Mutual Diffusion in Concentrated Polymer Solutions under a Small Driving Force

A theory is presented for mutual diffusion in concentrated polymer solutions under a small driving force. The crucial concept is that the interdiffusion of polymer and solvent causes deformation of the polymer component. A memory integral contribution to the solvent flux is developed from the transient network and reptation models; analytical formulas for measurables are derived for a polymer behaving like a Maxwell fluid. For sorption experiments, non-Fickian behavior is predicted when the polymer relaxation time matches the sorption time scale, that is, when the diffusion Deborah number is ~O(1). The predictions agree with non-Fickian behavior observed in classical and oscillatory sorption experiments. The analysis clarifies the potential value of the oscillatory sorption technique.