Sharp fronts due to diffusion and stress at the glass transition in polymers

We derive and analyze a model for sharp fronts in glassy polymers. We take the major effect of a diffusing penetrant on the polymer entanglement network to be the inducement of a differential viscoelastic stress. This couples diffusive and mechanical processes through a viscoelastic response where the strain depends upon the amount of penetrant present. Analytically, the major effect is to produce explicit delay terms, via a relaxation parameter, to account for the fundamental difference between a polymer in its rubbery state and the polymer in its glassy state, namely the finite relaxation time in the glassy state owing to slow response to changing conditions. We produce concentration profiles in good agreement with observations on sharp front formation. In addition the model can account for the phenomenon of sorption overshoot.