Isothermal Diffusion in Systems with Glasslike Transitions

Following Simon, we define fluid systems with a ``glasslike'' transition as systems which above the transition temperature Tξ are, and below Tξ are not in internal chemical equilibrium with respect to a set of unspecified internal parameters of even tensorial rank. We present the flow equations for the chemical components of such systems in various frames of references. In particular, in a mass-fixed frame of reference, besides a variation in the Onsager coefficients, the flow equations below Tξ are subject to a different set of subsidiary conditions (the ``new'' Gibbs—Duhem equations). We also investigate the consequences of the assumption of sorption equilibrium at the surface of our diffusion system. We find that below Tξ these systems will possess history-dependent diffusion coefficients and be subject to time-dependent surface concentrations. We can relate these time dependencies to the relaxation of the internal parameters of the system below Tξ.