MASS-TRANSPORT AND MECHANICAL-PROPERTIES OF SOLID POLYMERS

A general mathematical formulation is proposed for the description of the diffusion of low molecular weight species into a polymer matrix, in the presence of significant stress and deformation fields. The model is based on the usual momentum and mass balance equations; a crucial point is that it makes use of constitutive equations for the stress and for the diffusive mass flux which are not chosen independently of each other since they must obey precise thermodynamic restrictions; the latter are found in rather general terms. Due to the strong coupling between the mechanical and the diffusive problems, the transfer rate is in general non Fickian and is affected by the deformation gradient field, by the deformation at the external interface as well as by the mechanical boundary conditions which are exerted. The presence of a stress field results in some non-locality effects. The model was explicitly solved for the case of a non linear crosslinked network, described by the Flory Erman equation for the Helmholtz free energy.