A spatially nonlocal model for polymer-penetrant diffusion

Diffusion of a penetrant in a polymer entanglement network cannot be described by Fick's Law alone: rather, one must incorporate other nonlocal effects. In contrast to previous viscoelastic models which have modeled these effects through hereditary integrals in time, a new model is presented exploiting the disparate lengths of the polymer in the glassy (dry) and rubbery (saturated) states. This model leads to a partial integrodifferential equation which is nonlocal in space. The system is recast as a moving boundary-value problem between sets of coupled partial differential equations. Using singular perturbation techniques, sorption in a semi-infinite polymer is studied on several time scales with varying exposed interface conditions. Though some of the results match with those front viscoelastic models, new physically relevant behaviors also appear. These include the formation of stopping fronts and overshoot in the pseudostress.