1981_ o. olabisi_ interpretations of polymer-polymer miscibility_ j. chem. educ., 58, 944

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Table 1.

rzGGz

YMERS I TERPOLYMERS,I ETC.

RA N D O M A LTERN A TI N G G RA FT BLO CK STA R CO h'I"POLYBLENDS I

MECHA NICAL MECHANO-CHEMICAL CHEMICAL POLYB LEND S SOLUT IONS CAST&11*11?1111&,&,Th e domain sizeo fthis blend is larger than that representative late) (PMMAJ, multiphase polymer blend results, regardlessof miscihilitv: conseaue ntlv. the blend is m ul ti~ ha se t the of the intensitv of mixine. and reeardless of the tem wr atu re.. .given tempe rature , pressure, an d composition. If, however,the tem pera ture of this blend is dropped to 80°C, a single-phase tra nspa rent homogeneous mixture results. Th at is, the

domain size is smaller than the characteristic critical domainsize. Th is behavior for PS-PVME polymer blend is summa-rized (5) or a rang e of compositions in Figure 1.At any com-position, the system is immiscible at emperatures above theuppe r curv e (filled circles) and comp letely miscible below thelower curve ionen circlesl. Th e soace between t he two curves~ ~~ . ~ .reflects th e kinetic natu re of the domain formation; it alsoi l l u ~ t r a t e shat the d rk in e forces for the misciI11t.-immiscil)le

pressure, andcornpo sit& of th e blend. Th at is, m>scibilitjcan not be mechanically forced, and for systems such as this,the critical domain size remains a hypothetical concept; it

cann ot be measured.I t must also be noted tha t the critical domain size as a de-

fining concept of polymer-polymer miscibility is useless foran investigator interested in macroscopic properties usefulin practical industrial problems. For that investigator, amiscible blend is tha t which exhibits a single glass transitio ntemp eratu re (Tg) and miscibility implies homogeneity of themixture UD to a scale whose dimension is akin to tha t re-

transition are thermodyn&ic in origin and tha t the transition sponsible ;or the cooperative move ment associated with th eis observable if. an d onlv if. enoueh clusters have formed biz elass transition tem oerature.enough domains creating sufficient refractive index differ- - Th is T, definition ignores the presence of domains or mi-ences. In orin ci~ le.herefore. a critical domain size could be crodomains rich in one constituent ~ o lv m e r r the other some asu red for rl;osesystems exhibiting partial miscibility. On long as the blend in question yields a sjngieT, Because of this .the oth er ha nd, if one fluxes PS and po lyh et hy l methacry- it may appear to be a much less rigorous criterion; however.

Volume 58 Number 11 November 198 1 94 5



free energy (not relative to th e pure constituent, but to someintermediate composition) and the free energy becomes morenegative as the mixtures phase-separate further. Th e quali-tativ e criterion is a degenerate form of Gibb's criteria inas-much as it neither distinguishes unstable from stable statesnor gives any und erstanding of th e concept of metastability,which is so impo rtant in phase separation mechanisms. For

example, in their study of the thermally-induced phase sep-aration behavior of PS-PVME, Nishi et al. concluded th atthere a re two modes of phase separation phenom ena in thispolyblend (5). These modes are nucleation add growthmechanism and spinodal decomposition phenomena. Asshown in Figure 2, the solid line is the cloud-point curve, thefilled circles repre sent regions in which nuclea tion and grow thpredominate, t he open circles represent spinodal decompo-

it is more like a degenerate f orm of the definition based on 180 -

sition regions, and thedashed-curve represents theline of demarcation betweenthe two modes. In the nucle-ation and growth region, theresult was a finely dispersedtwo-phase s t ructure whosefinal droplet size as wellas the

inter-particle size depen ds onth e tim e scale of the experi-me nt an d on the rate of diffu-sion. In the spinodal decom-position region, the decom-posed system was character-ized by phase interconnectivityin both the minor and majorphases-a structure reminiscentof the co-continuous phasesthat have been observed inothe r systems.

This observed behavior canbe understood in term s of thethermodynamic stability of abinary system. Consider, forexample, Figure 3which illus-trate s the free energy of mixingas a function of conce ntrationfor a binary liquid systemshowing partial miscibilitywith the associated phase di-agram (6). On the phase di-agram, the boundary betweenthe s table on e-~ ha se egion

phase separation. In a truly miscible amorphous polymermixtur e in the molten sta te, a region rich in one constituentpolymer or another would n ot grow; because there is no drivingforce for phase separation, it would be stable to a wide range 160

of time-temperature-pressure excursion. If the amorphous

60 I0 0.2 0.4 0.6 0.8 1

$J

Figure 2. Tempraturecampasition phase diagram for polystyrenepaly(vinyI

methyl ether) mixtures. Phase separations by what appears to be spinodal

mechanism(0)nd nucleation and gowih mechanism(*)reobserved under

microscop. The dashed curve represents the line of dem arcatian betwee n the

two mwpholagies.

(Reprimed from Nishl. T., Wang, T. T., and Kwei, T. K., ~ c mm o l e c ~ l e s ,,227

(1975). Copyright by the American Chemical Society.)

-I

and the metastable com<osi-tions is called the bino dd, and ~ i g u r e . Free energy of mixing as a function of concentratian in a binary liquid system showing p mi ai miscibility.

the boundary between me?- (Reprinted h om Koningsueld. R.. Kleintlens, L. A., andSchoffelers, H. M.. m e Appl. Chem..39, I 1974). CopyrigM by imer-

stable and unstable composl- national Union of Pure and Applied Chemishy.)

mixture were immiscible, such regions would grow rapidlywith time, and th e mixture, in th e solid state, would satisfyneither the T, additivity criterion nor th e ph ase homogeneity 140 -criterion.

Theoretical Viewpoint

From the point of view of statistical thermodynamics,miscibility implies homogeneity on a scale equivalent to th erange of intermolecular forces. Th is is neithet satisfied by theT, criterion, the phase separation criterion, nor by the usualqualitative criterion given in several tests th at th e Gibb's freeenergy of mixing must be negative for a system to be ther -modynam ically stable. Mixtures are often unstable a t negative

946 Journal of Che mical Education



tions is called the spinodal. A finite undercooling below the

binodal down to a temperature Tz esults in the formation ofnuclei which grow depending on the length of time the un-

dercooling is maintained and on the rate of diffusion. As the

temperature decreases the diffusion rate decreases while the

rate of nuclei formation increases; he net result is a maximumrate of growth several degrees below the binodal. At equilih-

rium and a t temperature Tz,he final compositions of the

dispersed two-phase system are represented by 'P2'and 'Pf.On the other band, a sudden undercooling below the spinodalresults in a spontaneous and continuous decom~os itionnto

two phases with a high level of phase interconnec&ity in both

the minor and the major phases. The growth originates, notfrom nuclei, but from small amplitude composition fluctua-

tions which are always present in the equilibrium liquid state.The characteristic features of spinodal decomposition are

succinctly described by the following:

(a) It is an unstable process; it requires no activation.(h) It is diffusion-controlled;he diffusion coefficient for spinadal

decompositionis always negative.(c) It is an isothermal prwess.(d) It occurs coherently.(e) Forliquid crystalline systems, he two coexisting phases exist

on the same lattice; for amorphous isotropic materials, theinterwoven structures of the two coexisting phases would beuniform yet random.

The phase diagram shown in Figure 3 is only one of the

manv forms that anv auasi-binarv mixture could assume. Th ediff&ent t y p e oili&l phase beha\ior that could he observed

are illusrrnted (1)n Virure 4I) iar ram A represents wmpleremiscibility; B represenis a systemexhibiti<g an upper critical

solution temperature behavior (UCST); C represents a system

with lower critical solution temperature behavior (LCST);Drepresents a system with closed miscibility behavior; E rep-

resents a mixture with both UCST and LCST and F repre-

sents a mixture whose UCST and LCST merge to yield anhourglass phase diagram. Experimental examples for one or

more of these phase behaviors exist for solvent-solvent, sol-

vent-polymer, polymer-polymer, or solvent-polymer-polymer

mixtures.

The LCST behavior is exemplified by PS-PVME (51,poly(styrene-co-acrylo~itrile)-poly(methylethacrylate) and

poly(styrene-co-acrylonitrile) polycaprolactone (7).Severallow molecular weight polymer mixtures exhibit the UCST.

Some of these oligomeric mixtures exhibit the unusual two-peaked coexistenw curves usually referred co as himodality.

t3imcxiality has been demtmstrated for a low mulecular weight

1)olyityrene-polyisopreneystem (6)nd for a low molecularweight 1)0ly(o-methylstyrene-co-vinyl oluene) when mixed

with n low molwular weieht oolvhutene (81. similiu hehavior

has been observed for l&h^molecular weight epoxy and co-

polyester co-mixed with 1,l'-, 2,2'-tetrachloroethane ( 9 ) . r-

regular asymmetry of th e critical concentration has also been

observed in the exoerimental cloud-voint curve for low mo-Icrular weight n~ixrures f polyisoburylene and polv(dimethylsiloxane) 110~.rrrrular as\mmetry manifests itself ns a shift

of the ext'remum h i n t from low Eoncentrations of the highmolecular weiaht polymer to high concentrations of that

polymer.

Predicting Polymer Polymer Misclbllity

At this juncture, i t is well to emphasize tha t the state of

immiscibility of a polymer blend do& not preclude its utility;multiphase blends have made respectable inroads into the

commercial scene. Because of their specific advantages,multiphase polymer blends have found utility in applications

requiring improved impact strength, toughnesi,environ-mental stress crack resistance, wear resistance, flame ret-

srdance. ozone resistance, fatigue, ~rocessahilitv. dditive.

acceptance, resistance to s"nlig6t discoloration, and reduced

compression set. Furthermore, anti-slip, anti-block, and low

+z +2

Figure4. Schematic o liquid-liquid temperature-compositian phase diagrams.Shaded areas represent the temperature-composition regimes where phase

se~arationccurs.(Reprinted from Olabisi.0. .Robeson. L. M.. and Shaw.M. T.. "Polymer-PolymerMiscibility." AcademicPress. New Ywk.N.Y.. 1979.Copyright by AcademicPress Inc.)

coefficient of friction represent an additional se t of propertiesthat can he improved with appropriate choice of immisciblepolymers. All of these properties are achieved by the addition

of a small-to-moderate amount of one oolvmer t o another

polymer which is the continuous phase. The major advantagesof miscible amornhous oolvmer blends derive from the fact.that thew is only ,ml, continuous single ph ;~ ie er the entirecunct:ntration ranre. Thus. the miscil~lc lend is rhnrncwrized

by average or ah&e average mechanical property, absence of

shear-induced ~ h a s eeparation, and absence of additive mi-gration. This ciass of polymer blends finds utility in perma-

nent plasticization and in applications where it is necessary

to increase or decrease the heat distortion of a polymericsystem at will with the addition of a suitable miscible

polymer.

Semi-Empirical Rule of MixturesGenerally, blending technology rests on the premise of

property additivity although the additivity principle is not

strictly valid for the majority of polymer blends. Although"additivity" need not he simple arithmetic, for a quasi-binary

miscible blend, extensive experimental data suggest that the

following arithmetic semi-empirical mixture rule is oheyed

by the glass transition temperatures (Tg)nd other propertiessuch as the density, refractive index, dielectric constant,

thermal conductivity, heat capacity, thermodynamic prop-

erties, elastic moduli, viscosity of liquid mixtures, and surfacetension of liquid mixtures (11 .

P = plml p2m2 1414~ (1)

Volume 58 Number 11 November 1981 947



I 2

Figure 5. A schematic of eqn. 1 llustrat ing the possible patterns Of properly

dependenceoncomposition or a miscible polyblend.There isa rangeof values

within which the additivity principle is presumed to be obeyed.

Figure6. Composition dependence for the flexural and tensile sbengths forme

polyblendof paly(methy1methacryiate>poly(a-memy1 styrenelmethyi meth-

acrylate/acryIonitrile) terpalymer.

IRepr ntcd rom Olaolsi.0 .anaFarnham. A G . mCaoprx. S Esle~. M.,~ E a m r ~ . . llflpnase Polymers. Advances n Chemistry Series. 176.Chapler

29. 19791 Copyr ght OY the Amerncan Chemoca Soc ety.,

where P is the proper ty of interest , 4 th e concentrat ion, and. .I isan interaction rvrm which MI he po si~ive , egative,ur zero.I f 1 i.;zero, the ruleofm ixture s (add itivity principle, isobeye d;if i t is positive. the polymer hlend property w u d d he hettertha n the weighted average of the constituent pol yn ~er s ndth e polymers-are said to be synergistic with e ach other; if 1 snegative, the polymer blend prope rty would be below wh atone would expect from simple averaging an d the system could

948 Journal of Chemical Education

Figure 7. Semi-logarithmic plot of equation 2 (Y 1.01for various values of

A illustrating he possible palterns of property dependence on composition or

an immiscible polyblend. WhenA - , thedispersed phase s"son'': when A- . the disoersad ohare is "hard."

(Adaptnd lrom Niclren. L. E , Roo ning IhePropertiesof M xtures." New Yon .

h Y . 1978. Copy, gnt OY Mace D~kusr,nc,

be referred t o as non-synergistic. The hehavior is illustratedin Figure 5.Positive deviations from linearity have been oh-served in the T, hehavior of poly(viny1 nitrate)-poly(viny1acetate) mixtures in which strong intermolecular interactionsare present. The hehavior hasualso been observed in theco m ~ o s i t i o n e~ e n d e n ce f t h e t en si le s t ren gt h an d t h eflrx&il strength o fa m iscihle hlend oi a brittle polymer u,itha ductile polvmer asexem plitied hs Ficure 6 which illustratesth e data-f oi poly(a-methyl s tyr&e/methyl methacrylate1

acrylonitr i le) terpolymer-poly(methy1 methacrylate)(PM M A) hlend (12). Conversely, a miscible blend can exhibitnegative deviation from linearity in tensile strength andmodu lus when th e crystallization of one polymer is depressedby the addition of a miscible polymer. Phase morphologydicta tes th e behavior of such a system.

In the case of a quasi-binary immiscible polymer hlendconsistine of a continuous phase and a d i s~ er se d hase , an-othe r se$-empirical mixture rule is obeyed by suc hbr op eki esas elastic moduli, shear modulus, electrical conductivity,therm al conductivity, dielectric constant, thermal expansioncoefficient, diffusion coefficients, and the viscosity of sus-pensions (11); it is, however, not obeyed by failure Go pertie snor by toughness properties.



where +z is the concentration of the dispersed phase constit-uent, 0 5 A 5 m depends on the shape and orientation of thedispersed phase as well as the nature of the interface. B de-pends on the relative values of the properties PI,P2, gnd A ,and W s a reduced concentration term which is a function ofthe maximum packing fraction. The behavior of eqn. (2) is

illustrated in Figure 7. Note that no distinct maximum is everexhibited howe;er beneficial the nature of the interface as-suming, of course, that the chemical individuality of the

constituents is retained. That is, the property (described byeqn. 2) of the polymer hlend is never higher than tba t of theconstituent whose property value is the-higher of the two. Astriking exception to th is rule is the toughness properties ofrubber-toughened plastics. In these systems, the general im-misicihility has been turned into a unique advantage by usingsome selected ohvsical. chemical. andlor ohvsiochemical.techniques to induce, within the m&iphase polymers, somesor t of microscopic phase development known to be so im-por tan t in the mechanism of toughening. Extensive experi-

mental data has shown tha t the toughness property of thesesystems depend strongly on the phase morphology and tha t

toughness properties could be maximized if an optimum do-ma& structure is achieved. Hence, in almost all cases, a givenproperty of an immiscible hlend is never what one would ex-

pect from simple averaging. Nonetheless, the additivity con-cept has been generally applied, in a crude sense, in themodification of such properties as modulus, impact strength,thermal oxidative resistance, processability, environmentalweatherabilitv. color. hardness. heat resistance. flame ret-

ardance, domain mo;phology, thermal expansivky, thermalconductivitv. comoressibilitv. and refractive index. In all the.applications involving immiscible mixtures, one polymerphase is alwavs the continuous phase in contrast to the ao-&cations involving miscible blends where the property ad-ditivity principle is often possible over the entire composition

range. Overall, the approach has been quite successful as ev-idenced by the recent market statistics (13).

Probably the strongest motivation for blending is thecostlperformance characteristics achievahle. An expensivepolymer whose property spectrum is much higher than isneeded for a new application may be blended with an inex-pensive polymer whose property spectrum is such that theresulting polymer mixture has a costlperformance ratio whichmakes it very attractive for the given application. Thus , thenew standard of performance demanded by the new applica-tion is satisfied hv a mixture of commerciallv available oolv-

mers without the-need to develop a new po1;mer or to investin a new plant.

ThermodynamicASDects

Some polymer science literature contains the misconceptionthat polymer-polymer miscihility occurs whenever the freeenergy of mixiig is negative.

Indeed, it is a necessary, hut not asufficient condition, thatthe free enerw of mixing for a miscible nolvmer blend must"be negative. For a homogeneous single-phase blend, AG,i,is negative. However, depending on the shape and location of

the co-existence curve, the same hlend could achieve an evenlower free energy sta te by splitting into two phases via thenucleation and growth or spontaneous spinodal decomposi-tion. In Figure 3,the concentration corresponding to the crestof the free energy curve for Tz fits the situation under con-sideration. For this and any other concentrations, the ther-modynamic misril,ility is go;.erned by thr subtle deulili d t h cconrentrntiondependence uf thr Gilhs free energy uf mixing.

For example, a system is miscible if and only if the second

derivative of AG,i, with respect to concentration is positive;

that is,

(a2AGmax/dh2)~.r0 (4)

where +2 is the volume fraction of polymer 2. The complete

Gibb's criteria for thermodynamic miscihility is embodied inthe following relations tha t define the loci of miscihility fora binary or quasi-binary system (14):

A = A ' ; Aw2 = Am' (5 )

(a2AGmi,/a022)~.~0 (6)

(8AGmi,/a023)~,~(a2AGmix/J20dp,~0 (7)

where p1and pl ' are the chemical potentials of polymer 1 nthe two equilibrium phases.

The first condition (eqn. (5))defines the binodal curve ofthe phase boundnr" for the system, the st wnd (eqn. (61) 111:-

fines thv a d ~ i l u yimit ur the spinudul, and the last teqn. 171)

nrescrihes the temoerature. pressure. concentration, andmolecular weight dependen& of thecri tic al points or theconsolate state . Th at AG,i, is negative within the miscibleregion is only a degenerate form of these Gibb's criteria. If oneaccepts this degenerate form, one can develop a simple meansof predicting the miscibility of polymer blends based on anymolecular model so long as its free energy can he expressed inthe form of the Flory-Huggins (15-18) combinatorial entropy

terms plus the correction function for concentration, tem-perature, and molecular weight.

where V , s the interacting segment volume which is taken asclose to the molar volume of the smallest polymer repeat unitas possible, @ is the volume fraction, x is the degree of poly-merization in terms of the reference volume V ,and X IP is theFlorv-Humins interaction oarameter which is related to the...enthalpy o t the inrrrnctiun of the polymer repeat units eachof vulume \'.. Fur hirh ~o lvm ermixtures x m , the first two

terms on the right-hgnh side of eqn. (8)vanish (AS,, - )and the condition that AG,:, be negative reduces to thecondition tbat t he enthalpy of mixing he negative; tha t is,

AGmix RTxn-=-

v $102 < 0V .

(9)

Early attempts a t predicting the miscihility of polymer

hlend concentrated on the use of Hildehrand's (19) solubilityparameter 6 as popularized by Bohn (20) and defined by

In its simplest form, this approach presumes that the onlysource of a net unfavorable interaction is a difference in sol-uhility parameters hetween the constituent pd?.mers in thehlend. Berause it is unfavorable, it must heminimized by se-lection of an alte rnate polymer whose solubility parametermatches or yields a lower solubility parameter difference. In

spite of the tremendous amount of work in this area, the sol-ubility parameter approach has been a dismal failure in pre-dicting miscihilitv of ~olv mer lends. Further attempts were. -made iirst by wn~bin inghesolubility parameter with an es-

timateof the ~ol ari tvnd then hsnttemptinr! toaccount for

the donating and accepting ~ i o ~ e r t i e sf the hydrogenbonding effects. These refinements have been beneficial, hut

they have failed to provide a predictive scheme which, withoutusing any solution parameter , predicts polymeric structureswith enhanced probability of exhibiting miscihility.

Another at tempt a t predicting the miscibility of polymerhlend relies on eqn. (I ), which reduces to the condition that

the xlzhe negative. Indeed, the importance of specific inter-actions has been pointed out by several investigators (4,5,21) .

Volume 58 Number 11 November 1981 949

1981_ o. olabisi_ interpretations of polymer-polymer miscibility_ j. chem. educ., 58, 944

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