3588
J. E. MARKAND G. B. THOMAS
The Temperature Coefficient of the Unperturbed Dimensions of Polyisobutylene’a
by J. E. Mark and G. B. Thoma@ The Department of Chemktry, The Polytechnic Institute of Brooklyn, Brooklyn, New York
11,901
(Received June 10, 1966)
Intrinsic viscosities of polyisobutylene in n-hexadecane over the temperature range 30130” are reported. These results, in conjunction with published heats of mixing of this polymer in n-alkanes, indicate a value of -0.28 X deg-’ for the temperature coefficient d In (r2)o/dTof the unperturbed chain dimensions of polyisobutylene. This value is in good agreement with that obtained from force-temperature measurements on polyisobutylene networks as reported by other workers.
Introduction A quantity of fundamental importance in the analysis of spatial configurations of polymer molecules is the temperature coefficient d In (r2)o/dTof the mean-square end-to-end distance of the chain unperturbed by longrange interactions. Its utility in the correlation of theory and experiment has been demonstrated for a number of long-chain molecule^.^-^ This coefficient has been determined in a variety of ways : (i) stress-temperature measurements on elongated, amorphous networks of the polymer in either the swollen or unswollen state;3~7~10,11 (ii) swellingtemperature measurements on networks in athermal solvents;12 (iii) intrinsic viscosity-temperature measurements in athermal s 0 1 v e n t s ; ~ ~ ~and ~ l J ~(iv) intrinsic viscosity determinations in a series of solvents at their respective 0 temperature^.'^ The chains are in their unperturbed configurations in (i)15 and (iv)16 and thus corrections for long-range interactions are unnecessary; in (ii) and (iii), the athermal nature of the solvent facilitates the required correction of the chain dimensions to their unperturbed value. Special difficulties, however, attend the use of method iv. Specific solvent effects on (r2)ohave been demonstrated for both polar and nonpolar polymers under 0 c o n d i t i o n ~ . l ~ -It~ ~is thus essential that solvents chosen for this method of determining d In (r2)o/dT ~ *require~~ be as structurally similar as p o ~ s i b l e ; ~this ment, unfortunateh freauenth. .ignored, was successfully met in a study of atactic polystyrene in the 1chloro derivatives of normal decane, undecane, and dodecane a t the appropriate 0 temperat~res.1~ The importance of the specific solvent effect had not The J~urnalof Physical ChemiEtTy
been established at the time of an early analysis of intrinsic viscosities of polyisobutylene fractions in benzene, phenetole, and anisole under 0 condition^.^^ (1) (a) Presented before the Polymer Division at the 152nd National Meeting of the American Chemical Society, New York, N. Y.,Sept 1966. (b) Taken from a thesis presented to the Graduate School of the Polytechnic Institute of Brooklyn in partial fulfillment of the requirements for the M.S. degree, June 1966. (2) C. A. J. Hoeve, J . Chem. Phys., 32, 888 (1960). (3) A. Ciferri, C. A. J. Hoeve, and P. J. Flory, J . Am. Chem. SOC.,8 3 , 1015 (1961). (4) C. A. J. Hoeve, J . Chem. Phys., 35, 1266 (1961). (5) K.Nagai and T. Ishikawa, ibid., 37, 496 (1962). (6) P. J. Flory, V. Crescenzi, and J. E. Mark, J . Am. Chem. SOC.,86, 146 (1964). (7) J. E. Mark and P. J. Flory, ibid., 87, 1415 (1965). (8) A. Abe, R. L. Jernigan, and P. J. Flory, ibid., 88, 631 (1966). (9) P. J. Flory, J. E. Mark, and A. Abe, ibid., 88,639 (1966). (10) J. E. Mark and P. J. Flory, ibid., 86, 138 (1964). (11) J. E. Mark and P. J. Flory, ibid., 87, 1423 (1965). (12) J. E.Mark, J . Phys. Chem., 68, 1092 (1964). (13) P. J. Flory, A. Ciferri, and R. Chiang, J . Am. Chem. SOC.,83, 1023 (1961). (14) T. A. Orofino and A. Ciferri, J . Phys. Chern., 68, 3136 (1964). (15) P. J. Flory in “Lectures in Material Science,” P. Leurgans, Ed., W. A. Benjamin, Inc., New York, N. Y., 1963. (16) P. J. Flory, “Principles of Polymer Chemistry,” Cornel1 University Press, Ithaca, N. Y.,1953. (17) A. R. Shultz and P. J. Flory, J . Polymer Sci., 15, 231 (1955). (18)U. Bianchi and V. Magnasco, ibid., 41, 177 (1959). (19) K. J. Ivin, H. A. Ende, and G. Meyerhoff, Polymer, 3 , 129 (1962). (20)T. A. Orofino and J. W. Mickey, Jr., J . Chem. Phys., 38, 2512 (1963). (21)V. Crescenai and P. J. Flory, J . Am. Chem. Soc., 86, 141 (1964). (22) U.Bisnchi, J . PoEymer Sci., A2, 3083 (1964). (23) T. G Fox, Jr., and P. J. Flory, J . Am. Chem. Soc., 73, 1909 (1951).
TEMPERATURE COEFFICIENT OF POLYISOBUTYLENE
The value d In (r2)o/dT = -1.1 X deg-l estimated3 from these results is a t variance with that obtained from force-temperature measurements a t conX deg-1. Since values stant p r e ~ s u r e ,-0.09 ~ of d In (r2)o/dT obtained by different methods are almost invariably in good agreement, the discrepancy is probably due to different specific solvent effects in the three systems studied,14 and thus the value obtained from these viscosity measurements is thought to be ~nreliable.~~ It is the purpose of the present study to determine this important quantity from intrinsic viscosities of polyisobutylene in n-hexadecane over a wide temper* ture range. Heats of mixing of the polymer in this solvent and in other n-alkanes have been measured calorimetrically.25 The temperature coefficient of (r2)0 for polyisobutylene should be calculable from the temperature dependence of its intrinsic viscosity in nhexadecane without recourse to approximations or assumptions required in methods iii and iv.
3589
=
0.42
t
0,401
,
I
40
0
A sample of polyisobutylene26was fractionated from a tant. The fraction chosen for these studies constituted 23% of the original sample and had a molecular weight of 5.48 X lo5 on the basis of its intrinsic viscosity in toluene at 30°.27 Approximately 0.1% by weight of X-phenyl @-naphthylamine was added to the n-hex* decane (Matheson Coleman and Bell, 99% pure, olefinfree) to inhibit oxidative degradation of the polyisobutylene at elevated temperatures. Viscosities were measured in a Cannon-Ubbelohde viscometer having a capillary diameter such that kinetic energy corrections to the efflux times were negligible. Solutions were prepared by weight and concentrations C a t each temperature were calculated using specific volumes and thermal expansion coefficients of n-hexadecane% and polyis~butylene.~~ Efflux times, reproducible to &0.05%, were obtained for solvent and each of four solutions at 30,55,80,105, and 130°, the maximum temperature fluctuation being a few hundreths of a degree. The constancy of efflux times at even the highest temperature indicated the absence of significant polymer degradation. Relative viscosities16 qrel ranged from 1.15 to 1.55.
Results Intrinsic viscosities [q] obtained by extrapolation of both In qrel/C and reduced specific viscosities qsp/C to infinite dilution are plotted vs. temperature in Figure deg-l 1. The value of d In [q]/dT = -0.176 X obtained by least-squares analysis of these results is in
I
,
I
I
I20
80
0
T in 'C
Figure 1. Intrinsic viscosity vs. temperature for polyisobutylene in n-hexadecane.
qualitative agreement with the value -0.11 X deg-1 obtained from more limited measurements on polyisobutylene in n-hexadecane. 23 The coefficient d In (r2)o/dT was calculated from d In [q]/dT using the relationshipsw
C P [ ( ~ ~ ) ~ / M ] ~ ~ ~ M ' / W(1) ~ ~ ( ~ T ) - ' / ~ ( V ~ /[(r2)~/M]-1/Z NAV~) x [VI =
a5 -
a3 =
Experimental Section 1% solution in benzene at 30°, using acetone as a precipi-
I
M1/"('/2
- XI)
(2)
where CP is a universal constant for gaussian coils and in thermodynamically good solvents has a value of approximately 2.1 X 1021for [q] in dl g-l, (r2)oin cm2, and the molecular weight M in g mo1e-1.16 The quantity a = [(r2)/(7-2)01'/~is an expansion factor arising from long-range interactions, v and VI are the specific volume of polymer and molar volume of solvent, respectively, N A is the Avogadro number, and x~ is a parameter characterizing the interaction of polymer and solvent.16 Solving eq 1 for the temperature coefficient of (r2)oand using eq 2 to eliminate the temperature coefficient of a givesI3
- a-2)d In [q]/dT - a-2)[ ~ P z PI - ('/2 - xi)-'(dxi/dT) I
d In (r2)o/dT =
(I ~
(5/3
(3)
~~~~
(24)Failure to appreciate this point is probably also the source of the discrepancy [G. Moraglio, European Polymer J., 1, 103 (1965)l between the results of thermomechanical and viscometric measurements on cis-l,4polybutadiene, and casts considerable doubt on the interpretation given to intrinsic viscosity-temperature studies [I. Sskurada, A. Nakajima, 0. Yoshisaki, and K. Nakamae, Kolloid-Z., 186, 41 (1962)]of methyl methacrylate polymers of various steric compositions. (25)G.Delmas, D.Patterson, and T. Somcynsky, J . Polyner Sci., 57,79 (1962). (26)Vistanex L-100,generously provided by the Esso Research and Engineering Co., Linden, N. J. (27) T.G Fox, Jr., and P. J. Flory, J . Phys. Colloid Chem., 5 3 , 197 (1949). (28) G. Egloff, "Physical Constants of Hydrocarbons," Vol. V, Reinhold Publishing Corp., New York, N. Y.,1953. (29) N. Bekkedahl, J. Res. Natl. Bur. Std., 43, 145 (1949). (30)P. J. Flow and T. G Fox, Jr., J . Am. Chem. SOC.,7 3 , 1904 (1951).
Volume 70,Number 11 November 1966
3590
J. E. MARKAND G. B. THOMAS
where PI = (l/V,)(dVl/dT) and 0 2 = (l/v)(dv/dT) are thermal expansion coefficients of solvent and polymer, respectively. All quantities are to be evaluated at 353.2"K, the average temperature of the viscometric measurements. On the basis of dilatometric results, p1 = 0.952 X deg-1,28 and PZ = 0.551 X deg-1.29 The parameter x1 and its temperature coefficient are estimated from calorimetric results of Delmas, Patterson, and Somcynsky.26 Their use of the Prigogine cell theory of polymer solutions in the interpretation of observed heats of mixing of polyisobutylene in a number of n-alkanes gives the expression x1
= 43.2T-'
+ 0.355 X 10-3T
(4)
for polyisobutylene in n-hexadecane. At 353.2"K, XI = 0.248 and dxl/dT = 9.1 X deg-l. The appropriate value of cy was calculated from eq 2 using [ ( r 2 ) 0 / ~ ] ' 1= 2 77.4 x 10-10 cm (g/rno1e)-'/~,23 = 308.7 cc mo1e-1,28v = 1.105 cc g-1,29 and M = 5.48 X lo6 (see above). Use of the above quantities gives CY = 1.515 and the final result, d In (r2)o/dT = -0.28 X deg-l. The value of the term (1 - CY-^)(^/^ - xl)-l (dxl/dT) deg-l; thus in this was found to be only 0.02 X case even relatively large errors in x1 and dxl/dT resulting from inherent limitations of the cell theory of solutions would not significantly affect the value of d In (r2)O/dT. Similarly, adoption of suggested modifications of eq 1 and 2 would be of little consequence in the present context: (i) substitution of [17] = 2.9 X 1021[(r2)~/M]"l'1M'~'cy2~43 for eq lS1 gives d In (r2)o/dT = -0.19 X deg-l, and (ii) reduction of the numerical factor in eq 2 by one-half32 gives -0.25 X deg-l.
Discussion The value of d In (r2)O/dTfor polyisobutylene obtained herein is in good agreement with the small negative value obtained from force-temperature measure-
The Journal of Physical Chmietry
ments on elongated networks of the p ~ l y m e r . ~A molecular interpretation of the chain extension and its temperature coefficient for polyisobutylene has been given in terms of a chain model having rotational states at j=82°.2,33These skeletal rotational angles are associated with a helix having sixteen chain bonds per five turns, this conformation being suggested by early X-ray diffraction studies of crystalline polyisobutylene.84 There is now evidence,%however, of considerable distortion of this simple helix. In addition, calculation^^^ of intramolecular energies of conformations of the polyisobutylene chain indicate the existence of accessible rotational sequences in addition to those manifested by the chain in the crystalline state. In view of the above findings, it seems obvious that the rotational isomeric state model originally suggested for polyisobutylene2t33 requires considerable revision. Such calculations are in pr~gress.~' Acknowledgment. The authors wish to acknowledge several very helpful comments from Professor P. J. Flory of Stanford University.
(31) M.Kurata and H. Yamakawa, J . Chem. Phys., 29, 311 (1958); M.Kurata, H.Yamakawa, and H. Utiyama, Makromol. C h a . , 34, 139 (1959). (32)W.H. Stockmayer, J . Polyner Sci., 15, 595 (1955). (33) 0.B. Ptitsyn and Yu. A. Sharanov, Zh. Tekh. Khim., 27, 2744, 2762 (1957). (34)A. M.Liquori, Ada Cryst., 8 , 345 (1955). (35) c. Bunn and D. R. Holmes, DkCU88iOn8 Faraday soc., 25, 95 (1958). (36) P. De Santis, E. Giglio, A. M. Liquori, and A. Ripamonti, Nuovo Cimento, 26, 616 (1962). (37) NOTEADDED IN PROOF.Recently published force-temperature measurements on polyisobutylene networks a t constant volume at 18' (G. Allen, G. Gee, M. C. Kirkham, C. Price, and J. Padget, Preprints of The International Symposium on Macromolecular Chemistry, Tokyo and Kyoto, Japan, Sept 28-0ct 4, 1966) give d In (r*)o/ d T = -0.27 (f0.12) X deg-', in excellent agreement with the result of the present investigation.
w.
