Effect of partially immobilizing sorption on permeability and the diffusion time lag

Abstract

The gas permeability and diffusion time lag may exhibit varying degrees of pressure dependence for glassy polymers. The sorption isotherm appears to consist of contributions from both Langmuir and Henry's law terms in such systems. This “dual sorption” theory advanced in the literature pictures gas held by the Langmuir mode as being completely immobilized. In the present paper, this model is extended to accommodate different degrees of partial immobilization of gas sorbed by this mode using two different formulations. One uses a transport expression based on concentration gradients while the other is based on chemical potential gradients. The predictions are that: (1) total immobilization results in a constant permeability with a time lag which strongly decreases with pressure; (2) no immobilization results in a constant time lag with a permeability which decreases strongly with pressure; and (3) incomplete immobilization results in both the permeability and time lag decreasing with pressure but neither as strongly as in the other limiting cases. The differences which may arise by the two formulations of the model are discussed.