Steady State Transport Phenomena in Non-Ideal Permeant-Polymer Systems

Summary

The so generally used Fick’s first law of diffusion with the material current density proportional to concentration gradient of the penetrant is inapplicable to even the simplest uniform homogeneous polymer membranes which as a rule are not ideal. The nonideality shows up in a nonlinear increase of sorbed penetrant with applied pressure of gas or concentration of liquid. That modifies the concentration gradient in the membrane. The same effect can obtain as a consequence of the finite compressibility of swollen membrane under the applied pressure gradient in the hydraulic experiment. In both cases the membrane becomes nonuniform under the influence of concentration or pressure gradient in spite of the fact that it is uniform in a gradient free environment. But the true driving force is in all cases the gradient of the chemical potential of the penetrant and not that of concentration. The deviations of sorption, partition and diffusion coefficients from ideality in highly swollen and in plastically deformed polymer films can be to some extent described by the change of fractional free volume as a consequence of the finite amount of sorbate present. A new effect may occur in the hydraulic experiment. With increasing swelling the membranes exhibit a substantial viscous flow permeability which may be orders of magnitude larger than the diffusive permeability. It cannot be described in terms of diffusive transport.