May, 1951
INTRINSIC VISCOSITY RELATIONSHIPS FOR POLYSTYRENE
Acknowledgment.-The authors are indebted to Joyce C. Fox who carried out the major
1915
part of the experimental work. ITHACA,
RECEIVED SEPTEMBER 22, 1950
N. Y .
[CONTRIBUTION FROY THIC DEPARTMENT OF CHEMISTRY OP COBNELL UNIVERSITY I
Intrinsic Viscosity Relationships for Polystyrene1 BY T. G Fox,J R . ] ~AND P. J. FLORY Intrinsic viscosities of polystyrene fractions (M = 7.0 X lo4 t o 1.27 X 1Oe) have been determined in various solvents a t several temperatures. Critical miscibility temperatures 9 in the limit of infinite molecular weight were found t o be 307 and 343°K.for polystyrene in cyclohexane and in ethylcyclohexane, nspectivel From intrinsic viscosities measured in these solvents a t temperatures equal to their respective e's, K in the equation [7r= KM%u8 was found to be about 8.0 X 10-4 a t 34" and about 7.3 X lo-' a t 70". Present data, as well as other data from the literature, are well represented by the a8 = 2+1Cy(1 e/T)MVswhere u is the factor representing the above equation in conjunction a i t h the relationship d linear expansion of the polymer coil due to interactions. The entropy of dilution parameter $1 has been found t o be about 0.1 for the solvents with cyclic structures; for methyl ethyl ketone is about 0.01. The universal viscosity constant Q in the relationship K = @(rt/Id)'/s has been calculated t o be 2.1 X 10" on the basis of data of Outer, Carr and Zimm on molecular dimensions of polystyrene in solution as deduced from the dissymmetry of scattered light. The root-mean-square distance separating the ends of a polystyrene chain in the absence of interactions of the polymer segments with their environment, apart from hindrances t o free rotation, is calculated to be 730 A. at 25" for a polystyrene of M = lo6; the calculated distance for free rotation is 302 A. In benzene, a good solvent, a t 25", LY E 1.5 and the root-mean-square distance between the ends of the chain is ca. 1100 A. The polystyrene molecule appears to be more extended than is one of polyisobutylene having the same number of chain atoms.
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solvent and temperatureg* lo have been reported by several investigators] and more recently the mean-square extension T2 of polystyrene chains has been obtained in various solvents through measurements on the angular dissymmetry of light scattered by dilute solutions.l*J* For the [ q ] = KM1/3cu3 (1) successful application of equations (1) and (2), - LY3 = 2 +L.lcM(i - e/T)Mi/Z (2) however, intrinsic viscosities at the temperature T = 8 are virtually required for reliable evaluation K = Q(Z/M)'/n (31 of K; this constitutes the k s t step in the deterCM = 27(26/'/~a/~N)(~z/vl)( M/?):/z mination of all other quantities appearing in the = 1.4x 10-24 (G~/v,)(Q/K) (4) above equations. Such measurements have been The various quantities appearing in these equations carried out in the present investigation. With are defined in preceding papers.*t5 their aid, previously reported intrinsic viscosity Equations (1) and (2) have been subjected to data (and some additional results reported here) rigorous test in their application to precisely and results of chain dimension measurements are measured intrinsic viscosities of polyisobutylenes6J interpreted in the light of the relationships preover wide ranges in molecular weight and tempera- sented above. ture and in a number of different solvents. The Experimental adxquacy of these relationships has been coniirmed and the various parameters have been evaluated. Materials.-Four polystyrenes were prepared The present paper is concerned with the similar treat- by bulk polymerizations of styrene a t 60' in the ment of intrinsic viscosities of polystymne, and with presence of benzoyl peroxide according to the the deduction from such data of the ratio a / M method described elsewhere.I2 Details of the characterizing the configuration of the chain, and the polymerizations are summarized in Table I. The determination of the thermodynamic parameters 0 polymers were fractionated by the addition of and $1 for polystyrene in several solvents. Experi- methanol to their dilute (1to 2 g./100 cc.) solutions mental data on the dependence of intrinsic viscosities in methyl ethyl ketone a t 30°.12 Seven of the of polystyrenes on molecular weights and on fractions were selected for the work reported here. The percentage of the corresponding whole polymer (1) This investigation was carried out at Cornel1 University in conrepresented by each of these fractions] t0geth.r nection with the Government Research Program on Synthetic Rubber with their viscosity-average molecular weights M under contract with the Office of Rubber Reserve, Reconstruction Finance Corporation. are listed in Table I. The latter were calculated (2) Rohm and Haas Company, I n c , Philadelphia, Penna from the intrinsic viscosities in benzene using the (3) P. J. Flay, I . Chum. Phys., 17,303 (1949). relationship* Joururm,,78, 1904 (1961). (4) P. J. Flory and T. G Fox, Jr., THIS Introduction The results of the application of the theory of intramolecular interactions in dissolved polymer molecules to the interpretation of their intrinsic viscosities are sumrnerized in the equations3i4
(6) See also in this connection, P. J. Florp and W. R. Krigbaum, J . Chem. Phys., 18, 1086 (1960). (6) T. 0 Fox, Jr., and P.J. Flory, J . P1p. Colloid Chum., 68, 197 (1949). (7) T.G Fox, Jr.. and P. J. Flory, TIXISJOUBNAL, 79, 1909 (1861). ( 8 ) R. H.Ewart and H. C. Tingey, Abstracts of papers presented at the 111th Meeting of the American Chemical Society, Atlantic City, N. J., April 14-18 (1947).
log Be = (log
I?]
+ 4.013)/0.74
(5)
(9) L. H. Cragg and J. E. Sirnkins, Con. J . Research, BP7, 961 (1049). (lo) F. D.Kunst, Rcc. irao. ckim., 69, 126 (1960). (11) P. Outer, C.I. Cprr and B. H. Zimm, J . Chcm. Phys., 18, 830
(1950). JOURNAL, 70, 2384 (1948). (12) T . G Fox, Jr., and P. J. Flory, THIS
T. G Fox,JR.,
1916
AND
The solvents employed were of high purity and were freshly distilled before use. TABLE I POLYSTYRENES U S E D FOR
Desiguation
18A 14A" 11~" 3D"
FRACTIONATION
Mole % dodecyl mercaptan
Mole %
peroxide
0.006 0.04 0.5
Extent of reaction,
0 0 0 0.055
1.0
POLYSTYRENE FRACTIONS U S E D I N
Designation
%
14 26 22 28
M. 800,000 350,000 150,000 45,000
THESE STUDIES
Whole polymer. %
-
M.
18AF1Bb 9 1,270,000 14AF1 12 540,000 18AF5 8 360,000 3DF2' 14 92,000 llAF4 13 89,000 3DF3' 19.5 70,000 9 43,600 3DF8 a The preparation and fractionation of polystyrenes 3L,, 14A and 11A were described previously.12 b This fraction was prepared by a refractionation of polystyrene fraction 18AF1.
Intrinsic Viscosity Detenninations.-The solution viscosities were measured with a Ubbelohde No. 1 viscometer employing techniques which have been described in detail elsewhere.? Since the effect of the rate of shear on the observed specific viscosity qsp should be small for polymers having intrinsic viscosities in the range of those used here, i.e., for [q]
