A theory for species migration in a finitely strained solid with application to polymer network swelling

Abstract

We present a theory for the behavior of a solid undergoing two interdependent processes, a macroscopic or mechanical process due to the deformation of the solid and a microscopic or chemical process due to the migration of a chemical species through the solid. The principle of virtual power is invoked to deduce the basic balances of the theory, namely the mechanical force balance and the transport balance for the chemical species. In combination with thermodynamically consistent constitutive relations, these balances generate the basic equations of the theory. Keeping in mind applications involving the swelling of polymer networks by liquids, a specialization of the theory is presented and applied to study the influences of mechanical and chemical interactions on equilibrium states and diffusive dynamical processes. It is shown that the possibility of a mechanically induced phase transition is governed by two parameters: the Flory interaction parameter and a parameter given by the product between the number of cross-linked units per unit reference volume and the molecular volume of the liquid molecule. As for diffusion, it is shown that the theory is able to describe the pressure-induced diffusion in swollen membranes.