the microstructure of porous building materials: study of a cement and lime mortar

Transport in Porous Media 14: 219-245, 1994. 219 @ 1994 KluwerAcademic Publishers. Printed in the Netherlands.

The Microstructure of Porous Building Materials: Study of a Cement and Lime Mortar

R C. PHILIPPI , R R O S E N D O YUNES, C. R FERNANDES, and

E S. M A G N A N I Mechanical Engineering Department, Federal University of Santa Catarina, Cx.P.476, Floriandpolis, SC, Brazil

(Received: 16 June 1992)

Abstract. Building materials such as cement mortars and concrets present a very broad distribution of pore sizes, from some tenths of angstroms to several micra. This distribution is very important in establishing their macroscopic properties, e.g., vapor adsorption and desorption and moisture transfer. It is, thus, important to develop procedures to analyze the microstructure of these materials in the full range of pore sizes. In the present work, two complementary methods are used for obtaining the pore sizes distribution of a cement and lime mortar, often used as a building coating material. Electron scanning microscopy is used for pore sizes greater than 1250 A, from a sequence of pictures taken with magnifications from 25 x to 12500x, for highly polished surfaces. The heterogeneous spatial distribution of pores is discussed, related to the problem of the geometrical reconstitution of porous structure. For pore sizes smaller than 1250 A, adsorption isotherms obtained at 30 ~ are used. Molecular physical adsorption is supposed to be the dominant adsorption mechanism in a wide range of relative humidities and modeled using the De Boer and Zwikker theory. This is confirmed by a very high correlation coefficient equal to 0.994 for the present case, for values of RH smaller than 80%. Capillary condensation is supposed to become significant at the point where the adsorption curve deviates from the linear behavior as predicted by the De Boer and Zwikker theory, and the Broekhoff and De Boer theory is used for predicting the pore size distribution from the adsorption isotherm, starting from the deviation point and increasing RH. The results show the pore size distribution between 200 A and 13 #m.

Key words: Pore sizes distribution, sorption isotherms, electron scanning microscopy, moisture, porous building materials.

1. Introduction

The materials commonly used in buildings exhibit a large range of pore diameters.

This is the case of building materials based on hydraulic agglomeration such as

cement mortars, lime mortars, concrete and related materials. The manufacturing

process produces an heterogeneous material made-up of sand and/or gravel particles

and a very fine textured liants paste, which is the object of study of the present

work. Pore diameters may range from some tenths of angstrom to several micra,

contributing to establish the peculiar physical characteristics of these materials

with respect to moisture sorption and transfer. The behavior of these materials in building structures is strongly related to their

properties with respect to moisture sorption and transfer. Moisture is responsible for

220 P.C. PHILIPPI ET AL.

mold growth and affects mechanical resistance, aesthetic patterns and durability of the fabrics. Permeability to water vapor and heat transfer are dependent on moisture content, contributing to modify the energy balance of the building, and the thermal comfort and healthy conditions of its inhabitants.

Van der Kooi (1971) used the Philip and de Vries theory to study the effect of capillary transport of liquid water - in addition to vapor transport - on the rate of moisture transfer in cellular concrete. This work has greatly contributed to modify the concept of water vapor permeability for materials presenting an appreciable fraction of gel pores, like mortars, concrete and other cement paste aggregates. In fact, it was usual, in this field, to consider only vapor transport in calculations of moisture transfer and prevention of condensation (Van der Kooi, 1971), a good practice for insulation materials such as mineral wool and polyestirene, with large pores, but meaningless for materials presenting higroscopicity and capillary effects.

The hydraulic properties of these materials are strongly related with their microstructure and, in the last decade, several works have been undertaken for studying the microstructure of cement paste aggregates. Electron scanning microscopy of fractured and polished samples, neutron and X-ray scattering have been used for direct investigation. Allen and co-workers (Allen, 1982; Pearson et al., 1983; Pearson and Allen, 1985), Knab et al. (1984), Lange et al. (1990) and Jennings (1988) may be mentioned, without aiming completeness.

Mercury porosimetry has also been used as an auxiliary indirect tool, taking its well known limitations into account (Winslow and Lovell, 1981; Fernandes and Philippi, 1989; Pedrini et al., 1990; Daian, 1986).

Sorption isotherms using nitrogen and water vapor have been obtained for cement based building materials and theoretical models have been used for molecular physical adsorption - mainly BET (Brunauer et aI., 1938), GAB (Bizot, 1983) and de Boer and Zwikker (Adamson, 1982) - and for capillary condensation - mainly BJH (Barret et al., 1951), Broekhoff and de Boer (1967, 1968) and percolation methods (Wall and Brown, 1981; Mason, 1982; Neimark, 1986). The works of Badmann et al. (1981), Daian (1986), Merrouani (1987), Perrin (1985), Quenard (1989) and Saliba (1990) should be mentioned.

The purpose of this paper is to present a study of the microstructure of a cement and lime mortar commonly used as a building coating material. In the first part, micrographies of the porous structure are presented, taken using an electron scanning microscope and shown as two-dimensional pictures with magnifications from 25x to 12500x. These pictures show the heterogeneous character of the sample studied, displaying the great complexity of its porous structure. In a second part, the sorption isotherms are presented together with the experimental details concerning their obtention. The mathematical models for studying vapor adsorption are also presented, as theoretical tools for obtaining the distribution of micropores, which are inaccessible to electron microscopy.

THE MICROSTRUCTURE OF POROUS BUILDING MATERIALS

TABLE I. Grain sizes distribution for the sand used in the mortar.

Diameter (/~m) 105-149 149-210 210-250 250-297

% (in mass) 11 70 10 9

221

2. Materials and Methods

Samples were prepared using a mass proportion of 8:2:1 (fine sand, lime and Portland cement, respectively). The mass of water used was 25% with respect to the mass amount of the mixture. Table I shows the grain size distribution of the sand, as obtained by Quadri (1988). This sand did not present soluble salts as showed by weighting, after washing. The components were mechanically mixed and molded as rectangular 5 mm thick samples, for reducing curing time and water sorption tests.

The samples were taken out of the molds at the 5 th day but curing took about 60 days. The chemical reaction of carbonation,

Ca(OH)2 + C O 2 --+ CaCO3 + H20

has been observed to develop very slowly from the surface of the sample to the core. The reaction rate depends on the temperature and relative humidity. Phenolphthalein was used as an acid-base indicator for observing the carbonation progress and the tests were only begun after completion of this reaction over the whole thickness of the samples.

Dry mass was determined by drying the samples at a standard state corresponding to 200 ~ After drying, the samples were placed in a chamber containing molecular sieve during 24 hours, for cooling. The definition of a standard state is a difficult point. Using smaller temperatures, apparently, does not allow to eliminate all the physically adsorbed water on the surface of the pores. In addition, tests made using a differential scanning calorimeter showed that there is no liberation of chemically bonded water for temperatures below 300 ~ However, submitting the samples to higher temperatures can introduce thermal stresses which should modify the microstructure of the samples by, e.g., fissuring, see Allen (1982).

The dry density has been measured for parallelepiped-shape samples as the ratio between dry mass, as defined above, and the volume, measured with a 10 .2 cm resolution micrometer. Dry mass was measured using a 10 .4 g resolution Sartorius balance. The value obtained was 1.71g/cm 3 with a standard mean deviation of 0.05 g/cm 3.

The porosity was measured using a nitrogen porosimeter (Core Laboratories Inc) giving 0.31, with a standard mean deviation of 0.02.

The samples were prepared for electron scanning microscopy and for isothermal water vapor sorption. It is necessary to work with highly polished surfaces for quantitative analysis of pores distribution, in using the micrographies. The polishing

222 P.c. PHILIPPI ET AL.

procedure of the samples took several months, before the correct method was found, without contamination of the surfaces with abrasive grains or mechanical removal of solid pieces from the sample.

Impregnation of the porous space is necessary for polishing, giving the required mechanical resistance to the samples and enabling the polishing processes to be done without removal of solid grains from the surface. A resin (XGY from Ciba Giegy Society) mixed with ethyl-alcohol was used for the impregnation, which was performed under vacuum for preventing air bubbling.

Polishing of the samples was made in several stages. In the first stage, a 600 grade sandpaper was used to eliminate the surface excess of resin resulting from impregnation. The samples were then submitted to a polishing sequence using diamond powder diluted in lubricants and applied using impregnated soft sails: grain sizes of 15, 9, 6, 3, 1 and 0.25 #m were used. Polishing times varied between some hours and 25 hours. An ultrasonic source was used between any two sequential processes for eliminating diamond crystals adhering to the surface, which could contaminate the next sail and damage the surface.

After polishing, the resin was then evaporated at 350 ~ in an evacuated quartz tube at 10 #m Hg pressure. Resin evaporation allows the surface of the pores to receive a thin layer of gold for electronic emission, giving the required definition to the pictures and must be done in absence of oxygen to prevent chemical reactions with the resin and carbonization of the surface.

3. Electron Scanning Microscopy

Electron scanning microscopy of fractured and polished samples has shown to be an important tool for the investigation of microstructures. A Philips PSEM 500 scanning microscope, was used at the National Atomic Energy Commission, Buenos-Aires, Argentina. The microscope was operated at the emissive and refrac- tive modes. In the first operation mode, only secondary electrons emitted by the surface are detected whereas in the second mode, retrodiffused electrons are also detected. The best results were obtained at the emissive mode, giving a better definition of the porous space with respect to the solid matrix, and a resolution near 100

3.1. GEOMETRICAL HIERARCHY IN THE MICROSTRUCTURE

Figure 1 presents a 25 x magnification picture of a polished surface of the sample, showing the grains of sand with 100-200 #m mean width, air inclusions with the same dimensions and the cement and lime paste, which appears as an homogeneous material between the solid grains. Several cavities which appear on the picture as macropores, are, in fact, the result of mechanical removal, from polishing, and must not be considered in the analysis.

THE MICROSTRUCTURE OF POROUS BUILDING MATERIALS 223

Fig. 1. Electron scanning micrography of a polished surface of the sample. Magnification: 25• Each trace corresponds to 100 #m.

An extended network of narrow fissures, 3 #m width appears at the 200 x magnification picture, Figure 2, around the grains and establishing bridges throughout the whole medium, for liquid and vapor transport. The origin of these fissures can be attributed to thermal stresses and, also, to the curing process. Apparently, the lime present in the mixture could contribute to increase fissuring, however, no study was undertaken to find the origin of such fissures. Paulon and Monteiro (1991), using X-rays diffraction, have found a transition zone between the cement paste and the aggregates, with a smaller mechanical resistance. Fissures around the sand grains were always found, even at fractured surfaces from samples conserved at ambient temperatures and dried at 75 ~ Figure 3. As explained in Section 2, heating of the samples to evaporate the epoxy-resin, could also be important for increasing fissuring and this means that care must be taken in simulating moisture transfer, using the results of quantitative analysis for the porous space measured in these pictures. Nevertheless, the presence of fissures in mortars has been shown by several authors using direct means of investigation (Knab et al., 1984; Jennings (1988)), or indirect ones. Saliba (1990) has used networks of fissures to simulate moisture transfer in cement mortars, finding a better agreement with experimental

224 e.C. PHILIPPI ET AL.

Fig. 2. A 200• magnification electron scanning micrography of a polished surface of the sample showing an extended network of fissures. Each trace corresponds to 10 #m.

results. In our own experiments, using mercury porosimetry, a critical injection pressure of ~ 100 psi was found, for the cement and lime mortar, corresponding to a throat diameter of 3 #m, which is the mean width of the fissures, Figure 4.

Impermeable 10-20 #m width alumine particles from cement am noticed at the 800 x magnification picture, Figure 5.

The products of cement and lime hydration appear in detail as porous islands (Figures 6-8) using magnifications higher than 3200• Figure 7 shows the inner structure of these particles as a network of gel and small capillary pores (d < 2000 A) surrounded by larger capillary pores. Gel pores are very important since they yield the hygroscopic properties of a porous material, i.e., its water vapor sorption characteristics. Apparently, these pores are not homogeneously dispersed in the hardened paste, but concentrated, forming isolated clusters of connected gel pores, surrounded by larger pores.

Both the size and spatial distribution of capillary pores can be described using the pictures shown in the present paper. Modeling using several different scales are necessary, if one wants to increase accuracy in describing moisture sorption and transfer in such a kind of material - which is typically heterogeneous (see also


Fig. 3. Electron scanning micrography of a fractured surface of the sample. Magnification: 200x . Fissures are apparent between the grains of sand and the cement and lime paste. Each trace corresponds to 100 #m.

Quenard, 1989). In fact, the pictures show a geometrical hierarchy with respect to the distribution of pores. This means that different scales will exhibit different pore space geometries.

3.2. CORRELATION FUNCTIONS FOR THE SPATIAL MULTI-SCALE

DISTRIBUTION OF PORES

The pictures, such the ones shown in Figures 1-8, give information concerning the size and spatial distribution of pores, at several scales. Numerical reconstitution methods of the porous space, have been conceived by Quiblier (1984) and Adler, Jacquin and Quiblier (1990) for pore distributions which may be described using a single-scale network. For the present case, the intrinsic heterogeneity of the medium does not allow to use a single-scale network for numerically describing the pores size distribution and topology. It is thought that three different scales could be enough for the numerical description of the cement and lime mortar studied in this paper.

In the first scale, a 100 #m measuring unit was used for describing the distribution of impermeable sand grains. A rectangular grid made-up using 100 #m • 100 #m unit cells was superposed to the 25 • and 50 • magnification pictures. The

2 2 6 a c. PHILIPPI ET AL,

o I:ST I N J E C T I O N x 2 ND I N J E C T I O N

10 3 ~ �9 EJECTION . -

I , , . -

2 10 :-,

LLI "*,,

03 03 LIJ rY [3_

>_ 101 , I

r l ~

<~ ._J _J [1_ <[ (D

100 . . . . 100 90 80 70 60 50 40 50 20 IO 0

MERCURY SATURATION (%)

Fig. 4. Mercury intrusion curve for the cement and lime mortar. Critical injection pressure corresponds to 100 psi, which is related to a porous diameter of ~ 3/~m.

cells were made black for macropores, white for solid particles and gray for the cement and lime paste, respectively. Gray cells represent porous sections at which the pore sizes are smaller than the measuring unit (100 #m in the first scale).

In the second scale, the same procedure was used, superposing grids of 1.25 • 1.25/zm unit cells over the 200 x and 400 x magnified pictures, for describing the fissures network and the smaller solid particles.

The third scale was, initially, chosen 2500 #t to describe the porous structure of the cement and lime paste, using the 3200x and 6400x magnification pictures.

The whole process of binarization was, initially, done manually, by using trans- parent sheets, and, later, automatically, by using an HP IIC scanner, with 256 gray levels, and image analysis procedures in a PC 486 computer. With the manual procedure, smaller scales were prevented, since the necessary resolution was not reached even with the greater magnification pictures (12500x), due to spatial effects in the pictures.

The use of computerized image analysis procedures enabled the use of 1250 ,~ as the third scale, working over the 3200 x magnification picture, which represented the smaller magnification for the cement and lime paste.


Fig. 5. A 800 x magnification electron scanning micrography, showing impermeable alumine particles in the cement and lime paste. Each trace corresponds to 10 #m.

Figures 9(a) and 10(a) show some results of the binarization procedure for the second and third scale, respectively.

Following Adler et al. (1990) a phase function can be introduced,

Z(x) = 1 when x belongs to the pore space, and 0 otherwise, (1)

where x denotes the vector giving the position in the plane of the picture of a section of the porous medium, with respect to some arbitrarily chosen origin, and at a given scale. In fact, x denotes the set of 2-uples (Xl, x2), where Xl, x2 are integers, multiples of the measuring unit. The apparent porosity, i.e., the void fraction at the selected scale can be obtained as:

c = (Z(x)), (2)

where ( ) means statistical average in the sample space. The self-correlation function can, also, be written as,

<Z(x) - ~><Z(x + u) - ~> R(u) = <(Z(x) - ~)2> , (3)


Fig. 6. Electron scanning micrography of the cement and lime paste. Magnification: 3200 x Each trace corresponds to 1/~m.

for each arbitrarily chosen u, where u is a displacement in the plane of the porous section.

Assuming an isotropic porous distribution, the self-correlation function will only depend on u =1 u I and can be written as,

((Z(xl , x2))(z(xl + ~, x2))) - ~2 R(u) = (4) _ g2

As implied by this last equation, the self-correlation function can be obtained by displacing the picture over itself in the Xl direction (or x2), using multiples of the cell dimensions and measuring the void fraction related to the intersection, i.e., the frequency of outcomes corresponding to two superposed black cells. This procedure gives a covariogram, Quiblier (1984),

c (~ ) = [Z(xl, x2)Z(xi + ~, ~2)]. (5)

Figures 9b and 10b shows the self-correlation function for the porous section modeled in Figure 9a and 10a, respectively. For high values of u the self-correlation function oscillates around zero, taking negative values. This behavior has also been


Fig. 7. Electron scanning micrography of the cement and lime paste. Magnification: 6400 x. Each trace corresponds to 1/zm.

observed by Adler et al. (1990) and can be due to a weak statistical representability of the binarized images such as the one shown in Figures 9 and 10. Superposition of several binary images taken from different porous sections, at the same scale, reduces this effect.

Reconstitution methods of porous media from pictures, conserving pores size distribution and correlation function are now being improved, to describe the size and spatial distribution of capillary pores. Unfortunately, it is not possible to quantitatively describe the size distribution of gel pores from the pictures, as the necessary resolution was not reached even with the highest magnification (which corresponds to 12 500•

Sorption isotherms will be used in the next section to give quantitative information about the size distribution of gel pores present in the cement and lime paste.


Fig. 8. Electron scanning micrography of the cement and lime paste. Magnification 12 500 • Gel and small capillary porous appears as concentrated in porous islands. Each trace corresponds to 1 #m.

4. Sorption Isotherms: Experiments

Solid surfaces can capture water vapor molecules: these molecules have a great affinity with the sin-face, due to their dipole moment, and displace air molecules previously adsorbed (Adamson, 1982). As it is well known, the amount of water vapor adsorbed at a solid surface increases with the relative humidity. For porous materials, the sorption isotherms are modified by capillary condensation which is related to moisture filling of pores by vapor condensation.

Sorption isotherms were obtained, for the cement and lime mortar, in conven- tional Pyrex dryers containing saturated salt solutions. The dryers were placed in a temperature controlled oven at 30 ~ Spatial variation of temperature, inside the oven, were reduced by using fan ventilation and were periodically monitored with thermocouples. Spatial fluctuations of 0.2 ~ were measured. Time fluctuations of temperature were also measured being everytimes smaller than 0.5 ~ even for the longer runs, which took about 8 weeks. An auxiliary cooling system was needed for controlling temperatures in summer. The salts used in the experiments were chosen following the French standard NF X 15-014 and the solutions were


(a)

0.8

0.6

n-

c 0

~ 0.4

8

0.2

1 1 5 10 15 20 25

- 0 . 2 _u

Micron (b)

Fig. 9. (a) Binary representation of the 200• magnification micrography (Figure 2). Each unit cell corresponds to 1.25 [tm. Solid matter is represented by white cells and pores by black ceils Gray cells represent porous matter with pore diameters smaller than 1.25/am. (b)


-0.2

0.6 re

C 0

"~ 0.4

8 0.2

50OO 1000O 15OOO 2OO0O 250OO

Ca)

0.8

Angstroms Co)

Fig. 10. (a) Binary representation of the 3200x magnification micrography. Each unit cell corresponds to 2500 A. Pores are represented by black cells and white cells corresponds to porous matter with pore diameters smaller than 2500 A. (b) Self-correlation function for Figure 10(a).

THE MICROSTRUCTURE OF POROUS BUILDING MATERIALS

TABLE II. Experimental results for the water content in isothermal sorption at 30 ~ Samples dried at 200 ~

RH Adsorption Mean deviation Desorption Mean deviation (%) (g/g) (%) (g/g) (%)

07 0.0014074 8.47 - -

12 0.0016856 10.75 0.00338911 i3.72.

22 0.0026609 10.03 - -

33 0.0035324 4.68 0.00457439 5.17

43 0.0042997 8.37 0.00592956 4.87

52 0.0050059 10.17 0.00729290 8.17

63 0.0056888 9.68 0.00796476 12.82

80 0.0074165 4.12 0.01340605 2.95

91 0.0105782 4.15 - -

96 0.0216000 3.91 0.06641211 4.20

233

prepared mixing the salts with distilled water until salt deposition. For adsorption, thin samples, 5 mm thickness, previously dried at 200 ~ were put in the dryers containing salt solutions and equilibrium conditions were verified by weighing the samples periodically. Specific measures have been taken to avoid disturbing the experiments during the weighing, conserving the samples inside the dryers. Once equilibrium was reached the samples were weighed, dried and weighed once more, in the Sartorius 10-4g resolution balance, to measure possible changes in the dry mass between the beginning and the end of the experiments. Several samples have been used inside each drier for measuring data dispersion. The experimental procedure for desorption was the same as described above, starting with samples previously saturated with distilled water at atmospheric pressure.

Figure 11 shows the sorption isotherms measured using the 200 ~ standard drying state. Although hysteresis is put in evidence starting from near 30% relative humidity, apparently, capillary condensation becomes significant only after 80% RH in adsorption experiments. Table II shows some details of the sorption experiments, for each value of the relative humidity, giving the mean deviation for each experimental result. It is clearly seen that the difference between the measured values of the water content in the adsorption and desorption experiments, is significantly greater than the experimental deviation found in each process.

Equilibrium at 100% relative humidity is very difficult to be achieved in adsorption experiments. In fact, as it will be seen in the next section, some pores may remain two-phase thermodynamically stable systems even at very high relative humidity. If the pores are supposed to be spherical, pores larger than 2000 A in diameter will be filled with water only at relative humidity higher than 99% (see Table III). The experiments at 100% relative humidity have been performed by placing the samples in an atmosphere in contact with distilled water, using ventila-


0 . 0 8 0 -

t o

E

I-.- z LLt F- Z 0 (...)

0s W

<~

0.060-

0 . 0 4 0 2

oo2o2

0 . 0 0 0.00

�9 ADSORPTION ISOTHERM

i i i i i I

O. 20 O. 40 0.60 O. 80 1.00

RELATIVE HUMIDITY ( h )

Fig. 11. Sorption isotherms at 30 ~ for samples dried at 200 ~ C, showing data dispersion. Hysteresis is put in evidence from near 30% RH, but capillary condensation is only apparent after ~ 80% RH.

tion to accelerate the equilibrium process, at two different temperatures: 5 ~ and 30 ~ At the beginning, mist in the chamber indicates a 100% RH atmosphere, but placing the samples inside reduces the overall relative humidity as indicated by the disappearance of mist. After some weeks, mist appeared again, indicating that equilibrium was reached between the atmosphere inside the chamber and the superficial pores. The samples were weighed, beginning from this time.

Since the variation of the water density is smaller than 0.5%, at the above temperatures, there is, apparently, no reason to have any difference between the mass of liquid water adsorbed by the samples in adorption processes, at 100% RH, except for the reasons concerning the experimental procedures themselves: how much time is necessary to reach equilibrium in adsorption, at 100% RH? What is the influence of bubbling with respect to the amount of retained water, in a wetting process? What is the influence of air dissolution in water?

Figure 12 shows the influence of the temperature over the time evolution of the moisture content adsorbed by the samples, at 100% RH, resulting from readings during a period of about 6 months. Lower temperatures accelerate the achievement of equilibrium: in fact, the samples became saturated with water after nearly 2 months, at 5 ~ whereas, at 30 ~ equilibrium was, apparently, not yet reached,

0 . 0 2 0 -

v

I-- Z I.nl I-- Z 0 (D

L,d o ADSORPTION AT 5~

ADSORPTION AT 50~

I IIIII I I I I I I I I I I I I I I I I I I I I I I I I I I I I I i I I I l

50, O0 100100 15010 0 ~OlOO

0.015-

0 . 0 1 0 '

0.005-

o.oo 0.00


DAYS

Fig. 12. Kinetics of the isothermal adsorption at 100% RH and two different temperatures 30 ~ and 5 ~

even after the whole 6-months period. Decreasing the temperature will enhance air dissolution and decrease surface tension. However, in the liquid phase, viscosity will also increase and, in the gas phase, the diffusion coefficient of water vapor in air will decrease. Assuming local equilibrium in a given point of the core, the matrix potential, at a given time, will be given by ~I' ,,~ -or cosO/r where r is, roughly, the radius of the greater pore filled with liquid, in the core. This potential is related to the relative humidity (Broekhoff and De Boer, 1967, 1968). Decreasing the temperature will increase the surface tension cr and reduce gJ (and the relative humidity, h) whereas, at the surface, gJ = 0, independently of the temperature, because, as verified by direct observation, the atmosphere inside the chamber remains, almost always, at 100% RH (as confirmed by the presence of mist). Preliminary calculations showed, however, that the increase in Ah between the surface and the core, due to the present temperature reduction is very small, and any further conclusion about the effect of temperature on adsorption kinetics deserves more accurate studies.

The above results indicate that the value of 0 = 0.181 g/g, corresponding to saturation, shoud be taken to represent the equilibrium value of moisture content at 100% RH, in sorption experiments.


5. Modeling Isothermal Vapor Sorption

Vapor sorption has been modeled for materials presenting high hygroscopicity by considering the thermodynamical stability conditions of two phase systems in single cavities of simple geometry, such as cylinders or spheres. Adsorption or desorption curves are used in the full range of vapor pressures starting from saturation, where the available surface area to molecular physical adsorption is zero, and decreasing the vapor pressure by steps computing, at each step, the pore volume related to the critical pore diameter, from stability conditions (Broekhoff and De Boer, 1967, 1968).

Building materials present a very broad distribution of pores and, as it was seen in the last section, an ill-defined sorption behavior near saturation, with a great sensitivity to changes in relative humidity. It is thus impossible to start the calculations from saturation, due to the uncertainty in the values of water content for high values of relative humidity.

In addition, data on molecular physical adsorption of water vapor on solid surfaces does not suffices to establish universal characteristic isotherms (Adamson, 1982), as is the case for nitrogen adsorption, which has been widely employed in studying sorption isotherms. In fact, data on nitrogen physical adsorption allows to establish a universal curve relating the statistical thickness of nitrogen adsorbed layers, at 78 K, to the relative pressure, independently of the adsorbent material. It is thus possible to estimate the magnitude of the surface potential at the adsorbed layer surface and its role in settling the critical vapor pressure for pore liquid filling. Unfortunately, this is not the case for water vapor adsorption and the potential in the liquid water layer due to the attraction field with the pore surface must be calculated from the available data, for the specific material being used (Badman et

al., 1981). In the present paper, the pores are supposed to be spatially unrelated. Only

the adsorption curve is considered and the contribution of pores topology to the adsorption process is considered to be small. In fact, the spatial distribution of pores would not contribute to the adsorption process, strictly, in the case of vapor adsorption at zero gas pressure, when the accessibility of the pores to vapor is not modified by air blockage. In the present case the sorption experiments were performed at atmospheric pressure. In this case, bubbling can play an important role in the establishment of sorption characteristics at atmospheric pressures, since it allows blocked air to leave small cavities, when the liquid pressure increases at the adjacent pores.

Spatial distribution of pores has been taken into account by some authors, Wall and Brown (1981), Mason (1982), Neimark (1986), by using percolation networks of randomly distributed pores. As it can be seen in Figures 1-10, there is a strong statistical correlation for the spatial distribution of pores, in the present porous material, which is essentially non-homogeneous. It is not apparent that percolation networks, with pores homogeneously disposed at random, could explain their

THE MICROSTRUCTURE OF POROUS BU1LDING MATERIALS 237

sorption characteristics. In addition, only gel pores and small capillary pores will be considered here and these pores are disposed in porous islands in the cement and lime paste (see Figure 8), surrounded by larger cavities with about 0.5-1.0 #m diameters. These cavities will not impose restrictions to vapor accessibility.

5.1. MOLECULAR PHYSICAL ADSORPTION OF VAPOUR ON THE POROUS SURFACE

Water vapor is supposed to be adsorbed on a plane porous surface for relative humidity values smaller than the value corresponding to the beginning of the hysteresis cycle - in fact, somewhat higher due to the different critical points for liquid water emptying and filling of pores. This range of relative humidity is relatively large, suggesting a small contribution of micropores filling to the overall adsorption behavior, and was used to give the necessary data to estimate the porous surface area and surface potential.

Thermodynamical equilibrium between liquid and vapor phases separated by a plane surface is described by:

= ( 6 )

where #v is the chemical potential of vapor:

#~ = #~o(T) + m T In h. (7)

#~o(T) is the chemical potential of saturated vapor at temperature T, 9l > is the universal gas constant and h is the relative humidity. The chemical potential of the condensed phase:

= + (8)

where #Zo(7-) is the chemical potential of free liquid water at temperature T, and g~(t) is the value of surface potential at the surface of the condensed layer, corresponding to thickness t. Following de Boer and Zwikker (Adamson, 1982)

qJ(t) = e0 e x p ( - a t ) , (9)

where eo is the interaction potential at the surface and a is a constant related to the molecular polarizibility of water (Adamson, 1982, p. 250):

a - - do

where do = diameter of the adsorbed molecule, oz = polarizibility of the adsorbed molecule (Adamson, 1982, Table VIM), and d is the distance of separation between the induced charges.

The above equations give the thickness t of the condensed layer as a function of the temperature T and the relative humidity h:

t = l l n - e ~ l l n In 1, (10) a 91T a h


which can be multiplied by the porous surface area So to give the adsorbed volume of water:

Va = S ~ So In In 1. (11) a 9IT a h

The above equation means that the adsorbed volume of water Va must be a linear function of In ln(1/h), if the role of micropores filling is meaningless in some range of relative humidity, where the porous surface may be considered as a plane, i.e., where the curvature radius of the adsorbed layer is much greater than its thickness. This equation can also be used for estimating the numerical values of So and co as correlation parameters obtained from experimental data, when the parameter a is known. In the present work, the value of a was taken as 0.3449 • l0 s cm -1, by using the data from Adamson and by supposing d = do~2, in the lacking of any other data.

Figure 13 show the results obtained at 30 ~ for a cement and lime mortar dried at 200 ~ Capillary condensation is not meaningful for h < 80%, although the hysteresis cycle begins at 30% (Figure 11). This behavior is apparent from the adsorption curve (Figure 11), and has also been noted by Neimark (1986) for mesoporous adsorbents. The linear behavior of the adsorption isotherms, in this range of values of the relative humidity, is confirmed by a very high correlation coefficient equal to 0.994.

5.2. PHASE STABILITY IN SPHERICAL CAVITIES

Filling of pores with liquid water was conceived by Broekhoff and de Boer (1967, 1968) as a consequence of thermodynamical instability of two phases systems made up of a condensed and a vapor phase. The reader is referred to their original work for details in the developments.

Pores will be considered as spherical cavities of radius r with an spherical interface with a radius r - t (Figure 14). Increasing the relative humidity will increase t and the variation of the free enthalpy, G, of the two-phase system can be written as:

dG = #vdNv + lzldN~ + erdA,

where dNl = - d N v is the number of moles condensed, cr is the surface tension of the liquid phase and dA is the change in the interfacial area between the two phases. At equilibrium,

dG = O,

giving a relation between the thickness of the adsorbed liquid film and the relative humidity, h, for a given pore radius, r.

If the two-phase equilibrium is stable,

d2G > 0, (12)


0 . 0 5 0 - - �9 EXPERIMENTAL ADSORPTION ISOTHERM

- - - - - DE BOER AND ZWIKKER MODEL

0.025"

.-S j . o.ozo

E

F- 0.015 Z Ld F-

t~l k.-

O.O05-

SAMPLE D

0 , 0 0 ~ F n I I I I I I I I l I T [ I I I I I I I I l l I I I I I I i I I I I q J i l l I I [ I I I 1 I I I t I I I I ] ~ F I - .oo -,,.oo - .oo - z o o -1.oo o,oo .oo

~n [~n ( ] / h ) ]

Fig. 13. Use of the De Boer and Zwild<er model, [14], for isothermal adsorption at 30 ~ The model is satisfied for h < 80% with a correJation coefficient of 0.994 for the experimental data. The deviation from the linear behavior is attributed to capillary condensation, for h > 80%.

Fig. 14. Thermodynamic stability of 2-phase systems in spherical cavities.

which is valid when t < t*, where t* is the critical thickness of the condensed phase, calculated equating the above stability condition to zero and corresponding to the transition thickness for liquid water filling:

t* = __1 In [ 2crMz ] (13) a [ ( r - *)2pz(-a 0)J '


TABLE III. Calculated values of the critical thickness of physically adsorbed water t* and crtitical RH, h*, for spherical cavities.

r (AngstrOm) t* (AngstrOm) h* (%)

50 6.4 78.3 100 10.6 89.1 200 14.8 94.7 300 17.3 96.5 400 19.0 97.4 500 20.3 97.9 600 21.4 98.3 700 22.3 98.5 800 23.1 98.7 900 23.8 98.9

1000 24.4 99.0 2000 28.5 99.5

where Ml is the molecular mass of water and Pt is the mass density of liquid water. The equilibrium condition, given by dG = 0, can be used to calculate the critical

relative humidity, h*, above which there will be a complete filling of pores of radius r with liquid water,

2crMl -91T In h* - ~( t*) . (14)

( r - t*)p

Table III gives the values of the critical thickness t* and the corresponding critical values of the relative humidity h* for spherical pores with a radius between

o

50 and 2000 A.

5.3. CALCULATION OF VOLUME DISTRIBUTION OF PORES

At each relative humidity, hi, the total amount of water, Vi, taken-up by a porous material in contact with water vapor is considered to be composed of physically adsorbed water at the porous surface, Va,i, and capillary water, Vc,i, filling the smaller cavities:

Vi = Vc,i + ga,i. (15)

Calculations start at the relative humidity ho, which denotes the point where the adsorption curve leaves the straight line behavior as predicted by de Boer and Zwikker theory (see Figure 13). Let So be the total porous surface area available for physical adsorption, calculated as above (Equation 11). For the first step, i = 1, ho is increased by a small amount dh, and the capillary condensed and physically


adsorbed water are calculated using,

= (So - Sl) , vc, (16)

Va, l = S l t l (17)

where S1 is the surface area available to physical adsorption at relative humidity hi = ho + dh, t I is the thickness of the adsorbed layer at hi, calculated using Equation (10), and r I denotes the radius of the spherical cavities filled at hi, calculated from the stability conditions (see Table III). The surface area $1, can be calculated by adding the two above contributions, Equations 16-17, and equating the result to the measured value of the total amount V1 of adsorbed water at hi, as prescribed by Equation (15). At an arbitrary step i, the surface area available to physical adsorption can be written as:

i -1 ri -- ~ j : l Vc,J) - Si - l -3 (18)

Si = ri t i - - - - 3

The cumulative volume Vi of pores with radii smaller than ri is finally calculated, as the difference between the measured value and the product Siti, at each step i.

Figure 15 shows the evolution of capillary condensed and physically adsorbed water, when the relative humidity is increased from zero to near 100% RH. As it could be expected the curve of VaXh presents a maximum near 96% and decreases from this point, as the pores are filled with liquid water resulting from vapor condensation.

It is important to note that the present results do not imply that all the pores in the sample material have diameters greater than do (ho), where ho is the value of RH where, the adsorption isotherm deviates from the linear behavior, as predicted by De Boer and Zwikker theory. This only means that the contribution of these pores to the volume of the porous space is very small and cannot be computed from the adsorption isotherms. They will, thus, just behave as throats, distributed in the porous space and imposing restrictions to vapor accessibility in desorption process, contributing to hysteresis. This can be deduced from Figure 11, showing that hysteresis persists down to h ~ 30%.

The above comments are specially true if one considers that the contribution in number of pores always increases as the diameter decreases.

6. Results and Discussion

Figure 16 presents the pore sizes distribution obtained using the adsorption isotherms for pore diameters smaller than 1250 angstroms. The results obtained from electron microscopy are also presented, for pore diameters greater than 1250 A. The cumulative volume of small pores with diameter smaller than 1250 A was calculated as 0.075 cm3/cm 3, which corresponds to 24.59% of the total porous

242 P.c. PHILIPPI ET AL.

0.12

0.1 + Adsorption Isotherm I ' [

Physically Adsorbed Water

~ 0 . 0 8

~O.OB 8

0.04

0,02

0 ~ t lllll I I I I l

0.86 0.88 0.9 0.92 0.94 0.96 0.98 1

Relative Humidity. h

Fig. 15. Physically adsorbed and capillary condensed water for increasingly values of the relative humidity at 30 o C, for cement and lime mortar samples.

volume. This result has been confirmed by electron microscopy, by calculating the volume fraction of pores with diameter greater than 1250 A, from the pictures given in Figures 1-8. A volume fraction of 73.55%, with respect to the total porous volume, was calculated from electron scanning microscopy for pore diameters greater than 1250 A, independently from isothermal adsorption data. Initially, with the manual procedures, the calculation was done, using binary representations of the 3200x magnification picture, performed with 2500 A cells. The results were 35% for pores diameters smaller than 2500 A (using the adsorption isotherm) and 64.8% for pore diameters larger than 2500 *. These results are astonishingly good, taking the limitations involved in the calculations into account: in both cases the calculated values for the porosity were within the experimental incertitude of its corresponding measured value (6.45%).

It must also be kept in mind that, in the present work, only the first part of the adsorption curve was used, for h < 99%, which is less sensitive to interpolation errors, compared to the narrow range between 99 and 100% RH, where the present porous material takes-up about 65% of its maximum moisture content.

Another important result is displayed in Figure 17, where ln(Vs) is plotted against ln(D), Vs(D) -- (1 - e) + V(d < D), takes account of the volume fraction of the solid matrix (1 - c) and the volume fraction of pores with diameters smaller than D, c is the porosity and the volume fractions are taken, here, with respect to the total volume of the sample. V~ corresponds to the volume fraction of solid which would be apparent, at each scale D, if the pores with diameter d < D, were computed, at this scale, as part of the solid matrix. It is seen that the calculated

T H E M I C R O S T R U C T U R E O F P O R O U S B U I L D I N G M A T E R I A L S 243

0.35

0.3

0.25

E 0.2

:~ 0.15

0.1

0.05

0 I - - - - ~ - - - - '

100 1000 10000 100000 1000000

D (Angstroms)

Fig. 16. Pore sizes distribution for the cement and lime mortar using the results of isothermal adsorption at 30 ~ (d < 1250 A.) and electron scanning microscopy (d > 1250 A).

0

-0.05 ~ In Vs

-0.1

-0,15

:~ -0.2

-0.25

-0.3

-0.35

-0.4 I - t I I I ' - - t

5 6 7 g 9 10 1l

In O

Fig. 17. Scaling law for the pore sizes distribution in the range 200A < D < 50000 (including the fissures). Vs is the volume of solid matter apparent at each scale D, i.e.,

including the volume of pores with diameters smaller than D. D is given in .~. The correlation coefficient for the linear regression is 0.9909.

values of ln(Vs) follows a linear fitting against ln(D), with a correlation coefficient of 0.9909, in the the range 200 A < D < 50 000 A, of pore diameters, including the fissures. Using Mandelbrot fractal theory, Mandelbrot (1983), this means that the volume distribution of pores follows a scaling law, with, in the present case, a fractal dimension Df = 2.9329. This result will be further exploited in a next paper.

The authors expect the present work to be a valuable contribution for the knowledge of the microstructure of porous building materials, in what concerns the role of very small sized pores in setting-up sorption properties. Although


electron scanning microscopy is an important tool for microstructure investigation, it is very difficult to use it for the investigation of very small pore sizes, where sorption isotherms appear to remain a very important investigation method.

Acknowledgements

This work was supported by CNPq (Conselho Nacional de Desenvolvimento Cientffico e Tecnol6gico). R R. Yunes and C. E Fernandes were supported by CAPES (Coordenag~o de Aperfeiqoamento do Pessoal de Nfvel Superior). The authors wish to acknowledge M. Ipohorski of the National Atomic Energy Commis- sion (Buenos Aires, Argentina), for the support in the electron scanning microscopy, Cenpes/PETROBRAS for the mercury intrusion curves, IPEN/USP for the unavail- able guidance in precise polishing procedures of abrasive materials and J. F. Da~an (Institut de M6canique de Grenoble, France) for many fruitful discussions about the main ideas presented in this work. The authors also knowledge the support of Laborat6rio de Materiais (A. N. Klein) and Laborat6rio de Plantas Medicinais (R. Yunes) of UFSC/Florian6pololis.

References

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the microstructure of porous building materials: study of a cement and lime mortar

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