Generalized Dual Sorption Theory

Abstract

A theory is formulated to explain certain classes of negative and positive deviations from Henry’s law which are frequently observed in sorption plots of penetrants in polymers. Sorption is visualized as a process in which there are dual modes: either the penetrant molecule is normally dissolved and is free to diffuse or it is immobilized, as in a sink or well. It is the second process which gives rise to deviations from normal behavior. To explain negative deviations from Henry’s law, the solubility of the penetrant is analyzed as the sum of the contributions from these two modes. A diffusion equation, which is a modification of Fick’s second law, is derived for the rate of sorption. Numerical solutions are found for the resulting nonlinear partial differential equation using finite difference techniques. A very good correspondence of the theory and data is observed for several polymer-penetrant pairs. In the case of positive deviations from Henry’s law, the polymer network swells to expose more sites, increasing the sorption level synergistically. A statistical analysis of the phenomenon of clustering is used to aid in interpretation of the sorption isotherms. Fick’s law is modified to include a rate equation for clustering (assuming a first order reversible reaction). The correlation of the data with theory is quite good; not only in predicting the behavior of sorption transients, but also in yielding the effective steady-state diffusion coefficients.