Sorption Isotherms of Gases by Polymer Membranes in the Glassy State: An Explanation Based on the Nonequilibrium Thermodynamics

Abstract

Sorption isotherms of glassy polymers are concave to the pressure axis, and the absolute sorption levels are almost an order of magnitude higher than that of rubbery polymers on the relatively low-pressure side. There are several models to interpret this behavior, and the dual sorption model is the most widely accepted one among them. In the present work, sorption isotherms were first derived from permeation data with several gases for four polymer membranes which might be representative of the dual sorption model: two of them were in a glassy state (cellulose acetate and polyamide), the third one was a block copolymer which was composed of a glassy polymer and a rubbery polymer at the measuring temperature, and the fourth one was a Nafion membrane which was taken as a model membrane because of its channel structure with adsorption sites of charged groups supported by a rubbery polymer. These results did not necessarily support the dual sorption model. Subsequently, the validity of the underlying assumptions of two other sorption models for glassy polymers, that is, the matrix model and the deformation model, were examined and a new equation for the sorption isotherm with an ordering parameter was derived, which implied that the glassy polymer was in a nonequilibrium state and changed from the glassy to the rubbery state by absorbing the gas.