Coupled stress-diffusion: Case II

In this paper, a macroscopic continuum formulation is developed for predicting Case II diffusion in polymers. This formulation is based on micromechanical considerations in that the free energy density for the solvent-polymer system is calculated using information from the microscopic structure of the system. Formulation here means a complete set of governing balance equations and constitutive laws that may be used to solve initial boundary value problems. The analysis begins with the development of the proper statements of momentum and mass balance for a mixture of a solvent and a polymer capable of undergoing a solvent induced rubber-glass transition. Subsequently, the expression for the local reduced entropy inequality is derived and used to determine the form of the constitutive relations in terms of the free energy function for the mixture. An extension of the Flory-Huggins free energy of mixing to the transient case is then presented. The result of this formulation is a complete set of coupled field equations. An example initial boundary value problem is then solved to demonstrate that the qualitative features of Case II diffusion behavior are replicated.