min.,

and then mixed 2 min. more in a small, power-driven, open-tub mixer. Batches re-mixed 30 see, after slump test.

Slump Test: As in Series 254-8.Molding: As for cubes in Series 254-9, except 15 per batch.Measurements: As in Series 254-8.Drying: As in Series 254-8.Composition of Hardened Specimens: Computed as in Series 254-8. See Table A-30.Chemical Analyses of Dried Granular Samples: See Table A-31. Determinaticms

by same procedure as in Series 254-9.ComprewiveStrength: See Table 6-1, Part 6.Flexural Strength and Modulus of Elasticity: From prisms made from same ma-

terials in same proportions as in Series 290. See Table A-32.Adsorption Data: See Table A-33.

Description of specimens made in series 954-13

Specimens: 2-in, cubes Wde of cement-silica pastes.Cements: See Tables A-l,to A-3. Cements were prepared in the laboratory mill from

plant-made clinkers, Three grinds of each clinker were made, one with no addedgypsum, one with enough added gypsum to give a total SO, content of about 2,4 per-cent, and one with enough to give about 5 percent 80,. Blends were made to givecements having 1.5, 2.0, 2.5, and 3.5 percent SO~and specific surface area (Wagner) of1800 cm’/g.

Pulverized Silica: Lot 15918. Specific surface area (Wagner), 6000 cm2/cm3.Weight Proportions: Cement: pulverized silica: water = 1.0:0.714:0.5.Mixing: Each batch was mixed with a kitchen-type mixer 2 min., allowed to rest 3

min., and then mixed 2 min. more. ~lixing water was cooled before use to give batch

temperature of 73 * 2 F after mixing.

Molding: Three cubes were molded from each batch.Mea~urements: As in Series 254-8.Curing: In water at 73 F. Curing water replaced with fresh water after first 24 hr.,

twice weekly thereafter.Drying: As in Series 254-8.Composition of Hardened Specimens: See Table A-34.Analyses of Granular Samples: SeeTable A-35.Compressive Strengths: See Table 6-7, Part 6.Adsorption Data: See Table A-36.

Series 954-16

The specimens of thk series were prepared for the heat of adsorption studies describedin Part 4.

Cements: The cements used were 16186 and 16189, which were prepared from twoof the groups of cements described in Series 254-1L No. 16186 was a blend of two ce-ments prepared from clinker 15367, the blend having a specific surface area of 3200CmZ/gby the permeability method. No. 16189 had the same specific surface area, being

a blend of cements prepared from clinker 15623. The clinkers were of Type I and TypeH compositions, respectively.

TA

BL

EA

-36-

AD

SO

RP

TIO

ND

AT

AFO

RSE

RIE

S95

4-13

Wat

.a+

mel

ltIat

imm

mec

taf fo

rbl

edin

eA

ge28

days

P/P

.

Tot

iRW

ater

Ret

aine

dat

Rel

ativ

eV

apor

—In

dica

ted,

g/g

Cem

ent

Cfi

zlke

r1536

7R

ef.

No.

13-2

BW

*IC

=0.

488

:ela

tive

Vap

orP

r=ur

e‘g

cem

ent

Clin

ker

1536

7R

ef.

No.

13-2

we/

c=

0.49

3

.210

8.2

504

.266

0.2

903

.310

1.3

317

.354

0.3

610

.376

.5.3

833

.404

6.4

466

.578

1*

Clin

ker

1536

7R

ef.

No.

13-3

W.f

c=

0.48

9

PIP

.C

fink

er153

67R

ef.

No.

13-I

BW

.fc

=0.

486

clin

ker

1536

7R

ef.

No.

13-4

W.1

.$=

0.49

1

Cfi

nker

1536

7R

ef.

No.

133B

W*A

=0.

488

.193

8.2

295

.243

8.2

631

.277

4.2

961

.315

9.3

224

.339

6.3

495

.373

0.4

313

.617

6

.215

1.2

527

.265

3.2

749

.286

1.2

957

.324

5.3

563

.384

7.3

995

.417

4.4

591

-620

6

W* .09

.20

.36

.47

.61

.69

.7.5

.81

.84

.89

.96

SS

D

.208

3.2

462

.261

9;&

s

.325

8.3

439

.351

0.3

681

.377

9.3

987

.443

5.6

223

.211

5.2

500

.263

1.2

737

.289

32%

5:

.356

3.3

821

.398

7.4

131

.451

5.6

2?9

.215

8.2

.550

.268

1.2

779

.292

0Sl

&

.361

1.3

%2

.403

4.4

157

.454

3.6

199

T,

Clin

ker

1562

3R

ef.

No.

13-5

W.f

c=

0.47

0

1W

ater

Ret

aine

datR

efat

ive

Vap

orhu

reIn

dica

ted,

ghcement

PIP

*C

linke

r15

367

Ref

.N

o.H

L4B

We

/C=

0.49

2

.203

5.2

407

.251

8.2

607

.270

6.2

783

.300

2.3

310

.356

9.3

752

.394

1.4

498

.630

8

Cfi

nker

1569

9R

ef.

No.

13-9

W./c

=0.

498

Clin

ker

1562

3R

ef.

No.

13-6

W.jc

=0.

474

Clin

ker

1562

3R

ef.

No.

13-7

Woj

c=

0.47

3

.151

5.1

737

.183

8.1

919

.200

4

:%%

.258

0.2

931

.311

2.3

312

.386

1.5

965

Cfi

nfm

r15

699

Ref

.N

o.13

-10

W.lc

=0.

499

.199

2.2

346

.247

8.2

568

.270

4.2

771

.30L

UI

.332

2.3

6fxl

.373

9.4

113

.461

4.6

210

w. .081

.161

.238

.322

. 31j

.53

.70

.81

.85

.88

.96

SS

D

.151

8.1

779

.183

3.1

923

.201

8.2

072

.226

1.2

520

.278

3.2

988

.322

4.3

858

.577

2

.150

9.1

744

.184

3.1

910

.200

9.2

054

.223

8.2

596

.281

6.3

1X13

.316

9.3

699

.595

9

.144

4.1

671

.177

3.1

846

.193

1.1

989

.216

2.2

565

.292

0.3

115

.329

2.3

834

.605

4

.193

722

90.2

423

.250

4.2

618

.269

3.2

891

.321

5.3

519

.360

3.3

W0

.44$

X3

.611

0

hid

al

next

page

)(c

—

P/

P.

w. .081

.161

.238

;%2

.53

.70

.81

.85

.88

.96

SS

D

SS

D=

Wat

erco

nb*

Thi

sfk

gure

ispr

otU

%-

Non

-eva

pora

l

Clin

ker

1569

9R

ef.

No.

13-1

1Z

c./c

=0.

499

.191

7.2

247

.237

3.2

462

.256

1.2

643

.282

8.3

144

.350

1.3

587

.392

0.4

526

.630

8

Tot

alW

ater

Ret

aine

dat

Rel

ativ

eV

apor

Pre

ssur

eIn

dica

ted,

g/g

cem

ent

Cfi

nker

1569

9R

ef.

No.

13-1

2W

.je=

0.4W

3

.183

9.2

156

.21$

33.3

346

.243

9.2

507

.266

7.3

0S2

.341

1.3

511

.376

2.4

390

.60s

7

ofgr

anul

arsa

mpl

e,sa

tura

ted,

surf

ace+

yfo

rsa

mpl

eth

atha

dbe

end

Iyin

corr

ect.

By

com

pari

son

with

ofh.

rs,

itsh

ould

beab

out

0.61

7.W

8~;

pip,

=ab

out

24x1

0-.

1 an

dre

a.st

urat

ed.

Cfi

nker

1549

8R

ef.

No.

13-1

5W

*IC

=0.

493

.200

4.2

352

.247

2.2

558

.257

7.2

717

.294

5.3

243

.350

7.3

675

.392

7.4

444

.56c

m

Cfi

nker

1549

8R

ef.

No.

13-1

6w

e/c

=0.

491

.189

5.3

232

.235

2.2

430

.254

8.2

581

.278

1.3

162

S47:

.385

7.4

407

.574

3


llpechwns: The specimens were 1J@3-in, neat cement cylinders, nominal w/c D=0,50 by weight, The pastes were mixed with a kitchen-type mixer, following the 2-3-2schedulo described for earlier series, (Ile specimens were cured continuously in wateruntil they were used,

I?esults of Ezperimrmts: Experimental procedures rind the results are given in Part 4of the text,

Sork Q54.18

This series comprises several experiments using the high-vacuum uckrption appara-tukl,

Corwnts: The cemente used were 13495, 13723-IQ, 14675, rmcl 15305, These arecements of about average Type I composition,

Specimens; The original specimens were neat-cetnent pastes, As explained in thetext., the samples made with cements 15365 and 13723-IQ were granules preparedpreviously for Series 254-9 (Ref, 15A,age 180days) and 254-K413(Ref. lQ), respectively,The original specimens from which granular samples were taken were 2-in. cubes,

The specimen made with cement 13495 was a slab, cast on edge, shout 0.25 cm thickand 10 cm square, The paste was mixed with a kitchen-type mixer, 2 min. mixing, 3min. rest, followed by 2 more min. of mixing, w/c = 0,5 by weight. The mold wasstored under water immediately after casting. When the paste was 1 day old, thesquare was cut into 1x1OXO.25cm slabs and these were stored in sealed bottles contain-ing water-saturated cotton, After 7 years and 116 days of such storage, one of the1x1OXO.25slabs was ground on a plate-glass surface with water and powdered emeryuntil the thickness was reduced to an average of about 0.3 mm. This thin slab was usedfor adsorption measurements.

The specimen made with cement 14675 was a cylinder about 3 cm in diameter by 4 cmhigh. The original water-cement ratio was 0.12 by weight. The cement was mixedwith the water by kneading with a stiff spatula on a steel plate. The moist mix was thenloosely packed into a steel mold. By means of a close-fitting plunger and hydraulicpress, the sample was compacted. The applied pressure was 24,000 lb/in~, which wasjust enough to bring water to the surface of the specimen. A cross-section of the speci-men at time of test was free of visible voids.

The cylinder was removed from the mold immediately after caeting and then curedcontinuously under water in a covered can. It was 4 years 29 days old when used forthese experiments.

The sample for adsorption measurements was obtained by sawing out a thin slabparallel to the vertical axis of the cylinder and grinding it to a thickness of about 0.3turn as described above. The eample used actually comprised two such slabs, each about1.2 x 3.8 x 0,03 cm.

Test Results. All the experimental data are given in the text.


Part 3. Theoretical Interpretation of Adsorption Data*

CONTENTS

B.E.T. theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...470

Thetheory ofcapillary condensation.. . . . . . . . . . . . . . . . . . . . . ...0.473

Combining the B.E.T. and capillary condensation theories. . . . . ...476Effect of soluble salts on adsorption curves . . . . . . . . . . . . . . . . . ~..477

Application of the B.E.T. equation(A). . . . . . . . . . . . . . . . . . . . . . ...479Method ofevaluating Canal V~. . . . . . . . . . . . . . . . . . . . . . . . . . ...479

The relationship between V~ and non+vaporable water, w“, forsamples cured at70-75 F........ . . . . . . . . . . . . . . . . . . . . . . . . . ...482

Thespecific surface of hardened paste. . . . . . . . . . . . . . . . . . . . . . . . ..4S8

Computation of surface area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..4S8Verification of surface areas as computed from V~..... . . . . . . ...489

Results from hardened paste . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...490

Specific surface intermsofwn c..... . . . . . . . . . . . . . . . . . . . . . . ...490

The specific surface of steam-cured paste . . . . . . . . . . . . . . . . . . . . . . . .492

w/Vm curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .493

Minimum porosity and the cement-gel isotherm . . . . . . . . . . . . . ...495Estimation of pore- and particle-size . . . . . . . . . . . . . . . . . . . . . . . ...496

Data on relative amounts of gel-water and capillary water. . . ...498

Summary of Part 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...499

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...503

Whe characteristics of the cementi mentioned in this section may be found in the Appendix to Part 2

47o JOURNAL OF THE AMERICAN CONCRETE INSTITUTE December 1946

The adsorption isotherms obtained from hardened cement paste areidentical in several respects with those obtained from other materialsthat are very different in chemical and physical properties. For examplewhen glass spheres(i) * or oxide-coated cathodes of radio tubes(z) are ex-posed to nitrogen vapor (at the temperature of liquid air), or when a planemercury surface is exposed to CClq vapor (11 C), (3Jthe adsorption curvesobtained are of the same type as those for water vapor on cement paste.Also, the same type of curve is obtained when crystalline solids such astitanic oxide, stannic oxide, zinc oxide or pulverized quartz are exposedto water vapor at room temperature(l), Moreover, curves of the sametype may be obtained with different vapors on the same solid(s).

The similarities just mentioned exist not only among materials thatare not porous, that is, materials on which adsorption is confined tothe visible surfaces, but also among many porous solids having negligiblesuperficial surface areas. With suitable vapors the following materials,some porous, some not,” all give the same type of isotherm: buildingstone @J; cotton (’, ‘j; asbestos fibre(g); wood fl”); wood pulp(n); carbonblack(lz~; titania gel, ferric oxide gel, rice grainsf13); cellophane; bone-char@); cellulose; silica gel(17);proteins; soils (lg);wool@o).

It appears therefore that the curves found for portland cement pasteare not characteristic of the particular substances composing the pastebut represent some factor common to many dissimilar substances. Wewill see in what follows that this common factor is probably nothing otherthan a solid surface that has an attraction for the adsorbed substance.

B,E.T. THEORY

Various theories have been advanced to explain the taking up ofgases and vapors by solid materials(6), Among the most recent, and atpresent the most useful, is the theory of Brunauer, Emmett and Teller,(2I, 22) known as the multimolecular-adsorption theory, or the B.~.T.

theory for brevity. It is beyond the scope of this paper to discuss theB.E,T. theory in full; reference should be made to Brunauer’s book(s)or to the original papers for an adequate treatment. However, it isnecessary to review here the main features of the theory.

The theory rests on a concept advanced earlier by Langmuir, Thetaking up of a gas by a solid is considered to be the result of a physicalattraction between the molecules of the gas and the surface molecules ofthe solid. t This field of force is believed to arise from three different

*See references end of Part 3,tChemmal reaction with the solid in not excluded by the theory but it will not b cormidered here,


causes, or to be made up of three different forces that are known collec-tively as van der Waal’s forces. Hence, the process under discussion iscalled van der Waal’s adsorption. These forces are of a lesser order ofintensity than those involved in most chemical reactions, but theymay be effective over greater distances.

A solid surface exposed to a continuous bombardment of gas moleculescatches and holds some of the gas molecules, at least momentarily. More-over, when the gas is also a vapor such as water, the molecules caught onthe surface are in a condensed state and may be considered as a separatephase. Hence, when they are adsorbed, the molecules must give uptheir latent heat of vaporization. Besides this, adsorption usually isaccompanied by a further evolution of heat which may be said to repre-sent the energy of interaction between the solid and the condensed sub-stance; this is called the net heat of adsorption.

Some of the adsorbed molecules acquire enough kinetic energy toescape from the force field of the solid surface. The over-all result is acontinuous interchange between the surface region and the interior ofthe vapor phase, but the average molecular concentration at the solidsurface remains higher than that of the interior of the vapor phase byvirtue of the surface attraction,

The derivation of the mathematical statement of the theory startswith the assumption that the rate of condensation is directly proportionalto the frequency of impact between the solid and the vapor molecules,which frequency is proportional to the vapor pressure when temperatureis constant. The rate of evaporation is expressed as a function of theamount of energy a condensed molecule must acquire to escape from aparticular situation in the condensed phase. In the derivation of themathematical expressions that have found use, only two situations of amolecule in the condensed phase are recognized: (1) a molecule maybe condensed on bare surface; (2) a molecule may be condensed on alayer of previously condensed molecules. It is assumed that a moleculein the second situation can escape when it acquires energy exactly equalto its heat of vaporization; a molecule in the first situation must acquirea different (usually greater) amount of energy to escape, In otherwords, the net heat of adsorption is assumed to be zero for all moleculesnot in the first layer. *

The theory requires that at any given vapor pressure the amountadsorbed is directly proportional to the surface area of the solid,

A logical extension of the assumptions made in the derivation isthat at the saturation pressure there is no limit to the number of layersthat might be condensed on an open surface.

*Brunauer,Emmett, and Teller have publishedm equationrepresentingthe aaaum tion that the netPheat of adsorption from the aeoond layer aleo differs from aero. Thra equetion inoludm a so the aseumptlon

that the Paoldng of moleoulan in different in the Ilrat from that in the suooeeding layers. Th& aquetion deeenot cppear to have found uee (See Raf, 21, P, 813).

47s? JOURNAL OF THE AMERICAN CONCRETE INSTITUTE December 1946

The most widely used mathematical statement of the theory is thefollowing expression:

w—.v.

in whichw=

v. =

P .p, =

c(p/p8)

(l– P/P8)(l –p/p8+c(p,p*) )”””””.”””.”””””””. (A)

quantity of vapor adsorbed at vapor pressure pquantity of adsorbate required for a complete condensedlayer on the solid, the layer bei~g 1 molecule deepexisting vapor pressurepressure of saturated vapor

C is a constant related to the heat of adsorption as follows:Q,– Q.

C=ke RTwhere

k is a constant assumed to be 1,0 in computations.QL = normal heat of condensation of the vapor per mole of vaporQI = total heat of adsorption per mole of vapor(QI – QL) = net heat of adsorption per mole of vaporR = the gas constantT = absolute temperaturee = base of natural logarithms

Owing to the assumptions made in the derivation, eq. (A) wouldbe expected to hold only for adsorption on exterior surfaces. It couldhardly be expected to hold for surfaces on the interior of a porous solidwhere unlimited adsorption would obviously be impossible. Brunauer,Emmett, and Teller recognized this and introduced another constantn which was intended to be the maximum number of layers adsorbed.The resulting four-constant equation does not fit any known data from aporous adsorbent over the whole pressure range. However, Pickeft(2sjdiscovered a way to improve the derivation of the B.E.T. four-constantequation and supplied a better expression. This equation has the samefour constants as the original. It fits many adsorption curves over about90 percent of pressure range. In some cases it conforms to the extremes,but in the middle range the theoretical curve is above the experimental,There are also many curves that this equation does not fit in the high--pressure range. One reason for this will be explained in connection withthe theory of capillary condensation, discussed below.

In general, the four-constant equations did not prove to be veryuseful in this study; hence, they are not given here. However, the three-constant eq. (A) can be used to represent the low-pressure part of thecurve precisely. Of the three constants, p, is the same for all curvesand C is the same for most of them. Consequently, in most cases ad-sorption characteristics can be represented by V,,, alone.


THE THEORY OF CAPILLARY CONDENSATION

Conclcmsation of vapor in a porous cement paste seems to be mostadequately explained by a combination of a theory based on the energyavnilaldc ut the solid surface, such as the B. E,’J’, theory discussed above,and a theory based on energy available at the surface of a liquid, theci~~)illary-c:oxlclt!rlsatiorl theory,

The (:apilltily-corldens~~tio]l theory rests on the fact that the surfaceof a liquid is the seat of tivailable energy, The molecules at the surfaceof M litl~]i(l not l)eing completely surrounded by other molceulcs of likekind are under an inwardly dircctcd intermolecular force, When a givenbody of watnr is cha,nged in shnpe so m to increase its surface area, workmust be done against the forces tending to draw the molecules out of thesurfmo, Consequently, when left to itself, a small body of liquid tendsto become spherical, since that is the form giving a minimum of surface,

This phenomenon has an effect on the vapor pressure of the liquid,How this comes about can be seen by considering the behavior of waterin a small glass cylinder, as sholvn in Fig, 3-1, The solid curve at the top

B-\,/

‘.--~.

:———~-

—.—- .

— ——-— —— —

———

.——— — .——

———-

_—

—— —

=.— .—— .

———=.— ———=

Fig. 3-I

represents the meniscus of the ]vatcr surface, O\~ing to the surface

tension, which strives to straighten the meniscus, that is, to reduce its

curvature and thus reduce the surface area, the water in the vessel is

under tension. Consequently, the vapor pressure of the \vater in thetube will be Icss than normal for, the existing temperature. The greaterthe curvature of the meniscus, the greater the tension in the ~vatcr and

hence the lower the vapor pressure. The relationship between surface-

curvature and vapor pressure ]vas ~vorked out by Lord Kelvin. It may

be written

2(TMin p/p8 = – —

dfm’r” ”””””””’”’””””””””’” ““”””””””””’””””(1)

474 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE December 1946

wherep, = vapor pressure over plane surface at temperature T, the

saturated vapor pressurep = the existing vapor pressure over a concave surfacea = surface tension of liquidd, = density of liquidM = molecular weight of liquidR = the gas constantT = absolute temperatureT = radius of curvature of the circular meniscus

Under the conditions pictured in Fig, 3-1 the greatest curvature thatthe liquid can have is limited by ~the radius of the container. Whenthe liquid surface has this curvature, the liquid can be in equilibriumwith only one vapor pressure, p, corresponding to the radius of curvaturer, as given in eq, (1). If the pressure of the vapor is kept below p, allthe liquid in the vessel will evaporate. If the pressure is maintainedabove p, some vapor will condense, increasing the amount of water in thevessel. But under the conditions pictured, condensation would lessen thecuryature of the liquid as indicated by the dotted line and there would bea corresponding rise in the equilibrium vapor pressure. If the vaporpressure is kept equal to the saturation pressure, that is, the maximumpossible over a plane surface at the existing temperature, condensationwill proceed until the tube fills and the surface curvature disappears(r = m).

The minimum relative vapor pressure at which the liquid in thevessel can retain its meniscus depends on the maximum possible curvatureof the meniscus. ‘1’his in turn depends on the bore of the cylinder.‘.I‘:al)!c3-1 gives an idea of the curvature required to prodllce a giveneficct on vapor pressure.

The main point to note in Table 3-1 is that the surface must havea high degree of curvature to produce an appreciable effect on the vaporpressure of the liquid. For example, if the radius of curvature is 0.1micron, the vapor pressure is 99 percent of the normal value, p,. Aradius of curvature of 0,0015 micron would reduce the pressure to 50percent of p,. The figures given should not be taken too literally; they

are undoubtedly in error through the low-pressure range, for the equationtakes no account of the fact that the physical properties of the liquid

are affected by capillary and adsorption forces. The table serves only toindicate what the order of magnitude of the curvatures must be when

capillary condensation occurs.An “adsorption curve” of almost any shape could easily be accounted

for by the capillary condensation theory. The simplest approach is to1magine first that the voids in a porous solid are cylindrical pores of


TABLE 3-I—RELATIONSHIP BETWEEN AQUEOUSRELATIVE VAPOR PRESSURE AND RADIUS OF CURVATURE

Calculated from Kelvin’s Ecmation—Temperature = 25 C

Relative vaporpressure, p/p@

0.100.200.300.400,500.600.700,800,900,950.980,991.00

-—..———

Radius of curvatureof meniscus

cm

4,6x 1O-S6.6 X1 O-’8.8XKH

11,5 x 10-815,2 X 10-820.8 x10-829,5 x10-847,2 x1 O-B

100,0 X 10-8204.0 X 10-8532.0 X 10-8

1052.0 X 10-8m

microns

.0005

.0007,0009.0012.0015.0021.0030.0047.0100.0204.0532.1052m

——-.-

various sizes and that when a cylinder is partly filled, the radius ofcurvature of the liquid meniscus equals the radius of the cylinder. At agiven pressure p, all cylinders smaller than the corresponding r (seeeq. 1) would become or remain full and all larger than r would becomeor remain empty. The shape of the curve would therefore depend on therange of sizes presept and the total capacity of each size.

This simple analogy led Freyssinet (24)and others before him to con-sider an adsorption curve to be a means of ascertaining pore-size distribu-tion in systems of submicroscopic pores. However, a naturally formedporous solid so constituted is hardly conceivable. It is much more likelythat the pore spaces resemble those in an aggregation of particles. Theshapes of the particles may be spherical, fibrous, or between these ex-tremes. Capillary condensation could occur in the interstices in themanner illustrated in Fig, 3-2. At the point of contact between twospheres there is a space of wedge-shaped cross section. Condensationin this space would form a circular lens around the point of contact andthe liquid would present a curved surface, Similarly, where two prismaticbodies make contact, water condensed in the region of contact wouldpresent a curved surface, somewhat as shown.

In the circumstances pictured, the water surface would have twocurvatures. Hence, in this case Kelvin’s equation would take the generalform

UMh p/p8 = – —

()~+~ . . . . . . . . . . . . . . . . . . . . . . . . . ...(2)

d~RT r, r2

whererl and rs are the principal radii of curvature.

476 JOURNA!. OF THE AMERICAN CONCRETE INSTITUTE December 1946

For the conditions shown in Fig. 3-2 one of the r’s would be negative.Since the structure of paste is probably granular, fibrous, or perhaps

plate-lilic, it is evident that Kelvin’s equation provides no simple wayof computing the size of the pores; it only gives the effe~tiue curvatureof the water surface. It can, however, explain the condensation of vaporin a porous solid, and we will sce evidence in the data indicating that apart of whnt is here called adsorbed water in cement pastes is taken upby capillary condensation.

COMBINING THE B.E.T. AND CAPILLARYCONDENSATION THEORIES

When adsorption of a vapor occurs in a porous solid of granular orfibrous structure, the liquid surfaces are certain not to be plane. Theywill be concave, at least in some regions. Therefore, the free surfaceenergy of the solid and the free surface energy of the condensed liquidmust both be causes of condensation. *

13runaucr, Emmett, and Teller tried to take this factor into accountby adding a fift,h constant representing the release of the surface energy ofthe liquid when two adsorbed layers mcrget2$. This five-constantequation is very unwieldy and it embodies the assumption questioned byPickettt’3J. Also, it rests on the oversimplifying assumption that ad-sorption is occurring only between plane parallel surfaces.

By the B.E.T. theory, vapor would be expcctcd to condense uniformlyover all the available surf ace. But in a porous body, the surface tension

Fig. 3-9—.—*SIXl’al’t4


of the liquid must influence the distribution of the condensed water,whether it is primarily responsible for the condensation or not. Thus,in Fig. 3-2, B.E,T. adsorption could lead only to a uniform layer of con-densate around each sphere, but surface tension would require the liquidto collect as shown, for the condition pictured is the most stable onepossible under the circumstances, This follows at once from the factthat if the liquid shown in the lens were spread evenly over the twospheres, the total surface area of the liquid would be increased and thework done would be equal to the product of the increase in area and thesurface tension of the liquid.

If, as assumed in the B.E.T. equation, only the molecules in thefirst layer lose more than their heat of condensation, then all but thefirst layer should tend to collect in the lens. However, Harkins andJuraf27J have shown that the adsorption forces probably affect more thanthe first layer. Therefore, the net heat of adsorption probably representsthe heat from several layers. This being true we can expect the adsorbedlayer to vary in average thickness with the curvature of the liquidmeniscus, the greater the curvature the greater the tendency for ad-sorbed molecules to collect in the lens.

On account of the effect of liquid surface tension the relationshipbetween water content and vapor pressure depends on the characteristicsof the pore system. Since the characteristics of the pore system. are notpredictable from any adsorption t~eory, it follows that no general equa-tion can be expected to apply to all porous bodies over the whole pressurerange, Since, however, no appreciable capillary condensation is to beexpected below about 0.4p,, general theories may be expected to applyin this low range of vapor pressures.

As will be seen, little quantitative use ,is made of these theories, exceptthe B. E. T. eq.. (A) applied to the range p = 0.05 p, to 0.40 p,. IIow-ever, many features of the interpretations given rest on the theoriesdescribed above, That is, it was possible to use the theories qualita-tively even where the mathematical expressions intended as expressions ofthe theoretical concepts were found to be inadequate.

Effect of soluble salh on adsorption curves

The foregoing discussion is based on the assumption that the adsorbedliquid is pure water. However, in hardened portland cement paste thewater will contain dissolved salts, principally Ca(OH)Z, NaOH and KOH. *At any given water content the observed reduction in vapor pressure isdue not only to the capillary and surface effects described above, butalso to the dissolved salts. The magnitud; of the effect of the dissolvedsalts can be estimated from the vapor-pressure isotherms of the salt

*Becau of ita low volubility, Ca(OH)~ can be ignored.


solutions and the amount of dissoiwxl :1,1kuli in the sample of hardenedpaste.

Vapor-pressure data (28)for aqueous solutions of NaOH and KOH aregiven in Fig. 3-3. The lowering of vul)~)r pressure due to the alkalies canbe determined from these curves, f{)r W]Y given concentration of thealkalies.

The amount of dissolved alkali in hardened paste probably variesconsiderably among the different samples. Sample No. 254-11-2 is con-sidered to be representative of the average. The original mortar wasprepared from cement 15758 (we/c = ().4[;) and was cured 28 days inwater, The cement originally contained 0.3 percent NaZO and 0.4 per-cent h-ZO which, in g/g of cement, corresponds to 0.0019 and 0.0024of NaOH and KOH, respectively. An unknown portion of these alkalies

undoubtedly remained in the unhydratecf cement and can be consideredinsoluble for the present purpose. Some of the soluble alkali was

leached from the sample during the 28-day period of water curing. Thereis also reason to believe that some of it was adsorbed by the solid phase

and thus effectively kept from the solution. Hence, the sample as testedmust have contained considerably less than 0.004 g of soluble alkali

(total of NaOH and KOH) per g of cement. The adsorption isothermfrom this sample is given in Fig. 3-4, upper curve. This curve pre-sumably represents the combined effect of surface adsorption, capillarycondensation, and disso~ved alkali, The lower curve in Fig. 3-4 showsthe amount of water that could have been held by 0.004 g of sodiumhydroxide at any given relative vapor pressure above about 0.07 p,,the vapor pressure of a saturated solution of sodium hydroxide at 25 C.(See Fig. 3-3.) Since the actual amount of alkali must have been lessthan 0.004 g, the amount of water that could have been held by thealkali alone would be represented somewhere below the curve as drawn.

It thus becomes apparent that at pressures below about 0.8 p, onlya very small part of the total water taken up by this cement paste couldbe amounted for by the dissolved alkalies. In the range of higherpressures, the possible effect of the alkali is greater. As p/p, approaches1.0, the amount of ]vater that could be held by the alkali approachesinfinity. Since, however, the topmost point of the curve is establishedby saturating the granular sample with liquid water, its position isdetermined by the capacity of the sample and the assumption that, atsaturation, p/p, = 1.0, In this case the capacity of the sample was 0.33g of water per gram of original cement. With 0.004 g of alkali in 0.33 g ofevaporable water the relative vapor pressure would be slightly below 1.0.

Since the effect of the alkali is small, no correction for its effect hasbeen attempted; the topmost point is always plotted at p/p, = 1.0, and


24 I ,

x

Qzo -

k

$~ lb

EmL

:12 I

wa0

=“ 8

? ~NaOH:’

( I00 !

@’d “2 “3 “4 P7P$’6 “7.8 .9 !.0

Fig. 3-3 (above>Vapor pressure iso-th;~m;$~ aqueous solutions of NuOH

S = Satureied !olufion

Fig. 3-4 (ri ht>Estimation of effect of7dissolved a koii on adsorption isotherm

v.. I I ro~

.8 .9 I

all other points are treated as if their positions were determined bysurface adsorption and capillary condensation only.

Differences in the amount of soluble alkali among various samples,

within the range that might reasonably be expected, probably have little

effect on the lower part of the curve, the part that is used in the analysespresented below. However, such differences probably produce consider-able effects on the shapes of the upper parts of the curves and hence

contribute to the difficulty of interpreting the upper parts.

To minimize the effect of dissolved alkali, most of the specimens were

stored in water for the first 28 days of their curing period to leach someof the alkali from the specimens. Longer periods of water storage were

avoided because of undesirable leaching of Ca(Oll)Z.

APPLICATION OF THE B.E.T. EQUATION (A)

Method of evaluating C and V~

The constants G’and V~ were evaluated in the manner recommendedby Brunauer, Emmett, and Teller. Eq. (A), written in the form

lx c–l-—=:–+=X, (x = p/pJW1—zvmcm

lxshows that a plot of experimental values for – — against z should

W1—z


c–1give a straight line. The slope of the line will be —

Vmcand the inter-

cept on the #-axis will be l/V~C. The application of this method to

data from cement pastes ‘is illustrated in Fig, 3-5 and in Tables 3-2and 3-3. Two of the four diagrams represent data obtained by the air-stream method, and the others represent data obtained by the high-vacuum method.

TABLE 3-2—TYPICAL DATA FOR COMPUTING V.. AND C

Data obtained by air-stream method

I Iw

lx@!J &/!G!te

.—I&x w l-z

Ref. 25A11-11-Cement 16213

1

Ref. 254-8-15A-l&Cement 153651

0.09 0.0267 0,099 3.790.20 0.0348 0.250 7.180.36 0.0464 0.562 12.10.47 0.0539 0.887 16.5

—Ref. 2&l+16A-270A—Cement 15365

0,081 0.0187 0.0873 4.680,161 0.0264 0.192 7.270.238 0.0310 0.312 10.00.322 0.0359 0.475 13.20.360 0.0400 0.563 14.10.530 0.0500 1.127 22.6

C! and V~ can be computed conveniently from the intercept on the1$0

z-axis and from the ordinate at z = 0.5. Thus, when - — = ,WI— Z

C = 1 – ~; and when x = 0.5, V. = ~C w. In Fig. 3-5A we see thatx

when~~=O, z=WI—Z

Therefore,

C=l+L=0,053

– 0.053 and when x = 0,5, l/w = 19.3.

19.8, and V~ =1 + 19.8

X ~.3:= 0.0272 )( 19.8 .

PHYSICAL PROPERTIESOF HARDENED

24 1 1Rei? 1/-11 .Cemeni 16213

20 — w/c= 0.493 /

Air-Streom Method/

16

&fil?

08

M /

.

C-Jo 0.1 02 0.3 0.4 05

x (=P/Ps)

t I I40 — Ref 254-18

Cement /’767S %’WC = 0.12High -Vacuum Meth od

35

30 /o

c

25

lx/

WE

20

15- ~%

10. [

. m Adsorption

. Zm’ ,,

5 .

G,~o 0,1 0,2 0.3 0,4 0.5

x (=P\P\)

PORTLAND CEMENT PASTE 481

Fig, 3-5—Typical plots of the kindDoto Irom Tablej

Ref 9-15A 6mo. o

Cement 15365

’20— YC = 0,244 /

Air-Stream Method

16

& *I2 G

8

4 L

/k’’ioo o,

-.059-.03, )’ ‘ “2X(=P;:) 0’4 0’5

!6

Hfgh. Vocuum k?ethod

14-Cement 13565

9-ISA -180 1

12

10 ,

& +x

8Q

+

b

4

2

+’

!

-,031 0 0,1 0.2 0.3 0,4 0.5-,026 x (’ P/Ps)

used for evaluating C and V~3-9&3-3.

The nomenclature used here is the same as that used by Brunaueret al. except that they used V for the volume of gas adsorbed, whereashere w is used for weight adsorbed. w is expressed either in grams pergram of dry hardened paste (evaporable water removed) or as grams pergram of original cement. Having become accustonied to thinking of V.as a factor proportional to surface area, we have somewhat illogicallyretained this symbol, but express it in grams instead of cc.

48$? JOURNAL OF THE AMERICAN CONCRETE INSTITUTE December 1946

TABLE 3-&lYPICAL DATA FOR COMP(JTING Vm AND C

Data obtained by high-vacuum method

I I

?R) g/:of lxdry paste 1+X z TX

Ref. 254-18-9-15A-180-Cement 15365

0.055 0.0227 0,0598 2.630.073 0.0249 0.0790 3.170.104 0,0284 0,117 4.130.193 0.0347 0,240 6,910.244 0.0400 0.322 8.060.349 0.0455 0.534 11.70.472 0.0542 0.885 16.3

1

0.0550.0730.1040.1930.2440.3490.472

Ref. 254-K4B-lQ-Cement 13723

0.0369 0.0598 1.620.0397 0.0790 1.990.0435 0.117 2.690.0540 0,240 4.400.0587 0.322 5.490,0686 0,534 7.780,0819 0.885 10,8

Ref. 254-13-Cement 14675

0.064 0.0552 0.0684 1.24 ‘-0.155 0.0646 0.1835 2.340.193 0,0675 0.2395 3.550.249 0.0720 0.3310 4.600.350 0.0817 0.5380 6.580.446 0.0910 0.8040 8.84

THE RELATIONSHIP BETWEEN V. AND NON-EVAPORABLE WATER (Wn)

FOR SAMPLES CURED AT 70-75 F

The quantity V~ is considered to be proportional to the internal surface

area of the sample. Since the specific surface of mi crocrystalline materialis negligible compared with that of colloidal material, V~ is also con-

sidered to be proportional to the amount of colloidal material in thesample. The quantity w. represents the amount of non-evaporable

water in both colloidal and non-colloidal material. Therefore, if a givencement produces the same kind of hydration products at all stages of itshydration, the ratio VJW. should be constant for any given cementunder fixed curing conditions. However, the ratio of colloidal to non-

colloidal hydration products should be expected to differ among cementsof different chemical composition. Hence, the ratio ‘VJwfi should be

different for different cements.


V~ and w. are plotted for several different cements and differentmixes and ages, in Fig. 3-6 and 3-7. The points in most of the diagramsshow a considerable amount of scatter. Some of this is due to randomexperimental vagaries and some of it is apparently due to variations indrying conditions discussed earlier.

In view of the fact that the variations show no consistent influenceof the original water-cement ratio or of the age of the sample, the rela-tionships indicate that for any given cement the ratio VJW. is inde-pendent of age or water-cement ratio.

If the points fell on a straight line through the origin, that wouldindicate that the ratio of colloidal to non-colloidal products is preciselythe same at all stages of hydration, The data are not sufficiently con-cordant to indicate definitely whether this is so or not. There is somereason to believe that the reactions during the first few hours cannotproduce exactly the same products as those that occur later, Partic-ularly, the gypsum is usually depleted within the first 24 hours and thusthe reactions involving gypsum cannot occur at later periods.

If calcium sulfoaluminate as produced in paste is non-colloidal, theratio of colloidal to non-colloidal material should he lower during thefirst 24 hours than it is at any later time. The effect on the graph wouldbe that of causing the proportionality line that holds for the later ages tocut the w~-axis to the right of the origin. AS said before, the plotteddata do not indicate definitely where the inxercep~ should be. They doindicate, however, that if the intercept is to the right of the origin, itis nevertheless near the origin, as indeed it should be in view of therelatively sma[l amount of calcium sulfoaluminate that is formed. Tosimplify the handking of the data, we have assumed that the line passesthrough the origin and thus have considered the ratio of colloidal to non-colloidal material to be the same at all ages i’or a given cement.

Fig, 3-6 represents the data from Series 254-8 and 254-9. It represents5 different commercial cements that had been used in experimental high-ways. The data on this series are the least concordant of all obtained inthe investigation.

Fig. 3-7 represents cements prepared from 5 other commercial clinkers.Different plant grinds of each clinker were blended to give each cement aspecific surface of 1800 sq cm per g (Wagner).

The ratios determined for the cements in each of these two groupswere averaged. The results are shown in Table 3-4.

The figures in the third cohmn give the mean values and those inthe fourth give the probable error of the mean. Those in the last columngive the probable error of a single test value and thus reflect the degreeof scatter of the data.

484 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE December 194@

I I I 1,?2:?’”1 I04 , .$4- 1

,.

.03. . x

03

0? 02 /

,01 / 01

al

%g’ o

,16 20 21 ,08 .12 .16 ,20 ,24wn-arams Der arem of dru oaste

u I I

Cement/.50/3J

,05— C#r /;.

~pe~ Jr< {800cm Y9

,04

,0?

.01

0

graA of ‘$ry pi!!te “’2 “b “70 ’24

Eo Mix A. 8 Series.?S4 -9x cA Series 254-8

Fig, 3-6-Relationship between V~ and W. for pastes of Series 954.9


C6 wCements Prepmed {mm Cl!nk.?!S498 Cements Prepared from Clinker /5623

CjS - 62/

C3S 46C2S /3

m — C5— C?s 3/

:% ‘;. 7C,J! 4.8Cq,4F !3.2

n4 04/

&. 0

. #

.03 D3d o

02 ,02/

. Cement M758 o Cement 15756

.01 . ,, IW98 -/.s Lto%so> .01gm

wn- grams per gram of dry paste

~ .26

-0@merits Pre~red from Clinker 15670

C,s 37Gs 52

~ .05— C, A .?.4 /

C*,+/ .5.7

E~ 04 -

m

L 03al

/n.

,020 Ccinent 15?63

~ ,, x r, 16{981 & ,, 15699

. 1S670-2%S03b

1 00 I

>E.04 ,00 ,12 .16 20 ,24

wn-grams per

“06cements Preporedfiom Clinker 15367C,3 46C2S 28

.0s—C, A !4,3C4A: 6.?

04

.03

.020 Cenwnf 15754. ,J 162/3a ,, !62{4

.0! . f, /5367-1.5%

0 ,12 ,16 ,Zograr%of ‘$;g p%e

,%Cements Pmpored fiOm Clinker 15699

C3S 48,05— C.?x 29

CJ A 10cqa~ 7,6

04 — — —

.03

Em 1

0 Cement 1576{

,01 . ,, !s699-L5% &‘?Oz3L73

.J6 .20 .?4wn-9rams pergram of dry paste

Fig. 3-7—Relationship between V~ and w. for pastes of Series 954-11 and 254-13


TABLE 3-4-MEAN VALUES OF vm/w. FORTWO GROUPS OF CEMENTS

ASTM Mean value Probab16error Probable errorCement classifi- Of of mean of singlevalue

No, cation* vm/w.

Serie~254-9

14930J & .304 .00392 .017615007J ,272 .00216 .008915011J II .27215013J

.00242I

.0102,244

15365.00259

I.0107

.254 .00239 .0115

Series 254-11

15498 III “- .24815623

,00131 .003.271

15670 ?f.00405 .008

,29515367

.00411 .010.258 .00244

15699 I.006

,262 .00203 .004

*ASTMdesignationC-ISO-40T.Theolamifioation here ie based only on the oomputed quantities of thefour major oompoundm The surface area recpriremente are uot met in all caeea.

To evaluate the effect of composition, the assumption was made thatthe form of the relationship would be

v.– = .4(,70 CWS)+ B(% C2LS’) + c(%) CA) + D(Z C4AF)Wfl

The values of the coefficients were determined first from 200 items of datarepresenting about 50 different cements. Then, owing to the fact that lbOof these items represented only 5 cements (Series 254-9), a second analysis

was made excluding the data from Series 254-9. The results of the twoanalyses were as follows:*

For 200 items of data:

[.

.00326 (~oCWS)+ .00251 (~oC,A)Eq. (3): ~“ = * “%(%ca$) + * 00004

w. =1=.00016

+ .00549 (%C,AF)* .00030 1For 100 items of data:

v.,

[.

.00230 (% C&) + .00320 (~oCz@ + .00317 (%C,A)Eq. (4): — = * 00012

Wn =1=.00006 * .00016

+ .00368 (~, C4AF)=1=.00046 1The two equations give similar coefficients for CJ3 and C@ but con-

siderably different coefficients for CSA and CdA~. However, applied tothe same cements, the computed results are not far different, except for

*Seefootnote, Part 1, page 121.


certain compositions, This is shown by the data given in Table 3-5.

Here the observed mean values of V,./wn for the cements appearing inFig. 3-6 and 3-7 are compared with values computed from composition.

It appears that the value of Vn/wfi can be computed from composition

with fairly satisfactory accuracy by means of either equation. However,eq. (4) probably gives the more correct evaluation of the effect of varia-

tions in composition, since individual cements appear in the analysiswith approximately equal weights.

The influence of composition as given by eq. (4) is illustrated in Table

3-6.

The results given in the last column of the table show that the in-fluence of composition on this ratio is not very Iarge. The variation

occurs mainly among those cements whose compositions differ from the

average chiefly in C&, C~AF or both.

TABLE 3-5—COMPARISON OF OBSERVED ANDCOMPUTED VALUES OF V./w.

@meritNo.

15013J1536515367*15699

Average

15007J15011J15623*

Average

14930J15570’

Average

ASTMtype

IIII

IIHII

IVIV

HI

Mean V./w.observed

0.244*0.0030.254*0.0020.258+0.0020.262+=0.002——0.254

0,272 s=0.0020,272*0.0020.271+0.004

0,272

0,304*0,0040.295+=0.004——0,300

0,248+0.00115498*

*Thisitemrepresentsall cementsmadefromthiscliaker.

VJuJ,, computed fromcompound composition

Eq. (3)

0.2530.2550>2530.254

0.254

0.2690.2630.284

~, 272

0,2980.284——0.291

0.243

Eq. (4)

0.2560.2600,2580.25.5

0.256

0.2640.2570.272

0.264

0.2860.281

0.284

0.249

The theoretical significance of the coefficients of eq. (3) or (4) foundby the method described is not certain, mainly because of the lack ofdefinite knowledge concerning the chemical composition of the hydrationproducts. The data support arguments given elsewhere to the effectthat the hydration products of the alumina-bearing ~ornpounds are notmicrocrystalline as they are when these compounds are hydrated alonein an abundance of water; instead, the coefficients for C~A am-l C4A F,


TABLE 3-6-INFLUENCE OF CHEMICAL COMPOSITION ON V./wn

Type ofcomposition

Type I Normal CAHigh CSA

Type II High ironHigh silica

Type HI NTormal(7,.4High C!.4

‘rype IV High ironHigh silica

Computed compound compositionpercent by wt.

(73/s I C,s4545

4140

5959

2533

2928

2941

1313

4854

C,A

9.714.0

5.46.4

10.414,0

6.22,3

C,AF

7.55.0

14,89.7

7.65,0

13,85.8

Computed

v.;n Eq. (4)

0.2550.256

0.2590.279

0.2380.240

0.2820,277

taken literally, indicate that, per gram of compound, these compoundscontribute to the total surface area of the hydration products, that is, to

V~, as much as or more than do the two silicates, ~vhich are known toproduce colloidal hydrates. In any event, the analysis shows that ho\v-ever the AIZOSand FefOS enter into combination in the hydration prod-

ucts, they must appear in solids having a high specific surface.

The coefficient of C~i3 is less than that of CZS’. This result is com-

patible with the data of Bogue and I,erchf29Jshowing that both compoundsproduce a colloidal hydrous silicate, but only C~S produces micro-crystalline Ca(OH)2. The indications are that Ca(OH)z does not de-compose under the drying conditions of these experiments. Hence, theoccurrence of Ca(OH)z contributes to W. but contributes

vtn.very little to

THE SPECIFIC SURFACE OF HARDENED PASTE

Computation of surface area

From the derivation of the B. IZ.T. equation it follows that the surface

area 01 the adsorbent should bc equal to the product of the number of

adsorbed molecules in the first layer and the area covered by a singlemolecule. Hence, when V., is expressed in grams per gram of adsorbent

(dry paste),

s==a’, ““N—.. .................... . ...... .M

(5)

where

S = the surface area of the adsorbent, sq cm per gal = the surface area covered by a single adsorbed molecule

PHYSICAL PROPERTIESOF HARDENECIPORTLAND CEMENT PASTE 489

N = 6.06 x 1023, the number of molecules in a gram-molecular wt.(Avagadro’s number)*

M = molecular weight of the adsorbed gas.

The value of al has been estimated in several ways. Livingstonf30Jfound a value for water of 10.6x 10-’6 sq cm per molecule. Gans,Brooks, and Boydt4j used the same figure. Emmettf31) gave a formula forcomputing al from the molecular weight and density of the condensedvapor which gives nearly the same result if the normal density of wateris used. As will be shown, values for molecular area obtained in this waywhen introduced into eq. (5) actually give surface areas S that are inclose agreement with the results obtained by other procedures. Hence,for water we may write,

S = 10.6 X 10-’6 X 6.06 X 10~3V~

18

=(35.7 X10’) V~sqcmper g . . . . . . . . . . . . . . . . . . . . . . ...(6)

Verification of surface areas as computed from Vm

Gaudin and Bowdishflj used pyrex-glass spheres calibrated by micro-scope measurements. Low temperature adsori]tion of nitrogen gavealmost exactly the same specific surface as that computed from the meansize of the spheres. Ha rkins and Juraf3z) developed a me$hod of measuringsurface area by first covering particles with a complete film-of adsorbedwater and then measuring the heat evolved when the particles wereimmersed in water, The results obtained by this method were com-pared with those from the B.E.T. method for 60 different solids. For58 of the 60 solids the areas by the Harkins and Jura method differedfrom those obtained by the B.E.T. method by no more than 9 percent.Emmett (Z5’31’3S)presented an extensive array of data showing that where-ever particle size can be checked directly, as with the electron micro-scope, the results of the B.E.T. method look reasonable, to say the least.Because of such evidence as this, the B.E.T. method has been put touse by many investigators during the past few years.

The examples cited above were chosen from experiments made onsoli& that are non-porous. It i.s believed that V~ also gives the internalsurface area of porous solids, provided that the molecules of the adsorbateare small enough to penetrate the pores and reach all parts of the surface.The fact that V~ is evaluated from data in the low pressure range only,and hence where capillary condensation in the pores is not a factor,supports this belief. With respect to cement paste, the pores are con-sidered to be the spaces vacated by evaporable water when the sample isdried. The drying may be accompanied by irreversible shrinkage so that the

*6.023 x 10?~is now the accepted value for Avagadro’s number. This did not, come to our attention untilall the computations were ,oornpleted. Since other factors are uncertain, it dd not seem worth while tomake the slight corrections mckcated.

49o JOURNAL OF THE AMERICAN CONCRETE INSTITUTE December 1946

dried sample may not faithfully represent the original paste. The extentof the irreversible alteration is not known but it is considered to be small.Evidence of this is found in the fact that the total pore space, as measuredby the total evaporable water, is not greatly altered by the drying;in fact the data indicate that it is increased. (See Table 9, Part 2.)Hence, V~ is considered to give tbe internal surface area of the solidphase in the dried samples. If drying affects the measured surface area,it, would probably be in the direction of making it smaller.

In the remainder of this discussion it is assumed that V~ as determinedin this investigation is proportional to the surface area of the solid phase.It will be seen that this assumption leads to highly significant results.Thus the assumption seems justifiable.

Results from hardened paste

The magnitudes of the surface areas and the rates at which surfacedevelops during hydration as computed from eq. (6) are indicated byTable 3-7.

The figures pertain to the whole solid phase; that is, they are basedon the combined weights of the hydration products and residue oforiginal ciinker. ‘llerefore, the specific surface of the hydration productsis higher than the highest figure given except any that might representcompletely hydrated cement.

Specific surface in terms of Wn

Since V~ = kw., the specific surface of a paste can be computed if Wnis known, and if k for the particular cement is known. That is,

,Y--=35 .7x10 °k ~ . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . ...(7)c c

s— =35.7 X1 O’IC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (8)‘w,,

.41s0

s 35.7 X 108 k Wn _ 35.7 X 108 k W./C—.. . . —

l+wJn/c ““””””””’””””””””’. (9)

t; + w. c-l-w.

Eq, (7) gives the surface area per unit of original cement, and eq, (9)gives it per unit of dry paste.

For the types of cement given in Table 3-6 the surface area per unitweight of non-evaporable water is as given in Table 3-8,

The non-evaporable water content may lie anywhere between zeroand about 0.25 g per g of cement. Hence, according to th~se equationsthe specific surface may lie between zero and about 2.1 to 2.5 millionsq cm per g of original cement.

pHYSICAL Properties OF HARDENED PORTLAND CEMENT PASTE 491

Periodof

hydra-tion,days

7

;;56

1%365

TABLE 3-7–TYPICAL FIGURES FOR SPECIFICSURFACE OF HARDENED PASTE

Specific surface of paste for cementsindicated; w./c = 0,45 (approx. )

—14930J 15761 15365 15013JCWS23% cd 45% cd 4570 cd 40%C,A 6% C,A 10% cd 13% cd 1470

Millions of sq. cm. per g of:

cement

0,761,021.331.751.892.102.10

dry cementpaste

. —0.71 —0.921.19 1351.54 —1.62 1.961.78 —1,76 —

— —dry cement

paste— —

. 1,211.55

1=8 1,941.96

122 2,02— 2,14— —

drypaste

1.061,321.641.621.661.75—

cement drypaste

— —1.32 1,131.50 1.281.71 1.461,89 1.572.04 1.672,07 1,69— —

TABLE 3-8—SPECIFIC SURFACE OFHARDENED PASTE IN TERMS OF NON-EVAPORABLE WATER CONTENT

Type ofcement vm/wn (= k)

Type I Normal CA 0.261High C3A 0.256

Type 11 High iron 0,259High silica 0.279

Type 111 Normal C8A 0.238

17ypeIV High iron 0.282High silica 0.277

s/wn

9,3x1069.2x106

9,3x NY10,0 XI08

8.6 XI0’3

10.1x 1069.9 X1O’

Of course it cannot be literally true that S = O when ‘w. = O, sincethe initial surface area is that of the original cement. As measuredby adsorption, the specific surface of unhydrated cement is much higherthan that measured by methods previously used. Using a cement havinga specific surface of 1890 sq cm per g (Wagner), Emmett and DeWitt @4Jfound a surface area of 10,8OOsq. cm. per g by the nitrogen-adsorptionmethod. By the air-permeability method, this cement would showabout 3500 sq. cm. per g, which is probably close to the true macroscopicsurface area. The difference between the macroscopic surface area and

that as measured by adsorption might be due to microscopic, or sub-microscopic, cracks in the clinker grains. Surfaces of such cracks would

be measured by the adsorption method, but not by the other. Since such

49s! JOURNAL OF THE AMERICAN CONCRETE INSTITUTE December 1946

cracks have not been commonly reported, it seems more likely that thedifference is due to a slight coating of hydration products on the grainsurfaces. As shown above, an average cement shows about 9.3 x 106 sqcm per g of non-evaporable water. Hence, to account for the 7400sq cm difference between the two results, it is only necessary to assumethat the cement had “hydrated to the extent of

7400= 800 x 10-6g of non-evaporable water per g of cement,

9.3 x 106

or 0,08 percent of the weight of the cement. Such a small amount ofhydration could easily occur during the normal handling of a sampleduring humid weather.

Whether the true surface area of the cement is of the order of 3000or 10,000, it is clear that the initial surface area is negligible comparedwith that which finally develops,

THE SPECIFIC SURFACE OF STEAM-CURED PASTE

The effects of high-temperature steam-curing on the adsorption char-acteristics of cement paste were shown in Part 2, p. 300. In terms of theB,E.T. theory, the effects are as follows:

cVm, g/g of cement

V~, g/g dry paste

Sp. surface, sq cm per g of cement,millions

Sp. surface, sq cm per g of dry paste,millions

v./wn

‘w., glg Ofcement

R~~r~4i;

curing

15,4

0.037

0.032

1.32

1.15

0.241

0,1537

Ref. 14-6Steamcuring

20

0.0020

0.0018

0,071

0.062

0,012

0,1615

The figures for V~ and specific surface of the steam-cured specimenare probably not very ‘accurate because of the extreme smallness of theamounts of water taken up in the low-pressure range. The order ofmagnitude relative to the normally cured material is probably correct,however, The result indicates that all but about 5 percent of the colloidalmaterial was converted to the microcrystalline state by high-temperaturesteam curing.


w/Vm CURVES

The samples of hardened paste used in these studies contained unde-termined quantities of unhydrated material. Consequently, the weightof the adsorbent material could not be ascertained directly, a circumstancethat increases the difficulty of interpreting the adsorption data. Theproblem was simplified by expressing the amount of adsorption, w, interms of the surface area of the solid phase. Since the surface area isproportional to V~, the ratio w/V~ could be used without computing thesurface area.

Typical w/V~ curves are shown in Fig. 3-8. The uppermost curve

represents the paste in a mortar specimen having wtc = 0.587, cured sixmonths; the middle curve represents the paste from a richer mortar

specimen of the same age, w/c = 0.439. The lowest curve representsthe data given in the first group of Table 3-9. These data include water-cement ratios ranging from O.12* to 0.32 by weight. The table showsthat after long periods of curing and for w/c within this range, w/V~is virtually the same for all samples at all vapor pressures. (In the

lower range of pressures, w/ Vm is always the same for all samples exceptfor the effect of differences in C, t) The triangular points plotted inFig. 3-8 represent the average values from this group.

7, \ I 1 1

I. fief .-14, ./= - ,m?by Wf

6 —–.,, 9-!5,v.. .439A seeTOble 29 ond text

11Cured Wet /80 days

5 ------ -~

w/vm 4

3 -–-—-

1

0 ,1.7.3,45.6 .78 .910

P/P~

Fig. 3-8 (above>EKect of original w/con w/Vm curves

Fig. 3-9 (right>Effect of wet-curingon w/Vn curves P/P5

*This very dry paste was m~lded ,hy means of a press.tSee dmcuss]on m Part 4: Sigmficance of C of the B.ILT. Equation.”

TA

BL

E3-

9-T

YP

ICA

Lw

/va

tD

AT

A

Dat

aob

tain

edby

air-

stre

amm

etho

d,ex

~pt

asno

ted,

and

take

nfr

ompl

otte

dcu

rves

.

Ref

.N

o.C

emen

t25

4-N

o.

8-1

9-1

9-1

9-4

9-10

!2-1

3{J

-]3~.

1.j~

9-15

A*

2541

8”

Avg

.

1493

0J14

930J

1493

0J15

007J

1501

3J15

365

1536

515

365

1536

514

675

Net

w/c

.G9

.309

.316

.324

.319

.319

.244

.244

.12

9-14

1536

5.4

399-

1415

365

.439

9-14

1536

5.4

399-

1515

365

.587

2541

813

495

.44s

J1

*Dat

aob

tain

edby

high

-vac

uum

met

hod

~pp%

pW

8ter

mn?

ento

fsat

urat

ed,s

~Est

imat

ed.

vm

a,

Age

,dg

w/V

.at

valu

eof

pjp.

indi

cate

ddr

y—

——

——

——

—“

days

cpa

ste

0.4

0.5

0.6

0.7

0.8

0.9

0.95

SSD

t‘“

+.

——

——

——

Sam

ple

sfo

rw

tich

Vm

.z=

abou

t4V

m

447.

365

180

ML

)18

018

0

lZ 180

4yr

.

21 21 21 H 25 20 33 33 92

.045

.043

.042

.041

.043

.039

.041

.031

.031

.019

1.56

1.52

1.52

1.48

1.55

1.52

1.55

1.57

1.55

1.40

1.53

1.66

1.72

1.72

1.72

1.80

1.77

1.75

1.80

1.77

1.60

1.74

7

mpl

esfo

rw

hich

V.a

.>

4Vm

180

19.0

491.

5028

.046

1.52

i:.0

301.

55lJ

19.0

481.

557

yr.

.055

1.55

otin

clud

edin

aver

ages

)rf

ace-

dry

sam

ples

.

1.82

1.90

1.90

1.96

2.00

1.98

1.98

2.00

2.02

1.8Q

1.94

—,

—1.

752.

041.

802.

081.

852.

151.

802.

041.

751.

95

—.

2.05

2.12

2.12

2.23

2.17

2.25

z% 2.25

2.05

2.17

2.32

2.40

2.40

2.42

2.40

2.52

2.47

2.50

2.50

2.30

2.43

2.82

2.82

2.85

2.88

2.75

2.92

2.92

2.75

2.90

2.75

2.84

3.07

3.10

3.10

3.15

2.95

3.20

3.20

3.18

3.20

3.10

3.12

3.99

3.89

3.88

3.99

3.73

4.25

4.02

3..5

8

3.9

3.91

——

..

_2.

302.

653.

173.

605.

222.

352.

753.

403,

905.

852.

553.

054.

005.

258.

202.

343.

163.

203.

655.

232.

202.

502.

903.

254.

20

.88

.86

.86

.87

.86

.87

.87 — — — .867

—,.

WJC

.180

7.1

704

.162

0.1

8.35

.187

7.1

815

.178

9—

.155

4—

.89

.222

1.9

0.1

841

.91

.140

0—

——

—


In Fig. 3-9 the effect of prolonging the period of wet-curing on a given

paste is shown together with the lowest curve of Fig. 3-8 for comparison.

Minimum porosity and the cement-gel isotherm

Considering Fig. 3-8 and 3-9 together we may conclude that thedensest paste possible contains a pore-volume equal to the volume of thequantity of adsorbed water represented by about 4V~.

The shape of the lowest curve in Fig. 3-8 also seems to represent alimit that is approached as the pastes are made denser. Hence, forbrevity we will call the lower curve of Fig. 3-8 the cement-gel isothermor just gel-curve, when the meaning is clear. The part of the totalevaporable water equal to 4 V~ will be called gel water.

When a paste is such that at saturation it contains a quantity ofevaporable water equal to 4V ~, we may infer that all the originallywater-filled space has become filled with porous hydration products.Thus, in such a paste the space outside the unhydrated clinker residuehas only the porosity of the cement-gel itself.

When a paste is such that at saturation it contains a quantity of waterexceeding 4 V~, the excess over 4 V~ is believed to occupy residual spaceoutside the cement-gel. Water occupying this space is called capillarywater in this discussion. It should be understood that this distinctionbetween capillary water and gel-water is arbitrary, for some of the gel-water may be taken up by capdlary condensation and is thus not differentfrom the rest of the capillary water-so far as the mechanism of adsorptionis concerned. The distinction is justified by the fact that, in a saturatedpaste, the quantity of gel-water always bears the same ratio to theamount of gel, whereas the water called capillary water can be presentin any amount according to the porosity of the paste as a whole.

Fig. 3-8 and 3-9, which are typical of all other w/V~ curves obtained,show that among various samples any increase in pressure up to about0.45 p. is always accompanied by approximately the same increment of

adsorption, regardless of differences in porosity. * From this we mayinfer that the capillaries (the spaces outside the gel) do not begin tofill at pressures below about 0.45 p,. At higher pressures, however,a given increment in pressure will be accompanied by an increment ofadsorption that is larger the greater the porosity of the sample. Thismay be taken as direct evidence of capillary condensation. The amountof water held by capillary condensation at any given pressure is repre-sented by the vertical distance of the point in question above the gel-curve.

These ideas can be represented by a model such as is illustrated inFig. 3-10. In A the shaded areas represent cross sections of spherical

*Such differences w there maybe are due to differences in C of eq. (A), as is explained h Part 4.

496 JOURNAL OF THE AMERJCAN CONCRETE INSTITUTE December 1946

A B

Fig. 3-10

bodies of cement gel with non-colloidal particles (microcrystalline hy-drates and unreacted cement) embedded in them. Between the bodiesis interstitial space containing capilliry-condensed water, here picturedas lenses around the sphere-to-sphere contacts. The water content of thesystem is assumed to be below saturation, as indicated by the curvatureof the lenses. At saturation, the interstitial space would be filled withcapillary water, making the total water content equal to 4 V~ plus thevolume of capillary water.

Thus, if we consider the system pictured in Fig. 3-1OA to be the samplerepresented by the upper curve of Fig. 3-8, at equilibrium with thepressure p = 0.8 p,, the water content of the spheres (the gel-water)would be 2.44 V~, the capillary water would be 0.56 Vm, making a totalof 3.00 Vm. At saturation the gel-water would be 4V~ and the capillarywater 2.83 V~, making a total of 6.83 Vttt.

Fig. 3-1OB represents a paste at the same stage of hydration as thatrepresented in 3-1OA but with a lower original w/c. Here the spheres ofgel have merged into one body, eliminating all capillary water. Thelowest w/V~ curve in Fig. 3-8, the cement-gel isotherm, would correspondto this case.

Estimation of pore- and particle-size

With data obtained from specimens containing no capillary space (asdefined above) we can estimate the order of size of the elements of thesolid phase and of its characteristic pores. Pore-size can be estimatedfrom the hydraulic radius

Hydraulic radius = m =volume of pores

area of pore-walls

Pore volume is the space occupied by evaporable water and, in apaste without capillary space, this is equal to the volume of the gel~~:itcr, i.e., the volume of 4T7~. The area of the pore-walls is given by(!q. (6).

,s = 35.7 x 106 Vm


Hence,

4 vmvom.

35.7 x loWm

whereVO= specific volume of the gel-water.

It will be shown later than the specific volume of the gel-water is about0.90, Hence,

4 x 0.90m= = 10.01 x 10-8 cm35,7 x 106

or approximately 10A. *

The average size of a pore in the gel having a given hydraulic radiuscan be estimated by assuming that the cross section of the pore resemblesa rectangular slit, Let b, h, and L be the width, thickness, and length,respectively, of the slit. Then

hbL hb

m = (2h + 2b)L = 2(h + b)

Solutions of this equation for various values of h and b are given below:h=b ;m=l/4bh=2b ;m=l/3bh=4b ; m=4/10bh=lOb ; m = 10/22 bh = 100b ; m = 100/202 b

Thus, as h/b is made larger, m approaches ~ b as a limit. This meansthat the width of the pores is at least twice and at most four times thehydraulic radius. Since m was given as about 10~, it follows that the

average pore is from 20 to 40~ across, probably closer to 40A than to20~ if the particles are other than spherical.

The order of size of the colloidal particles cannot be computed directlybecause there is no way to correct for the volume of non-colloidal material,i.e., microcrystalline hydrates and unhydrated clinker. However, it isof interest to estimate the size without such correction since the volumeof non-colloidal hydrates is relatively small and data are available forsamples containing very little unhydrated clinker. The estimate is madeby finding the size of spheres in an aggregation of spheres that wouldhave the same total volume and surface area as dry hardened paste. Thesize of sphere is given by the relationship

3T=–s’

*A- Angstrom unit = 10J cm


wherer = radius of sphere in cmS = surface area in sq cm per cu cm

S = d,~where

dP = density of dry paste, g per cu cmand 8 = surface area of dry paste, sq cm per g,

For a typical paste cured at least 6 me.,dP = 2.44 g per cu cmS’ = 1.8 x 10s sq cm per g

3r= = 68 x 10-8cm,2,44 X 1,8 X 10E

say 70A.

This indicates that if the solid phase were an assemblage of equalspheres, each sphere would have a diameter of about 140~, The unitsof colloid material are probably smaller than this, but not very muchsmaller since most of the hydration product is colloidal and since therewas probably little unhydrated material in the specimen on which thisestimate is based.

These figures give a picture of a material made up of solid units averag-ing about 140A in diameter, with interstices averaging say 20 to 401%across. This should, of course, be taken only as an indication of theorder of size of the elements of the fine structure. It indicates, forexample, the necessary resolving power of a microscope capable of dif-ferentiating these features of hardened paste.

*****

It is hardly necessary to add that the authors hold no belief that thegel develops as spheres or that the pores are rectangular slits of uniformcross section. Those assumptions were made only for convenience ofillustration and computation. The bodies of hardened gel could be inthe form of submicroscopic plates, filaments, prisms, or of no regularform at all. However, as developed above, the evidence points to theconclusion that the gel is a solid having a characteristic porosity.

Data an reiative amounts of gel-water and capillary water

The relative amounts of gel-water and capillary water in saturatedsamples at various stages of hydration are shown in Fig. 3-11 and 3-12,for the materials of Series 254-9. The shaded portion of each columnrepresents gel-water and the open portion capillary water. These chartsbring out again the fact that for specimens of sufficiently low water-cement ratio, prolonged curing eliminates all capillary water.


In mveral instances there is an indication that the ratio of capillaryto gel-water increases after a minimum is reached. Whether this isreal or the result of experimental vagaries cannot be told without furtherexperiment, If it is real, it might be due to the leaching of soluble ma-terial from the paste during the curing period. Such leaching would beexpected to increase the porosity of the paste. It might also be due to acoarsening of the gel-texture by the formation of microcrystals at theexpense of colloids. If so, the change is of considerable significance,Present data warrant no conclusions on this point,

There is a rather definite indication that the gel is able to fill but alimited amount of space, regardless of the length of the curing period.This is brought out in Fig. 3-13, where w,/V~ (wC = evaporable water)at saturation is plotted against w/c for all specimens cured 180 days orlonger. This shows again that the minimum possible evaporable water

content is about 4Vn and further that all samples having original water-cement ratios greater than about 0.32 by weight will contain some

capillary water. The empirical relationship illustrated can be repre-

sented approximately by the equation

w,— = 12.2 (W/C – 0.32)v. 1W/C k 0,32

whereWCis the capillary-water content of specimens cured 6 months or more.

SUMMARY OF PART 3

Adsorption isotherms for water on hardened portland cement pastesshow the same characteristics as those for vapors on many differentorganic and inorganic materials,

The process of adsorption and the conditions for equilibrium are ex-plained in terms of the Brunauer-Emmett-Teller (B.E. T.) theory andthe capillary condensation theory.

The B.E.T. eq. (A) is used for representing data over the range p =0,05 p, to 0.45 p,. The equation is

w------- —.v. (l–z)(:– z--cz) ””””””””””’”””””””” ‘“”””

where

(A)

w = weight of evaporable water held at equilibrium with pressure p,

V~ = quantity of water required for a complete condensed layer onthe solid, the layer being 1 molecule deep on the average,

C = a constant related to the heat of adsorption,x = p/p, where p, = saturation pressure and p the existing pressure.

500 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE December _1946

cement 14930 J, - ,

‘r—————— -18

1 ‘“L- 0.30917

lb

15

II -

K 10-&

9-

‘9-

7-

6 -

5-

4 -

3

2 -

1

0-

11(-

14m54mla9447

RerN.9-I

Cement 15013 J. – C

“r—————13-

~~-0.324!2-

II -

10 -

9 -~“Vm * .

2

RevNo9-10

S 2?.7, C*S 55.8, C,A 6.1, C,AF

~/c. 0.424

jp,Surf, 2040 cm~g

I

).573 (b+!Wo

8:

Age in Daysnef, No. 9.2

39.4, CZS 296, C,.4 139, 1

‘%. 0.443

Rm NU9.3

IF 7.2, Sp. surt 1800 cm~g

7 14 28 % 90 1?4

Fig. 3-11 —Effect of hydration on w/V~

RefNc,9-12

Notw Figuresover columns are compressive strengths of ‘l-in. cube$, psi.


cement 8so07J. - Q ~aO, c,s 291, c>A613 c.Ar 1°5. ‘D ‘Urf 20!5 cmy9.II

‘$.0,316 ~ * ‘YC”Q433m i i ,w@’””

—. I

-w_Vm

Am in De..Qef N. 9.. L, N. 9.5”

cement !5011$,,

r

‘Z-0316,3

,2

!,

,0

,

8- i

*W

6

5

.

3

2

v

451, C,s 29.1, C,.467,

‘YC.043Z

;.

Age in DaysRef. . 9-6 9.,N.,.9

rl.r N. ,-7

&

Vm

Fig. 3-1 %—--Effect of hydration on w/V~Note: Figure! over columnsare comrwesslvestrengths0[ %lni cubes, Psi.


II

10E

>9 -

\

f’ (j

0- --!

~7 -y

$60

al c1

Z5 -~

●0 0

0n4 Q

m 8 ~“;3 -—gz

1-1 -

0 ;0.1 0.2

‘/c (b~Weigh~”4 0“5 0.4Fig, 3-1 3—Empirical relationship between total evaporabie water perunit V~ and ariginal water-cement ratio for samples cured 180 days

ar longer

V~ and C can be readily evaluated from experimental data and p,is a constant depending on temperature. C is about the same for allpastes. Hence differences in adsorption characteristics are indicated bydifferences in V~.

The non-evaporable water content, w~, is regarded as proportionalto the total amount of hydration products. Since Vm is proportional to

surface area and since practically all the surface is that of the colloids,V~ is considered to be proportional to the colloidal material (gel) only.

The ratio VJw. is considered to be a constant for any given cement.lt is influenced by compound composition about as follows:

v.— = 0.00230 (%C&) + 0.00320 (%C,tl) + 0.00317 (%C,A) +w.

0.00368 (~oC&’)Among the different types of cement VJW. varies from about 0.24 to

0.28.

The above equation implies that the hydrate of each compound iscolloidal or at least that all compounds occur as constituents of a com-plex colloidal hydrate.

The specific surface of hardened paste can be computed from therelationship S = 35,7 x 106 Vm. It increases with the period of curingand reaches about 2 million sq cm per g of original cement.


The specific surface of the hardened paste is related to w. as follows:

s– = 35.’? x 106 ii,Wn

where lc is a constant for a given cement. Among the different typesof cements, S/wn ranges from about 8.6 x 106to 10 x 106.

None of the relationships given above apply to paste cured at hightemperature. Under steam pressure a sample cured 6 hours at 420 Fshowed only 0.07 x 106 sq cm of surface per g of cement, as comparedwith 1.3 x 106for a paste cured 28 days, or about 2.0 x 106for long curing,at room temperature.

When adsorption data are expressed in terms of w/V~ and p/p,, theresult is an isotherm based on the relative amount of gel. Such curvesare virtually identical for all cement pastes over the pressure range p =0.05 p, to 0.45 p,.

For pastes in which the total evaporable water content is about 4V~,the curves are identical for the whole pressure range.

For pastes having capacity for evaporable water exceeding 4V~, theexcess is taken up over the pressure range p = 0.45 p, to p = p,.

The evaporable-water capacity is smaller the lower the original water-cement ratio and the longer the period of curing, but it cannot be re-duced below about 4V~.

Evaporable water in excess of 4 V~ is believed to occupy interstitialspace not filled by gel or other hydration products. The water in thisspace is called capillary water. The rest of the evaporable water is heldwithin the characteristic voids of the gel and is called gel water eventhough some of it might have been taken up by capillary condensation,

When the total evaporable-water capacity = 4V~, the specimen con-tains no space for capillary water.

From the surface area of the solid phase, and its characteristic porosity,the average pore in the densest possible hardened paste is estimated tobe from 20 to 40~ across.

From the volume of the solid phase and its surface area, the orderof particle size, expressed as sphere diameter, is estimated at 140~.

Data on the relative amounts of gel-water and capillary water invarious samples are given graphically,

REFERENCES

(1) A.M. Gaudin and F. W. Bowdish, Mining Technology,v. 8 (3) pp. 1-6 (1944).(2) L. A. Wooten and Callaway Brown, J. Am. Chem. Sot. v. 65, p. 113 (1943).(3) H. Cassel, Trans. Faruday A’30c.v. 28, p. 177. (1932). Quoted by Brunauer in

Ref. 5, p..289.


(4) D. M. Cans, M. S. Brooks, and G, E. Boyd, Znd. Eng. (Xem (Anal. Ed.) v. 14,p. 396 (1942).

(5) Stephen Brunauer, The Adsorption of Gases and Vapor:, Vol. 1, Princeton Uni-versity Press (1943).

(6) J. W. McBain and John Ferguson, J. Ph~s. Chern. v. 31, p. 564 (1927).(7) Urquhart and Williams, J. Teztile Inst. v. 40, p. T439 (1924).(8) S. E. Shephard and l?. T. Newsome, Ind. En.g. Chem. v. 26, p. 285 (1943).(9) L. M. Pidgeon and A. Van Winsen, Can. J. Re8. v. 9, p. 153 (1933).(10) E. Filby and 0. Maass, Can J. Res. V. 13, Sec. B., p. 5 (1935).(11) C. 0. Seborg, F. A. Simmonds, and P. K. Baird, Znd. Eng. Chern.v. 28, p. 1245

(1936).(12) W. R. Smith, F. S, Thornhill, and R. I. Bray, Ind. E~. Chem. v. 33, p. 1303

(1941).(13) K, S. Rae, J. Phys. Chem., v. 45, p. 500 (1941).(14) V. L. Simril and Sherman Smith, Znd. Eng. Chem. v. 34, p. 226 (1942).(15) V. R, Dietz and L. F. Gleysteen, J. Res., Natl, Bur. of Stds. v. 29, p. 191 (1942).(16) J. D. Babbitt, Can, J, Res. v. 20, p. 143 (1942),(17) L. A. Reyerson and Cyrus Bemmels, J. Phys. Chem. v. 46, p, 31 (1942).(18) Henry B. Hull, J, Am. Chem. So., v. 66, p. 1499 (1944).(19) Lyle T. Alexander and M. M, Haring, J. Phys. Chem. v. 40, p. 195 (1936).(20) J. B, Speakman, Trans. Faraday Sot, v. 40, p. 6 (1944),(21) S. Brunauer, P. H, .Emmett, and E, Teller, J. Am. Chem. Sot. v. 60, p. 309

(1938).(22) S. Brunauer, L. S. Deming, W. E. Deming, and E. Teller, J. Am. Chem, Sot.

V. 62, p. 1723 (1940).(23) Gerald Pickett, J. Am. Chem. Sot. v. 67, p. 1958 (1945).(24) E, Freyssinet, Science et Industr-ie (Jan. 1933).(25) P. H. Emmett, Ind. Eng, Chem. v. 37, p. 639 (1945).(26) Ref. 5, p. 168.(27) W, D. Harkins and G, Jura, J. Chem. Phys. v. 11, p. 560 (1943) and J. Am.

Chem. Sot. v. 66, p. 919 (1944).(28) International Critical Tables, Vol. HI. For iVaOH, pp. 296 and 369. For

KOH, pp. 298and 373.(29) R. H. Bogue and Wm. Lerch, Ind. Eng. Chem. v. 26, p. 837 (1934), or Paper

No. . 27, Portland Cement Association Fellowship, National Bureau of Standards,Washington, ‘D. C.

(30) H. K. Livingston, J. Am. Chem. Sot. v, 66, p. 569-73 (1944).(31) P. H. Emmett, Aduance.s in Colloid Science, Interscience Publishers, Inc., New

York, 1942, p. 6.(32) Wm. D. Harkins and Gee. Jura, J. Chem. Phys. v. 11, p. 431 (1943).(33) P. H. Emmett, Symposium on New Methods for Particle-Size Determination

in the Subsieve Range, p. 95, A.S.T. M. Publication, 1941.(34) P. H. Emmett and T. DeWitt, lnd. Eng. Chem. (Anal. Ed.) v. 13, p. 28 (1941),


Part 4. The Thermodynamics of Adsorption of Water on Hardened Paste

CONTENTS

Theheat of adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...550

Thenetheat of adsorption .,...... . .,.,,,,..,.,....,..,.,,.,.,.551Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551Evaluation of total net heat of capillary condensation. , , . . . ., , 551Evaluation of total net heat of surface adsorption. ., . . 552Thetotal netheat of adsorption.. . . . . . . . . . . . . . . . . . . . . . . . . . . 552Net heat of adsorption and heat of wetting. . . . . . . . . . . . ., , . . . 553

Measurement ofnetheat of adsorption. . . . . . . . . . . . . . . . . . . . . . . . . . 553

Materials and procedure, .,.,.,... .,, .,,,,..,,,,.,.,,...,,.553

Experimental results., . . . . . . . . . . . . . ., . . . . . . . . . . . . . . . . . . . ...555

Comparison of net heat of adsorption of water by cement pastewith that ofwater on other solids. . . . . . . . . . . . . . . . . . . . . . . . . 559

Comparison of heat of hydration with net heat of adsorption. . 559

The free-energy and entropy changes of adsorption.. ., . . . . . . . 563Underlying concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...563Internal energy . . . . . . . . . . . . . . . . . . ., ...,,,.....,..,....,...565Enl,halpy, free energy, and unavailable energy, ., . . . . . ., . . . 565

Relationship between net heat of adsorption and decreases in in-ternal energy, enthalpyj free energy, and entropy. . . . . . . . ., . 567

Relationship between change in vapor pressure and change in freeenergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567

Estimation of decrease in entropy from experimental results, . . . 568

Significance ofchange in entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571

The energy of binding of water in hardened paste. . . . . . . . . 574

550 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE January 1947

Net heat of adsorption and C of the B.E.T. eq. (A) . . . . . . . . . . . . ...577

Swelling pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...578

Limited-swelling gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...578Idealized cement gel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...579

Derivation of equation for swelling force. . . . . . . . . . . . . . . . . . . . .579

Relation of idealized behavior to that of cement paste or concrete, 582

Mechanism ofshrinking and swelling. . . . . . . . . . . . . . . . . . . . . . . . . ...582

Volume change as a liquid-adsorption phenomenon. . . . . . . . . ...582

Volume change as a capillary phenomenon. . . . . . . . . . . . . . . . ...584

Relationship between change in volume and change in watercontent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..587

Capillary flow and moisture diffusion. . . . . . . . . . . . . . . . . . . . . . . . . ...588Inequalities in free energy . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . ...589

Effect of temperature changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...589

Effect onswelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...590

Effect on diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...591

Combined effect of stress, strain, and temperature gradients, . ..591

Summary of Part 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...592

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...595

This discussion pertains to the energy changes that take place whenwater is adsorbed by hardened cement paste. The relationship of thesechanges to such physical effects as shrinking and swelling, capillaryflow, and moisture diffusion will be considered briefly. Comparisonsare made of the energy of binding of evaporable and non-evaporablewater. Ana,lysis of the energy changes into the two main forms of energyand consideration of the relative amounts of each are of interest in con-nection with the question of the extent to which water is modified whenit is adsorbed on the solid.

THE HEAT OF ADSORPTION

As pointed out in Part 3, the adsorption of a vapor by a solid can belikened to the process of condensation both with respect to the kineticsof the process and the nature of the forces involved. Therefore, it mightbe expected that the heat liberated when the vapor is adsorbed wouldbe comparable to the heat of liquefaction of the vapor. When thecomparison is made, it is usually found that the heat of adsorptionexceeds the heat of liquefaction. In the adsorption of water vapor onhardened cement paste, the heat of adsorption for the first incrementsof water added exceeds the heat of liquefaction by about 65 percent of


the latter. This excess can be attributed, directly or indirectly, tointeraction of the adsorbed molecules with the surface of the solid,

DefinitionsTHE NET HEAT OF ADSORPTION

The excess of the heat of adsorption over the heat of liquefaction iscalled the net heat of ad807ption. If Q represents the heat of adsorptionand QL the heat of liquefaction, then Qa, the net heat of adsorption, isdefined by,

Q. = Q- QL.,.., . . . . . . . . . . . . . . . . ...(l)The definition just given amounts to regarding the adsorption of

the vapor as a two-step process, as follows:

(1) Vapor at the saturation pressure, P,, condenses to liquid, therebyliberating the heat of liquefaction, QL.

(2) The liquid water is then adsorbed, liberating the net heat ofadsorption, Q.. In this step, the water comes to equilibriumwith vapor at a lower pressure, p.

As pointed out before (Part 3), the free surface energy of the solidand the free surface energy of the condensed liquid must both be causesof adsorption in a porous solid such as hardened paste. Hence, the netheat of adsorption must have its origin in at least two sources. At lowvapor pressures, the net heat of adsorption has its origin in the inter-action of the adsorbed molecules with the solid surface. When thepressure is increased above 0.45 p,, where capillary condensation becomesa factor, the surface of the water film formed at lower pressures diminishesand becomes zero, or nearly zero, at saturation. The destruction of thewater surface is accompanied by the liberation of the heat of water-~urface formation. Thus, the net heat of adsorption is the sum of twoterms, the net heat of surface adsorption and the net heat of capilla7ycondensation. That is,

Qa=Qs+Qc)......(2)where

Q. = net heat of adsorption,

Q, = net heat of surface adsorption, andQ. = net ‘heat of capillary condensation,

Evaluation of total net heat of capillary condensation

The total amount of heat arising from the destruction of water surface,ie., the total net heat of capillary condensation, when the paste goesfrom the dry to the saturated condition can be evaluated by means ofthe following considerations.

It may be assumed that the maximum extent of water surface is thearea of the solid surface. It would seem, however, thfi I, ti.is maximum

55$? JOURNAL OF THE AMERICAN CONCRETE INSTITUTE January 1947

could not exist at any vapor pressure. At low vapor pressure, the filmwould be incomplete, even when V., g are present, because of the chancedistribution of molecules among the layers described in the B.E.T.theory. At higher pressure, the water film would be partly destroyedby capillary condensation. At saturation the water surface would dis-appear completely except for a negligible area about equal to the super-ficial area of the granules composing the sample. Nevertheless, eachllnit of solid surface was covered by a water film at some stage prior tothe elimination of the film surface, and the total net heat of capillarycondensation should be the same as if the formation of the, wat& surfaceand its disappearance occurred consecutively.

In accordance with the assumption just stated, the total net heatof capillary condensation, Q,l, is

Qct=shc , . . . . . . . . . . . . . . . . . . . . . . . ...(3)where S = internal surface area of paste, sq cm, and

h, = heat of water-surface formation, cal per sq cm.

According to Harkins and Jura,f’j h, = 118,5 ergs per sq cm at 25 C, or118,5 X 2.39 X 10-8 = 2.83 X 10-8 cal per sq cm,. Also by eq. (6) ofPart 3,

S = 35.7 X 10’ V~ sq cm.

Therefore,

Q,, = 2.83 X 10-’ X 35.7 X 10’ X V~–lOIV~, saylOOV~cal . . . . . . . . . . . . . . . . . . . . . . . . ...(4)—

Evaluation of total net heat of surface adsorption

The total amount of heat arising from the interaction of the adsorbedmolecules with the solid surface, i.e., the total net heat of surface ad-sorption is given by

Q,, =l% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(5)

where Q,~ = total net heat of surface adsorption, cal per g of paste,S = internal surface area of paste, sq cm per g of paste, andhd = total net heat of surface adsorption, cal per cm2of paste.

Hence,Qs~=35.7x 10’vJ, . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(6)

If it can be assumed that h, is the same for all pastes, and this is a reason-able assumption that will be used, then

Q3 = Const = ~Vm “ ““” ””””””””””””””””””””””’”’””””’”

. (7)

The totol net heat of adsorption

The total net heat of adsorption will be the sum of the total net heat ofsurface adsorption and the total net heat of capillary condensation.


Thus,

Qat=Qet +Qct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(8)= kv. + 100V. = (k + 100)V?II

*******

At low vapor pressures, only the net heat of surface adsorption ap-pears. At higher pressures the net heat of capillary condensation alsoappears. There isat present no basis forevaluating either term at anystage short of saturation.

*******

Net heat of adsorption and heat of wetting

When adsorption is considered to bethe two-step process mentionedabove, step (2) immediately suggests a comparison of the net heat ofadsorption with the heat of wetting.

Distinction must be made between the heat evolved when a solidsurface is immersed in a body of liquid and the heat evolved when the,surface is wetted by causing a film to spread over the surface. The heatof immersion exceeds the heat of spreading-wetting by the heat offormation of water surface.

The total net heat of adsorption, Qa~, must be very nearly if notactually, equal to the heat of immersion of the hardened paste. Thisfollows because the water surface at saturation is virtually zero, aspointed out above. This means that if a sample of hardened paste isbrought to saturation by adsorption of vapor no measurable amountof heat will be evolved if it is immersed in water.

The net heat of surface adsorption is comparable to the heat of spread-ing-wetting. If the thickness of the film is not a factor, i.e., if the inter-action of the adsorbed molecules with the solid surface affects only thefirst layer of molecules adsorbed, the net heat of surface adsorption isstrictly comparable to the heat of spreading-wetting, except for thepossible effect of narrow crevices. (In cement gel, s~me water may beheld in crevices so narrow that a water surface cannot form.) If thethickness of the film is a factor, the net heat of surface adsorption differsfrom the heat of spreading-wetting but the amount of the differencecannot be evaluated. However, the total net heat of suriace adsorptionshould be equal to the heat of spreading-wetting of what may be calleda complete film, i.e., a film so thick that the effect of interaction at thesolid surface is no longer evident.

MEASUREMENT OF NET HEAT OF ADSORPTION

Materials and procedure

The net heat of adsorption was. measured, using two different hardenedpastes. From each paste twelve granular samples were prepared by

5.54 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE January 1947

P/P5

9

8

7

b

5

/w Vm

A

~LC;yt v,. 9/9 ‘n

dry cement 9/9 cmtpost?

—/6[86 0.0417 0.0502 0,205

16[89 0,0307 0.0355 0.155

Fig. 4-1 (abave~Adsorption isotherms ofsamples used for heat of adsorption

measurements.

Fig. 4-2 (right)-w/Vm curves for thesamples used in heat of adsorption mecssure-

ments.Data from Tables 4-1 and 4-$!.

P/P,

first removing the evaporable water and then exposing the samples todifferent humidified air streams according to the method already de-scribed (Part 2).

When the samples had reached equilibrium, each was sealed in aseparate glass ampoule, each of the twelve samples from a given pastebeing at equilibrium with a different vapor pressure. Such sampleswere prepared in triplicate.

The adsorption isotherms are shown in Fig. 4-1. The total watercontents are plotted in order to show also the non-evaporable watercontents. The values for p/p, = 1.0, which ordinarily represent thewater contents at saturation, were not measured for these samples; thepoints shown for this pressure represent the water contents before thesamples were dried the first time.

w/V~ curves are given in Fig. 4-2. The broken line is the curve forcement-gel, as discussed in Part 3. Both pastes evidently containedspace for capillary water.

The heat of adsorption was measured by the same heat-of-solutionprocedure that is used for measuring the heat of hydration of cement. *The procedure is first to dissolve the dry paste, measuring the heat

*Federal Specification SSC-158a-Seo. 31.


evolved, and then to dissolve a similar sample of paste containing ad-sorbed water. The indicated reactions. are

Paste + acid-solution + nHzO ~ solution of pasteHeat evolved = QOcal per g of dry paste. . . . . . . . . . . (9)

Paste + nHzO + Paste.nH20Heat evolved = Q. cal per g of dry paste. . . . . . . . . . (Iti)

Paste.nHzO + acid-solution ~ solution of pasteHeat evolved = Q, cal per g of dry paste. . . . . . . . . .(11)

wherePaste = dried paste

Q. = heat of solution of dry pasteQ, = heat of solution of paste containing n grams of

evaporable waterQ= = net heat of adsorption.

By Hess’s law,

Qa=Qo–Qp......... (12)This process, in effect, transfers the adsorbed water from the sample tothe solution. Hence, the heat of vaporization does not appear and, on theassumption that the heat of solution of the adsorbed water in the acid iszero, the method may be regarded as giving the net heat of adsorptiondirectly. *

The heat-of-solution method was adopted mainly because at the timethe project was planned the heat-of-solution calorimeter was alreadyset up. The results obtained are not altogether satisfactor~-, for inseveral cases the variation in the observed net heat of adsorption amongcompanion samples was as great as or greater than the difference in heatcontent due to differences in adsorbed-water content. This results insome uncertainty as to whether certain observed differences are sig-nificant or not.

It should be noted that eq. (12) does not take into account the factthat Qo and QP may represent the heats of solution of samples con-taining different amounts of adsorbed air. This inaccuracy must beaccepted, for we have no knowledge of the change in adsorbed air con-tent, or of its heat of resorption. However, the inaccuracy is probablysmall, owing to the relative smallness of the amount of air adsorbed atroom temperature under a pressure of 1 atmosphere.

Experimental results

The experimental results are recorded in Tables 4-1 and 4-2. In Fig.4-3 the net heats of adsorption are plotted against the equilibrium vaporpressures of the respective samples of each of the two cement pastes.They are plotted in this way to facilitate estimating the total net heats

*The small heat eflect of charging n moles of water vapor from pressure p, to P is considered negligible.


TABLE 4-1—ADSORPTION AND HEAT OF ADSORPTION DATA FORPASTE MADE WITH CEMENT 16186

0.50 (and C

P /P*

o

.081

,161

.322

.39

.46

.53

.60

.70

.81

,88

.96

1.0 I

ted wt.,)9 days.

~

Original w/caverage of A, 1

Sa#$e

ot corrected for bleeding). Ref. 16-OIA,Heat of mlutior af orig. cement = 623 cal

-

nnd C. V~ = 0.0502 g/g ig]I Ignited wt. Am at test-27 !x

Wateradeorbed

-

[eat ofdutioncal /gCn. wt

537.5539.0538.0

538,2

525,4527,1

526.2

523.2525.2

524.2

520.6521,3

G

z518.9518.9

519.3

519.5520.8519.3

519,9——519.1520.1516.9

618.7

517.5519.1——518.3

517.9516.5515.7

516.7

515.6516.6

516.1

513.9515.0——514.4

510.0514.3509.8

511,4

509.5+

Net heat ofadsorption

cal~~of:.—dry ign.

paate wt.

dw,)f :

ign.wt.

.2031

.2051

.2042

.2041’

T

KYEvap.watm!3/KIgn.wt.

da—.dry

mate

of:

ign.wt.

Wfvm

o

0.76

drypasta . —

o 000 :

-6- T-

A-12 ,2aB-24 .2aCt

.1688

.1702,1696

.1695

000

G---00Avg.

239

A-11AB-23a

.2010

.2014.2418.2427

.0322

.0312.0387.0376

9.6 12.29.5 11.8

Avg. .2012

.2092

.2091

.2422

.2517

.2520

.0381 .0317 .0381

A-7aB-19a

.0404

.0389.0486.0469

GZ

11.4 14.311.0 13,8

Avg. .2092

.2258

.2254

.2518 .0477 .0396 279

242

0.95

1.37

A-9aB-21a

.2717

.2716

.2716

.2810

.2813

.2832

.0370

.0552.0686.0665

.0676

.0779

.0762

.0790

.0777

13.3 16,913,8 17.6

13.5 m—_

Avg. .2256

.2336

.2334

.2352

.0675

.0777

.0859

.0950

.1024.—

.1243——

.1507

.0561

.0648

.0632

.0656

A-10aB-22ac-log

13.7 17.515.7 20.115,0 19.2

14.7 G.0645Avg.

A-8aB-20aC-%

.2340

.2399

.2397

.2428

.2818

,2886.2889.2924

1.55

1.71

1.89

376

.0711

.0695

.0732

.0855,0838.0882

.0358

.0956

.0929

.0963

14.0 18.014.1 18.214.5 18.8

G3 GAvg.

A-laB-13aGlg

.2408

,2483.2473.2496

.G——.2550.2541

.2900

.2987

.2980

.3005

.0713

.0795

.0771

.0800

364——14.2 18,414.6 18.916.3 21,2

ii; xi— —15.3 20.015.2 19.9

Avg. .2991.—.3068.3062

.0789

.0862

.0839

.0949

.1037

.1011

388

A-3aB-17a

Avg. .2546 .3065 .0350

.1033

.1012

.1044

.1024

.1249

.1220

.1258

2.04

2.48

3.00

3.48

4.28

398

428——

442.—

474

534

—.14.8 19,617,0 22.516.8 22.3

A-4aB-16ac+

.2726

.2714

.2740

,3280.3271,3300

Avg. . 272? .3284 .1031 .1242

.1523,1490

.1266

.1236

—l—————A-2aB-14a

.2954

.2938

.2946

.3554

.3541

z

16.2 21.916.5 22.4

.1251Avg.

A-3aB-15a

.1506I

17.1 23.717.5 24.0

.3175

.3121.3820.3761

.1487

.1419

.1453

.1789

.1710

.1750 F31Z8Avg. .3148

.3477

.3431

.3522

.3790

.4183

.4135,4241

.1749

.1789

.1729

.1826

.1781

—

r from il

. —19.4 27.517.5 24.719.8 28.2

A-hB-18aC-6g

Avg.

,2152.2084.2199

.2145.3477

.3997

.4002

.3976

,3992

.4186

.481

.2145— —

I5,5Avg.

*Non-evapo,277 .277 – I 28.71 572$

nition loss; no dry sample available. $Ei ,imatedmated graphica


TABLE 442—ADSORPTION AND HEAT OFPASTE MADE WITH CEMI

= 0.5 (not corrected for bleechng). Ref. 16-02Aand C. Heat of solution of mi~ sement = 606 ct

ADSORPTION DATA FOR4T 16189B, and C. V~ = 0.0355 g/g [email protected] wt.,/gignitedwt. Ageat test42 to 44days.

Original w,averarce of A.

Net heat of ITotal ter

bed,of:

ign.wt.

o00

F-’-

ads(

Cal

drypaate

000

%-

ption IHeatgoluti[

cal/@Ign. w

542.:546. i546. t

G

z539,1540, f

G

Li534, C537 .(

G

z535.4

(47—.dry

paate

er,of:

m

: of:&

ign. v.wt.

w/v,P/P

—

o

ign.Wt.

drypfkst(

. 137E

.1340

.1336

.1350

.1602,1557,1562

.1574

.1682

.1634,1641

,1652—-

,1741.1757

G——-

,1803.1813

.1810——.1905.1857.1876

.1879

.1943

.1907

.1914

.1921

.2011

.1976

.1984

XG.—.2153.2149.2145

.2149

.2333

.2385

.2384

.2635

.2572

.2604

.3062,3058.3003

.3041

.3991

.3372

.3894

G

:0

i--x

.021{

. 022{

ZE

G.030!.030

.030i

.0401

.0421

A-24.2gB-12.2cCt

Avg.

.1594,1547.1542

——,1501

.1847

.1798

.1803

.1816

-6-0

,025:

.0349

.0458

.0539

0

lea—.—

268.—

327——.

360

375———

380

406—-—

456

501——

535

552

572$

timd.ed

.0253

.0251

.0261

G

.0356

.0340

.0348

.0348

5.15.95.1

x0.72.081—-

.161—

.322—.

,39—

.46

A-19gB-70C-19C

.1950

.1887

.1894

G

.2010,2028

Avg. 0.98

1.34

1.54

1.72

1.36

2,03

2.60

3.40

4,15

5,50

B-9oC-21O

,0463.0486

.0474

.0535

.0556

.0546

.0515,0597.0623

Avg.———B-1OCC-22C

Avg.

.2019.—.2082.2098

.0411

.046:, 048;

.0472

053(.0517. 054C

534.7

G534.1

533.5

G533,2532.6

531.7

528.7532.2533.6

9,6

10,910,3

G

11.6

13.1EL 5

G13.013.013,9

.2090

,2209,2144.2165

A-20gB-80C-20C

10.610,711.4

Avg.

z13g ‘–B-1oC-13C

.2173

.2253

.2202,2209

.2221

.2331

.2282

.2290

.2301

.2496

.2482

.2476

.2485

.2752

.2753

.0612 .0529

,0568,0.567.0578

.0612

.0659

.0655

.0667

.0660.—.0737.0735.0748

10,9

11.011.410.6

13,514.013.0

Avg. .53—

.60

.70—

.81—

.88

.0660-—

.0740

.—

.0924

.1191

.1445

.1965

.2983

.0571

,0636.0636.0648

531,5

527.7

5G.4

530,0

526.6529.0530.7

11.0

11.8

1~6

13.5

14,5

112

14.4

A-17gB-5cC-17C

Avg. .0640

G.0809.0810

.0799

z.1049

.1046

.1295

.1246

.1270

.1697

.1718

.1669

.1695

—

.0740

.0902

.0935

.0934

=

.1205

.1211

.1208

.1496

.1447

11.7

12.513,712.7

13.0

14.014.0

15.617.115.8

A-16gB-4cC-160

Avg. 528.8——528,2528.8

528.5

526.7537. a

526.7

518.9526.8523,3

525.0

16.2

B-2cC-14C

Avg.——B-3.C-15C

.2752

.3043

.2969

14.0

14.914.4

G

17,2114.314.7

G

17.8

Avg. .3006 .1472

.1966

.1984

.1924

19.0

A-18gB-6CC-18C

,3550,3531.3466

.3516

,4627.4489.4515

X14

Avg. .96—

1.0—

.1958

.298

19.6

ABtc

Avg.

*Non-evapo

8.65 —ivaih

—ble water. tE mated graphic~ y from ]ition loan; no


P/Ps

Fig. 4-3 (left)-Heat of adsorption vs.relative vapor pressure.

Data from Tables 4-1 and4.%

Fig, 4-4 (above)--& vs. P/p,

m

P/Ps

adsorption for the saturated samples, which were not measured,ofThe terminus of the lower curve was e~timated to be at 20.3 cal per g ofignited weight. Then, in accordance with eq, (8) the total net heat ofadsorption was assumed to be proportional to V~ and the terminus ofthe upper curve estimated on this basis. That is,

(Q.t)I _ (Qat)2—— —(Vm)l (V?J2

From the data given in Fig, 4-3 and from the estimated value of (Q.,) Iwe have the following:

(Q.JI = 20.3 cal per g ign. wt.(Vm)l = 0.0355 g per g ign. wt.(Vm)2 = 0.0502 g per g ign. wt.

Hence,

(Q.t) JWJ 1 = 20.3/0.0355 = 572 Cal w’ gand

(Q~Jz = 572 X 0.0502 = 28.7 cal per gReference to the upper curve of Fig. 4-3 will show that this estimateresults in a reasonable terminus for that curve.

According to the discussion leading up to eq. (8) the amount of heatevolved by adsorption at a given pressure should be proportional, ornearly so, to the amount of surface covered at that pressure. Accordingto the B.E,T. theory, the fraction of the total surface that is coveredat a given relative vapor pressure is the same for all absorbents havingthe same value for the constant C. This could be strictly true onlyin the absence of capillary condensation, unless the various absorbentshad pores of exactly the same size and shape. Thus, at least for the lowpressure range, ~re could predict from theory that the relationship be-


tween Q*/ V~ and p/p, should be the same for both samples, at least UP to

P = 0.45 p,.The relationship found between QJV~ and P/Pt for the two cement

pastes is shown in Fig. 4-4, If pIotted separately the two series ofpoints would be judged to describe different curves. However, in viewof the possibility of considerable experimental error, it is doubtfulwhether the differences are significant, at least in the lower range ofpressures. At any rate, dhlerences in the lower range cannot be accountedfor on the basis of current theory, In the upper range the separationof the curves might be due to a difference in size and shape of the poresand hence to a difference in the rate of change of water surface withchange in pressure, The curves as drawn indicate that only those pores,or those parts of the pores, that fill at pressures above 0.6 p, differ insize and shape.

Comparison of not heat of adsorption of water by comwrt paste with that of water onothor solids

The total net heat of adsorption, Qat, was estimated above to be 572 V~.

Since V~ = 35 ~ ~ ~od, the heat per unit of surface =572

35.7 x 108

= 16 x 10-8cal per sq cm of solid surface or 16 X 10-? X 4.18 X 107 =670 ergs per sq cm of solid surface. Harkins and Boyd(2J measured theheats of immersion in liquid water of several different solids. The resultswere as follows:

Bai5’Od 49o ergs per sq cm of solid surfaceTiOZ 520Si 580sio2 600ZT02 600A’nOz 680ZrSi04 850

Graphite 265It is evident that the total net heat of adsorption for water in

hardened cement paste is about the same as the heat of immersion ofvarious non-porous minerals. As brought out before, the heat of im-mersion per sq cm of surface of these minerals should be about equalto their total net heats of adsorption per unit of surface if they wereporous absorbents.

Comparison of heat of hydration with net heat of adsorption

In another project, W. C. Hansen* measured the non-evaporable watercontents and the heats of hydration on a group of 27 commercial cementscomprising all types, The samples were neat pastes, W[C = 0.40 by

*Formerly of PCA laborat ory. At present, Manager, Research Laboratories, Universal AthM Cement Co.


Ea) 2’Ea) ,20 -u

Q-0 .!807Lal .16 -a

~ .!4 -

<

$ .12 -

~.

al.10 -

,: .08-

~: .06 -

Lom .04 -

:? .02-

. 2800y3

5 + Sf+’ronthsZo

&’eat %Hy#atio~~ cala~er $~e~~nt

Fig, 4-5—Relationship between heat of hydration and non-evaporable water.

630

k

:--- .-.=w~=- ‘=- ‘-wr- ‘-–*

g

‘:~!~::”o .10 .20 .30 .40 .50

Water Content - g per g ignited sample

Fig. 4-6—Heat of solutiarr data for pastes made with cement 16186.

Data fromTable 4-1.


630 1 r f r ,I I I

fi - -~.--wt-+--+-t-.___ ye_____ t_+_T+_

Q1

“: 590 -.-> 580 Mm+of

0)% ydrafion

L 5.70-al

:560 \/( z)

(J \ [‘ 5s0 ,c0 \ \ --- ------ -—-—- ---- .- --

“< 540\

Nef% 520 Cal/g >Heof ofz 530 - - Adsorptiono ,

--———. -—r

_- .-- ——- .—--

~ 520u ‘Esfimofed

= 510-i

500J ! I ! I I I 1 I.10 .20 .30 .40 .s0

Water Content -9 per g ignited sample

Fig. 4-7—Heat af salutian data far pastes made with cement 16189.

Data fromTable 4-%

weight (not corrected for bleeding). The y were cured in sealed vials at70 F for periods ranging from 7 days to 1 year. The heat of hydration ateach age was determined by the same heat-of-solution method describedabove. The non-evaporable water content was determined by themethod already described (Part 2).

The results are shown in Fig. 4-5. This graph indicates that theheat of hydration is directly proportional to the non-evaporable watercontent, and that the proportionality constants for the different cementsdiffer, but do not differ widely.

Fig. 4-6 and 4-7 bring out the relationship between heat of hydrationand heat of adsorption for the two samples used for the present study.In each diagram the point plotted for zero water content represents theheat of solution of the original cement. All the other points representthe hardened paste after 27 days of wet curing. In Fig. 4-6, for example,we see that the heat of solution of the original cement was 623 cal perg and that after hydration the heat of solution was 509.5 cal per g.*The difference, 113.5 cal, is the heat of hydration. When the evaporablewater was removed before determining the heat of solution of the hy-

*This particular point was not obtained dir$ctly but was astimated from Fig. 4-1 in the manner alreadydescribed. The same is true of the lowest point m Fig. 4-7.


drated cement, the heat of solution was 538.2 cal per g. The differ-ence between 538.2 and 509.5, or 28.7 cal per g ignited weight, is thetotal net heat of adsorption, Q~f. The other points on the curve repre-sent samples containing intermediate amounts of evaporable water.

The heat of hydration per gram of non-evaporable water is about 555 calfor 16186 and 520 cal for 16189, which values agree fairly well with thedata given in Fig. 4-5. These values are computed from the slopes ofthe lines marked A in Fig. 4-6 and 4-7.

The heat of reaction of the non-evaporable water alone is 416 cal perg of non-evaporable water for 16186 and 390 cal per g for 16189, Thesefigures (based on lines B) indicate that the heat of reaction of the non-evaporable water is different for cements of different chemical com-position.

From these results we may picture the heat of hydration as devel-oping in the following way:

(1) Chemical reactions between the cement and water in the freshpaste produce new solid phases in which the non-evaporablewater is an integral part. These reactions release a definiteamount of heat for each unit of water combined, but theamount is different for cements of different chemical com-position. (For cement 16186 the amount is 416 cal per g ofnon-evaporable water, or 416 X 0.204 = 84.8 cal per g ofcement.)

(2) AS the new solid phases (the reaction products) form, theyadsorb water and the net heat of adsorption is released.This, according to the above estimates, is 572V~ cal per gfor all cements, and is equal to the heat of immersion of thedried paste. (For the paste made from cement 16186 thisamounts to 572 x 0.0502 = 28.7 cal per g of cement. )

(3) The total heat of hydration is the sum of the heat of combina-tion of the non-evaporable water and the net heat of adsorp-tion (84.8 + 28.7 = 113.5 cal per g for 16186).

The amount of heat that adsorption generally contributes to thetotal heat of hydration can be estimated from the data given above. Let

Q, = heat of reaction of the non-evaporable water, cal per g.Then

Q, = ~1% ,

wherekl = a constant for a given cement. Also, as assumed before,

Q.t = 572 V* cal per g .Since

w~=ksV~,


wherelc, = a constant for a given cement (see Part 3),

Q.c__ _~2;572 V.

Qr lclwn klkz

or Qat 572

Q, + Q.t = k,k, + 572The data for the two cements discussed above are:

Ce~~t Qatk, Q, + Q.,kl ——

16186 416 4.07 0,2516189 392 4.39 0.24

This shows that for the cements cited the total net heat of adsorptionof the evaporable water is about H of the total heat of hydration.

The results from these two cements suggest that the ratio of theheat of adsorption to the heat of combination of the non-evaporablewater is a constant, or nearly so. However, the close similarity in thiscase is evidently fortuitous. Q, is the heat of combination of the waterthat is a part of the solid phase and Q=, depends on the surface area ofthe solid phase, Hence, only Q, is appreciably influenced by chemicalcomposition and the two quantities therefore should not always bearth,e same ratio to each other. However, for most portland cements

cured under the same conditions, the ratios probably do not differwidely from those found for these two cements.

THE FREE-ENERGY AND ENTROPY CHANGES OF ADSORPTION

Underlying concepts

It will be shown that the net heat of adsorption represents a change inthe internal energy of the system in which the reaction takes place,As expressed by Glasstone, [3)the internal energy content of a substance‘(is made up of the translational kinetic energy of the moving molecules. . . of the energies of rotation and vibration within the mole-cule, of the internal potential energy determined by the arrangements ofthe atoms and electrons and other forms of energy involved in thestructure of matter. From the standpoint of thermodynamics, however,it is not necessary to know anything about the structure of the atom ormolecule, and so it is sufficient to divide the internal energy into twoparts only: these are (a) the kinetic energy of translation or, in brief, thekinetic energy, and (b) all other forms of energy. ” For the present pur-pose this statement can be amplified by adding that it is not necessaryto distinguish energy resident at the surface of a phase from energywithin the phase, It can all be regarded as internal energy.

564 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE Janua~ 1947

Although the princides of thermodynamics can be applied withoutknowledge of the mechanism of the change from the initial to final condi-tions, it seems helpful to picture what is believed to occur.

In the introduction to this section, adsorption was likened to thewetting of a solid by immersion in a liquid or by the spreading of a liquid

film. Although in the following discussion this analogy is not explicitly

used, the treatment is not in conflict with the concept set forth earlier.In the earlier discussion, emphasis was placed on the change from the

completely dry to the completely water-covered or saturated state. In the

following discussion attention is centered on changes from one inter-

mediate state to another.As indicated in Part 3, a field of force exists over the surface of the

solid matter of the hardened paste. When molecules, in this case water

molecules, enter this force field, they are attracted to the surface. In thedirection normal to the surface the force field of the surface supplementsthe normal cohesive forces between water molecules. The result is

that the proportion of molecules having enough energy to escape from

the adsorbed liquid’ during a given time interval is less than normalfor the existing temperature. The vapor pressure is correspondingly

below that of free water at the same temperature.

The mean specific volume of adsorbed water is ‘less than that of freewater (see J&t 5). The adsorbed water thus appears to be in com-pression. This observation has led to the belief that adsorbed wateris in the same state as would be produced by an external compressiveforce of sufficient magnitude to reduce the specific volume of free waterto that of adsorbed water. This conclusion was reached by Lamb and

Coolidge(’) from their experiments showing that for the adsorption of thevapors of eleven different liquids, the net heats of adsorption were

roughly proportional to the compressibilities of the respective liquids.However, for several reasons this is regarded as an oversimplified inter-pretation of the data. We may note in the first place that increasing

the external pressure on a Ijquid densifies it and raises its vapor pressure.Although adsorption densifies the liquid, it decreases the vapor pressure.In the second place we may note (as will appear later) that the changein entropy caused by applying an external force is very much smaller

than that caused by adsorption, unless the applied force causes a changeof state. An external pressure produces a uniform compression through-out the liquid. The force of adsorption acts, like gravitation, on the

water molecules individually and the effect therefore must vary with thedistance from the surface, or from the centers of greatest attraction,according to the gradients in intensity of the force-field.

lt seems reasonable to regard the net heat of adsorption as repre-senting the result of changes in the internal structure of the water

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMEN-i PASTE 565

(changes in the association and orientation of the molecules) and in the

potential energy of the water molecules caused by the mutual attraction

betw-een the water molecules and the surface. The surface of the solidprobably remains structurally unchanged.

Internal energy

A system in a given state is regarded as possessing a definite quantityof internal energy. The system may undergo a gain or a loss of internal

energy by a gain or a loss of energy in the form of heat, by doing me-chanical ~vork, or by having mechanical work done on it. In thermo-

dynamics, heat gained by the system and work done by the system are

conventionally regarded as positive quantities.

According to the first law of thermodynamics the increase in internal

energy is equal to the difference between the energy gained as heat andthe energy lost by the system if it does mechanical work on its sur-

roundings during the process. That is,

A~=~–zv, . . . . . . . . . . . . . . . . . . . . . . . . . ..(13)

whereAU = increase in internal energy,

Q = heat gained, andw = work done by the system.

When the external pressure is constant, the work term is proportional tothe increase in volume. That is,

w= PAv, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. (14)in which

P = the constant external pressure, and

Av = the increase in volume of the system.

It is conventional to subtract the initial value from the final to obtain

the increment. For example, AU = Uz – U1 and AV = VZ – vi.

The increment is called an increase whether in any given case it is posi-

tive or not. In the case of adsorption the final energy content and thefinal volume are less than the corresponding initial values. Hence, it

is advantageous to write in terms of decreases, that is, in terms of– AU, – Av, etc. This is done in the rest of this discussion.

Enthalpy, free energy, and unavailable energy

For reactions at constant pressure it is customary to let— AH=– AU– PAV . . . . . . . . . . . . . . . . . . . . . . . (15)

— AH is usually called the decrease in heat content, but, as ~villbe seen,it is generally not that and is preferably called the decrease in cnthalpy. (GJ

The decrease in enthalpy accompanying an isothermal adsorptionrepresents a decrease in tmo general classes of energy, namely, jweenergy and unavailable ene~gy. That is,


-AH= –AG– TAB, . . . . . . . . . . . . . . . . . ..(16)where

- AG = decrea~e in free energy,– All = decrease in entropy, and

T = absolute temperature,The term – TAS represents the decrease in unavailable energy for

an isothermal reaction, It is that part of the total energy decreasewhich, at constant temperature, cannot be converted into external work,If released, it can appear only as heat. Therefore, the unavailableenergy can be regarded as stored heat. * In the freezing of water, it is thelatent heat of freezing, Without reference to underlying concepts,entropy, S, can be regarded simply as a capacity factor giving thequantity of stored heat in calories per degree of temperature aboveabsolute zero. Hence, TS is the quantity of stored heat, and TAS achange in stored heat, in calories or in whatever energy unit is adopted,

The decrease in free energy, - AG, that accompanies an isothermalreaction at constant pressure is that part of the enthalpy-decrease thatmight be converted into external work, It is that which promotes allspontaneous processes at constant temperature and pressure. In thiscase it is the energy that promotes hydration, adsorption, swelling,capillary flow, and moisture cliffusion. Such processes always take placein such a way as to tend to equalize initial differences in free energy.Thus adsorption occurs when the free energy of the free water or freevapor is greater than the free energy of the adsorbed or capillary co~-densed water, Moisture diffusion occurs when adsorbed or capillary-condensed water in adj scent regions is at different free-energy levels,The free energy per mole of a given substance is known also as its chemicalpotential, or thermodynamic potential,

For the conditions of most of these experiments (adsorption in smallgranules of paste at constant temperature and atmospheric pressure) thedecrease in free energy may be assumed to appear entirely as heat. Butif work is done by the process, as for example against forces tending torestrain swelling, the free energy expended for such work will not appearas heat. t

*This concept is developed at length in an office memorandum by H. H. Stein our. (Special Report No. 1,Series 330, 1945).

tVery recent developments in this subject indicate, that adsorption in a comparatively rigid solid such ashardened paste should not be conmdered to be oocurpng pnder a constant external pressure of 1 atmosphere.Since, m a rlgld body, 6w,elhng Or ahrmkase may elve rise to elastm forces that act on the adsorbed layer,the pre~ure on tbe layer Ls,a functmn of the degree o,f Byell!ng of the sate, and hence of P/p, aa shown inthe sectmn below on Swelling Pressure. fSuch a varmt]on m externa pressure wax dealt with by A. B.D.Cassie. See “Adsorption of Water by Wool,” Trans. Faradau Soc. v. 41, p. 458 (1945) and earlier papers hyBarkas. in the same journal.

Caesle assumed that the swelling of dry woo! fiber produced tension in the fdamenta of the fiber and oom-

?IIIIYs,wolk state and the .dasty bonds that bold the maw togetbe~shmdd therefore be considcmd free ofression in the adsorbed water. This amumptmn may not ady to cement paste. The gel ia formed in the

stress m that state, rather tkm m the dry state ae, aaeumed by Cass!e. . However, since the eam,e reasoningmay be appbed to the gr?w~h of wool fiber, Cames results seem to mdlcate that the reaaol.mg m incorrect.In view of theea uncertamt]es and the recent date of Cawe’a paper, the apthors have adopted the usualprocedures and assumptions for the present paper. A more exact analyma wdl not be attempted until moreexperimental data are avadable.


We may note in passing that AUof eq. (15) is in the present case thesmall contraction accompanying adsorption from the liquid state. Itamounts, on the average, to about 0.13 cc per cc of water adsorbed.Hence, for an external pressure of 1 atmosphere, 108 dynes per sq. cm.,

w = 0,13 X 108 ergs

or 0.13 X 10s X 2,39 X 10-8 = .003 cal per g of water adsorbed, Tinusit is seen that the work term of eq. (15) is negligible and hence the net heatof adsorption represents the change in internal energy of the system.

Rolatlonshlp between net heat of adsorption and decreaseshr ]nternal energy, enthalpy, free energy, and entropy

Since by eq. (13), (14), and (15) –AH = – Q, it follows from eq, (16)that:

-Q= -( AG+TAS), . . . . . . . . . . . ..(17)-AG= - (Q– Z’AS),. . . . . . . . . . . . . . ..(18)

-AS=-(Q-AG)

T ‘ ““”’””’”-””””’”(19)

– AG cam be computed from the vapor pressure, as will be shown below,and AS can be estimated from the measured value of – Q and the cor-responding value of – AG.

Relationship between change in vapor pressure and change in free energy

As said before, adsorption can occur only when water in the free statehas a higher vapor pressure than it has after it is adsorbed. When waterin the free state is adsorbed, the change in its free energy is equal to thecorresponding change in the free energy of its vapor. Hence, the changein free energy when water changes from one equilibrium condition toanother can be calculated from the corresponding change in the freeenergy of the water vapor.

The relationship between change in free energy and change in vaporpressure may be written

dG=vdp, o . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(20)

where v and p are the volume and pressure, respectively, of 1 mole of

vapor at temperature T. Hence, if PI is the initial equilibrium vapor

pressure of the free water and PZ the pressure after adsorption, the

change in free energy is, for such a finite change,

AG= ~pzvdp . . . . . . . . . . . . . . . . . . . . . . . . . . .pl

(21)

Assuming that the vapor behaves as an ideal gas, we have

RTrJ = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (22)

P


Thus,

JPZ dp

AG=RT —. .(23)plP ‘“””””’”””””’””””’””’”’

or,AG = RT in pz/pl (cal per mole of water), , . . . . . . . . . . . (24)

This is the change in free energy when,, 1 mole of free water, or watervapor, at vapor pressure pl is adsorbed by a paste under conditions suchthat the pressure after adsorption is pz. The decrease in free energywhen the initial vapor pressure is the saturation pressure, ps, and thefinal pressure is a smaller pressure, p, is given—in calorie~ per g of watertaken up—by the following equation:

RTAG=–%ln p/p, . . . . . . . . . . . . . . . . . . . . . ..(25)

where M = the molecular weight of the adsorbate,

For our experiments,M = 18,02 (molecular weight of water)R = 1.986 cal per deg per moleT = 298 K.

Using these values and letting h p/p, = 2.303 Iogla p/ps, we obtain— AG = – 75.610g10p/p, calperg of water . . . . . . . . . . . . . .. (26)

It is to be noted that the solid phase is not directly represented in thisequation for reduction in free energy (eq. 26). It is indirectly repre-sented by the difference between p and p,. Since temperature is con-stant and since condensed water is present, p can be smaller than p,only through the action of a solute or some agency external to the water.The nature of this agency is immaterial so far as the thermodynamicrelationships are concerned.

Estimation of decrease in entropy from experimental results

From eq. (19) it is seen that the decrease in entropy can be obtainedfrom the difference between – AG and – Q. In the present case, – Q =Q=, the net heat of adsorption in cal per g of adsorbent, an integral

quantity. * But the decrease in free energy, – AG, is given by eq (26)

as the calories lost per gram of water adsorbed when 1 gram of waterhaving vapor pressure p, is added to a large quantity of paste havingvapor pressure p, the quantity of paste being so large that the addedgram of water does not change the vapor pressure. In other words,— AG is a differential. It is therefore necessary to obtain the differentialnet heat of adsorption in cal per g of adsorbed water. This can be doneby differentiating the empirical Q. vs. w relationship.

*Note that the tabulated valum of Q., the heat lost, are given as positive quantities. This is customary inrecording adsorption data. Hence, the recorded values must be multiplied by — 1 before being used inthe thermodynamic equations in place of Q.


The Q. vs. w relationship found in these experiments is similar tothose found by Katz@J and others for various materials. Katz foundthat these curves could be represented by empirical equations of theform

Qa=2 . . . . . . . . . . . . . .Bi-w’

. . (27)

where Qa = net heat of adsorption, cal per g of solid,w = vapor adsorbed, g per g of solid, andA and B = constants for a given system.

Differentiation gives

dQa AB

‘=(B+w)2 ””””’”’””’””””””dw. . . . . . . . (28)

The constants A and B of eq. (27) and (28) can be obtained by usingthe following form of eq. (27):

:+:;=A

This shows that if experimental values of w/Q~ are plotted against w, astraight line should result, from which the constants can be evaluated.The data for the two pastes used in this study are given in Table 4-3.

The corresponding values of w/V~ and w/Q~ up to p = 0.81 p, areplotted in Fig. 4-8. The points for 16186 lie close to a straight line.

Those for 16189 appear more erratic, but between w/V~ = 1 and w/V~= 2 they seem to follow the same line as the other points. At any rate,

P/P.

0.0

0.0810.1610.3220.390.460.530.600.700.810,880.961,00

TABLE 4-3—DATA OR EVALUATING CONSTANTS&OF NET HEAT F ADSORPTION EQUATION

I

Cement 16186

Q.iG-

cal,/g

23:279342376364388398428442474534572

0

0.760.951.371.551.711.892.042,483,003.484.285.50

t-g/calx 10’

3.183.404.004.124,704.885.135.806.797,348,029.6

Q.K

cal)g

Cement 16189

18:268327360375380406456501535552572

%-

0

0.720.981,341.541,721,862,082.603.404,155,508.65

;g/calx 103

—.

4,03.664,104.284.594.905.125.706.807,769.95

15.10


~ Fig. 4-8—Plot for evaluating constants ofnet heat of adsorption equatian.

~Vm

no distinction between the two pastes seems justifiable on the basis of

these data alone.

The constants for the line as drawn are

B= 0,0020 ; ~ = 500;

2 B

E. = 000152; A=655T7m;

A“

B = l,31V~ ; AB = 858V~’,

Hence, for these experimental data,

Q. 655 W/ Vm—.v. 1.31 +w/vm’” ””’’”’”’””””’”””’

(29)

and

dQo 858—.dw

. (30)(1.31 +w/vm)2’ ”””’ ””’ ”””’”.”.

Solutions of eq. (26) and (30) are given in Table 4-4 and in Fig. 4-9.These data show, for example, that if 1 g of water were added to a verylarge quantity of paste having a water content corresponding to p = 0,2

P,, the quantity of paste being so large that the addition of 1 g would notchange the vapor pressure, the total heat evolved would be 154 cal per gof water. Of this total, 53 cal per g would be due to the change in freeenergy. The curves and tabulated data based on the equations represent


Fig, 4-9— Comparison ofdifferential net heat of ad-sorption with change in freeenergy.

—AG from eq. (95).

‘Q fromeq. (99)dw.

P/Ps

the original data rather closely between p = 0.05 p, and p = 0.5 p, atleast for 16186. For lower pressures, the trend of the dQJdw curve isuncertain. This will be discussed more fully below.

Table 4-5 gives solutions of eq. (19) and thus gives the change in un-available energy and entropy for the same data as Table 4-4. Thesedata show that for the pressure range p = 0.05 p, to p = 0.5 p,, from 60to 70 percent of the heat-loss represents unavailable energy. For adsorp-tion of water on cellulose over the same pressure range, Babbitt(7j foundthe change in unavailable energy to be 44 to 60 percent of the total,This may be taken to indicate that when water is adsorbed by cementpaste, it undergoes a similar but somewhat greater change than it doeswhen it is adsorbed by cellulose.

Significance of change of entropy

The decrease in entropy is shown in the last column of Table 4-5.That these are relatively large changes in entropy may be judged bycomparing them with the change in entropy of water in the variousphysical and chemical processes given below:

(1) For water at 25 C an increase in pressure from 50 atm. to 400 atm.causes a decrease in entropy of 0.0023 cal per g per deg. (8J

(2) The transition of water to ice at O C is accompanied by an entropydecrease of 0.29 cal per g per deg.(g)

57$2 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE January 1947

TABLE 4-4-COMPUTATION OF DIFFERENTIAL NET HEATOF ADSORPTION dQ./dw AND FREE ENERGY A G

dQa 858

7W = (1.31 + w/vm)’ ; - ‘G = – 75’6 ‘“fl’o~’~’

P/P* w/v. * 1.31 + w/vm (1.31+W/vm)t

>0,05 0>7 1:6 3:6.10 0.76 2.07 4.28.15 0.92 2.23 4.97;20 1.05 2.36 5.57.30 1.30 2.61 6.81.40 1.52 2.83 8.01.50 1.75 3.06 9.36

*Values taken from curve in Fig. 4-2.

2?820017215412610792

– AG

TABLE 4-5-COMPUTATION OF DECREASE IN UNAVAILABLEENERGY, – TAS AND DECREASE IN ENTROPY, – AS

-TAS=$$+AG

Z’=298K

P/Pa w/vm*

>0.05.10.15.20.30.40.50 1.75

dQ.z

cal/g

500

24820017215412610792

*Values taken from curve in Fig. 4-4. TAS from e

– AGcal/g

—

G7662

::3023

(19).

&766253403023

– TALScal/g

—

la124110101867769

– AScal/gF

0:00.420.370.340.290.260.23

(3) At 25 C, a pressure of about 9000 atm. will change liquid water to asolid of density 1.35 (specific volume 0.74) known as ice VI. Thischange in phase is accompanied by a decrease in entropy of 0.26 cal perg per deg. (9J

(4) The entropy change of a system comprising CaSOi and HzO whenthe CaS04 acquires two molecules of water of hydration can be computedas follows :f’”)

Compound. Entropy, S, at 25 CCaSO~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25.52Hg0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.5

Total . . . . . . . . . . . . . . . 59.0 cal/degCaSOi.2H~0 . . . . . . . . . . . . . . . . . . . . . . . 46.4

– AS = 12,6 cal/deg


If this decrease in entropy of the system is ascribed wholly to thewater, as is done in the calculations for adsorption, —AS’in cal per g ofwater is

12,6— = 0.35 cal per g per deg2X18

(5) For the system NaJIO, and H,O reacting to form Na2S0,.10H,O,the change in entropy of the system expressed in terms of the water is,when computed as above, also —0.35 cal per g per deg. @Oj

(6) For the system CaO and H,O, reacting to form Ca(OH)Z, the changein entropy, computed and expressed as above, is – 0.49 cal per g per deg.(1 a)*

A comparison of these figures with those in the last column of Table4-5 shows that the data have the following indications with respect tothe change of state of the water adsorbed in the low-pressure rangeindicated by the decrease in entropy:

(1) The change in entropy is far greater than could be produced bypressures lower than the pressure required for solidification of water at25 C.

(2) The change in entropy is fully as great as that corresponding to thetransition from normal liquid to ice VI, or to water of crystallization,

(3) The change in entropy for the water taken up at very low pressure,p = 0.05 p,, may be as great as the change accompanying the Changefrom normal water to hydroxyl groups chemically combined in Ca(OH),,

The third conclusion is less valid than the other two. As will bebrought out below, there is reason to question ~vhether eq. (27) and (28),on which Table 4-5 is based, are of the correct form for the low pressurerange, about p = 0.05 p, and below. If it is not, the estimated – AS’may be considerably in error in the direction of being too large, Evidencecan be found to show that —AS reaches a maximum in absolute valuebelow p = 0.05p~. At very low relative vapor pressures, the absolutevalue of AS may be about the same as that estimated for p/p, = 0,50.This would indicate that the estimated decrease in entropy is the re-sultant of several factors and that the full significance of the entropydecrease cannot be seen until these factors are known in detail.

*In Part 2, in connection with Table 5, it w~s po,inted out that the equilibrium relative vapor pressme ofwater over Cd) may be, much less than that given m the table. The ewdence for th}s statement is found i“the values for change m ent~opy and, enthalpy for the system CaO-H!O. (The enthalpy change is 847cd/g of water. The equilibrmm relntwe vapor pressure may be calculated by reversing the steps in theprocedure for c?lculatmg the entropy change of ad80rptm”, The result m P[P, = 5.6 x 10-10. This is tohe comprtred with 1.3 x 10-4 gwen ]n Table 5, Part 2. Although the c?l$ulated vxlue may be somewhatin error, the error is not likely to ,be great enough to account for a mllhon-iold difference., The experi-mental value is open to more question. It is derwed from measurements of the relatlve efficlen cy of desic-cants. The conditions were such as to warrant the conclusion that the vidue of I)IP* cannot exceed thatgiven; the true value can be much less,

No evidence has been obtained in this laboratory that an of the desiccants listed in Table 5, Part 2,Y“actually removed water from ,Ca(O13)z. If the calculated, vn ue M accepted as being of the right Order of

magnitude, then tbe dehydration of Ca(OIJ); by these desmcnnts would not be expected.

574 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE Janua~ 1947

In general, the data indicate that some of the adsorbed water under-goes a pronounced modification, but the nature of the modificationcannot be deduced from the data alone. In Part 3, reasons were givenfor considering the adsorption process to be a physical cne—van derWaal’s adsorption. These data are generally compatible with thatview, although the estimated – AS values in the low pressure rangeappear to be rather larger than might be expected. Thus, the possi-bility of some of the water being taken up by a chemical process is notprecluded by these data.

THE ENERGY OF BINDING OF WATER IN HARDENED PASTE

The heat of adsorption is a measure of the energy that must be sup-plied to enable adsorbed water molecules to break away from the forcefield of the adsorbent and become vapor. Similarly, the net heat ofadsorption (dQa/dw) is a measure of the energy required to restoreadsorbed water to the normal liquid state. That is, the net heat ofadsorption is a measure of the energy of binding between the evaporablewater and the solid phase. In the same way, the heat of reaction of thenon-evaporable water is a measure of the energy of its binding.

In this connection the value of dQJdw when evaporable water =zero is of special interest, According to eq, (27), this value is equal to

A/B. For the data of Fig. 4-9, A/B = 500 cal per g. Steinbergerfll)remarked that when the vapor pressure is near zero, the surface is sosparsely populated with adsorbed molecules that the molecules can beregarded as having no effect on each other, and therefore the net heat ofadsorption at the limit where, in this case! w/ V~ approaches zero is ameasure of the binding energy of the evaporable water molecules in thegel. In this case it has the further significance that it should also be ameasure of the energy of binding of the least firmly bound part of the non-evaporable water. This will become evident when it is remembered thatin Part 2, Tables 3 and 4, it was shown that the water content of thesample dried over Mg(C104) 2,2H20 is a point on a smooth curve relatingwater content to vapor pressure. If the chosen drying agent had beenPZO,, the non-evaporable water contents would have been 80 percent ofthe present values, and the evaporable water contents would have beencorrespondingly highe~. For example, in Fig, 4-6, the non-evaporablewater content would have been 0.163 instead of 0,204, If the heat ofreaction of the increment of water (0.204 — 0.163) is the same as the

average for all the non-evaporable water, the heat of solution of the dry

sample would have been 555 cal per g, represented by the point of inter-section of line B and the ordinate at w = 0.163. If the heat of reaction

PHYSICAL PROPERTiESOF HARDENED PORTLAND CEMENT PASTE 575

of this increment is less than the average, the heat of solution would fallbelow line B.*

Similarly, had a desiccant of higher vapor pressure been used, the non-pvaporable water content would have been higher and the heat of solu-tion of the dried sample lower, the point falling somewhere on the curvenow representing evaporable water. The average heat of reaction of thenon-evaporable water would have appeared lower.

It is thus clear that the maximum net heat of adsorption cannot begreater than the minimum heat of reaction of the non-evaporable water.Since the minimum heat of reaction of the non-evaporable water cannotbe greater than the average for all the non-evaporable water, the maxi-mum net heat of adsorption cannot exceed the average heat of reactionof the non-evaporable water and is probably less.

This is rather positive evidence that eq, (28) cannot represent thedata all the way to w = 0. Hence, the value 500 cal per g for w = Oobtained from eq, (30) cannot be accepted; it is too high, t This conclusionis represented by the curved dotted lines in Fig, 4-8, The line termina-ting at w/Qa = 2.40 X 10-8 g per cal corresponds to the average heat ofreaction of the non-evaporable water in sample 16186, 416 cal per g,It is therefore the lowest possible terminus for the line representing thatsample. The other point, at 2,55 X 10-s g per cal, is the lowest possibleterminus for sample 16189. It corresponds to the average heat of re-

action, 392 cal per g of non-evaporable water.

As discussed in Part 2, one microcrystalline hydrate known to occurin hardened paste is Ca(OH)Z. The heat of formation of this compoundfrom CaO and HZO is about 15,260 cal per mole.flzj Expressed on thebasis of the water, as for the net heat of adsorption or the heat of re-action of non-evaporable water, this amounts to about 847 cal per g ofwater. This figure is to be compared with the 392 and 416 cal per gof water found as the heat of reaction of the non-evaporable water forthe two paste samples, It is thus apparent that a considerable portionof the non-evaporable water in hardened paste has much less energy ofbinding than the part that is in Ca(OH)Z. From the relationship pointedout above it follows also that the most firmly bound adsorbed water isloosely bound as compared with that in Ca(OH),.

The total net heat of adsorption has already been shown to be about572V~ cal per g of sample, ‘1’he average for the gel water alone istherefore about 572V~ + 4V~ = 143 cal per g of gel water. We cannow observe that the maximum net heat of adsorption is of the order of400 cal per g (392 cal per g of water for one paste and 416 cal per g for the

*It could not fall very far below line B, however, since the curve would still have to PWS through thepoint ht w = 0.204 in line with the smooth curve. It is estimated that the lowest point m Fig. 4-6 thatwould meet this requirement would be at about 550 cal per g and w = 0.163.

tThis conclusionmaybe true also with respect to the use made of eq. (28) by Katz, Steinberger, Babbitt,and othere.


Fig, 4-1 O—Estimate of the netheat of adsorption for the waterin the first layer,

600

500- ●

● (I400 -

0

g~e ;

300 -t

?

200 -0 /6/86

100- . !6/89

2 3 4

%“ 9/9

other). How much of the adsorbed wotcr has this relatively higher

energy of binding cannot be told from these data. I-Iowcver, an estimatecan be made of the average binding energy of the first layer with the aidof Fig, 4-10. This is a plot of Q~/V~ vs. w/V~ for both sets of data upto about w/ Vm = 3, This shows that the average net heat of adsorptionof the first layer is about 300 cal per g of water for 16186 and about270 cal per g for 16189, This estimate embodies the assun]ption thatall the water taken on in the low pressure range is held in the first layer,that is, that the layers form consecutively as the pressure is raised.This is probably not true. According to the 13.13.T. theory, u’hen w/V~

= 1.0, p = about 0,2 p, and about 85 pcrccnt of the water would bc in

the first layer at this pressure. The rest would bc in higher layers. Such

a correction, very doubtful as to accuracy, would indicate an averagenet heat of adsorption of about 320 to 350 cal per g of water in the firstlayer.

Data published by Harkins and Jura(lsj are instructive in this respect.These authors found, by direct calorimetric measurement, the net

heat of adsorption of water on anatasc (titanium dioxide) to be asfollows :

Average for:

lst layer . . . . . . . . . . . . . . . . . . . . . . . 3G4calperg of water2nd layer . . . . . . . . . . . . . . . . . . . . . . 76

3rdlaycr . . . . . . . . . . . . . . . . . . . . . . . 25

4th layer . . . . . . . . . . . . . . . . . . . . . 4.4

5th layer . . . . . . . . . . . . . . . . . . . . . . . 2.2 (?)

Allabove 5 . . . . . . . . . . . . . . . . . . . . . 1.7 (?)

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 cal pcrgof water

Since these quantities ~vere computed from experimental data on the

assumption that the layers formed consecutively, the average per layer

is directly comparable with the figures obtained from l?ig. 4-10 without


correction for the overlapping of layer-formation, Thus, 364 cal per gfor the first layer adsorbed on anatase is comparable with 270 to 300for the first layer on dried paste. At least a part of the difference is due

to the presence of air in our experiments, for the adsorption on anatase

occurred in a high-vacuum system. The general indication is that the

first layer of water on cement paste is bound with about the same energy

as the first layer on anatase.

A comparison of the average heats for successive layers is not feasiblebecause the shapes of our curves are undoubtedly influenced by capillarycondensation and the presence of air.

NET HEAT OF ADSORPTION AND c OF THE B.E.T. EQ. (A)

As previously indicated, the constant C of the B.E.T. eq. A is relatedto the heat of adsorption as follows,

Q, – QL

C=ke RT

where

QI = heat of adsorption for the first layer, cal per mole,

QL = heat of liquefaction, cal per moleR = gas constant = 1.986 cal per mole per degT = absolute temperaturek = constant

Brunauer et al. assumed that constant k does not differ significantly fromunity, and, hence, that

Q1 –– QL = 2.303 R1’ Wlo c

This assumption no longer appears valid in the light of the derivation ofthe equation by statistical-mechanical methods recently reported byCassie. (23) On the contrary, it appears that k is of the order 0.02 or less.It follows that (QI – QL) calculated on the assumption that k is unitymust be too low. However, in some cases, k might approach unity so that

(QI – QL) calculated On this assumption would wwach the eweri-mental values.

The experimental data obtained by the air-stream method show that,for cement pastes, about 90 percent of the values of C lie between 17 and23. For the particular samples used in the calorimeter tests, C = 22.On the assumption that k is unity, C = 22 corresponds to 102 cal per g.

This is to be compared with 472 cal per g found experimentally. Thatis, the value of k appears to be far less than unity.

Similar results were obtained in the adsorption of water on non-porous absorbents by Harkins and Boyd, as shown by the followingdata :(14)


I<ind of (:%;.) (Ol$?p)solid

TiO, (anatase) 133 445~a~$,quartz) ’139 511

178 416

Here also k must be much less than unity to account for the results.The analysis made by Cassie clarifies somewhat the significance of

C, making it appear as a factor which expresses the distribution ofmolecules between the first and higher layers and placing less emphasisupon its relationship to the heat of adsorption, At the same time, itclarifies the significance of constant V~. So long as k was assumed to beunity, the discrepancies between calculated ‘and experimental net heatof adsorption raised doubts about the acceptance of Vm on theoreticalgrounds. Now it appears that this doubt can be dissolved to a con-

siderable extent, though not completely. In any case, it may be notedthat the acceptance of V~ as a measure of surface area, discussed in Part3, rests mainly on the outcome of empirical tests, rather than on literalacceptance of the assumptions used in the derivation of the B.E.T.equation,

SWELLING PRESSURE

Limited-swelling gels

When some kinds of gel are placed in contact with a suitable liquid,they imbibe liquid and swell until they have become molecular or colloidalsolutions. This is called unlimited swelling. The same gels with anothertype of liquid may imbibe only a limited amount and show correspond-ingly limited sweUing. Such observations suggest that the tendency toswell on coutact with a liquid is a manifestation of a tendency of thematerial to dissolve or at least to peptize to the colloidal-solution state,When swelling is of the limited type, the tendency of the liquid to pene-trate and disperse the solid is evidently opposed by cohesive forces thatbind the mass together.

Portland cement gel in water belongs to the limited-swelling class,Like other gels of its class, it is not able to swell beyond the dimensionsestablished at the time of its formation. However, it will shrink onloss of evaporable wat~r and swell when evaporable water is regained.

As mentioned elsewhere (see Part 2) it undergoes a permanent shrinkage

on first drying; that is, only a part of the initial shrinkage is reversible,

When the tendency of a swelling body to expand is resisted, the bodymay be able to exert great force. For example, dry wooden wedgesdriven into rock seams will split the rock when the wedges are allowed


to take up water, a method of quarrying used by the ancient Egyptians, (Lb)It is thus understood that swelling is a movement of the solid units

of the gel that can be prevented only by suitable application of force.

The magnitude of the force required to prevent swelling, the so-calledswelling pressure, can be ascertained from a consideration of the free-

energy changes that occur when a swelling body takes up a liquid at agiven constant temperature.

Idealized cement gel

In the following derivation it will be assumed, contrary to fact, thatthe solid particles of the cement gel are not interconnected. Also, thepossible effects of any non-gel constituents will be ignored. It will beassumed that these disconnected gel-elements are colloidal particlesand that they are packed together in such a way that all interstitialspace is filled with adsorbed water. Thus we assume that we are dealingwith a highly concentrated colloidal solution. These assumptions makeit possible to ascertain the conditions governing the movements ofadsorbed water in an actual paste, without the modifying effects ofelastic forces in the solid phase Also, it eliminates the complicationintroduced by the presence of capillary space. This will be dealt withlater.

The thermodynamics of the swelling of such an idealized gel canbe treated as if the gel were a true solution. The swelling pressure isrelated to vapor pressure in the same way that osmotic pressure is relatedto vapor pressure. The following treatment follows Glasstone’s treatmentof osmotic pressure.tlej (See also references (7) and (1l)).

Derivation of equation for swelling force

Imagine a vessel containing the idealized gel, its water content such

as to give a vapor pressure less than that of pure water at the same tem-perature. If pure water were placed in contact with this gel, the gelwould imbibe water and swell until the vapor pressure of the waterwithin the gel became equal to the vapor pressure of pure water, If theexternal pressure on the gel (which acts alike on both the solid and theliquid phases) were increased sufficiently, the vapor pressure of thewater in the gel could thereby be made equal to that of free water at thesame temperature. Under this higher external pressure, the gel would beunable to imbibe water and swell. The increase in pressure required toprevent swelling when a dry or partially dry gel has access to free wateris, as said above, defined as the swelling pressure.

Let Ps = existing external pressure,P = external pressure on the gel when it is in equilibrium with free

water under external pressure P,,P – P, = AP = swelling pressure,


G, = free energy of pure water at external pressure P,, andG = free energy of adsorbed water at external pressure P,.

The increase in external pressure required to equalize the free energiesof the adsorbed and free water is given by the following expression

)G,=G+ ~;,(~ ~dP. . . . . . . . . . . . . . . . . (31)

For a system such as this the change in free energy with pressureat constant temperature can be shown to be equal to the rate of change involume of the system with change in water content—on the molar basis,

the “partial molal volume” of the adsorbed water, ~. That is,

()AG .~

~ ?’ “ ““’’’’”””’’”””””’”””’”””””(32)

Hence,

G,= Gi- ~;~dP. . . . . . . . . . . . . . . . . . . . ..(33)8

The increase in free energy of the adsorbed water that takes placewhen the external pressure is increased can be expressed in terms of thecorresponding changes in vapor pressure. If

G = free energy of adsorbed water under initial external pressure, P,and G, = free energy of adsorbed water under external pressure P,then G, – G = AG = increase in free energy when external pressure israised from P, to P. The respective free-energies are related to vaporpressures as follows:

G= G,+ RTln p/p, . . . . . . . . . . . . . . . . . . . . . . ..(34)and

G~=G, +RTlnp,/p, , . . . . . . . . . . . . . . . . . . .. (35)where

G, = free energy of free water in a chosen reference state, andp, = vapor pressure of free water in the chosen reference state.

Hence,G,– G= AG=RTln p,/p ..,...... . . . . . . . ..(36)

and, by eq. (33)

J

P–VdP=– RTln p/p,. . . . . . . . . . . . . . . ..(37)

Pa

An exact solution of eq. (37) for swelling pressure \vould require knowl-edge of the relationship Iwtween the specific volume of the adsorbedwater and change in water content. “1’his relationship is unknown; in a

real paste containing capillary water M well as gel water it must be rather

complicated. Although the water is densified by adsorption forces in a


partially dried sample containing capillary water, it is also subjectedto capillary forces that tend to extend it. Without knowledge of the—relationship, it is necessary to assume V to be independent of pressureand hence a constant. On this assumption, integrating eq. (37) gives

P–P, =AP=–!~ln p/p,. , . . . . . . . . . . .. (38)

In terms of ordinary logarithms and specific volume, ~ becomes Mufand the swelling pressure becomes

AF’=-R~2,30310g10p/p, . . . . . . ... ... . . . . . . . . . . . . ..(39)M Vf

Solutions of eq. 39 are given in Table 4-6. The value of specificvolume of adsorbed water used in these computations is 0.87, the meanspecific volume of the gel water. (See Part 5), This value is no doubttoo low for swelling at high vapor pressures and too high at low pressures,but it should be preferable to the specific voiume of free water, ordinarilyused for this computation.

TABLE 4-6—COMPUTED POTENTIAL SWELLING PRESSURE

RT—2.303 log,,p/p,; 7’ = 298K; M = 18.02; Uf= 0.87; R = 82.07 cc, atmAP = – ~fv,

per deg pcr mole; W = – 3593 loglop/p, atmospheres or AP = – 52,810 loglOp/p, psi

P/Pa

1,000.950,900,800,700.600.500,400.30

&veiling pressure, AP——-

it mospheres

8:165348557797

108114301879

psi

117:241951188181

11710159002101027620

Computed values such as those given in Table 4-6 have never beensatisfactorily tested experimentally, owing to experimental difficulties.

For an idealized gel, there is little reason to question the results, exceptfor the error introduced by assuming the specific volume of the adsorbed

water to remain constant. At least, they are in line with general ob-

servations as to the enormous forces that sw-elling bodies are able to

develop when the tendency to s]vell is restrained.

It should be understood that the pressures indicated cannot exist

unless the movement of swelling is prevented; the so-called swellingpressure is really the potential pressure. Also, the potential pressures


given correspond only to a condition wherein a specimen at initial vaporpressure p is exposed to liquid water or to vapor of pressure p,. If thespecimen is exposed to vapor having a pressure p’ such that p’ is greaterthan p but smaller than p,, the potential swelling pressure may be com-puted from the pressuie ratio p/p’.

Relation of idealized behavior to that of cement paste or concrete

A hardened cement paste or concrete differs from the idealized geldiscussed above, The gel in the paste is not composed of discrete particlesbut is apparently a coherent, porous mass held together by solid-to-solid bonds, Moreover, it contains microcrystals and aggregate particlesthat resist the shrinkage of the gel, Consequently, swelling (or shrink-age) in concrete is partially opposed by the elastic forces developedthroughout the mass according to the relationship

AP6 =LYAV . . . . . . . . . . . . . . . . . . . . . . . . (40)where

a = the coefficient of compressibility,AP, = change in elastic force, andAV = change in over-all volume of concrete.

Thus, a change in volume induced by the swelling or shrinking of the gel

may be partially opposed by a force that is, presumably, proportional to

the change in volume.

However, swelling pressure, as defined above, should be very nearlythe same for concrete as for the idealized gel, for if the swelling is pre-

vented, AV of eq. (40) is zero and the increase in external pressure required

to prevent swelling is only that required by eq. (39), However, the re-

quired increase in external pressure per unit gross area of concrete may

be less than AP of eq. (39) if the adsorbed water is effective over less than100 percent of the cross-sectional area of the concrete. In other words,the maximum externally manifested swelling pressure could be less thanthe theoretical, but not greater.

MECHANISM OF SHRINKING AND SWELLING

Volume change as a liquid-adsorption phenomenon

When volume change is regarded as a swelling phenomenon, as wasdone in deriving cq. (39), the force is considered to arise from attraction

between the liquid and the solid surface. In regions where the solid

surfaces are separated slightly, the solid-to-solid attraction tends todraw the solid surfaces together, and at the same time the solid-to-liquid attraction tends to draw the water in between the surfaces. Ifthe water is exposed, its tendency to evaporate or its surface tension,or both, give rise to an opposing force that tends to draw the waterout of the adsorbed layer. Thus, the adsorbed water in the gel is the


subject of competing forces, and when these opposing forces are in equilib-rium the rate of volume change is zero.

From this conception of the mechanism of shrinking and swelling

it would appear that the over-all volume change of the paste should be

proportional to the change in spacing of the solid bodies that are heldapart by adsorbed water. This spacing should decrease as adsorbed

water is withdrawn and increase as adsorbed water is added. Since thefirst layer is much more strongly held than the higher layers, the volume

change should be of the order of magnitude that could be accounted for

by changing the spacing of the particles by only 2 molecular diameters,about 5 or 6 i%ngstrom units, per particle.

To see whether this is within the bounds of possibility, we may con-

sider the data on the particle-size of the solid phase. Imagine the

solid matter to be made up of equal spheres having a specific surface

equal to that of the hardened paste. The spheres are in some character-

istic array that encloses voids equal to the observed pore-volume in the

paste. The addition of an adsorbed layer of water will be regarded as

equivalent to increasing the sphere radii and hence their center-to-centerspacing. The corresponding change in over-all volume is related to thechange in radius by the ~vell known relationship for small changes,

AV 3Ar—. —, . . . . . . . . . . . . . . . . . . ,. .,., . . . . (41)v r

wherev =

Al’ =r=

Ar =

over-all volume,

change in over-all volume,

sphere-radius, andchange in sphere radius.

When hardened paste is dried to equilibrium with a very low vaporpressure, virtually all the adsorbed water is removed. Hence, thepossible change in volume may be computed from the thickness of theadsorbed layer and the particle-size of the solid phase. The thickness ofthe adsorbed layer may be conservatively estimated at one water-moleculediameter, or about 2,7A. The equivalent sphere radius of the pasteparticles is estimated at 70~ (see Part 3). Hence,

AV 3X2,7=016—. —.v 70

That is, a change in particle spacing corresponding to the addition or

loss of one molecular layer per particle Woultd, under the assumptionsgiven, result in an over-all volume change of 16 percent.

Shrinkage measurements on thin, neat-cement slabs, W~/C = 0.5

by weight, showed a linear shortening of 0.7 percent when all the evapor-able water was removed. This corresponds to a volume-shrinkage of


about 2 percent, or about one-eighth the amount theoretically possible,Thus, it appears that the loss or gain of the first adsorbed layer could

more than account for the observed amount of volume change. Thesmallness of the observed volume change, relative to the calculated,could be explained as being duc to the restraining effect of non-shrinkingbodies embedded in the gel, and elastic forces developed at points wherethe gel particles are joined by solid-to-solid bonds.

However, the figures shoukl not be taken too literally. If the particlescomposing the mass are not of equal size and shape, the above com-putation dots not apply exactly, Ho\vever, unless the simplifyingassumption leads to ?s much as an eight-fold error, which seems un-likely, the conclusion that swelling could be due to changes in adsorbed~vater content is Tvcll\vithin the limit of possibility.

****

It, should be observeci particularly that by the theory outlined abovethe change in volume is not considered to be the result of forces actingon the solid phase. Instead, the change is assumed to be the result ofan unbalance of the forces acting on the adsorbed water, and the con-sequent changes toward establishing an equilibrium between thoseforces.

Volume change as a capillary phenomenon

The shrinkuge and swelling of rigid porous bodies that undergo volumechanges much smaller than the corresponding changes in water contentare regordcd by some 0s cupillary phenomena. l’lummw and I)orc, (17)for example, describe shrinkage of some soils as the result of tension inthe capillary ]vater. The reaction of this tension produces compressivest,ress in the solid phase and thus causes a reduction in volume or length.The force of capi nary tension is given by the following equation flgl.

()F=u ~+~ , . . . . . . . . . . . . . . . . . . . . . . (42)rl rZ

where F = force of capillary tension,r = surface tension of ~vater, andT1and TZ= principal radii of curvature of the rnenisci.

The curvature of the water surface is determined by the size and shapeof the pores in the solid. Apparently the pores are such that as thewater content of the body diminishes, the curvature (concavity) of thewater surface increases (the radius decreases) and thus the shrinkageforce increases.

Swelling on increase in water content can be accounted for by thistheory only by assuming that shrinkage produces elastic strains andthus, when the shrinkage force is released, elastic recovery causes ex-pansion,


When concrete undergoes shrinkage for the first time, it is unable toregain its original dimensions when it becomes resaturated. This canbe accounted for in terms of the capillary theory by assuming that thestresses of shrinkage cause plastic flow in the solid phase. Hence, thepermanent shrinkage, that is, the irreversible part of the initial shrinkage,can be regarded as permanent set.

According to the capillary-tension theory, any porous body containingsmall liquid-filled capillaries should contract as the water is removeduntil the evaporable water content and vapor pressure pass the limitbelow which a meniscus cannot exist. When this limit is passed, thebody should expand. In concrete, this limit might be found at, thewater content corresponding to p =0.45 p,; it certainly ~vould be foundat some pressure greater than p = 0.00. However, concrete and, asMummer and Dore~’7J point out, fine-grained soils shrink and swellwith changes in moisture content even when the moisture content is toolow for the existence of a meniscus. In concrete at least, shrinkage isat a maximum when the evaporable water content is zero. * It is thusapparent that the capillary theory alone will not suffice,

The relationship between tension in the capillary water and volume

change of cement paste can be clarified with the aid of Fig. 4-11. Here,as in Part 3, the paste is represented by a model composed of spheres.Each sphere represcmts gel substance together with its associated voids

(gel water) and non-gel solids. The interstices between the spheresrepresent capillary spaces outside the gel. t

Each sphere of Fig, 4-11 is supposed to contain gel water and be in a

state of swelling determined by its water content. The water content

Fig. 4-11,

40

6

‘Shrink:we Pmlmbl. v incrc:w.s further with loss of some of the non-cvwporab]e water on heating in dryair. S0 data MC avuil:>h]c. Itowmzr.

tIt lnu.t 1,. en,pl,:wim I th:lt the nuthors, do not Imuw the skwes of the solid bodies co!nposing hard-ened p:~ste (except for sumll :I!!IuurILs o,f ,nimm~eopw m:lteri:ll) or Itow they are linked together. Themwlel M ,ofl, ere,l only he(t Luse tl]e Wndltwlls pi(:tured thereky ore such :Ls to give the smne adsorptionCbwllctcrlstlm :1sIl:trdellc<l Cc!!)et)tp:lstc.


in turn is determined by the existing vapor pressure. The capillarywater is represented as lenses around points of contact or near-contactbetween the spheres. The volume of water in each lens is determinedby the curvature and position of the spheres and the curvature of thewater-surfaces. The latter is determined by the existing vapor pressureaccording to the relationship

;-+:=–-~- ln p/p, . . . . . . . . . . . . . . . . . . . . . . .Mvju

(43)

wherer-l and r-2 = principal radii of water-surface curvature,

u = surface tension of the water,

and the other symbols have the same signific~nce as before. Eq. (43) isthe Kelvin equation discussed in I’art 3.

For finite values of 1 + 1 the capillary water is in tension, the tensilerl Ti

force F being

(44)

Comparison of this with the swelling-pressure equation (cq. 39)shows, as must needs be, that for equilibrium with a given vapor pressurep, capillary tension equals potential swelling pressure. That is, potentialswelling force is the result of the tendency of water to enter the gel and

capillary tension opposes that tendency; at equilibrium the two forcesbalance. *

Fig, 4-11 is drawn so as to depict a condition in which the gel is onlypartly covered with capillary-condensed water. In those areas notcovered, the tendency of the water mohwulcs to enter the gel is opposedby their tcndcmcy to evaporate. This has the same effect as tensionarising frox]l a meniscus.

It lMS been remarked before that the classification of gel water andcapillary ~vater adopted in this discussion is somewhat tirbitrary. Someof tho gel wo,tcr muy occupy space beyond the force-field of the solidrnatcrial and may therefore be properly classed as capillary water.

Nevertheless, even if a less arbitrary dcfrnition of capillary water ~vere

adoptccl, the concepts clcvcloped above would seem to apply: ‘rho

spheres in l’ig, 4- I 1. would represent the gel-substance together with

what,evcr part of the total water-fillable SP:LCC is predominantly in-——

*St! irtly slm:kkin~, the frrc enmOic,s of the adsorbed water and capillary water are equal at equilibrium,ralhcr th:lll tk~ Il!lcusity Of fOK<:eS. ‘1’hot is, at equilibrium

AI+! = F?/ (Eq. (3!)) 1111(I(44))Sinm V( for tlb. al sorbed water is not the same M that for capilhtry water, AP and P rtmrlot be exactly e<iual.‘rhc dmrusaior, in the text, thou~b prwhnps not rigorously correct, Iea,l$ to c~qily vlsllali~ed ~OncePts thatdloui(l not b,, u,slc:~tlil,g.

PHYSICA!- PROPERTIES OF HARDENED PORTLAND CEMENT PASTE 587

fluenced by van der Waal forces. The interstices would represent therest of the water-fillable space in the paste,

Relationship between change in volume and change in water content

According to the concepts set forth above, swelling and shrinkingshould depend on the amount of adsorbed water in the gel, That is,presumably,

AV=k A~, . . . . ... . . . . . . . . . . . . . . . . . . . . .. (45)m

where k is a proportionality constant connecting change in over-allvolume, AV, with change in the amount of adsorbed water, Aw~,per unitsurface of the gel, as represented by V~. In th,e range of vapor pressureswhere capillary condensation takes place (p> 0.45 p,), any change inadsorbed-v’ater content would be accompanied by a change in capillarywater content, Aw., so that Aw~, the change in total water content =Awa + Awe. Hence,

AV=; (Azu~-Aw,) . . . . . . . . . . . . . . . . . . . . . ..(46)m

It follows from this that the change in over-all volume will bc relatedto the total change in water content differently in different samplesaccording to the ratios of adsorbed water to capillary water in the re-spective samples, We should expect, therefore, that the greater theratio Aw,/Aw~l the smaller the average AV/Aw~ for a specimen con-taining a given amount of gel.

A wholly satisfactory experimental check of this deduction cannotbe offered at this time because available volume-change data pertain toshrinlmgc aceomp:inying resorption whereas data leading to the evalua-tion of Vm and WOare derived from adsorption measurements. How-ever, shrinkage data bear out eq. (46) in a general way. The best avail-able examplc of this is given in l?ig, 4-12, re~resentiug a part of a study

of shrinkage by ~i~kctt.(19, It was found that the course of shrinkage

durin~ the dr~ing of a concrete prism could, be represented by an equa-tion analogous to the heat-flow equation. If shrinkage were directlyproportional to the concomitant water-loss, the same equation shouldapply also fo watm-loss. I?ickett found, however, that the water-loss-vs.-timc curve could ]Iot be reprcscmted by a single equation of theheat-floy type. But, by assuming that two classes of water are lostsimultaneously dilring drying, the loss of water in each class followingits owm law, he could represent the experimental results with two equa-tions of the heat-flow type, This is shown in Fig. 4-12. Pickett calledthe water that seemed to be unrelated to shrinkage W. and the restWb. The relative proportions W. and Wb assumed for the computationswere arrived at by trial. In the figure the “a” water is represented


60 I I 1 I I I f 1200

50 — — 1000

2 . . Loss of Water 2m.%

Fig. 4-1 Q—Time rela-tionships for shrinkageand water-loss fora con-crete specimen stored inair at 50 per cent rela-tive humidity,

“‘hrinkagel~,.,

10

v

Size : 2x2x114 in.Concrete: I :4.5 mix

~

200

oo~10 20 30 40 50 0

Days Drying

by the computed curve marked W.. The ‘W’ water is represented bythe computed curve marked Wb, which also represents shrinkage whenappropriate ordinate scales are used. The sum of the ordinates ofthese two curves gives the curve marked W. + Wb. The crosses repre-sent the observed total water-losses and the circles the observed shrinkage.

Thus Pickett’s experimental data support the deduction expressedin eq, (45) and (46) that volume change is directly proportional to a partof the total water-loss, It remains for future experiments to prove ordisprove the deduction that the part responsible for volume change isthe adsorbed water. It is of interest in this connection that in Fig.4-12 the “b” water constitutes 60 percent of the total lost at 50 percentrelative humidity. The highness of this proportion suggests that shrink-age is proportional to the loss of gel water rather than to the loss fromthe first adsorbed layer only. This indicates that W. of eq. (45) includesabout the first four layers of adsorbed water.

CAPILLARY FLOW AND MOISTURE DIFFUSION

In connection with this discussion of the thermodynamics of adsorp-tion, about all that need be said about capillary flow and moisturediffusion is that these phenomena take place as a result of inequalitiesin free energy. Under isothermal conditions, capillary water will move


if the effective radius of curvature (see eq. (42)) is not the same on allexposed surfaces of a continuous body of capillary water. In Fig. 4-11it is apparent that the addition of water, by condensation or otherwise,to the outer concave water-surfaces, would decrease the curvature ofthose surfaces. Water would therefore flow inward until the innerwater-surfaces would have acquired the same curvature as the outer.

Where capillary water is absent, adsorbed water will move along anycontinuous surface if a gradient in the f;ee energy. of the adsorbed waterexists. If an inequality in free energy exists between water on discon-nected areas, the transfer of water will occur by distillation through thevapor phase. If surface migration and distillation are both physicallypossible, both will occur simultaneously, However, in an extremelyfine-pored substance such as the gel in hardened paste, most of thetransfer is believed to be effected through surface migration.

inequalities in free energy

Inequalities in free energy under isothermal conditions arise from

inequalities in moisture content, as shown indirectly by the water-

content-vs.-vapor-prcssure isotherms shown in Part 2. Hardened cementpaste is of such nature that a change in moisture content of a givenregion in the paste, however slight the change may be, changes the free

energy of the water in that region. *Inequalities in free energy under isothermal conditions may also

arise from deformations of the solid phase. In Fig, 4-11 we can see that

if the spacing of any pair of spheres were changed, the surface curvatureof the ]vat,er lens v-ould likewise change. This would require a redistri-bution of moisture to restore equality in free energy of the capillarywater throughout the system. Also, a change in external pressure actingon the adsorbed water would change the free energy of the adsorbedwater, as indicated by eq. (32) and (33),

Thus inequalities in stress and strain produce inequalities in the freeenergies of both the adsorbed water and capillary water and therebyinduce redistributions of moisture within the mass. This, as has beenpointed out by Lynam, t20J Carlson, (22) and others, is an importantfactor in the gradual yielding of concrete under sustained stress knownas creep or plastic flow. The changes in moisture distribution causelocalized shrinking and swellings with consequent changes in the de-formation of the body as a whole.

EFFECT OF TEMPERATURE CHANGES

The experimental part of these studies has not included measure-ments of the effect of temperature changes. However, some of these

*If, however, the external pressure on the adsorbed water changes at the same time, the relationshipbet ween water content and vapor pressure will not be tbe same as when external preesure remains constant.See later discussion.

5UI JOURNAL OF THE AMERICAN CONCRETE INSTITUTE January 1947

effects can be deduced qualitatively with the aid of the theories andprinciples introduced above.

Effect on swelling

It was shown in eq. (44) that at equilibrium the capillary tension equalsthe potential swelling pressure. That is,

[]AP=F=u ~+~ =–

RT—2?zp/p8, . . . . . . . . . . . . . . ..(47)

rl rg Mu[

Since an increase in temperature causes an expansion of the adsorbedwater, the surface curvature of the water in the lenses must decrease.Moreover, the surface tension of water decreases with increase in tem-perature. Hence, the capillary tension must decrease with increase intemperature, provided the water content remains constant. This inturn would mean that an increase in temperature would cause expansionowing to swelling, in addition to the thermal expansion. JiIo}vever, ifthe specimen is initially saturated, no change in swelling pressure canoccur because for this condition capillary tension is zero, or insignifi-cantly small. Obviously, ifthespecimen contains noevaporable water,no swelling due to moisture can occur when the temperature is increased.

Evidence of this may be found in data published by Meyers. (2’) Thecoefficients of thermal expansion of neat cement and concretewere measured at various degrees of saturation, with res~lts asin Table 4-7.

TABLE 4-7—MEYERS’ DATA ON THERMAL EXPANSIONFOR SATURATED AND PARTLY SATURATED SPECIMENS

(Temperature range 70 to 120 F)

prisms

shown

Thermal coefficientin millionths

for condition indicated— --

Seall$~toroage After soakingfor 1 week

Normal portland cement 10.3 5.7Concrete (flint aggregate) 8.1 4.9Cement-sand mortar 1:1 6.3High-CSA’cement 1!:2 5.6

Note that the sealed specimens * show much greater expansion thanthe same specimens after soaking. According to the foregoing discussion,the figures in the last column represent the true thermal coefficientof the solid phase, whereas those in the first column represent the com-bined effect of thermal expansion and swelling caused by the decrease inswelling pressure.

*The specimens were stored in copper-foil jackets with soldered seams. Even though sealed they couldnot remain fully saturated,


It was stated above that if all the evaporable water is removed, a risein temperature would not cause swelling. This too is confirmed byMeyers’ data, as shown in Table 4-8. These data show that drivingout all the evaporable water (or most of it) reduced the thermal co-efficient of a specimen below that of the same specimen in the partiallysaturated state. Comparison of Tables 4-7 and 4-8 indicates that thethermal coefficient for the “bone-dry” and saturated states are aboutequal.

TABLE 4-8–MEYERS’ DATA ON THERMAL EXPANSION—EFFECT OF EXTREME DESICCATION

(Temperature range 70 to 120 F)

Thermal coefficientTy e

OF’in millionths

for condition indicatedmaterial — —

Before Dr$dllow:kdrying

——. — .—— —— ———High early strength cement 6.0White cement l::i 6.5,~m,mal Portland cementConcrete (limestone aggregate)

6.0::: 2,1

Meyers found that the introduction of a liquid that does not causeswelling, kerosene, did not change the thermal coefficient appreciably. *

Effect on diffusion

If temperature gradients are established in a concrete mass, watermust move in the direction of descending temperatures. This followsfrom rather simple considerations. An increase in temperature in anyregion of the mass must be accompanied by an increase in the watervapor pressure in that region in accordance with the Clausius-Clapeyronequation. Water then moves toward the regions of lower temperaturewhere the vapor pressure is lower.

The movement of water thus induced is accompanied by shrinkage inthe regions where the temperature is increased which tends to offset theexpansion due to swelling and thermal expansion. Conversely, in theregions where the temperature is lowered, swelling tends to offset theshrinkage and thermal contraction. However, these effects cannot beevaluated quantitatively at present.

Combined effect of stress, strain, and temperature gradients

It can readily be seen that deformations of the solid phase and tem-perature changes together or separately cause moisture movements in

*It should be observed t,hat a single tl}ermal coefficient cannot correctly be essigned to a givens ecimemof roncrete. The “coeficlent” is, a var,mble that changes with evaporable water content. The fumtionmust be such that the coefficmnt M a mlnlm urn for the bone-d;y and saturated states and a ,maximum f?rsome intermediate evapor?ble water c,on~en~. hleyers’ data ]ndlcate that the variation with change mevaporable water content M far from mmgn]fican t.


concrete, The separate effects may combine in different ways so thatthey may offset or augment each other at a given point in the mass,During a period of heating, cooling, or changing external force, theseparate effects may combine in different ways at different times at thesame point, The over-all result is that in concrete subjected to changingexternal forces or temperature or both, the evaporable water must be in acontinual state of flux. If the ambient humidity also fluctuates, theinternal moisture movements are still further complicated, Possiblythese effects have an influence on the ability of concrete to withstandweathering,

SUMMARY OF PART 4

(1) This part deals with energy changes of adsorption and with theirrelationship to shrinking and swelling, capillary flow, and moisturediffusion.

(2) The net heat of adsorption is the heat in excess of the normalheat of condensation that is released when water vapor is adsorbed.The total net heat of adsorption of hardened paste is approximatelyequal to the heat of immersion of the adsorbent.

(3) The net heat of surface adsorption is that part of net heat of ad-sorption that has its origin in interaction of the adsorbed moleculesand the solid surface. It is related to the heat of spreading-wetting andin cement paste is equal to about 472V~, *

(4) The net heat of capillary condensation is the total heat of water-surface formation, It is about equal to the difference between the heatof immersion and the heat of spreading-wetting, In cement paste itis equal to about 100V* cal per g,

(5) The net heats of adsorption at 11 different initial water contentswere measured, using two different samples of hardened paste.

(6) The total net heat of adsorption was found to be about 572V~cal per g or about 670 ergs per sq cm of solid surface. This is about thesame as the heat of immersion of various mineral oxides in water.

(7) Among portland cements of all types the total heat of hydra-tion ranges from about 485 to 550 cal per g of non-evaporable water.Data from two cements indicate that of this amount about three-fourthsis due to the heat of reaction of the non-evaporable water and the restis due to the net heat of adsorption of the evapora,ble water.

(8) The total internal energy change of adsorption is equal to thechange in enthalpy minus a small “PAo” work term representing the con-traction in volume under constant external pressure that accompaniesadsorption. The enthalpy change is thus essentially equal to the net heat

*V~= weight of adsorbed water required to cover the surface of the solid phase with a monomoleoulmlayer.


of adsorption and is the sum of the free energy and unavailable energychanges, i.e.,

Q. = AH = AG + TAS’,where

– Q. = net heat of adsorption,AH = change in enthalpy,AG = change in free energy,AA’= change in entropy,

T = absolute temperature,TAS = change in unavailable energy.

(9) The free energy ch?nge of water that occurs when the water be-comes adsorbed can be expressed in terms of vapor pressure change alone.When the initial and final vapor pressures are p, and p, respectively,

. AG = – 75.6 loglop/ps.where

p = existing vapor pressureps = saturation vapor pressure

(10) Unavailable energy is equal to the difference between the netheat of adsorption and the corresponding free-energy term, i.e.,

TAS’=Q.-AG.(11) Entropy change, Afl, is an indication of the extent to which

adsorption modifies the adsorbed water. The data show that for waterisothermally adsorbed at low vapor pressure the entropy change of

adsorption is of the same magnitude as that accompanying solidifica-

tion, or the combining of water in a salt as water of crystallization.

(12) The differential net heat of adsorption is the differential of the

Q.-vs.-w relationship, It is at a maximum for the first increment ad-

sorbed, and becomes zero with the last increment at p = p,.

(13) The maximum differential net heat of adsorption is about 400

cal per g of water. This is also the minimum heat of reaction of thenon-evaporable water. Expressed on the same basis, the heat of com-

bination of water in Ca(OH) 2 is 847 cal per g of water. This shows that

the maximum energy of binding for evaporable water and the minimumfor non-evaporable water is much less than that of the bond of water

(i.e., hydroxyl groups) to calcium.

(14) The average net heat of adsorption of the gel water appears to beabout 143 cal per g of gel water. The average for the first layer of ad-sorbed water appears to be about 270 to 300 cal per g. These figuresare probably too low owing to the effect of adsorbed air.

(15) The logarithm of the constant C of the B.E.T. equation~s theoreti-cally proportional to the net he?t of adsorption. Recent work has shownthat assumptions concerning the proportionality constant made by


B.E.T. are invalid and that values of net heat of adsorption based onthis assumption aro too low.

(16) Cement gel belongs to the limited swelling class of gels.(17) S\vclling pressure i~ the increme in Pxternal pressure required to

prevent swelling It can be estimated from the following relationship:

R TAP = – — 2.303 loglOp/p, ,.

Mu,where

Al’ = swelling Immure, excess over normal external

pressure,R = the universal gas constant,

M = molecular weight of aclsorbate,u, = specific volume of adsorbate.

This gives the pressure required to prevent the isothermal swelling ofa gcl dried to vapor pressure p when it has access to Irec water,

(18) The externally mi~nifested s]velling pressure of concrete lvol~ldprobably bc less than that calculated from the above equation.

(] 9) ‘JIM order of magnitude of the total volume change of hardenedcement paste can be accounted for on the assumption that the changeis due to the removal or addition of the first layer of adsorbed watermolecules.

(20) rrotal volume change cannot bc regarded solely as a capillary

phenomenon, since expansion does not occur ~vhen the cvaporable water,

and hence meniscuses, disappear. When capillary }vater is present,capillary tension is equal to swelling pressure ~vhcl~the system is atequilibrium.

(21) Experimental data show that volume change is directly pro-portional to a part of the total change in water content. This agreeswith 19, which implies that volume change is independent of the changein capillary-water content. The data suggest that volume change maybe proportional to the change in gel-water content, rather than to thechange in the first layer only.

(22) Capillary flow or moisture diffusion or both occur under isothermalconditions when there are inequalities in the free energy of the evapor-able water in different regions in the specimen. Inequalities in freeenergy under isothermal conditions arise from inequalities in moisturecontent, from deformations of the solid phase, and from inequalities inexternal pressure on the adsorbed water, Resulting moisture movementis an important factor in plastic flow.

(23) An increase in temperature causes a decrease in swelling pressureof partially saturated pastes and thus causes an effect on volume changein addition to the usual thermal expansion. Evidence of this is found indata obtained by Meyers.

PHYSICAL PROPERTIES OF HARDENED PORTLAND CEMENT PAS1”E 595

(24) Changes in external forms and changes in :~n~l,icnt tempcratl[re

and humidity keep the evaporable water of a partially saturated specimen

in a continual state of flux. This possibly influences durability.

REFERENCES

(1) Wm. D. Harkins and Gee. Jura, J. Am, Chem. Sot. v. 66, p. 1362 (1944).(2) Wm. D. Harkins and Gco. E. Boyd, J. Am. Chem. Sot. v. 64, p. 1197 (1942),

Table I.(3) Samuel Glasstone, Ph~sical Chemistry (D. Van Nostrand, 1940), p 175.(4) A. B. Lamb and A. S. Coolidge, J. Am. Chern. Sot. v. 42, p. 1146 (1!)20).(5) Luke E. Steiner, Introduction to Chemical Thermodynamics (McGraw-I-Iill, 1941),

p. 46.(6) J. R. Katz, Ergibnisse der Exacten Naturwiss v. 3, p. 316 (1924); v. 4, p. 154

(1925); Trans. Faraday S’oc. v. 29, p. 279 (1933).(7) J. D. Babbitt, Can. J. Res. v. 20? Sec. A, p. 143 (1942).(8) N. E, Dorsey, Properties of Ordznary Water Substance (Reinhold, 1940), Table

123, p. 267.(9) Ref. 8, Table 201, p. 467.(10) R. R. Wenner, Thermochemical Calculations (McGraw-lIill, 1!141), pp. 177 and

216.(lea)(11)(12)(13)(14)(15)(16)(17)

p. 60.(18)

Ref. 10, p. 178.R. L. Steinbergerj Textile Research v. 4, p. 451 (1934).Ref. 10, p. 44,Wm. D. Harkins and Gee. Jura, J. Am. Chem S’oc. v. 66, p. 919 (1944).Ref. 2, Table VI.H, l’reundlich, CoUoid and Capillary Chemistry (E. I’. Duttcm, 1!)22), p. 073.Ref. 3, p. 659.F. I.. Hummer and S. hf. Dore, Soil Mechanics and Folmdations (1’ihnall, 1940),

N. K. Adam. The Phvsics and Chernistrv of Surfaces (Oxford [Jniversit.v Press,1930); pp. 8, 9.

. . .

(19) Researrh Reports of the Portland Cement Association ltescarch I.aborwtory,Al)pendix 3, July 1942, ur,published.

(2o) C. G. Lynam, Growth and Movement in Potihrnd Ceownt Concrete (oxford Uni-versity Press, 1934).

(2I) S. 1,. IIeyers, in-d. Eng. Chem. V. 32, p. 1107 (1$!0).(22) R. \\’. Carlson, Proc A. S. T. M., v. 35, Part 11, p 370 (1935).(23) A. B. D. Cassle, Trans. Farada~ SrIc. v. 41, p. 450 ( 1!W3).


Appendix to Parts 3 and 4

This appendix gives tables of non-evaporable water, ton, water required for the firstmonomolecular layer of adsorbed water, V~, the ratio V~/wn, the B.E.T. constant C,and the computed surface of the dry paste for all the series used in this discussion.

In estimating Vm for some of the groups of data from plots oflx~ ~z versus w,*

the same value of C could be used for all items in the group. In other groups the datacould be represented best by using different values of C for different items, In some in-stances the points were too few and too scattered to establish the slope of the line. Whenthis was true, a value of C was estimated and the line was drawn in such a way as toconform to the experimental points and the assumed value of C as closely as pmsible.

The samples of Series 254-265 were dried over concentrated H#O, instead ofitfg(CZOi)2.2~~@. This aocounts for the relatively low ratio of V~/w” and low valuesof C for this group.

Wee Part 3.

TABLE l—V., C, COMPUTED SPECIFIC SURFACEAND OTHER DATA FOR SERIES 254-!265”

Cement 14502

V.t, g per g of:u., g per g Of: ____Age —~: z)riginal Dry Original Dry .J!!L

t%,c

cementday~t i

paste cement paste run

1.—— —- ] I “1 I lL—————323 110 .160506 110 ,179506 110 .183512 110 .200515 110.518 110

;j;:

521 110 ,219

,024

,030.031.030.037.036.037

,0210.0266.0287.0272,0336.0311.0324

,152.168,172.150,160.1.58,170

S,611,75,57,s5,26,73.7

, , 1 I I 1

Sp. surfaceof drypaste,ems/g

miUions

0.75:.;:

0:971.201.111.16

*%mpleS of this group were dried over concentrated ~2~04 instead of over M17(C104)L2HIO as in the othertests. tApproximate.

CementNo.

14NM-lAQ14SW-lPC14!IO0-lSC

14901 -2.4fJ14902-21’C14903-2SC

14904-3AQ14905-3PC14906-3SC

149074AQ14908-iPC14909-4SC

14!)1O-5AQ14911-5PC14912-WC

14913-6AQ14914-6PC14915-6SC

TABLE !?-kAND C

Netw/c

. 3S2,388.446

.391

.393

.424

.425

.411

.476

.406,3044s3

.460

.464,480

,410.423.437

——

*tie

test,days

—120120126

126133133

162162173

173200200

204204212

212222222

w.,

Originscement

.2171

.2225,2274

. 222s

.2273

.2271

22S4.2261.2344

.21S5

.2249

.2255

. 22s2

.2294,2252

.2206

.2253

.2240

; of:

Drypaste

. 17s4, 18~Ij. 1s53

.1822

. 1X52

. 1s51

.1859,1869.1906

,1797.1836.1840

1s5s1s66183s

. 1s07

.1829

. 1s30

D SPECIFIC S()R SERIES $!54

v.,,-——

2riginacement

,057,0560.5s

,054.056.056

.061

.063

.063

.060

.060

.059

.059,060.062

.062,060.060

: of:

Drypaste

.047

.046

.047

.044,046.046

.050

.052

.051

,049

,04904s

,048.049,051

.051

.049

.049

tFACEMRB

v.—w.

.269,253.254

.24223S

,248

.268

.27826X

,273.267.261

25s,262,276

. 2s2

.266

.268

c

::IS

181818

181s1s

18181s

18

;:

1s1818

S:i ~;f.

paste,cm2/gmilhons

1,681.641.68

1.571.571.64

1.791.S61.82

1,751,751.71

1.751.711.82

1.s21,751.75


TABLE 3—V. C, COMPUTED SPECIFIC SURFACEAND OT~ER DATA FOR SERIES 954-K4B

CeNm3nt

13721-1S13722-1P13723-IQ

13730-4s13731-4P13732-4Q

13733-5s13734-5P13736-5Q

13736-6S13737-8P1373S-6Q

13740-7P13741-7Q

13762-11P13753-llQ

13763-15s13764-15P13765-15Q

13766-16S13767-16P13768-16Q

13778-20S1377LI-20P13780-20Q

Netw/c

,470.473.425

,463.460

,.450

.427,453,456

,471

.Z7

,473,480

.445,440

,485

. Ii5

. ;4

.456

.472

.462

.436

A$

test,days

174180180

144138138

150146150

196191191

164171

164172

202190202

322223223

170167176

w“, &!/i?of:.——higinal!ement

K,2332,2290

,1786,1772,1773

,1650,1589,1650

,2148,2297.2220

.2395,2390

,1864.1896

.2173,2109.2201

,2096,2256,2250

,2308.2329.2262

Drypaete

.1824,1891,1863

,1515.1505,1506

,1416,1371.1416

,1768.1868,1817

,1932.1929

.1571

.1594

.1785

.1742

.1804

,1733.1841,1837

.1875

.1889

.1845

v!?!, f

)rigirmlcement

.0634

.0618

.0697

.0486,0426.0447

,0591,0637,0559

.0682

.0617

.0537

.0530

.0597

.0545

.0553

,0594.0640.0623

.0611

.0565

.0569

of:

Drypaete

.0518

.0501

.0486

,0412.0362.0330

.0486

.0518,0457

,0550,0498

,0463.0446

.0490

.0450,0453

,0491.0522. 0s09

.0496

.0458

.0464

v“

“Yz

.284

.265,261

.272

.240

.252

,275.277,252

,28526s

. 28S,,280

,275,238,2.51

,283.284.277

,265,242.2.52

——

c

181818

1s181s

Is1818

1818

1818

181813

181818

181818

S:i S#

paste,~m2/g

millions

1.851.7E1,74

1.47,1,291,36

1.741.851,63

1,961.78

1,621,59

1,751,611.62

;,%

1:82

1.771.641.66

I

TABLE 4—Vm C COMPUTED SPECIFIC SURFACEAND OT~Eh DATA FOR SERIES 254-8

Age w., g/g of:Ref.

Vm, gfg of: S:i Su;f.Net —— ——— v. c

No. t%, w/c oriKiey: Dry Original Dry z paete,days paste cement paste ~~?fg

millions

Cement 14930J

254-8-1 447

I

.312 .1808 .1530

I.053.045

I

.294 21.0

I

1,61

254-8-2 362 ;44; .2006 .1671254-8-3

; (l:: ; ::5) .310 21,0 1,83362 ,2101 ,1736 .313 21.0 1,94

Cement 15007J

254-8-28

I479 .351

I.1!380

I.1652.063 .052

I.316 18,0* —1.86*

254-8-29 440 .464 .2169 .1782 .0.58 .048 .268 17.0 1.70254-8-30 479 .59.5 .2323 .1885 .060 .049 .256 20,6 1,73

Cement 1501 lJ

254-8-40 I478

I.319 .1843 .1556

i

.051 ,043

I,276

254-3-41

18.0

I

1.54368 .442 ,2102 .1737 .058 .048 .276

254-8-42

16.4 1.73368 .596 .2218 .1815 .062 .051 .280 15.0 1.81

Cement 15013J

254-8-46 339

I.333.2185 .1793

I.052

I.043.239 19.2 1.53

254-8+7 333 ,454 .2407 .1940 .058 .047 ,242 17.6 1.67

254-8-48 333 .599 .2527 .2017 .057 .04.5 ,224 17,6 1.63

lx*Estimat-ed; -— vs. z doss not give straight line.

ru l-z


TABLE 5—V. c COMPUTED SPECIFIC SURFACEAND OThElt DATA FOR SERIES 954-9

y Wn,glg of: Vm, dg of:g:

S:f yr;.—— — &*

test, ::rie:; Dry Original Dry cdays

paste,paste cement paat.e ‘n ~~ llg

millions— — ——

Cement 14930J; w/cat 2 hr. 0.309

:5i9il 7 .0804 .0744 — .021 T Y— 18 o,70—;::;; .0004 .027 ,024 ; ;;; 18 0.88

:: .0967 .034 ,031 1s56

1,11; ;:;; .1144 .043 ,038 ,330 18 1,35

.1302 .046 ,040 ,3041%

1,41.1620 ,1400 .050 .043 .310 :?

3651,55

,1704 ,1456 .049 .042 .290 21 1,51—. —

w/c at 2 hr .0,424— — ——

~9-2 7 :::;; ,0739 .021 ,020 .288 18 0.71Mix B ,0933 ,028 ,025 .276 18 0,92

;; .1165 .1044 ,037 ,033 ,310 1.195; .13.52 .1191 ,049 ,043 ,363 ;: 1,54

.1735 .1470 ,033 :04!5 ,306l~i

1,62.1853 .1564 ,039 ,050 ,310 ;: 1,7X

365 1%3 ,1634 .050 ,049 ,302 21 1.76——— —. — — . .

w/c at 2 hr. 0.573—. — — —.254-9-3 7 .0822Mix C

,0760 ,022 ,020 ,270 18 0,73.0896 ,0822 .028 .026 ,313

::0,02

.1214 .1083 .043 .038 .351 ;:.56

1,36.1638 ; ;::! .049 .042 ,298 16 1,50

1s50 .0.55 .0461%

.298 1s 1,66,2008 ,1672 ,056 .047 .279 18 1,66

365 ,2142 .1764 .069 .057 .324 18 2,04—.--— —— —— —— . — . — —.

Cerne nt 15007J; WIc at 2 hr. 0.318—.--—.——— —— —— — — — — ——. .?X;oi4 7 —. 1250 .111s ,036 ,032 ,2s4 18 1,17

,1404 .1231 .041 ,036 ,296::

18 1,30.1538 ,1332 .042 .036 ,276 1,31,1681 .1439 ,047 ,040

% . 172!J.281 ;: 1,44

.1474 .048 ,041 ,276 2; 1,45180 ,1835 ,1550 ,048 ,041 .265 10 1,46

_—_-. — —— —— — — — —w/c at 2 hr. 0.432—— —— — — — —. ——

piy 7 ,1334 .1177 ,036 .032 .270,1498

1,14.1303 .042 ,037 .278

;:

;: 1.29.1714 .1463 04!5 .038 .265

5(i18 1,30

,1647 ,1559 . (349 ,041 .266 fi8 1.48I!)24 .1614 ,056 .0’47 ,290

l%_ ,2018 _-, 167920 1,67

.0.55 .046 ,271 16 l,ti3_——-——_-. — — — — — ————

w/c at 2 hr. 0.582

$;;060 7 1500 ,1330 —.037 ,032 :;;; I ;; 1,13.1634 .140: ,042 ,036

;:1,20

1839 1553 ,050 ,0’42 27256

18 1.51:2035 . llwlo .0.33 ,044 ,259 18 1,57

:10 .2049 ,1700 .056 ,046 .272 1f; 1,66180 .2132 17J7 .060 .050 ,283.- 20 _1.78——. . ..—.

Cement 15011J; w/. at 2 hr. 0.338

254-9-7 7——

,1= 1020 ,033 ,029Mix A :% I :;

1.05.1333 .1176 .036

::,012 1,13

.1430 ,1251 ,04,5 .0405[i

1,42,1357 .1347 .046 ,040 .296 ii 1.43

90 . llM3 .1411 .043 ,037 .263 22180

1.33.1705 .1457 04!5 ,038 ,264 25

:651.37

.1760 .1497 .048 ,041 ,273 25 1,46——w/c at 2 hr. 0.433

~;i9~8 7’ .1228 . 10!34 ,037 .033 ,304.1527 .1325 ,038

22 I 1,19-–.033

&,247 27

.16541,17

,1419 .045 ,039 ,27256

23..1781

1,38,1512 .047 .040 ,266 23 1,44

!J913 ,1606 .0511%

.043 ,267 23.1086

1.53.1657 .0.56 .046 .280 16 1,66

*Calcul:. ted before rounding V* values to 2 significant figures. (Concluded on p. 599


TABLE 5--CONCLUDED— !- 1

Agep:.

w., g/g of: Vln, g/u of:.— V.,*

t%, Original Dry Eiginal –days

Dry ~cement paste cement paste

c

s:; y;f,

paste,~m2/g

millions(__———— I 1— I — I — I

Cement 15011J; w/c at 2 hr. 0.570—.— ——

:5;969 7 ,1314 .1161 .034 .030 ,261 27 - 1,08.1567 .1355 .039 .034 ,252 22 1.22

;: .1756 .1494 ,047 .040 26S 18 1,43,1953 ,1634 .034 .045 .274 17 1.60

% .2046 .1698 .058 ,046 .272 16 1.65180 .2136 ,1760 .057 ,047 ,266 16 1,671—..———1—l l—l l—l—l

Cement 15013J: WIICat 2 hr. 0.324—— — .— —..$jilo 7 .1488 ,129.5 .036 ,031 .240 21 1.11

.1639 ,1408 .039 ,033 ,236 20::

1.19.1711 ,1461 .043 ,036 ,250 23 130.1802 ,1527 ,046 ,039 .254 22

::1,38

.1913 lfi06 ,047 .040 .248 1,42180 .1877 ,1580 .051 ,043 ,272 ;; 1,54

_——— .— .— . . — ——W/C at>2 h r. 0.443

—.— —— —— —— —.~:;9il 1 7— ,1556 .1346 .037 .032 ,235 1,13

,1828 ,1545 ,042 .036 ,232 ;!;:

1.28.1770 ,1504 .048 ,041 ,271 21 l,4ft

56 ,2085 ,1725 .053 .044 .254 18 1.57,2152 ,1771 .057 ,047 ,203 15

1%1.67

,2356 ,1907 ,058 ,047 ,248 16 1,69.—— —— — — —_—_

wic at 2 hr. 0.611—. —— ——~;;9612

—————

7 ,1583 — ,1367 ,033 ,029 ,211 27 1.03.1828 ,1545 .040 .034 21{] 21

E1 21

2[M8 ,1686 .046 .038 ,220 21 1.36., ,2208 ,1809 ,055 $)4; ,250 16%

1,02,2357 ,1907 .058 ,245 19

180 .24471 67

,1966 . OXI ,047 ,239 17 1.68

Cement 15365;. w/. at 2 hr. 0.322

~;oil 3 7 .1326 ,1171 .034 .030 ,2.541515

24 ‘,1316 . 0J7 .032 243 24

E 14S8 ,1295 .044 ,038 ,294 2056 .1786 ,1515 .047 .040 .264 22{)0 ,1789 1318 .048 ,040 2f)i’ 20

180 ,1815 .1536 ,Oifi ,039 _l__?,;6 ~~_--_— —— .— ——w/cat2 hr. 0.439

~;;!li14 13!34 .1223 ,0341:

::;; I ::;; 2C 1.06,1711 ,1461 ,04J

2820 1,:32

,1841 1.55,; Os.i .046 2!1!5 1!1 1 li4.56 .2105 .1739 05; ,045 ,26190

1, Ii!.2150 ,1770 ,056 .046 .263 i: 1,66

180 ,2224 ,1819 .060 ,049 26!3 1!) 1.,73

WIC at 2 hr. 0.587

254-9-15klix C

7 .1530 ,1327 ,037 .032 .242 2s 1.15,1855 1.565 .04.5 03s

‘H,241 22 1,33

,2102 ,1737 .035 ,043 ,261 1!) 1.fi2.x3 ,2213 1s12 ,057 .047 2X) 22 1.68

1’-~__l: ] :Ri:i

1s67 ,062 .051202!)

,271 1{, 1.81,060 . 04s ,’235 lo 1.70

-— .—-. —. — — — .—— —

wfc at 2 hr. 0.244_—— __ —. —-. — _— ___2:4-!)-16A 7 ,1152 ,1033 0!!8 ,025Neat,

.2441259

Cement.1118 .030

;:.027 .242

.1338 .1196 ,032 (j~~ ,2:4256 13qfi .1225 ,034 OX) 24(1

1452 ,1268 ,034 .030 ,2361:: ,1.534 ,1345 .035

Isotherm A.031 2.)0

270 .1691 ,1446 ,032 02xIsotherm B

1!13270 .1722 ,1469

————— ’031 l-f12L. 2..

333333333:3331:)1(i

f), f)o(),<,H

(). !)01.051,071,0!)0,9!)o,g~

*Calculated before rounding V.,values to 2 sigl]ificant figures.


TABLE 6—Vm, C, COMPUTED SPECIFIC SURFACEAND OTHER DATA FOR SERIES !254-11

CeNmOent

15;58

15156

15163

15761,!

15754,,

1621316214161981.5669

11-111-211-311-411-511-6,11-711-811-911-1011-1111-1211-1311-14

11-111-211-311-411-511-611-711-811-.911-10

w., g/g of:w/0 —— —

Original Dry2%. cement paste

—— —— .

.334

.460

.318,446,324,437.334.468,328.449,443,448,444.452

.334

.460

.318,446,324,437,334.468.328,449

Vnr, g/g of:——— .

Original Drycement paste

— —Age at test 28 days

.1912

.2227

.1492

.1684

.1335

.1487,1798,21201!3512301

f

*Cakmla8ed before rounding ,V~ values to 2,

,043.050.034,03,502s

.031,041,049

.044

.050

.047,048.032.028

at test !30 days

.1605 .047—

.1821 ,054,1298 ,043.1441 ,0445.1178 .041,1293 ,0445,15’24 .048,1749 ,055,1632 ,047.1871 .038

at test 6 days

,037.042.031,031.026,028,035,042,037,042,040,040.029

,025

,039,044,037,038,036.039.040().!5

.039~

V2*

w!!

2W2,254,2s1,267,307.305.251.266.256256

.273,258.296,262

.245

.244

.287

.267

.304

.303264Ml

,241.250

c

H181818181818181818181821

21

;?18181818181818

S:i S&f.

paste,cm? /g

millions

1.311.491.101.110.921,001,251,481.331,501,431,441,050,92.—

1,411,591.331,371.281,401.441.621,411,67

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASIE 601

TABLE 7—V., c, COMPUTED SPECIFIC SURFACEAND OTHER DATA FOR SERIES !254.13

Ref.No.254-

13-113-213-313413-lB13-2f313-3D13-4f3

S03 W*, 6A?,of: V.n, g/g of: S:i .9urYf.wf c content —— V.*

of Original Dry Original Dry2a;r.

G c paste,cement, cement paste cement paste ~m9/gpercent’ millions—.————— —1— I

.493

.493,489.491,4864s8

.488,402

Cements made from clinker 15367


13-17

I.476I I

,1108,0997 .031 ,028

I,282

13-18 .479 ;:1 .1182 ,1057 .034 (XJO .28713–19 .483 2,5 ,1842 1555 .042 0J6 ,23113-20 .486 3.5 .2087 .1727 .050 ,042 .241

*Calculated before rounding VIIIvalues to 2 significant figur-.

18,0

I1,01

18,0 1,0818.0 1.2818,0 1,49


16-OIA16-0113ltj-olcAvg..— .—— —.16-02A16421316-WCAvs.

16-(I3A16-03f316-(HC16-03J)Avz.———.

TABLE 8—V., C, COMPUTED SPECIFIC SURFACEAND OTHER DATA FOR SERIES $!54-16

— —— —

Age w“, E/g of: Vm, g/g of:11t

OrigirmlV.*

test, l)ry (lriginal ‘Dry -w: cdays cernen t paste cement paste

IIMad on moximum weixhts atti~ined during adsc

272729

42

::

—— .—

.51),.,~,

fi363

,137,513.io

,1336.1350

,12:37,12.10,1306,1312,1274——..——

,053,0:,3,052,053

.037O:W

,036,036

.036,037fj39

,039,038_ .—

,044,044()’43044

,032,030,031.031

.——,032VU0J4

,034,033

Based cm weights }Lttinle heat-of-solutiorme,asaremeuts were made—. ————

16-01.\16-0113

1

~ I ;;Xl:;

IltiS8

l-l,051 o~~—

I17(Y2 ,050

16-OIC,041

29 20-J2 ,1696 -—

AVE. .2041 ~fj(j~ .050 042—-——..—.. I .——. ———

16-WA .}~ 15!M 1375 .036 ,0311O-O2L+16-02CAvg.

__::__, -_:gj I ~% _g ;%

*C&.ulated before rounding V,. \)al um to 2 significantfiiwrea.

on teat,259—.258,2562.58———

,230.228,233.230—.—,255,268~fjo

.258!258

22222222

2222

222222

-—— l—

2-i6 I 22

,223 22224 22

.23: 22,227 22

y su;f.

paste,~m2/g

millions

1, 56—-1,571,551,56

1,131.081.111,11

1.121.151,211,211,17

——

1..511,47

1,49

1,091.081,1’21.10——


Part 5, Studies of the Hardened Paste by Means of Specific-Volume

Measurements*

CONTENTS

Classification of water in saturated paste according to mean specificvolume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...670

Mean ratio of(l–uJtowfi/w/. . . . . . . . . . . . . . . . . . . . . . . . ...686

Lower limit of mean specific volume of total water. . . . . . . . ...687

Estimation of the bulk volume of the solid phase and volume ofcapillary water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...688

Estimation of the absolute volume of the solid phase. . . . . . . . . . ...690

Method of measuring volume of solid phase. . . . . . . . . . . . . . ...690

Choice of displacement medium . . . . . . . . . . . . . . . . . . . . . . . . . ...692

Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...694

Specific volume of non-evaporable water. . . . . . ., . . . . . . ...695

Specific volume of gel water . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...696

Computation of volume of solid phase from non-evaporablewater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...696

Limit of hydration for pastes of high cement content. . . . . . ...704

Limit of hydration with capillary water continuously a-vailable.706

Estimation of volume of unreacted cement. . . . . . . . . . . . . . ...707

Graphical summary of data on volumes of various phases inhardened cement paste . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...708

Some practical aspects of the results. . . . . . . . . . . . . . . . . . . . . . . . . ...708

General summary of Part 5........ . . . . . . . . . . . . . . . . . . . . . . . . ...710

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...712

*The characteristics of the cements mentioned in this section may be found in the Appendix to Part 2.

670 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE February 1947

CLASSIFICATION OF WATER IN SATURATED PASTEACCORDING TO MEAN SPECIFIC VOLUME

The total water content of a saturated sample of hardened paste hasalready been classified according to its evaporabilit y, i.e., into evaporableand non-evaporable water. We have seen also that the evaporablewatel w.n be subdivided into gel water and capillary water on the basis ofvapor pressure data. The following discussion will show that the sameconclusion can be reached on the basis of the mean specific volume of thetotal water.

The non-evaporable water is regarded as an integral part of thesolid phase in hardened cement paste. In becoming a part of the solidmaterial some or all of it may have lost its identity as water. Never-theless, the absolute volume of the solid phase can be considered as beingequal to the original volume of the cement plus the volume of the non-evaporable water. If the absolute volume of the original cement, theabsolute volume of the whole solid phase, and the weight of the non-evaporable water are known, a hypothetical specific volume can beassigned to the non-evaporable water such as will accoufit fo: the knownvolume of the solid phase. This hypothetical specific volume is knownto be less than 1.0; that is, the non-evaporable water occupies less spacethan an equal weight of free water. Moreover, the physically adsorbedpart of the evaporable water also has a specific volume less than 1.0.Thus, in any given specimen the mean specific volume of the non-evaporable and adsorbed water is less than 1.0.

On the other hand, any capillary water present will either be in a

state of tension or under no stress at all. If the specimen is not saturated,so that the vapor pressure of the contained water is less than p, but more

than about 0.45 p,, capillary water will be present and under tension.

(The magnitude of the tension is theoretically equal to the potentialswelling pressure. See eq. (39), Part 4.) If the paste is saturated, so

that p = p,, the capillary water will be under no tension, Hence, whencapillary water is present, but the paste is not saturated, the specificvolume of the capillary water will be greater than 1.0, and if the specimenis saturated, the specific volume will be 1.0, except for a slight effect ofthe dissolved salts.

Thus, we can divide the total water content of a saturated specimeninto two categories:

(1) Water that has a specific volume less than 1.0;

(2) Water that has a specific volume equal to 1.0.

The part of the total water in a saturated paste that has a mean

specific volume less than 1.0 will be called compressed water for want of


a better descriptive term, As applied to adsorbed water, the term isappropriate, if used with the reservations discussed in Part 4. Appliedto non-evaporable water the term can hardly be taken literally. It does,however, fit the fact that non-evaporable water occupies less space as apart of the solid than it does when free.

The weight-composition of the. total water in a sample of saturatedpaste can be expressed as follows:

wl=wd+ we, . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . (1)

where

wd is the weight of the compressed water, g andw, is the weight of the capillary water, g,

The volume of the total water can be expressed as

wlut=wdud+wc,........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

where vd is the mean specific volume of the compressed water, and

v! is the mean specific volume of the total water.

The specific volume of the capillary water is assumed to be 1.0.

Since w, = wl – wd, eq. (2) can be rewritten

~d(l–~~)=wt(l–u~).... . . . . . . . . . . . . . . . . . . . ...(3)

Experimental values of the mean specific volume of the total watercontent, vf, were obtained by direct measurement. If the weight of thecompressed water also could be measured, its mean density could beobtained by means of eq, (3), However, this cannot be done directly.It can be estimated by making certain assumptions, as will be shownbelow.

Of the water, wd, that has a specific volume less than 1.0, a part is thenon-evaporable water and the rest is adsorbed water, specifically, waterwithin the range of the force-field of the solid phase. That is,

Wd=w*+wa, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)

where W. is the weight of non-evaporable water, g and

W. is the weight of adsorbed water, g.

For samples made with a given cement we may safely assume that

W==ll’w n, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (5)

where B’ is a constant for the particular cement. That is, it is assumedthat the amount of adsorbed water is proportional to the total amountof hydration products* which in turn is in proportion to the amount of

*BecauaeW._ V~_ w. for a given cement.


non-evaporable water, Hence,w~=wn+B’ w*=(l+B’)w~ =Bw~, . . . . . . . . . . . . ...(6)

Substitution from eq. (6) into eq. (3) gives

~~=l–B(l–~d)wJ....... . )........,..,...(7)Wt

Eq, (7) shows that a plot of experimentally determined values ofVtversus the corresponding values for wJwt should give a straight linebeginning at v, = 1 when w~/wt = O and having a slope which wouldequal the product of the decrease in mean specific volume of the com-pressed water and the factor B, which is the ratio of the total amount ofcompressed water to the non-evaporable water, eq. (6), Experimentaldata are given in Tables 5-1 to 5-8.

The mean specific volumes of the total water, vt, were determinedas follows: Granular samples were dried to remove all the evaporablewater. A portion of each dried sample was analyzed for non-evaporablewater, portland cement, and pulverized silica, when present. Anotherpart of the dried sample was brought to the saturated, surface-dryc6ndition by the method described under “Experimental Procedures”(Part 2), and the amount required for saturation was noted. Thisamount, added to the non-evapol able water, gave the total water con-tent of the sample, The specific volume of the saturated sample was thendetermined by a conventional pycnometer method, using water as thedisplacement medium.

Examination of these tables will show how the mean specific volumeof the total water was computed. In Table 5-2, for example, columns5, 6, and 7 give the weight-compositions of the saturated granular samples.Column 8 gives the measured density of the same granules.

Columns 9, 10, 11, and 12 give the weight-composition of 1 cc ofeach saturated sample. The values were obtained by multiplying thecorresponding values in columns 5, 6, and 7 by the density of the satu-rated sample.

The volumes of cement in 1 cc of each saturated sample appear incolumn 13. These were obtained by multiplying the values in column 9by the respective specific volumes of the original cements as measuredby displacement of kerosene.

‘l’he figures in column 14 are the differences between the total volumes

and the volumes of the cements as given in column 13. The difference

was taken to be the volume of water. This involved the assumption that

the air content was zero. For these particular neat cement specimens

the air contents of the original specimens were very low. In the mortar

specimens from which the samples represented in other tables were ob-

TA

BL

E5.

1-C

OM

PO

SIT

ION

SO

FG

RA

NU

LA

RS

AM

PL

ES

US

ED

INA

DS

OR

PT

ION

OF

ME

AN

SP

EC

IFIC

VO

LU

ME

OF

TO

TA

LW

AT

ER

CO

NT

EN

T

(1)

Cem

ent

No.

(2)

(3)

(4)

(5)

(6)

(7)

Gra

ms

per

gof

sat’d

sam

ple

Ref

.A

ge,

DC

*C

emen

tN

on-

Eva

p.

h’o

.da

ysev

ap.

wat

erw

ater

——

.—

Seri

es25

4MR

B(8

)(9

)(l

o)(1

1)

AN

DO

TH

ER

TE

ST

SA

ND

CO

MP

UT

AT

ION

AN

DO

TH

ER

FA

CT

OR

S

(12)

(13)

(14)

,D

ensi

ty.

Gra

ms

per

ccof

satu

rate

dsa

mple

satu

-—

——

—ra

ted,

Cem

ent

?4..-

!E

va~;

Tot

alg

/cc

evap.

wat

erw

ater

——

1!

1l—

Clin

ker

NO

.I

Vol

s.per

un

itvo

l.sa

t’d

sam

ple

Cem

ent

‘1

–

—-1

_cem

ent

(15)

(16)

(17)

Avv

f:?

w.

1–V

Iw

ater

LU

%IW

1V

I

II

——

-—14

S98

1

1.4Q

‘12

00.

3155

1489

90.

6S5

1Pc

0.14

90.

167

120

1

2.04

0

I

1.397

I

0.3

04

I

0.3

41

I

0.6

45

I

0.4

41

I

0.559

0.3

155

I

0.8

67

0.4

7P

0.6

86

0.1

53

0162

2.0

40

1.3

99

0.2

82

l~go

o”lS

C126

0.3

12

0.3

30

0.6

42

0.4

41

0.5

59

0.3

15.5

0.6

64

0.1

51

0.1

86

1.9

76

1.3

12

0.2

?)8

0.8

71

0.4

36

0.2

65

0.3

68

0.6

66

0.4

14

0.5

86

0.8

84)

0.4

47

0.2

68

,,

t1

1I

11

l—l

II

1-1

II

Clin

ker

No.

2

14901

Iw/y—

——

——

——

——

——

__10

3’75Ik

!d0-

’49IO

1sO]:0

04j

1345

I02

WI

OSG

I-I0

G60

-Io-

427

\0573

[06681.0

453

I0291

——

,_

(lin

ker

No.

2—

——

—14904

3.%

Q162

0.3

155

0.6

71

0.1

53

14903

3PC

162

0.1

75

2.0

20

]1.3

55

1

0.3

09

0.3

34

0.6

63

0.4

28

0.5

72

0.3

1.5

.50.6

71

0.8

63

0.4

66

0.2

94

0.1

54

0.1

74

2.0

13

14906

3S

C173

0.3

155

0.6

45

0.3

10

0.3

.50

0.1

52

0.2

03

1.9

39

I;:

E0.6

60

0.4

26

0.5

74

0.2

95

0.8

70

0.4

70

0.3

94

0.2

77

.-.

-—0.6

89

0.3

95

0.6

05

0.8

78

0.4

28

0.2

85

Clin

ker

N-o

.4

14907

4A

Q173

14908

0.3

155

0.6

85

4PC

0.1

50

0.1

65

!200

0.3

155

2.0

45—

I1.4

01

0.3

07

0.6

77

0.1

52

0.3

37

0.6

44

0.1

71

0.4

42

0..

558

0.8

66

0.4

77

0.2

s12.0

28

14909

4S

C2oi

l1.3

73

0.3

08

0.3

47

0.6

55

0.4

33

0.5

67

0.3

155

0.6

46

0.1

46

0.2

08

1.9

36

1.2

51

0.8

66

0.2

83

0.4

70

0.4

03

0.2

85

0.6

86

0.3

95

0.6

05

0.8

+32

0.4

13

0.2

86

——

Clin

ker

NO

.5

;;;;?

I;;g

ZO

A0.3

155

::35;

-F

*~-=

——

——

——

—204

0.3

160

1.2

86

0.3

81

0.6

76

0.4

06

0.5

94

0.8

79

0.4

36

0.1

88

1.9

78

1.3

07

0.2

99

0.

27S

14912

xc212

0.3

72

0.6

71

0.4

13

0.5

87

0.3

144

0.6

46

0.1

46

0.

20s

1.9

30

1.2

47

0.8

75

0.2

82

0.4

46

0.4

01

0.2

80

0.6

83

0.3

92

0.6

08

0.8

90

0.4

13

0.2

66

—

Clin

ker

h-o

.6’

14913

6.4

(J212

0.3

155

14914

0.6

77

0.1

49

6PC

0.1

73

I2.0

26

222

0.3

155

1.3

72

0.6

72

0.1

.52

0.3

02

0.3

.50

0.6

52

0176

2.

00s

0.4

33

0.5

67

0.

S70

0.4

63

T

I—l_

_l_

_l_

_!I_

1.3

49

0.3

05

0.3

53

14915

MC

222

0.6

58

0.4

26

0.5

74

0.3

155

0.6

58

0.1

47

0.1

94

1.

!+64

1.2

92

0.

2s9

0.8

72

0.4

64

0.3

81

0.2

76

0.6

70

0.4

08

0.5

92

0.8

84

0.4

31

0.2

69

*For

mos

tof

thes

ece

men

tsa.

was

not

mea

sure

d.

Th

efigu

re0.3

155

isth

eav

erag

efo

rth

ose

that

wer

ern

ea.w

red.

Avg

.0.2

79

TA

BL

E5-

2-C

OM

PO

SIT

ION

OF

GR

AN

UL

AR

SA

MP

LE

SU

SE

DIN

AD

SO

RI?

TIO

NA

ND

OT

HE

RT

ES

TS

AN

DC

OM

PU

TA

TIO

NO

FM

EA

NS

PE

CIF

ICV

OL

UM

EO

FT

OT

AL

WA

TE

RC

ON

TE

NT

AN

DO

TH

ER

FA

CT

OR

S

(1)

Cem

ent

Nu.

(2)

(3)

(4)

(5)

(6)

(7)

, Gra

ms

per

gof

sat’d

sam

ple

:::

Age

,n

oC

emen

t?$

On

-E

vap.

day

sev

ap.

wat

erw

iter

Ceu

Seri

es25

4-K

4B(8

)(9

)(1

0)(1

1)(1

2)(1

3)(1

4)

Den

sity

.G

ram

spe

rCC

ofsa

tura

ted

Sam

p]e

Vol

s.pe

run

itsa

tu-

——

——

VO

1.sa

t’d

Sam

ple

rate

d,C

emen

tN

on-

Eva

P.

Tot

al—

—g

/cc

evap

.w

ater

wat

erC

emen

tl–

wat

erce

men

t

nts

Mad

efr

omC

linke

rN

o.i

(15)

(16)

Av:

f::y

w%

u.a

ter,

GV

t

(17)

l–v{

w.

/w

,

13721

1-s

174

0.3

195

0.6

48

0.1

45

13722

0.

20s

1-P

180

0.3

21.5

1.9

25

1.2

47

0.2

79

11::~

-10.

679

0.3

98

0.6

02

0.8

86

0.6

41

0.4

11

0.1

50

13723

0.2

09

1.’3

10

1.2

24

1-Q

180

0.2

87

0.6

86

0.3

94

0.6

06

0.2

77

0.3

216

0.6

66

0.1

52

0.1

82

1.9

80

1.3

19

0.3

01

0.8

83

0.3

60

0.6

61

0.4

18

0.4

24

0.2

80

_——

0.5

76

0.8

71

0:4

55

0.2

84

Cem

ents

Mad

efr

omC

lin

ker

NO

.4

13730

4-s

—144

13731

0.

31O

O*

0.6

62

10.1

18

‘4-P

0.2

22

1.$

53

1.2

93

138

0.2

30

0.4

34

0.6

64

0.4

01

0.5

99

O.3

1O

O*

0.6

61

0.1

17

0.2

22

1.9

60

1.2

96

0.

2FJ

0.4

35

0.9

02

0.6

64

0.3

46

13732

4-Q

138

0.4

02

0.

59X

0.3

100*

0.

66!7

0.1

19

0.2

12

1.%

11.3

2.5

0.2

36

(J.g

ol0..

345

0.4

20

0.6

56

0.4

11

0.5

89

0.8

98

0.3

60

.—1

l__l

1!

l——

i—_–!

!!

l——

lI

11

Cem

entsM

ad

efr

omC

lin

ker

h’o

.5

0.2

83

0.2

87

0.2

83

13733

5-s

150

O.3

1O

O*

0,6

68

0.1

10

0.2

22

1=.9

60

13734

1.3

09

0.2

16

0.4

35

0.6

51

0.4

06

0.5

94

5-P

146

O.3

1O

O*

0.6

63

0.1

03

0.2

32

1.9

36

1.2

84

0.2

03

0.0

12

1373.5

0.4

49

0.6

52

‘O.

332

0.2

65

0.3

98

~Q1.5

00.3

100*

0.6

61

0.1

09

0.2

30

1.9

37

1.2

80

0.6

02

0.2

11

0.9

23

0.3

11

0.4

46

0.6

.57

0.2

48

0.3

97

0.6

03

0.9

18

0.3

21

0.2

55

Cem

ents

Mad

efr

omC

linke

rh’

o~6

——

——

13736

6-S

106

0.3

162

0.6

63

0.1

42

0.1

95

1.9

66

1.3

03

0.2

79

0.3

83

13737

6-P

191

0.3

172

0.6

.58

0.1

51

0.1

90

0.6

62

0.4

12

1.9

56

0.5

88

1.2

87

0.2

95

0.8

88

0.3

72

0.4

21

0.2

66

13738

6-Q

191

0.3

186

0.6

61

0.1

47

0.1

92

0.6

67

0.4

08

1.9

74

1.3

05

0.5

92

0.2

90

0.8

88

0.3

79

0.6

69

0.4

42

0.4

16

0.2

.53

0.5

84

_——

_0.8

73

0.4

33

0.2

93

Cem

ents

Mad

efr

omC

lin

ker

.NO

.7

—

—.—

——

13740

I7-F

164

o.3190t

0.6

43

——

13741

0.1

54

0.2

04

1.9

26

1.2

38

0.2

97

j0.3

1J3

0.6

90

7-Q

171

0.3

95

o.3190t

0.6

46

0.1

54

0.2

04J

1.9

34

0.6

05

1.2

49

0.8

77

0.2

98

I0.3

87

0.4

30

0.6

85

0.2

86

0.3

98

0.6

02

0.8

79

_—.

_0.4

35

0.2

78

Cem

ents

Mad

efr

omC

lin

ker

h’o

.11

13752

1l-

P—

164

O.3

1O

O*

0.6

60

0123

0,2

18

1.9

51

13753

11-Q

1.2

88

0.2

40

172

0.4

23

0.6

65

0.3

100*

0.6

63

0.1

26

0.2

12

0.3

99

0.6

01

0.9

04

0.3

61

0.2

66

l.!)%

1.2

97

0.2

46

0.4

15

0.6

61

0.4

02

0.5

98

_——

0.0

05

0.3

72

0.2

55

——

——

——

Cem

ents

Mad

efr

omC

lin

ker

No.

15

——

13763

15-s

202

0.3

160

0.6

51

0.1

41

13764

0.2

08

15-P

1.9

32

196

1.2

58

0.2

72

0.3

182

0.4

02

0.6

74

0.3

’38

0.6

02

=“

0.4

04

0.6

66

0.1

41

0.1

93

1.9

76

0.2

65

1.3

16

13765

1>Q

202

0.3

222

06.5

40.2

79

0.3

81

0.6

60

0.1

44

0.2

02

0.4

19

0.5

81

1.%

31.2

77

0.8

80

0.4

23

0.2

81

0.3

95

0.2

34

—–1

0.6

76

0.4

11

0.

s89

0.8

71

0.4

16

—.—

—0.3

10

——

——

——

——

(Con

clud

edop

posi

tepa

ge.)

{Tab

le5-

2co

nclu

ded)

Cem

ents

Mad

efr

omC

3ii

No.

16_—

——.—

——

——

13766

16-S

—322

0.3

190*

0.6

47

“=0.2

18

1.9

18

1.2

41

0261

0.4

18

0.6

79

0.3

96

g:g~

:;:;

:13767

16-P

0.3

84

223

0.2

86

0.3

190*

0.6

56

0.1

48

0.1

96

1.9

52

1.2

81

0.2

89

0.3

83

0.6

72

0.4

09

0.4

30

0.2

81

1376S

223

0.3

190*

0.6

66

O.K

XI

16-Q

—.

——

——

—0.1

34

1.9

76

1.3

16

0.2

96

0.3

64

0.6

60

0.4

20

0.5

80

0.8

79

0.4

48

0.2

70

Cem

ents

Mad

efr

omC

lin

ker

No.

20

—.

——

13778

20-s

170

0.3

18Q

0,6

48

0.1

50

0.2

02

1.9

42

1.2

58

0.2

91

—=

0.3

92

0.4

00

0.6

00

0.8

78

—%

zz--

13779

20-P

167

0.3

190

0.4

26

0.6

48

0.1

51

0.2

01

1.9

54

1.2

66

0.2

95

0.3

93

0.6

88

0.4

04

0.5

96

0.8

66

13780

20-Q

176

0.3

197

0.4

29

0.3

12

0.6

63

0.1

50

0.1

87

1.9

84

1.3

15

0.2

98

0.3

71

0.6

69

0.4

20

0.5

80

0.8

67

0.4

45

0.3

99

.—.—

.——

‘*A

ssu

med

valu

efo

rTyp

eIV

cem

ents

-Den

sity

ofce

men

t=

3.22

;u.

=0.

310.

tAve

rage

valu

efo

rT

ype

Ice

men

ts.

Ave

.0.

278

TA

BL

E5-

3-C

OM

PO

SIT

ION

SO

FG

RA

NU

LA

RS

AM

PL

ES

US

ED

INA

DS

OR

PT

ION

AN

DO

TH

ER

TE

ST

SA

ND

CO

MP

UT

AT

ION

~O

FM

EA

NS

PE

CIF

ICV

OL

UM

EO

FT

OT

AL

WA

TE

RC

ON

TE

NT

AN

DO

TH

ER

FA

CT

OR

S

(1)

p;;

7-1 7-2

7-3

7-4 7-5

7-6

7-7 7-s

-17-S

-27-s

-37-s

47-s

-5

(2)

Age

,m

o. 6 6 6 6 6 : 6 6 6 6 6

Seri

es25

47

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(lo)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

Gra

ms

per

gof

satu

rate

dsa

mpl

eG

ram

spe

rcc

ofsa

tura

ted

sam

ple

Vol

s/un

itvo

l.sa

t’d

sam

ple

—C

3ens

ity,

——

——

——

——

Cem

ent

Sand

Avv

~;?

~nN

cm-

Eva

p.62

i%u-

Cem

ent

Sand

Non

-E

vap.

To-

oC

emen

tSa

nd1–

VI

evap

.w

ater

rate

d,ev

ap.

wat

er(+

d~:}

dfw

ater

,G

w./w

,w

ater

gjcc

wat

erv,

0.7

72

0.5

9s

0.5

54

0.4

67

0.4

20

0.3

22

0.2

84

0.7

09

0.5

74

0.4

71

0.3

97

0.3

77

0.;

99

0.2

49

0.3

31

0.3

49

0.4

52

0.4

93

0.T

31

0.2

35

0.3

16

0.3

51

0.1

26

0.1

05

0.1

01

0.0

96

0.0

99

0.0

75

0.0

65

0.1

54

0.1

33

0.1

15

0.0

99

0.0

93

0.1

03

0.0

98

0.0

96

0.1

06

0.1

33

0.1

51

0.

15s

0.1

37

0.1

62

0.1

79

0.1

88

0.1

79

Ckn

ent

14675:

Den

sitv

ofce

men

t=

3.1

43

ZIC

C:

uc

=0.3

182

2.2

68

2.2

70

2.2

78

2.2

37

2.1

44

2.0

9s

2.0

84

2.1

04

2.0

24

2.0

00

2.0

00

2.0

19

0~52

0.5

67

0.7

40

0.7

48

0.9

48

1.0

27

0.~

65

0.4

70

0.6

32

0.7

09

0.2

86

0.2

38

0.2

30

0.2

15

0.2

12

0.1

57

0.1

35

0.3

24

0.2

69

0.2

30

0.1

98

0.1

88

—.

0.2

34

0.5

20

0.2

22

0.4

60

0.2

19

0.4

49

0.2

37

0.4

52

0.2

85

0.4

97

0.3

17

0.4

74

0.3

29

0.4

64

0.2

813

0.6

12

0.3

28

0.5

97

0.3

58

0.5

88

0.3

76

0.5

74

0.3

61

0.5

49

I

o.55s

0.4

32

0.4

02

0.3

32

0.2

86

0.2

15

0.1

s8

0.4

75

0.3

70

0.3

00

0.2

53

0.2

42

0.;

70

0.2

13

0.2

78

0.2

81

0.3

56

0.3

86

0.Y

m0.1

77

0.2

38

0.2

67

0.4

42

0.3

98

0.

3s5

0.3

90

0.4

33

0.4

29

0.4

26

0.5

25

0.5

30

0.5

23

0.5

09

0.4

91

0.8

50

0.5

50

0.2

73

0.8

65

0.5

17

0.2

61

0.8

58

0.5

12

0.2

77

0.8

63

0.4

76

0.2

88

0.s

71

0.4

27

0.3

02

0.9

05

0.3

31

0.2

87

0.9

1s

0.2

91

0.2

81

0.8

58

0.5

30

0.2

68

:;.8

;:0.4

51

0.

24S

0.3

91

0.2

s10.8

87

0.3

45

0.3

28

0.

S94

0.3

42

0.3

10

n 2 52

-1

Avg

.0.2

84

~AB

LE

5-4-

CO

MP

OS

ITIO

NO

FG

RA

NU

LA

RS

AM

PL

ES

US

ED

!NA

DS

OR

PT

ION

AN

DO

TH

ER

TE

ST

SA

ND

CO

MP

UT

AT

ION

AN

DO

TH

ER

FA

CT

OR

SO

FM

EA

NS

PE

CIF

ICV

OL

UM

EO

FT

OT

AL

WA

TE

RC

ON

TE

NT

Seri

es25

4-8

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(lo)

(11)

{12)

IG

ram

sper

gof

satu

raw

dsa

mple

Gra

ms

per

ccof

satu

rate

dsa

mple

.4::

;Iz

=x

x:-

%:%

:‘Q

~—

‘— ~.a

,er

IW

a’li

on-

1‘E

vap.

evap

.-a

ter

Iw

ater

gle

eev

ap.

wat

erI_

I::

3-1

~448

~0.6

45

0.1

02

8-.

2i

363

I0.4

9~

0.2

38

x-3

~363

I0.4

01’

0.3

25

(13)

(14)

(15)

(16)

(17)

(18)

Vol

s/u

nit

vol.

sat’d

sam

ple

~1

Cem

ent

\S

ilic

aI

,~e{

ent~

%j~

~’

~~

1!

1+

fjilic

a)l

t’~

~

Cem

ent

14930;

Den

sity

ofce

men

t=

3.2

18

g/cc

;u

.=

0.3

108

0.1

16

‘0,1

37

2.1

57

I~:~

~;:

0I

j:;g

x’0.5

46

0..

432

l—~-l

z%W

-”~-

0.

0s3

0.1

00

0.1

65

2.0

70

0.3

42

0084

0.5

49

0.3

20

0.

18.5

0.1

90

[2.0

04

0.3

81

0.5

49

0.2

.50

0.2

45

.

Cem

ent

15007J;

Den

sity

ofce

men

t=

3.1

89

gjcc

;u

.=

0.3

136

10.9

20

j0.3

06

1

8-2

8i

481

0.6

23

0.1

12

0.1

23

0.1

41

2.1

15

1.3

18

8-2

!7!

441

0.4

74

0.2

76

~—

——

-lmq

%im

m-

“-/-

Tzr

0.2

37

0.1

03

0.1

47

2.0

!23

8–3

0441

0.3

59

,0.4

01

0.9

92

0.5

78

0.0

83

0.1

57

2.0

78

I0.7

46

,0.8

33

0.1

72

I0.3

26

0.4

98

]0.2

34

\0.3

13

0910

,0

340

0.2

61

.——

I

Cem

ent

15008;

Den

sity

ofce

men

t=

3.1

81

g/cc

;..

=0.3

144

8-3

2)

464

—,—

——

—.—

—‘—

0.5

20

1-–

0.1

97

IO

.I1O

i0.1

73

8–3

3~

464

I0.4

00

\0.3

29

\0.0

88

\0.1

82

?:%

:[

::%

~::

%:

i%:

‘%:

::U

~8:%

\::

;28:%

:I

::::

:~

::::

::$

;,—

—

Cem

ent

1501

IJ;

Den

sity

ofce

men

t=

3.2

04

g/cc

;..

=0.3

121

——

R1~’-i

!’%R

’i:~

!%?

1i:%

1i:E

j!%

;%:

;3&

~g

i;,

3

!:%

~!::

~!%

?i

:Yilm

-

0.2

88

—b

1

Cem

ent

15012J;

Den

sity

of

cem

ent

=3.1

91

gjcc

;r.

=0.3

134

,——

——

—,

—1—

——

—

::::

~j:g

I::

;::

I:,

;=~

:,j&

[:,

;;:

~;,

%~

:,;:

;~

0.4

50

0.

20s

0.3

.58

0.5

66

I0.3

09

0.1

69

0.5

22

0.6

55

0.1

7.5

0.3

74

0.9

22

J0.5

49

I0.2

47

=’

0.2

12

0.2

46

0..

507

0.9

23

0.3

20

0.2

40

Cem

ent

15013J;

Den

sity

ofce

men

t=

3.1

63

g/cc

;z’

.=

0.3

162

——

$346

\442

i0.6

63

I0.0

49

I0.1

45

0.1

43

i2.0

89

1.3

85

IO

.102–’

~~’–

~2!W

U&

I0.4

38

0.0

38

C):~~;-

1-0

.870

0.5

02

z8+47

s–48

__l

I__

l—1—

l——

l_J_

JJ_

__—

l—.

434

0.5

10

,0.2

04

0.4

13

I0.3

03

I8:%

::1:8

;:&

%,

::%

:~

:::A

:0.3

30

0.3

29

0.1

56

0.2

68

,0.3

60

0.4

32

0..

368

0.2

61

0.2

65

0.2

28

0.5

11

~::

:%0.3

67

0.2

73

Cem

ent

15014J;

Den

sity

ofce

men

t=

3.1

75

g/cc

;u

.=

0.3

150

*5O

.44:

I0.4

79

0.2

17

I0.1

18

I0.1

86

I::

}::

~::

:EI

:,;;

:!

:,jg

:I

0595

I0.%

5

—,—

——

——

——

1..

957

=51

0.3

80

0324

i0,0

96

I0.1

99

1.9

36

——

1.

,0571,0

532

IU

%g%

1-1

-~~

——

i’

A*.

g.O

.245—


.:.—.——

~’ 0“Kz

TA

BL

E5-

5-C

ON

TIN

UE

D

Ser

ies

254-

9(9

)(lo)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(1s)

(19)

Gra

ms

per

ccof

satu

rate

dsa

mple

l~O

ls,u

itvO

I.sa

t$d*

ampl

el\

I(1

)(2

)(3

)(4

)(5

)(6

)(7

)

Gra

rmper

gof

satu

rate

dsa

mpl

e—

—R

ef.

w/c

Age

,C

emen

tSi

lica

Ncm

-E

.vaP

.N

o.da

ysev

ap.

wat

erw

ater

(s)

Den

sity

mtu

-l’a

ted,

g/cc

872)

;D

2.1

20

2.1

20

2.1

14

2.o

97

2.0

85

2.1

32

2.1

70

2.1

36

2.0

94

2.0

92

2.C

Q4

2.0

70

2.1

71

Cem

ent

Silic

aN

on-

Eva

p.

evap.

wat

erw

ater

——

—A

~wi.

~~~

Tot

alC

emen

tSi

lica

1–8,

wat

er(c

~m;n

t.w

ater

,G

%/w

,+

sili

ca)

u;—

—.

—313(C

[

o.49s

0.4

94

0.5

03

0.5

35

0.5

40

0.

4S

2

0.4

51

0.4

63

0,4

94

0.

49s

0.4

77

0.5

22

0.4

10

0.2

09

0.2

21

0.2

20

0.

1s5

0.1

83

0.2

92

0.3

10

0.3

00

0.

2s2

o.2s2

0.2

70

0.2

79

0.4

30

0.9

1s

O.

2S

50.2

83

0.9

19

0.3

14

0.

25S

0.9

12

0.2

4s

0.2

53

0.

S97

0.3

6s

0.2

843

0.

S9S

o.37s

0.2

70

O.m

0.3

67

0.2

73

Cem

ent

0.0

s7-0

.073

0.0

83

0.0

94

0.0

9s

0.0

83

54107JI

O.

16S

0.1

60

0.1

55

0.1

61

0.1

61

0.1

43

0.1

44

0.1

50

0.1

62

0.1

5s

0.1

56

0.1

s60.1

29

mitv

ofce

men

t=

3.18

9s

:C:

0.

=

0.35

60.3

39

0.

32S

0.3

38

0.3

26

0.3

05

0.3

12

0.3

20

0.3

39

0.3

26

0.3

13

0.3

44

0.2

30

tinue

d

0.33

40.

325

0.32

10.

235

0.33

20.

274

0.28

00.

274

0.26

60.

265

0.25

40.

260

0.19

3

—.—

1.0

ss1.0

37

1.0

25

1.0

s91.0

59

0.

S74

O.

S92

o.S

74

0.8

4s

0.8

4.5

0.

Slo

0.s

30

0.6

17

0.1

42

0.1

55

::;;

:

0.2

04

0.1

77

0.1

39

0.1

43

0.1

55

0.1

72

0.1

64

0.

17s

0.1

30

,432

5S

2

33s

.433

.570

3O

pp,

7

z 5s.

194 7

i: 56

56

1%

7

;: 2s 56

194

365 7

;: 28

56

1%

7 14

28

X 1s0

0.5

55

0..

589

0.5

86

0.4

91

0.4

8s

0.7

76

0.8

25

0.7

99

0.7

50

0.7

49

0.7

17

0.7

41

1.1

44

0.4

57

0.4

54

0.4

59

0.4

80

0.

4s5

0.4

34

0.4

10

0.4

26

0.4

52

0.4

53

0.4

76

0.4

61

0.3

77

0.5

03

0.

4s9

0.4

85

0.5

10

0.5

08

0.4

10

0.4

11

0.4

09

0.4

05

0.4

04

0.4

04

0.4

01

0.2

84

0.2

62

0.

27S

0.2

77

0.2

34

0.2

33

0.3

64

:::%

o.35s

0.3

56

0.

35s

0.3

58

0.5

27

0.06

40.0

s70.0

74

0.

0s2

o.0s2

0.0

86

0.0

60

0.9

09

0.3

0s

0.2

95

0.9

20

0.3

09

0.2

59

0.9

15

0.3

14

0.2

70

0.9

10

0.3

45

0.2

61

0.

99s)

0.3

44

—0.8

83

0.2

41

0.3

43

0.9

20

0.3

17

0.2

53

.—

Avg

.0.2

73

Cem

ent

1501

1J;

Den

sity

ofce

men

t=

3.20

4gj

cc;

m=

O.

0.6

66

0.6

1S

0.6

55

0.6

55

0.6

34

0.6

43

0.6

S3

O.6

S3

0.4

34

0.4

90

0.4

93

0.4

93

0.4

92

0.5

15

0.4

94

0.3

95

0.4

03

0.

3s7

0.3

71

0.4

00

0.3

92

0.4

56

0.

43i

o.4s7

0.4

50

0.4

46

0.4

54

0.4

8JI

0.4

89

0.4

05

0.4

64

0.4

57

0.4

58

0.4

62

0.4

79

0.4

66

0.4

33

0.4

17

0.4

32

0.4

55

0.4

63

0.4

35

D.1

02

D.1

63

D.1

19

D.1

19

D.1

37

D.124

0.0

s90.0

S3

D.3

64

0.2

68

D.2

69

0.2

69

0.2

66

0.2

31

0.2

61

0.

3s4

0.3

86

0.

38S

o.’3

s90.3

52

0.3

s1

0.0

76

0.

0s2

0.0

94

0.0

94

0.0

99

0.1

06

0.1

16

0.1

20

0.0

53

0.0

75

0.0

s2o.

0s2

o.0ss

o.09s

0.0

9s

0.0

52

0.0

63

0.

06S

0.0

72

0.

0s2

0.0

84

0.1

5s

0.1

33

0.1

43

0.1

43

0.1

29

0.1

27

0.1

32

0.1

34

0.1

49

0.1

67

0.1

57

0.1

57

0.1

54

0.1

56

0.

14s

0.1

s80.1

49

0.1

56

::;:

;

0.1

44

2.2

08

2.2

14

2.

05s

2.2

0s

2.2

22

2.2

06

2.1

76

2.lM

l

2.

1s2

2.1

15

2.1

31

2.1

23

2.1

20

2.1

05

2.1

18

2.1

16

2.1

52

2.1

30

2.0

s02.0

88

2.1

27

1.4

71

1.

36S

1.3

48

1.4

45

1.4

09

1.4

18

1.4

66

1.4

75

0.9

47

1.0

36

1.0

51

1.0

47

1.0

43

1.0

84

1.0

46

0.

S36

O.S

67

0.s

24

0.7

72

0.3

36

0.s

24

0.2

25

0.3

61

0.2

45

0.2

63

0.3

04

0.2

74

0.1

50

0.1

36

0.7

94

0.5

67

0.5

73

0.5

71

0.5

64

0.4

86

0.5

53

0.s

13

0.8

31

0.8

26

0.8

439

0.7

35

0.s

10

0.1

68

0.

1s2

0.1

93

0.2

07

0.2

20

0.2

34

0.2

52

0.2

59

0.1

16

0.1

59

0.1

75

0.1

74

0.1

87

0.2

06

0.2

08

0.1

10

0.1

3s

0.1

45

0.1

50

0.1

71

0.1

79

0.34

40.

303

0.29

40.3

15

0.

2S

70.2

s0O

.2S

70.2

89

0.3

25

0.3

53

0.2

35

0..

333

0.3

2s

O.3

2S

0.3

13

0.3

55

0.3

21

0.2

22

0.3

49

0.3

49

0.3

06

0.5

12

0.4

88

0.4

s70.5

22

0..

5437

0.5

14

0.5

39

0.5

4s

0.4

41

0.5

12

0.5

10

0.5

07

0.5

13

0.5

34

0.5

21

0.4

65

0.4

57

0.4

77

0.4

99

0.5

20

0.4

85

0.4

59

0.4

27

0.4

21

0.4

51

0.4

40

0.4

43

0.4

s40.4

60

0.2

96

0.3

23

0.

32S

0.3

27

0.3

26

0.3

38

0.3

26

0.2

61

0.2

71

0.2

57

0.2

41

0.2

61

0.2

60

0.0

85

0.1

36

0.0

92

0.0

99

0.1

14

0.1

03

0.0

56

0.0

51

0.2

99

0.2

13

0.2

15

0.2

15

0.2

12

0.1

83

0.2

08

0.3

06

0.3

12

0.3

11

0.3

04

0.2

76

0:3

05

9-7

0.9

1s

0.2

63

0-.

350

0.9

06

0.3

11

0.3

02

0.8

96

0.3

43

0.3

04

0.9

03

0.3

43

0.

2S

30.9

01

0.3

65

0.2

71

0.8

97

0.3

36

0.2

67

0.8

94

0.3

99

0.2

66

9–s

0.9

31

0.2

37

0.2

91

0.9

12

0.2

98

0.2

95

0.9

06

0.3

04

0.3

09

0.9

12

0.3

01

0.2

92

0.8

90

0.3

29

0.3

35

0,

S97

0.3

69

0.2

80

9–9

(CO

nch

l

——

L___

__A

vg.

0.2

90

ite

pag

e.)

(Tab

le5-

5co

nclu

ded)

Cem

ent

1501

3J;

Den

sity

ofce

men

t=

3.16

2g/

cc;

v.=

0.31

62

0.4

74

0.4

79

0.4

83

0.4

91

0.4

89

0.4

13

0.4

61

0.4

59

0.2

57

o.4t?

00.4

64

0.4

74

0.4

01

0.4

28

0.4

WI

0.4

43

0.4

12

0.4

36

.324

.443

.611

—,

—0.8

78

0.8

71

0.8

67

0.%

60.%

50.8

75

-0.4

11

0.4

47

0.4

51

0.4

67

0.4

92

0.4

98

0.2

97

0.2

89

0.2

95

0.2

87

::::

:

9-1

o

9-1

1

9–1

2

.——

9–1

3

9-1

4

9–1

5

9-1

5A

0.6

86

0.6

89

0.6

80

0.6

80

0.6

76

0.5

58

0.5

31

0.5

04

0.2

31

0.4

90

0.4

33

0.4

53

0.3

96

0.4

06

0.3

87

0.3

82

0.3

01

0.3

44

0.0

66

0.0

57

0.0

63

0.0

57

0.0

62

0.2

30

0.2

33

0.2

53

0.6

48

0.2

51

0.3

14

0.2

89

0.4

01

0.3

71

0.3

88

0.3

83

0.4

84

0.4

24

0.0

59

0.0

84

0.3

83

0.0

81

0.0

84

0.1

25

0.2

48

0.2

45

0,3

31

0.2

32

0.2

43

0.2

67

0.4

09

0.3

56

0.3

84

0.3

60

j;:;

;

— — — — —

0.1

02

::);:

0.1

23

0.1

29

0.1

05

1.4

93

1.4

98

1.4

74

1.4

65

1.4

59

1.2

47

1.1

21

1.0

72

0.5

42

1.0

23

0.!310

0.9

4.5

0.

XX

IO

.X

66

O.S

23

0.6

04

0.6

39

0.7

23

0.1

44

0.1

24

0.1

36

0.1

23

0.1

34

0.5

14

0.4

92

0.5

38

1.5

20

0.5

24

0.6

60

0.6

03

0.8

70

0.7

92

0.$

525

0.6

07

1.0

27

0.8

91

0.2

22

0.2

46

0.2

51

0.2

65

0.2

78

0.2

35

0.1

75

0.1

96

0.0

96

0.2

13

0.1

95

0.2

23

0.1

37

0.1

58

0.1

68

0.1

77

0.1

51

0.1

77

0.3

18

0.3

04

0.3

06

0.3

32

0.

2!3

70.2

37

0.5

40

0.5

50

0.5

57

0.5

67

0.5

65

0.4

72

0.4

72

0.4

74

0.4

66

0.4

63

0.4

61

0.3

94

0.3

54

0.3

39

0.1

71

0.3

23

0.2

88

0.2

99

0.2

72

0.2

74

0.2

60

0.2

54

0.2

02

0.2

29

0.4

75

0.4

62

0.3

30

0.4

.56

0.4

63

0.4

39

0.3

6.5

0.3

44

0.3

03

0.3

38

0.3

31

0.3

17

0.2

68

0.2

69

0.2

56

0.2

53

0.2

53

—

0.5

41

0.5

52

0.5

48

0.5

51

0.5

53

0359

0.0

54

0.0

47

0.0

51

0.0

46

0.0

50

0.1

93

0.1

85

0.2

02

0.5

72

0.1

97

0.2

48

0.2

27

0.3

27

0.2

98

0.3

10

0.3

03

0.

3S

60.3

3.5

0.0

48

0.0

68

0.3

30

0.0

66

0.0

68

0.1

02

0.2

01

0.1

94

0.2

65

0.1

82

0.1

90

0.2

09

0.3

31

0.2

77

0.3

01

0.2

78

0.2

74

— — — — — — —

0.0

83

0.9

02

0.0

41

0.1

02

0.0

93

0.1

07

0.9

26

0.8

88

0.9

05

0.8

87

0.9

06

0.

!378

0.3

51

0.3

79

0.3

38

0.3

94

0.3

81

0.4

13

0.2

11

0.2

96

0.2

81

0.2

87

0.2

46

0.2

95

0.9

05

0.8

99

0.W

X3

0.8

99

0.8

98

0.8

97

0.0

63

0.0

74

0.0

79

0.0

84

0.0

71

0.0

84

0.1

41

2.1

70

0.1

49

2.1

34

0.1

46

2.1

26

0.1

50

2.1

06

0.1

45

2.1

22

0.1

47

2.1

02

—.—

0.3

06

0.4

43

0.3

18

0.4

76

0.3

10

0.4

78

0.3

16

0.4

93

0.3

08

0.4

5!3

0.3

09

0.4

86

—1

_l_.

_—l

____

___

Avg

.0.2

82

Cem

ent

15365;

Der

ur

ofce

men

t=

3.13

5E

lcc

=0.3

.—

0.1

27

0.1

81

0.8

77

0.1

75

0.1

82

0.2

71

—.

0.1

98

0.3

3.5

0.2

20

0.3

11

0.1

53

0.2

22

0.2

.55

0.2

96

0.2

61

0.2

78

0.2

49

0.2

71

0.5

33

0.5

31

0.3

75

0.5

51

0.5

39

0.5

20

—,—

.—

.322

.439

.587

.244

0.6

94

0.6

71

0.4

52

0.6

63

0.6

68

0.6

34

0.5

30

0.5

13

0.4

.45

0.5

08

0.4

98

0.4

78

0.3

90

0.4

07

0.3

76

0.3

90

0.3

87

0.3

99

0.

76.%

0.7

72:

0.

767(

0.7

71[

0.7

71(

o.7

79(

o.77G

1.4

90

1.4

48

1.0

36

1.4

30

1.4

51

1.3

75

1.1

43

1.0

79

0.

9!5

0I

.0.5

91.0

38

0.9

95

0.8

40

0.8

44

0.7

84

O.m

l0.7

92

0.4

77

0.4

70

0.3

40

0.4

78

0.4

69

0.4

59

0.4

34

0.4

62

0.4

32

0.4

80

0.4

79

0.4

74

0.4

01

0.4

54

0.4

49

0.4

67

0.4

73

0.8

95

0.8

85

0.9

07

0.3

68

0.8

70

0.3

83

0.3

71

0.4

14

0.4

08

0.4

63

0.4

84

0.4

79

0.2

83

0.2

78

0.2

27

0.2

85

0.2

69

0.2

45

0.9

06

0.3

34

0.2

81

0.9

0s

0.3

63

0.2

53

0.9

04

0.3

66

0.2

62

0.8

82

0.4

10

0.2

73

0.8

87

0.4

20

0.2

69

0.8

93

0.4

16

0.2

57

0.5

35

0.5

15

0.7

06

0.4

83

0.5

06

0.5

56

0.1

60

0.1

85

0.1

75

0.2

23

0.2

27

lj.~

zl

0.3

19

0.3

24

0.3

03

0.3

21

0.3

13

0.3

10

0.4

79

0.5

09

0.4

78

0.5

44

0.5

40

0.5

31

0.0

60

0.1

42

2.1

.54

0.0

76

0.1

61

2.0

74

0.0

79

0.1

57

2.0

85

0.0

86

0.1

63

2.0

53

0.

0s9

0.1

67

2.0

46

0.1

02

0.1

63

—

0.8

81

0.7

38

0.3

01

0.7

39

0.7

30

0.1

29

0.3

06

0.1

58

0.3

34

0.1

65

0.3

27

0.1

77

0.3

35

0.1

82

0.3

42

0.’4

35

0.

4!?

20.4

92

0.5

12

0.5

24

—

0.5

19

0.5

10

0.5

20

0.5

11

0.5

15

0.92

20.2

97

0.2

62

0.9

23

0.3

21

0.2

71

0.9

13

0.3

35

0.2

60

0.0

12

0.3

46

0.2

54

‘o.

903

0.3

47

0.2

80

——

—-l

–1.6

95

1.7

30

1.7

18

1.7

27

1.7

33

— — — — — —

0.4

59

0.4

48

0.4

52

0.4

49

0.4

47

0.8

84

0.3

76

0.2

09

0.8

78

0.4

27

0.2

86

0.8

69

0.4

48

0.2

92

0.8

79

0.4

72

0.2

57

0.8

68

0.4

89

0.2

70

0.—

%3

O.z

l0~36

——

—A

VE

.0.2

68

—l—

1.7

54

0.2

!)7

I0.2

14

0.5

11

0.4

41

—

TA

BL

E5-

6-C

OM

PO

SIT

ION

SO

FG

RA

NU

LA

RS

AM

PL

ES

US

ED

INA

DS

OR

PT

ION

AN

DO

TH

ER

TE

ST

SA

ND

CO

MP

UT

AT

ION

SO

FM

EA

NS

PE

CIF

ICV

OL

UM

EO

FT

OT

AL

WA

TE

RC

ON

TE

NT

AN

DO

TH

ER

FA

CT

OR

S-S

erie

s25

4-11

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(s)

(9)

(10)

(11)

(12)

(13)

(14)

(1.5

)(1

6)

(17)

(1s)

Gra

ms

per

gof

satu

rate

dsa

mple

Gra

ms

per

ccof

satu

rate

dsa

mple

Vol

s/u

nit

vol.

sat’d

sam

ple

—D

ensi

ty,

——

——

——

—R

ef.

Age

,C

emen

tS

ilic

aN

on-

Eva

p.

Cem

ent

IS

ilic

a—

Avv

~~p

U%

L-

l–?u

satu

-C

emen

tS

ilic

aN

on-

Eva

P.

Tot

alh

’o.

day

sev

ap.

wat

er(C

~m

–en

tw

ater

,G

rate

d,

wat

erw

ater

w.

fw

{ev

ap.

TV

ater

g/cc

I1

“’ate

’—

——

-1—

——

——

+si

lk)

UC

_——

—.

Clin

ker

N0.

2;C

emen

t15

758

;D

ensi

tyof

cem

ent

3.10

7;r.

=0.

3219

;SP

.su

rf.

1800

(tur

b.):

3567

(per

m.)

——

—.

——

—

I1

-11

–128

0.66

50.

071

0.11

40.

151

2.I1

O1.

403

0.15

00.

240

0.31

9G

—11

-20.

452

0.50

00.

056

0.49

20.

237

0.09

s0.

164

0.s8

0

L

0.42

92,

03s

::;%

1.01

90.

4s3

0.20

00.

334

0.S3

411

–10.

328

0.1s

2%

0.65

90.

490

0.07

20.

91s

0.12

6-0

.14s

2.O

W0.

375

11–2

’30

0.50

21.

380

0.15

10.

264

0.31

00.

574

0.44

40.

0.57

0.49

90.

213

0.11

20.

869

0.46

00.

285

0.17

32.

014

1.01

10.

429

0.22

60.

348

0.57

40.

325

0.16

10.

514

0.89

50.

394

0.26

6—

——

—.—

——

——

——

11-3

114

11-3

11-4

——

11–5

11-6

11-5

11-6

——

—

Clii

ker

No.

3;

Cem

ent

1.5

756;

Den

sity

ofce

men

t.3.1

74;

..=

0.3

151;

SP.

surf

.1800

(tu

rb.);

3060

(per

m.)

zE

EE

EE

EIm

iEE!E

EIE

HE

EEE

Clin

ker

h’o

.4;

Cem

ent

15763;

Den

sity

ofce

men

t3.2

15;

t%=

0.3

110;

SP.

surf

.1800

(tu

b.);

2760

(per

m.)

——

-—

——

28

0.6

84

0.0

73

0.0

63

0.1

80

2.1

48

1.4

69

0.1

57

0.1

35

0.3

87

l—‘—

——

0.5

22

0.4

57

0.0

59

\0.4

84

r

0.9

27

0.2

59

28

0.5

34

0.2

38

0.0

54

0.1

7.5

2.1

37

1.1

41

0.5

09

0.1

15

0.2

82

90

0.

6&

50.3

74

0.4

89

0.3

55

0.1

91

0.0

91

0.0

89

0.1

56

0.4

54

0.9

2S

0.2

35

2.1

69

0.3

06

1.4

42

O.lw

0.1

93

90

0.5

08

:::;

:\

$::

;0.

44s

0.0

74

0.2

37

0.0

76

0.4

78

0.9

00

0.1

80

2.0

78

0.3

64

0.2

75

1.0

56

0.4

92

0.1

58

G.32S

0.1

s50.4

87

0.9

15

0.2

97

0.2

86

II

)——

I——

l—l—

i—!—

,—,

—l—l

—l—l

—

~1—

-—28

11-8

28

11-7

90

11-8

90

Clin

ker

No.

5;

Cem

ent

15761;

Den

sity

ofce

men

t3.1

55;

m=

0.3

170;

SP.

surf

.18041

(tu

rb.);

2951

(per

m.)

rr

.—

0.6

74

0.0

.57

0.1

09

0.1

59

Z.1

14

1.4

25

0.1

20

0.2

30

0.3

36

0.5

66

0.5

16

0.

20s

0.0

96

0.1

81

0.4

52

0.0

45

0.5

4)3

0.8

89

2.0

38

1.0

52

0.4

24

0.4

06

0.1

96

0.3

69

0.2

73

0.5

65

0.3

33

0.1

59

0.6

72

0.5

0s

0.0

49

0.1

21

0.1

58

0.8

99

2.0

97

1.4

09

0.1

03

0.2

54

0.3

47

0.3

31

0.2

91

0.5

85

0.4

47

0.0

39

0.5

03

0.2

14

0.1

07

0.5

14

0.1

76

0.8

79

2.

03s

1.0

25

0.4

36

0.2

18

0.4

34

0.2

79

0.3

59

0.5

77

0.3

25

0.1

64

0.5

11

0.8

86

0.3

78

0.3

02

~.

——

——

——

——

——

Clin

ker

No.

1;

Cem

ent

15734;

Den

sity

ofce

men

t3.1

35;

m=

0.3

190;

SP.

surf

.lW

O(t

urb

.);

3417

(per

m.)

T11–9

28

—‘Iz

;Zw

GQ

wx

—‘—

‘——

0.6

57

0.1

43

1

2.1

44

0.1

91

0.2

40

0.4

49

0.0

72

0.4

79

0.8

76

11–1

028

0.4

94

0.4

39

0.

2s2

0.

07il

0.3

26

0.1

91

0.4

83

0.8

94

11-9

90

0.6

58

0.

12s

0.1

34

2.1

36

1.4

05

o.i6

90.3

72

0.2

73

0.

2S

60.2

85

11-1

090

0.5

59

0.

44s

0.4

93

0.2

32

0.1

14

0.0

64

0.4

88

0.1

51

z.O

w0.8

73

1.0

11

0.4

76

0.4

88

0.2

34

0.3

30

0.2

60

0.5

64

0.3

23

0.1

79

0.4

98

0.8

83

0.4

15

0.

2s2

.——

——

——

——

——

—

Clin

ker

No.

1;

Cem

ent

16213:

Den

sity

ofce

men

t3.1

35;

cc=

0.3

190;

SP.

surf

.2426

(per

m.)

——

——

——

—

11-1

,12s

Io.

494

]o.

265

Io.

0S

5I

0.1

.56

]2.1

10

I1.0

42

[0.5

59

I0.1

79

I0.3

29

[O

.WS

[0.3

32

I0.2

10

I0.4

5s

I0.9

02

[0.3

52

[0.2

7s

Clin

ker

No.

1;

Cem

ent

16214;

Den

sity

ofce

men

t3.1

35;

m=

0.3

190;

SP.

surf

.2923

(per

m.)

—11-1

2~1~[-

l0.0

91

I0.1

59

[2.0

86

[1.0

24

I0.5

40

]0.1

90

[0.3

32

I0.5

22

~“

0.3

27

I0.2

03

I0.4

70

I0.9

00

[0.3

64

~—

.——

.——

(Con

clu

ded

oppw

+it

epag

e)—

——

(Tab

le5+3

conc

lude

d)

Clin

ker

No.

4;C

emen

t16

198;

Den

sity

ofce

men

t3.

215;

m=

0.31

1@a.

surf

.32

OO

(per

m.)

II-I

,]z,

[0..

50.3

I0.2

58

[0.0

55

Io.

*84

Ixl

1.0

.58

\0.5

43]

0.1

16

I0.2

87

[0.5

03

F~~~~

Clin

ker

No.

4;

Cem

ent

15669;

Den

sity

ofce

men

t3.2

15;

m=

0.3

110;

Sp.

surf

.3810

(per

m.)

.—

E44

MQ

3!L

?4J2

43?2

1HL

I04

’8I

0’25

I03

”I

05’6

[0=

7/=

]0-

-I

0--

I0-

=I

0-24

0A

w.

0.2

74

TA

BL

E5-

7-C

OM

PO

SIT

ON

SO

FG

RA

NU

LA

RS

AM

PL

ES

US

ED

INA

DS

OR

PT

ION

AN

DO

TH

ER

TE

SSA

ND

CO

MPU

TA

TIO

NS

OF

ME

AN

SP

EC

IFIC

VO

LU

ME

OF

TO

TA

LW

AT

ER

CO

NT

EN

TA

ND

OT

NE

RF

AC

IOR

S-S

enes

254-

13(1

)

Ref

.N

o.

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(lo)

(11)

(12)

(13)

(14)

(15)

(16)

(HI

Gra

ms

per

gof

satu

rate

dsa

mpl

eG

ram

spe

rcc

ofsa

tura

ted

sam

ple

Vof

sIun

itvo

l.rs

at’d

-pie

S03

——

——

Den

sity

,—

——

——

——

Co:

ent

Cem

ent

Silic

aN

on-

Eva

P.

satu

-C

emen

tSi

lica

Ncm

-

l_l_E_z_2iiZ

Eva

P.

evap

.w

ater

rate

d,ev

ap.

wat

erem

ent,

%w

ater

g/cc

wat

er—

.—

—C

linke

rN

o.1

(153

67);

Den

sity

ofce

men

t*=

3.13

5;m

=0.

319

(18)

13-1

1.5

0.4

28

0.3

06

0.0

92

0.1

75

2,0

34

0.8

71

0.6

22

0.1

87

13–2

1.9

0.2

56

0.4

36

0.5

43

0.3

12

0.0

92

0.1

60

2.0

67

0.2

78

0.9

01

0.6

45

0.2

34

0.1

90

0.3

31

0.4

38

0.5

21

0.2

87

1

0.3

99

0.3

44

0.2

94

13-3

2.4

0.2

43

0.4

70

0.4

28

0.3

06

0.0

89

0.1

77

0.9

02

0.3

65

0.2

69

2.0

27

0..

368

0.6

20

O.lw

134

0.3

59

3.5

0.4

29

0.3

06

0.5

29

0.0

83

0.1

82

3.0

67

0.2

77

0.8

87

0.6

33

0.2

33

0.1

72

0.3

76

0.4

90

0.5

48

0.9

09

0.2

34

0.2

72

0.2

s30.2

38

0.4

79

.—0.8

74

0.3

14

0.4

01

.—__

Clin

ker

No.

1(1

5367):

Den

sity

ofce

men

t*=

3.1

35;

u.

=0.3

19

13-l

B1.

50.

427

0.30

50.

090

0.17

82.

026

0.86

50.

618

0.18

20.

361

IE

Erm

0.5

43

13-2

B1.9

0.4

28

0.3

06

0.0

92

0.1

73

2.0

28

0.8

68

0.6

21

0.1

87

0.2

51

lXIB

2.4

0.4

28

0.3

06

0.0

92

0.5

23

0.1

74

2.0

87

0.8

93

0.6

39

0.1

92

0.3

63

144B

3.5

0.5

55

0.4

26

j0.3

05

0.0

87

0.1

82

1.9

69

0.8

39

0.6

01

0.1

71

0.3

58

0.5

29

.—

——

Clin

ker

h’o

.3

(15623)

;D

ensi

tyo

fce

men

t*=

2.1

75;

v.=

0.3

15

——

——

13-5

1.5

0.4

36

0.3

12

I0.0

66

0.1

86

2.0

40

II

EE

EE

Em

rm

0.8

89

0.6

36

EW

52.0

0.4

33

0.3

09

0.0

65

0.1

93

2.0

28

0.8

78

0.6

27

1>7

2.5

0.4

33

0.3

09

0.0

66

0.1

93

2.0

16

0.8

73

0.6

23

13-8

3.5

0.4

31

0.3

08

0.0

62

0.1

99

2.0

22

0.8

71

0.6

23

——

—C

lin

ker

No.

5(1

5670)

;D

ensi

tyo

fce

men

t*=

3.1

55;

n.

=0.3

17

13-9

1.5

0.4

28

0.3

06

0.0

85

0.1

81

2.0

31

0.8

69

II

E_M

aEm

m0.6

21

0.1

73

——

13-1

02.0

0.4

30

0.3

07

0.0

83

0.1

79

2.0

33

0.8

74

0.6

24

0.1

69

13–1

12.5

0.4

26

0.3

04

0.0

82

0.1

87

2.0

18

0.8

60

0.6

13

0.1

65

13-1

23.5

0.4

30

0.3

07

0.0

79

0.1

83

2.0

27

0.8

72

0.6

22

0.1

60

.——

——

Clin

ker

N0~2

(15498);

Den

sity

ofce

men

t*=

3.1

08;

z.=

0.3

22

—!—

—

13-1

31.5

0,4

43

0.3

15

0.0

92

0.1

50

2.0

10

0.8

90

1—1

EEIE

T!Z!

!EEI

EE=

0.6

33

__l0

.185

13–1

42.0

0.4

42

0.3

16

0.0

88

0.1

.54

2.0

52

0.9

07

0.6

48

0.1

81

——

——

——

——

—

*ES

ect

ofva

ryin

ggy

psum

negl

ecte

d.

(1)

Ce&

rnon

t

.—TA

BL

E5-

8-C

OM

PO

SIT

ION

SO

FG

RA

NU

LA

RS

AM

PL

ES

US

ED

INA

DS

OR

PT

ION

AN

DO

TH

ER

TE

ST

SA

ND

CO

MP

UT

AT

ION

SO

FM

EA

NS

PE

CIF

ICV

OL

UM

EO

FT

OT

AL

WA

TE

RC

ON

TE

NT

AN

DO

TH

ER

FA

CT

OR

S

Seri

es25

4-14

.A

ge,

28da

ys(2

)(3

)(4

)(5

)(6

)(7

)(8

)(9

)(1

0)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

Gra

ms

per

gof

satu

rate

dsa

mple

Gra

ms

per

ccof

satu

rate

dsa

mpI

eV

ofs/

unit

x-o]

.sat’d

sam

ple

Ref

.v.

—D

ensi

ty,

——

——

——

—C

emen

tS

ilic

aN

on-

Eva

P.

sLlt

u-

Cem

ent

‘Sili

caA

\TO

n-E

vaP

.T

otal

Cem

entl

Siiic

a~g

m-t

%%

.2-

::_

,N

o.ev

ap.

-.va

ter

rate

d,.

evap

.w

ater

wat

erw

ater

g[cc

rw

ater

,w

ater

+si

lica)

W.

—

——

15!?

54

14–1

0.3

176

0.4

37

0.3

12

1.3

756

14–5

C.3

111

0.4

36

0.s

11

16215

14–1

10.3

1’3

00.4

30

0.3

07

161%

514–1

20.3

216

0.4

38

0,3

13

—

Cu

red

24

hr.

at43

C,

27

days

at23

C

o.0s5

0.1

66

2.0

64

0.9

02

0.6

44

0.1

75

I

——

0.066

0.3

43

*.1s7

z.0

40

0..

518

=x

0.4

72

0.8

89

0.6

34

0.1

35

0.9

11

0.3

3s

0.2

63

0.3

s10.5

16

0.2

77

0.2

3S

0.

0s7

0.1

76

2.0

37

0.

S7(i

o.62s

0.4

s50.9

40

0.2

62

0.

2.%

0.1

77

0.0

s0o.

35!)

0.5

36

0.1

70

0.2

79

0.2

35

2.

07s

0.4

s60.9

10

0.6

50

0.!)0

70.3

30

0.2

s20.1

66

0.3

53

0.5

19

0.2

93

0.2

44

0.4

63

0.s

92

0.3

20

0.3

3s

—.—

——

Cu

red

2S

days

at23

C

15954

14–2

0.3

176

0.4

33

0.3

09

0.0

87

0.1

71

15756

144

0.3

111

0.4

3.4

0.3

10

0.0

67

0.1

89

—=1

m%

;;{!

E::

%8:

1?3

!16186

14–7

0.3

190

0.4

27

0.3

0.5

0.0

91

0.1

77

0.6

19

0.1

8.5

0.

3;9

o.&

40.5

77

16195

14–s

0,3

216

0.4

26

0.3

03

0.

0S

60.1

83

2.0

24

0.s

62

0.6

17

0.1

74

0.3

70

0.5

44

0.2

77

——

——

——

——

Cur

ed24

hr.

at5

C.

27da

vsat

23C

1-——

0.2

3s

o.4&

I0

.90

70

.33

60.2

77

0.2

3s

0.4

s70.9

33

0.2

62

O.z

m0.2

33

0..

496

O.a

ol0.3

40

0.2

91

0.2

32

0.4

91

0.9

03

0.3

20

0.3

03

——

Cu

reci

24

hr.

at4

C,

27

days

at23

C—

——

—=86

14–9

0.3

190

0.4

2.5

0.3

04

0.0

90

0.1

s0—

——

16195

2.0

22

0.

8!5

90.6

13

0.

1s2

0.3

64

0.-

614–1

00.3

216

0.4

33

0.2

74

~—

0.4

95

0.3

10

0.0

85

0.1

72

2.0

.39

0.8

92

0.

63S

0.1

75

0.3

54

0.9

07

0.3

23

0.2

79

0.

5%

40.2

S7

0.2

40

0.4

73

_-—

——

_—

0.s

94

0.3

31

0.3M

.—A

uto

clav

eat

3.5

0F

for

6h

r._—

-_15756

l~lfi];~

~l~

z~l~

l——

‘——

‘——

——

——

——

O13b712.2

ti-l

1.0

28

I0.7

35

I0.1

66-1

0.2

JJ9

I0.4

75

[0.3

20

[0.2

76

I0.4

4M

I0.S

51

@491

0.4

27

.—

—.

—


tained, the air contents were considerable. However, it is believed thatthe small granules taken for these measurements were smaller than mostof the air voids and therefore would contain little air, if any.

Column 15 was obtained by dividing the figures given in column 14by corresponding figures in column 12.

Plots of o, vs. wfi/w, for most of these data are given in Fig. 5-1 to 5-4.Since v~ depends on the measured volume of the saturated, granular

samples, and the computed volume of the original cement and (whenpresent) pulverized silica, small inaccuracies in measurement haverather large effects on v,. Moreover, any inaccuracies in the correspond-ing figures for non-evaporable water, due either to errors or to inadvertentdepartures from the standard. drying condition discussed ear~ier, contrib-ute to random scattering of the plotted points. Nevertheless, when allthe plots are considered together, they support the conclusion that thetotal water content is made up of two components, one being free waterand the other being water having a mean specific volume less than 1.0.

This conclusion may not seem wholly convincing in view of the ratherwide scatter of points in some cases and the fewness of the points inothers. If so, one should consider that the main factor determining themagnitude of W. is the length of the period of hydration. In the graphsfor Series 254-9, Fig. 5-3, the points represent ages ranging from 7 daysto 6 months or a year. In every case, the sample at zero age would haveto be represented by a point at w. = O, v, = 1.0, for at that time allthe water would obviously be free. Consequently, the only uncertainty iswhether the real relationship is a straight line beginning at v~ = 1.0, ora curve, beginning at that point. If the real relationship were a curvebending upward from the line as now drawn, it would indicate that thespecific volume of the compressed water that is combined when W*is largeis greater than when w. is small. If the curve turned downward, the indi-cation would be the opposite. In either case the indication would be thatthe products formed at one time would be different from those formed inthe same paste at another time.

There is some basis for believing that the products formed at firstare different from those formed later. During the first few hours thereactions with gypsum are completed, as mentioned before. Also, theproducts formed from the finest flour in the cement would differ fromthose formed later because of the difference between the composition ofthe flour and that of the coarser particles. However, the effects areapparently not large. This was shown earlier when discussing the re-lationship between VWand w (Part 3). All things considered, it seemsjustifiable to assume that one straight line represents the data for anygiven cement and accordingly that both B eq. (6) and Vd eq. (7) areconstant for a given cement.


E3 1.0z I 1

>f4675

Cement-Silico Posteru

.% 0.9 8>al$& 0.8~ \a)$ 0.70 .2 .4 .6 .8 Lo&

w

Fig. 5-1 (above)-w versus ~~

Series954-7

Fig. 5-!2 (right)-w versus ~

Series254-8

1,

Cemenf /4930J

09- \

08- \

1.0

t5007J

0,9

>+

hod

ilEEEB3: 1.0>

15011JLQ“G 0.9

rn

& o,~

m&j 1.0

z

0.9

0,8

%


1.0 ICement 14930 J

o0.9

Q8

:ml‘0 .2 .4 .6 .8 .

‘l&w

Fig.5-3+; versus ~

series Q54.9

1.0Clinker /5699Cement 15761

0.9

0.0>41,0

Clinker 1536?.@ CemenfsJ5 754

al O.y162f3

3% f6214

g

~ 0,8<

f ILO

m Clinker /56 .?3p Cement 15756u>0.9< >

08\

i=.2 .4 .6 .8 1.0

MLw

WIFig, 5-4-vt versus ~

S*llot 954.11,954-13


Mean ratio of (1 - W) to wn/wt

As stated before, the compressed part of the total water is consideredto be the sum of the non-evaporable water and the adsorbed water. Thedegree of compression of the adsorbed water is probably the same for allcements. This is indicated from data on the heat of adsorption alreadyconsidered. The degree of “compression” of the non-evaporable watermight be different for different cements, however, since there are differ-ences in the proportions of the various reaction products. For example,the proportion of Ca(OH)Z should depend on the C3S content of theclinker, and the amount of aluminate-hydrates should vary with theC’3A content. With this in mind, the data were classified according to

(1 – v,)CSA content, and for each class the values of — w6re averaged

w./wt

separately. The results are shown in Table 5-9.

Application of methods of statistical analysis indicate that the largestdifference between the mean ratios of the group are not larger than couldbe accounted for by chance variation alone. Nevertheless, some of thevariation must be due to differences in the chemical compositions of thecements, as mentioned above,

On the whole, the data seem to support the presumption that(1 - vJ/(wn/wJ varies with the composition of the cement but at the sametime they show the influence of cement composition to be small, Cer-tainly the random variations are too great to warrant trying to evaluatethe effect of cement composition from these data, Accordingly, eq, (8)below, representing the grand average, will be applied to all cementsalike in further treatments of the data:

V:=l –0.279w~/w, , . . . . . . . . . . . . . . . . . . . . , ..,,..,...(8)

According to Table 5-9, this equation will give u, for an individual itemwith a probable error of about 7 percent. The degree of agreement be-tween the data and the equation is shown in Fig. 5-1 to 5-4. In eachdiagram the line represents eq. (8),

TABLE 5-9-RATIO OF MEAN SPECIFIC VOLUMEOF TOTAL WATER TO Wn/WI

Type ofcement

Low C8AMed. (74High CaAGrand avg.

Meanl–v,wn/wt

0.2790.2s30.2780.279

Probableerror

ofmean

* .0028==.0024* .0015* !0015

Probableerror

of singlevalue

* .0259+ .0137+ .0129* .0204)

Numberof

samples

883170

189


Lower limit of mean specific volume of total water

From eq. (8) it is apparent that the greater the weight-fraction ofnon-evaporable water, wti/wt, the smaller will be the mean specificvolume, v~, However, there is an upper limit to w~/wj and hence alower limit to vt, This conclusion follows from the fact that the evapor-able water content of a saturated paste cannot be less than about 4Vm(see Part 3), That is, the minimum amount of evaporable water is

we = Wt —Wq= 4V~ (min.) ,

or

Wt—— 1 = 4: (min.) ,Wn

Since VJw. = k, for a given cement,

Wt— = 1 + 4k (min.) ,w~

or

w.

, ; 41$‘maX’) ‘-.=—Wt

From the values for h, i,e,, VJwn, for different types of cement givenin Table 3-6, Part 3, the limits of wt/w. and wtJwt were computed withthe results given in Table 5-10.

TABLE 5-1 O—LIMfTS OF W./W, AND Wt/Wn

FOR DIFFERENT TYPES OF CEMENT

Type I

Type II

Type III

Type IV

T&:;;

Normal C3AHigh C3A

High ironHigh silica

Normal CdHigh CU4

High ironHigh silica

v.

0.2550.256

0.2590.279

0.2380.240

0.2820.277

w,

‘W”

2.022.02

2.042.12

1.991.96

2.132,11

W.—

‘lot

0.500.50

0.490.47

0.500.51

0,470.47

From these results we may conclude that Jhe non-evaporable watercannot become more than about one-halj the total water content oj a saturatedpaste.

From the data given in Table 5-10 and the empirical relationshipgiven in eq. (8), the mean of the specific volumes of the non-evaporablewater and gel water can be estimated. That is, when w~/w~is a maximum,


w,/w~ is between 0.47 and 0.51. For most oements w~/w~would be about0.60, Hence, the lower limit of v~is about

(w) min. = 1- (0.279 X 0.60) = 0,860,

Sinoe these con~ideration~ pertain to paatea in which the total evaporablewater = 4V~, hence, to paetea containing no space outside the gel, itfollows that 0,860 ia the mean 8pecij$c volume oj the total water in a 8aturatedsample that contahu? no capillary water out8ide the gel,

Estimation of tho bulk volume of tho solid phaw and volumo of capillary water

With the mean of the specific volumes of the gel water and non-evaporable water established, as given above, it is possible to computethe bulk volume of the solid pha~e and the volume of capillary water atany stage of hydration,

The bulk volume of the solid phase is here defined as the sum of theabsolute volumes of the solid material in the hardened paste and thevolume of the pores that are characteristic of the gel. In other words,it is the sum of the volumes of the gel-substance, the pores characteristicof the gel, other hydrates, and residues of unhydrated clinker, Or, for asaturated paste, the bulk volume of the solid phase is the sum of thevolumw of the solids plus the volume of the gel water. It differs fromthe over-all volume of the paste by the volume of the capillary water,

The volume-composition of a unit volume of paste can be expressedin terms of its weight-composition as follows:

Cvc+(wn+wo)vd+wc= 1 !where

c = weight of cement, g per cc of saturated paste,W. = weight of non-evaporable water, g per cc of saturated paste,Wv = weight of gel water, * g per cc of saturated paste,w, = weight or volume of capillary water, g per cc of saturated paste,v. = specific volume of original cement, andud = mean specific volume of (wn + w~) ,

Let

V~=l– Wo=CVc+(U). +U)o)vd

where

V~ = bulk volume of solid phase.Since w, = 4V~, and V~ = kwn (see Part 3), WO= 4kwn .Hence,

VBGCVc+ Wn(l+dk)Vd . . . . . . . . . . . . . . . . . . . . . . . . ...(g)

Thk equation holds for VB = O to V~ = 1.0.

*In this equation WO,the weight of the gel water, may be identical with w., the weight of the adsorbedwater appearing in eq, (4). However, until this is proved it in necasaary to assume that a saturated gelmay contain some water held by capillar condensation, that is, that gel water may compriee both adsorbed

1water and capillary water. However, t e term “capillary water” as used in thin discussion includen onlytb~ water that in in excms of tbe gel water.


For an average Type I cement, for which k = 0.255 (see Table 5-10)and v, = 0.315, and for vd = 0.860 as given above, this reduces to

v~=1+55wn—, . . . . . . . . . . . . . . . . . . . . . . . (lo)

c v~ c

The significance of this equation is illustrated in Fig. 5-5. Thisdiagram gives the bulk volume of the solid phase, or of capillary water,per unit volume of paste at any stage of hydration for any paste. Forexample, if a paste was originally 0.3 cement and 0.7 water by absolutevolume, by the time it had hydrated to an extent such that the non-evaporable water is 0.2 g per g of original cement, the bulk volume ofthe solid phase will be 0,63 and the volume of the capillary water willbe 0.37 cc per cc of paste, The other lines give the compositions atlesser degrees of hydration, At win/c = O, a point on the line gives, ofcourse, the original water or cement content of the fresh paste, byabsolute volume. The increaseclearly seen in this diagram,

F (,9 wI,),8 ,65 * ,3 ,2

of Pm+; (*C., )

It should be noted that for

in volume due to hydration is also

Fig, 5-5-Graphical illustration of eq. (10)

VB =[ 1

1 + 5.5: CV*

any given stage of hydration (givenwn/c) there is a certain cement content above which the paste can con-tain no capillary water. For example, as shown in Fig. 5-5, when wn/c =0.1, capillary-water content is zero when the absolute volume of theoriginal cement is 0.65 cc per cc of paste; or, when w~/c = 0.2, w, = Owhen the cement content of the paste is 0,48.

Conversely, for a given cement content there is a degree of hydrationat which capillary water disappears, This conclusion is restricted,however, by the fact that for any given cement, wn~c cannot exceed acertain limit, which is usually about 0.25. This topic will be consideredfurther after the following discussion of the absolute volume of the solidphase in hardened paste,


ESTIMATION OF THE ABSOLUTE VOLUME OF THE SOLID PHASE

The absolute volume of the solid phase in hardened paste is definedhere as the sum of the volumes of all the hydrated solids and the volumeof the unreacted cement. For a saturated paste it differs from the over-all volume by the volume of the evaporable water and from the bulkvolume of the solid phase by the volume of the gel water. It cannotbe determined from the weight of the evaporable water because the meanspecific volume of the evaporable water varies with the porosity of thepaste and the extent of hydration of the cement. For that reason, at-tempts to measure the specific volume of the solid phase were made.

Method of measuring volume of solid phase

In preliminary work, the volume of the solid phase was computedfrom the displacement of the dried granules in water and in other liquids.Owing to the effects of adsorption and to other factors which will bediscussed presently, it was necessary to adopt an inert gas as the dis-placement medium and to develop special apparatus—a volumenometer—for the purpose. This apparatus and its operation are describedbelow,

The apparatus developed for measuring the volume of the solid phasein a hardened paste is illustrated in Fig. 5-6. The volumenometerproper is that part, shown with surrounding water bath, which is lo-cated between stopcocks, 1, 2, and 5. This comprises:

(1) A sample bulb, 8, which is ~oined to the rest of the apparatusthrough a standard-taper, ground-glass joint, and which can be cut offfrom communication with the rest of the system by means of stopcock3.

(2) A mercury barometer, B, for measuring the pressure within thevolumenometer.

(3) A burette bulb, V, the free volume of which can be altered atwill by introducing or withdrawing mercury through stopcock 5, thusaltering the gas pressure within the volumenometer.

(4) A stopcock, 4, which enables the sample bulb to be evacuatedwithout evacuating the rest of the volumenometer.

Stopcock 2 connects with a line to the vacuum pump. Beyond stop-cock 5 is a mercury reservoir R. The pressure in the volumenometeris maintained at somewhat less than atmospheric so that mercury willsiphon into bulb V when R is open to the air and stopcock 5 is open.To withdraw mercury from V, the side-tube on R is connected to thevacuum pump by means of rubber tube T and is evacuated beforestopcock 5 is opened.

Stopcock 1 connects the volumenometer to a helium reservoir H indirect communication with a mercury manometer M, which gives the


H

8

/2 “ ——————i

Fig. 5-6

difference between atmospheric and helium pressures. Stopcock 6 con-nects with the helium supply through two cold traps (not shown) filledwith activated charcoal for removing impurities.

Tests are made with the volumenometer to obtain the free volumeof the sample bulb S (up to cock 3) with and without a sample in place.The absolute volume of the sample is then found by difference. Volumesare measured by determining the volume of mercury that must beadmitted to bulb V in order to restore the helium pressure in the volume-nometer after the cock to the evacuated sample bulb is opened.

At the start of a volume measurement the mercury is withdrawnfrom bulb V until only the capillary remains filled. The flask R with

69s! JOURNAL OF THE AMERICAN CONCRETE INSTITUTE February 1947

its content of mercury is then removed, weighed, and replaced. Next, thevolumenometer inclusive of the sample bulb S is evacuated through cock2 using a mercury diffusion pump backed by a Cenco-Hyvac pump. Ifthe volumenometer is already filled with pure helium beyond stopcock 4,this cock can be left closed. After evacuation, stopcocks 2 and 3 areclosed and 4 is opened. Helium is then admitted through cock 1 untilthe desired pressure, somewhat less than atmospheric, is obtained.Readings are taken on the lower level of mercury in barometer B untila steady, reliable value is obtained. A micrometer microscope readingto 0.001 mm is used. After the reading has been obtained, a littlemercury is withdrawn to flask R to eliminate any air that may havebecome trapped at the mouth of the siphon-tube when the flask wasreplaced after the previous weighing. This clears the line for subsequentmanipulations.

Next, stopcock 3 is opened, admitting helium to the sample bulb,and the pressure drops. The pressure is then restored by opening stop-cock 5, thus allowing mercury to flow into bulb V. The mercury contentof V is adjusted until the reading taken on barometer B is the same asbefore the helium was admitted to the sample bulb, The apparatusis allowed to stand in this condition with further additions of mercurywhen necessary, until it is obvious that the -desired reading is beingmaintained. Then the weight of flask R and its content of mercuryis found and subtracted from the previous weight. When the weight ofmercury given by this difference is multiplied by the specific volume ofmercury, the volume of the free space in the sample bulb is obtained.

When bulb S contains a paste sample, the times required for evacua-tion and for helium contact are necessarily much longer than when thevolume of the empty bulb is measured. Experience with cement pasteshas indicated that overnight pumping out and one or more days ofcontact with the helium are advisable,

Choice of displacement medium

The displacement medium was chosen on the basis of results of pre-liminary tests given in Table 5-11. The object in making these measure-ments was to find a medium that would measure the space occupiedby the evaporable water, or its complement, the space occupied bysolids. The medium should be able to penetrate any region that can bereached by water, without undergoing the volume change that waterdoes.

The upper half of the table represents data obtained by pycnometermeasurements; the lower half represents results obtained with gases asdisplacement media using an earlier form of the volumenometer de-scribed above. These data were obtained when the methods were being


TABLE 5-11

Volume of 1 gof dry sample forsamples indicated: (cc)

Displaadment- ——— ————— —20Q 1s 39 40 41 42 62 N.B.

. — — ———— —Liquid displacement fluids

— . . — —— —Water .395 — .392 — .389 ,391 — ,450Acetone .408 .404 — — — — .424 —Carbon tetrachloride — —Toluene

.465 —G9 .Z4 ❑ ~ — — — —

— — . — — — —Gaseous displacement fluids— — . — — — .—

Air . — .327 .362 .336 .338 .312Hydrogen .392 .422 ,392 .396 — .&6Helium .G4 .Z3 — — — — — .420

N. B.-Silica-gel Lot 15106.

developed and may not be very accurate; however, they serve wellenough for the present purpose.

The wide differences among the results shown in Table 5-11 are due,we presume, to such factors as differences in size of molecule and dif-ferences in the interaction between the solid and the fluid. The size ofthe molecules of the various gases is about the same as that of water,or slightly smaller; but the organic liquids have molecules considerableylarger than the water molecule, as shown by the following data:

Kind of I Molar I Relativeliquid volume volume

WaterAcetone ;: i::Carbon tetrachloride 5.3Toluene 1% 5.9

I

Since the sizes of the molecules of the organic liquids ranged from fourto six times that of the water molecule, the gases were preferable so faras this factor is concerned.

Among the gases, air and hydrogen proved to be unsatisfactorybecause they were adsorbed by the solid material. In air, the apparentspecific volume of the hydrated cement appeared to be little or no higherthan that of the original cement. This obvious absurdity was probablydue mainly to the adsorption of oxygen. Hydrogen is adsorbed also; ithappened to give apparent displacements virtually the same as thosein water. These results with air and hydrogen left only the inert gasesas being able to meet the requirements with respect to molecule-size andabsence of interaction, for these gases have small molecules and besides

694 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE Februa~ 1947

are not adsorbed to a measurable degree at ordinary temperature andpressure. Helium was chosen because it was readily available and hadbeen used by others for the purpose.(1)

It cannot be said that the displacement of a sample in helium is an

accurate basis for computing the space that had been occupied by

evaporable water. An inaccuracy would arise from the salts that appearas solids in the dry paste but which are in solution in the saturated paste.

The error from this source is probably small. Another inaccuracy,

perhaps more serious, arises from the ability of water to swell the solidand thus possibly to open up and enter regions that are inaccessible to

an inert gas. Whether or not helium is excluded from any regionsaccessible to water is not known. The existence of such regions does notnecessarily imply an inaccuracy in the helium determination, That is,

if the loss of water from such a region causes a shrinkage equal to thevolume of water lost, the helium measurement would correctly indicatethe density of the solid phase and the space available to the water eventhough the helium were not able to penetrate it. However, if the volume

change in such a region is not equal to the volume of water 1ost fromthat region, the helium displacement will not accurately indicate the

space available to water. This is a question which must be left open forthe present. However, it “might be noted that the possibility of a gel-shrinkage equal to the amount of water removed from the gel is not asremote as might at first be supposed. Although it is true that the

over-all volume-change is only about 1/40 of the volume of water re-moved, there is evidence that the gel itself undergoes much greater

shrinkage than the specimen as a whole, the difference being due to

mechanical restraints.

Other sources of error are inherent in the apparatus itself. Althoughthe apparatus was constructed and manipulated with care, leakage

through the stopcocks seemed to occur occasionally, Also, the readings

of the mercury level in the barometer with the micrometer microscopewere sometimes affected by changes in the shape of the meniscus in the

course of the manipulation of the apparatus.

EXPERIMENTAL RESULTS

Many measurements were made on samples of various descriptions,but the original determinations were later found to be in error becausenot enough time had been allowed for the helium to penetrate the finestructure of the granules. As was found for carbon black by Rossman andSmith, (z)the first period of rapid penetration is followed by a very longperiod of slow penetration. Different pastes differed in the time re-quired for the attainment of practical equilibrium. In one case 5 or 6days of contact seemed to be necessary. The procedure finally adopted


was to evacuate the sample for 1 or 2 days and then to maintain contactwith the helium for 1, 2, or as many days as were necessary to establishapparent equilibrium. Even under these circumstances it was difficultto attain as good duplicability in repeat tests as was desired, partlybecause the long time periods increased the effects of any slight leaks,These sometimes developed at the stopcocks.

Test measurements had to be repeated several times to obtain valuesfor the specific volume of the non-evaporable water with an apparentaccuracy of about + 0.01 cc per g. Only four different samples weretested by the final technique, but the cements represented a considerablerange of compositions. The specific volumes of the dried pastes (about6 months old) were all found to be close to 0.41 cc per g (density:2,44 g per cc). From the individual values the specific volume of thenon-evaporable water was computed as explained below.

Specific volume of non-evaparable water

The volume of the solid phase can be considered as being equal to thesum of the volumes of original cement and the volume of the non-evap-orable water, That is,

V,=cvc+ wnvn, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(11)

where

v* = volume of solid matter,v. = hypothetical specific volume of non-evaporable water, and the

other symbols have the same significance as before,

The specific volume of the non-evaporable water may have no literalsignificance, since at least a part of the non-evaporable water probablyloses its identity when it enters into chemical combination with thecement constituents. Nonetheless, a figure can be obtained whichrepresents the increase in volume of solid phase per gram of w:~ter com-bined with the cement and which is thus virtually the specific volumeof the water. Since this specific volume does not vary widely amongcements of various compositions, general use can be made of it forestimating the absolute volume of the solid phase from the non-evapor-able water content, This makes available for this study a considerablenumber of data from samples on which helium-displacement measure-ments were not made.

The hypothetical specific volume of the non-evaporable water canconveniently be computed from the following form of eq. (11):

V, – c v,v. = ,,..,,. ,., ,,, . . . . . . . . . . . . . . . . . . . . . . . (12)

w.

The values of v. found from the final, most reliable experimentswere as follows:


Computed compositionCeg~t

CaS I CZS I C,A I C&F ‘“I l—--- 1—[

13721-1P 44,8 26,3 12.7 6.6 0.8213738-6Q 56.4 17.6 10.5 0.8313765-15Q 42.4 28.9 ::: 0.8113779-20P 53.0 15,5 1::! 11,5 0.82

In the computations that follow on is taken as 0,82 for all cements,on the basis of the results tabulated above,

Specific volume of gel water

With the data now at hand, the approximate specific volume of thegel water can be estimated,

Let V, = mean specific volume of gel water;W* = weight of gel water;

V.w. + Vowo= Vtwt.In a saturated sample, made of normal Type I cement, containing nocapillary space,

w. = 0.50 Wt ;Wg = 0,50 Wt ;2)1 = 0.860 ; andv. = 0,82 ,

Hence,

0,860 – 0.50 X 0.82Vg= = 0.90, approximately.

0.50

Computation of volume of solid phase from non-evaporable water

Eq, (11) can be written

v8_1+v@g . . . . . .. . . . . . . . . . . . . . . . . . . . . ,, ..,.., (13)c v. v~ c

This gives the ratio of the volume of the solid phase to the volume of theoriginal cement in terms of the non-evaporatde water (g per g of cement)and the ratio of the specific volume of the non-evaporable water to thatof original cement, v./vC. For any given cement vn/v, is constant andindeed the same value may be used for various cements without intro-ducing much error. In the following computations V. is taken as 0.82 forall cements, v. is the measured value when known and 0.317 when no

0.82 or 0.82measured value is available. That is, the value is either — —

v, 0.317

= 2.59.Computations of solid-phase volumes are recorded in Tables 5-12

to 5-16. These data include results from five different cements and three


TABLE 5-1 9-COMPUTATION OF VOLUME OF SOLID PHASE

Cement 14930Ju. _ o~2 = 2.64; Cd 23 percent; Cd 66 percent; Cd 6 percent; CAF 10 percent;- -0.31v.Specific surface = 2040 sq cm per g; Computations based on eq. (12)

(1) (2) (3) (4) (5) (6) (7)

g: c VoAge, % L cc per

Seri;s we/c dfkys c v. cc of v,254-8 & 9 (g?g) paste

—. ——Mix A

—.%,1 .q:9 7 ,080 1,21 ,!Y8 .60

,099 1.26 .6341 I( :: ,107 1,28 “ .64‘1 1( 56 .129 1.34 “ .671( (d 90 ,150 1.40 “ .70II II ,162 1.43 “ .71(1 :; ; ;;: 1!45 .72

!3-1 ,;;1 447 , 1.48 ,;;4 .73I

Mix B.— ——

9;2 ,4:4 7 .080 1.21 ,418 .51:103 1.27 “ ,53

(1 (( & .116 1,31 ‘( ,55(( (1 56 .135 1,36 “ ,57(( {1 ,174 1.46 “ ,61I( I( 1% ,185 1.49 “ ,62

365 ;;;: 1.52 ,63:2 .;:3 362 1,53 .;;7 ,62

Mix C

9;3 .5:3 7 .082 1,22 ,~?7 .42.090 1.24 .43

(( (1 :: .121 1.32 “ .46(( (( 56 ,164 1,43 “ .5011 (( .185 1.49 ;; .5211 (( l.:

!!.2 1 1.53 ,53

365 .24 1.56 ,54:3 ,;;5 362 .210 1.55 , ii8 .52

different mixes and from six to eight different curing periods for eachcement. The increases in solid volume during the course of hydrationare shown for each of the cements in Fig. 5-7. *

These curves show that during the first month or so the average rateof hydration of a given cement is greater the greater the original water-cement ratio. After the first 3 months the rate is very low. Becauseof this the data do not indicate very definitely the trends of the curvesat the later ages, Nevertheless, it is clear that even with the slowhardening cements, hydration virtually ceases within a year.

*Fordescriptionof mixa see S-254-8 & 9, Appendix to Part 2.


TABLE 5-13—COMPUTATION OF VOLUME OF SOLID PHASE

Cement 15007JUn_ 0.82_.— = 2.61; CVS48 percent; CZ.S29 percent; (78A 7 percent; C,A F 10 percent;u, 0.314

Specific surface = 2015 sq cm per g; Computations based on eq. (12),

(1) (2) (3) (4) (5) (6) (7)

;:;.v,

c v,

Series $:;; ?- “cc per

we/c c v,254-8 & 9

cc of(g/g)

v,paste

_—. — . .— —. ——— .—— — ____Mix A

—r.316 7 ,126

(1 .140(, ;: ,154,( .168“ % .173

180 ,184;;4 480 ,198

—.

——.1.331.361,401,441,451,481,52

—,493(t

,,i,,,

,:;1———

.. —,— —_

.66,67.69.71.72.73.71

————

9-5 ,433 7 .133(t

1.35 ,+4:61, ,150,56

1,3911 (( : .171

,581,45 ‘1

(( 1( 56.60

.185 1,48 “{1 1( .62

,192 1,50 ‘(1( 1;: ,202

.621,53

8:29 ,464,64

——–-i440 .217 1,57 3;8 ,62

—— ———Llix C

—— .—

9-6 – .570 7 ,156 1.41(( (C .3:7 – ‘- ,49

.163 1.42(1 (i ;:

,49,184 1,48 ‘(

(1 (( 56.51

,204 1,53 “1( ,, .205

.531,54 “ I

1%.53

.213 1.56;30 ;;5 440 ,232

.541,61 .;:0 .55

Table 5-17 gives the volumes of the solid phase in pastes that hadapparently closely approached the rnaxirnurn possible extent of hydra-

tion. The average results from each mix are plotted in Fig. 5-8. Thisdiagram is like Fig. 5-5 except that the solid volume rather than bulkvolume is shown. Fig. 5-9 represents a Type I cement cured 6 months.

The original specimens were truncated cones of 4-in. base diameter, 1~-in, top diameter, and 6-in. altitude. Some were made of sand-cement

mortar; others from cement and pulverized silica. * (See Table 5-18.)

These two diagrams show that as the cement approaches ultimatehydration the volume of the solid phase per unit over-all volume of paste

is directly proportional to the original cement content of the paste for

*ForcompletedwcriptiomseeAppendixto Part 2, Series254-7.


TABLE 5-14--COMPUTATION OF VOLUME OF SOLID PHASECement 15011J

~ – 0“82 = 2.63; Cd 45 percent; C& 29 percent; CSA 7 percent; CAF 10 percent;v. 0.312Specific surface = 1835 sq cm per g; Computations based on eq. (12).

(1) (2) (3) (4) (!5) (6) (7)

Ref. c v.No. Age, 5 L cc per

Series wO/c days c UC cc of v.254-8 & 9 (g;g) paste

——Mix A

9-711

‘(

11

(1

11

:40

.114

.133

.143

.156

.164,170.176.184

Mix B

9-81111(,1[

L1

.432,’

1.30 .+?21.351,38 “1.41 “1.43 ‘(1.45 “1.461.48 . ;L

.64

.66

.68

.69

.70

.71

.72

.72

,—,123.153,165,187,191.199.210

Mix C

1.321.401.431.471.501.521.55

.413‘,(1

,,

,,

. ;;0

,54.58.59.61.62.63.64

—9:9 .$?2 7 .131 1.34 .350 .47

.157 1,41 ,( .491( ,1

;: .176 1.46 “ .51,1 (t .195 1,51 (1 .53‘, 1(. i! .205 1,54 “ .54

180 .214 1,56 .55L2 ‘;;5 368 .222 1,58 ;;0 .54

those pastes in which the original cement content does not exceed about

45 percent of the over-all paste volume. For this lower range of cement

contents the position of the line OB corresponds to wn~c = 0.224;hence, eq, (13) becomes

1V,=l.58c V, ~vC~ 045 . . . . . . . . . . . . . . . . . . . . . . . . . . .(14)

For pastes having cement contents greater than 45 percent of theover-all volume, the ultimate volume of the solid phase in the hardenedpaste is not directly proportional to c v.. Instead, the relationship, asshown in Fig. 5-8, is

1V8=0,5+0.5C?JC 045~Gu, =10 . . . .. c. . . . . . . . . . . . (15)

Eq. (14) is represented in Fig. 5-8 by line OB; eq. (15), by BC.


TABLE 5.1 5-COMPUTATION OF VOLUME OF SOLID PHASE

Cement 15013J

V“ 0.82- = — = 2.60; C&’39 percent; C$tJ29 percent; CA 14 percent; CU4F 7 percent;V. 0.316Specific surface = 1810 sq cm per g; Computations based on eq, (12).

(1) (2) (3) ‘ (4) (5) (6) (7)

ft$. c V.a

Age, & L cc perSeries w./c days

2548 & 9CG cc of

(g;g)v,

paata.—

1,391.431,441,471,501.491.57

y; 1 .443 ‘ 7

r: ;

.156 1.4111

.410 .58.183 1,48 “

1( 1(.W

;; .177 1,46 “(( 11

A&56 ,208 1.54 “

<1 Ii ,215 (1 .641% ,236

L7 . ;;3.66

333 .241 . ;5 .66

Mix C—— ,

7 ,335 .471( .49;: J( .5156 11 .5390 II ,54

.55:~ , ;;9 .56

%12 I .q;l

1( (1

(( ((

{1 (1

({

~8 .599

Mix A

7 .149.164

:; .171.180

: .191.188

in .218

Mix B

.158

.183

.203

.221

.236

.245

.253

1.561.611.63

1.411.481.531.581.611.641.66

Lines OD and DC in F’ig. 5-8 represent the bulk volumes of the solidphase (see Fig. 5-5) corresponding to the solid volume$ representedby OB and BC. Line OD corresponds to eq. (10) with win/c = 0.224.For a saturated paste vertical distances in the area above OD representcapillary water; those in the area between ODC and OBC represent gelwater; those in the area OBCO represent non-evaporable water.

In Part 3, data were presented showing that the evaporable watercannot be less than 4Vm. (V~ = weight of water in first adsorbed layer.)It was shown that as a consequence of this the maximum weight ratioof the non-evaporable to the total water would be between about 0.47and 0.51, depending on the type of cement. For a Type I cement itwould be about 0.50. It is of interest to compare these weight ratioswith the volume ratio indicated by BC in Fig. 5-8. (The points along


TABLE 5.1 6-COMPUTATION OF VOLUME OF SOLID PHASECement 15365

~ . 0.82 _2,57; C& 45 percent; Cd 28 percent; Cd 13Percent; cd~ 7 Percenti

u“ 0.319SDecificsurface = 1640 sq cm per g; Computations bawd on eq. (12).

(1) (2)

“ ‘oc ‘4 ~’) Lk ‘:

Sales254-8 & 9


this line represent cements of average Type I composition.) To makethis comparison it is necessary to convert the volume ratio representedby BC to the corresponding weight ratio:

w~v~=O.5wW, (Fig. 5-8) . . . . . . . . . . . . . . . . . . . . . . . . . ..(l6)

V~= 1 – 0,279 ~ (eq. (8) ).w~

w= 0.82 (assumed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. (17)

Substitution of eq, (8) and (17) into eq. (16) gives

w.. = 0.52.Wt

Thus, the maximum weight ratio of W. to w, as estimated from thespecific-volume measurements is higher than that estimated from theadsorption measurements by 6 percent of the smaller value. Thisdiscrepancy is probably the result of applying eq. (8) for V, instead ofexperimental values for the particular cements represented in Fig. 5-8,using the approximate value 0.82 for v., and using the estimated weight

1.10

1.60 I we/c.3?3iMix C> .+

1,50 ,. ‘9. . ~2qf

9’ K,, A

‘1.40 ,309

$ !30 Cemenf /4930J

EC# 23%

~ 1.20 C,J -56 ~~u CJA 6 ,,

1,10 C4A/-,0 ,,

-ii 2040 Crn2jgc 1,00

!.70

1.60

1.50

1.40

I 30

I 20

1.)0

Loo

‘&.-

1,70I I

% Mix c160 ~ix = Wo[c~.370, 1.60

\ .

: 150A 7“ ,4>, ~

> * ~‘150

.316; 14.20. I

140

“ I.w - Cement 15007J 1,30 rem ,“ t /50/3 JC3S 44%

u 120 C2S .29C,s 39!Z

120 Czs 29,,C3.4 7,, L-3.4 /4,,

0-110 C’JAF {0,

InI !0 c#.4F 7.,

20/5 Cn+ 1810 Cm 2/~~ KO I000 ;

10 15 20 25 30 35 40 45 50 55 60 65Cl.

;!70

m 1.604-01s0

ECenwnf 15365

CJS -45%3120 C2S -28,,

C3A -/3,,1.10 C4AF- 7,’

[640 Gnqg1,00-

0 S 10 15 20 25 30 35 40 45 50 55 60 65

Per!od of Curing -weeks

Fig. 5-7—increase in valume of solidphase

Period of Curing -weeks


)W4COU3’N03,&b*r-l-,, .!..

RwR,. ..,.is%..—

I

I

I


ratio based on an average ratio between V~ and W. that may be in errorby as much as 10 percent for a particular cement.

It may be concluded that Table 5-10 and line BC of Fig, 5-8 are sub-stantially in agreement in howing that the maximum possible weightartio of non-evaporable watw to total water is about ~,

Limit of hydration for pastes of high cement cantent

As already noted, line BC appears to be an upper limit to the amountof hydration (in terms of w.) that can occur in pastes of high cementcontent. The data at hand are not sufficient to prove whether this is anabsolute limit or whether, given sufficient time, the points will graduallymove higher. However, the fact that one of the points represents awater-cured paste 4 years old gives strong support to the suppositionthat the line as shown marks the upper limit. The significance of theposition of line BC and whether or not its slope remains the same maynot at first be apparent, Consider the following alternative possibilities.

(1) The process of filling the available space with hydration productscould be likened to filling a vessel with like-size spheres; at any givenstage in the filling the total void space in the vessel would represent theunfilled space plus the pore space between the spheres; the void space

TABLE 5-1 8-COMPUTATION OF THE VOLUMES OF THE SOLIDPHASE IN SPECIMENS FROM SERIES 254.7

Cement 14675

v—’=l+u~ . ~ 0.82= — = 2.68c Uo %c’rlo 0.318

Ref. co, (1 + 2.6: W#C)@O

2%:7w“/0 1 + 2#5s(wn/c) co per

co of 00/00 of pasta

— TI-[z: ‘-b =Ivl 6 mm~1~1 6 m...—— — ——. . ___ _

Mortar spacirnenn. — — — . . . . _7-1 .1445 .1485 ,16267-2

1.37 1.38 1.42.1585 .1605

,654 .76.1763 1,41 1.41 1.46

.77 .79

7-3 .1665.534 .75 .76

.1705 .1817 1.43 1.44.78

7-41.47

,1895.615

.1870.74

.2046.74

1.49 1.48.76

7-5 .20461.53 .477

,2115.71

.2351 1.53 1.65 1.61.71 .73

.2115,421 .64 .65

.2275 .2337 1,55,68

H1,59 +.:NJ

.2155,354 ,55

.2275 .2303 1.66 1,59 ,.57

.306 .48 :Z .49. — — — — — — — —— _c%ment-sili ca specimens

— — . . — . — . . . _3M 62d 6 mo. 36d 63d 6 mo. 35d 63d 6 mo.

. — — — — —7-1s .1995

— — —.2007 .2160

7-2S1.52 1.52 1,56

.2133.472

.2164.72

.2324,72

1.56 1.66; ’11

7-3s1,60 .421 .65

.2246.66

.22707-4s

.2433 1,58 1,59 1,63 .373 ,59.2323

.69.2303 .2497 ;fy

.617-3s

1.59 1,64.2351

.340 .64 .54 .56.2304 ,2456 . 1.59 1.63 .326 .52 .62 ,53


. .Orlglnd Cam*nt-hactlon cdOver.all Pad9 VOlum*

(. CVC)

i “0~g.s

yB,

+’- d,.

!J ‘ / Age 6 Months

~g, ~, /

8. Mortor specimens

.x - Comonf.SilicO $mcimens .

Et Commt /46753!+~

OrlOlnelCement-Fraction of Ovar.dlPaste Volume

Fig. 5-8 (left) —Relationship between volume of solid phase and original cement contentat virtually ultimate hydration

Data fromTablo S.17

Fig, 5-9 (right)-Relationship between volume of solid phase and volume of originalcement

Data fromTablo 5-10Sac Arwandlx to Part S for deswlption of orlolnal smelmons

within the vessel could not be reduced below the total volume of thespaces between the spheres when the vessel is ful 1 of spheres.

(2) The process could be likened to that of filling a vessel with rela-tively large spheres and then sifting in smaller spheres that could occupythe spaces between the larger spheres,

If the amount of non-evaporable water reached a point on the lineBC and then remained there regardless of the length of the period ofcuring, thus indicating an unchanging ratio between evaporable and non-evaporable water, the indication would be that the hydration productshave a characteristic minimum porosity that cannot be reduced. Thiswould indicate that the space becomes filled by a process analogous tothat described in (1). If with continued hydration the slope of BCshould become smaller, this would show that the ratio of non-evaporableto evaporable water gradual] y increases and that the colloidal hydrationproducts become less porous as hydration proceeds. This would indicatethat the space becomes filled in the manner pictured in (2); that is, thepores of the gel first formed would become partly filled by hydrationproducts formed at a later time. As pointed out above, the fact thatthe specimen cured 4 years is represented by a point on BC of Fig. 5-8

is strong evidence that the porosity of the hydration products does notdecrease as hydration proceeds. Hence, hydration seems to be a process

of forming new products without changing the characteristics of productsalready formed.


This evidence that the hydration products have a characteristicporosity is compatible with the theory of formation of the gels, When thesolid material precipitates from solution, the colloidal particles initiallyformed by the aggregating molecules are drawn together by interparticleforces having an intmsity characteristic of the system, The gel is pic-tured as a mass of colloidal particles drawn together in random arrange-ment and held by the forces of flocculation and probably to some extentby rudimentary, submicroscopic crystal growths, If the particles com-

posing the gel (the “micelles”) are larger than the normal spaces in thegel, later deposition of new gel in such spaces would seem unlikely, (SeePart 34)

Limit of hydtat,ion with capillary water continuous,!y available

For mixes falling to the left of point B, the time required for the solidphase in a given paste to attain a volume represented by a point on theline OB is greater the greater the original cement content of the paste.(It should be noted that time is not represented in Fig. 5-8 or 5-9.)But apparently this line is reached eventual] y and it marks a limit to theamount of hydration even though capillary water is present in the paste,Such a result would be expected if the position of line OB corresponded tocomplete hydration of all the cement. However, complete hydrationprobably does not occur except in cements of unusually high specificsurface. Observations by Brownmiller@J on pastes of w/c = 0,4 byweight (c v. = 0.44 cc per cc of paste) indicate that all but the coarsestparticles of cement, probably those having diameters less than about 40microns, become completely hydrated if water-cured long enough.According to Brownmiller, a Type III cement of about 2600 specificsurface appeared to be about 99 percent hydrated at the seventh day.A Type I cement, specific surface 1800, appeared about 86 percenthydrated at the 28th day. In a section from concrete pavement 6 yearsold, the cement (specific surface unknown but probably not over 1800)in the part photographed appeared to be completely hydrated exceptfor one 75-micron particle.

Fig. 5-10 gives data obtained in this laboratory on the influence offineness on the extent of hydration as indicated by the non-evaporablewater content. These results indicate that the ultimate increase in solidvolume per cc. of original cement is smaller the coarser the cement. Thesaindications that coarse particles of cement remain unhydrated for anindefinite period even when free water is present show that the apparentcessation of hydration is, for cements of ordinary fineness, not due to theattainment of chemical equilibrium. Apparently, the gel around thecoarser cement grains becomes so dense that water cannot penetrate it.Absolute stoppage of flow through the gel is hardly conceivable, however.


It is more likely that water continues to penetrate to the cement butdoes it so slowly that we are unable to detect the effect.

Estimation al volume of unreacted cement

The amount of unreacted cement in hardened paste can be expressedas follows:

v,,.— =l–nw~ , . . . . . . . . . . . . . . . . . . . . . . . . . . .. (18)Cv, c v,

where

vu.—. volume of unreacted cement per unit volume of originalm. cement, and

n = cc of cement reacted per cc of non-evaporable water.

As said before, we have no data on the amount of unreacted cement in thespecimens used in these studies. However, from Brownmiller’s observa-

tions, mentio~ed above, it seems reasonable to assume that at ultimatehydration, about 90 percent of a Type I cement becomes hydrated.

Making this assumption, assuming that wnjc = 0.24 at ultimate hydra-tion, and letting vn/v, = 2,59, we obtain

0.1 = 1 – n(2.59 x 0.24).

Hence, n = 1.45.

With n thus estimated we may write

V,,c—=1–3.75wn/c . . . . . . . . . . . . . . . . . . . . . ..(19)Cvc

It should be understood that this relationship is only a rough estimate.The value of n will depend on the fineness of the cement, the coarserthe cement, the smaller n. For example, if when wn/c = 0.24 thecement is actually completely hydrated, n would equal about 1.6; if 80

PeriodOfWa+wCur{.~,weeks

Fig. 5-1 O-Effect of fineness of grinding onrate and amaunt of hyd;ation

Cement14560C,S-6057& C,S-l 7%,C3A-7qo, c4AF-13~o

708 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE February ~947

percent hydrated, about 1.3. The purpose of the computation is toshow the order of magnitude of n ahd to provide a baais for showing,in the following section, how the correct data would be representedgraphically if we had them.

Graphical summary of data on volumes of various phases in hardened cement paste

Fig, 5-11 gives a summary of the relationships brought out in thepreceding discussions,

It should be understood that the diagrams represent average values.The slope of BC (eq. (15)) would vary slightly among pastes made withdifferent cements, according to differences in the ratios w~/w, for thevarious cements, Likewise, the relationship between the slope of OB(eq. (13)) and that of OD (eq. (9)) depends on V~/wfi. The slope of OBat ultimate hydration would be smaller the coarser the cement. More-over, the slope of OE (eq. (18)) would depend on the fineness and othercharacteristics of the cement.

With respect to eq. (18), it should be clear that thk equation canhold only up to the ordinate of point B. Beyond that point the locusof the point representing unreacted cement must be the straight line EC.

At Opercent hydration, only the diagonal line would appear, represent-ing unreacted cement and capillary water, At this stage, the capillariesare the spaces between the original cement grains. The manner in whichthe new phases develop as hydration proceeds maybe seen by comparingthe four diagrams in consecutive order.

SOME PRACTICAL ASPECTS OF THE RESULTS

No attempt was made in this paper to discuss the implications of thedata and the relationships that have been, presented. However, thefollowing fairly obvious matters may be pointed out:

(1) Pastes in which the original cement constitutes more than46 percent of the over-all volume cannot become hydrated to thesame extent as pastes containing less cement. In terms of weightratio, this meahs that if we/c is less than 0.40, ultimate hydrationwill be restricted. Therefore, conclusions about the extent ofhydration of cement in ordinary concrete should not be drawn fromdata obtained from standard test-piecee--w/c = about 0.25. (Thenumerical limits mentioned above probably are different for cementsof different specific surfaces; the coarser the cement the lower thelimiting we/c, For specific surfaces between 1600 and 2000, thefigures given are satisfactory.)

(2) The average rate of hydration is lower the lower w~/c, There-fore, the age-strength relationship for ordinary concrete cannot bethe same as that for standard test pieces of low we/c.

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE 7W

25Y. of Ultimate Hydrstion

‘0/c (by wf.).8 .6S .4 3 .2

50% of Ultlme+e Hydration

‘o/c W ~).8 .6.5 .4 .3 ,2

original Cement, Frection of Over.,‘n/c” o.ob

.s!% 7S% of Ultimate Hydrationg

We/C (by wt.)

I.8 b .5 A .3-

I Paste Volume (= Cvc ) “-wn/c =0.12

100% of Uljimete Hydration

,8 ,~$~b~ wt.).2

1 , t 1 r , .

Original Cement, Fraction of Over-all Paste Volume (= Cvc) “- ‘-wn/c = 0, !8 wn/c = 0,24

Fig. 5-11 —Relationship between volumes of various phases in soturated hardened pasteand original cement content

(3) The substance that gives concrete its strength and hard-ness is the solid material formed by the hydration of portlandcement, In Fig. 5-11 this cementing substance is represented bythe vertical distance from OEC to ODC at the point on the scale ofabscissas representing the original cement content of the paste.The capillary spaces, when present, are distributed through this


substance and weaken it. Therefore, the cementing substance (notthe paste as a whole) has its maximum possible strength if thehardened paste can be represented by the ordinate passing throughpoints E, B, and D, or by any ordinate to the right of that one.

(4) It might seem from the foregoing paragraph that a pasterepresented ky the ordinate through EBD has the maximum possiblestrength and therefore that still richer pastes (necessarily moldedunder pressure) would be no stronger. However, a limited amountof data obtained from specimens molded under high pressure in-dicates that the strength of the paste as a whole increases as thecomposition is made to fall farther to the right of the ordinate pass-ing through EBD, In view of the evidence that the density of thecementing substance is the same in all such pastes, it is concludedthat the increase in strength is due to the decrease in the thicknessof the layer of cement between the particles of mineral aggregate,In this connection, the unreacted cement may be considered to be apart of the aggregate, The increase may also be due in part to an

increase in the degree of “self-desiccation” of the gel, which would

be expected to increase with the proportion of unreacted cement,

(5) The hydraulic radius of the pores in the paste and the porosityare smaller the smaller the proportion of capillary space in thehardened paste. The hydraulic radius is at its lowest possible

value when the composition of the hardened paste can be repre-

sented on the ordinate passing through points E, B, and D of Fig.5-11. Porosity of the paste as a whole continues to decrease as thecomposition is made to fall farther to the right, but the hydraulicradius is not further reduced.

(6) The permeability of hardened pastes to fluids under externalpressure probably depends almost entirely on the proportion of

capillary water, owing to the extreme smallness of the gel-pores.Hence, permeability is practically zero when the paste can berepresented by the ordinate passing through points E, B, and D.This is discussed further in Part 7.

GENERAL SUMMARY OF PART 5

Nomenclature:

c = cement, g per g of saturated paste

W1 = total water, g per g of saturated paste

W. = non-evaporable water, g per g of saturated paste

wa = compressed water, g per g of saturated paStew, = capillary water, g per g of saturated paste

w. = adsorbed water, g per g of saturated paste


WO= gel water, g per g of saturated pastev, = specific volume of cementvi = (( {i “ total waterVn = (( (( {{non-evaporable waterVd= (( (t i( compressed water

(( ((= “ gel water: = ratio of adsorbed water to non-evaporable waterB=(l+B’)k = ratio of Vm to w.

Vm = constant of B.E.T, equation, proportional to surface area ofthe gel

VE = bulk volume of solid phase, It differs from the over-allvolume of the paste by the volume of the capillary spaceoutside the gel,

V, = volume of solid matter in the, paste

vu,= volume of unreacted cement in the pasten = cc of hydration product per cc of non-evaporable water

(1) The total water in a saturated specimen can be divided into twocategories: (a) tlfat which has A specific volume less than 1,0; (b) thatwhich has a specific volume equal’ to 1,0, All the water having aspecific volume less than unity is called compressed water, It comprisesthe non-evaporable water and a part of the evaporable water,

(2) The mean specific volumes of the total water contents were com-

puted from the measured volumes of the saturated granular samples andthe volumes and weights of the ingredients, assuming that the cementretained its original volume.

(3) The mean specific volume of the total water in a saturated pasteis given by the expression

wn/w~ can vary from zero to about 0.50. Hence, the mean specific volume

of the total water varies from 1.0 as a maximum (w. = O) to about 0.860as a minimum (w./w~ = 0.50). Among different types of cement,w./wt (maximum) ranges from 0.47 to 0.51.

(4) When wnj’w, = about 0.50, the sample contains no capi!lary water.

Hence, 0,860 is the mean of the specific volumes of the non-evaporablewater and the gel water.

(5) The mean specific volume of the gel water is estimated to beabout 0.90; that of the capillary water is 1.0.

(6) The bulk volume of the solid phase as a fraction of the over-allvolume of the paste is given by the expression

71s! JOURNAL OF THE AMERICAN CONCRETE INSTITUTE February 1947

LB=l+~n ; (1 + 4JC)‘~ (for 0< Vj3 <1)c Va Vtl

For an average Type I cement, k = 0,255 and VB becomes

[V.E!= 1+6.SU 1c VLI

(7) The absolute volume o; the solid phase as a fraction of the totalpaste volume is given as

[v,= 1+~.~ 1c Vo

(8) The ratio of the so~d v~lume after hydration to the solid volumeof the original cement, . V,/(c v,), varies from 1.0 when wJc = O to

about 1.63 when wn/c is maximum. The upper limit is probably lowerthan 1,63 for cements coarser than those used in this study (1600 to 2000sq cm per g and maybe slightly higher for finer cements.

(9) For pastes having original cement contents greater than about0,45 of absolute volume, the ultimate solid volume is about

1.v,=o.5+(Mcvo ~45~@d~10

(10) The extent of hydration in water-cured pastes having originalcement contents below 0.45 by absolute volume is apparently limited bythe relative amount of +40 micron particles in the original cement. Inthe richer pastes it is limited by the space available for the hydrationproducts.

*****

For comments on some practical implications of the results, see thesecticm immediately preceding this General Summary.

REFERENCES

(1) A. J. Stamm and L. A. Hansen, J. Phys. Chem. v. 41, p. 1007 (1937); G. F.Davidson, J, Teztile In-d. v. 18, T175 (1927); Stephen Brunauer, The Adsorption ojGases and Vapors, v. 1 (Princeton University Press, 1943), Chapter XII.

(2) R. P. Rowman and W. R. Smith, Ind. Eng. Chem. v. 35, p. 972 (1943).(3) L. T, Brownmiller, Proc. ACI, v. 39, p. 193 (1943).


Part 6. Relation of Physical Characteristicsof the Paste to CompressiveStrength*

CONTENTS

Mlation of paste structure to compressive strength . ... . . . . . . . . . . .S45The ratio of increase in solid phase to available space . . . . . . . ...846Thegel-space ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...848fitititio~ of~, vs. Vn/w. relatio&tip... ,, . . . . . . . . . . . . . . . ...848Effect ofsand particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...849

Influence ofgypsum content of cement. . . . . . . . . . . . . . . . . . . . ...851

Effect ofsteam-curing, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...853

Dkcuseion and summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...854

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...857

The compressive strengths of mortars and concretes depend on manyvariable factors. The effects of some of the factors, particularly certainproperties of the hardened paste, will be discussed in this section.

The ratio of increase in solid phase to available space

At the time when fresh cement paste of normal properties first congeals,its final volume is established except for a relatively minute expansionin volume that occurs during subsequent hydration and the small volumechanges that accompany drying and wetting. Therefore, the spaceavailable for the increase in volume of the solid phase is initially equal tothe volume occupied by water.

$,rhe ~haracter~tic8 of the ~emen~ mentioned in t~m ~ecti~n may be found in the Appendix to Part 2.

846 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE March 1947

We may tentatively assume that the increase in strength that accom-panies an increase in extent of hydration is a function of the increasein the volume of the solid phase per unit of volume of initially water-filled.9pace. In this connection it seems logical (though not essential) to con-sider the volume of the solid phase to be the sum of the volume of thesolid matter and the folume of its associated voids, that is, to considerthe bulk volume of the solid phase, rather than its absolute volume.(See Part 5.)

As shown in Part 5, the increase in bulk volume of the solid phaseis about

0.860 (w. + 4T”m,

W. is the weight of the water that has become a part of the solid phase andtherefore represents the increase in absolute volume. 4V~ is the weight ofthe water required to fill the voids of the gel. 0.860 is the mean of thespecific volumes of these two classes of water. Hence,

increase in solid phase = o,860(wn + 4vm). . . . . . . . . . . . (1)

original space available w.

where WOis the original water content after bleeding.

l’or any given cement, VJW. is a constant (see Part 3). Hence,the solid-space ratio is, in general,

X’=0.860; (l+4k) . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(2)

or

( -)x, = ~ 860 ~ l_+ 417C. . . . . . . . . . . ...!. . . . . . . . . . . . .

w. k(3)

where X’ = ratio of increase in solid phase to original water content.It will be shown that compressive strength, f,, is related to X’ by anempirical equation of the form

fc=rnx’ + B........................(4)

where m is the slope of the empirical line and B, its intercept on the j’.axis.

Substitution for X’ from eq. (2) and (3) gives

fC=M’~m + B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(5)w.

and

jc=jjJf’!.!l+B..................................(6)Wo

PHYSICAL PROPERTIESOF HARDENED

where

()M’ .0.860 ~ m .

PORTLAND CEMENT PASTE 847

The constants M’ and B can be evaluated by plotting observed valuesof fC versus VJwO or wm/wo. Such data for four different cements aregiven in Tables 6-1, 6-2, and 6-4* and are plotted in Fig. 6-1 and 6-2.The points represent mixes A, B, and C of Series 254-9 and the cmixesused in Series 254-11, where they were the same as A and B of 254-9.The curing periods ranged from 7 days to about 1 year.

The straight line drawn in Fig, 6-1 represents the relationship

j. = 120,000 ~ –3600 . . . . . . . . . . . . . . . . . . . . . . . . . . . . (7)w.

It will be noted that the deviations of the individual points from this lineseem to be random. That is, there is no indication that the points for anyparticular age or cement or mix can be distinguished by their positionswith respect to the line, In view of the fact that VJW. (i.e., k) differsconsiderably among the four cements, it seems that strength is not muchinfluenced by this ratio. If w. represents all the hydration products andV~ only the gel (material of high specific surface—see Part 3), this in-

BI I

,,.,,,~,;y, .,:7,”;::;;.”,%J.~):W ~ ,,,4, ,4 :. , , ,,, /; ; ““d “’ ‘d $ ‘1 ‘“ . L“,.,,., ,, ,. . ,. ,..a ,,.!,, ., ,, , m ,7*~ “— ‘

.“w– ,8s

g,2 — J !3$10%

ga

$ x

$b

y

!4 -

a

~------- ------- (s.)240 oO*- 3600)

u?/

//0 --1-

, 002 Ma 00; 006 080 082 014 016 O\*V@

Fig. 6-1 (left)-Relationship between compressive strength and V~/wo for cementslow in C,A

Data hornTables 6.1,6-9, ~ 6-4, Se!ie$954-8.9 & 11

Fig, 6-9 (right)-Strength versus wtJw. for the same materials represented in Fig. 6-1series 954.0.9 a 11

*All Part 6 table~ follow text PP. S58 to 864.


dicates that strength depends primarily on the gel and is therefore littleinfluenced by differences in w. when Vm is fixed.

This point is illustrated further by Fig. 6-2, where j, is plotted againstwn/w.. The straight line has the slope Mlc where M = 120,000 andk = 0.285, the mean value of k for the four cements. That is, the equa-

tion for the line is f, = 34,200 %“ – 3600. Although the points scatter toW.

a similar degree, the scattering in Fig. 6-2 differs from that in Fig. 6-1in that there is clear evidence of segregation of the triangles (representingcement 1501lJ) whereas in Fig. 6-1 the points are rather well mixed.

The gel-space ratio

It thus appears that the increase in strength is directly proportionalto the increase in VJwo regardless of age, original water-cement ratio,or identity of cement. Accordingly, it appears advisable to discard

the assumption that strength is a function of the ratio of the total in-crease in solid phase to available space, in favor of the assumption that itis a function of the ratio of the volume of the gel to the original spaceavailable. We may call this the gel-space ratio. Thus, we may assumethat

X=& . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(8)w.

where X = gel-space ratiod = proportionality between V~ and the total volume of the

gel,

Substitution of eq, (8) into eq, (4) gives

jc=M~m+B !........... ,,,.,,,.,.., . . . . . . . . . . . . (9)w.

where M = mfl. Comparison of eq. (9), (6), and (4) shows that theabove is merely a redefinition of the. meaning of the slope of the linerepresented by eq. (4), the new definition taking into account the obser-

vation that k need not be included. Eq. (7) is thus now defined as therelationship between strength and the gel-space ratio.

Limitations of j, vs. V~/w, relationship

Although the four cements represented in Fig. 6-1 differ considerably

in CSS and CZS content, they are all similarly low in Cd. When cementsof various C3A contents are included, the j, vs. VJw. relationship isfound to be influenced by the C3A content of the cement. This is illus-trated in Fig. 6-3 and 6-4 (plotted from data of Tables 6-1 through 6-7),

in which cements of various C8A contents, including the cements of Fig.

6-1, are represented, Fig. 6-3 represents cements of low CSA content;


Fig. 6-4, those of medium or high C,A content. In each diagram, thediagonal line represents eq. (7).

In Fig. 6-4 it will be seen that the strengths developed by cementsof medium or high (7,A content were in general lower than would becomputed from eq. (7). (Certain exceptions will bc discussed below. )The conclusion follows that cements of different CSA contents developdifferent strengths at the same value of V~/wo, at least among thosecements containing more than about 7 percent CSA (computed).

Before further discussion of the relation between cmnent composi-tion and strength, it is necessary to consider some other factors.

Effect of sand particles

In Fig. 6-3 and 6-4 three different series of tests are 1eprcsented. Se] ies254-9 comprised three mixes, A, B, and C, as described previously (seeAppendix to Part 2). Mix A contained sand and cement only. hlixesB and C contained sand and pulverized silica of cement fineness, theamount of the silica being 33 percent and 73 percent of the weight of thecement, respectively. Series 254-11 comprised mortar mixes of the same

proportions as mixes A and B of Series 254-9. The data from these twoseries are, therefore, directly comparable. On the other hand, the datafrom Series 254-13 (appearing in Fig. 6-3A, B and Fig. 6-4A, B, andD) represent specimens containing only cement and pulverized silica,the amount of silica being 71 percent of the weight of the cement. Thequestion, therefore, arises as to whether the results from Series 2~~-13are comparable with those from the other two series.

In this connection it is of interest to examine Fig. 6-4C, which repre-sents data obtained from mixes A, B, and Cf, and from neat cement.This is the only case where neat cement and mortar can be compared.Note that the strength of the neat cement at a given VJWO exceeds by aconsiderable margin that of the specimens containing sand (No. 4 maxi-

mum size). The points appearing immediately below those representing

neat cement are the ones representing mix A, which contained no pul-verized silica, and mix B, which did contain silica. The results indicate,therefore, that the introduction of sand lowered the strength. It ispresumed that the decrease in strength resulting from the introductionof sand is due to the decrease in homogeneity with respect to elasticproperties, and possibly to a modification of the mode of failure asdescribed by Terzaghi.flJ* On this basis one ,,would not expect the in-troduction of pulverized silica to affect the strength adversely, owing tothe smallness of the silica grains. Therefore, it would seem that neatcement specimens or specimens containing only pulverized silica aaaggregate would not be directly comparable with specimens containingrelatively coarse sand particles.

●See references at end of text, Part 6.


20 I

(@ iem,n, 15763I

Clinker 15670lb

-Eq. 7

12.

/

8.

/5 2.S%SC,4 I cemenf !5 763

4,0 13,~ c, s C,5[C,A C*.4F[SO<34 s4[2 6 li~

m

S?%/,04 .08 .1.? .16 20 24

x ‘d% Sr-.;es .754.//

‘ef, 254-/3

“.- .?0.I

k @ kemenf 149303

I

j lb -

~.

-g 12-

Gk“

o

t8

z

%d [ I ccmd !4930 J

=4 c>f Ct> ]C,.4IC4AJIS0,-p z.! 56 I 6 [ 10 1/.6

: 0- A ~

m“.04 .08 .12 ,s6 ,20 .24

v~w,~ Serk ?54-9

.:.; 20-

+ Q >emen;/5011.l

8 lb.

0

1?Ypx

x8

/ f“.4 I cement 15011J

* C,5 Ic>s IC,A c#[so .!~512917 /0 1/4

@oA04 .06 12 .\& 20 24

vmpo Ser,es254-9

20 I I I

@ g;;;;;:;~j(6

[2/

o

8L5& 3.57.$0=

4 / y I cemen~ I 5756c, s C>9IC,J G74aI%<9 261 5 ( u 1).7

00/.04 ,LM .12 .16 .?0 24

‘m/wo series ,?544/0! 254/320

I I I@j Cement 15007J

o16

12. &

x

8

/ F

A

4 [ Cenle”? 1500?1<, s c, s [ C,.4 c< A/ 1so<da 2917 [101/.s

L00

/.04 08 .12 .16 20 .74

~m/wo 3<,;,,2S 4-9

Fig. 6-3—Strength versus gel-space ratioData fromTables 6-1, 6-!?,6-3, 6-4 and 6-7

Key to symbols

o-Mix Ax-Mix BA-Mix ~❑1.f+erie$954.13, cement-silica pa$tes

However, the trend of the neat-cement points is such as to suggest

that the strength of the neat cement and mortar would be equal at aboutV~/w~ = 0.10. It happens that most of the points representing the

cement-silica specimens of Series 254-13 fall near this point or lower onthe V~/w~ scale. Also, it may be observed that the strengths of these

cement-silica specimens were about the same as or lower than the strengths

obtained from the mortar specimens having equal values of Vm/w.. It

thus appears that, at least within the range of gel-space ratios thatembraces the results from Series 254-13, the introduction of sand hadlittle or no effect on strength and therefore that the mortars and cement-


20 1

@ C.m.n?15758Clinker 15498

lb

12/’”

3.s8 ,, 5

Loh%so,

4 / ‘ t C*mm~l s758CIsl C.A C,dflsot

61 /? I /0 8 [ /.6

“?GO /

..,1 ,,, !6 .20 ,24

x vm/wOr.<

Ser;es 260.11,, 2s 4-/3

~ ‘m/wo S,r;@S 254-9.=m:20

I I I~ @j Cement f5013J

0 t6u

12/ o 6

0%

8 ,.

/ $

? c

4 r cement Iso/3 Jb c, J Czslc,. C,.4FIS0,

.“ J, 29 I 1+ 7 11.7

00/,,04 .08 12 16 ,20 24

hp. SW;,. 254-9

‘PFPt%Hi12 I /

/

?,s, fl~ 0083..4- \“* / S%so,

4 / 7 I ( ‘*men+ I5761

00/.04 .08 ,1’2 ,16 .20 ,24

vm/% serh3 254 -If,, 2s+13

VmpvoSer[e5 ?54-11

,, 254-/3

Fig. 6-4-Strength versus gel-space ratioData fromTables6-f, 6-5, 6.6, and 6-7

Key to symbols:

Mix Ax-Mix BA.Mix C❑l-series !254-13 cement-silica pastes

silica pastes can be compared directly in this instance. As brought outbefore, this indication is supported by the trend of the neat cementpoints appearing in Fig. 6-4C.

Influence of gypsum content of cement

The data from Series 254-13 offer a clue as to the cause of the relativelylow strengths at a given VJw. produced by the high C3A cements. Thesedata are given in Table 6-7 and are plotted in Fig. 6-3 and 6-4, as rmm-tioned above. In this series, four cements were prepared from each offive different clinkers. The 6’03 content in each group of four cementsranged from 1.5 to 3.5 percent. Cement-silica cubes were made andtested after 28 days of water curing.

85$! JOURNAL OF THE AMERICAN CONCRETE INSTITUTE March 1947

Note first the diagrams for the cements prepared from clinkers 15498,15699, and 15367 in Fig. 6-4-medium or medium-high CaA cements.

In each case, increasing the gypsum content increased the strength to avalue equal to or slightly greater than the mean of the low CSA cements asrepresented by eq. (7) (that is, by the diagonal line).

As remarked above, it is somewhat questionable whether the dataof Series 254-13 are comparable with eq. (7), Hence, the indicationsof the data must be taken with some reservation. However, it maytentatively be concluded that the relatively low strengths, at a givenVJwo, of cements of the type noted above can be increased and brought

into line with the strepgths of low C8A cements by appropriate increasesin gypmm content.

This conclusion was reached first by Lerchf2j in an investigationcarried on parallel with this one. By means of calorimeter measurementsof the rates of reaction and of strength and shrinkage tests, he foundthat the relatively low strength of high CW4 cements was associatedwith a premature depletion of gypsum during the early stages of hard-ening. Maximum strengths were produced when the gypsum contentwas so adjusted that the dissolved gypsum did not become depletedduring the first 24 hours. Marked reductions in drying shrinkage alsoresulted from such an adjustment in gypsum content. Lerch’s resultshave been confirmed in some respects by Whittaker and Wessels. (3)

It should be noted particularly that increasing the gypsum contentof cements prepared from clinkers 15498 and 15367 increased the strengthand at the same time reduced the ratio VJW.. Since WOwas substantiallythe same for the different cements of a given group, this indicates thatthe reduction in the gel-space ratio was due to a reduction in the amountof gel. Thus we have a reduction in gel associated with an increase instrength whereas the normal effect would appear to be a reduction instrength. This apparent anomaly cannot yet be explained with assur-ance. However, it appears that the observed increase accompanyingthe decrease in gel content could be the result either of a change in thecomposition of the gel or of a reduction of the proportion of a gel havinglittle intrinsic strength. Lerch(2J has pointed out that gypsum combineswith C3A to form calcium sulfoaluminate, most of the reaction takingplace during the first few hours. Therefore, if the hydrate of C3A is

colloidal, as other evidence indicates, and if calcium sulfoaluminate ismicrocrystalline, the greater the amount of ,eulfoaluminate produced,the smaller V~ should be. With the type of cement considered here,the C3A content is in excess of the gypsum on a combining-weightbasis, and therefore the amount of calcium sulfoaluminate depends onthe proportion of gypsum,


Hence, it appears that with medium- and high-CaA cements, an

increase in gypsum content reduces the ultimate amount of colloidalhydration product of C3A. If this product is a hydrous calcium aluminategel, it might have a weakening effect on the paste through an intrinsicweakness of such a gel. Another possibility is that the C8A that does notreact with gypsum becomes a constituent of a complex aluminosilicategel. Presumably, it has a weakening effect on the gel.

The explanation given above is comfiatible with the results obtainedfrom one of the low-C~A cements but is possibly not in accord with theresults from the other. As shown in Fig. 6-3, increasing the gypsum

content of the 1ow-CSA cements prepared from clinker 15623 had littleeffect on either strength or gel-space ratio. This result is in accord withthe above explanation, But with the cements pfepared from cliriker

15670, very low in CSA, increasing the gypsum content greatly increasedthe gel content and slightly reduced the strength. This result is def-

initely not explained above. It might be that in this high-silica, low-

&Os type of cement, the gypsum produces a colloidal hydrate, or causes

some normally non-colloidal product to appear in the colloidal state.In either event th’e new colloidal product would have to be such as tohave little effect on strength; that is, it would have no strength of its

own and have no effect on the strength of the gel fol med from othercompounds. This matter will probably not be satisfactorily explained

until new information on the constitution of hydration products isavailable.

Whatever the correct explanation may be, it is apparent that the

strength of hardened paste depends on its chemical constitution as well asits gel-space ratio. This is substantially the same conclusion reached

earlier by Bogue and Lerch. (A1

Effect of steam curing

The experiment with a steam-cured paste made of cement and pul-verized silica was described in Part 2 and Part 3. No strength testiwere made on this material, but the effects of the steam treatment can beestimated from the data published by Menzel.@) These data show thatsteam-cured mixtures of cement and pulverized silica were as strongas or stronger than companion specimens cured normally, ‘The adsorp-

tion data mentioned above indicate that the gel content of steam-curedmaterial is not over 5 percent of that of the specimen normally cured for28 days. This seems to be a clear demonstration that the gel-space

ratio is not the controlling factor when curing temperature and pressure

are variable. At least, it proves that the relation of j. to VJWO found forspecimens cured at one temperature and pressure will not hold at anotherwidely different temperature and pressure.


Menzel’s data indicate that among specimens cured at differenttemperatures ranging from 70 to 350 F, the properties of the specimensshow no differences that are disproportionate to the difference in curingtemperature, This is particularly well illustrated by the data on shrink-age. The plot of total shrinkage at 35 percent relative humidity vs.temperature of curing, results in a smooth curve having a negative slopethat diminishes slowly and rather steadily with increase in temperature,(See Menzel’s Fig. 8,) Likewise, the initial rate of water-loss increasesprogressively as the curing temperature increases. From this we con-clude that the j,-vs,-VJw* relationship must change progressively as

the temperature of curing is increased above normal. Presumably, itwould change also if the temperature were lowered.

DISCUSSION AND SUMMARY

Werner and Giertz-Hedstrom@J found that strength could be expressedas a function of the volume of solid phase per unit volume oj hardenedpaste, The solid phase was defined as the volume of the original cementplus the water that is not evaporable in the presence of concentratedHz80& The plotted data of Werner and Giertz-Hedstrdm (see theirFig. 9) showed that ,the increase in strength was approximately pro-portional to the increase in the volume of the solid phase over the initialvolume in the fresh paste. Thus, the relationship found was virtuallythe same as that shown in Fig. 6-2 of this paper.

Lea and Jones(7) found a fairly good relationship between fixed waterper unit of original cement and strength. The fixed water was determinedon neat pastes, w/c = 0.25, and the strengths on 1:2:4 concrete cubes.Since w,/c of the concrete was a constant, a measure of the extent ofhydration would also be virtually equivalent to our w~/w~. However,since the extent of hydratioh was estimated from companion specimensof much lower we/c, the shape of the curve obtained was no doubt in-fluenced by the difference between the rate of hydration of the neatcement and that of the same cement in concrete.

Giertz-Hedstrom@J concluded from these experiments and those ofseveral other investigators that “it is thus possible as a first approxi-mation to regard strength as a function of the degree of hydration andindependent of the kind of cement. ” However, he goes on to say,i(.,. . this can obviously not be the whole truth, as emerges for in-stance from the spreading of test values. ” He points out also that testsby Bogue and Lerch on pastes made of pure Cd and Cd3 “indicate thatthe silicate gel, which is the sole cause of the hardening of dicalciumsilicate, is also chiefly responsible for the hardening of tricalcium silicate,but is to a certain extent helped hereby calcium hydroxide.” However,the data of Bogue and Lerch are of doubtful significance with respect

PHYSICAL PROPERTIESOF I+ARDENED PORTLAND CEMENT PASTE 855

to this particulm question. The original water-cement ratios of thepastes were not equal and therefore a measure of the extent of hydra-tion alone was not an adequate description of the concentration of thehydration products in the space available to them.

Freyssinet@J introduced two factors that he regarded as measuresof important physical properties of hardened paste. These are:

(1) The “concentration of the cement,” defined as:

volume of hydrated cement

volume of hydrated cement + volume of non-combined water’

(2) The total area of the interstitial surfaces per unit volume ofpaste.

It will be seen that (1) represents the concept on which Giertz-Hedstrombased his analysis and that (2) is similar to the gel-space ratio as usedby the authors.

Any attempt to express the strength of concrete or mortar as a func-tion of only one independent variable is certain to meet with but limitedsuccess, at best, for the lesson that more than one independent variableis involved. We have seen that in some combinations of paste and sand,the sand lowers the strength below that of the strength of pure paste ofthe same composition. Another factor influencing the strength ofmortars and concretes is the existence of minute fissures under the aggre-gate particles, especially the larger particles. These fissures are theresult of unequal settlement of paste and aggregate during the plasticstate. (l” 11112)They occur to clifferent degrees with different materialsand proportions.

Another factor influencing strength is the air content, the higher theair content the lower the strength, other factors being equal. Weymouth[13Jfound that among plastic mixes the air content of fresh concrete dependson the water content and sand-cement ratio. He found also that the aircontent is approximately constant in different mixes of the same materialsif the slump is constant. Therefore, variations in consistency of thefresh concrete will result in variations in strength of the hardened con-crete (when other factors are equal) because of the corresponding varia-tions in air content. The effect of air introduced by air-entrainingagents is now well known. @4)

Also, although pertinent data are lacking, we may surmise that thestrengths of adhesion between the hardened paste and the aggregatediffer among concretes made with aggregates of different mineral com-position. This will account for differences in strength, especially tensilestrength.


All these independent factors influencing strength are secondaryto the strength of the paste. Nevertheless, thsy cannot be ignored eitherin theoretical studies or construction practice. In the tests describedin the foregoing pages most of these factors were absent, or were kept asnear constant as possible. Consequently, the results depended mainlyon the properties of the hardened paste. However, the problem ofevaluating the factors influencing the strength of the paste is not muchless complicated than that of the concrete as a whole. The degree ofsuccess achieved in this direction is indicated by the following summaryof the results described in the foregoing pages.

(1) The strength of 2-in. mortar cubes made with cements of nor-mal gypsum content and low CW4 content (less than about 7 or 8percent) cured continuously wet at about 73 F conformed (within* 10 percent) to the following relationship, regardless of clifferencesin age 01 original water-cement ratio:

Compressive strength of 2-in. cubes, psi = 120,000 ~~ – 3600.Wo

(2) Under the same curing conditions, mortar cubes made withcement of medium or high CSA contents, containing the normalamount of gypsum, produced strengths that are too low to conformwith the above equation.

(3) Some cements of medium or high CSA content could be broughtinto conformity with the above equation by increasing the gypsumcontent, the required increase differing among different cements.Increasing the gypsum content of such cements reduced the gelcontent of the hardened paste.

(4) The tests indicated that with cements low in CSA both thegel-space ratio and the strength may be unaffected by an increasein gypsum content, or the strength may remain unaffected whilethe gel-space ratio is increased. In the last-mentioned case, theresults were not in conformity with the equation.

(5) The relationship between strength and V~/w, given in theabove equation did not apply to specimens cured at temperaturesother than about 73 F.

(6) In general, strength could be expressed as a function of thevolume of the hydration products and the space originally availablefor them, only when factors such as cement composition and curingconditions were not available.

When cements of ordinary CSA content are compared, the findingsgiven above show that the strength at a given Vm/w~ is highest for the10W-C3A cements. It should be noted that this observation does not


pertain to the rate of hydration or the rate of strength development,

Cements high in CSA usually hydrate more rapidly and develop higherearly strengths than those low in (7SA, The conclusion mentioned means

that when two pastes of the same original water-cement ratio reach

the same degree of hydration, as indicated by their gel-space ratios, thecement having the lower C3A content will probably have the higher

strength.

REFERENCES

(1) K. Terzaghi, Proc. A.S.T.M., v, 45, p. 777.(2) Wm. Lerch,A.S.T.M, Preprint A-4, 1946. SeeA.S.T.M. Bulletin, Jan. 1946.(3) A. G. Whittaker and V. E. Wessels, Rock Produds, v. 48, p. 95 (Aug. 1945).(4) R. H, Bogue and Wm. Lerch, Ind. Ew. Chem. v. 26, p. 837 (1934) or Paper No.

27, Portland Cement Association Fellowship (Aug. 1934).(5) Carl A. Menzel, Proceedings, ACIV.31,P. 125(1934).(6) D. Werner and S. Giertz-Hedstrom, Zemd, V. 20, pp. %4, 1000 (1931).

(7) l’. M, Lea and F. E. Jones, ~. Sot. Chern. Ind. v. 54, p. 63T (1935).

(8) S. Giertz-Hedstrom, ‘[The Physical Structure of Hydrated cement s,” Sym-

posium on the Chemistry of Cements, Stockholm, 1938.

(9) EL Freyesinet, ~tience et Irdu.sttie (Jan. 1933).

(10) H. J. Gilkey, Eng. News-Rewrd, v. 98, p. 242 (1927).(11) T. C. Powers, Proceedings, ACI v. 25, p, 388 (1929); Bulletin 2, P.C.A. F@-

search Laboratory (1939).(12) I L. Collier, Proc, A.S.T.M., v. 30, Part II, p. 731 (1930).(13) C. A. G. Weymouth, Proc. A.S.T.M., v. 38, Part II, p. 354 (1938).(14) C. E. Wuerpel, ‘Proceedings ACI v. 42, p. 305 (1946); (See particularly bibliog-

raphy in this paper).


TABLE 6-l—STRENGTHS AND GEL-SPACE RATIOS FOR SERIES 254-11

Ref. StrengthMix we/c Age, 2-in. cubes, w./c vm/c

(&4)wn/wo v./wo

days psi— —. —

Cement 15758; clinker 15498; V~/wn = 0.248— — —

11-1 A .334 28 11760 .171 .043 ,512 .12990

11-2 B11660 .191 .047 .572 .141

.460 28 8320 .196 ,050 .426 .10990 8810 .223 .054 .485 .117

— — . . —— — —Cement 15756; clinker 15623; V~/wn = 0.27i

— — . — — . .11-3 A .318 28 9750 .123 .034 .387 .107

1;;;; .149 .043 .468 .13511-4 B .446 %/ .132 .035 .296 .078

90 9010 .168 ,045 .377 .101— — — — . —

Cement 15763; clinker 15670; VJw. = 0.295. — —. . —

11-5 A .324 28 7170 .092 .028 .284 ,08690 12420 .134 .041 .414 .126

11-6 B .437 28 4610 .101 .031 .231 .07190 8990 .149 ,045 .341 .103

— — . — —Cement 15761; clinker 15699; Vn/wm = 0.262

— . — . —1 — —

11-7 A .334 28 8660 ,162 .041 .485 .12390

11-8 B9200 .180 .048 .539 .144

.468 28 6850 .185 .049 .395 .10590 7620 .212 .055 .453 .118

— — . . —— . .Cement 15754; clinker 15367; v~/wn = 0.258

— — — — .11-9 A .328 2s 11820 .170 .044 .518 .134

90 13460 .195 .047 .594 .14311-10 B .449 28 7970 .197 ,050 .439 .lli

90 9110 .230 .057 .512 .127. — __ . — —.—


TABLE 642—STRENGTHS AND GEL-SPACE RATIOS FOR CEMENT 14930J—

SERIES 954.9

vm/wn = 0,304

Strengthwe/q Age, 2-in, cubes, wn/c vm/c wn/wo vm/wo

days pal— — —

8-1I

.309

8-1 .311

9-2

8-2

7

;:5690

i%’

Mix A,—

49507960

1028012970142101541017260

,080.099.107.129,150.162.181

%i-.027.034.043.046,050.053

.259

.320

.346

.417

.485

.524,.582

Mix B

.424 7 25804320

;: 693056 9860

111801:: 12310

.443 362 11910

.080

.103

.116,135.174.185,201

.021

.028

.037

.049,053.059.062

9-3

6-3

,573

.595

,068.088,110,139.149.162.170

Mix Cl— l—

I 1230 I .082I .0221! 2140 .090 .02828 I 3940 I .121 I .04356 6200 ,164 .04990 7580 ,185 .055

8280 .201 ,056% 7940 .210 .066

l—l 1 I——

. —

.189,243.274,318.410,436,452

.143

.157

.211

.286

.322

.350

.353

.050,066,087,116.125.139.140

,038,049,075,086,096.098,111


TABLE 6-3-STRENGTHS AND GEL-SPACE RATIOS FOR CEMENT 15007J–

SERIES 254-9

Vn/wn = 0.272

Ref. Strengthw./c Age, 2-in. cubes, wn/c v./c

(&ii4)wn/w. vm/wo

days psi——

Mix A,— , ——

94 .316 7 ‘ ,036 .399 ‘.041 ,443,042 ,488,047 .532,048 ,648,048 ,588

8-28 .344 .064 .576l—l , l— I

Mix B— —

9-5 ,433 7 6380 .133 .036 ,0838080 ,150 .042 ,097

& 9400 .171 .045 .10456 11OKI .185 .049 .11390 11600 ,192 ,056 .129

12150 .202 .055 .1278-29 .464 E 11120 ,217 .058 .125

—— . —— l—

9-6

8-30

,570

.695

9660118301281015310156001678014970

.126

.140

.154

.168

.173

.184

.198

,307,346.395.427.443

7

&5600

- —Mix C

4060 –

62807070784085407780

,156.163.184,204,205,213.232

.114

.130

.133

.149,152,152,186

I

:467.468

.037 ,274

.042 .286

.050 .323,053 ,358.056 ,360,060 ,374.060 .390

.065

.074

.088

.093

.098

.105

.101———


TABLE 6.4-STRENGTHS AND GEL-SPACE RATIOS FOR CEMENT 1501 lJ–

SERIES !254-9

Vm/ws = 0.272

Ref. Strengthwe/c Age, 2-in. cubes, w./c vm/c wn/w. vm/w.

(s%54) days psi— —- —_ .

9-7 .316

8-40 .319

9-8 I ,432

8-41 .442

9-9 I .582.— —

8-42 .595

7

7

;:5690

180368

Mix A-1 l—

.114

.133,143.156,164,170,184

-1 l—

Mix B

5550714089009500

107201102011500

Mix C

.123

.153

.165

.178,191.199,210

.131

.157

.176

.195,205.214.222

,033,036,045,046,043.045.051

.361

.421

.453

.494

.519

.538,576

.104,114,142,146,136,142.160

——- ——

.037,038,045.047,051,056.058

-l—

.285

.354,382.412.442,461.475

.—

.034 .225

.039 .270

.047 .302

.054 .335,056 .352.057 .368,062 .373

——.086,088.104,109,118,130.131

,058.067.081,093,096.098.104

86S? JOURNAL OF THE AMERICAN CONCRETE INSTITUTE March 1947

TABLE 6-5-STRENGTHS AND GEL-SPACE RATIOS FOR CEMENT 1501 3J—SERIES !254.9

V~/wm = 0,244

Ref. Strengthwe/c Age, 2-in. cubes, wn/c vm/c

(SM4)Wnjw. vm/wo

days psi.— — .

Mix A

9-1o

8-46

,324

.332

9-11I

.443

8-47 .453

.— —9-12 .611

I

8-48 .599—.— —

6620796087809680

106101102010820

Mix B

4010494061206740760080609040

Mix C

2250275034804180428045205210

— .

— .

,149.164.171,180.191,188.218

.156

.183

.177,208.215,236,241

.036 .460

.039 ,506,043 ,528.046 .555,047 .590,051 .580.052 I .656

,037.042.048.053.057.058.058

— —.158 .033.183 .040,203 .046.221 ,055.236 .058.245 .059.253 ,057

.352

.413

.400

.470,485.533,532

,259.299.332.362.386.401.422

.111

.121,133.142.145.158.157

——

.084,095,108,120,129.131.128

,054.065.075.090.095.096.095


TABLE 6-6—STRENGTHS AND GEL-SPACE RATIOS FOR CEMENT 15365—SERIES 954-9

v./wn = 0,254

Ref. Strengthw./c Age, 2-in. cubes, wn/c Vmlc W!JWO vm/w.

(SN;54) days psl—. — —

Neat cement——— .—— — . —. — .

9-15A ,244 7 14440 .115 .028 .471 .11514 14640 .126 .030 .515 .12328 17600 .136 .032 .556 .13156 17960 .140 .034 .573 ,139

20000 ,145 .034 .594 ,1391:: 20500 .155 .036 .635 .148

. —— ——Mix A

—— ..— — -—— ——-— — —— — _.9-13 .319 7 8380 .133 .034 .417 .107

10380 .152 .037 .476 .116:: 11550 .149 .044 .467 .13856 11800 .179 ,047 .561 .147

12170 .179 .048 .561 .1501:: 12760 .182 .046 .571 .144

——— . — —— —. — .Mix B

[

—— —— — —9-14 .439 7 5340 .139 .034 ,316 .078

7170 .171 .043 .390 .098;: 8480 ,184 .054 .419 .12356 9400 .210 .055 .478 .12590 9870 ,215 ,056 .490 .128

180 9940 .222 ,060 .505 .137—. —.. — ———— —— .—. ——. —z

_—_— —9-15 .587

II

——.—————l——

Mix C

7 I 3220 I .153————

4670 .186$: 5680 .210

6280 .221;: 6320 .230

180 I 6720 \ .255———

— _—-.—-037 .260

.045 .317,055 .358,057 .376.062 .392.060 \ .435

——

.

——.063.077.094.097,106,102


TABLE 6-7—STRENGTHS AND GEL-SPACE RATIOS WITH THE AMOUNT OFGYPSUM IN THE CEMENT AS A VARIABLE—SERIES 954-13

Cement-silica ~astes

so, 28-dayRef. cont. of strength wn/c v,n/c Wnl% vm/wo

we/c cement, 2-in. cubes,(s!&54) percent psi

—— —

13–113-11313-213-2B13-313-3B13-413-4B

—.——

13--513-613-713-8

————.493 1.5.486 1.5.493 1.9

..— —13-1313-1413-1513-16


6970 .2156640 .2127630 .2116870 .2168090 .2087610 .2158240 .1948250 ,204

—— ——.059 .435.058 .436.056 ,428.058 .442.054 ,425.055 .441.048 .395.050 .414

—————.———Cements made from clinker 15623

— .——. — . —. — .————.470 7530 ,152 ,038.474 ;:: 7440 .151 .038.473 2.5 7440 .152 .038,480 3.5 7000 .144 .038

——. —— ———Cements made from clinker 15699

13--9 .49813-10 .49913-11 .49913-12 .498

.488

.487

.493,491

———

13-1713-1813-1913-20

,323 .081.319 .080.321 .080.300 .079. ———

1.5 8120 ,208 .0532,0 8120 .199 .0502,5 8550 .200 .0493.5 8710 .190 ,(347

.——.— _—— ———.. —Cements made from clinker 15670

I——-——, —(—--

.120

.119,113,119.110.113.098.102

1.5 7510 .199 .053 .4002,0 8160 .194 .052 .389

7860 .192 .049 .385$: 7530 .184 .046 .369

—. I l— l—— l—


.476 4240 .111 ,031,479 M 4440 .118 .034.483 2,5 4070 .184 ,043.486 3.5 3800 .209 .050

—-— —— __ ——— —...————

.426

.409,405.387

,106.104.098.092

——

.109lo!!

,099,096

-————... - —---___.233 .065,246 .071.380 ()&J.431 .103


Part 7. Permeability and Absorptivity”

CONTENTS

Permeability of hardened portland cement pask. . . . . . . . . . . . . . ...865Darcy’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...865Permeability equation for hardened paste.. . . . . . . . . . . . . . . . . ...866Comparison with data of Ruettgers, Vidal, and Wing.. , . . . . . ...868Theoretical minimum permeability . . . . . . . . . . . . . . . . . . . . . . . ...872Relationship between permeability of paste andpermeability ofconcmte. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...873

Theabsorptivity ofhardened paste.... . . . . . . . . . . . . . . . . . . . . . . ...873Relationship between absorptivity and the capillary porosity. . ..874Dependence of K. on initial water content of the specimen. . . ...877Relationship between absorptivity and permeability. . . . . . . . . ...877

Sumryof Part 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...879Permeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...879Absorptivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..8$0

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...880

PERMEABILITY OF HARDENED PORTLAND CEMENT PASTE

The following discussion deals with the relationship between thephysical properties of hardened paste and the rate at which water mayflow through a saturated specimen of paste under a given pressuregradient. In view of the results published by Ruettgers, Vidal, andWing,(’) we may assume that such flow takes place in accord withDarcy’s law.

Darcy’slawDarcy’s law for low-velocity flow, first found empirically from experi-

ments with flow through beds of sand, may be written

dq 1 = K+ . . . . . . . . . . . . . . . . . . . . . . . . . . . .Zz

,..... (1)

where

dq =

z

A=Ah =

L .

KI =

rate of volume efflux, cc per see,

area of the porous medium, sq cm,

drop in hydraulic head across the thickness of the medium, cm,thickness of the medium, cm, and

a constant depending on the properties of the porous mediumand the kinematic viscosity of the fluid, cm per sec.

KI of eq. (1) depends on both the properties of the medium and ofthe fluid. Thus, KI represents the permeability of a porous medium to aspecified fluid at a specified temperature. The following, more generalexpression is preferred:(2)

*The characteristic of the cements mentioned in thb section may be found in tbe Appendix tO part 2.


dq 1 _ K, AP’——— . . . . . . . . . . . . ,. 04.+ ,., ,., ,,, ... . . . . . .%2 v L

(2)

in which

. viscosity of fluid, poises, dyne-see per sq cm,

AP~ = pressure drop across the medium, dynes per sq cm, and

KS = coefficient of permeability, sq cm.

In terms of hydraulic gradient rather than pressure differential

dq 1 = K,g d, Ah

Z2. . (3)

qL ‘ “””’”’’””””””””””””””””””””’” ““””

where df = density of the iiuid, g per cc, and

9 = acceleration due to gravity, cm per sec per sec.

As Muskatfz) has pointed out, the coefficient of permeability, K%,is a constant determined by the characteristics of the medium in question

and is entirely independent of the nature of the fluid.

Permeability equa~ian for hardened paste

In the following discussion, the theoretical coefficient of permeabilityof hardened paste will be evaluated analytically from the original cementcontent, the non-evaporable water content, amd V~ (see Part 3). This isaccomplished by means of the following relationship found theoreticallyby Kozeny(’j and verified experimentally on beds of granules by Car-man :(44

K,=ke m’. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(4)

where k = a dimensionless constant,

E = ratio of pore volume to total volume, and

m = hydraulic radius.

For the derivation of this equation reference should be made to the

original articles by Kozeny and especially those by Carman. The

equation rests on the assumption that the particles composing the bedhave a completely random packing, and on the use of hydraulic radius inPoiseuille’s equatiom for capillary flow. The hydraulic radius is

void-volume Em= =_ . . (5)

surface area of void-boundaries ,s ”””””””””’”’

Hence

K,=?c ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(6)32

Various experiments of Carman and those of Fowler and Hertelf5) showthat k = 0.2 can be assumed for a wide variety of media,

Applied to beds of relatively large particles, eq,. (6), with k = 0.2,was found by Carman to be a satisfactory basis for predicting permea-


bility from the total porosity of the bed and the specific surface of theparticles, Applied to certain fine-textured media, the equation wasfound to give permeability coefficients that were much too high if thetotal porosity was used for e. Carman found such to be the case forbeds of clay. (*J By assuming that a certain amount of the interparticlespace was not effective in transmitting water, Carman was able to obtainagreement between the theoretical and experimental results. Powers@)and Steinour(Tj adapted the Kozeny equation (eq. (4)) to the rate ofbleeding of portland cement paste and found that a similar modificationwas necessary. These different experiments show that for certain fine-textured media,

.fe=e — a(l —c), . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...!.(7)

where e = total porosity,

E* = effective porosity, anda = amount of immobile fluid per unit volume of solids in the

medium.

Steinourf7) found that for fluid flow through concentrated suspensionsof particles, a depended on

(1) the amount of fluid chemically or physically combined with theparticle surfaces,

(2) the angularity of the particles, and

(3) the presence or absence of flocculation of the particles.

In a solid porous medium such as hardened paste, item (1) would be theamount of fluid attached to the pore walls, item (2), the irregularityof the wall surfaces, and item (3), the variations in cross-sectional areaalong the conduits through the medium.

For cement pastes, the total porosity, q may be taken as being equalto the volume of the total evaporabIe water. According to eq. (7), theeffective porosity, Q, should be smaller than the total by some quantityproportional to (1 – c), the volume of the solid phase. However, theeffect of the three items mentioned above can be taken care of ade-quately enough for the present purpose by assuming that the amount ofwater in a saturated paste that remains immobile is proportional to thetotal surface area, regardless of the cause of its immobility. Thus, sincethe total surface area is proportional to V~,

e. = we –k~vm . . . . . . . . . . . . . . . . . . . . . . . . . . . .!........(8)

where we = total evaporable water in cc per cc of hardened paste,

Let wJV. = N. Then

e~=VJN- Al) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(9)

The total surface area in the paste is


8=(35 .7xlo’)vm ... . . . . . .. c!.!..... , . . . . . . . . . . ..(10)(See Part 3,)

Using c. for e and substituting from eq. (9) and (10) into eq, (6) gives

k

“= (35.7 xlo’)’vm(N –k1)3””’ ””’o” ”’’”””’”’ “’(11)*

(In the above equations V~ is in g per cc of paste.) Since,

k = 0.2 (Carman),

eq, (11) may be written

K2=15.7x lo-’7vm(N –kl)3 . . . . . . . . . . . . . . . . . . . ..(12)

Eq, (12) gives the coefficient of permeability in terms of three factorsthat are constant for a given sample. V~ and N are measurable. How.ever, kl is unknown and cannot be evaluated without further permea-bility tests,

Comparison with data of Ruettgers, Vidal, and Wing

No experimental data are available for checking eq, (12) quantita-tively. However, Ruettgers, Vidal, and Wingf8j published the results ofpermeability tests on neat cement made with a special cement resembling

the present A. S,T,M. Type II, except that it was considerably coarser

than present-day cements (15 percent retained on No, 200). From theirplotted results, the coefficients of permeability for neat cement cured 60

days were estimated to be as shown in the last column of Table 7-1,

Before comparing the results of the tests and the computations the

basis of the computations must be explained. To compute the permea-

bility of the specimens tested by Ruettgers, Vidal, and Wing, Vmand thetotal eva~orable water for the saturated state must be known and avalue for kl must be assumed, However, only the nominal water-cementratio, the composition of the cement, and the heat of hydration of thecement were available. The cement content was estimated from thenominal water-cement ratio. wn/c was computed from the relationship

heat of hydration = 525 wn/c (see Part 4)

and found to be about 0,15, From the composition of the’ cement andeq, (4) of Part 3, Vm was estimated at 0.256 w..

Ruettgers, Vidal, and Wing gave their results in terms of K1 of eq.(l), in ft. per see, whereas eq. (12) is in terms of K’ of eq. (3). A com-parison of eq. (1) and (3) shows that

K, _ KZdH— —_.v

*It mcy bc noted that, in deriving eq. (11) from eq. (6 , th~tetal surface in contact with the flowing waterLb precumed to be equal to the etyface area of the no d phace cc meceured b water-vapor adsorption.

i’ThIC ic exrmtly correct If the only Immobde water ICthe.firet adeorbed layer an If the eurfaee area of thetit adeorkf layer ic eqrml to the surface area of tbe eohd ph~e. At recent there ic no way to oheok the

1validity of the final equation, except crudely by the r.mconcblenenc of t e remdtc obteined.

TABL

E7-

1—C

OM

PU

TATI

ON

OF

CO

EFFI

CIE

NT

OF

PER

MEA

BILI

TYFR

OM

EQ.(

13)

K,

=0.

5X

I&U

V-(

N–

k,)’

0.25

6X

w/c

I&3-

wn/

c(n

om)

c=

vm/c

pin

to

0.5

1.2

20.1

50.0

38

0.6

1.0

90.1

50.0

38

0.7

0.9

80.1

50.0

38

0.8

0.9

00.1

50.0

38

1.0

0.q

60.1

50.0

38

1.2

0.6

60.1

50.0

38

*Est

imat

edby

extr

apol

ati

on.

tBM

imate

dby

inte

rpol

atio

n.

v. —.C

c 0.04

7

0.04

3

0.03

7

0.03

4

0.02

9

0.02

5

w.

—w

.c

=w

e/c

0.35

0.45

0.55

0.65

0.85

1.05

we/

cK

,co

mpu

ted

(ft

per

see)

XlW

5$

rk,

=l

k,=

2k~

=3

9.2

139

6

11.8

2720

15

14.5

4536

2%

17.1

7059

48

22.3

——

—

27.6

——

—

- kr=4

3 10 22 38 — —

15”

100

550t

1830

3730

8530


For water, d, = 1, q = 0.01, and g = 980 may be assumed, Hence,

Kl, in cm per sec = 98000 K*,

orKl, b ft per sec = 3220 Ke,

Therefore, from eq, (12)

KI = 50 X10-i4V~(N -kl)8ftper sec. . . . . . . . . . .. (13)

To be strictly consistent, we would have converted the weights of thetotal evaporable water to volumes. However, such a refinement seemedunnecessary in view of other uncertainties. Therefore, the estimatedweights in grams per unit volume of paste were used.

To itl, the immobile-water factor, no value could be assigned fromknown or estimated values of physical composition. Four values weretried, as shown in Table 7-1. The assumption k] = 1.0 amounts toassuming that only the first adsorbed layer is immobile. The assumptionthat ?cIis greater than 1 is, of course, that the immobile liquid is morethan the amount in the first adsorbed layer.

In Table 7-1 the first indication to be noted is that the computedvalues are less than the experimental values in all cases. Only for thepaste of 10west water-cement ratio do the two values approach equalityand then on]y when kl is given its minimum value. Even here, theapparent agreement may be fortuitous because the experimental valuegiven was obtained by an uncertain extrapolation. The second pointis that the observed permeabilities increase with increase in w/c muchfaster than the computed values. Had the computation been basedon net rather than nominal w/c, the divergence at high w/c wouldhave been even greater. Possibly the lack of agreement and the diver-gence just noted are the result of some fault in the theory on which thecomputations are based, but it cannot be accepted as proof of such faults.There is good reason to believe, as shown in the following paragraph,that the discrepancies between observed and computed values can beaccounted for on the basis of decreases in the degree of homogeneity oftest specimens accompanying increases in w/c.

Both Powers@j and Steinourf7cj found from studies of fresh pastemade of water and normal’ portland cement that for w/c’s up to about0.5 by weight, the flocculated cement particles formed a continuousstructure having a permeability that could be computed from a modifica-tion of the basic Kozeny.equation (eq. (4)). At such water ratios, themass of paste constitutes one continuous floe, and the permeability ofthe mass as a whole depends on the floe texture. At very high dilutionthe particles form floes that are more or less independent of each other.The permeability of such a mass is not determined by the floe texture,but largely by the size of the individual floes and their concentration.


In an intermediate range of w/c’s, the fresh paste exhibits some of the

qualities of both extremes. The permeability is determined in part byfioc texture and in part by channels that develop in the flocculated mass.This condition is denoted by the appearance of localized channels dur-ing the bleeding period. In either the intermediate or the high range ofw/c’s, the effective size and number of the conduits through the mass ofparticles cannot be computed from the composition of the mass as awhole, because such masses do not have the homogeneity assumed inthe computation.

The homogeneity of a fresh paste, or the lack of it, probably persistsin some degree after the paste hardens. Hence, it is probable that forhardened pastes having w/c’s greater than 0.6, or thereabouts, * thepermeability of a test disk is determined not only by the permeabilityof the hardened paste, but also by vertical channels that represent dis-continuit,ies in the paste—the discontinuities that developed during thebleeding period. In the neat cement disks in question, such channelswould extend from the top surface well into the interior and thus greatlyincrease the permeability of the disk as a whole. The higher the orig”nalw/c above the minimum at which channels develop, the greater the num-ber and size of such by-passes around the relatively dense, homogeneousmaterial composing the bulk of the hardened paste.

It is probable that even if channeling did not occur, eq. (13) wouldnot correctly represent the permeability of hardened pastes of all de-grees of porosity. This mar be inferred from Fig. 5-11 of Part 5. Fromthis figure we may recall the earlier conclusion that saturated, hardenedcement pastes may contain only the gel water, or they may containboth gel water and capillary watel, depending on the original water-cement ratio and the extent of hydration. Capillary water is absentwhen the total evaporable water is equal to 4V~. It is possible that thepermeability of a given paste depends on the p~rmeability of the gelitself and on the size and number of the capillaries outside the gel.The hydraulic radius of these capillaries would be

w. — 4V. = V.(N - 4)

s= s,

whereS, = superficial area of the gel, andi? = we/v?n .

Sc is not known. It is probably much smaller than the total surface areaof the solid phase as indicated by Vm. If so, the permeability of thecapillary space would be of a higher order than that of the gel itselfwhen w, is greater than 4 Vm.

*The limiting water ratio depends on the characteristics pf the cement, particularly its, specific surface,and on the character and amount of subsieve aggregate. Ammtrammg agents tend to rruse the limit.

879

The

JOURNAL OF THE AMERICAN CONCRETE INSTITU[E March 1947

discrepancies between computed and observed values of K1seen in Table 7-1 are in accord with the considerations expressed above.That is, it appears that the permeability of pastes of relatively highw/c is probably determined in major degree by the by-passes around thehydration products, or in other words, by residues of the originai water-filled space not filled by gel or other hydration products; but in pastesof low w/c, well cured, the permeability of the paste as a whole is fixedmainly by the permeability of the gel and the amount of gel per unitvolume of paste.

Theoreticalminimum permeability

For rich pastes the minimum permeability attain~ble can be estimatedfrom eq. (13) on the assumption that the equation is valid at least forpastes in which w, = 4V”. The composition of such pastes may beexpressed as follows:

Cvc+ Wnun+ ‘wgvg= 1 ,where

c = original cement, g per cc of paste,W*= non-evaporable water, g per cc of paste,WV= gel water, g per cc of paste, andv,, v., and V. = the respective specific volumes.

On the basis of data given in Part 5, letw. = 3.9vmW. = 4vm

Vn = 0,82, and

Va = 0,90.

Thenvm=o.147(1 –cv.) c. . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(14)

Hence, noting that N = 4, we obtain from eq. (13),

K, = 50 X 10-’4 X 0.147(1 – CU,)(4 – k,f. 7.4 X10-14 (l–cv,) (4–klj . . . . . . . . . . . . . . . . ..(15)

Eq. (15) show-s that K, can be zero when CV, = 1 or when itl = 4. The

condition that cu. = 1 means that the paste is a voidless mass of un-hydrated cement, (As shown in Part 5, CV,as high as 0.72 can be prod-

uced by molding the paste under high pressure. Normally, it is near0.50.) -Hence, the CVCterm cannot make K1 zero. Constant kl has aminimum value of 1. Its maximum value is not known but it is notlikely that it can be as great as 4 since this would mean that all thewater in such pastes is held immobile by the solid surface. It seems more

likely that only the first layer could be wholly immobile and hence that

hardened paste cannot be absolutely impermeable. If this is assumed,the minimum permeability would be of the order of 10-’2 to 10-18ft. persec.


These estimates indicate that well cured, neat paste of low w/c ispractically impermeable. (Ruettgers, Vidal, and Wing(’) give the per-meability of granite as ranging from 2 to 10 X 10-lz ft, per sec.)

Relationship between permeability of paste and permeability of concrete

This subject was discussed fully by Ruettgers, Vidal, and Wing andtherefore requires only brief mention here. Introduction of aggregateparticles into paste tends to reduce the permeability by reducing thenumber of channels per unit gross cross-section and by lengthening thepath of flow per unit linear distance in the general direction of flow.However, during the plastic period, the paste settles more than the aggre-gate and thus fissures under the aggregate particles develop. In satu-rated concrete these fissures are paths of low resistance to hydraulicflow and thus increase the permeability of the concrete. In general,with paste of a given composition and with graded aggregate the per-meability is greater the larger the maximum size of the aggregate. Ob-viously, the permeability of concrete as a whole is much higher than thetheoretical permeability as developed above for a homogeneous medium.

The above discussions indicate that for well cured concretes havingwater-cement ratios above about 0,5, the permeability is determinedlargely by the by-passes around the gel and the by-passes around thepaste in the concrete structure as a whole.

THE ABSORPTIVITY OF HARDENED PASTE

The term “absorptivity” pertains to the characteristic rate at whichdry or partially dry paste absorbs water without the aid of externalhydraulic pressure.

For pastes containing capillary space outside the gel, it is believedthat the water is taken in by two different processes. The water entersthe capillary system under the influence of capillary force, i.e., surfacetension. Probably most of the water entel ing the gel, if not all, isdrawn by adsorption forces. The resistance to the inward flow into thecapillary system should be indicated by the coefficient of pel meability ofthe saturated paste, The resistance to the flow into the gel, where theinitial flow presumably takes place along surfaces of unfilled channels,would probably not be determined by the permeability, but by a co-efficient of diffusivity.

These suppositions are supported by several considerations alreadydiscussed. Perhaps the most pertinent consideration is that illustratedby Fig. 4-12, Part 4. This shows that the evaporable water lost when asaturated specimen is exposed to a relative vapor pressure of 0.5 couldbe divided into two classes—one that was lost rapidly without apparentrelation to shrinkage, and one that was lost more gradually and wasdirectly related to shrinkage.


No attempt will be made here to derive a theoretical relationship forabsorptivity. However, an empirical relationship between absorptivityand capillary porosity will be shown.

Relationship between absorptivity and the capillary porosity

It can be shown (see later) that for either capillary penetration ordiffusion, the absorption of water during a short initial period, under

proper experimental conditions, follows the relationship

l=(Kat)~,. , ., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(16).ii

where q/A =

K. =

amount of water per unit area absorbed in elapsed timet, anda constant characteristic of the absorbent, in its initialstate of dryness, called the coefficient of absorptivity. Ithas the dimensions sq cm per sec.

Ko was evaluated for several mortar prisms, 2 X 2 X 9% in., that hadbeen water-cured and then dried in air of 30 percent relative humidityfor 6 or 7 months. They were broken into halves transversely and thencoated with paraffin so that only the broken end was exposed. Eachspecimen was then suspended under water at 73 F from one end of abeam-balance and its change in weight with time was recorded. Plot-ting q/A vs. the square root of time for these specimens produced straightlines for about the fi@ 60 minutes.

Two different kinds of cement were used, with the following two mixesfor each cement:

Parts by weight.—

g: Cement Stml?d Pulverizedr3i1ica

—29041 &-43 1 1.63 —

29042 &44 1 2.30 0.33

The pulverized silica was of about the same specific surface (sq cm percc) as the cement. The mortars were plastic when fresh and relativelyhomogeneous after hardening, since the paste had relatively low bleedingcapacity and the paste content was relatively high. (The above mixesare the same as mixes A and B described in Appendix to Part 2.) Thecompositions of the specimens were the same as those given in Table A-30, first four lines, Appendix to Part 2. The results of absorptivity tests,together with data derived from Tables A-30 and A-33 are given inTable 7-2.

We may surmise that the coefficient of absorptivity depends on theporosity and on the size of the pores of the specimen, As remarked


TABLE 7-Q-ABSORPTIVITY DATA

Kc (observed),w. c,

p:sq om per secx 10~

:Cp$ g per g~;r 0.86 x 0.86 X 0%6 ; — —cc of cc of (1 + 4k) (lX+#:) (lx+w4k) sp~c, sp#,

spec. spec, spec, n

—— . — — . . .Cement 15758 A,S.T.M. Type III, k = 0.248*. .— — . . . _

290-41 .252 ,755 ,129 1.71 .220290-42 ,250

.032.542

13.5t,106 1.71 ,181 .069 23,5 2%;

. — — . — . .Cement 15756 A,S,T,M. Type II, k = 0.271*

. — —— . . _,290-43 .255 .769 .095 1.79 ,17029044 ,252

,085.560

27.4 28.0.074 1.79 .132 .120 73.5 76.1

—— ——— —-— . . — .*SeePart 3, Fkz. 3-7A and B.tDoubtful result based on first 15 minutes only. Others are based on about first hour.

above, it is probable that the initial, comparatively rapid adsorptiontakes place almost exclusively in the capillary system. That is, althoughthe gel is not saturated, the gel pores are so small that very little watercan enter them, as compared with the amount that enters the capillarysystem during a limited time. On this basis, we may write

Ka=f(pc, ?’.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(17)

where p. = volume of capillary pores per cc of mortar—the capillaryporosity, and r, = effective radius of the capillaries.

The capillary-porosity can be estimated conveniently in terms of thewater content of the fresh mortar (after bleeding) and the increase in thevolume of the solid phase due to hydration. That is, the capillaryporosity is the difference between the increase in volume of the solidphase (due to hydration) and the original volume of pores:

where V~

and C

From Part

where 0.86

w.

PC= WO— VB— CVC, . . . . . . . . . . . . . . . . . . . . . . . . . . . .. (18)= bulk volume of the solid phase, including gel pores and

unhydrated cement, in cc per cc of specimen,

= cement content of specimen, grams per cc of specimen.

5, eq. (9),

VE = @ –0.86(l +4k)W~, . . . . . . . . . . . . . . . . . . . . . ..(19)

= ?)d= mean of the specific volumes of gel water and non-

evaporable water, and

= non-evaporable water, grams per CCof specimen.

Hence, from eq. (18) and (19),

p, = w. – 0.86(1. + 4k)w . . . . . . . . . . . . . . . . . . . . . . . . . . (20)

As shown previously, there is no satisfactory way of evaluating the

size of the capillaries. However, capillary radius is at a maximum


before hydration begins and becomes zero when all original capillaryspace ( = W.) becomes filled with hydration products. At intermediatestages the relationship may be such that capillary radii are about thesame among different pastes when the original capillary space in eachpaste is filled to the same degree. To the extent that this is true,

rc=$[Wo –O.86(l+4k)Wfi]. . . . . . . . . . . . . ..0 . . . . ..(21)

A comparison of eq. (17), (20), and (21) indicates that K. shouldbe some function of W. – 0.86(1 + 4k) W. only. The nature of thefunction is indicated by the plotted experimental data given in Fig, 7-1.

I00 , ,

90 - I

180

d

70 –

60 1

Ka so .

x 10740 I

30 - tach p~~et ;~;~ent~ -

20 / [ 0. Cement IS 758

x- ,,.? 15756

10 -/ ‘

o?.&s6&a#;;oint -

..-

Or I , J

0 .02 .04 .06 .08 .10 .12 .14 .16 .18 .?0

Fig, 7-l—Empirical relationshipcoefficient of absorptivity an Jporosity

%rloi 954 and NO

betweencapillary

Wo - 0.86 (l+4k) Wn

It should be noted that according to eq. (21), capillary radius becomeszero when 0.86(1 + 4k) W. = W., that is, When capillary porosity iszero. Hence, if the assumptions made in arriving at the basis of plottingused in Fig. 7-1 are valid, or approximately so, the curve should appearto go through the origin. Fig, 7-1 shows that a reasonable curve throughthe points could pass through or very near the origin. This only illus-trates, however, the relative smallness of the gel pores, for it is certainthat K. is not zero when capillary porosity is zero. The curve probablyshould intercept the Ka-axis slightly above zero, possibly about as indi-cated in Fig. 7-1.

The empirical curve probably does not indicate the relationship be-tween Ka and capillary porosity corvectly, for no account is taken of thefact that the capillary pores were not entirely empty at the start of theabsorption test, However, at p = 0.5 p,, reached by resorption, thecapillaries are probably not far from empty. The presence of capillarywater in the specimen at the start probably reduces K. below what itwould be if the capillaries were entirely empty, but it probably does notinfluence the indications as to the trend of the curve as capillary porosityapproaches zero, the matter of interest here.


On the whole, these absorptivity data support other indicationsthat the capillary pores are much larger than those in the gel, and that

relationships given in Part 5 distinguish between water held in capillaryspaces and that held in the pores of the gel with satisfactory accuracy.

It should be remembered that when W. = 0.86(1 + 4k)W~, that is,when capillary porosity is zero, the specimen must be such that, whensaturated, the total evaporable water = 4V~. (See Part 3.) Theseabsorptivity data thus constitute a significant independent check of theconclusion reached from other considerations, that the weight of thewater required to saturate the gel is equal to 4V~.

Dependence of K. on initial water content of the specimen

It must be remembered that the value of K= for a given specimen willdepend on the initial water content of the specimen, at least for watercontents high enough to partly fill the capillaries. If the specimens werefirst dried completely and then allowed to adsorb vapor before theabsorption test, K. would probably be about the same for all initial

water contents up to that corresponding to about p = 0.45 p,. Thisfollows from the evidence presented earlier indicating that the capillariesdo not begin to fill by capillary condensation below about p = 0.45 P8

and that the initial rapid absorption takes place almost exclusively inthe capillar~es, when capillaries are present. For specimens dried onlyby resorption, data now available do not indicate clearly how low thefinal vapor pressure must, be to empty the capillaries completely. Such

data as there are indicate that the required pressure might be as low asp = 0.1 pd, though theory indicates that it might be about p = 0.3 p,.(O)

Relationshipbetweenabsorptivityand permeability

In view of the evidence given above, we may conclude that the initialrapid absorption of water by paste containing capillaries outside the gelis predominantly capillary absorption. Consequently, the rate ofabsorption should be, according to Darcy ’s law,

’91 =(s’d, A~g,, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (22)d~~ q L

in which (Kz), is the coefficient of permeability for flow through the

capillary system alone, d@h is the hydraulic head in g per sq cmcausing the flow, and L is the depth of the saturated layer in which theflow is taking place.

For horizontal capillary penetration

g djAh = u()

~+~ , . . . . . . . . . . . . . . . . . . . . . . . . . ..(23)*rl rf

—*Eq. (23) is bryed on the,msumption that t,he angle of contact between the meniscus and the solid bound-

‘?is zero. Thm awumpt]on seems permwble m th10 case because of tbe etrong attraction between the

m Id and the liquid and because of the extreme sl,owness of the movement of the meniscus. It would not bepermissible, however, ,for specl?lens that ~rmtam atearat,es or other a‘water-repellent” substa!icw or forcoarsely porous matermls In which tbe cap!llary penetrritmn IS rapd.


whereu = surface tension of water, dynes per cm,

9 = acceleration due to gravity,rl and rz = principal radii of curvature of the menisci.

Carman f4djhas shown that()r: + ~ can be replaced by the recipro-

cal of the hydraulic radius. That is,

~+~’~ .......................................(24)rl r2 6C

where. volume of the capillaries per unit volume of the specimen,

and ;= surface area of capillary boundaries.For our data,

s s. s..=‘vm(iv -4)’”””””””””””””””””””

. . . (25)er, w. — 4vm

in whichs. = superficial surface area of the gel, and

we = total evaporable water.

We may note also that

L.ef= qV.(N –4)A’ ”””””””’”””’””’””””””””

. . . (26)

where A = exposed area of the specimen.Substitution from eq. (23), (24), (25), and (26) into eq. (22) gives

dq 1 _ (~2). ~ s. V.(N – 4)i4

Zz q Vm(ly – 4) q

[ 1‘@2b4a8c! . . . . . . . . . . . . . . . . . ..(27)=V 9

All the quantities within the brackets are constant for a given specimen.Hence, we may write

J“=k- lb’(K2)cA2 ~ so

which, when integrated, gives

2=[?gscli’iA

From eq. (16) and (28) it follows that

. . . . . . . . . . . . . (28)

2(K,). ~ s,Ka=— . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (29)

vIt thus appears that if the superficial surface area of the gel were known,the coefficient of permeability for flow through the capillary system


(which is virtually the total flow) could be computed from the coefficient

of absorptivity as determined from the initial rate of absorption. How-

ever, S. cannot be measured by any method now available. We maysurmise that in a fresh paste, where the hydration products exist mainly

as a thin coating on the cement grains, the superficial area of the hydra-

tion products, &, must be virtually the same as ‘that of the originalcement grains. While hydration proceeds, either an increase or a de-crease in So is conceivable. If the cement grains were sufficiently sep-

arated, and if hydration merely enlarged the grains, S. would increaseuntil the boundaries of the grains began to merge. After a certainextent of this merging, S. wo~uld begin to decrease and would eithereventually reach zero—if the paste were sufficiently dens~or somefinite minimum value. (See Fig. 5-11, Part 5.)

SUMMARY OF PART 7Permeability

(1) The permeability of well cured neat cement paste of low w/cis, theoretically,

KI = 50 x 10-14vm(N – k,)s

in which KI = coefficient of permeability to water in ft per sec.;V~ = amount of water required to form the first adsorbed

layer, g per cc of paste;

N = ratio of total evaporable water to Vm; andkl is a constant depending on the amount of immobile water per

unit of solid surface-kl is probably near 1.

(2) For pastes in which N is considerably greater than 4, the permea-

bility is much higher than the theoretical value computed from the

above equation. This is believed to indicate that the flow in such pastes

is predominantly in the capillary spaces outside the gel and, in testson neat-cement disks of high w/c, through vertical channels formed dur-

ing the period of bleeding.

(3) The theoretical permeability of pastes containing no capillaryspace outside the gel is

1

LKI = 0.7 X 10-12(1 - Cic) 045< ~vc < ~ o==,

whsre c = cement content, g per cc of paste and v, = specific volume ofthe cement. K1 cannot be zero in practice because CV.must be less than1. At CV. = 0.45, approximately the minimum cement content of pastescontaining no capillary space outside the gel, K1 = 1 X 10-12. Accord-ing to Ruettgers, Vidal, and Wing, this is of the same order as the per-

meability of granite.

(4) The permeability of concrete is generally much higher thanthe theoretical permeability owing to fissures under the hggregate that


permit the flow partially to by-pass the paste and owing to the capillariesin the paste that permit the flow in the paste to by-pass the gel,

Absorptivity

(1) The absorption of water by a dry specimen during the first 30 to60 minutes follows the relationship

9- = (Kat)* ,A

in which q/A = the amount absorbed per unit of exposed area and Ka =the coefficient of absorptivity at t = time.

(2) The empirical relationship between K. and capillary porosityindicates that Ka is near zero when capillary porosity is zero. Hencejthe empirical relationship indicates that the initial absorption takes placealmost exclusively in the capillaries outside the gel, when such capillariesare present.

(3) The theoretical relationship between absorptivity and permeability is

T

in w~ich (Kz), = the coefficient of permeability for flow through thecapillary system of the paste; u and q = surface tension and viscosityof water, respectively; g = gravitational constant; S, = superficialsurface area of the gel. This pertains to specimens in which the capil-laries are initially empty, or nearly so. S, has not been measured, Itprobably diminishes as (Kz)c diminishes. If so, K. is a relative measureof (Kz)..

REFERENCES

(1) A. Ruettgem, E, N, Vidal, and S. P. Wing, Proceedings ACI v. 31, p. 382 (1935).(2) M. Muskat, The Ffow of Homogeneous Fluiak throWh Porous Media (McGraw-

Hill, 1937), p, 71.(3) J. Kozeny, S. B. Akad. Wie.s. Wire, v. 136, Part IIa, p. 271 (1927).(4) P. C. Carman (a) Symposium on New Melhoak of Particle Size Distribution t%

the Subsime Range, A.S.T.M, Publication (1941), p. 24.(b) ~. Agr. i%i. V. 29, p. 262 (1939).(c) J. Sot. Chem. Ind., v. 57, p. 225 (1938).(d) Sail Scienti v, 52, p, 1 (1941).

(5) J. L. Fowler and IL L, Hertel, J. Appli@ Ph~s. v. 11, p. 496 (190).(6) T. C. Powers, “The Bleeding of Portland Cement Pas@, Mortar and Concrete,”

Bulletin 2 of the Research Laboratory, Portland Cement Association, 1939.(7) H. H. Steinour (a) P.C.A. Research Laboratory BuUetin 3, 1944; or Ind. Eng.

Chem. (b) v. 36, p. 618 (1944); (c) v, 36, p. 840 (1944); (d) v. 36, p. 901 (1944).(8) Discussion of paper by A. Ruettgere, E. N. Vidal, and S. P. Wing, ProceediWe

ACI V.32, P. 378 (1936).(9) L. H. Cohan, J. Am. G%em. Sot. v. 66, p. 98 (1944).


Part 8. The Freezing of Water in Hardened Portland Cement Paste*

CONTENTS

Theoretical freezing points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...934

Application of Washburn’s equation. ., ., ., . ...935

Apparatus andmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...937

Test samples ...,..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...937

Dilatometers . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . ...937

Freezing and thawing procedure,.. .,, ,, ..,,...,,,.,.,..,..937

Description of cryostat . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . ...939

General aspects ofexperimental results. . . . . . . . . . . . . . . . . . . . . . ...940

Dilatometer curves . . . . . . . . . . . . . . . . ... ... ,., ,.. .,. ,., . . . ..9w

Effect of hydration during the experiment. ., . . . . . . . . . . . . ...942

Effect ofdissolved material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...943

Detection of freezing by means of the change in dielectric con-stant. .,..,.....,......,,. . . . . . . . . . . . . . . . . . . . . . . . . ... .943

Method of estimating the amount of ice from the melting curve.. ..944

Effect oftoluene onthernelting curve. .,, . . . . . . . . . . . . . . . . . . . ...948

Quantities of ice formed in various samples..,. ., . . . . . . ..950

Influence ofsoluble alkalies.....,.. .,. .,, . . . . . . . . . . . . . . . . ..~~

Theoretical amount of freezable water at a given temperature. ., ..950

Locus oficein the paste . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..95o

Relation of freezing to drying . . . . . . , . . . . . . . . . . . . . . . . . . . . ...958

Relation of freezable water to total evaporable water. . . . . . .. ,958

Relationship between the amount of water unfreezable at a giventemperature and the 25 C vapor pressure isotherm . . . . . . . . . . .961

Theoretical relationship . . . . . . . . . . . . .,.............,...,,,.961

Comparison of theoretical and empirical relationships... . ..963

*The characteristi~ of the cements mentioned ia this section may be found in the Appendix to Part 2,

934 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE April 1947

Equations for estimating maximum freezable water from the non-

evaporable water content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...965

Saturated pastes containing no freezable water . . . . . . . . . . . . . . . . ...966

Final melting points for specimens not fully saturated. . . . . . . . i . ..966

Summary of Part 8,., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...967

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...969

This part of the paper contains data on the amount of ice that canexist in hardened portland cement paste under given conditions. Alsosome theoretical aspects of the data are considered.

THEORETICAL FREEZING POINTS

From the fact that the evaporable water in hardened paste exhibitsdifferent vapor pressures when the sample is at different degrees of satura-tion, we could anticipate the now known fact that not all the evaporablewater in a saturated paste can freeze or melt at a fixed temperature. Thiscan readily be deduced from Fig. 8-1, which is a diagram illustrating(on a distorted scale) the relationship between the vapor pressure andtemperature for water and ice. The upper curve represents the relation-ship for pure water under the pressure of its own vapor, p,. Similarly,the curve marked “ice” represents the relationship for ice under thepressure of its vapor, pi. The vapor pressures of the two phases areequal only at point A. This is the only point where the free energiesof the ice and pure water are equal and hence the only point where iceand pure water can coexist. If a salt is added to the water, the vaporpressure of the solution bears a nearly fixed ratio to the vapor pressureof pure water at all temperatures, as indicated by the line marked “so-lution.” (The position of this line depends on the salt concentration,)Pure ice can coexist with the solution only at point B, which is at atemperature below OC.

It is clear, therefore, that the evaporable water in a saturated hard-ened paste will not begrn to freeze at O C because of its content of dis-solved hydroxides. Moreover, when freezing begins, and pure iceseparates from the solution, the solution becomes more concentrated andthus the freezing point is lowered further. It follows that the evaporablewater will freeze progressively as the temperature is lowered.

At this point we recall the discussion in Part 3 showing that the

reduction in the vapor pressure of evaporable water is caused not onlyby the dissolved salts but also by capillary tension and adsorption. At


IFig. 8-1 —Phase equilibrium diagramfor water and ice (distorted)

P

4.58mm

o

T, “C

saturation the effect is due entirely to dissolved material, but as theevaporable water is removed the effect of capillary tension and adsorptionincreases, and it exceeds that of the dissolved material after only a little

of the evaporable water has been removed, A given reduction in, vaporpressure signifies the same reduction in freezing point, regardless of

the mechanism by which the reduction is effected. Hence, we may con-

clude that if the icc separates from capillary water or adsorbed water inthe same way that it does from a solution, the freezing point will be the

same as for a solution of the same vapor pressure.

Application of Washburn’s equation

The reduction in freezing point for such a system can be ascertainedfrom the following semi-empirical relationship given by WashburntlJ*

log,o ~i = 1’1489t + 1,33 X 10-5t2 – 9.084 X 10-8t3 , . (1)Ps 273.1 + ~

in which

pi = vapor pressure of ice at temperature t,

p. = vapor pressure of pure water at temperature i, andt ~= temperature, deg. C.

Let P = vapor pressure of evaporable water in cement paste,—.

*Seereferencesenrlof Part 8.


Then, where the ice and the evaporable water are in equilibrium, thatis, at the freezing point, p = pi, and

log,Op/p, =eqi (l). . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(2)

Thus, eq. (1) gives the relative vapor pressure of water (or solution) thatwill be in equilibrium with ice at any given temperature. In other words,it gives the freezing temperature corresponding to any given value ofp/p, for the system. A plot of this equation appears in Fig. 8-2.

1.00

0.90

/aso

P/~a70 /

0.60 /’

0.s0

O.w -90 -M -70 -60 -50 -40 -30 -20 -lo 0

Temperature~C

Fig, 8-9—Relationship between P/p, and freezing point

Eq. (1) gives substantial y the same result as the following equationgiven by Kubelkaf2j:

T.–T 2vfuf_ =— ,., ,,. . . . . . . ,., ,,. .,, .,, . . . . . . . . . . . .7 (3)T. rq

where To = normal freezing point, deg. K,T = freezing point in capillary system, deg. K,

fff = molar volume of fluid,

Uf = surface tension of fluid,r= radius of curvature of fluid surface, and

9 = latent heat of fusion of fluid.

This equation was derived from thermodynamic considerations, takinginto account the influence of capillary tension. It involves the assump-tion that the liquid phase is in tension while the ice is under normalpressure,


One of the objects of this investigation waa to verify eq. (1) as appliedto cement paste, or to find an empirical substitute for it. It is apparent

that from the correct relationship the amount of water in a saturated

paste that is freezable at any given temperature could be obtained from

the adsorption curves, after applying temperature corrections. That is,

the amount of freezable water could be obtained from the sorption

characteristics measured at 25 C, for example, after correcting the valueof p/p. at 25 C to what it would be at the freezing point.

To apply eq, (1) to the freezing of water in cement paste is tantamountto assuming that the ice forms as a separate microcrystalline phase,the crystals being so large that they exhibit the normal properties ofice, and that the ice is under normal external pressure. As will be seen,the experimental data do not definitely confirm these assumptions, butthey indicate that the assumptions are substantially correct, at leastfor the freezing of saturated pastes. The causes of uncertainty will bediscussed later.

APPARATUS AND METHODS

Test samples

The test samples were granules of cement paste or cement-silica paste.They were obtained by the method described in Part 2. The originalspecimens (cylinders or cubes) were crushed and sieved, the particlescaught between the No. 14 and No. 28 sieves being taken for the freezingexperiments. Each sample was treated as follows:

The evaporable water was removed from the granulated sample bydrying in vacuo over Mg(CUIA)z.2H@ + Mg(CZOt)z.4H@. Then waterwas added to the dry granules in such quantity as to saturate them. Thisprocedure is described in Part 2.

Most of the sample prepared in this way was then transferred to adilatometer, without packing the granules in the bulb. All operationsinvolved in the transfer were carried out in a water-saturated atmosphereto minimize losses of moisture from the sample.

Dilatometets

A drawing of a typical dilatometer is shown in Fig. 8-3. This isessentially the same instrument used by Elsner von Gronowfaj in hisexperiments with hardened paste and by Foote and Saxton,f4J Jones andGortner,@) and Bou youcos,@) who studied various materials.

Freezing and thawing procedure

The sealed dilatometer was placed in a cryostat (initially at roomtemperature) with the stem vertical. During the ensuing night, the


n Fig. 8.3 (left)-Sketch of typical dilatometer

}

Scale

f

CopilloryImm. lD,

,.:,,. .+::,;:...,: :,.. , >.: ”,. Somple,%... ,.,,.:..,:.:,,.:.. .:”.:J.I....:.

Section ofGfoSS Rod

Fi , 8-4 (below)-Sketch of apparatus used for filling‘fdl atometers with toluene

E

temperature of the cryostat was allowed to drop gradually to about– 20 C. The bulb of the dilatometer was then cooled quickly to about– 78 C by placing it in a mixture of solid carbon dioxide and alcohol. Thestem was connected to a vacuum pump through the apparatus shown inFig. 8-4. After the air was removed, toluene in bulb D was caused to flowinto the dilatometer by manipulating flexible connections and pinchclamp E which admitted atmospheric pressure. By repeating suchmanipulations, all the space surrounding the frozen grains, as well as thebore of the capillary stem, was filled with toluene.

After the level of the toluene in the stem had been adjusted to a pointnear the bottom of the scale, the top of the calibrated stem was sealedto prevent loss of toluene by evaporation. Then the loaded dilatometerwas transferred back to the cryostat, still at about —20 C, withoutallowing the sample to thaw during the transfer. The final dilatometerreading at —20 C was taken the following morning,

After the initial – 20 C reading was obtained, the temperature wasraised stepwise, allowing time for the level of the toluene in the stem tocome to rest after each change in temperature. A constant level wasusually established in about one-half hour, but each temperature wasmaintained for at least 1 hour.

The procedure described above was used for most of the data dis-cussed herein. Other data were obtained ehrlier when the methods wereless well developed. In some cases, the saturated sample was sealed in


Fig. 8-5<ryostot used for freezing studies

Lelt-Over.all viewAbove-Top of C~yO1tdi Proper

the dilatomcter and the toluene was introduced with the aid of a vacuumpump without first freezing the sample, Although the granules werewetted with toluene before they were subjected to low pressure, thisprocedure probably resulted in a small loss of evaporable water. Also,the top of the dilatometcr stem was sealed only with a rubber cap. Thispermitted a small loss of toluene during the course of the experiments,The samples prepared in this manner were usually started above thefreezing point and the freezing curves as well as thawing curves wereobtained.

Description of cryostat

The cryostat used in these experiments is shown in Fig. 8-5 and dia-grammatically in Fig. 8-6. It consists of an alcohol container G, equippedwith cooling coils. Within this container is a double-walled glass vesselalso containing alcohol, This is the cryostat proper. It contains anelectrical heating coil, not shown, a motor-driven stirrer, C, and a mer-cury-toluene type thermoregulator, B. The temperature of the alcohol


To RdaY //0V 0 ~ Topofentiofnhr Fig. 8-6-Freezing studyapparatus

t \

Q

[

is indicated by the 8-junction copper-constantan thermopile, T, having

its cold junction in melting ice outside the cryostat, as indicated. Thee,m.f. of the thermopile is measured by means of a Type K potentiometerand suitable galvanometers. A single dilatometer, D, is shown. Actually,four dilatometers could be accommodated simultaneously.

GENERAL ASPECTS OF EXPERIMENTAL RESULTS

Dilatometer curves

Results of a typical experiment on a saturated sample are given inFig. 8-7. Beginning at point A, the temperature was lowered stepwise

and the corresponding changes in dilatometer readings were observed.These changes were converted into volume change, the volume at –0.2 Cbeing taken as the reference point. As shown, the points describethe straight line AB. This represents the thermal contraction of the

whole system, p yrex-glass bulb, toluene, and water-saturated sample.At about – 7.5 C, point B, a sudden expansion occurred, giving the riseBC. Further cooling produced the curve CD. Since CD does not fall

as steeply as AB, we may conclude that further expansion accompanied

the change from – 7.5 to – 25 C.

PHYSiCAL PROPERTIESOF HARDLNED PORTLAND CEMENT PASTE 941

A- -1

Fig. 8-7—Typical results ofdilatometric study of saturatedsample

‘“””46 -24 -22 -20 -18 -lb -14 -12 -10 -8 -6 -4 -2 0 2 !, , , I i

Temperature, “C

Beginning at – 25 C (point D) the temperature was raised stepwise

and the curve D to H was obtained. A comparison of the slope of AB

with the various slopes of DH shows that each increment of temperaturecaused expansion up to point E. But the expansion accompanying each

increment of temperature was less than the normal thermal expansion.

This indicates a progressive melting of ice. Along EF, contractionoccurs, showing that the contraction due to melting exceeded the thermalexpansion. At temperatures above G, the volume increase is due to

thermal expansion only, as shown by the parallelism of GH and AB.The results described above are typical of all such tests made on

saturated granules of paste. During the time when the points fell alongAB, below – 0,2 C, the water remained in a supercooled state. All the

water that might have frozen between —7.5 and —0.2 C changed toice at – 7,5 C, In various experiments the extent of supercooling ranged

from about – 5 C to – 12 C. Sometimes freezing was started by tappingthe stem of the dilatometer. It seems likely that at other times chance

vibrations determined the extent of supercooling,The fact that DE and DC do not coincide is probably another mani-

festation of hysteresis, We have already seen that the progressive dropin freezing point indicates a corresponding progressive drop in relativevapor pressure of the unfrozen evaporable water. The freezing of a part

of the evaporable water has an effect on the unfrozen evaporable watersimilar to the loss of evaporable water by drying. Likewise, the meltingof ice has an effect like that of increasing the evaporable water contentof a partially dry specimen. Hence, by analogy we can see that the

freezing curve is a resorption curve, with temperature representing vaporpressure. The melting curve is conversely an adsorption curve.


Fig. 8*8—Freezingthawing of silica gel .015-

,010-

m -

A(J

o .

u03 -

; *IO -

; 31s -

,g :~ -

al-,03s-p

m mm -s

. ,%eezicg

u -.05 - 0 Thowing

MO -

:0ss - /’

-’~13 -1? -11 -10 .9 -8 -7 .6 -5 -4 -3 -2 -1 0 I 2 345

Temperature, “C

110 , ! , ,~

$lj Im -

‘IIo Freezing

8x Thawing

$93 -

jw

Fig. 8-9—Results of ex- fperiment for measuring mfreezing and thawing of T 10-ice in hardened cement ~paste by the dielectric &’method %0-; -i-; -i-; i-i-i-1012 345678

Temperature, “C

The curves DE and DC in Fig. 8-7 show, by comparison with AB,that the contraction per degree on melting is less than the expansion perdegree on freezing. This result is as would be anticipated” from the factthat the decrease in evaporablc water content per unit decrease in p/p,

is, in the upper range of pressures, less than the increase in evaporablewater content per unit inercasc in p/p8.

Effect of hydration during the experiment

A significant feature of Fig. 8-7 is the position of point G with respect

to A. Point G is that at which all ice disappears—the final meltingpoint. The fact that it is below A shows that the volume of the systcm

dccreascd permanently during the freezing and thawing cycle. * Re-

peated cycles o% onc sample showed that shrinkage incrcmcs with eachcycle. It was suspected that the shrinkage was due at least in part tohydration of ccmcnt in the sample during the test. To check this possi-

*rrhi~ plrticu]ur example showed a considerably great w permanent c]1311!zcthan dill other.% lt repcewm tsa test made before the pmctice of senliw! the dihtometer stem was ndopted. Consequently, most of thechange may be due to loss of toluene.


bility, some special tests were made on silica gel, Fig, 8-8 gives theresult.

The amount of evaporable water that was in this sample of silica gel

is not known exactly, owing to losses of moisture during the, pr~paration

of the dilatometer. However, it is believed to have been slightly more

than the amount required to saturate the granules of silica gel. Thefeature to be noted especially is that the volume after the cycle was

completed was almost exactly the same as the original volume at the

same temperature. The same degree of reversibility was found in threeother tests on silica gel.

In view of the results obtained from silica gel, it was concluded thatthe permanent contraction in volume such as is shown in Fig. 8-7 is

due, at least in part, to continued hydration of the cement during the

course of the experiment. Such an explanation is plausible, even though

the original material had been cured under water for several months,

because the granulation of the original specimen exposed fresh clinkersurfaces and admitted Water into fine gel structure that had become par-

tially desiccated in the whole specimen (see Part 2).

Effect of dissolved material

One other feature of Fig. 8-7 should now be noted, Point G, the finalmelting point, is slightly below 0 C. This is the effect of dissolved

materials, chiefly alkalies. It will bc seen later that the final meltingpoint of one of the samples was – 1.6 C!, owing to its unusually highalkali content.

Detection of freezing by means of the change in dielectric constant

Alexander, Shaw, and NIuckenhirn studied the freezing of yaterin soils and other porous media by means of the accompanying change in

dielectric constant, (7) The dielectric constant of water is about 80 andthat of ice about 4. By using the material to bc tested as the dielectric

medium between the plates of a fixed condenser, these authors were

able to follow the course of ice-formation by measuring the change in

capacitance of the condenser.

Through the courtesy of Horace G. Bycrs, Chief, Soil Chemistry andPhysics Research, U, S. Dept. of Agriculture, Washington, D. C., Mr.Alexander very kindly tested a saturated, granular sample of hardenedpaste for us. The results are shown in Fig, 8-9. Since this representsbut a single run, we cannot assume that all the features shown aresignificant. Nevertheless, they are of considerable interest in connec-tion with the interpretation of the results obtained by the dilatometermethod.

In Fig. 8-9 the scale of ordinates gives- the dial readingsparatus. An increase in reading denotes an equal decrease in

of the ap-the capaci-


tance of the fixed condenser and hence a decrease in the dielectric constant

of the sample. The curves show that in the range above O C, loweringthe temperature decreased the dielectric constant of the sample, Asthe temperature fell below zero, the water in the sample remained in a

supercooled state. At –4.5 C, freezing was started by tapping thecondenser, producing the change in dielectric constant indicated. Low-ering the temperature further caused a further decrease in dielectricconstant, the decrease being greater than could be accounted for by alinear extrapolation of the curve for the supercooled system. After thetemperature reached – 9.3 C, the temperature was raised stepwise andthe melting curve was obtained. The final melting point was at – 0.7 C.This depression below O C may be due entirely to the alkali content,but it is probably due in part to a slight loss of moisture from the samplethat occurred while it was being transferred to the fixed condenser.

The final melting point appears to be exactly on the cooling curve,indicating that the sampie returned to its initial state at the end of thecycle. However, the slope of the thawing curve above O C is not thesame as that of the corresponding part of the freezing curve. This mightindicate a permanent change in the dielectric constant of the sample.Such a change would take place if some of the originally evaporablewater would become non-evaporable through reaction with unhydratedcement. Since the sample was in the fixed condenser for four days, someadditional hydration is not unlikely.

On comparing these results with those given in Fig. 8-7, we findthat the major features of the results obtained from the dilatometermethod were found also with the electrical method, (A possible excep-

tion is the evidence concerning the permanent change in the sample

during the cycle.) It seems, therefore, that supercooling and hysteresis

are not peculiarities of the dilatometric method but are characteristicof the paste.

METHOD OF ESTIMATING THE AMOUNT OF ICEFROM THE MELTING CURVE

Curves such as that shown in Fig. 8-7 show the algebraic sums of

simultaneous expansions and contractions that accompany changes intemperature, To estimate the amount of ice that exists at any given

temperature it is necessary to ascertain the net expansion, that is, thedifference between the existing volume at the given temperature and thevolume that the system would have had, had no freezing occurred. This

difference was not determined with exactness for several reasons discussedbelow.

In those tests where the specimens were cooled stepwise, as in thecase represented in Fig. 8-7, the volume change that would have occurred


Fig. 8-1 O—Specific volume of waterat a pressure of 1 atmosphere

N, E. Dorsey, Properties of OrdinarvWater Substance (New York} Rein.hold Publishing Corp., 1940Table 94

I 1 1 1 1 # ,.,4 .!2 -10 .B -6-4-202* 6919*1*

Temperature, “C

had no ice formed could be estimated with satisfactory accuracy fromthe slope of the line established while the freezable water remained in asupercooled state. However, in the majority of tests only the meltingcurve was obtained and’ the volume change in the system when it wasfree from ice could be observed only in the range from O to +2 C. Anextrapolation of the line so established into the range below O C involves

an assumption that the coefficients of expansion of all parts of the systemare, in the absence of ice formation, constant throughout the tempera-ture range involved, usually – 20 to +2 C, So far as the solid phase

of the paste and the pyrex bulb are concerned, this is probably not farfrom true, With respect to the water and toluene, however, such an

assumption is at variance with fact.

As may be seen in Fig, 8-10, water expands as the temperature is

changed in either direction from +4 C, Hence, the volume change of the

water is in the same direction as that of the rest of the systcm only when

the temperature is above +4 C, Therefore, it follows that at readings

taken between O and +2 C, the volume change of the water is oppositeto that of the rest of the system over all parts of the curve. However,

Fig. 8-10 shows that the mean coefficient for the water in the O to +2 Crange is much different from what it is over a 12-deg. range below O C.

Hence, a meam slope established by data in the O to +2 C range cannotbe the same as the mean slope in the lower range. It is necessary, there-

fore, to find a means of determining the mean S1OPCover the lower range

from the empirically established mean slope in the O to +2 C range.

This may be done as follows:

946 JOURNAL OF THE AMERICAN CONCRETE INSTITUTE

Let V. = volume of contents of bulb at O C, or volumeat O C,

v, = volume of contents of bulb at temperature t,Vdt = volume of pyrex bulb at temperature t,

April 1947

of pyrex bulb

WOand zI~l= volume of solids in bulb at O and t, respectively,Vboand vbt = volume of evaporable water in bulb at O and t, re-

spectively, and

v,Oand v,: = volume of toluene in bulb at O and t, respectively.

The apparent change in volume for a specified temperature change willbe

(v, – v.) – (Vd, – VO) = V, – Vd, = AV.

From the above definitions it follows that

AV = (Vat – V..) + (Vbt – Vbo) + (W – v..) – (Volt – v.)

Avavat =V.o+z At, etc., for each term of the above equation.

Hence,

AV &—= ~+~+~– A+............................(4)At

The mean coefficients for each part are as follows:

For the solid phase of the paste:

Ava—. 32 X 10-6 v., (Ref. 8)At

For water:

AVb:- – 50 X 10-’ Vbo,for O to 2 C (See Ref. 10 and Fig, 8-10)

z

~Vb_ --: – 216 X 1o-” ti,5.,for O to – 12 C (See Ref. 10 and Fig, 8-10).,!JL

For toluene:~l,c—.At

Au,~=

For the bulb

1051 x 10-0v,, for o to 2 c

1038 x 10-6v,, for O to – 12 C (Ref. 9)

(Pyrex-brand glass):

A vd— = 10 x 10-’ Vo (Ref. 11).At

These figures substituted into eq. (4) give

~06 Al’= 32va~– 50v~. + 1051v,0 – 10V~,for 0t02 C............(5)

z


and

~08 AV= 32va. – 216v~o+ 1038v,~ – 10V~, for O to –12 C. . . . ...(6)

z

Let m = mean slope of dilatometer curve, AV/At, from O to 2 C, andm’ = mean slope from O to – 12 C.

Then, from eq. (5) and (6)

108(m’ – m) = – 166vbo+ 13VC0and

_ = ~ _ 166zJbo+ 13v.Om’loem ““’’ ””’’’ ”’” o’”’”’’’’’”’’’” (7)

m

Thus the ratio of the mean slope from O to – 12 C to that from O to 2 C isfound in terms of the amounts of water, tib., and toluene, v,., and the ex-perimentally established slope above O C. As applied to any specific casethe line represented by eq, (4) was extended to – 15 C and in some casesto – 20 C, This was necessary because data on supercooled water below

– 12 C were not available.

With the mean slope of the line representing the supercooled systemthus established for each test, the amount of ice at any given ten~pera-ture was estimated from the difference between the observed volumeand the corresponding computed volume of the supercooled system, thisdifference being the observed net expansion. Let

Av = net expansion,B~ = expansion resulting from freezing 1 gram of water at

the existing temperature, andWf = amount of ice (freezable water).

Then

Au

“=x”””””””’”’””’”’’’’’”””” ‘“’”’’’’’””’””’,, (8)

BI is itself a function of temperature, since the coeffkicnts of expansion

of water and ice differ both in magnitude and sign. Table 8-1 gives values

of l?~ at various temperatures calculated from values of the specific

volume of icc and water assembled by Dorsey. (lo)

The method of obtaining the amount of ice in the dilatometer de-scribed above obviously decreases in accuracy as the temperature be-

comes lower. This is due not only to the inaccuracy of the experimentalvalue for m but also to limitations on the use of Table 8-1. As will be

seen Iatcr, the water that freezes above a dilatometer temperature ofabout —6 C is almost entirely capillary water. But below – 6 C, someof the gcl water is extracted and freezes with the capillary water: Sincethe mean specific volume of the gel water is about 0.90 (Part 5), Table 8-1does not correctly represent the volume change of gel water on freezing.


TABLE 8.1—VOLUME CHANGE OF 1 GRAM OF WATER WHENFREEZING OCCURS AT GIVEN TEMPERATURES

VolumeT#p) change,

( =mjt)

0.0907- !.0 0.0904– 1.5 0,0903- 2.0 0.0902– 2,5 0.0900- 3.0 0.0898– 3.5 0.0897– 4.0 0,0896– 5.0 0.0892– 6.0 0.0889- 8.0 0.0881-10.0 0.0872–12.0 0.0863–15.0 0.0849–20,0 0.0812

Because of these considerations, the method of obtaining w~ describedabove cannot be considered reliable below about – 15 C, A preferableprocedure would be to establish the- slope by supercooling the sampleas far as possible, after the final melting curve has been obtained.

EFFECT OF TOLUENE ON THE MELTING CURVE

Owing to the fact that the paste granules were surrounded withtoluene, it is necessary to consider the effect of the toluen.e on the position

of the melting curve. This will be done indirectly by considering its

effect on water vapor pressure.

At any given temperature below O C, equilibrium between ice andcapillary water can be maintained because of the effect of capillary ten-sion on the free energy of the water. The fact that with ice presentthe capillary tension is maintained indicates that the unfrozen capillarywater either becomes separated from the ice so as to maintain its menis-cus, or else it retains its continuity and remains in contact not onlywith the ice but also with the external phase. Such contact might bemaintained through channels too small to be frozen at the existingtemperature. If the external phase is air, as in the electrical methoddescribed earlier, the capillary tensiop will depend on surface curvatureand the interracial tension at the air-water interface (i.e., the surfacetension), according to Kelvin’s equation. (See Part 3.) If the externalphase is toluene, the capillary tension will depend on surface curvatureas before, but now it will depend on the interracial tension at the toluene-water interface rather than the tension at the air-water interface. There-


fore, the melting curves of the granules submerged in toluene should notbe the same as when the granules are exposed to air.

We can estimate the effect of substituting a toluene-water inter-face for an air-water interface by making use of eq. (3). Let

u. = surface tension of water against air,u.~ = interracial tension, water against toluene,To = normal freezing point of water, deg. K,

AT1 = depression of freezing point with sample in contactwith air,

ATZ = depression of freezing point with sample in contactwith toluene, and

let the other symbols have the same meaning as before. Then,

AT1 2V,—.To ~ ‘w

and

ATZ 2vf—= —To rq ‘w’ ‘

We may assume that vf and q are the same in both cases. Hence,

ATI u..—.A~t – u.,

Interracial tension and surface tension are functions of temperature.For the air-water interface, we may obtain satisfactory figures for giventemperatures from published datai. For the toluene-air interface nodata are available except for 25 C. For the similar liquid, benzene, thetemperature coefficient is given as – 0.058 for the temperature range 10to 40 C. We will assume that this holds for toluene and for the lowertemperature range.

On the basis just described, the following results were obtained:I I I

SW cd n“

dei$ C—ad

O , 75.64 37.6 2.01

-5 I 76.33 I 37.8I

2.02

-10 \ 77.00 I 38.1 I 2.02I I I

Hence, it may be concluded that

ATI = 2AT2, approximately.

That is, the depression of the freezing point with the sample in contactwith air would be about twice the amount observed in these experiments.Or, the amount of water freezable in these experiments at – 15 C, for


example, is about the same as would be freezable at —30 C if the sampleswere exposed to air.

QUANTITIES OF ICE FORMED IN VARIOUS SAMPLES

The amounts of ice formed in various samples are given in Tables8-2 to 8-6 and compositions of the samples in Table 8-7. The relation-ships between ice-content and temperature are given graphically in Fig.8-11 and 8-12. The results are analyzed further in succeeding sections.

Influence of soluble alkalies

The curves shown in Fig. 8-11 and 8-12 show that the final lneltingpoint differed among the various specimens. These differences arebelieved to be due to differences in the amount of soluble salts, partic-ularly the alkalies, in the evaporable water. The basis for this con-clusion is more clearly indicated by the data as arranged in Table 8-8.

It will be noted that with three of the five cements, the final meltingpoint is higher the higher the original water-cement ratio. This is un-doubtedly the result of the leaching out of alkalies during the 28-dayperiod of water storage; the higher w~/c the higher the rate of leaching.

The dissolved alkali not only lowers the final melting point but alsothe amounts of ice that can exist at lower temperatures. The effectis probably proportional to the concentration in the part that remainsunfrozen, What this concentration is, or how it changes with tempera-ture, cannot be told from information now available, mainly because theeffects of adsorption by the solid phase on both the solvent and thesolute cannot be evaluated.

THEORETICAL AMOUNT OF FREEZABLE WATERAT A GIVEN TEMPERATURE

Locus of ice in the paste

In the majority of the tests considered here, the samples were firstcooled to – 78 C. This is the temperature at which ice has about thesame vapor pressure as the non-evaporable water. (See Part 2.) Hence,if equilibrium is reached, all the evaporable water should be frozen.However, it should be observed that the jreezing in place of adsorbedwater is very unlikely. As shown in Part 4, when water is adsorbedit undergoes a change, as indicated by its decrease in entropy. The in-dications are that the entropy change of adsorption is greater than thataccompanying the transition from water to ice. It hardly seems possiblethat water that has already been changed to such an extent could becaused to crystallize only by lowering the temperature. To be con-sidered also are the relative sizes of the gel pores and the capillaries. Asshown in Part 3, the hydraulic radius of the gel pores is estimated to beabout 10~. The average width of the pores is probably between 2 and

TABL

E8-

2-M

ELTI

NG

-CU

RV

ED

ATA

FO

RS

AM

PLE

SM

AD

EW

ITH

CE

ME

NT

1575

4(F

orco

mpo

siti

ons

ofsa

mpl

es,

see

Tab

le8-

7.)

Ref

.10

-4;

,/C=

0.32

,/c=

0.45

90da

ys

Ref

.10

-3;

t

28&

yS

,/C=

0.62

Ref

.10

-1;

(

28@

ST

emp.

,de

g.C

x(–

1)90

days

Wf

/c

Wf/v.

28&

yS90

days

Wf/

cw

r/v.

wf/

cw

j/v.

wf

/cW

f /vm

Wf/

cW

J/V

nt

wf/

c — — —

— — —

.0G

9.0

287

.037

6.0

417

.043

2.0

452

.046

7.0

485

.050

7.0

539

.058

3.0

622

.064

8.0

672

.073

4

— — — Oxo

0.59

0.77

0.85

0.88

0.92

0.95

0.99

1.03

1.10

1.19

1.27

1.32

1.37

1.50

— —

.M:5

.074

4.0

909

.107

5.1

207

.129

4.1

350

.140

4.1

445

.155

6.1

655

.177

9.1

893

.199

3.2

093

.227

0

— — 0<6

1.40

1.72

2.03

2.28

2.44

2.55

2.65

2.73

2.94

3.12

3.36

3.57

3.76

3.95

4.28

.016

5—

.055

7.1

160

.162

7.1

897

.224

3.2

452

.260

2.2

724

.282

9.2

916

.305

5.3

172

.339

6.3

616

.374

9.3

919

.424

0

0.29

0Z9

2.07

2.91

3.39

4.01

4.38

4.65

4.86

5.05

5.21

5.46

5.66

6.06

6.46

6.69

7.00

7.57

.o%

.1;

5.1

562

.175

1.2

061

.225

9.2

387

.248

2.2

547

.263

6.2

773

.288

5.3

096

.326

7.3

397

.355

9—

027

0.1

0.15

0.25

0.50

——

——

.cZ

4.0

663

.076

2.0

898

.099

6.1

045

.109

3

—.

0>0

1.09

1.25

1.47

1.63

1.71

1.79

—2.

092.

562.

873.

383.

703.

914.

074.

184.

324.

554.

735.

085.

365.

575.

83

0;5

0.65

0.85

0.92

1.00

1.05

1.10

1.16

1.24

1.33

1.47

1.56

1.65

1.83

2.07

.015

7.0

293

.038

4.0

415

.044

9.0

473

.049

6.0

520

.056

0.0

600

.066

3.0

704

.074

4.0

823

.093

0

0.75

N 2.0

2.5

3.0

3.5

.1i4

21.

871.

932.

052.

162.

382.

532.

662.

853.

22

:117

7.1

250

.131

6.1

449

.154

2.1

622

.173

8

4.0

5.0

6.0

8.0

10.0

12.0

15.0

20.0

Fin

alM

elti

ng

Poin

t

.196

5

–0.

05”

–0.

05°

–0.

5°–

0.5°

–0.

25”

–o.2

0°

Tem

p.,

deg.

C

x

C-1

)

0.1

0.25

0.

50

0.75

1.

0 1.

5 2.

0 2.

5 3.

0 3.

5 4.

0 5.

0 6.

0 8.

0 10

.0

12.0

15

.0

20.0

Fi

nal

Mel

ting

Poin

t,

TABL

E 8-

J-M

ELTI

NG

-CU

RVE

D

ATA

FOR

SA

MPL

ES

MAD

E W

ITH

C

EMEN

T 15

756

(For

co

mD

ositi

ons

of s

amD

Ies.

se

e Ta

ble

S-7.

)

Ref

. 10

-C;

w,/c

=

0.34

29 d

ays

- wJ

]c

.OG

l .0

242

.039

1 .0

469

.060

0 .0

717

.080

2 .0

889

.095

1 .I0

13

.113

9 .1

218

.135

4 .1

413

.146

8 .1

563

.172

1

- wJ

/vna

0<8

0.67

1.

09

1.30

1.

67

1.99

2.

23

2.47

2.

64

2.81

3.

16

3.38

3.

76

3.92

4.

08

4.34

4.

78

Ref

. 10

-B;

zoo/

c =

0.48

29 d

ays

wJ/c

wJ

/vm

.0&o

1.

21

- .0

916

2.35

.1

156

2.96

.1

345

3.45

.1

637

4.20

.1

864

4.78

.2

068

5.30

.2

196

5.63

.2

311

5.93

.2

410

6.18

.2

578

6.61

.2

732

7.01

.2

934

7.52

.2

988

7.66

.3

079

7.89

.3

184

8.16

.3

431

8.80

- 0.

1”

Ref

. 10

-A;

w,/c

=

0.67

29 d

ays

wJ/c

wJ

/vm

.025

2 0.

60

.099

4 2.

37

.175

5 4.

18

.226

0 5.

38

.262

4 6.

25

.312

8 7.

45

.348

9 8.

31

.372

7 8.

87

.391

0 9.

31

.407

1 9.

69

.419

8 10

.00

.445

9 10

.62

.462

4 11

.01

.485

9 11

.57

.494

2 11

.77

.503

0 11

.98

.515

7 12

.28

.541

7 12

.90

- 0.

05”

_-

I R

ef.

10-1

4;

w,/c

=

0.45

90 d

ays

WI/c

w/

/v,

.027

3 .0

558

.081

6 .0

957

.116

1

: E

.154

9 .1

636

1724

: 1

863

1972

20

24

.225

1 .2

343

.247

7 .2

691

0”

0.58

1.

19

1.74

2.

04

2.47

2.

79

3.07

3.

30

3.48

3.

67

3.96

2%

5.73

- --

--

-

Ref

. 10

-13;

w

,/c

= 0.

63

90 d

ays

w//c

wJ

/vm

.044

8 - 0.91

.1

289

2.63

.2

056

4.20

,2

16s

4.42

.2

638

5.38

.2

910

5.94

,3

13s

6.40

.3

322

6.78

.3

476

7.09

:%

El

.396

5 8.

09

.417

5 .4

305

:%

.440

1 8:

98

:Z

Ei

O0

TA

BLE

8-4-

ME

LTIN

G-C

UR

VE

DA

TA

FO

RS

AM

PLE

SM

AD

EW

ITH

CE

ME

NT

1575

8(F

orco

mp

osit

ion

sof

sam

ples

,-

Tab

le8-

7.)

Ref

.10

-12

l./C

=0.

32R

ef.

10-1

1;lo

/c=

0.45

Ref

.10

-10;

9./C

=0.

62T

emp.

,de

g.C

x(-

1)91

day

s91

day

s28

&b

Jll

91d

ays

Wf/

cw

r/v.

Wf/

cW

fW.

—.——

.OE

M0Z

5.0

335

0.76

,040

60.

92,0

462

1.05

.049

31.

12.0

510

1.16

.052

91.

20.0

583

1.32

.061

31.

39.0

674

1.53

.072

71.

65

Wf/

c

.OX

O.0

510

.071

4.0

919

.104

5.1

146

.122

2.1

272

.132

1.1

384

.144

5.1

546

.162

4

w//v.

wJ

/cW

fW.

Wf

/cw

r/v.

WfW.

——

——

0.25

0.50

0.75

.lii

o.1

723

.204

8.2

386

.263

6.2

799

.292

5.3

031

.313

1.3

229

.335

6.3

575

.374

1.3

848

.402

4.4

363

.052

90.

96.1

042

1.89

.147

42.

68.1

766

3.21

.202

73.

68

o% 1.00

1.40

1.80

.017

7.0

358

.053

8.0

724

——

.oii

9.0

197

.027

6.0

324

.037

9.0

418

.044

9.0

520

.058

2.0

694

O:ii

0.47

0.66

0.77

0.90

0.99

1.07

1.24

1.38

1.65

1.0

1.5

2.0

2.5

3.0

3.5

4.0

5.0

6.0

2.05

2.25

2.40

2.49

2.59

2.71

2.83

3.03

.084

4.0

933

.103

1.1

039

.108

2.1

169

.125

6.1

397

.147

3

.227

2.2

415

.254

0.2

586

.265

7.2

820

.290

9.3

118

4.13

4.39

4.62

4.70

4.83

5.13

5.29

5.67

8.0

10.0

12.0

15.0

20.0

Fina

lM

elti

ngPo

int

.078

3.0

857

.092

4●

1.86

2.04

2.20 —

3.18

3.29

3.46 —

.325

7.3

376

.322

9

5.92

6.14

6.42 —

,076

51.

74.0

793

1.80

*—

–0.

85”

.167

8.1

566

3.01

.176

3*

.167

33.

22*

—

–0.

9°–

0.2.

5°–

0.25

°–

0.15

°–

O.1

OO

~ept

i

x(–

1)

0.75

1.0

1.5

2.0

2.5

3.0

3.5

4.0

5.0

6.0

8.0

10.0

12.0

15.0

20.0

Fin

alM

elti

ngPo

int

TABL

E8-

5—M

ELTI

NG

-CU

RV

ED

ATA

FO

RS

AM

PLE

SM

AD

EW

ITH

CE

ME

NT

1576

1(F

oreo

mD

ositi

ons

ofsa

mde

s.se

eT

able

8-7.

)

Ref

.10

-6;

we/

c=

0.32

28da

yS

wf/

cW

!lv.

— — —.0

316

.045

5.0

515

.056

8.0

615

.069

7-.0

747

.083

0.0

888

.092

8.0

942

.096

4

–1.

6°

— — — 0.77

1.11

1.26

1.38

1.50

1.70

1.82

2.02

2.16

2.26

2.30

2.35

Ref

.10

-2;

u

28d

aJ

W

wf

/cW

f/V

m

——

——

.085

4.1

199

.135

7.1

459

.154

7.1

630

.177

9.1

918

.213

0.2

289

.241

0.2

542

.278

0

–0.

9°

1.71

2.40

2.71

2.92

3.09

3.26

3.56

3.84

4.26

4.58

4.82

5.08

5.56

/c=

0.45

90da

ys

wf/

c?0

//V

~

. 0=1

.089

2.1

083

.120

1.1

296

.137

1.1

431

.155

0.1

664

.183

7.1

949

.204

6.2

152

.231

0

–0.

85°

0<4

1.59

1.93

2.14

2.31

2.45

2.56

2.77

2.97

3.28

3.48

3.65

3.84

4.12

Ref

.10

-5; W

O/C

=0.

63

28C

kb

yS

wf/

cw

r/vm

.106

31.

93.1

894

3.44

.254

84.

63.2

858

5.20

.310

05.

64.3

240

5.89

.337

66.

14.3

478

6.32

.365

5.3

793

::E.4

012

7.29

.414

57.

54.4

235

;:::

.437

3.4

425

8.04

–0.

5°

TA

BLE

8-6-

ME

LTIN

G-C

UR

VE

DA

TA

FO

RS

AM

PL

ES

MA

DE

WIT

HC

EM

EN

T15763

(For

com

posi

tion

sof

sam

ples

,see

Tab

le8-

7.)

Ref

.10

-9;w

e/c

=0.

31R

ef.

10-8

;W

e/C

=0.

44~f

.1&

7;W

O/C

=0.

62

Te&

pe

x(:1

)

Dil

.N

o.5

Dil

.N

o.6

28d

&iy

S91

days

Wf/c

uv/

v.

28d

ays

Wf

/cW

fm.

28&

yS

W/

/c

Wf/v

.W

f/c

wf/

v.

0.10

0.15

0.25

0.50

0.75

.011

2

.0~6

.100

3.1

352

,160

0.1

914

.212

8.2

276

.239

1.2

456

0.34

1>8

3.04

4.10

4.85

5.80

6.45

6.90

7.24

7.44

7.64

.009

2

M>8

.090

8.1

269

.152

5.1

827

.203

6.2

177

.229

4.2

386

.246

7

.W39

2

.lfi

o.1

903

.204

8.3

041

:= .412

3.4

306

.445

2.4

566

.470

5.4

889

.497

3.5

061

.515

3.5

272

.550

0

1.12

.0<6

0<2

.022

80.

76.0

459

1.53

——

.W<8

.0;4

.035

8.0

430

.053

8.0

603

.065

2.0

698

.072

7.0

768

0:5

O:w

0.94

1.13

1.42

1.59

1.72

1.84

1.91

2.02

2.16

.077

2.0

932

.104

6.1

128

.118

5.1

231

.127

3.1

347

2.57

3.11

3.49

3.76

3.95

4.10

4.24

1.0

1.5

2.0

::; 3.5

4.0

.252

3.2

639

5.0

6.0

8.0

10.0

12.0

15.0

20.0

Fin

alM

elti

ng

Poi

nt

4.49

4.59

4.79

4.94

5.03

5.15

.082

2.0

875

.093

9.0

983

.101

4.1

037

.104

5

8.00

8.28

8.57

8.83

8.90

8.98

9.18

.256

3.2

658

.137

8.1

437

.148

1:1

509

.154

5

2.30

2.47

2.59

2.67

2.73

2.75

.273

1.2

828

.291

3.2

937

.296

2.3

028

.275

7.2

814

,284

6.2

892

.296

3*

15.7

1—

–0.

05°

–0.

05°

0.05

°–

0.05

°–

0.05

°—

*Not

avai

labl

e.


TABLE 8-7-COMPOSITION OF SAMPLES USED IN DILATOMETERS

(For cement characteristics, see Appendix to Part 2.)

Composition, g/g of cementg: Age, -?& ~n

—— .

days c W6 Wt (*, v. %—T c -1- C T

— . . ——

——10-4 I 281041o-1 %1o-1 9010-3 2810-3 90

I——

— .10-c 281O-B 281O-A 2810-14 9010-13 90- .

Cement 15754; V~/w~ = 0.258

0.32 0.176 0,213 0.389 0.064 0.045 4.73 -0.32 0.189 0.220 0.409 0.065 0.049 4,490.45 0.207 0.351 0,558 0,076 0.053 6.630.45 0.237 0.335 0.572 0,081 0.061 5.500.62 0.217 0.536 0.753 0.081 0.056 9.570.62 0.235 0.538 0.773 0.088 0.061 8.82

Cement 15756; V~/wn = 0.271

0,34 0.134 0.272 0.406 0.0510.48 0.145 0.443 0.589 0.0520,67 0.154 0.648 0.802 0.0570.45 0.172 0.391 0.563 0,0630.63 0.182 0.611 0.793 0.066

Cement 15758; V~/w~ = 0.248— — .10-12 28 0.32 0.168 0.224 0.392 0.05810-12 0.32 0.179 0.227 0.406 0.06110-11 % 0.45 0.204 0,353 0.557 0,07410-11 0.45 0.211 0.365 0.576 0,0761o-1o ;: 0.62 0.218 0.555 0.773 0.0781o-1o 91 0.62 0.222 0.535 0.757 0,083— — —

Cement 15761; VJW. = 0.262

0,036 7.560,039 11.360.042 15.430.047 8.320.049 12.47

0.042 5.330.044 5.160.051 6.920.052 7.020.054 10.280.055 9.73

1

16-6 28 0.32 0.158 0.248 0,406 0,057 0.041 6.0510-2 28 0.45 0.190 0.390 0.580 0,069 0.050 7.8010-2 90 0.45 0.215 0.381 0.596 0.078 0.056 6.8010-5 28 0.63 0.209 0.613 0.822 0.083 0.055 11.15— — .

Cement 15763; V~/w~ = 0.295

10-9 28 0.31 0.101 0.278 0.379 0.045 0.030 9.2710-9 91 0.31 0.130 0.237 0.367 0.056 0.038 6.2410-8 0.44 0.113 0.424 0.537 0,048 0.033 12.8510-7 % 0.62 0.119 0.624 0.743 0.050 0.035 17.83

4 times the hydraulic radius. Thus the average gel pore is estimated to

be between 20 and 40A wide. The width of the average capillary cannot

be estimated very accurately, but it is at least 10 or 20 times the widthof the gel pore. Owing to the fact that the melting point of a crystalis Iower the smaller the crystal—for crystals in the colloidal size-range—any ice that might form in the gel pores would have a lower melting pointthan that of the ice in the capillaries. It seems, therefore, that if the gelwater freezes, it first moves out of the gel and then joins the ice already

PHYSICAL Properties OF HARDENED pORTLAND CEMENT pASTE 957

I

I

I

I

3k

Temperature,‘C Tempweture,”c

Fig. 8-11 —Relationship between ice content and temperature for samples made withcements indicated

1

I

1

1

1

:

Temperature,”C

7

6

5

4

3

2

I

o

I I lkJ ‘}”- I I

t--H.

3 \ I I \

4

2

0-20 -16 -16 -14 -(2 -10 -8 -6 -4 .2 -0

I I I I I [ 1-,,

Temperat.re,”C

Fig. 8-1Q—Relationship between ice content and temperature for samples made withcements indicated


formed in the capillaries. The movement of the water could be either bysurface migration or by distillation.

Relation of freezing to drying

As mentioned before, the process of freezing out gel water would befundamentally the same as removing it by evaporation, In either case,the equilibrium vapor pressure of the gel water at any time is determinedby the degree of saturation of the gel. Consequently, the amounts offreezable and unfreezable water should be determinable in terms of thevapor pressure isotherm. For the conditions of these experiments, theadsorption isotherm may be used.

TABLE 8-8—INFLUENCE OF ALKALIES ON FINAL MELTING POINT

“ 15754

15756

15758

15761

15763

*29days.t91 days.

Alkali contentof cement, percent

Na,O

0.17

0.05

0.30

1,13

0.05

K20

0.16

0.17

0!40

0.44

0.22

Total

0.33

0.22

0.70

1,57

0.27

I Final meltingpoint, deg. C

we/c

28 days

0.32 –0.500.45 –0.250.62 –0.05

0.34 –o. 10”0.450.48 –:1O*0.630.67 -;05

0.32 –0,900.45 –0.250.62 –0.15

0.32 -1,600.45 –0.900.63 –0.50

0.31 –0.050.44 –0.050.62 –0.05

90 daya

–0.50–0.20–0.05

T—o—

–0.85t–0.251’–0.lot

–ii85—

–o.05t——

Relation of freezable water to total evaporable water

We have already seen (Part 3) that the water content that producesa given vapor pressure in the lower range of pressures is the same per unitV~* for all samples. Therefore, for the lower range of vapor pressures,and hence for the lower range of freezing temperatures, the amount ofunfreezable water at a given temperature por unit V~ should be thesame for all samples. Thus if we let

*V” is the constant in the f3.f3,T. equation thst represents the quantity of water required to cover thesurface with a single layer of molecules. It is considered to be proportional to the surface area of the solidphase and a measure of the gel content of well hydrated samplw


WC= total evaporable water,w. = unfreezable water, andWt = freezable water,

then Wf we—.—V~ Vm– u’”””””’”””””””””””””””””’”” ““’”””

,. (9)

where u = wJV~ and is a constant for a given temperature.

From eq. (9) it can be seen that plotting wf/V~ vs. wJV~ shouldproduce a straight line having a slope of unity for whatever range oftemperatures wJV~ is actually constant. Such plots are shown in Fig.8-13 for six different temperatures. In each diagram the solid straight

line has a slope of 1.0 as required by eq. (9). With the exception of thoseobtained above – 6 C, the experimental points conform fairly well tothis slope. Hence, we may conclude that for temperatures of about – 6 Cor lower, the following empirical relationships may be used for estimating

the amount of freezable water:

()Wf we– 4.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

y- .6. = ~-

()

Wf W*– 3,7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~m .10. = ~m

()

w/ w*– 3.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,. (12)

~~ .15. = ~~

(lo)

(11)

The temperatures indicated are for freezing in toluene. For freezing inair, the temperatures should be multiplied by 2, as shown in a preceding

section. That is,

(wJ).6J in toluene = (wf).1~. in air, etc.

Reference to Fig. 8-13 shows that at a dilatometer temperature of– 6 C or higher, the amount of freezable water is roughly proportional tothe amount of capillary water, w. – 4V~, the proportionality constantsbeing about 1.0 at –6 C, 0.86 at –4 C, 0.7 at –2 C, and 0.6 at – 1 C.This indicates that in this upper temperature range, the. amount of waterextracted from the gel by freezing is negligible. Below - 6 C, the con-tribution from the gel water is appreciable. As already mentioned itcould contribute a maximum of 4Vm at about – 78 C.

It should be noted that eqs. (10), (11), and (12) can be used only forestimating the maximum amount of freezable water. If a specimen werecooled only a few degrees below its final melting point, as is frequently

the case for concrete exposed to the weather, the amount of freezable

water would probably be smaller than would be indicated by theseequations because of the hysteresis in the vapor-pressure-vs.-water-

content relationship. very little specific information on this point can

be given until more experimental work is done.


14 ,

12- Dilatometer Temperature= -I”C

@w

/

‘%.’

6 -

4

2

00? 460‘Y& ‘2 ‘4 “ ‘8

)4

1?- D=!er Temp?ratuE. -4° C

o0 -

8-

‘fhm

6

4-

2

co24b8 h

‘?( “ ‘4 ‘ ‘

8

4 . Y’

12- @!:atometer Temperatwe.40”C

&N -

‘%.’ o

b -

.4 -

.

2 -

002468‘W; “ ‘4 “ “

(L

12 Dilatometer Tsmperatu,V. .2°C

@o

8-

6-

4

2

‘0246 8W’O ‘2 ‘4 ‘6 18%

!4- /

12- Dllatometer TemperaWe. -6-C

@D-

8-

6-

4- .

2-..

% 2 4 b 0

‘fi: ‘4 ‘ ‘

(2 b 8

.14

Dlatomeier ‘remerature..15.c‘7“ ~_r??‘d-

8-

b-

4-

.2-

OOZ 468

;m ‘= ‘4 “ ‘8W

Keg to Sgmbols . - 15754x. ,576,. . ,S,s,g.- !5763a. 15756

Fig. 8-1 3—Relationship between maximum freezable water content and total evaporablewater in saturated pastes

PHYSICAL PROPERTIESOF HARDENED PORTLAND CEMENT PASTE %1

RELATIONSHIP BETWEEN THE AMOUNT OF WATERUNFREEZABLE AT A GIVEN TEMPERATURE AND THE 25C VAPOR

PRESSURE ISOTHERM

Theoretical relationship

As mentioned before, one of the objects of this investigation was toestablish the relationship between melting point and vapor pressureso that the amount of water freezable at a given temperature could beestimated from sorption data alone. As pointed out in connection withFig. 8-1, at any given temperature below O C, the vapor pressure of theunfrozen evaporable water must be the same as that of ice at the existingtemperature. On the assumption that the ice exists as a pure, micro-crystalline phase under atmospheric pressure only, we can ascertainits relative vapor pressure at given temperatures from eq. (1) or (2). Theresults of such computations are plotted in Fig. 8-2. That curve showsthat at – 30 C, for example, the vapor pressure of ice is about 0.75 p,,where p, is the saturation pressure at – 30 C. As shown above, theamount of water freezable at, – 30 C is about the same as the amountfreezable in the toluene-filled dilatometer at – 15 C.

To estimate the point on the 25 C adsorption isotherm correspondingto a given relative vapor pressure at a lower temperature, we may usethe Kelvin equation (see Part 3):

()lnp/p.=-M$ ;+! . .....................r~

whereP/p, =

M=Vf =g, =

rl and r-z =R=

T=

Leth25 =h, =

U25 =at =

Then

in h2~ =

relative vapor pressure,molecular weight of the fluid,molar volume of the fluid,surface tension of the fluid,principal radii of surface curvature of the fluid,gas constant, andabsolute temperature.

P/P, at 298 K (25 C),pip, at temperature T,surface tension at 25 C, andsurface tension at temperature T.

_ 025 M(Vf)25

():+!

R298 r, r-.

(13)


where

T = the lower temperature, in deg. K, and the other symbols have thesame significance as before. Hence,

in hzs UZ6 T (2},)2s—=.- —— ,, ...,. ,. .,,.,, ,., ..,., ,in h, cr~298 (vf)~

. ..<. (14)

The ratio (Vj)2Sto (Vj)tvaries so little from 1.0000 over the temperaturerange involved here that it can be taken as unity at all temperatures.

The ratio of fJ25/C~can be evaluated from the relationship

u: = 75.64 – 0.1391t – 0.00003t2 (Ref. 12) . . . . . . . . . . . (15)

Solutions of this equation are given below in Table 8-9:

TABLE 8-9--SOLUTIONS OF EQ. (15)

nt CM

de:. C—Ut

—— — ——25 71.97 1,0000

0 75.64 0.9515

-4 76,19 0,9446–6 76.46 0.9413–8 76.75 0.9377

– 10 77.06 0.9339– 12 77.47 0.9290–15 77.79 0.9251

– 20 78.30 0.9192

– 30 79.54 0.9048

The above data, substituted into eq. (14), give the results shown inTable 8-10.

TABLE 8.1 o-SOLUTIONS OF EQ. (14)

de;. C

—o

–4–6–8

– 10– 12– 15

– 20

–30

273,1

269.1267,1265,1

263.1261,1258.1

253.1

243.1

h,from hz,

Fig. 8-2

1.000 1.000

0.958 0.9650.945 0.9530.927 0.939

0.908 0.9240.893 0.9110.86.5 0.890

0.823 0.859

0.746 0.806


According to the foregoing discussion, the amount of ice formed in

the dilatometer at – 15 C, for example, is about the same as that which

would form in the same sample exposed to air at – 30 C. Table 8-10shows that the water remaining unfrozen at this temperature wouldhave a relative vapor pressure of 0.806 at 25 C. Thus, if all the assump-

tions made above are valid, the amount of unfrozen water in a sampleat – 15 C in the dilatometer should be approximately the same as theevaporable water content of the same sample having a relative vaporpressure of 0.806 at 25 C. The extent to which the data bear out this

assumption will be shown after the empirical relationship has beenexamined.

Comparison of theoretical and empirical relationships

Consider a given sample in a dilatometer at – 15 C. It will contain a

certain quantity of unfrozen evaporable water in equilibrium with ice.We have already seen that to maintain equilibrium between the sameamount of unfrozen water and ice in the absence of toluene, the tem-perature would have to be – 30 C. At this temperature the ice, andhence the unfrozen water, would have a vapor pressure of 0.746 pa (seeFig, 8-2). According to Table 8-10, the corresponding vapor pressureat 25 C would be 0.806 p,. Similarly, for dilatometer temperatures of– 10 C and – 6 C, the corresponding vapor, pressures at 25 C would be0.859 and 0.911, respectively.

Table 8-11 gives the ratio of evaporable water, w, to V~ in samples atequilibrium with these pressures at 25 C. These data were obtainedfrom smooth isotherms, representing samples almost identical with thoseused in the freezing experiments. They represent the theoretical amountsof unfrozen water at clilatometer temperatures of – 6 C, – 10 C, and–15 c.

The experimentally observed amounts of unfreezable water are indi-

cated by the intercepts of the straight lines in Fig. 8-13 D, E, and F.These intercepts represent experimental averages, comparable with thegrand averages given in Table 8-11.

The two sets of figures may be compared in the following table:

IDilatometer Unfreezable water, ~/V~

temperature,deg. C Observed Theoretical Ratio

—— —.——— ——— .—–6 4.00 3.72 ~08– 10 3.70 3.25 1.13– 15 3,20 2.93 1.09


TABLE 8-11—RATIO OF EVAPORABLE WATER TO VmIN HARDENED PASTESREPRESENTATIVE OF THOSE USED IN FREEZING STUDIES

w/V~* at p/p, (25 C)Wolc indicated

&0.911 0,859 0.806

—. —_____ .—Cement 15754

—.—— .—0.33 28 3.35 3.050.33

2.853,10

0.45 E2.75

3,60 ::E0.45 90

3.003.45 3.10 2.90

Avg. 3.38 3, (){] 2.88

Cement 15756—.——— —— ————

0.32 28 4.10 3.450.32 90

3.053.45 3.05

0.452.85

4,40 3.700.45

3.20% 3.90 3,30 2.95

—— ——Avg. 3.96 3,38 3.01

—— ——. ——— ——— —Cement 15758 —

0.33 28 3.70 3.200.33

2.8090 3.35 2.95

0.46 282.70

3.80 3.35 3.050.46 90 3.70 3.25 2.90

Avg. 3,64 3.19 2,86————— __

Cemen~15761——— . . —

0.33 28 3.80 3.30 2.950.33 90 3.50 3,050.47

2.803.80 3.?’0 2.95

0.47 :: 3.55 3.20 2.90

Avg. 3.66 3.21 2.90

Cement 15763——— —.—. _—

0.32 28 4.25 3.65 3.250.32 90 3.45 3.05 2.750.44 28 4.35 3.65 3.250.44 90 3.85 3,25 2.85

——Avg. 3.98 3,40 3.02

——Grand Avg. 3.72 3.25 2,93

*W = ewiporable water, g/g cement; V~ = constant from 11.E.T. eq. A, gfu rement


This indicates that the observed amount of unfreezable water averagesabout 10 percent greater than the theoretical amount. Such a differencecould be due to the smallness of the ice crystals, which would tend tolower their melting point, Or it might be due to an error in the theoreti-cal figure arising from the assumption that the effects of temperaturechanges on the solutions in the paste are the same as for pure water.

The degree of agreement between the observed and theoretical valuesis such as to warrant estimating the amount of water freezable at a giventemperature from the 25 C isotherm,

EQUATIONS FOR ESTIMATING MAXIMUM FREEZABLE WATER FROM THENON-EVAPORABLE WATER .CONTENT

The maximum amount of water in a saturated paste that may befrozen at a given temperature maybe estimated from the non-evaporableand total water contents. The bases for such estimates are developed

below:

Eq, (9) may be writtenWf = W* — Uvm .

Since, for an average cement,V~ = 0.26 w. (Part 3, eq. (4)),

andw~=wt —wn,

thenWf = Wt –w~(l+0.26u) : . . . . . . . . . . . . . . . . . . . . . . . . .. (16)

Using the values of u given in eqs. (10), (11), and (12), we obtain(W~).~0=w, –2.04w~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(17)(w~).]oo=w, –l.96w~ . . . . . . . . . . . . . . .. . . . . . . . . . . . . ..(18)(wj)-lso =w, –1.83wm . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(19)

The above equations may be used when the total water content of thesaturated paste is known. When only the original water-cement ratiois known (corrected for bleeding), the relationships developed below maybe used,

On the assumption that the volume of the hardened paste is the sameas that of the fresh paste after bleeding, we may write.

wo=wtv~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (20)Since

V~= 1 – 0.279 ~ (Part 5, eq. (8)),

Wo= Wi – 0.279 W. . . . . . . . . . . . . . . . . . . . . . . .......... (21)

Substitution into eq. (16) giveswf = Wo+ 0.279wm — w.(1 + 0.26u)

=w. –(0.721 +0.26u)w~ . . . . . . . . . . . . . . . . . . . . . .. (22)

966 JOURNAL OF THE AMEI?ICAN CONCRETE INSTITUTE April 1947

Again using values of u from eqs. (10), (11), and (12) we obtain

(W,).(y =wJo-1.76w~ ; . . . . . . . . . . . . . . . . . . . . . . . . . . ..(23)(Wj)-lOO= ~O–l.68W~ ; . . . . . . . . . . . . . . . . . . . . . . . . . .. (24)(w,).l~O=wO–1.55 w,, . . . . . . . . . . . . . . . . . . . . . . . . . . ..(25)*

It should benoted that all these empirical equations give the amountsof water freezable in the dilatomcters, with the saturated paste in contactwith toluene, As mentioned before, the temperature drop requiredto freeze equal amounts of water in the absence of toluene is, theoreti-cally, two times the temperature in degrees C indicated, i.e,, —12 C,– 20 C, and – 30 C, respectively.

SATURATED PASTES CONTAINING NO FREEZABLE WATER

For the range of temperatures over which the equations derivedfrom eq. (9) were found to apply, it seems that the freezable water con-tents of some saturated hardened pastes should be zero. For example,eq. (25) indicates that Wf = O when w. = 1.55 w.. Thus, when hydra-tion has proceeded to the point where win/c = 0.2, wJ/c = O when we/c =0.2 X 1.55 = 0.31. In other words, according to eq. (25), a saturatedpaste having an original water-cement ratio of 0.31 would contain nowater freezable in the dilatomcter at —15 C after w./c has increased to 0,2,This may not be literally true since all saturated pastes contain a quan-tity of evaporablc water equal to at least 4V~, all of which is theoreti-cally freezable at about – 78 C, and parts are freezable at higher tem-peratures, as indicated by the vapor pressure isotherm for gcl water.However, in pastes in which the gel fills all available space (we = 4VW)freezing may not occur because of the difficulty of starting crystalliza-tion in such extremely small spaces. If ice did form in the dilatometerexperiment with such a paste, it probably would form as a separate phaseon the surface of each granule, This remains a matter for speculation,since no tests were made on pastes containing no capillary space.

Whether or not freezing can occur within such pastes, the quantitythat could form at ordinary freezing temper~tures is so small that it canbe regarded as zero from the practical point of view.

FINAL MELTING POINTS FOR SPECIMENS NOT FULLY SATURATED

As would be expected, the final melting point, that is, the highesttemperature at which ice can exist in a specimen of hardened paste, islower the lower the degree of saturation of the specimen. This is shown

*NOte:Anequnt,imsimilarto eq. (25)WaSgivm in an earlier publication, Proc. AC1 v, 41, p. 245, orP.C.A. Research Laboratory Bulletin 5, eq. (3). ‘Ilmt equation was based on a preliminary analysis of thedata presented in thk paber. The difference between the two equations is due mainly to a difference inthe assumed relationship between w. and to’. In the earlier equation; the relationship for the particularsamples used in the freezing studms was used. In this paper, eq. (23) was used instead. For some unknownreason the difference between the w. and w values for the samples used in the freezing study were ahnormal-lY high.


Fig. 8-1 4—Meltingcurves for saturatedand partially satu-rated pastes

\] 04

\l-20 -18 -16 -14 -!2 -10 -8 -6 -4 -2 0°

Temperature, “C

by the data plotted in Fig. 8-14. The upper curve represents a fullysaturated specimen, and the other two lesser degrees of saturation, as

indicated. The results agree approximately with eqs. (10), (11), and (12)r

which were derived empirically from tests on saturated samples.

For the sample represented by the middle curve, the amount of

evaporable water was 3.9 V~. By eq, (10), the amount of water freezable

at —6 C should be

()Wf= 3.9 – 4.0,

K -@

This indicates that none of the water present was freezable at – 6 C,which agrees roughly with the observed fact that the final melting pointwas --6.5 C.

Similarly for the lowest curve, the amount of water freezable at – 15 Cis indicated by eq. (14) to be 0.3 V~. The experimental data show thefinal melting point to be – 15.5 C. This result may be considered asindicating substantial agreement between the equation and the obser-vation.

SUMMARY OF PART 8

(1) Dilatometer studies were made on neat cement and cement-

silica pastes to determine the amounts of ice that can exist in hardened

paste under given conditions.

(2) Under the conditions of these tests, freezing did not occur on

cooling until after the saturated samples had been supercooled 5 to

12 c.(3) When freezing occurred, further cooling caused more ice to form.

(4) Raising the temperature step wise from – 20 to +2 C or highershowed that the melting was progressive. This result is as would be


predicted from the known effects of dissolved salts, adsorption, and

capillary tension or, the vapor pressure of the evaporable water.

(5) The final melting point in a saturated paste (temperature at

which the last increment of ice disappears) ranged from – 0.05 to – 1.6 C.

The temperature seemed to depend on the alkali content of the cement,the higher the alkali content, the lower the final melting point.

(6) The ice is believed to form in the capillary space outside the gel.

It is unlikely that the gel water freezes in place, although, at low tem-

peratures, it contributes to the ice.

(7) The maximum amount of water, tot, that can freeze at a given

temperature, can be estimated from the total cvaporable water content,w,, and l’~ by use of the following empirical equations:

(w,).,. = w. – 4.0Vm(W,)-lly = w. – 3.7vm(W,).MO = W, – 3.2V~

(8) The maximum freezable water content may be estimated in termsof the total water content, wI, and the non-evaporable water content,

wn, as follows:

(Wf).~. = W, – 2.04wn(wf)-lo. = W, – 1.96w.

(W,)-~~O= W, – 1.83wn

(9) The maximum freezable water content can be estimated from the

original water content, w., and w., as follows:

(W,)+. = Wo – 1.76w.(Wf)-l(y = w. – 1.68W.(W,)-ly = w. – 1.55wn

(10) The temperatures given in the above equations are for freezing

in a toluene-filled dilatorneter, For freezing in air, the same equations

apply (theoretically) if the temperatures (deg. C below zero) are multi-

plied by 2.

(11) Under freezing conditions differing from those used in these

experiments, the amount of freezable water may be less than the amountindicated in the above equations, owing to the hysteresis in the sorption

isotherms.

(12) The compositions of pastes that can contain practically nofreezable water can be estimated from the above equations.

(13) The maximum amount of water freezable at a given temperaturecan be estimated from the 25 C isotherm with the aid of Fig. 8-1 andTable 8-10.

(14) When a paste is not fully saturated, the final melting point islower than that for the same paste when saturated. The maximum


amount of freezable water in a paste at a given degree of saturation can

be estimated approximately from the 25 C sorption isotherm and Fig.

8-1.

REFERENCES

(1) E, W. Washburn, Monthly Weather Review v. 52, p. 488 (1924); InternationalCritical Tables v. 3,210 (1928).

(~) p. Kubelka, z. Electrochem. v. 38, p. 611 (1932).(3) H. E. von Gronow, Zement,v. 25, pp. 485-90 (1936).(4) H. W. Foote, B. Saxton, J. Am. Chem, A’oc.v. 39, pp. 627-30 (1917).(5) I. D. Jones, R. A. Gortner, J. Ph~s. Chem. v. 36, pp. 387-436(1932).(6) G. J. Bouyoucos,Mich. Agr. CollegeExp. Station Tech. Bull. No. 36 (1917);

also,~. Agr. Research v. 8 ,pp. 195, 217 (1917).

(7) L. T. Alexander, T. M. Shaw, and R. J. Muckenhirn, Proc. i%il S’ci. Sot. Am.v. 1, p. 113 (1937). Also, L. T. Alexander and T. M. Shaw, J. Phys. Chem. v. 41, p. 955(1937).

(8) S. L. Meyers, Znd. Eng. Clzem. v. 32, p. 1107 (1940).(9) J. S. Burlew, J. ~m. Chem.Sot. v. 62, p. 690 (1940).

(10) N. E. Dorsey, Properties of Ordinury Water Substance (New York: ReinholdPublishing Corp., 1940), Table 100.

(11) G. Jones and F. C. Jelen, J. Am. Chem. Sot. v. 57, p. 2532 (1935).(12) Ref. 10, p. 514.


Part 9. General Summary of Findings on the Properties of Hardened

Portland Cement Paste

CONTENTS

Intr~UCtiOn . . . . . . . . . . . . . . . . . . . . . , .,.,........,......,......972

General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...972Paste porosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...973

Capillary pores . . . . . . . . . . . . . . . . . . . , ..,,.,,.,.....,.......973Gel pores, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..g75

Surface area of the solid phase in hardened paste. ,.. . . . . . . . . ...976Mean size ofgel pores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...976Size of capillary pores . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...977Permeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...977Absorptivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...978Properties ofwater in hardened paste. . . . . . . . . . . . . . . . . . . . . . . . ...978

Non-evaporable water . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . ...978Gel water,,.......,,..,....,,,.. , .,...,........,........979Capillary water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...980

Physical state of the hydration products. . . . . . . . . . . . . . . . . . . . . . ,981Energy changes of hydration, adsorption, and capillary condensa-tion . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . ...982

Heat of hydration . . . . . . . . . . . . . . . ., .,...............,,..,.982Total netheat of surface adsorption. . . . . . . . . . . . . . . . . . . . . ...982Netheat of capillary condensation. . . . . . . . . . . . . . . . . . . . . . ...982Total netheat of adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...982Enthalpy change of adsorption,.. . . . . . . . . . . . . . . . . . . . . . . . ...982Decrease in free energy . . . . . . . . . . . . .,,...,......,...,.,...983Decrease in entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..9s3Energy of binding of water in hardened paste . . . . . . . . . . . . ...983

Volume ch&nge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..9s4Mechanism ofshrinking andswelling. , ., . . . . . . . . . . . . . . . . ...984Swelling pressure . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..9MCapillary tension, . . . . . . . . . . . . . . . . . ., . . . . . . . . . . . . . . . . . . . ..9fj5Relationship between change in volume and change in watercontent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...985Contraction in volume of the system cement + water . . . . . ...986Self-desiccation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...986

Capillary flow and moisture diffusion . . . . . . . . . . . . . . . . . . . . . . . ., .987Effect of temperature changes at constant moisture content . . . . ...988

Effect on swelling. , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...988Effect on diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...988Combined eflect of stress, strain, changes in humidity, andtemperature gradients.....,.,,.. . . . . . . . . . . . . . . . . . . . . . . ...988

Factors governing the extent and rate of hydration of portlandcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , ...,..,988

Extent of hydration ., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...988Rate of hydration . . . . . . . . . . . . . . . . . .,, . . . . . . . . . . . . . . . . . ...989

Relation of paste porosity to compressive strength. . . . . . . . . . . . ...989Freezing ofwater in hardened paste... . . . . . . . . . . . . . . . . . . . . . . . ..9Wl

97s! JOURNAL OF THE AMERICAN CONCRETE INSTITUTE April 1947

INTRODUCTION

In this, the final part of the paper, the concepts concerning the char-acteristics of hardened paste that have emerged from this study are setdown in brief, It is not implied that the concepts are new and unique.

On the contrary, they agree in general with previously expressed viewsof those who have believed the colloidal state of the hydration products

to be a dominant characteristic of the hardened paste. However, it isnow possible to consider these characteristics in more detail and on a

quantitative or semi-quantitative basis,

This summary includes only the facts and relationships that can beset down with a minimum of discussion, The reader should not dependon this part alone for an understanding of the subject, since the finerpoints of interpretation and many significant details and illustrativegraphs are omitted.

Some of the relationships given below do not appear in the precedingparts of the paper, but they are derived from relationships alreadygiven,

In the preceding parts of this paper the sequence of topics was deter-mined according to the requirements for an orderly development of con-cepts and interrelationships between variables. In this summary it isassumed that the reader is familiar with the background material and thesubject is presented, as far as possible, in the form of an analysis of theproperties of hardened paste.

The following should be noted carefully before proceeding with thesummary: All the data and relationships discussed below pertain onlyto specimens cured continuously at about 70 F. Without modification,the y do not apply to other curing conditions.

GENERAL

Many of the technically important properties of concrete can beattributed to the peculiar nature of the hydration products of portlandcement. The hardened paste is considered to be not a continuous, homo-geneous solid, but rather to be composed of a large number of primaryunits bound together to form a porous structure. The chemical con-stitution of the units of this structure is not definitely known. However,it appears that many significant characteristics are dependent notprimarily on chemical constitution but rather on the physical state ofthe solid phase of the paste and its inherent attraction for water.

The extreme smallness of the structural units of the paste, the small-ness of the interstitial spaces, and the strong attraction of the solidunits for water account for the fact that changes in ambient conditionsare always accompanied by changes in the moisture content of the hard-


ened paste; moreover, these factors account for the changes in volume,strength, and hardness that accompany changes in moisture content.They also account for the peculiarities of the relationship betweenice-content and temperature when saturated or partially saturatedpaste is cooled below the normal freezing point of water.

Various findings concerning the properties of the solid phase in hard-ened paste, and the interaction between the solid phase and evaporablewater, are summarized in the following sections.

PASTE POROSITY

The pores in hardened portland cement paste are here considered tobe the space in the paste that may be occupied by evaporable water.Evaporable water is defined as that which exhibits a vapor pressuregreater than about 6 X 10-4mm Hg at 23 C. It is roughly equivalent-tothe amount lost when a saturated paste is oven-dried at about 105 C.

The pores in a paste (exclusive of entrained air) are of two kinds:capillary pores and gel pores. The relative proportion of each kind canbe determined from suitable data and the relationships given below.

Capillary pores

Before hydration begins, and during the time when the paste remainsplastic, a cement paste is a very weak solid held together by forces ofinterparticle attraction. These forces probably act across thin filmsof water at points of near-contact between the particles. The water-filled spaces between the particles constitute an interconnected capillarysystem. After the plastic stage, when the final reactions of hardeningbegin, the capillary channels of the fresh paste tend to become filled withsolids produced by the reaction between water and the constituents ofcement. This process rapidiy reduces the volume and size of the capil-

laries, but apparently does not destroy their continuity. The volume of

the capillaries at various stages of hydration can be estimated withsatisfactory accuracy from the relationships given below.

Before hydration starts,

pc= w, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)

where p. = volume of capillary pores, andw = volume of water. *

Eq. (1) is correct only for an instant after the cement and water aremixed. Solution and reaction begin at once, the average rate during

the first 5 minutes being higher than during any subsequent 5-rein.period. Within the initial 5-rein. period, the rate of reaction decreases

*In this and the following equations. cgs uni,~ are interided and the same symbol is used for either weight(grams) or volume (cc) of free water. That M, w (general term for free water), W* (net free water afterbleeding), and w. (capillary water) all are assumed to have, a SP~CIfiC volume of 1.0 and thus may represent;;it:;. grams m CC. The as8um@10n that specific vOlum~ w Unity lntrOduoea no error of practical impm-


abruptly and becomes very low. This low rate persists, under normal,controlled laboratory conditions, for a considerable period, usually aboutan hour. If the paste has been stirred continuously during the period ofrapid initial reaction, or if it is restirred at the end of that period, it willremain plastic during the ensuing, relatively dormant period. If leftundisturbed, the paste will “bleed” and its volume will thereby bediminished. After bleeding, its porosity (now equivalent to the remainingwater-filled space, entrained air neglected) will be approximately

Ilc=w–(v l r-w ), . . . . . . . . . . . . . . . . . . . . . . . . . . ...(2)where w. = original water content after bleeding, grams (or cc),

VB = total volume of solid phase including increase due tohydration and pores in the gel,

c = weight of cement,v. = specific volume of the cement, i.e., the volume of a unit

weight,(VB – CV.) = increase in volume of the solid phase due to hy-

dration.

The volume of the solid phase at any stage of hydration can be evalu-ated as follows:

~B=cv, +0.86(l +4k)zv~, . . . . . . . . . . . . . . . . . . . . . . ...(3)where 0.86 = mean specific volume of the non-evaporable water and

gel water,ii = a constant characteristic of the cement, and

W. = weight of non-evapora”ble water. *

Eliminating VB and CV.between eqs. (2) and (3) gives

p.=wo– 0.86(l+ 4k)w~ . . . . . . . . . . . . . . . . . . . . . . . ...(4)

k will range from 0.24 to 0,28 among different cements, but for an average

Type I cement, k = 0,255 (see Part 5) and eq. (4) becomes

pc=wo–1.74wn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(5)

At early stages of hydration, that is, during the first few hours, when

w. is very small, eqs, (4) and (5) probably do not represent the facts veryaccurately because the numerical constants were evaluated from dataobtained over a range of ages during which reactions involving gypsum

could not occur. Therefore, the constants are probably not quite correct

for periods during which gypsum-reactions are taking place to an ap-preciable extent.

From eq. (4) it follows that capillary porosity is zero when

0.86(1 + 4k)w. = w.,

or for an average cement, when 1,74wn = w. (SCCeq. (5)). For example,

when wn/c = 0,2, pc = O if we/c is equal to or less than 0.2 X 1.74 = 0.35.

*Non-evaporable water ia that having a vapor pressure equal to or leas than about 6 X 10-~ mm HO at23C, It includes chemically combined water.


The highest possible water-cement ratio at which P* can be made zeroby prolonged curing depends on the magnitude of the highest possiblevalue of w. and on k. Both (w.)m.. and ~ depend on the characteristics

of the cement. (w~)~~. depends principally on the degree to which thecement approaches complete hydration, which, in turn, depends prin-

cipally on the proportion of the cement that is made up of particles finerthan about 50 microns. (The coarsest particles fail to hydrate completely

even though the wet-curing period is long. ) It is related also to thecomputed chemical composition, as shown by the following relationship

for WWafter six months of water-curing at 70 F.*

Wn/C = 0.187 (C3S) + 0.158 (C2LS)+ 0.665 (C3A) + 0.?13(C4-4F),. . . . (6)

where the symbols in parentheses represent the computed weight-pro-portion of the compound indicated. This relationship may be considered

to represent the average value of w~/c when the cement is not far from

its ultimate degree of hydration, provided that wJc is not less than about

0.44 and that the specific surface of the cement is betwden 1700 and 2000,

by the Wagner turbidimeter. For finer cements (wn/c)~a. will be higher,

but not much higher. For coarser cements, it Will be lower to a degree

about proportional to the residue on the 325-mesh sieve. For cementshaving a specific surface of about 1800 (Wagner), (w~/c)~~. ranges from

about 0.20 to 0.25, the higher value corresponding to cements relativelyhigh in C3S and CSA.

Likewise, k is related to computed compound composition as follows:

k = 0.230(CS8) + 0.320 (C,S) + 0.317 (C3A) + 0.368 (C4AF) . . . . . . (7’)

This relationship holds for any age with accuracy sufficient for mostpurposes.

With an average Type I cement, capillary pores will be present, evenat ultimate hydration in any paste having an original water-cement ratiogreater than about 0.44 by weight.

Gel pores

The quantity (VB – rz) appearing in eq. (2) and implicitly in eq. (4)is the increase in volume of the solid phase including the pores that are

characteristic. of the hydration products, presumably the pores in the gel.Consequently, the total porosity of the paste is greater than that givenby the above equations, That is,

f)~=p, +fl o, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(8)

where p; = volume of total pores,p, = volume of gel pores, and

p, = volume of capillary pores.

*This empirical relationship was not given in receding parts of this paper. It was establi,qhed by thexmethod of least squares umng about 100 ]tems of ata.


The volume of gel pores is given approximately by the following relation-ship:

pO=0.9X 4V~=3.6Vtm,. ..,.... . . . . . . . . . . . . . ... ...(9)

where 4V~ is the weight of water that would saturate the gel, Vm is afactor proportional to the surface area of the gel (see eq. (12)), and 0.9is the mean specific volume of the water in saturated gel.

For any given cement,

Vm=lcwn, . . . . . . . . . . . . . . . . . . . . . . . . .!, .,, ., . . . . . . ..(10)

where k is the same constant that appears in eqs. (4) and (7), Hence, foran average cement, for which k = 0,255,

pO=0,92ww, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. (11)

SURFACE AREA OF THE SOLID PHASE IN HARDENED PASTE

The surface area of the solid phase in hardened paste is computedby the following relationship

s=(35.7x lo’)vm, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(12)

where S = surface ‘area of solid phase, sq cm, andV~ = grams of water required to forma complete monomolecular

adsorbed layer of water on the solid surface.

Since Vm = kwn, and since k = 0.255 for an average cement, the surfacearea of a hardened paste made from an average cement can be obtainedfrom W. by using the following relationship:

S = (35,7 X 106)0.255w.=(9.1 xlo’)wn. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(13)

In a typical paste, w./c = 0.6, the surface area per unit volume of pastereaches about 2.4 X 106 sq cm at ultimate hydration.

Since the internal surface area of the paste is predominantly that ofthe gel, Vm is here usually considered to be proportional to the surfacearea of the gel, SO.

MEAN SIZE OF GEL PORES

The mean diameter of the gel pores is probably between 2 and 4 timesthe hydraulic radius. The hydraulic radius is evaluated as follows:

mO=p~l~SO, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (14)

where mg = hydraulic radius of gel pores, cm,p, = volume of gel pores, cu cm, andS, = surface area in the gel, sq cm,

Thus, from eqs. (9) and (12),

3.6vm=10 XIO-8cm . . .. c. ...<..... (15)

‘o = (35.7 x 106) Vtn


Hence, the mean diameter of the gel pores is from 20 to 40 Angstromunits.

SIZE OF CAPILLARY PORES

The mean diameter of the capillary pores cannot be determined fromdata now available. However, results of absorptivity tests indicate thatthe capillary pores are very much larger than the gel pores, exceptperhaps in pastes in which the gel nearly fills the available space.

PERMEABILITY

A saturated, hardened paste is permeable to water. Under a givenpressure gradient and at a given temperature, the rate of flow is a function-of the effective hydraulic radius of the pores and the effcctivc porosity.The general theoretical equation for this function! called the coefficientof permeability, is

Kl=50x10-’4 V~(N–k1)3, . . . . . . . . . . . . . . . . . . . . ..(16)

in which ~1 = coefficient of permeability to water, in ft pcr SCC,

V~ = weight of water requirccl for the first adsorbed layer, g percc of paste,

N = ratio of total evaporablc water to Vm, andkl = a constant interpreted as the number of layers of immo-

bile water per unit of solid surface, or the differencebetween total and effective porosity.

Indications of a limited amount of data arc that eq. (16) would giveresults in reasonable agreement with experiment (Ruettgers, Vidal, andWing) only for pastes in which N is not greater than about 4, that is, forpastes containing no capillary space. For such pastes, the theoreticalpermeability is given by

K, = 2.0 x 10-1’(1 – Cw)0.45 s Cv. s 1.0

where c = cement content, g per cc of paste, and

v, = specific volume of cement.

This result indicates that cement gel has about the same degree ofpermeability as granite (Ruettgers, Vidal, and Wing).

For pastes containing much capillary space outside the gel, actualpermeability exceeds the theoretical by a wide margin. This is believedto indicate that in such pastes the flow is predominantly in the rela-tively large capillary pores outside the gel.

The permeability of concrete is generally greater than can be accountedfor from the actual permeability of the paste (Ruettgers, Vidal, andWing). This indicates that the water is able to flow through the fissures


that develop under the aggregate during the bleeding period and thus topartially by-pass the paste.

ABSORPTIVITY

The characteristic rate at which a dry specimen absorbs water ishere called the absorptivity of the specimen. The absorption during thefirst 30 to 60 minutes follows the relationship

q/A= (Kot)~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(17)

in whichq)A = the amount of water absorbed per unit area in time t,

andK. = coefficient of absorptivity.

An empirical relationship was found between K. and capillary porosity.

That is,

[ 1K~=j WO-0,86(l+4k)W~ , . . . . . . . . . . . . . . . . ..(18)

where the quantity in brackets is the capillary porosity,

W. = water content of original mix, after bleeding, g (or cc)per cc of specimen,

W. = non-evaporable water, g per cc of specimen, andk = a constant characteristic of the cement. (See eq. (3),

(7), and (10).)

The quantity 0.86(1 + 41c)Wnis the increase in volume of the solidphase due to hydration, When it equals W., capillary porosity is zero.The experimental curve showed that Ka was also zero, or nearly so, atthis point. Thus the data show that the initial absorption of waterby a dried specimen takes place almost exclusively in the capillary spacesoutside the gel.

PROPERTIES OF WATER IN HARDENED PASTE

In a saturated, hardened cement paste, three classes of water arehere recognized:

(1) non-evaporable water,(2) gel water, and(3) capillary water.

Non-evaporable water

Non-cvaporable water is defined as that part of the total that has avapor pressure of not over about 6 X 10-4 mm Hg at 23 C. It is a con-stituent of the solid material in the paste. Some of it exists as OH groupsin Ca(OIl) z; some, probably as water of crystallization in calcium sul-foaluminat.e. The rest is combined in the solid phase in ways not yet


known. Of this part, some may be combined chemically with thehydrous silicates and hydrous alumina-bearing compounds; some may beheld by van der Waal forces, that is, physical forces.

For purposes of volume-analysis, the non-evaporable water may betreated as an entity. Its volume added to that of the original cement givesthe absolute volume of the solid phase in the paste. Thus,

Vs=cv, +wnzb, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. (19)

where VS = absolute volume of solid phase in the paste,c = cement content of the paste,

W. = non-evaporable water content of the paste,v. = specific volume of the cement, andV. = mean specific volume of the non-evaporable water.

The specific volume of the non-evaporable water is an empirical factorthat will account for the observed increase in the absolute volume of thesolid phase per gram increase in amount of non-evaporable water. Itsvalue is about 0.82,

Gel water

The gel water is that contained in the pores of the gel. The pores inthe gel are so small that most if not all the gel water is within the rangeof the van der Waal surface forces of the solid phase. This is indicatedby the fact that the mean specific volume of the gel water is about 0.90.

The vapor pressure of the gcl water at a fixed temperature is a functionof the degree of saturation of the gel. The lowest pressure just exceeds6 X 10-4mm it 23 C, which is the highest pressure of the non-evaporablewater. The highest pressure is nearly, but not quite, equal to that ofpure water in bulk at the same temperature; the difference is due prin-cipally to the alkali hydroxides in solution. The vapor pressure at agiven intermediate degree of saturation may be any value between limitsfixed by the manner in which the existing water content was reached. Itwill be a maximum if the existing water content was reached by con-tinuous adsorption, beginning with a dry sample. It will be a minimumif the water content was reached by continuous resorption, starting witha saturated sample. Intermediate pressures will be found if the givenwater content was reached by adsorption after partial resorption, or if itwas reached by resorption after partial saturation by adsorption. Thesepeculiar relationships are due to hysteresis in the sorption isotherm.They are found only for water contents that fall within the hysteresisloop. The limits of the loop are not now definitely known.

The weight of gel water in a saturated paste is equal to 4V~, whereV~ is the weight required to form a complete mononlolccular adsorbedlayer on the solid phase. For volume analysis of the paste, the weight of

980 JOURNAL OF THE AMERICAN CONCRETE lNSTITU-I_E

the gel water may be used to determine the total volumeabsolute volume) of the solid phase in the paste. Thus,

VB=VS+0.9W0 =VS+3.6V~,. . . . . . . . . . . .

April 1947

(rather than

. . . . . . . , (20)

where VB = total volume (or bulk volume) of the solid phase,

VS = absolute volume of solid phase, andw~ = grams of gel water per cc of saturated paste = 4V~ .

Capillary water

Like the gel water, the capillary water is really a solution of alkaliesand other salts. The capillary water is that which occupies space in thepaste other than the space occupied by the solid phase together withcharacteristic pores of the gel. That is,

Wc=}7t —VB ) . . . . . . . . . . . . . . . . . . . . . . . . . .. (21)

where w, = volume of capillary water,

V, = over-all (total) volume of saturated paste, exclusive ofcavities,

VB = bulk volume of solid phase in the paste.

Practically all the capillary water lies beyond the range of the surface

forces of the solid phase, Hcncc, in a saturated paste, the capillary

water is under no stress and its specific volume is the same as the normal

specific volume of a solution having the same composition as the capillary

water.

In a partially saturated paste, the capillary water is subjected to tensilestress, This stress is due to curvature of the air-water interface and thesurface tension of the water, The magnitude of the stress is given by thefollowing equation:

F=–~~, ln p/p, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. (22)

where F = fOrCf3 of Capih’y kIM3iOn,

R = gm constant,.?1 = molecular weight of water,~)j = specific volume of water,p = vapor pressure of capillary water at the existing tempera-

ture,

P, = s~turation pressure Of water at the existing temperature, andin = natural logarithm.

The vapor pressure of the capillary water depends on the degree ofsaturation of the paste and on the factors arising from hysteresis discussedin the preceding section. However, if the existing vapor pressure isreached by continuous adsorption from the dry state, capillary waterdots not existin the paste at pressures below about 0.45 p8.


Since at vapor pressures greater than 0.45p, and less than p., thecapillary water is present and under tension, its specific voluime mustbe greater than 1.0 and a function of F of eq. (22). No attempt has beenmade to verify this experimentally,

Some of the gel water may be fundamentally the same as capillary

water. The distinction used here is made on the basis of relationship to

the solid phase. The quantity of gel water always bears a fixed ratio to

the quantity of hydration products, whereas the quantity of capillary

water is determined by the porosity of the paste.

PHYSICAL STATE OF THE HYDRATION PRODUCTS

Microscopic observation of hardened paste indicates that only Ca(OH),crystals and unhydrated residues of the original cement grains can readilybe identified. Other microcrystalline constituents, particularly calciumsulfoaluminate, may be present in small amount but are generallyobscured by the abundant “amorphous” constituents.

The size and volume of the pores in hardened paste indicate that thesolid material is finely subdivided, though the solid units are obviouslybonded to each other. If the units were equal spheres, the sphere diam-eter would be about 140~. Since the computations leading to thisfigure included the volume of microcrystalline constituents, the unitsof “amorphous” material must be somewhat smaller than just indicated.

The size indicated is definitely in the colloidal size-range. Since a gel is

defined as a coherent mass of colloidal material, it follows that the prin-

cipal constituent of hardened paste is a gel, here called cement gel.

The cement gel is composed of hydration products that contain allthe principal oxides: CaO, L%02,A1203j. and FezOs This is shown by thefact that the total surface area of the solid phase is related to the com-

puted cement composition in the following way:

v.— = 0.’230(C3~)+ 0.320 (C,S) + 0.317 (C,A) + 0.368 (C,AF) , . . . (23)w.

where the symbols in parentheses represent the computed weight-fraction

of the compounds indicated. The similarity of the numerical coefficients

and the magnitude of particle size given above show that all constituents

either may be present in a single complex hydrate of high specific surface

or they may be constituents of two or more different hydrates having

similar specific surfaces. The relative smallness of the coefficient of CVS

is in line with the fact that this compound hydrolyzes to give micro-

crystalline (low specific surface) Ca(OiY) z as one of it,s reaction products.


ENERGY CHANGES OF HYDRATIONADSORPTION, AND CAPILLARY CONDEN!$ATION

Heat of hydration

When cement and water react, the total amount of heat evolved isdirectly proportional to the total amount of non-evaporable water in thepaste, Thus,

total heat of hydration = constant X W. .

The proportionality constant varies with cement composition. For alltypes ,of portland cement, it ranges from 485 to 550 calories per gram ofnon-evapomble water.

The total heat of hydration is the sum of the heat of combination of thenon-evaporable water, the net heat of adsorption of water on the surfaceof the solid phase, and the net heat of capillary condensation,

Total net heat of surface adsorption

The net heat of surface adsorption is the amount of heat in excess ofthe normal heat of liquefaction that is evolved when water vapor in-

teracts with the solid phase. For all cement pastes,

Q,~=472V~calories (aPprox.), . . . . . . . . . . . . . . . . . . . . ..(24)

where Q,~ = total net heat of surface adsorption when the paste ischanged from the dry to the saturated state.

Net heat of capillary condensation

Adsorption at low vapor pressures causes the solid phase to becomecovered with a film of water having a surface area presumably equal tothe covered area of the solid phase. At pressures above 0.45p, adsorptionis accompanied by capillary condensation which progressively diminishesthe exposed water-surface as the pressure is raised. The heat evolvedfrom the destruction of water-surface is the net heat of capillary condensa-tion. When a paste is changed from the dry to the saturated state,

Q,~ = 100V~, calories (approx.), . . . . . . . . . . . . . . . . . . . . ..(25)where Q,~ = total net heat of capillary condensation.

Total net heat of adsorption

The total net heat of adsorption is the sum of the total net heat of

surface adsorption and the total net heat of capillary condensation. That

is,

Q.t = 472vm + loov~ = 1572V~, dories (approx.),. . . . (26)

where Q~t = total net heat of adsorption. This amounts to about fj70

ergs per sq cm of solid surface and is about the same as the heat ofimmersion of various minerals, particularly the mineral oxides, in water.

Enthalpy change of adsorption

The total net heat of adsorption (eq. (26)) is practically equal to the

decrease in enthalpy of the system. The decrease in enthalpy represents


the sum of the decrease in free energy and the decrease in unavailable

energy. Thus,

–AH=– AG– TAB, . . . . . . . . . . . . . . . . . . . . . . . . . .. (27)

where — AH = decrease in enthalpy,— AG = decrease in free energy,— AS = decrease in entropy,

T = absolute temperature, and— TAS = decrease in unavailable energy.

Decreasein free energy

Shrinking and swelling, moisture diffusion, capillary flow, and allother effects involving changes in moisture content of the paste at con-stant temperature are due to the free surface energy of the solid phase,or to the free surface energy of the water, or to both surface energies.All such effects are accompanied by a decrease in free energy and, inthis case, a decrease in entropy, but the forces producing these effects arederived solely from the free energy,

The decrease in free energy can be expressed as a function of the ratioof the vapor pressure of the adsorbed water to that of free water at thesame temperature without regard to the nature of the underlying solidphase.

— AG = – 75,6 loglOp/p,, cal per g of water . . . . . . . . . . (28)

It thus varies from zero when p = p, to a very large value when p is verymuch smaller than p,.

Decreasein entrapy

A change in entropy denokes some sort of internal change in the sub-stance or substances involved in a reaction. In this case, the change is

assumed to take place solely in the water as it changes from the free tothe adsorbed state.

The decrease in entropy was estimated for adsorption over the pressurerange p = o.05pa to p = o.5p,, The decrease ranged progressively

from – AS = 0.22 cal/g/deg at P = 0.5P, to 0.50 cal/g/deg at P = 0.05P,.

The magnitude of – AS indicates that some of the water is changedby adsorption in this range of pressures more than free water is changed byfreezing under ordinary conditions and as much as or more than freewater is changed by becoming water of crystallization. Water adsorbedat p = 0.05P, undergoes a change as great as the change from normalwater to hydroxyl groups chemically combined in Ca(OH) z.

Energy of binding of water in hardened paste

The net heat of adsorption (decrease in enthalpy) is a measure of the

energy that must be supplied to restore adsorbed water to the normalliquid state.


The maximum energy of binding of the adsorbed water is estimated atabout 400 cal/g of water, The average energy of binding of the firbt com-plete adsorbed layer is estimated at about 300 cal/g of water. Theaverage energy of binding of the gel water,is about 143 cal/g of gel water.These figures are probably somewhat too low inasmuch as the effect ofadsorbed air was neglected.

These values indicate that most of the non-evaporable water is lessfirmly bound than the water in Ca(OH) z for which the energy of binding is847 cal/g of water,

The capillary water cannot be considered “bound” in the same sense

as the non-evaporable water and gel water. The energy required toremove all the capillary water from a saturated paste, if that could be

done separately, would be 100V~ calories, regardless of the amount of

capillary water in the paste.

VOLUME CHANGE

Mechanism of shrinkage and swelling

Cement paste shrinks and swells as the cement gel loses or gains water.Swelling results when the surface forces ~f the solid phase are able todraw water into the narrow spaces between the solid surfaces. Themagnitude of the swelling can be accounted for by assuming that thetotal volume change that occurs when a dry” specimen is saturated isdue to the increase in spacing of the solid surfaces required to accommo-date a monomolecular layer on each opposing solid surface.

Shrinking results when water is withdrawn from the gel. It is prob-ably due to the solid-to-solid attraction that tends to draw the solidsurfaces together, though capillary tension and elastic behavior’ may alsobe involved.

By this theory, volume change is regarded as being the result of anunbalance in the forces acting on the adsorbed water. These forces arethe solid-to-liquid attraction and capillary tension. When the solid-to-liquid attraction and capillary tension are equal, the volume of the geiremains constant.

Swelling pressure

Swelling pressure is the force that would be just able to prevent waterfrom entering the gel. For isothermal swelling it is related to the mag-nitude of the free-energy change that would occur if the water enteredthe gel, Thus,

AP=AG/vf, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. (29)

where AP = increase over existing external pressure required to preventswelling,

AG = increase in free energy of adsorbed water when swellingoccurs, and


Vf = specific volume of adsorbed water, assumed to be inde-

pendent of pressure.

Or, in terms of the change in vapor pressure of the adsorbed water that

accompanies swelling,

AP=–RT—ln p/p, . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mvf

(30)

This equation is probably reasonably accurate (except for low values of

~/~8) for a hypothetical gel composed of discrete colloidal particles.When the gel is composed of interconnected particles and encloses stablemicrocrystals and aggregate particles, as in concrete, shrinking or

swelling is partially opposed by elastic forces. Hence, some difference

between the theoretical and actual swelling pressure should be expected.

Capillary tension

In a partially saturated paste the tendency of the water to enter thegel is opposed by tension in the capillary water. The force of capillarytension,

[1F=u~+~ =–RT—ln p/pa, . . . . . . . . . . . . . . . . .

rl r-z Mvf(31)

where u = surface tension of water,rl and rz = principal radii of curvature of the menisci, andv~ = specific volume of capillary water,

Thus, capillary tension and potential swelling pressure have the samerelationship to relative vapor pressure except for a difference in vf.* Whenthe vapor pressure of the gel water and the capillary water are equal,volume remains constant.

In saturated paste that contains no capillary water (we = 4V~) itwould appear that there could be no capillary tension. However, someof the gel water may actually be capillary water; that is, menisci maydevelop as the gel is dried, Whether or not capillary tension can developin the gel, the tendency of the water to evaporate from the gel wouldhave an effect on adsorbed water equivalent to capillary tension.

Relationship between change in volume and change in water content

When drying occurs, capillary water and gel water are lost simul-taneously. Since the resulting change in volume is due only to thechange in gel-water content, it follows, theoretically, that

AUI — AwcAV = (constant) 77 ) . . . . . . . . . . . . . . . . . . . . . . (32)

Vm

where AV = change in volume of specimen,Aw~ = change in total water content, grams,Aw, = change in capillary-water content, grams,

*See footnote, page 586, Part 4,


AWJ– Awo = change in gel-water content, grams, and(constant) = a value characteristic of the concrete in question.

(It probably changes slightly as curing proceeds.)

Vm is here considered to be a factor proportional to the amount of gel.Hence,

l–AZ

~~= (constant) VAW’. . . . . . . . . . . . . . . . . . ..< . . ..(33)m

Thus, the change in volume per unit change in total water content willdepend on the ratio of capillary water to total water.

Con~raction in volume of the system cement + water

When cement and water react, there is a diminution in the sum oftheir absolute volumes. On the assumption that the contraction is con-fined entirely to the water and that the over-all apparent volume of thehardened paste does not change after bleeding is over,

wtv~=wo, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (34)

where wt = weight of total water in the saturated hardened paste,Vt = specific volume (mean) of the total water, andWO= volume of original water in the paste.

The difference between w. and w~ is the amount of water that mustbe absorbed by the specimen during the course of hydration for thespecimen to remain saturated.

At any stage of hydration,

V~=l–0.279 w~,, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..(35)Wt

whereVt = mean specific volume of the total water (both evaporable

and non-evaporable) in saturated paste, andW. =. non-evaporable water, grams,

Hence,AvW=w~– wO=0,279wn, . . . . . . . . . . . . . . . . . . . . . . . .. (36)

where Avw= contraction of the water, cc.

Self-desiccation

If a specimen is kept sealed after its bleeding period, so that no extrawater is available to it during the course of hydration, the pores in thepaste will become partially emptied. This is here called self-desiccation.

The degree to which the pores become emptied can be estimated asfollows :

Let w. = evaporable water content of the saturated paste=Wt —wn.


Then

AVW—. ratio of elmpty-pore volume to total-pore volume (ignoringW* differences in specific volume),

and

Since w, = w. + 0.279w. ,

AVW 0.279w.—. . (37)we w. —0,721w~ ”””””””’”’”” ““”’””””’”””””””

This gives the deficiency in evaporable water on a weight-ratio basis,which is close enough to the volume ratio for practical purposes.

For an illustrative example, let zoo/c = 0.5 and wn/c = 0.2. Then,

Az). 0.279 X 0.2—.0,5 – (0.721 X 0.2)

= 0.16 . . . . . . . . 4. . . . . . . . . . .we

(38)

That is, in such a specimen and under conditions that prevent loss or gain

of water, the deficiency in evaporable water would be 0,16 glg of total

evaporable water, when hydration had proceeded to the point wherewn/c = 0.2.

Such self-desiccation is believed to be an important factor contributingto the frost resistance of concrete. Experimental evidence indicates

that when specimens of good quality are stored in moist air, or even

under water, they are unable to absorb enough water to compensate

completely for self-desiccation. Consequently, cement paste is seldom

found in a completely saturated state, and hence is seldom in a condition

immediately vulnerable to frost action,

CAPILLARY FLOW AND MOISTURE DIFFUSION

From the standpoint of thermodynamics, capillary flow and moisture

diffusion are considered to be the results of inequalities in free energy.Inequalities in free energy under isothermal conditions arise from

(1) inequalities in moisture content,

(2) inequalities in deformations of the solid phase, and

(3) inequalities in the external pressure acting on the adsorbed water.

When such inequalities arise, the evaporable water will always tend toredistribute itself in such a way as to equalize its free energy. This hasan important influence on plastic flow under sustained stress.


EFFECT OF TEMPERATURE CHANGESAT CONSTANT MOISTURE CONTENT

Effect on swelling

As mentioned above, potential swelling pressure and capillary tensionhave the following relationships at equilibrium:

[1AP=F=u ~+~ , . . . . . . . . . . . . . . . . . . . . . . . . ..(39)‘rI T2

At constant water content, a rise in temperature would expand the

capillary water and thus decrease its surface curvature. Also, it would

decrease the surface tension, U. Consequently, a rise in temperature

causes capillary tension to decrease and thus causes water to enter the

gel and restore equilibrium between AP and F. Thus, a rise in temper-ature at constant water content causes swelling in addition to the normalthermal expansion. The swelling of the solid phase would be absent ina dry specimen or in a saturated specimen where p = p,.

From the above it follows that the “thermal coefficient” of a givensample of concrete is not a constant, unless the sample is completelydry or saturated.

Effect on diffusion

When counteracting effects are absent, evaporable water moves in thedirection of descending temperature.

Combined effect of stress, strain, changes in humidity, and temperature gradients

In concrete subjected to changing external forces, changing tem-peratures, and fluctuating ambient humidity, the evaporable water mustbe in a continual state of flux. As a consequence, the concrete swells,shrinks, expands, and contracts under the changing conditions in ahighly complicated way, The separate effects may combine in differentways at a given point in the mass so that they offset or augment eachother. Possibly these effects have an influence on the ability of concreteto withstand weathering.

FACTORS GOVERNING THE EXTENT AND RATE OFHYDRATION OF PORTLAND CEMENT

Extent of hydration

The principal factors governing the ultimate degree of hydration,regardless of the time required, are the relative proportion of particleshaving mean diameters greater than about 50 microns, and the originalwater-cement ratio. Incomplete data indicate that cements containingno particles larger than 50-micron diameter (or thereabouts), becomecompletely hydrated if w~/c is not too low, The ultimate extent ofhydration appears to be about inversely proportional to the 325-meshresidue.


With any given cement the ultimate degree of hydration is propor-tional to the water content of the paste in all pastes in which w~/c isless than a definite limiting value. With an average cement the limitingvalue is about 0.44 by weight. That is, this is the lowest w~/c that willpermit the ultimate degree of hydration with an average cement. Pre-sumably, the greater the 325-mesh residue, the lower this limiting valueof we/c.

Rete of hydration

With other factors equal, the average rate of hydration is lower thesmaller we/c, except during a short initial period. Consequently, thetime required to reach ultimate hydration becomes longer as w,/c ismade smaller.

During the early stages of hydration, say during the first week ortwo, the rate of hydration is higher by a large factor, the higher thespecific surface. But during the later stages, the rates of hydration forcements of widely different specific surface cliffer comparative y little.

Self-desiccation influences the rate of hydration. As the pores be-come partly emptied, the vapor pressure of the remaining evaporablewater is corresponding y reduced. Experiments indicate that eventhough the remaining water is chemically free, its rate of reaction withcement is a function of its relative vapor pressure. If the relative vaporpressure in the paste drops below about 0.85, hydration virtually ceases.Consequently, sealed specimens hydrate more slowly than those havingaccess to water, and they may never reach the ultimate degree of hy-dration possible when extra water is available. This has a bearing on theeficiency of membrane or seal-coat curing.

The foregoing discussion indicates that conclusions concerning therate and amount of hydration of portland cement in concrete (w/c = 0.45to 0.70)should not be drawn from data on standard test pieces (w/c =0.25 *), Moreover, specimens cured in sealed vials should not be ex-pected to hydrate at the same rate and to the same extent as similarspecimens cured in water or fog. Also, it should be noted that forsamples in sealed vials, water separated from the paste by bleeding mustbe considered as extra water.

RELATION OF PASTE POROSITY TO COMPRESSIVE STRENGTH

The compressive strength of 2-in. mortar cubes is, with certain re-strictions, given by the relationship

j, = 120,000 Km – 3600, . . . . . . . . . . . . . . . . . . . . . . . . . . . .(40)w.

where f, is compressive strength, psi, and VJwo is considered to be a


factor proportional to the degree to which the gel fills the originallywater-filled space, here called the gel-space ratio, The relationship holdsfor all ages and apparently for all cements low in C*A (less than about7 percent computed).

For cement of average or high CSA content, and especially for thosehigh in both alkali and CSA the strengths obtained at a given VJw. arelower than those indicated by the equation. The results obtained withsome such cements can be brought into compliance with the equation byincreasing the gypsum content of the cement.

The relationship given by eq. (40) is considered to be empirical—neither fundamental nor general, Independent variables that are notadequately taken into account are as follows:

(1)

(2)

(3)

(4)

(5)

some features of cement composition,

effect of aggregate particles,

entrained air,

fissures under the aggregate particles that form during the bleeding

period, and

variations in curing temperature,

FREEZING OF WATER IN HARDENED PASTE

Owing to the nature of the relationship between water content andfree energy, as shown by sorption isotherms, the water in a saturatedpaste freezes or melts progressively as the temperature is varied belowthe normal melting point, An example of the progressive melting ofice in a particular frozen, saturated paste follows:

Amount AmountofTeti- of ice, ice, as percent

perature* .&l/gof of amountcement at–30 C

– :s5 0.:45 2:– 1.5 0.075– 2.0 0.093 ::– 3.0 0.109 52– 4.0 0.122 59– 5.0 0.131 62– 6.0 0.137 65– 8.0 0.147 70–12.0 0.168 80–16.0 0.181 86–30.0 0.210 100

*The temperature indicated are for samples exposedto air or water. For exposure to toluene, as in the ex-

BY 2.erimente, the figures for temperature should be divided


The capillary water is believed to freeze in place, at least under theconditions of the experiments. However, the gel water probably flows ordistills from the gel to the capillaries before it freezes.

The temperature at which the last increment of ice disappears onprogressive melting is here called the final melting point. It wouldbe the same as the initial freezing point, were it not for the occurrenceof supercooling.

The final melting point in saturated pastes ranges from about – 1.6 Cto about – 0.05 C. The depression of the final melting point is due todissolved material in the mixing water, principally alkalies.

The final melting point in a paste that is not fully saturated dependsnot only on the dissolved material but also on the degree of saturation;the lower the degree of saturation the lower the final melting point.

All the evaporable water is freezable, but a minimum temperatureof about – 78 C is required to freeze all of it.

At any given temperature between – 78 and – 12 C*, the maximumamount of freezable water in saturated paste is

Wf=we. —uvtn ;...... . . . . . . . . . . . . . . . . . . . . . . . . . . .. (41)

or, approximately,

wf=w:— W. (1 + 0.26u) $. . . . . . . . . . . . . . . . . . . . . . . . . (42)

or

w, = Ulo — (0.721 +0.26u)wn, . . . . . . . . . . . . . . . . . . . . ..(43)

in which Wr = freezable water,Wa = total evaporable water,Vm = factor here considered to be proportional to the gel con-

tent of the paste,W. = non-evaporable water, andu = a constant equal to w~/ Vm, where W. is the amount of

water unfreezable at a given temperature.

The following are empirical relationships for the maximum amountsof water freezable in saturated pastes at given temperatures, in terms ofw~ and w.:

(W/)-~y = W. – 1.76w.(w/).zo@= w. – 1.68wn(W,).so. = w. – 1.55wn

At – 12 Cf’, the amount of freezable water is equal to the volume of thecapillary water outside the gel. At lower temperatures gel water isfrozen, but the gel water probably leaves the gel and becomes a part ofthe ice already formed in the capillaries.

*Seefootnote below table on previous page.~he temperaturra indmated are the theoretical valuea for freezing in air or water. They correspond to

-6 C, -10 C, and – 15 C, reapeotively, for freezing in contact with toluene. (See Part 8.)

99S? JOURNAL OF THE AMERICAN CONCRETE INSTITUTE April 1947

At temperatures above – 12 C, the maximum amount of freezable

water is roughly proportional to the amount of capillary water, we — 4 Vm,or (approximately) W, - 1.76w.. The proportionality constants areabout 1.0 at –12 C, 0.86at –8 C, O.7at –4C, and0.6at –2 C.

The maximum amount of ice will not be present unless the temperaturehas previously dropped to a low value, – 50 C or perhaps lower. If themaximum cooling is only a few degrees below the final melting point, theamount of ice formed would probably be less than the amount, indicatedby the relationship given above. This is a result of the hysteresis in thewater content vs. free-energy relationship as indicated by the sorptionisotherms.

For practical purposes, the freezable water can be considered to beidentical with the capillary water. Hence, pastes that contain no capillaryspace outside the gel are considered to be without freezable water.

INDEX

Absolute volumecomp&s~ti;;20f mortar specimens, 310, 316, 318,

of solid phase in hardened pastecomputation of, 6!36-704, 712defined, 690method of memming, 690-92

Absorptivityand capillary porosity, 874-77, 880, 978coefficient of, defined, 873, 978and permeability, 877-80tests, 874, 875

A&sorbed water, 252described, 1I 2mecific volume of. 670

Adsorptionapparatus, 272, 282, 286, 288, 289, 302amount of, in terms of surface area of solid phase,

A02.0.5...- ..-curves, 278-80, 283-88data, 310, 311, 314, 315, 317, 319-26, 330, 331,

334, 335, 556, 557heat of, 5.50-51, 554, 556-,58, 574on interior of porous solid, 472, 476isotherms (see afso Isotherms, Sorption), 554net heat of, 477, 593 (see also Heat)

Adsorption characteristics of hardened cement

effec~o~age (extent of hydration), 289-91,297-.99, 302

effect of original w/o, 290-93, 302effect of soluble salts, 477

Air-stream apparatus, 271-74, 282, 286-9, 302Alkaliea, effect of, on final melting point of ice in

hardened cement paste, 943, 950,958“Amorphous”, use of adjective, 12? (footnote)Amorphous structure of hardened paste, 107

BET equation Aapphcatlon of, 479-482, 499and net heat of adsorption, 577-78

BET theory (see also BET eq, A), 499Cassie’s derivation, 577-78described, 470-2P]ckett’s modification of, 472

Binding of water, 110, 129, 984Brunauer, Emmett, Teller theory (see BET theory)Bulk volume of the solid phase in hardened paste

computation of, 688, 71<-12defined, 688, 846shown diagrammatically, 689

Calcium hydroxide, 107, 108, 129Calcium sulfoaluminate, 262, 301Calorimeter, heat-of-solution, 565Cepilkmy condensation

net heat of, 551-52, 592, 982theory, described, 473-74

combined with BET theory, 476-9Capillary flow, 588-89, 594, 987Capillary pores, 973-75Capillary porosity and coefficient of absorptivity, 876Capillary tension

force of, 584, 873, 985and volume change, 585, 985

c%’&~,%f495, 503,980freezing of, 947and gel water, relative amounts of, 498-501,and permeability, 710specific volume of, 670, 980, 981vapor pressure of, 980volume of, at any stage of hydration, 688

shown diagrammatically, 689, 709

981

Carbonation of samples, 257, 258Cement%el isotherm, defined. 495Cements-

chemical compositions of, 30.5.7lot numbers of, indexed by Series No., 304physical properties of, 308-9

“Colloid,” defined, 124 (footnote)Colloidal material in cement paste, V~ proportional

to, 482, 502Compositions

of granular samples, tablm of, 673-82of mortar specimens! 310, 316, 318, 328, 332of samdes usedin ddatometers, 950, 9E6

Compres~ed water, defined, 671, 686, 711Compressive strerigth

effect of gypsum content on, 851-53effect of sand particles on, 849-51and gel-space ratio, 848, 850, 851, 858-64, 989and paste structure, 845-54andsolid-smice ratio. 846

Crymtat, de~cribed and pictured, 939, 940

Darcy’s law, 865-66Dehydration isotherm, 111, 117Density data, 308-9Resorption curve, 278-80, 283-85Dielectric constant, detection of freezing by, 943,944Dilatomet.er studies, described, 938-41, 967Drying of sample8

in desiccators, 275isothermal, 256, 258-60in oven, 260

Electron microscope, use of, 108-9, 129Energy of binding, 574-77, 593, 983-84Enthalpy, 565-67, 592, 593, 982-83Entropy change, 564, 566-68, 571, 572, 593, 983Evaporable water

decrease with increase of curingdefined,, 252, 253, 973determination of, 263-65freezing of, 935methods of studying, 267

period, 302

Fixation of water, studies of. Part 2. n. 249..-Fixed water in hydrated cement compounds (see

a]so Non-evaporable Water), 262Flexural strength data, 329Flocculation of particles, 867Free e~4:~8j76, 565-68, 570, 571, 588-89, 593,

Freezable waterestimation of, 937, 959, 965, 966, 968, 991-92theoretical amount, 950, 956, 958, 959

Freezing of water in hardened portland cementpaste, Part 6, p. 845

Freezinf3:oint, diagram showing relation to P/ps,

Freezing studyappara@ 940dielectric method, 942-44procedure, 937-39of silica gel, 942, 943

Gel—cement gel, 578, 579, 706Gel pores (see PoretJGel-space ratio and strength, 848, 850-52,858-64

i

ii JOURNAL OF THE AMERICAN CONCRETE INSTITUTE

Gel waterdefined, 495, 503, 979specific volume of, 497, 6!26, 979

shown diagrammatically, 709Granular samplm

analyses of, 310:327, 329, 332compared with intact cubes, 268

Grinding of samples, effect of, on isobars, 114-16,130Gypsum content of cement, influence on strength,

851-53, 864

Heatof adsorption, net, 551-53

and C of the BET eq. A, 577, 593defined, 471, 551, 592differential, 568, 571, 572, 593and heat nf hydration, 559-63and heat of wetting, 553measurement nf, 553-63, 592total, 552, 592, 982in relation tn V~, 576

of capillary condensation, 551-52of combination of water in Ca(OH)g, 593of hydration of cement, 554, 559, 560, 592, 982of reaction of non-evaporable water, 562, 592of solution data, 560, 561of spreading-wetting, 553

Heat-of-solution methnd, 555Helium, wed as a displacement medium, 694High-vacuum apparatus

data4;$.ta,ad by merms of, 277-80, 283-8S,

described-,-269-71, 282, 302Hydrates of major portland cement compounds,

extent of dehydration, 261Hydration, extent of, 988-9

and cement content, 708in concrete vs. in standard test pieces, 989and cement fineness, 706, 708, 712, 975, 988and water content, 989

Hydration productscharacteristic porcaity nf, 706,physicaI state of, 981prop~7ena~to amount of non-evaporable water,

Hysteresis, sorption, 118,276,282,302,944

Ice, me Freezable WaterImmobile water factor, 87o, 872Internal energy, 563, 565, 567Intemarticle attraction, 973Interpretation of adsorption data, theoretical,

Part 3, p. 469Isobars

of A1203.3H20, 113apparatus for obtaining, 118, 120defined, 110, 129of Fe~O~,HzO, 114of hardened portland cement paste, 118-23, 130for hardened 3Ca0.8i01, 120of hydrates of chrnmium, 111and isotherms, relationship het wee~), 127of principal compounds in portbmd cement,

122-24.130for pyropbyllite, 115

Isotherms

‘do?ionat Ifferent degrees of hydration, 293for samples of equal w., 291, 292showing w. only, 291, 292

aPParat~ for determining, 126, 127cement-gel-, 495, 496, 554defined, 110, 130effect of dissolved alkali, 479of geh (silica gel), 116, 117, 130for hardened paste (hydrated cement),

130, 277, 286, 287, 470, 554nf hTaOH and KOH, 478of pure cement compounds, 128

124-27,

Kelvin’s equation, 473, 475, 476, 586

Leachi~$90f soluble material from teat specimens,

Light-miormcopc, uae of, 106-8

Materials, description of, Appendix to Part 2, p.Mean 8pecific volume

of gel water, 696, 711of non-e mporable water, 695, 711of total water content, VI

computed, 673-82, 711influence of cement composition on, 686

9, 711lower limit to, 687, 688method of determming, 672plntted vs. w~/w,, 684-85

303

Melting oint of ice in hardened pastec?define , 966, 991

effect of dissolved materials, 943, 950, 958, 991in uaste not fullv saturated, 968-69, 991

Methods of stud~ing barderied portland cementpaste, literature review, Part 1, P. 105

MicrocryataOine hydrates, 108, 129and stepped isobars, 112-16, 129, 130

Microcrystalline state, 107, 124, 129, 260, 487, 499Mixes, Appendix to Part 2, p. 303Moisture diffusion and capillary flow, 488-W, 987Multimolecular-ndaorption, thenry of, 102,470

Non-eva orable water$’define , 252, 253, 978

determination of, 257-63maximum, related to extent of hydration; fine-

neaa; co fnputed chemical composition, 975specific volume of, 670, 979

hypothetical, equatmn for computing, 695upper limit to, 687, 704

Particle-size, equivrdent, of colloids in cement gel,497, 498, 503

Permanent set in relation to shrinkage, 585Permeability

and absorptivity, 877-80coefficient of

defined, 866equation giving, 868, 879, 977observed vs. theoretical values, 869, 870theoretical, of hardened paste, 866

of har7~9$~ pastes and concrete, 710, 871-73,

minimuh, theoretical, 871, 872, 077—testt90~$p, Vidal, and Wing, 868! 869,

Poiseuille’s equation for capillary flow, 866Pore-size, 981

distribution, 475estimation of, 496, 503

Pore-volume, 495, 496, 981Pores

capillary, 973-75size of, 977volume of, equations for estimating, 973,

defined, 300gel, 975, 976

mean size of, 976, 977volume, equatione for computing, 976

Porosityand compressive strength, 989defined, 251, 973efiect of drying on, 266, 267effective, of cement pastes, 867total. of cement tmstes, 867, 975

974

Porou8 structure o; hydration ptnduct, 106, 972Pressure, swelling, equation for .579-82

INDEX iii

Ratio V~/W., 4W, 483,,502influence of composltmn on, 486-88

Reproducibility of results, 256, 274, 275

Samples, preparation of, 255, 256Satura~6~ Sg6~Plea, data on total water content,

Self-desiccation, 986, 987, 989Shrinkage

and gypsum content, 852Piokett’s equations for, 587, 588

Shrinking and swelling, mechanism of (see alsoVolume Change), 984

Solid phase in hardened paste, 562, 705absolute volume of, 690bulk volume of, at ,any stage of hydration, 688,

712, 974, 980ratio8~~ to available space, in relation to strength,

surface area of, 563, 976volume of

computation of, 696-701, 703, 704, 974increase in, diagram sbowimz 702

Specific surface data on harden~d paste (see alsoSurface Area), 308, 309, 491, 596-602

of steam-cured paste, 492Specimens

dt%criptions of, Appendix to Part 2, p. 303preparation of, Appendix to Part 2, p. 303; alao,

PP. 253-55Stability of hydrates, 260-3, 301Steam-curing,, effect of, 492, 503

on adsorption characteristic, 300, 301on strength, 853

Strength of hardened paste, 709, 716Supercooling, 941, 991Surface adsorption, see AdsorptionSurface area

computation of, 488, 502of hydration products, 490

related to cement ,composition, 981internal, of sample, proportional to V~,

90-2.503of steam-cured paate, 492, 503in terms of wn, 4$

Surface tension, 473, 477,873Swelling pressure, 578-82, 594, 984, 985

482

Tern erature changeife ect of, on moisture diffueion, 591, 695, 988

effect of, on swelling, 590, 591, 595,988

Thermal expansion, coefficients of, 59o, 591, ’388Thermodynamics of adsorption, Part 4, p, 549

Unfreezable water, 963, 964related to the 25° C vapor pressure ieotherm, 96 I

Unreaoted cement, volume of, estimated, 707shown diagrammatically, 70fI

Vapor pressure, 294, 473, 474, 477-79, 979Vm and C

data for computing, 481-83data from Series 254-265 and 254-MRB, 597data from Series 254-9, 5!)8-99data from Series 254-11, 600data from Series 254-13, 601

V~ and w“, relationship between, 484-88V~/w~ and compressive strength, 847Volume change, 973

as a capillary phenomenon, 584, 594as a liquid-adsorption phenomenon, 582, 594

Volume contraction (see also Volume Change)due to hydration, 943, 986

Volumenometer, described and illustrated, 690-92

w/Vm data, 493, 494, 500-2, 554wII/w. and strength, 847Waal’s, van der, adsorption, 112, 471,587, 979Water, mean thermal coefficients, 945-47Water-cement ratio, original

‘ffect ‘n ‘ard’nedPte’”295’’2g6effect Onshqpe of a sorption curve, 290-93Water of constitution, 252Water fixation, studies of (see also Fixed Water),

110-12, 129, 130as mfi of estimating nature and size of pores,

-..by means of freezing tests, 128

Wetting, heat of, and net heat of adsorption, 553

X-ray ~~jfi~9ations, of hardened cement, 109,

Young’s modulus of mortars, 328, 329

ZeOlitic water, 111, 112, 129

Printed in U.S .A.

Bulletin 1l—’’Shrink~ge Stresses in Concrete: Part l—Shrinkage (or Swelling),Its Effect upon Displacements and Stresses in Slabs and Beams ofHomogeneous, isotropic, Elastic Material; Part 2—Application of theTheory Presented in Part 1 to Experimental Results”; by GERALDPICKnTT,Me,rcb,1946.

Reprinted from .lourrud oj the American Concrete Institute (January and February,1946) ;&oceedirw6,42, 165,361 (1946).

Bulletin 12—’’The Influence of Gypsum on the Hydration and Properties of PortlandCement Pastes, ” by WILLIAMLERCH,March, 1946.

Reprintedfrom Proceeding, American i%.ietv jor ‘Z’esting Materials, 46, 1252 (1946).

Bulletin 13—’’Tests of Concretes Containing Air-Entraining Portland Cements orAir-Entraining Materials Added to Batch at Mixer, ” by H. F, GONNER-MAN, April, 1947.

Reprinted from Journal of the Arrwican Concrete Inst@Ae [June, 1944); Proceedings,40, 477 (1944); also supplementary de,ta and andyms, reprinted from Supplement(November, 1944); Proceedings, 40, 508-1 (1944),

Bulletin 14—”An Explanation of the Titration Values Obtained in the MerrimanSugar-SolubMty Test for Portland Cement, ” by WILLIAM LERCH,Mttrch, 1947.

ReprintedfromASTM Bulktin, No. 145, 62 (March, 1947).

Bulletin 15—’’The Camera Lucida Method for Measuring Air Voids in HardenedConcrete, ” by GEORGE J, VERBECK, May, 1947.

Reprinted from Journal oj the AmeAcan Concrete InaMute (May, 1947); Proceedings,43, 1025 (1947).

Bulletin 16—’’Development and Study of Apparatus and Methods for the Determina-tion of the Air Content of Fresh Concrete, ” by CARL A. MENZEL, May,1947,

Reprinted from Jourrwt of the American Concrete Institute (May, 1947); Proceeding.r,43, 1053 (1947).

Bulletin 17—’’The Problem of Proportioning Portland Cement Raw Mixtures:Part I—A General View of the Problem; Part II—Mathematical Studyof the Problem; Part IH-Application to Typical Processes; Part IV—Direct Control of Potential Composition”; by L. A. DAHL, June, 1947,

Reprinted from Rock Product., 50, No. 1, 109; No. 2, 107; No. 3, 92; No. 4, 122 (1947).

Bulletin 18—’’The System CaO-SiO,-H,O and the Hydration of the Calcium Sili-cates, ” by HAROLD H. STEINOUR, June, 1947.

Reprintedfrom Chemicrd l?wiem, 40, 391 (1947).

Bulletin 19—’ ‘Procedures for Determining the Air Content of Freshly-Mixed Con-crete by the Rolling and Pressure Methods, ” by CARL A. NIENXEL,June, 1947.

Reprinted from Pr’oceedinQn,AmericanSociety for Testing Materials, 47, 833 (1947).

Bulletin 20—’’The Effect of Change in Moisture-Content on the Creep of Concreteunder a Sustained Load, ” by GERALD PICKETT, July, 1947.

Reprinted from .70wrwlof the American Concrete Institute(February, 1942); Pro-ceedings, 3S, 333 (1942).

Bulletin 21—’’Effect of Gypsum Content and Other Factors on Shrinkage of ConcretePrisms,” by GERALD PICKETT, October, 1947.

Reprinted from Journal of the American Concrete Instittd6(October, 1947); PT’o-ceedings, 44, 149 (1948).

Bulletin 22—’ ‘Studies of the Physical Properties of Hardened Portland CementPaste, ” by T. C. POWERS and T. L. BROWNYAR~,March, 1948.

Reprinted from Journal of the American Concrete Institute(October-Deoenlber, 1946;January-April, 1947); Proceedings, 43, 101,249, 469, 549,669, 845, 933 (1947).

rx022[1]

Documents