Prediction of differential sorption kinetics near T_g for benzene in polystyrene

Abstract

A recent first principles theory for "anomalous" diffusion, which accounts for the effect of a protracted macromolecular response to a perturbation, is used to quantitatively predict the results from successive differential sorption experiments in the benzene/ atactic polystyrene system. The physical constants in the theory are evaluated for the conditions of the experiment without reference to any non-Fickian diffusion data. The theoretical predictions are in reasonable agreement with the experimental observations.

Perturbation analysis of Thomas and Windle's model of Case II transport

“…Of fundamental importance, the present analysis, together with previous works (Billovits and Durning, 1990, 1994Mehdizahdeh and Durning, 1990;Fu and Durning, 1993), shows that the relatively simple nonequilibrium thermodynamic results by Durning and Tabor (1986) can explain the essential characteristics of the most important experimental manifestations of viscoelastic diffusion in polymer/fluid mktures: The appearance of "two-stage" weight uptake in linear-perturbation, differential sorption experiments (Billovits and Durning, 1990, 1994Mehdizahdeh and Durning, 1990) and the appearance of Case I1 transport in sufficiently nonlinear, integral sorption experiments (Fu and Durning, 1993). These studies clarify the relationship between twostage uptake and Case I1 transport in the context of a first principles development.…”

Numerical simulation of Case II transport

“…It also assumes a simple functional form for the nonequilibrium free energy consistent with well-accepted molecular-level models of concentrated polymer solutions (transient network model, tube model). The theory correctly predicts 1-D linear viscoelastic behavior observed in interval sorptions without the use of empiricism (Durning, 1985;Mehdizahdeh and Durning, 1990). The framework is attractive for comparison with experiment because of its relatively simple mathematical structure and because all of the physical properties accounting for non-Fickian effects can be measured in independent mechanical experiments.…”

Desorption Overshoot in Polymer-Penetrant Systems: Asymptotic and Computational Results

“…The flux in (2.1a) can be derived by postulating that the chemical potential is a function of both C and σ [24], which in one dimension corresponds to the stress in the polymer network [24], [30], [31], [32]. In (2.1b), the coefficient of ∂σ/∂x has been chosen constant, in contrast to the models of Durning and colleagues [8], [28], [33].…”

“…Other physically appropriate forms for β and D are presented in [4], [8], [28], [33], [34], [35], [36], [37]. We examine a polymer that is initially saturated (and hence rubbery) and unstressed, which leads to the initial conditions…”