The effects of heterogeneities on memory-dependent diffusion

(Received 2 November 1992, accepted 25 March 1993)

Abstract
Case II diffusion is often seen in glassy polymers, where the mass uptake in sorption is proportional to time t instead of . A memory dependent diffusion is needed to explain such effects, where the relaxation function used to describe the memory effect has a characteristic time. The ratio of this time to the overall diffusion times is the diffusional Deborah number. Simple models show that case II results when the Deborah number is around one, that is, when the two time scales are comparable. Under investigation are the possible effects of the fact that the glassy polymers are heterogeneous over molecular scales. The averaging form given by DiMarzio and Sanchez has been used to obtain the averaged response. The calculated dynamics of sorption show that whereas case II is still observed, the long term tails change dramatically from the oscillatory to torpid, to chaotic, which are all observed in the experiments. The Deborah number defined here in a self-consistent manner collapses in those cases, but causes no other ill-effects.