COUPLED DEFORMATION AND MASS-TRANSPORT PROCESSES IN SOLID POLYMERS

A theory is developed for the effect of stress on the diffusion of a swelling penetrant into a linear viscoelastic solid. A constitutive equation for the Helmholtz free energy of the mixture is used to obtain expressions for the dependence of the stress tensor on the history of the deformation and concentration fields. For cases in which the solid has only a single relaxation time, the stress constitutive equation is consistent with the standard linear viscoelastic model for solid deformation. The expression for the free energy is also used to obtain an equation for the difference in the chemical potential between the solute and the polymer as a function of the trace of the stress and concentration histories; as a result, the theory is thermodynamically consistent. As an example, the analysis is applied to the case of solute transport into a thin rectangular slab, resulting in a new expression for the diffusive flux. © 1990, American Chemical Society. All rights reserved.