Thermodynamics of mixing polymers

THERMODYNAMICS OF MIXING POLYMERS* A. A . TAGER, T. I . SltOLOKHOVICH, I . M. SHAROVA, L . V. ADAMOVA

and Yu. S. BESSOl~OV A. M. Gor'kii State University, Urals

(Received 24 December 1974) Free energies Ag~, enthalpies Ahz and entropies TAsx of 1T~ixingwere calculated for eight p o l y m e r - p o l y m e r systems. I t was shown t h a t the polymer compositions studied, in respect of the shape of the curve showing the concentration dependence Agx, m a y be classified in three groups: stable, metastable and unstable. For a stable cellulose n i t r a t e - p o l y v i n y l a c e t a t e system a reduction in entropy was observed during mixing, which m a y be due to ordering of elements of the system. F o r metastable systems thermodynamic functions of mixing Ahx and TAsx are positive in one range of composition and negative in the other. An unstable p o l y m e t h y l m e t h a c r y l a t e - p o l y b u t y l m e t h a c r y l a t e system undergoes endothermic mixing over the entire range of composition and the free energy varies positively and entropy of mixing increases in this case.

A STI~CTLY quantitative approach to solutions of even low molecular weight. substances is not only limited by the range of considerable dilutions. An objective pattern of the behaviour of solutions, as noted correctly [1], can only be given by purely thermodynamic characteristics in the form of main thermodynamic functions (enthalpy, free energy, entropy) according to concentration and temperature independent of more or less likely hypotheses, assumptions and models. All this is not only applicable to electrolyte solutions, but is quite correct for polymer solutions and polymer-polymer systems. In the latter case, however, it appears much more complex, since many values normally determined cannot be measured. For example, polymer vapour pressure cannot be measured or the heat of mixing polymers cannot be directly determined; however, the latter can be calculated by the Hess law [2, 3]. We have recently proposed a similar method for calculating the free energy o f mixing polymers [4]. The sign and magnitude of this parameter is known to determine the direction of the process and the thermodynamic affinity of components, and the sign of the second derivative of free energy according to composition 82g/Ox~ determines the measure of thermodynamic stability of the binary system [5]. The method proposed is based on the fact that the Gibbs free energy G is. the same function of state as enthalpy H and is therefore independent of t h e * Vysokomol. soyed. AI7: No. 12,. 2766-2773, 1975. 3178

Thermodynamics of mixing polymers

3179

course of the process. Consequently, we are justified in formulating several equations similar to thermodynamic equations and calculating the value in which we are interested. mx of polymer I-4-m 2 of polymer I I = s o l u t i o n III--AGz solution I I I -4-solvent = solution IV--AGm

S

(1)

Solution IV may be obtained by another method. ml of polymer I~-solvent=solution I--AGI m s of polymer I I + s o l v e n t = s o l u t i o n II--AGn

]

(2)

solution I + s o l u t i o n II-=--solution IV--AGIv Hence it follows that

--,dG.-- AGnI= --AGI-- AGn-- AGIv

(3)

For very dilute solutions of AGiv-~ 0, the free energy of mixing of two polymers

--AGx=AGnI--(AGI~AGH) ,

(4)

where AGI, AG~I and AGm are free energies of mixing I and II of polymers and their mixtures with a general solvent, respectively calculated for 1 g polymer or 1 g mixture. If in a " d r y " polymer composition gravimetric proportions of each component are denoted by wl and w2, the average specific free energy of l g of this mixture m a y be expressed by the equation:

-- Agx= AGm-- (wlAGI + w2AGH)

(5)

All the foregoing is essentially equivalent to determining the free energy of solution for a mechanical mixture of two polymers of given composition and their mixed composition, while the difference between them is the free energy of mixing of two polymers. The method proposed was tested for m a n y polymer-polymer systems. Calculated values were compared with mixing enthalpies of these compositions and mixing entropies calculated. Several generalizations may therefore be made and numerous problems discussed. Thus, when dealing with first results of the determination of free energies of mixing, the view was expressed that thermodynamics cannot be applied to systems such as polymer mixtures. This cannot, of course, be accepted since thermodynamic ratios are successfully used for metastable systems [6]. It is precisely on the basis of a thermodynamic study of the system that we can determine whether it is stable, metastable, or labile. It is relevant here to cite Prigozhin and Defey, according to whom "very often metastable phases are also regarded as stable and naturally resistant since these phases have some general features which distinguish them from unstable phases" [5]. Frenkel' and Yel'ya-

3180

A . A . TAOER et

al.

shevich when e x a m i n i n g the principles of r e l a x a t i o n t h e r m o d y n a m i c s [7] corr e c t l y n o t e t h a t the " s t a t e of relative equilibrium will simply be t e r m e d equilibrium a n d p a r a m e t e r s of the s y s t e m in these states r e m a i n u n c h a n g e d for a fairly long time, c o m p a r e d with the e x p e r i m e n t a l t i m e . . . " Consequently, the v a l i d i t y of this cycle does n o t cause a n y d o u b t in e x a c t l y t h e same w a y as calculations previously m a d e concerning heats o f mixing o f polymers [2, 3]. Difficulties are involved in the e x p e r i m e n t a l d e t e r m i n a t i o n o f values AGI, AGH a n d AGnI a n d when miscalculating results. This is a highly a c c u r a t e exp e r i m e n t which requires v e r y sensitive a p p a r a t u s a n d v e r y extensive t h e r m o d y n a m i c calculations, to which a p p r o x i m a t e m e t h o d s of calculation h a v e to be applied. To determine AGI, zlGn and adsorption of a general solvent by sition. The adsorbate used should should be completely miscible with proposed.

AGIH it was proposed to obtain isothermal curves of individual polymers and mixtures of different compobe a general solvent for both polymers, i.e. polymers the latter, as required by the Hess law [8] and the cycle

TABLE 1. CHARACTERISTICSOF MIXTURES Mixture, No. 1

Polymers

Symbol

Composition

Adsorbate

Polymethylmethacrylate-polybutylmethacrylate

PMMA-PBMA

2:8;4:6; 5:5;6:4; 8:2

Acetone

Cellulose nitrate-polyvinyl acetate

CN-PVA

3:7;4:6; 5:5;7:3

Cellulose acetate-polyvinyl acetate

CA-PVA

3:7;5:5; 7:3

Cellulose acetate-cellulose, nitrate

CA-CN

1-5:8.5; 4:6;7:3

Polyvinylchloride-polymethylmethacrylate

PVC-PMMA

3:7;5:5; 7:3

Epoxy resin-polyvinylacetate

ED-5-PVA

Epoxy resin-SKN- 10 rubber

ED-5-SKN-10

Epoxy resin-SKN-18 rubber

ED-5-SKN-18

2:8;4:6; 5:5;6:4; 8:2 2:8;4:6; 5:5;6:4; 8:2 3:7;5:5; 6:4;8:2

Tetrahydro furan Acetone

Thermodynamics of mixing polymers

3181

To study adsorption, apparatus was used with helical McBain scales [9] (sensitivity of helixes b~ing 0.3-0.5 mm/mg). Vapour pressure was measured by U-shaped pressure gauges. Readings were taken of the values measured using a cathetometer. TABLE 2. CHARACTERISTICS OF POLYMERS

Polymer Cellulose nitrate Cellulose acetate Polymethylmethacrylate (mixture 1) Polymethylmethacrylate (mixture 5) Polybutyl methacrylatc Polyvinyl chloride Polyvinyl acetate (mixture 2 and 3) Polyvinyl acetate (mixture 6) Epoxy resin ED-5 SKN-10 Nitrile rubber SKN-18 Nitrile rubber

Brief description of the sample Industrial product, Industrial product, Industrial product, merization Industrial product,

11.9% N, acetyl number 52.3 obtained by bulk polyLSO-M

Industrial product of emulsion polymerization Industrial product S-65 Industrial product obtained from 'bead' polymerization Industrial product obtained from 'bead' polymerization Industrial product, 21-3°/0 epoxy groups Industrial product Industrial product

/t~w 83,000 81,000

790,000 98,700

960,000 107,200 280,000 104,000 450 250,000 250,000

Systems examined are shown in Table 1. Characteristics of individual components are shown in Table 2. Epoxy resin and nitrile rubbers are highly viscous oligomer liquids, mixtures of which were prepared in a vessel while heating. Before adsorption experiments all samples were treated at 50-60°/10 -2 tort and then further evacuated in an apparatus at 10-5 tort to constant weight. Other polymers and mixtures of given composition were investigated in the form of thin films obtained from 5~o solutions in acetone (samples 1-4) or tetrahydrofuran (sample 5). Finished films (5=20-30/~rn) were dried at 25° to constant weight in vacuum. Solvents were purified by well known methods, their constants corresponding to results in the literature. Figure 1 shows a d s o r p t i o n isotherms o f acetone v a p o u r for a P M M A - P B M A system. A d s o r p t i o n isotherms are also similar for o t h e r systems previously exa m i n e d [10, 11] a n d dealt with in this s t u d y . According to the n a t u r e of components, a d s o r p t i o n isotherms of mixtures m a y be situated between a d s o r p t i o n isotherms of individual c o m p o n e n t s (Fig. 1) or a b o v e a n d below them. A d s o r p t i o n isotherms should be obtained, w i t h the highest degree o f dilution possible, which is a r a t h e r difficult p r o b l e m as equilibrium v a p o u r pressure over the solution Pl differs v e r y slightly from s a t u r a t e d v a p o u r pressure p l , v e r y sensitive pressure gauges being required for m e a s u r e m e n t . Chemical potential difference per g solvent A/I~ was calculated from a d s o r p t i o n isotherms using e q u a t i o n Pl ~, Pl where M~ is the molecular weight o f solvent. 1

A/~= -M~ RT

in

(6)

3182

A.A. TxoE~ eta/.

Another even greater difficulty arises after t h a t - - t h e calculation of Ap2 which is carried out according to equation aA].L 1

W1 ~

aA/.g2

"~--W2 ~

~---~0 ,

(7)

where wz and w~ are the gravimetric proportions of solvent and polymer components in the solution formed in the course of ~isorption.

-

°

!

I~

A 2 •

j

× ~ nj O'5

o 8 •

0

]]1t

7

0-q

0.8 ~/~0

FIG. 1. Adsorption isotherms of acetone vapours for P M M A (1), P B M A (2) and a

•n~ture of PMMA-PBMA of 2 : 8 (3); 4 : 6 (4); 5 : 5 (5); 6 : 4 (6); 8 : 2 (7) composition. A general solution of differential equation (7) m a y be given as: A~z A/~----- -- f w~W-d~l( a ~ ) + C ,

~CO

(8)

Thermodynamics of mixing polymers

3183

where C is a constant which is found when A / ~ - . - - ~ , A/~s-*0. Therefore, t~ldng in formula (8) the upper limit of integration A/~I-'-- or, we obtain C-----0. Hence it is evident that the dependence of A/~S on Agl is given by the ratio J/tj

z~s=- I - ~ d(zg,)

(9)

--0o

Integral (9) cannot be accurately calculated since the curve showing t h e relation wl/w 2 (A/z1) when w2-~ 1, becomes infinite. Therefore, as is normally done, an approximate method of calculation should be used [12], consisting of two stages: approximate integration (by the Simpson formula) Apt

,d~'x

where A/12' is the minimum experimental value of the potential corresponding to the value closest to ws= 1 among the values measured and calculation of correction A in respect of the area not taken into consideration J#,'

The value of A is found by extrapolation of the curve which shows the dependence of A/z~' on wl which is linear in the region of w1 close to zero A/zs----Ags'-4-A

(12)

Values of A/6 and Aps being known the average free energy of mixing was calculated for solutions of different concentrations (per g solution)

Agm=Wl~px+WsZ~

(13)

The overall error of calculating Ag'~ (bearing in mind approximate integration) is ~ 1 0 % . Typical curves showing the dependence of Ag m on the composition of t h e solution are shown in Fig. 2. Since all samples were completely soluble in the solvents used, the curves were extrapolated in point ws=0. The value of A ~ being known (per g solution), AG m related to g polymer o r polymer composition was found from the equation ACre= Agm(mx +ms) = Agm, ms ws

where ml and m a are the weights of solvent and polymer, respectively.

(14)

3184

A . A . TAoss et ol.

I t is evident from curves of Fig. 2 that the Ag/w~ratio depends on concentration. We therefore examined the limit of this ratio (aAg'~/aw~)w~=o. This value has the geometrical significance of the tangent to the curve showing the relation of Agm~--f (we) at the point w2----0, which is equal to the length of the section 0.q

0 r~

i

l

c~:=f ~

~

IA

-0"4

-f.f

-2"8 m

~g , c,q/g

FIG. 2. Dependence of the average free energy of mixing on the composition of solutions in acetone for a PMM/k-PBMA system (see Fig. 1 for notations).

intersected on the ordinate axis when w~----1 (Fig. 2). This section is Ap2 when Apl----0. Hence

AG----1 g polymer. Alz~x/m (g) solvent. 0

(15)

Consequently, the AB section is the free energy of mixing 1 g polymer (or polymer composition) with an infinitely large amount of solvent. Values of AGI, AGII and AGm thus calculated were substituted in equation (5) and values of Ag~ were calculated for polymer-polymer systems. Figure 3 shows the dependence of average free energies, enthalpies and entropies of mixing of two polymers and their ratios in a dry composition. Values of Ah® were taken from a previous study [13] or determined b y the method described in this study. Values of TAs~ were calculated from the equation Ag~

Thermodynamics of mixing

31'85

polymers

=Abe=TAsk.

The Figure shows that various polymer-polymer systems are characterized by different relations of Ag~=f(w~), enthalpies and entropies of mi~ing being predominant, reflecting the interaction between polymers and the degree of ordering of the system. Regarding the form of relations the systems may be classified in three groups. c~

b

# PVA

..,

C

3

o,.~, 0,.8~CN

PVA

-#

3

PVC

PMMA

i

-8 -12

Z

12 8 4' CA -q -8

-12

CN PMMA 02

V

Oq

PBMA ED-5 06

o.6

SKN 10 SKN-18 PVA

!

Fro. 3. a-e--Variationofthermodynamicfunctions (J/g)withthecompositionofthe polymer: zlg:~ (1), Ahx (2), TAsx (3); f--variation of a v e r a g e free energy Agx for mixtures of: ED-5SKN-10 (•); ED-5-SKN-18 (2); ED-5-PVA (3).

The first group of systems is characterized by Ag~Oover the entire range of composition (the curve is convex downwards). These are thermodynamically stable systems, with which polymer components are completely miscible. The systems studied are: CN-PVA system previously obtained by Dobry [14] and the ED-5 PVA system. Components of the CN-PVA system are miscible with heat liberation (Ah~<0) and are characterized by negative non-combinatorial entropy of mixing. This means that different polymer macromolecules are packed in a more orderly fashion in the mixture than in the molecular phase. It is evidently the ability to form joint structures which is the main cause of mixing of these polymers. These systems are stable and the permanence of their operational characteristics may be guaranteed over a period of time. For the second group of systems (PVC-PM~IA, CA-PVA, CA-CN, ED-5 with SK_N-10 or SKN-18) there is a section on the curves showing the dependence of Ag~=f (w~) which is convex upwards (a2Ag/aw~
318~}

A.A. TAGF,net aI.

sist of three sections, i.e. the first derivatives of these parameters according t o composition show a discontinuity. These curves are obtained for several liquidliquid systems [15] which are separated into two phases. However, if for a liquid-liquid system separation is rapid, a two-phase metastable polymer-polymer system may be in this state for a considerably longer period of time. Factors of stability are the high macro-viscosity and the presence of intermediate layers, ideas of which were introduced by Voyutskii [16] and Kuleznev [17]. The segmental mutual solubility of both polymers in the intermediate layer is reflected by the negative value of Ag~. As shown previously [18], this form of curve showing heats of mixing corresponds to the phase equilibrium diagram, when on changing temperature t h e composition of both phases does not become the same. Consequently, these two phase polymer-polymer systems have no critical temperature of mixing. Thermodynamics of these systems predicts the unilateral diffusion of o n e component into the other, which was experimentally observed by Voyutskii, Kamenskii and Fodiman [19]. One part of the intermediate layer in which component A is diffused, becomes looser and softer, which is accompanied by positive values of Ah~ and A8x. The other part of the intermediate layer, from which diffusion takes place, is compressed and ordered, which is accompanied by heat liberation and a reduction of entropy [18]. Results shown in Fig. 3 mainly predict diffusion of PVC into PMMA, CN into PVA and CA into CN. The PMMA-PBMA system is in the third group of systems. The curve Ag~(w2) (Fig. 3b) of this system in the entire range of composition is in the positive range (Ag~0) and convex upwards (a2Ag/aw~0), which is evidence of the thermodynamic instability of this system. Mixing PMMA with PBMA is accompanied, over the entire range of composition, by a strong endothermic effect which does not enhance mixing and is evidence of interaction taking place mainly between homogeneous molecules, compared with heterogeneous ones. An increase of entropy on forming the PMMAPBMA system exceeds the combinatorial entropy of mixing of two polymers, calculated by Gee [20] and suggests that in the mixture heterogeneous molecules are less ordered, compared with packing in individual polymers, i.e. components of the system cannot form joint structures. This may be due to steric hindrance by a butyl radical which prevents dense packing. Kern [21] came to a similar conclusion on studying the effect of dimensions of the alkyl radical in polyalkylmethacrylates on interaction with PVC. The incompatibility of components of this system has also been confirmed by a dielectric method [22].

TransZated by E. SElYIERE REFERENCES

1. K. P. iYIISHCHENKOand G. M. POLOTRATSKII,Voprosy termodinamiki i stroyeniye vodnykh i nevodnykh rastvorov elektrolitov (Problems of Thermodynamics and Structure of Aqueous and Non-aqueous Electrolyte Solutions). Izd. "Khimiya", 1968

Mechanical properties of epoxy resin binders

3187

2. G. L. SLONIMSKII and G. V. STRUMINSKII, Zh. fiz. khimii SO: 1941, 2143, 1956 3. N. V. MTIEHAILOV, L . G. TOKAREVA and E. Z. FAINBERG, Vysokomol. soyed. 1: 404, 1959 (Not translated in Polymer Sci. U.S.S.R.) 4. A. A. TAGER, T. I. SHOLOKHOVICrH and M. V. TSHJPOTKINA, Vysokomol. soyed. A14: 1423, 1972 (Translated in Polymer Sci. U.S.S.R. 14: 6, 1594, 1972) 5. I. PRIGOZHIN and R. DEFEY, Kblmlcheskaya termodinamika (Chemical Thermodynamics). Izd. "Nauka", 1966 6. V. P. SKRIPOV, Metastabil'naya zhidkost' (Metastable Liquid). Izd. "Nauka", 1972 7. S. Ya. FRENKEL' and G. K. YEL'YASHEVIC~, Sb. Relaksatsionnye yavleniya v po]imerakh (Relaxation Effects in Polymers). Izd. "Khimiya", 1972 8. G. I. HESS, Termokhimicheskiye issledovaniya (Thermochemical Studies). Izd. AN SSSR, 1958 9. A. A. TAGER and V. A. KARGIN, Kolloidn. zh. 10: 455, 1948 10. A. A. TAGER, Vysokomol. soyed. A14: 2690, 1972 (Translated in Polymer Sci. U.S.S.R. 14: 12, 3129, 1972) 11. A. A. TAGER, T. I. SHOLOKHOVICH and Yu. S. BESSONOV, Europ. Polymer J. 11: 321, 1975 12. I. S. BEREZIN and N. P. ZHIDKOV, Metody vychislenii (Methods of Calculation). Izd. "l~auka", 1966 13. A. A. TAGER and Yu. S. BESSONOV, Dokl. AN SSSR 205: 1146, 1972 14. A. DOBRY and F. BOYER-KAWENOKI, J. Polymer Sci. 2: 90, 1947 15. V. P. BELOUSOV and A. G. MORACHEVSKII, Teploty smesheniya zhidkostei (Mixing Heats of Liquids). Izd. "Khimiya", 1970 16. S. S. VOYOUTSKII and V. L. YAKULA, Vysokomol. soyed. 2: 51, 1960 (Not translated in Polymer Sei. U.S.S.R.) 17. V. N. KULEZNEV and S. S. VOYUTSKII, Kolloidn. zh. 35: 40, 1973 18. A. A. TAGER and Yu. S. BESSONOV, Vysokomol. soyed. AI7: No. 11, 1975 (Translated in Polymer Sci. U.S.S.R. 17: 11, 19, 1975) 19. A. N. KAMENSKH, N. M. FODIMAN and S. S. VOYUTSKII, Vysokomol. soyed. 7: 609, 1965 20. G. GEE, Quart. Revs. London Chem. Soc. 1: 265, 1947 21. R. J. KERN, J. Polymer Sci. 33: 524, 1958 22. A. A. TAGER, V. D. KRASYUK, Sb. Sintez i fiziko-khimiya polimorov (Synthesis and Physico-Chemistry of Polymers). Ied. "Naukova dumka", No. 15, 1974

EFFECT OF ACTIVE DILUENTS ON MECHANICAL PROPERTIES OF EPOXY RESIN BINDERS* YE. ]~[.FILYAI~OV, ~E. M. BLYAKHMA!~, T. V. KRASNIKOVA, 0. G. TARAKANOV and ¥E. B. PETRILENKOVA All-Union Scientific Research Institute of Synthetic Resin Manufacture

(Received 2 January 1975) A study was made of the effect of a highly active diluent (ETF-10) on the mechanical properties of a solidified binder prepared from ED-16 epoxy resin. I t was shown that the use of this diluent enables low viscosity binders to be obtained without a * Vysokomol. soyed. AI7: No. 12, 2774-2778, 1975.