Nonequilibrium thermodynamic modeling of case II diffusion in glassy polymers

In this article, we formulate a nonequilibrium thermodynamic theory for case II diffusion in a glassy polymer. In the model, we integrate the three-dimensional elasto-visco-plasticity of a glassy polymer, the Flory-Rehner theory for polymer network swelling, and the kinetics law for solvent migration with the concentration-dependent diffusivity. Our theory is given in a general 3D tensorial form, which, therefore, can be used to model case II diffusion in glassy polymers with arbitrary geometries and under different mechano-chemical loading conditions. An intrinsic length determined by the combination of the polymer viscosity and solvent diffusivity arises from the theory, which dictates the size-dependent case II diffusion in glassy polymers. The theory developed in the article may provide important guidance for designing semi-permeable membranes, waterproof coating, and drug-delivery systems, where case II diffusion can commonly occur.