Elastic strain energy and forces on point defects in a two-phase medium
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The temperature dependence of the tracer diffusion coefficient D * of long deuterated polystyrene (c?-PS) chains of molecular weight M>MC, where Mc is the critical molecular weight for entanglement, diffusing into highly entangled PS matrices, each of molecular weight / > = 2 x l 0 7 , is studied using forward recoil spectrometry. It is found that the temperature dependence of D */T, reflected primarily in the monomeric friction coefficient, is accurately described by a Vogel equation. The constants that are used to fit these results are independent of M and are the same as those used to fit the temperature dependence of the zero shear rate viscosity of polystyrene.
I. INTRODUCTION It is now well established1"3 that the tracer diffusion coefficient D * of a long polymer chain of molecular weight M diffusing into a highly entangled melt varies as D*=D0M
2,
(1)
in accordance with the predictions of the theory of reptation.9'10 Theoretically, the constant D o depends on the molecular weight between entanglements and the Rouse mobility of the chain.10 Recently, Graessley showed that Do can be estimated from knowledge of viscoelastic parameters. :: The agreement between the estimated and experimental values is remarkably good.1"3'11 If these ideas are correct, the temperature dependence ofD V7 1 ought to be the same as that of the inverse of the zero shear rate viscosity rj0. Consequently, the Vogel equation, log( l/?70) = -A-B/{T-Tm) should describe the temperature dependence of D */T. The empirical constants B and Tx may be obtained from the Williams-Landel-Ferry (WLF) constants c1 and c2, which describe the time-temperature shift factor 1 2
aT(\ogaT
= Cl{T-
Tg)/[c2+
{T-
Tg)]
,
where Tg is the glass transition temperature of the polymer). Recent measurements by Nemoto and coworkers13 on the self-diffusion of ris-polyisoprene are consistent with this prediction. Measurements of values of the activation energy for diffusion at high temperatures, where the temperature dependence is Arrhenius, revealed values similar to those obtained from viscosity measurements over the same temperature ranges.3'8'14 Antonietti and co-workers find that the temperature dependence ofD * (notZ) */T) for polystyrene7 chains diffusing into an entangled matrix can be described by a WLF shift factor. However, the constants used to fit the data not only differed from the WLF constants cx and c2 202
J. Mater. Res. 1 (1), Jan/Feb 1986
http://journals.cambridge.org
for polystyrene but varied with the molecular weight of the diffusing chain. It is expected that the constants used to fit the D*vsT data should differ from those used for the D */T\% T data. Furthermore, their studies of the diffusion of shorter chains extended to much lower temperatures than those of the longer chains; perhaps the bulky molecule used as a tag affects the motion of these shorter chains at lower temperatures where the available free volume is smaller. These reasons may account for this discrepancy. In this paper we reexamine the temperature dependence of D
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