A Nonlinear Constitutive Behavior for Diffusion in Polymers.

Abstract : Non-linear diffusion is defined within the framework of Fick's laws where the diffusion coefficient, D, is a function of penetrant concentration, temperature and stress. It is also recognized that these same parameters are contained in a memory dependent free volume description of polymers. Combining the Stokes-Einstein equation for diffusion with a WLF shift function allows the Doolittle equation for free volume to be interpreted in terms of diffusion of penetrant. It is further shown that the history dependent diffusion law needs to be solved together with the usual stress-strain viscoelastic law at a material point in order to quantify the effect of diffusion on the stress field or vice-versa.