THERMODYXAMIC PROPERTIES OF POLYSTYRENE SOLUTIONS
213
SOME THERMODYSAMIC PROPERTIES OF POLYSTYRENE SOLCTIOSS' PAUL DOTY* Dcparttnent of Cheitiisti y, V n i c e r s i t y of S o t r e D a m e , .Yolie Dame, Indzaria
'
ASD
LIILTOS B R O W S S T E I S 3
AND
Lt"ILLIA.\I SCHLESER3
D e p a r t m e n t of Cheniistrg, Polytechnic Institute of Bi ooklgri. R Iooklyn, .Yew Fork Received A u g u s t 19? 1948
This paper presents some further u-ork on ;t thermodynamic investigation of polymer solutions which may be considered to have begun with studies on a typical polar polymer, polyvinyl chloride (4,5); the present u-ork is based on polystyrene as a representative of the class of non-polar polymers. Here we deal chiefly with the effect of structural features and temperature on the osmotic pressure of dilute polystyrene solutions. ;1more comprehensive investigation, including a study of concentrated solutions, has been completed (15) and Jrill be published later. ISTRODUCTIOX
The Flory-Huggins (7, 12) theory has brought a considerable understanding t o manp aspects of polymer-liquid systems. Being a first attempt to solve a difficult problem it is natural that some defects should soon become recognized. Gee (lo), for example, has explored its shortcomings in the region of phase separation. Meanwhile the authors of the theory and others have carried out refinements 11-hich bring it into closer relation with experimental observation. Perhaps the most fruitful aspect of these later efforts is to emphasize the interpretation of the coefficient of the square term in concentration in the expression for the free energy of dilution in terms of excluded volume. In summarizing in simplified form this point of view let us consider the corresponding coefficient B in t h e expansion of the osmotic pressure in terms of concentration:
In the Flory-Huggins theory
B where
=
RT (1,'2 1oov,pi!
,u)
represents the partial molar volume of solvent and p the partial specific
Presented :it t h e Twenty-second Sational Colloid Symposium, which was held under t h c auspices of the Division of Colloid Chemistry of the American Chemical Society at Cnmhridge. Massachusetts, June 23-25, 19-18. * Present address: Department of Chemistry, Harvard University, Cambridge, Massachusetts ? This paper n a s taken in part from a thesis presented in partial fulfillment of the requirements for the degree of .\faster of Science a t the Polytechnic Institute of Brooklyn, .June, 1947
214
P. DOTY, 31. BROJVNSTEIX, S N D W. SCHLEXER
density of the polymer. I n the absence of precise values for these tJ1-o quantities the values for the bulk substances are generally used. The quantity p is ;i semiempirical constant n-hose d u e is determined by the equality. It will be recalled that the coefficient B is essentially zero for liquid mixtures of small molecules which mix in all proportions without heat change. If this latter athermal condition ivere fulfilled for a polymer solution, B would be observed to be greater thanzero. This is essentially due to thefactthat apolymer segment \vi11 over a period of time have many fen-er contacts with other polymer segments than it n-odd have if all the polymer segments were cut free from each other, thus producing the situation found in the ideal solution just mentioned. At a constant molecular m i g h t a branched or cross-linked polymer will differ from a linear one in that a typical polymer segment will be constrained to move in a region of greater local concentration of other polymer segments and vi11 therefore enjoy more contacts n ith other polymer segments. Consequently the value of B for such a solution should not be as large as for the solution of the corresponding linear polymer. In other ~i-ords,since B (and therefore p) is essentially independent of molecular weight its value n-ill be diminished in proportion to the amount of branching or cross-linking in the polymer provided no other configurational aspects are changed in the polymer samples. However, certain conditions of polymerization such as the temperature can produce configurational changes in the molecules being formed and hence alter the value of p. The first part of this investigation is directed a t determining the magnitude of these effects on p. One of the direct applicatioiir of such determinations is in estimating precisely the p-value of a lightly cross-linked swollen polymer, inasmuch as such information is required for the accurate evaluation of p-values by the swelling techniquc (2, 3). I n the Flory-Huggins theory the free energy of dilution is given by the follon-ing expression
i2 ) where the ratio of the volume of polymer molecule t o the solvent nioleculc is denoted by m. It IT-as suggested that the temperature dependence of AI‘, c ~ ~ l t l CY’RT. This Lituation ibe adequately represented if p had the form 8 consistent Tvith the meager amount of experimental data available Hon-c~-c~i , tv-0 further questions arise: one regarding the concentration dependence ot @ and a , and the other regarding the correlation of the v a h e s of they(. t i \ [ ) constants v i t h molecular details of polymer solution. K i t h reference to i h c first point it has been clearly shown ( G ) that p increases with solute concentration for the rubber-benzene system and that in a number of cases it.. d u e is not at all predictable from the cohesive energy calculation commonly u>ed for ordinary non-polar solutions. The concentration dependence of’ 01 seems to follon- from thc discontinuous character of the solution, Tvhich becomes increasingly significant in the lon- concentration region (9, 18). Since p is observed in many c a w to he
+
T€IERMODTS.I.\IIL PROPCRTICS O F POLTSTYRLSE SOLUTIOSS
215
approyimately independent of concentration, it follon s that p should diminish u-ith increasing concentration in proportion to the reciprocal of a. This apparent comglementxy relationship is not TI ell understood at prewit. The foregoing d i m i 4 o n of the viriz.1 coefficient B leads to the expectatic 11 th:it p ihould :tlnays have a value of someirhat less than 0 5. In fact, Z m m (19) has shonn that for a particular shape of n coiled nicleculc it ~ ~ o u have l d a value of 037. In uther I\ord., in a dilute sollition a value of 0 5 corrcspondi to the cntropy of dilution of an ideal hinary syctem compoyed of small molecules. If one of the species conyiqts of long stiff iods n value of nbout 0.49 results, the exact value depending on dimensions. If the long molecule is not stiff hut flexible, i e . a polymer, a considerably smaller 7,-alueof is expected, OTTing to the larger entropy of mixing. The second part of thi. inw-tigation iq concerned TI ith tlie determination of pm d a-values of some polystyrene solutions in order to qee hon they fit into the interpretative scheme just summarized. ? SI’CRI\\IE>-TIL
DET i l L +
For the oqniotic presiire measurement:, on the thiee polymer> in the diisowries dcscribcd belon static wnioiiieterb conitriicted accord ng to t h r de-ign oi Kagner (17) uere employed For all other measurements a t lieimciitated dynamic osinometer 11 as ~ i ~ e dTliii . (,~nionieterrind its m:inipulaI ion ha1 c lxcn described previoidy 1.5). The pi obable ci ror in the osmotic pre-siiie me,twrenicnty is estimated to be lictnccn 1 0 10 and &0.20 mm., ticpending on the cunccntiation and teniperatiiic. of nieawrcment In the case of the polymer A, on TI hich niost of the tcnipcratm.e-d~pendentmeusiircments TI eie made, the molecular \I eight TI ,ii su T\ r!l established by many measurements tlLdit the intercept value corresponding to its molecii1,ir 11eight 1,i-a~used in fitting the high-temperature data to a straight line S o degradation iras detected a t the temperature employed Sewn polyityrcnc sampleq TT ere used in this inw>tigcition. The styrene from nhich they were made 11-as a middle fraction from a vacuum distillation of a commercial product (Don. Chemical Company) from IThich the inhibitor and nioistui e had been removed. The divinylbenzene uqed a z it cross-linking agent caontained about 30 per cent ethylvinylbenzene. The diisopropenyldiphenyl, mother cross-linking agent used, v a s pure. -111 polymerizations were carried to completion in several days in the absence of & l e d catalybt. The samples \Ihich n-ere soluble had some low-moleculzr-n eight species 1emoved before use. ‘The samples are listed in table 1 n i t h the polymerization temperature and the .mount of cross-linking agent used. Polymers C and D vere gels Jvhich snelled in solrents, the former almost \titbout limit. 1considerable amount of the soluble material in these samples \\as removed by the follouing pioceduie. &%itel2 clay, in toluene a t 53OC. the cut into small pieces. The pieces were transferred to fresh ollen polymer toluene, which ~ia:, rhanged every 2 day5 over u period of 8 days. Fragile points n-ere then remored, the pieces boiled in methyl ethyl ketone for an hour, and finally carried through an exhaustive drying procedure. It was shown that 131openyldiphcnyl
216
P. D U T Y . 11. IIIZOTVXSTEIS, . I S D TI-. SCHLESER
even a t room temperature these samples when swollen underwent simultaneously both chain scission and extraction of soluble polymer. This necessitated extrapolation of all sn-elling data back to zero time. The osmotic pressure \vas obtained by multiplying the difference in height in matched capillaries by the density of solvent. The use of solvent density here rather than solution density introduces no significant error. However, in calculating p from the slope (cidc supra) the partial specific density of the polymer cannot generally be replaced by the polymer density in bulk viithout introducing a noticeable error. This is due to the fact that the polymer is less dense in bulk than in solution. Vse is made here of the partial specific density data of Royer and Spencer ( 2 ) , in m-hich both the concentration and the temperature dependence partial specific density n-ere determined. I n the absence of accurate measurements on methyl ethyl ketone solutions the partial specific density of polystyrene in toluene i3 assumed to be valid here; this is at least approximately true ( 2 ) . TABLE 1 Details of p o l y m e r pieparatious SAMPLE
TEUPER4TURE
_ _ __
.1.. ..................... B . .. . . . . . . . . . . . . . . . . . . . . C. . . . . . . . . . . . . . . . . . . . . . . . .
D. ...................... E. . . . . . . . . . . . . . . . . . . F. . . . . . . . . . . . . . . . . . . . . . . . . ....
"C 130 130 130 130 70 70 70
I
CROSS-LINKING AGENT
-
-
-
Sone
0,030:; divinylbenzene Sonc 0 .00Z5~odiisopropenyldiphenyl 0 . 0 1 0 ~diisopropenyldiphenyl
THERMODYXAMIC EFFECTS O F HRASCHIXG
The osmotic pressure results for pblymers X and B are plotted in figure 1; those for polymers E, F, and G in figure 2 . In a11 cases the solvent is toluene. The osmotic pressure is measured in units of grams of force per square centimeter. It is apparent that in both groups the small amounts of cross-linking agent incorporated in the polymers have produced a noticeable lowering of the slope. Xoreover, the slopes for the two uncross-linked polymers are different. Presumably this is due to the different temperatures of polymerization, for Xlfrey, Bartovics, and >lark (1) found a similar difference in slope for samples of polystyrene polymerized at (j0"C. and 120'C. Because such an enormous excess of styrene \\as present in the polymeriz a t'1011 of polymers B, F, and ,C; it is permissible to conclude that practically all of the cross-linking agents entered into the polymer. On this basis it is possible to summarize the composite effects of the cross-linking and the temperature oi polymerization by plotting p against the number of cross-links per ten thousand monomer units. This ir done in figure 3. Decreasing the temperature of polymerization or increasing the amount of branching increases the value oi I.(.
THERMODYNAMIC PROPERTIES O F POLTSTYREKE SOLUTIOSS
I
,
t
217
- n\%
I
I
T
' I
0
0.2
0.4
OG
0.8
1.0
c (g./100ml.) FIG.1. Plot of t h c rcduced osinotic pressurc for po1ynicr.i A :rnd 13 i n toluene
at 28'C.
The data for polymer A ma\' lw found i n figurc 5.
0'
FIG.2. Plot
of
I
0.2
I
1
04 0.6 c (q./foo rn I.)
,
I
0.8
1.0
t h r rcduced osniotic prcssure for polymcrs E, F, :tnd G
111
toluctnc, : ~ 25"( t
branching decrease with 111creasing temperature. This seems so improbable that it is best dismissed in favor of the suggestion of Huggins (13), based on the assumption that the amount of randomness in the right and left disposition of styrene radicals along the extended carbon chain depends upon the temperature of polymerization. Thus if at lon- temperatures the styrene radicals were predominantly on one side of the chain for long intervals u stiff and rather regularly coiled molecule may resiilt. On the other hand, if a t high temperatures
a more nearly random nrrungenient TT ere produced, more flexible, irregularly coiled molecules Tvith greater internal shielding and 1mii.e lower p-values would result. The quantitative aspect3 of figure 3 are 01’ some interwt. \\-it11 ordinary precision in osmotic pressure me:isurenients values of p differing by 0.005 can readily be established. The re-ults shown in figure 3 jiidicate that ZL difference of one branch point per 25,000 nmimmer units between tn-o polymers corresponds
CROSSLINKS PER I 0 , O C O h:ONOMER UNI’rS
FIG.3. l’lut o f p :igniiist t h e nunibcr of cross-links per 10,000 monomer units. The upper dashed line corresponds t o niensiirenients in nicthyl ctliyl ltetonc; the others t o toluenr. solution 5 ,
to this difference and hence could be d e t e r t e d . 11 muyt bc yeinembeid that a cross-link formed by a divinylbenzene molecule erit ering two growing chains is approximately equivalent t o i11-o ordinary brnnch point such as may be formed by chain transfer. This effect offers no ~ v a yfoi determining the absolute amount of branching, for it does not establish the value of y correiponding t o :L completely unbranched polymer. Moreover, the polymers being compared miist h a w been prepared under comparable conditions in order to eliminate wch effects as apparently result from different polymerization temperatures. Finally, the effect of a given change in the amount of branching n-ill probably affect the vahie of ,u differently in different solvents, that. is, there will be a different slope
THERMODYSAMIC
PROPERTIES OF POLTSTYRENE
so1,rrIoxs
21!)
in figure 3 for different solvents. This is illustrated by the dotted line irhicll represents some less accurate measurements on polymers A and B, using methyl ethyl ketone for solvent. On the other hand the lack of dependence of this effect on molecular weight makes it unique among the several methods that have been suggested for estimating branching. The extrapolation of the data plotted in figure 3 makes available an estimatt. of the p-values for more highly cross-linked systems, i.e., gels. This is important because the application of sn-elling measurements on polystyrene-divinylbenzene gels to evaluate p for various liquids (2) is dependent upon knowing accurately the value of p for one liquid and the gel. From measurements of the swelling of a series of polystyrene-divinylbenzene gels of different composition in eaeli 01 several liquids Boyer and Spencer (2) shon- that the relative value of p T a i ie5 linearly with the amount of cross-linking agent. \Tre may then i\ith some confidence uze n linear extrapolation on the data plotted in figure 3. Thu
