Basis of Solubility versus TC Correlations in Polymeric Gas Separation Membranes

Gas molecules dissolve in dense rubbery matrices by occupying empty cavities created by thermal fluctuations in the matrix. In this paper, we describe the corresponding thermodynamics in terms of cavity formation and penetrant binding steps. We illustrate that the contributions of these processes to the sorption enthalpy can be estimated from experimental gas sorption and volume dilation data. A simple argument is provided to illustrate why the enthalpy change of cavity formation does not affect gas solubility, leaving behind the binding enthalpy as the relevant energy descriptor for penetrant sorption. The described procedure is accurate for systems in which the penetrant interacts with the polymer via dispersion forces and has been applied to analyze the solubility of hydrocarbons and perfluorocarbons in polydimethylsiloxane. Moreover, the two-step thermodynamic process for gas sorption considered in this work suggests a molecular basis of frequently observed correlations between gas solubility and gas critical temperature in rubbery and glassy polymers.