KAZUIIIKO SINOMIYA AND JOHN D. FERRY
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Vol. 67
VISCOELASTIC PROPERTIES OF POLYVINYL ACETATES. I, CREEP STUDIES OF FRACTIONS' BY KAZUHIKO XINOMIYA AND JOHR' D. FERRY Department of Chemistry, University of Wisconsin, Madison, Wisconsin, and Japan Synthetic Rubber Company, Yokkaichi, Japan Received April 22, 1963 Tensile creep measurements on three polyvinyl acetate fractions and shear creep measurements on five sharp fractions are reported. The range of molecular weights was from 5500 to 780,000 and the temperatures were brtween 19 and 143". The temperature dependence of the creep compliance was described by the method of reduced variables. The shift factors were identical for all fractions provided that each was referred to a separate reference temperature corresponding to iso-free-volume states. The treatment implies a fractional free volume which decreases with increasing molecular weight approaching an asymptotic value. At very high molecular weight, the fractional free volume a t 75" is f7d = 0.0532 (or f g = 0.026) and its thermal expansion coefficient is af = 5.9 x 10-4, in reasonable agreement with previous estimates. I n the transition zone, the creep compliance and hence all viscoelastic properties are identical in the iso-free-volume states. I n the terminal zone, the viscoelastic properties are characterized by the steady-state compliance, whose value (for the sharp fractions) is near that predicted by the Rouse theory, and the steady-flow viscosity, which is proportional to the 3.4 power of molecular weight. The viscosities of the sharp fractions agree very well with data of Long and of Fox and Nakaj-asu. The relaxation modulus in the terminal zone, d2rived from the creep compliance by approximation methods, agrees moderately well with the predictions of the Rouse theory in the molecular weight range from 10,500 to 262,000.
Introduction The viscoelastic properties of certain polyvinyl acetate fractions and blends of fractions, investigated by tensile stress relaxation, have been reported pre~ i o u s l y . ~We , ~ now present some creep measurements on polyvinyl acetate fractions. These were undertaken to extend the earlier work with (1) more direct determinations of the steady flow viscosity and steadystate compliance, which cannot be obtained from stress relaxation as reliably as from creep; ( 2 ) inclusion of fractionated samples covering a range extending to much lower molecular weights; (3) measurements in shear as well as extension, providing greater accuracy; (4) the basis for subsequent work on a large number of blends of fractions with widely different molecular weights, to be reported subsequently. Experimental Materials.-Three polyvinyl acetate fractions described earlier3 as IX, X , and X I were used for tensile creep nieasurements. Their molecular weights were recalculated from their intrinsic vkcosities, in acetone, using the relation of Matsumoto and Oyanagi4 =
1.08 x
1 0 - 2 ~ 0 ~ 2
(1)
and are given in Table I. Five fractions were used for she_arcreep measurements. These were kindly furnished by Dr. Y. Oyanagi; they had been polymerized in ethyl acetate a t 60" with ala'azobisisobutyronitrile as initiator, the conversion being less than 5%. They were fractionated by precipitation with nheptane from very dilute methyl ethyl ketone solutions. The elaborate fractionation procedure is described The molecular weights were also derived from intrinsic viscosities, with an empirical relation based on osmotic pressure data which deviates somewhat from eq. 1 a t the lowest molecular weights. The molecular weight distribution is believed to be sharper in these samples than in samples TX, X, and XI; ultracentrifugal analysis of molecular weight distribution is in progress. The fractions were dried in mcuo a t 80" for 1 week. For tensile measurements, thin films w x e cast on mercury, leached in water, and dried as described previously.2 For shear (1) P a r t XLII of a series on mechanical properties of substances of high molecular weight. (2) K. Kinomiya and H. Fujita, J. Colloid Sei., 12, 204 (1957). (3) K. Ninomiya, ibid., 14, 49 (1939). (4) RI. Matsumoto and Y. byanagi, J . Polymer Sei., 46, 441 (1960). (5) M. Matsumoto, "Kobunshi-jikkenkagak~~-koza,"Vol. 6, Kyoritsuhnpprtn. Tokyo, 1958, p. 1.
TABLE I
---
POLYVINYL AkCETATE FRACTIOXS
Tensile creep---Fraction M X 10-8
IS
x
XI
232 340 480
------Shear Fraction
D-15 B-7 1-8-11
1-A-4 12-E-2
creep------
M
x
10-8
5.5 10.5 112 263 780
measurements, disk-shaped samples were molded under pressure a t 1.50". Methods.-The tensile creep measurements on thin films were made with a chainomatic balance originally designed for stress relaxation studiesEbut modified for measurement of creep strain. Each creep run ordinarily was made over an interval of about 80 min., and the maximum tensile strain did not exceed 30y0. The shear creep measurements were made with the torsion pendulum of Plazek, Vrancken, and B e ~ = g emodified ,~ for measurement of very small torsional deformation.8 The optical path wa8 increased from 14.34 to 26.25 f t . The sample disk dimensions ranged from 0.9 to 3.5 cm. in diameter and from 0.05 to 0.35 em. in thickness. The height was measured a t each temperature in situ, immediately after lowering the t,hermostat to bring the sample housing int~oview. The maximum shear strain including viscous flow did not exceed 0.1 and was much less than this a t low temperatures.
Results Tensile Creep.-The t,ensile creep compliance, D,( t ), is plot,ted logarithmically in Fig. 1for fract'ioii XI at three different temperatures. Here the subscript p denotes that D(t) has been multiplied by Tp/Topo, where p and po are the densities a t T and To, respectively, and TO is a reference temperature chosen as 348°K.; this procedure permits temperature shift factors to be determined from horizont'al displacements. Similar curves were obt'ained for fractions IX (at 80.0, 92.2, and 104.6') and X (at 93.0, 108.1, and 121.3'). The results for each fraction were reduced to 75' by the method of reduced variables to give the composit'e curves illustrated in Fig. 2 . The many individual points for all different temperatures, not shown, lay mostly (6) K. Ninomiya, A. Kishimoto, and H. Fujita, Kobunshi-kagaku, 14, 504 (1957); n e are indebted to Professor Fujita for the use of this equipment a t the Department of Fisheries, Maiauru, Japan. (7) D. J. Plazek, 181. N. Vrancken, and J . W.Berge, T ~ a n s SOC. . Rheol., 2, 39 (1958). (8) K. Ninomiya, .I. R. Richards, and J . D. Ferry, J . P h y s . Chem., 67,327 ( I 963).
CREEPSTUDIES OF POLYVINYL ACETATE FRACTIOKS
Nov., 1963
/
1
I
I
2
3
loy t
2293
I
IS2'O
4
(set.).
Fig. 1.-Tensile creep compliance of sample XI, plotted logarithmically a t seven temperatures as indicated. The subscript p indicates multiplication by Tp/Topa.
C
-
5
I
b
,
I
3
2
I09 t
+J
4
(sed.
Fig. 3.--Shear creep compliance of sample 1-A-11, plotted logarithmically a t 13 temperatures as indicated. The subscript p indicates multiplication by TplTopo.
(r,
0
2
4
8
6
log t/a,(:jec.). Fig. 2.-Tensile creep compliance of three samples as indicated, plotted logarithmically after reduction to 75'.
within 2% of the composite curves. The shift factors UT used in the reduction followed thle WLF equation9 log UT
:=
+ T - To)
-cj0(T - To)/(cz0
(2)
with T o = 348'K., c1O = 8.86, and cz0 = 101.6. They are very close to those used for reducing earlier dynamic mechanical measurements on a polyvinyl acetate of broad molecular weight distribution. lo The latter can be represented either by the "universal" WLF parameters with TO= 349O, elo = 8.86, and cz0 == 101.6, or by an alternative choice1' equivalent to To = 348', clo = 8.13, and cz0 = 89.8. Shear Creep-The shear creep compliance, J p ( t ) ,is plotted logarithmically in Fig. 3 for fraction 1-A,-11 a t 13 different temperatures. Similar curves were ob(0) M. L. Williams, R . F. Landel, and J. D. Ferry, J. Am. Chem. Soc., 77. 3701 (1055). (IO) M. L. Williams and J . D. Ferry, J. Colloid Sci., 9, 479 (1954). (11) J. D. Ferry, "Viscoelastic Properties of Polymers," John TViley and Sons, I n c . , New York, W. Y., 1961, p. 210.
107 t/a,Csec.). Fig. 4.--Shear creep compliance of five samples as indicated, plotted logarithmically after reduction t o 75".
tained for fraction D-14 at 12 temperatures from 18.6 to 74.4'; for fraction B-7 a t 12 temperatures from 32.3 to 74.6'; for fraction 1-A-4 a t 14 temperatures from 39.1 to 102.8'; and for fraction 12-B-2 at 15 temperatures from 37.7 to 142.6'. The results for each fraction were again reduced to 75 O by the method of reduced variables to give the composite curves illustrated in Fig. 4. Here the individual
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