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The conformational and thermodynamic properties of poly-α-methylstyrene in various solvents
602
V. YE. EsxI~r e¢ td.
3. G. D. LITOVCHENKO, G. S. SOKOLOVA, A. V. VOLOIZH~A, G. I. KUDRYAVTSEV and 8. P. PAPKOV, Zh. prikl, spektroskopii 20: 455, 1974 4. Sh. SOBAJIMA, J. Phys. Soc. Japan 23: 1070, 1967 5. E. IIZUKA, Biochim. et biophys, acta 243: 1, 1971 6. V. A. PLATONOV, O. A. KHANCHICH and T. A. BELOUSOVA, Vysokomol. soyed. BI7: 726, 1975 (Not translated in Polymer Sci. U.S.S.R.) 7. B. Z. VOLCHEK, A. V. GRIBANOV, A. I. KOL'TSOV, A. V. PURKINA, G. P. VLASOV and L. A. OVSYANNIKOVA, Vysokomol. soyed. A19: 321, 1977 (Translated in Polymer Sci. U.S.S.R. 19: 2, 1977) 8. V. N. TSVETKOV, Ich. zap. Len. pod. in-ta im Gertsena, t. X, 1938 9. E. R. BLOUT and E. SHECHTER, Biopolymers 1: 565, 1963 10. V. N. NIKITIN, M. V. VOL'KENSHTEIN and B. Z. VOLCHEI(~ Zh. tekn. fiziki 25: 2486, 1955 11. P. CHATELAIN, Bull. Soc. Trans. Mineral et CrystaJlogr. 66: 105, 1943 12. M. M. KUSAKOV, V. L. KHODZHAYEVA, M. V. SIHSHKINA and I. I. KONSTANTINOV, Kristallograflya 14: 485, 1969 13. P. FLORY, Prec. Roy. Soc. A234: 73, 1956 14. F. A. BOVEY, G. V. D. TIERS and G. FILIPOVICH, J. Polymer Sei. 38: 73, 1959 15. B. Z. VOLCHEK and A. B. PURKINA, Vysokomol. soyed. A l l : 1563, 1969 (Translated in Polymer Sei. U.S.S.R. 11: 7, 1772, 1969) 16. I. SANDEMAN, Prec. Roy. Soc. A232: 105, 1955 17. M. TSUBOI, J. Polymer Sci. 59: 139, 1962
THE CONFORMATIONAL AND THERMODYNAMIC PROPERTIES OF POLY-~-METHYLSTYRENE IN VARIOUS SOLVENTS* V. Y~.. EsKrs, T. N. NEKaASOVA, U. B. ZHURAYEV, A. F. PODOL'SKII and A. A. TA-~A~ High Polymers Institute, U.S.S.R. Academy of Sciences
(Received 19 July 1976) Light scattering and viscometric methods have been used to determine the unperturbed dimensions K0 of a poly-~-methylstyrene produced by anionic polymerization (using the Stoekmayer-Fixman extrapolation), the number of solvent molecules No sorbed by the polymer chain unit, and the molecular packing density of the polymer in various solvents. Ke for polymethylstyrone (PMS) have been found to increase with the thermodynamic quality of the solvent. The mechanism of the solvent effect on K0 has been assessed after consideration of the energy of polymer-solvent reactions and of N,. An energy equivalence is assumed for changes in the unperturbed dimension under the influence of the solvent and the temperature. T ~ effect o f t h e s o l v e n t on t h e e q u i l i b r i u m o f c h a i n f l e x i b i l i t y ( u n p e r t u r b e d d i m e n s i o n s ) is one of t h e m o s t i n t e r e s t i n g b u t l e a s t i n v e s t i g a t e d p h e n o m e n a o f j n t e r m o l e c u l a r r e a c t i o n s w h i c h t a k e p l a c e in p o l y m e r solutions. V e r y l i t t l e i s * Vysokomol. soyed. AIg: No. 3, 525-532, 1977.
Thermodynamic properties of poly-a-methylstyrene
603-
k n o w n a t p r e s e n t a b o u t t h e m e c h a n i s m o f this effect, a n d a n e x c u s e f o r it is t h e purely empirical approach to this problem; only a wealth of experimental material w o u l d l e a d t o f i n d i n g a m e a n s o f s o l v i n g it. The dependence of unperturbed chain dimensions (and of a number of other p a r a m e t e r s ) in p o l y - 2 , 4 - d i m e t h y l s t y r e n e ( P D M S ) o n s o l v e n t p r o p e r t i e s h a d b e e n t a c k l e d b e f o r e [1] a n d s o m e o f t h e likely c a u s e s h a d b e e n e v a l u a t e d . T h e w o r k d e s c r i b e d h e r e deals w i t h t h e p r o p e r t i e s o f p o l y - g - m e t h y l s t y r e n e (PMS) i n 12 s o l v e n t s a n d t h e e v a l u a t i o n o f t h e r e s u l t s f o r it a n d for s o m e o t h e r p o l y m e r s . EXPERIMENTAL
PMS samples were synthesized by anionic polymerization of the monomer in T H F at --78°C; the catalyst was the disodium-a-methylstyrene tetramer (live polymer). T h e synthesis and the polymerization method have been described before [2]. The stereo-isomerism of the PMS samples was determined by proton magnetic resonance (PMR) spectrometry on a J E O L C-60 H L instrument at 180°C on 10% PMS solutions in o-dichlorobenzone. The contents of the iso I, hetero H and syndio S triades were calculated from the comparison of the respective signal intensities of the a-methyl groups; it was found to be: 1--10-14~o, H-46-49°~o, and S--39-42°~o in separate PMS samples. The NMR signal of the methyl groups was identified on the basis of earlier results [3]. (The authors are indebted to A. I. Kol'tsov and V. M. Denisov for the recording of the NMR spectra of the PMS). The molecular weights (mol.wt.) ~/w of the PMS samples were determined in toluene at room temperature (22°C) by the light scattering method in a "Sofica" photogonio-diffusometer. Six samples were examined; these had ~w in the range (3-2-75)× 10~. The J~fw/llTf~ ratio, determined by gel chromatography, was 1.05-1.12. Tile intrinsic viscosity [t/] was determined in an Ostwald viscometer at 25°C with 60-190 sac flow times of the solvents. The density and the refractive index of the solvents used were those contained in the Tables. The found [¢] and ~7fwwere used to determine the unperturbed dimensions of the PMS. molecules in various solvents by the Stockmayer-Fixman method [4]. The graphical data were processed by the method of least squares. The partial specific volumes ~ were determined at 25°C by the method described by Nekrasova and Eskin [5]. The temperature was 35°C where ~ and [t/] were determined in cyclohexane. The number of solvent molecules sorbed on a single polymer chain unit was determined by light scattering from the ~ of the polymer in the pure solvent and in solvent] /precipitant mixtures, using the Lange [6] method and that used earlier [1]. A number of normal aliphatic alcohols were used as the precipitants. RESULTS
T h e p a r a m e t e r Ke=q)'(k~/M) ~ in t h e [ti]e=KoM I ratio, w h i c h c h a r a c t e r i z e s t h e r e l a t i v e u n p e r t u r b e d coil d i m e n s i o n s ( R ~ / M ' ) w a s f o u n d b y t h e k n o w n g r a p h i c a l e x t r a p o l a t i o n p r o c e d u r e o f [tl]/M*=.f(M*) t o M * = 0 , w h i c h is b a s e d o n [4]:
[tl]/M ~----Ko-k- 0.035 ~ ' B M ~,,
( 1)
in which B=p[M~; p t h e o c c l u d e d v o l u m e o f t h e c h a i n u n i t ( s e g m e n t ) i n t h e
~04
V. YE. Esxrs eta/.
particular solvent; M0, its mol.wt. (R0~ is the mean square radius of inertia of t h e macromolecule, ¢ ' ~ 3 - 9 × 1024). Recent direct measurements of the statistical chain segment A in PDMS' and PS [7] confirmed the A differences in thermodynamically good and poor solvents found by extrapolating [~]/M~ to M ~ 0 by the Stockmayer method [4]. TABLE 1. SOMEOF T~E PARAMETERSOF THE INVESTIGATEDSOLVENTSANDTHE EXPERIMENTAL FINDINGSFOR PMS Solvent Cyclohexane Butylethylketone Isopropylbenzene Decalin Toluene Benzene Tetrachloroethylshe
Chloroform Chlorobenzene Diehloroethane Dioxane Pyridine
cal )/ /era ~ 8.2 8.3 8.6 8.8 8.9 9-2 9.3 9-3 9.3 9.9
10.0 10.7
~' Debye
2"7 0"4
VI, K0 × 10i, cm3/mole g/em3 108 144 139 156 106
7.2 7.5 8.9 8-3
9.7 10.0
89
K~ × 10a, g/era* 7.2 7.5 3.6 3.6 2-6 2.4
~8"9
1"2 1"6 2"0
80 102 79 86
2"2
11.2 10"2 9"3 9"8 ~9.6
2.2 2.7
3.0 3.6
N
0.5C 0.41 0-6C 0.58 0-64 0.6fi
0.5 -1.0 1.2 1.2 1.4
0.61
--
0.6e 1.2 0.64 0.62 0-7 0.60 0.9 0.63
v, em*/g 0"890 0.885 0.883 0"874 0.869
0.887
One gathers from the Table 1 results t h a t Ke~f(a) increases in a number of solvent solutions of PMA with solvent quality, and the measure of this is taken t o be the exponent a in
[~]-~K,aMa
(2)
The type of the Ko-~f(a) function (Fig. 1) is the opposite for PMA t h a n for PDMS, for which the K0 drops with increasing a [1]. We shall deal below with t h e reasons for this difference. Although Kamide and Moore [8] consider their extrapolation of the log K~ ~f(a--½) to a ~½ to be valid 0nly for a Re2 which is independent of the solvent, such extraplation yields K0 in the case of PMS which is very close to the K0 value obtained in cyclohexane (Fig. 2). The use of Ke found in non-ideal solvents will give points on the log Ko:f(a) curve which are also grouped around the line interesting the ordinate in Fig. 2 at a point close to t h a t for Ke in cyclohexane. It should be noted however t h a t K0 characterizes in eqn. (2) not the individual properties of a particular solvent, but merely points to the extent by which the polymer reacts with it and enhances the swelling of the coils as a function of chain length. In this connection it will be quite satisfactory to t r y and establish
Thermodynamic properties of poly-a-methylstyrene
605
how the polymer properties in the solvent correlate with the values which are a direct characteristic of the solvent molecule. These are at present the following 3 parameters: solubility parameter J1 (the cohesive density of the liquid is j2), which determines the energy of molecular interactions in the pure solvent, molar volume V1, and the dipole m o m e n t / ~ of the molecules in the case of polar liquids. We already mentioned before [5, 9, 10] t h a t the effect of dipole moment/~, associated with its polarizing action on the chain unit of the non-polar polymer (or with the dipole-dipole reaction in the case of a polar polymer), will greatly complicate the intepretation of the full picture of polymer properties in a range of solvent~. At this stage of the study one must therefore try to clarify, where possible, the direction of the specific effect of solvent molecule polarity. As regards the exponent a in eqn. (2) as a measure of thermodynamic quality of the solvent (for the particular polymer), its value incorporates all the mechanisms of the polymer-solvent interactions. This is particularly clear from the dependence of a on 51 which is given by one general curve regardless of solvent polarity, at least in the case of non-polar or slightly polar polymers (Fig. 3, curve 1). The largest a value is equivalent to Jl for PMS which is parameter J2 of the polymer (9.2-9.3 kcal~/cm~).
KO
P
11
-Y'O-
o
2
lg .q -0"5 l
0.5
0.5 FIe. 1
a
g'5
a
I 0"7
Fie. 2
F i e . 1. K~ × 10' as a f u n c t i o n o f a for P M S in v a r i o u s s o l v e n t s . FIG. 2. / - - l o g K~; 2 - - l o g K o as f u n c t i o n s o f a for P M S in v a r i o u s s o l v e n t s .
We shall now examine the 51 functions of two parameters directly connected with the polymer-solvent interaction, namely N,, the number of solvent molecules sorbed on average by a single chain unit, and the partial specific volume ~. One can see from the N,----f(al) and v--~f(J1) functions (Fig. 3, curves 2 and 3) t h a t the m a x i m u m sorption of solvent by the polymer (N,) and densest packing in solution (~ minimum) applies when Jl~-J2, which corresponds with a better thermodynamic quality of solvent a.
608
V. YE. E s x x s
et a/.
The reason for the parabolic shape of the J1 functions of a, N0 and ~ is thought to be the fact that the changes of the thermodynamic functions, especially of the internal energy are in a direct relation with (Ji--Jz) = (see [10, 11] for example). One can assume the sorption of the solvent molecules to be intimately linked with the molecular packing density of the polymer in the solutions. The iV, dependence of ~ is especially strong in the case of aromatic solvents and less in solvents with a saturated structure (Fig. 4). The reason for such a difference is probably the specific reaction of the aromatic solvent molecules with the phenyl branch of the polymer.
0"8
l'~
0"5 ~ ¢r
I
[
I
1
3
o
0"88
0.87 tf ~ la
+_ o
,
I
0"1/7V 0"~
!
[ °°
o
o
0"88 o
o o
o
o
o
0"87
0 I
I
9
io
Fzo. 3
4
I
1
I
0.+
0"8
/.2
Ns
Fro. 4
l~o. 3. /--Exponent a; 2--the number of sorbed molecules Na; 3--the partial specific volume ~; 4--K~, as functions of parameter Jl. FIo. 4. The partial specific volume 0 as a function of ~Ve for PMS in: /--aromatic; 2--nonaromatic solvents. I t was impossible to establish any noticeable effect of the bulk of the solvent molecules (V1) on the polymer properties which are discussed here. On turning now to the dependence of the unperturbed dimensions of the macromolecules on the solvent properties we notice that an intensification of the PMS reaction with the solven~ shifts the distribution of the isomeric state~ of the chain units towards an increase in the numbers of those with a less coiled conformation [12, 13], while the reverse is true in the case of poly-2,4-dimebhylatyrene [1]. The presence of the methyl group in ~-position in PMS thus subs~an-
Thermodynamic properties of poly-~-methylstyrene
60T
tially alters the energy balance of the reactions in the chains which also ought to include (as we shall see below) the sorption reaction. Typical is that in another polymer possessing an a-methyl g r o u p - - P M M A - - t h e unperturbed coil dimensions are also smaller in poor solvents t h a n in good ones [14]. One can also note that a further reduction in the solvent quality to below the ~ point (a<0.5) does not affect the chain flexibility, i.e. the K0 values are very similar in the case of butylethylketone (a~_0.4) and cyclohexane (a=0.5). Where the polymer reaction with the solvent is weak, the latter therefore does not affect the flexibility equilibrium of PMS. The relationship between K~ and 51 is not as distinct however as between K0 and a (Figs. 3, 4); there is only a tendency towards a Kt increase as 51 approaches 5t. This could mean that 51 is not the only factor on which the unperturbed dimensions depend in solution, and that there must he some other reasons for the changes in K~. As only some general theories have been suggested for explaining the solvent effect on the unperturbed macromolecular dimensions [15, 16], and the elaborations b y Burhard [17] disagree with the findings for PMS [1], we shall try here to find out whether one can associate K~ with the energy of the polymersolvent reaction. The measurements of the internal energy of dissolving the polymer, which correlates with (51--$2) 2, together with the entropy of mixing, determine the thermodynamic properties of the solution as a whole. It appears to follow from the discussion of the solvent effect on the total conformations of the chain units t h a t one must immediately turn to the energy of the chain unit reaction with its environment. The enrgy of intermolecular reactions is characterized in the liquid b y value 5~, and by 515~ in the case of mixtures (at least of non-polar components) [11]. The transition of the polymer chain unit from the solution into the hydrogenated monomer is linked in the partAcular solvent with the energy difference of its reaction with the environment (per 1 mole of chains), F~(5~1--522), in which V2 is the molar volume of the polymer. (This will be correct only for a pseudolattice model of the liquid when the coordination number Z in various solvents is regarded as being the same, and one neglects the actual conditions of molecular packing as t h e y are not easily calculated). As the range of solvents tested in this work contained liquids with 51<52 as well as 52>~1 the (5~1--5~) difference can be positive or negative in value. The assumption of dependence of K~ on the reaction energy with the environment cannot be coordinated with the similarly of the K~ values in solvents with 51<52 and 51>52 (see for example the K~ in dioxane and toluene: Table 1). This non-idcntity will disappear if one takes into account the additional energy of the chain unit reaction having some number Na of sorbed solvcnt molecules. The sorption energy Es had been determined by Lange [18] from the temperature dependence of ~ in the case of PS in toluene; this was found to be 0.9 kcal/mole. As N6 depends on solvent quality (Fig. 3, curve 2), it must have some peak value N o at 51---:5~(in the hydro-
608
V. YE. ESKI~ et ~ .
genaCed monomer). By bearing in mind the sorption, the entire change of t h e energy of the chain unit reaction with the environment AE (per mole of chain units) will equal: AE = V~= (~,--5,) + E s (N s--N°s) (3) Ea is fundamentally specific for a particular polymer-solvent pair. Although it was determined for only one such pair, we shall nevertheless regard it as approximately the same for various systems (which will be obviously correct only for non-polar polymers and solvents), i.e. to equal about 1 kcal/mole. For AE we shall write AE = -- V~= [(g~--~l) + 7 (Ns--N°)],
(3a)
in which ~=E,/5=V2. With z/E we also compared K~ for PMS and PDMS in various solvents (Table 2), and we shall assume 7 = 1 cal+/cm+ as ~2---10 cal+/cm + and V2---100 emS/mole for these polymers. The value of N o can be got by consecutive approximation from Ns=:f(AE) function or by extrapolation to gl=~= of Ns=f@~--Z,.I). The dependence of K1 on LiE is illustrated in Fig. 5a. I f one excludes the points belonging ~ the polar solvents, for which the energy o f interactions can differ from g~5,.V=, and the sorption energy is obviously much larger than 1 kcal/mole [18], the K~=f(zIE) linear function can be approximated b y a straight line with a slope characterizing the "energy factor" of the unperturbed coil dimensions dK~/K~d(AE). The calculation for which we took gz=9"3 cal+/cm + and Vz=-104 cm3/mole in the case of PMS, and 9.0 and 126 respectively for poly-2,4-methylstyrene, yielded a dK~/K~d(ztE) 0.6×10 -4 for the first, and --0.8 × 10 -4 for the second polymer. K tl3
•
0"37 0"J3
O,ql I
Q
e
l
0"5
]
"o
l!0
2
-3 E, kcal/rnole
/ ~
•
n
I
°
I
w
g
-,4 E pkcal/mole
~'kG. 5. The dependences of: a--K~, b--N=; on AE for: 1--PMS; 2--PDMS; in non-polar (blank circles), polar solvents (black circles). We shah now compare the "energy factors" of the unperturbed coil dimensions with the same values got by changing the solution temperatures. The dimensional increase must be attributed in this case to the energies CrT, in which Cr--par~ of the molar heat content of the polymer coonnected with the transitions due to conformation changes of the chains, and therefore value (2~02)+. There are no promising calculation results available for Cr. Its estimation gives C r = 1 cal/mole-
Thermodynamic propertieB of poly-~-methylstyrene
609'
• °C at 300°K in the case of P E [19] which makes about 6"5~/o of the total h e a t content Cv. Polymers with a more complicated chain unit structure ought t~ have a much smaller Cr, so t h a t a C r y 2 cal/mole.°C can be regarded as close to the t r u t h in the case of the polymers discussed here. (The Cv of PMS in solution w a s found to be 45 cal/mole. °C [20]).
0.06
0.02 -
I
O'G 0"5 2
I
~, OeOye
3
FIO. 6. The dependences of KI and of a for PMS on the dipole moment/2 of the solvent. The temperature coefficient was calculated for PMS and PDMS from d[~]/ /[t/] d T in a good solvent, i.e. toluene (between 24 and 75°C); it was found to be --3 × 10 -4 °C -1 (we show for comparison t h a t the dR/.RdT obtained for PS was 2.8× 10 -4 °C -I [21]). We thus found for d R / R d T about 1.5× 10 -4 (cal/mole} -~ which is close enough to the absolute value of the dK~/K~d(AE). The evaluation points to an energy equivalence between the unperturbed polymer chain dimensions under the influence of temperature and of the reaction with the environment (the solvent}. Of further interest is also to clarify the nature of the correlation between N s and AE. This dependence is shown in Fig. 5b for PMS' and PDMS. I t is in both cases (in non-polar solvents} a descending straight line. The slope of the l a t t e r was used to assess the d(AE)dNs, which was found to be about 2.0 kcal/mole for PMS and 1.7 kcal/mole for PDMS; the latter is 1.5-2 times larger t h a n the " p u r e " sorption energy of toluene on PS [19]. I t must be remembered however t h a t the AE together with the sorption energy include also the changes of lilac energy of the chain reaction with the environment, which also determined the d (AE}/dN, value. The monotonous nature of the N~----f(AE) function has obviously a physical meaning, i.e. t h a t the Ns decrease in a number of solvents is the direct consequence of the weakening of the polymer chain reaction with its low mol.wt, en-
V. Y~.. E s E i ~ e$ al.
-610
vironment. The nature of the dependences of K~ and N , on J E permits the assumption that desorption of the solvent molecules can be part of the mechanism which results in a change of the unperturbed polymer chain dimensions with temperature elevation. TABLE 2. THE ( J l - - ~ ) ' , (1V~-z¥,)- AND z~E-vALUE OF PMS AND POLY-2,4-DIMETHYLSTYRENE IN VARIOUS SOLVENTS
PMS (/V~= 1.6) Solvent Benzene
Toluene I)ichloroethano Chloroform Dioxane Tetrachlorornethane Decalin Isopropylbenzene Butylacetate p-Xylene Cyelohexane
J2--Jl
"0
,--N,
PDMS (N~=2.2) --~E, eal/molo
0.1 0"4 --0.6 0 --0.7
0.2 0-4 0.9 0.4 0.7
310 830 310 415 0
0.5 0.7
0-4 0.6
930 1340
5s--$1
1.1
--JE, cal/mole
--0"2 0"I --0"9
0.25 0.1 1.35
57 228 515
--1"0 0"4
1.75 0.3
860
0"5 0"2 1.1
N,--M#°
0.4 0.9
8O0 1030 1250
2280
I t is also possible to follow up the effect of solvent polarity on the reaction o f PMS in solution, which determines not only the thermodynamic quality of the ~olvent, b u t also the polymer chain flexibility. We illustrate as an example the dependence of a in eqn. (2), and of KS for PMS, on the dipole moment ~ of the solvent molecules. K~ and a decrease as g increases, and particularly a when ~u>2 Debye. Dondos and Benoit [14] stated that it possibly happenes that branches of the polar solvent molecules engage in the macromolecular chain units and that this must cause a reducticn of the unperturbed dimension KS. One cannot exclude another mechanism however b y which /~ affects the flexibility of polar polymers, namely the direct dipole-dipole reactions of the chain units with the polar environment which will change their conformations. KS will approach its value in a non-polar solvent when the temperature rises in both cases, or due to the association between bonds decomposing in the solvent molecules [14], or as result of their desorption from the polymer. The polymers which are used here have a low polarity and the effect of/~ on the K~ of PMS is of a secondary nature, affecting the thermodynamic quality of the solvent (causing an increase o f the 152--5,1 difference, an a decrease) as ~ increases [22]. An approximately parabolic type of dependence can thus be noticed on the solvent parameter J~ of PMS properties, such as is the exponent a in eqn. (2), the partial specific volume ~, and the number zVs of solvent molecules sorbed By the chain unit. The unperturbed dimensions of the PMS chain unit and Ns
Thermodynamic properties of poly-a-methylstyrene
611
are linear f u n c t i o n s o f the e n e r g y of t h e chain u n i t reaction with t h e low mol.wt. molecules o f t h e e n v i r o n m e n t , including t h e sorption e n e r g y of t h e l a t t e r on t h e polymer. Translated by K. A. ALLE~ REFERENCES
1. V. Ye. ESKIN, T. N. NEKRASOVA and U. B. ZHURAYEV, Europ. Polymer J. 11: 341, 1975; Vysokomol. soyed. A17: 2682, 1975 (Translated in Polymer Sci. U.S.S.R. 17: 11, 3085, 1975) 2. A. F. PODOLSKY, R. Ch. DASHKIN and A. A. KOROTKOV, J. Polymer Sci. 9, A I : 2259, 1971 3. K. C. RAMEY and G. L. STATTON, Makromol. Chemie 85: 287, 1965 4. W. H. STOCKMAYER and M. F. FIXMAN, J. Polymer Sei. CI: 137, 1963 5. T. N. NEKRASOVA and V. Ye. ESKIN, Vysokomol. soyed. AI5: 2429, 1973 (Translated in Polymer Sci. U.S.S.R. 15: 11, 2749, 1973) 6. H. LANGE, Kolloid-Z. und Z. Polymere 199: 128, 1964 7. V. Ye. ESKIN, S. Ya. MAGARIK, A. I. GRIGOR'EV and T. N. N'EKRASOVA, Vysokomol. soyed. A19: No. 5, 1977 (Translated in Polymer Sci. U.S.S.R. 19: 5, 1977) 8. K. KAMIDE and W. R. MOORE, J. Polymer Sci. B2: 809, 1964 9. V. Ye. ESKIN, N, A. ANDREYEVA and T. N. NEKRASOVA, Vysokomol. soyed. AIT: 1103, 1975 (Translated in Polymer Sci. U.S.S.R. 17: 5, 1264, 1975) 10. V. Ye. ESKIN, U. B. ZHURAYEV and T. N. NEKRASOVA, Vysokomol. soyed. AI8: 2529, 1976 (Translated in Polymer Sci. U.S.S.R. 18: 11, 2890, 1976) 11. G. MORAVETS, Makromolekuly v rastvore (Macromolecules in Solution). Izd. "Mir", 1967 12. T. M. BIRSHTEIN and A. B. PTITSYN, Konformatsiya makromolekul (Macromolecular Conformations). Izd. "Nauka", 1963 13. P. FLORY, Statisticheskaya mekhanika tsepnykh molekul (Statistical Meohanics o f Molecular Chains). Izd. "Mir", 1971 14. A. DONDOS and H. BENOIT, Makromol. Chemie 129: 35, 1969; Macromolocules 4: 279, 1971 15. S. LIFSON and J. OPPENH:EIM, J. Chem. Phys. 33: 109, 1960 16. A. VRIJ, J. Polymer Sci. 7, A-2: 1627, 1969 17. W. BURHARD, Makromol. Chemic 50: 20, 1961 18. H. LANGE, Kolloid-Z. und Z. Polymere 209: 29, 1966 19. B. WUNDERLICH and G. BAUER, Teploemkost' lineinykh polimerov (The Heat Contents of Linear Polymers). Izd. "Mir", 1972 20. A. I. KIPPER, G. V. KOTEL'NIKOV and V. Ye. ESKIN, Vysokomol. soyed. AI8: 1173, 1976 (Translated in Polymer Sei. U.S.S.R. 18: 5, 1349, 1976) 21. T. A. OROFINO, J. Chem. Phys. 45: 4310, 1966 22. L. A. UTRACKI, Polymer J. 3: 551, 1972
V. YE. EsxI~r e¢ td.
3. G. D. LITOVCHENKO, G. S. SOKOLOVA, A. V. VOLOIZH~A, G. I. KUDRYAVTSEV and 8. P. PAPKOV, Zh. prikl, spektroskopii 20: 455, 1974 4. Sh. SOBAJIMA, J. Phys. Soc. Japan 23: 1070, 1967 5. E. IIZUKA, Biochim. et biophys, acta 243: 1, 1971 6. V. A. PLATONOV, O. A. KHANCHICH and T. A. BELOUSOVA, Vysokomol. soyed. BI7: 726, 1975 (Not translated in Polymer Sci. U.S.S.R.) 7. B. Z. VOLCHEK, A. V. GRIBANOV, A. I. KOL'TSOV, A. V. PURKINA, G. P. VLASOV and L. A. OVSYANNIKOVA, Vysokomol. soyed. A19: 321, 1977 (Translated in Polymer Sci. U.S.S.R. 19: 2, 1977) 8. V. N. TSVETKOV, Ich. zap. Len. pod. in-ta im Gertsena, t. X, 1938 9. E. R. BLOUT and E. SHECHTER, Biopolymers 1: 565, 1963 10. V. N. NIKITIN, M. V. VOL'KENSHTEIN and B. Z. VOLCHEI(~ Zh. tekn. fiziki 25: 2486, 1955 11. P. CHATELAIN, Bull. Soc. Trans. Mineral et CrystaJlogr. 66: 105, 1943 12. M. M. KUSAKOV, V. L. KHODZHAYEVA, M. V. SIHSHKINA and I. I. KONSTANTINOV, Kristallograflya 14: 485, 1969 13. P. FLORY, Prec. Roy. Soc. A234: 73, 1956 14. F. A. BOVEY, G. V. D. TIERS and G. FILIPOVICH, J. Polymer Sei. 38: 73, 1959 15. B. Z. VOLCHEK and A. B. PURKINA, Vysokomol. soyed. A l l : 1563, 1969 (Translated in Polymer Sei. U.S.S.R. 11: 7, 1772, 1969) 16. I. SANDEMAN, Prec. Roy. Soc. A232: 105, 1955 17. M. TSUBOI, J. Polymer Sci. 59: 139, 1962
THE CONFORMATIONAL AND THERMODYNAMIC PROPERTIES OF POLY-~-METHYLSTYRENE IN VARIOUS SOLVENTS* V. Y~.. EsKrs, T. N. NEKaASOVA, U. B. ZHURAYEV, A. F. PODOL'SKII and A. A. TA-~A~ High Polymers Institute, U.S.S.R. Academy of Sciences
(Received 19 July 1976) Light scattering and viscometric methods have been used to determine the unperturbed dimensions K0 of a poly-~-methylstyrene produced by anionic polymerization (using the Stoekmayer-Fixman extrapolation), the number of solvent molecules No sorbed by the polymer chain unit, and the molecular packing density of the polymer in various solvents. Ke for polymethylstyrone (PMS) have been found to increase with the thermodynamic quality of the solvent. The mechanism of the solvent effect on K0 has been assessed after consideration of the energy of polymer-solvent reactions and of N,. An energy equivalence is assumed for changes in the unperturbed dimension under the influence of the solvent and the temperature. T ~ effect o f t h e s o l v e n t on t h e e q u i l i b r i u m o f c h a i n f l e x i b i l i t y ( u n p e r t u r b e d d i m e n s i o n s ) is one of t h e m o s t i n t e r e s t i n g b u t l e a s t i n v e s t i g a t e d p h e n o m e n a o f j n t e r m o l e c u l a r r e a c t i o n s w h i c h t a k e p l a c e in p o l y m e r solutions. V e r y l i t t l e i s * Vysokomol. soyed. AIg: No. 3, 525-532, 1977.
Thermodynamic properties of poly-a-methylstyrene
603-
k n o w n a t p r e s e n t a b o u t t h e m e c h a n i s m o f this effect, a n d a n e x c u s e f o r it is t h e purely empirical approach to this problem; only a wealth of experimental material w o u l d l e a d t o f i n d i n g a m e a n s o f s o l v i n g it. The dependence of unperturbed chain dimensions (and of a number of other p a r a m e t e r s ) in p o l y - 2 , 4 - d i m e t h y l s t y r e n e ( P D M S ) o n s o l v e n t p r o p e r t i e s h a d b e e n t a c k l e d b e f o r e [1] a n d s o m e o f t h e likely c a u s e s h a d b e e n e v a l u a t e d . T h e w o r k d e s c r i b e d h e r e deals w i t h t h e p r o p e r t i e s o f p o l y - g - m e t h y l s t y r e n e (PMS) i n 12 s o l v e n t s a n d t h e e v a l u a t i o n o f t h e r e s u l t s f o r it a n d for s o m e o t h e r p o l y m e r s . EXPERIMENTAL
PMS samples were synthesized by anionic polymerization of the monomer in T H F at --78°C; the catalyst was the disodium-a-methylstyrene tetramer (live polymer). T h e synthesis and the polymerization method have been described before [2]. The stereo-isomerism of the PMS samples was determined by proton magnetic resonance (PMR) spectrometry on a J E O L C-60 H L instrument at 180°C on 10% PMS solutions in o-dichlorobenzone. The contents of the iso I, hetero H and syndio S triades were calculated from the comparison of the respective signal intensities of the a-methyl groups; it was found to be: 1--10-14~o, H-46-49°~o, and S--39-42°~o in separate PMS samples. The NMR signal of the methyl groups was identified on the basis of earlier results [3]. (The authors are indebted to A. I. Kol'tsov and V. M. Denisov for the recording of the NMR spectra of the PMS). The molecular weights (mol.wt.) ~/w of the PMS samples were determined in toluene at room temperature (22°C) by the light scattering method in a "Sofica" photogonio-diffusometer. Six samples were examined; these had ~w in the range (3-2-75)× 10~. The J~fw/llTf~ ratio, determined by gel chromatography, was 1.05-1.12. Tile intrinsic viscosity [t/] was determined in an Ostwald viscometer at 25°C with 60-190 sac flow times of the solvents. The density and the refractive index of the solvents used were those contained in the Tables. The found [¢] and ~7fwwere used to determine the unperturbed dimensions of the PMS. molecules in various solvents by the Stockmayer-Fixman method [4]. The graphical data were processed by the method of least squares. The partial specific volumes ~ were determined at 25°C by the method described by Nekrasova and Eskin [5]. The temperature was 35°C where ~ and [t/] were determined in cyclohexane. The number of solvent molecules sorbed on a single polymer chain unit was determined by light scattering from the ~ of the polymer in the pure solvent and in solvent] /precipitant mixtures, using the Lange [6] method and that used earlier [1]. A number of normal aliphatic alcohols were used as the precipitants. RESULTS
T h e p a r a m e t e r Ke=q)'(k~/M) ~ in t h e [ti]e=KoM I ratio, w h i c h c h a r a c t e r i z e s t h e r e l a t i v e u n p e r t u r b e d coil d i m e n s i o n s ( R ~ / M ' ) w a s f o u n d b y t h e k n o w n g r a p h i c a l e x t r a p o l a t i o n p r o c e d u r e o f [tl]/M*=.f(M*) t o M * = 0 , w h i c h is b a s e d o n [4]:
[tl]/M ~----Ko-k- 0.035 ~ ' B M ~,,
( 1)
in which B=p[M~; p t h e o c c l u d e d v o l u m e o f t h e c h a i n u n i t ( s e g m e n t ) i n t h e
~04
V. YE. Esxrs eta/.
particular solvent; M0, its mol.wt. (R0~ is the mean square radius of inertia of t h e macromolecule, ¢ ' ~ 3 - 9 × 1024). Recent direct measurements of the statistical chain segment A in PDMS' and PS [7] confirmed the A differences in thermodynamically good and poor solvents found by extrapolating [~]/M~ to M ~ 0 by the Stockmayer method [4]. TABLE 1. SOMEOF T~E PARAMETERSOF THE INVESTIGATEDSOLVENTSANDTHE EXPERIMENTAL FINDINGSFOR PMS Solvent Cyclohexane Butylethylketone Isopropylbenzene Decalin Toluene Benzene Tetrachloroethylshe
Chloroform Chlorobenzene Diehloroethane Dioxane Pyridine
cal )/ /era ~ 8.2 8.3 8.6 8.8 8.9 9-2 9.3 9-3 9.3 9.9
10.0 10.7
~' Debye
2"7 0"4
VI, K0 × 10i, cm3/mole g/em3 108 144 139 156 106
7.2 7.5 8.9 8-3
9.7 10.0
89
K~ × 10a, g/era* 7.2 7.5 3.6 3.6 2-6 2.4
~8"9
1"2 1"6 2"0
80 102 79 86
2"2
11.2 10"2 9"3 9"8 ~9.6
2.2 2.7
3.0 3.6
N
0.5C 0.41 0-6C 0.58 0-64 0.6fi
0.5 -1.0 1.2 1.2 1.4
0.61
--
0.6e 1.2 0.64 0.62 0-7 0.60 0.9 0.63
v, em*/g 0"890 0.885 0.883 0"874 0.869
0.887
One gathers from the Table 1 results t h a t Ke~f(a) increases in a number of solvent solutions of PMA with solvent quality, and the measure of this is taken t o be the exponent a in
[~]-~K,aMa
(2)
The type of the Ko-~f(a) function (Fig. 1) is the opposite for PMA t h a n for PDMS, for which the K0 drops with increasing a [1]. We shall deal below with t h e reasons for this difference. Although Kamide and Moore [8] consider their extrapolation of the log K~ ~f(a--½) to a ~½ to be valid 0nly for a Re2 which is independent of the solvent, such extraplation yields K0 in the case of PMS which is very close to the K0 value obtained in cyclohexane (Fig. 2). The use of Ke found in non-ideal solvents will give points on the log Ko:f(a) curve which are also grouped around the line interesting the ordinate in Fig. 2 at a point close to t h a t for Ke in cyclohexane. It should be noted however t h a t K0 characterizes in eqn. (2) not the individual properties of a particular solvent, but merely points to the extent by which the polymer reacts with it and enhances the swelling of the coils as a function of chain length. In this connection it will be quite satisfactory to t r y and establish
Thermodynamic properties of poly-a-methylstyrene
605
how the polymer properties in the solvent correlate with the values which are a direct characteristic of the solvent molecule. These are at present the following 3 parameters: solubility parameter J1 (the cohesive density of the liquid is j2), which determines the energy of molecular interactions in the pure solvent, molar volume V1, and the dipole m o m e n t / ~ of the molecules in the case of polar liquids. We already mentioned before [5, 9, 10] t h a t the effect of dipole moment/~, associated with its polarizing action on the chain unit of the non-polar polymer (or with the dipole-dipole reaction in the case of a polar polymer), will greatly complicate the intepretation of the full picture of polymer properties in a range of solvent~. At this stage of the study one must therefore try to clarify, where possible, the direction of the specific effect of solvent molecule polarity. As regards the exponent a in eqn. (2) as a measure of thermodynamic quality of the solvent (for the particular polymer), its value incorporates all the mechanisms of the polymer-solvent interactions. This is particularly clear from the dependence of a on 51 which is given by one general curve regardless of solvent polarity, at least in the case of non-polar or slightly polar polymers (Fig. 3, curve 1). The largest a value is equivalent to Jl for PMS which is parameter J2 of the polymer (9.2-9.3 kcal~/cm~).
KO
P
11
-Y'O-
o
2
lg .q -0"5 l
0.5
0.5 FIe. 1
a
g'5
a
I 0"7
Fie. 2
F i e . 1. K~ × 10' as a f u n c t i o n o f a for P M S in v a r i o u s s o l v e n t s . FIG. 2. / - - l o g K~; 2 - - l o g K o as f u n c t i o n s o f a for P M S in v a r i o u s s o l v e n t s .
We shall now examine the 51 functions of two parameters directly connected with the polymer-solvent interaction, namely N,, the number of solvent molecules sorbed on average by a single chain unit, and the partial specific volume ~. One can see from the N,----f(al) and v--~f(J1) functions (Fig. 3, curves 2 and 3) t h a t the m a x i m u m sorption of solvent by the polymer (N,) and densest packing in solution (~ minimum) applies when Jl~-J2, which corresponds with a better thermodynamic quality of solvent a.
608
V. YE. E s x x s
et a/.
The reason for the parabolic shape of the J1 functions of a, N0 and ~ is thought to be the fact that the changes of the thermodynamic functions, especially of the internal energy are in a direct relation with (Ji--Jz) = (see [10, 11] for example). One can assume the sorption of the solvent molecules to be intimately linked with the molecular packing density of the polymer in the solutions. The iV, dependence of ~ is especially strong in the case of aromatic solvents and less in solvents with a saturated structure (Fig. 4). The reason for such a difference is probably the specific reaction of the aromatic solvent molecules with the phenyl branch of the polymer.
0"8
l'~
0"5 ~ ¢r
I
[
I
1
3
o
0"88
0.87 tf ~ la
+_ o
,
I
0"1/7V 0"~
!
[ °°
o
o
0"88 o
o o
o
o
o
0"87
0 I
I
9
io
Fzo. 3
4
I
1
I
0.+
0"8
/.2
Ns
Fro. 4
l~o. 3. /--Exponent a; 2--the number of sorbed molecules Na; 3--the partial specific volume ~; 4--K~, as functions of parameter Jl. FIo. 4. The partial specific volume 0 as a function of ~Ve for PMS in: /--aromatic; 2--nonaromatic solvents. I t was impossible to establish any noticeable effect of the bulk of the solvent molecules (V1) on the polymer properties which are discussed here. On turning now to the dependence of the unperturbed dimensions of the macromolecules on the solvent properties we notice that an intensification of the PMS reaction with the solven~ shifts the distribution of the isomeric state~ of the chain units towards an increase in the numbers of those with a less coiled conformation [12, 13], while the reverse is true in the case of poly-2,4-dimebhylatyrene [1]. The presence of the methyl group in ~-position in PMS thus subs~an-
Thermodynamic properties of poly-~-methylstyrene
60T
tially alters the energy balance of the reactions in the chains which also ought to include (as we shall see below) the sorption reaction. Typical is that in another polymer possessing an a-methyl g r o u p - - P M M A - - t h e unperturbed coil dimensions are also smaller in poor solvents t h a n in good ones [14]. One can also note that a further reduction in the solvent quality to below the ~ point (a<0.5) does not affect the chain flexibility, i.e. the K0 values are very similar in the case of butylethylketone (a~_0.4) and cyclohexane (a=0.5). Where the polymer reaction with the solvent is weak, the latter therefore does not affect the flexibility equilibrium of PMS. The relationship between K~ and 51 is not as distinct however as between K0 and a (Figs. 3, 4); there is only a tendency towards a Kt increase as 51 approaches 5t. This could mean that 51 is not the only factor on which the unperturbed dimensions depend in solution, and that there must he some other reasons for the changes in K~. As only some general theories have been suggested for explaining the solvent effect on the unperturbed macromolecular dimensions [15, 16], and the elaborations b y Burhard [17] disagree with the findings for PMS [1], we shall try here to find out whether one can associate K~ with the energy of the polymersolvent reaction. The measurements of the internal energy of dissolving the polymer, which correlates with (51--$2) 2, together with the entropy of mixing, determine the thermodynamic properties of the solution as a whole. It appears to follow from the discussion of the solvent effect on the total conformations of the chain units t h a t one must immediately turn to the energy of the chain unit reaction with its environment. The enrgy of intermolecular reactions is characterized in the liquid b y value 5~, and by 515~ in the case of mixtures (at least of non-polar components) [11]. The transition of the polymer chain unit from the solution into the hydrogenated monomer is linked in the partAcular solvent with the energy difference of its reaction with the environment (per 1 mole of chains), F~(5~1--522), in which V2 is the molar volume of the polymer. (This will be correct only for a pseudolattice model of the liquid when the coordination number Z in various solvents is regarded as being the same, and one neglects the actual conditions of molecular packing as t h e y are not easily calculated). As the range of solvents tested in this work contained liquids with 51<52 as well as 52>~1 the (5~1--5~) difference can be positive or negative in value. The assumption of dependence of K~ on the reaction energy with the environment cannot be coordinated with the similarly of the K~ values in solvents with 51<52 and 51>52 (see for example the K~ in dioxane and toluene: Table 1). This non-idcntity will disappear if one takes into account the additional energy of the chain unit reaction having some number Na of sorbed solvcnt molecules. The sorption energy Es had been determined by Lange [18] from the temperature dependence of ~ in the case of PS in toluene; this was found to be 0.9 kcal/mole. As N6 depends on solvent quality (Fig. 3, curve 2), it must have some peak value N o at 51---:5~(in the hydro-
608
V. YE. ESKI~ et ~ .
genaCed monomer). By bearing in mind the sorption, the entire change of t h e energy of the chain unit reaction with the environment AE (per mole of chain units) will equal: AE = V~= (~,--5,) + E s (N s--N°s) (3) Ea is fundamentally specific for a particular polymer-solvent pair. Although it was determined for only one such pair, we shall nevertheless regard it as approximately the same for various systems (which will be obviously correct only for non-polar polymers and solvents), i.e. to equal about 1 kcal/mole. For AE we shall write AE = -- V~= [(g~--~l) + 7 (Ns--N°)],
(3a)
in which ~=E,/5=V2. With z/E we also compared K~ for PMS and PDMS in various solvents (Table 2), and we shall assume 7 = 1 cal+/cm+ as ~2---10 cal+/cm + and V2---100 emS/mole for these polymers. The value of N o can be got by consecutive approximation from Ns=:f(AE) function or by extrapolation to gl=~= of Ns=f@~--Z,.I). The dependence of K1 on LiE is illustrated in Fig. 5a. I f one excludes the points belonging ~ the polar solvents, for which the energy o f interactions can differ from g~5,.V=, and the sorption energy is obviously much larger than 1 kcal/mole [18], the K~=f(zIE) linear function can be approximated b y a straight line with a slope characterizing the "energy factor" of the unperturbed coil dimensions dK~/K~d(AE). The calculation for which we took gz=9"3 cal+/cm + and Vz=-104 cm3/mole in the case of PMS, and 9.0 and 126 respectively for poly-2,4-methylstyrene, yielded a dK~/K~d(ztE) 0.6×10 -4 for the first, and --0.8 × 10 -4 for the second polymer. K tl3
•
0"37 0"J3
O,ql I
Q
e
l
0"5
]
"o
l!0
2
-3 E, kcal/rnole
/ ~
•
n
I
°
I
w
g
-,4 E pkcal/mole
~'kG. 5. The dependences of: a--K~, b--N=; on AE for: 1--PMS; 2--PDMS; in non-polar (blank circles), polar solvents (black circles). We shah now compare the "energy factors" of the unperturbed coil dimensions with the same values got by changing the solution temperatures. The dimensional increase must be attributed in this case to the energies CrT, in which Cr--par~ of the molar heat content of the polymer coonnected with the transitions due to conformation changes of the chains, and therefore value (2~02)+. There are no promising calculation results available for Cr. Its estimation gives C r = 1 cal/mole-
Thermodynamic propertieB of poly-~-methylstyrene
609'
• °C at 300°K in the case of P E [19] which makes about 6"5~/o of the total h e a t content Cv. Polymers with a more complicated chain unit structure ought t~ have a much smaller Cr, so t h a t a C r y 2 cal/mole.°C can be regarded as close to the t r u t h in the case of the polymers discussed here. (The Cv of PMS in solution w a s found to be 45 cal/mole. °C [20]).
0.06
0.02 -
I
O'G 0"5 2
I
~, OeOye
3
FIO. 6. The dependences of KI and of a for PMS on the dipole moment/2 of the solvent. The temperature coefficient was calculated for PMS and PDMS from d[~]/ /[t/] d T in a good solvent, i.e. toluene (between 24 and 75°C); it was found to be --3 × 10 -4 °C -1 (we show for comparison t h a t the dR/.RdT obtained for PS was 2.8× 10 -4 °C -I [21]). We thus found for d R / R d T about 1.5× 10 -4 (cal/mole} -~ which is close enough to the absolute value of the dK~/K~d(AE). The evaluation points to an energy equivalence between the unperturbed polymer chain dimensions under the influence of temperature and of the reaction with the environment (the solvent}. Of further interest is also to clarify the nature of the correlation between N s and AE. This dependence is shown in Fig. 5b for PMS' and PDMS. I t is in both cases (in non-polar solvents} a descending straight line. The slope of the l a t t e r was used to assess the d(AE)dNs, which was found to be about 2.0 kcal/mole for PMS and 1.7 kcal/mole for PDMS; the latter is 1.5-2 times larger t h a n the " p u r e " sorption energy of toluene on PS [19]. I t must be remembered however t h a t the AE together with the sorption energy include also the changes of lilac energy of the chain reaction with the environment, which also determined the d (AE}/dN, value. The monotonous nature of the N~----f(AE) function has obviously a physical meaning, i.e. t h a t the Ns decrease in a number of solvents is the direct consequence of the weakening of the polymer chain reaction with its low mol.wt, en-
V. Y~.. E s E i ~ e$ al.
-610
vironment. The nature of the dependences of K~ and N , on J E permits the assumption that desorption of the solvent molecules can be part of the mechanism which results in a change of the unperturbed polymer chain dimensions with temperature elevation. TABLE 2. THE ( J l - - ~ ) ' , (1V~-z¥,)- AND z~E-vALUE OF PMS AND POLY-2,4-DIMETHYLSTYRENE IN VARIOUS SOLVENTS
PMS (/V~= 1.6) Solvent Benzene
Toluene I)ichloroethano Chloroform Dioxane Tetrachlorornethane Decalin Isopropylbenzene Butylacetate p-Xylene Cyelohexane
J2--Jl
"0
,--N,
PDMS (N~=2.2) --~E, eal/molo
0.1 0"4 --0.6 0 --0.7
0.2 0-4 0.9 0.4 0.7
310 830 310 415 0
0.5 0.7
0-4 0.6
930 1340
5s--$1
1.1
--JE, cal/mole
--0"2 0"I --0"9
0.25 0.1 1.35
57 228 515
--1"0 0"4
1.75 0.3
860
0"5 0"2 1.1
N,--M#°
0.4 0.9
8O0 1030 1250
2280
I t is also possible to follow up the effect of solvent polarity on the reaction o f PMS in solution, which determines not only the thermodynamic quality of the ~olvent, b u t also the polymer chain flexibility. We illustrate as an example the dependence of a in eqn. (2), and of KS for PMS, on the dipole moment ~ of the solvent molecules. K~ and a decrease as g increases, and particularly a when ~u>2 Debye. Dondos and Benoit [14] stated that it possibly happenes that branches of the polar solvent molecules engage in the macromolecular chain units and that this must cause a reducticn of the unperturbed dimension KS. One cannot exclude another mechanism however b y which /~ affects the flexibility of polar polymers, namely the direct dipole-dipole reactions of the chain units with the polar environment which will change their conformations. KS will approach its value in a non-polar solvent when the temperature rises in both cases, or due to the association between bonds decomposing in the solvent molecules [14], or as result of their desorption from the polymer. The polymers which are used here have a low polarity and the effect of/~ on the K~ of PMS is of a secondary nature, affecting the thermodynamic quality of the solvent (causing an increase o f the 152--5,1 difference, an a decrease) as ~ increases [22]. An approximately parabolic type of dependence can thus be noticed on the solvent parameter J~ of PMS properties, such as is the exponent a in eqn. (2), the partial specific volume ~, and the number zVs of solvent molecules sorbed By the chain unit. The unperturbed dimensions of the PMS chain unit and Ns
Thermodynamic properties of poly-a-methylstyrene
611
are linear f u n c t i o n s o f the e n e r g y of t h e chain u n i t reaction with t h e low mol.wt. molecules o f t h e e n v i r o n m e n t , including t h e sorption e n e r g y of t h e l a t t e r on t h e polymer. Translated by K. A. ALLE~ REFERENCES
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