Case-II diffusion in polymers. II. Steady-state front motion

Abstract

We consider front formation and steady-state front motion in a one-dimensional polymer system undergoing case-II diffusion. The polymer system approximates a polymer sheet whose thickness is very small compared with its lateral dimensions. The osmotic pressure of Thomas and Windle (TW) is used in the theoretical analysis. The transient problem of front formation is formulated. It is found that the original coupled system of partial differential equations proposed by TW can be reduced to one equation. An exact solution of this equation for a diffusion front moving with a velocity V is presented. The solution allows us to predict the dependence of the steady-state velocity on material parameters and the equilibrium concentration of penetrant outside the sheet. The concentration and pressure profile ahead of the moving front is obtained. We also show that the TW Model predicts the existence of a Fickian tail ahead of the steadily moving front. Conditions for the dominance of the Fickian tail are determined. The predicitions of our theoretical analysis are then compared with concentration profiles of iodohexane diffusing into polystyrene determined from Rutherford backscattering spectrometry.