Diffusion in solids under strain, with emphasis on polymer membranes

A solute diffusing through a solid gives rise to a change in volume. This swelling can be viewed as a strain, and it is possible to obtain the accompanying stress using elasticity theory. The theory provides two ways by which stresses can be generated. The first comes from the condition of impenetrability where the system generates stress to exclude certain configurations during deformation. The second is due to imposed restrictions on the geometry during the swelling process. Larché and Cahn have provided the thermodynamics for such systems, from which the chemical potential can be used to obtain a phenomenological expression for flux and an expression for the solubility. These two are sufficient to obtain the sorption response in most systems. Solutions have been obtained here.