Contributions of diffusion and solubility selectivity to the upper bound analysis for glassy gas separation membranes

Prior analyses of the upper bound of permselectivity versus permeability, both theoretical and empirical, have assumed that this relationship is a consequence of the dependence of gas diffusion coefficients on the molecular diameter of the gases of interest. The solubility selectivity has been assumed to be invariant with permeability (and free volume). However, a few literature sources note that the solubility coefficient for specific families of glassy polymers correlate with free volume. A large database of permeability, diffusivity and solubility coefficients for glassy polymers was compiled to investigate this hypothesis. A critical analysis of the data demonstrates a modest solubility selectivity contribution to permselectivity as a function of free volume and, thus, permeability. The solubility selectivity (Si/Sj) generally decreases with increasing permeability (and free volume) when the diameter of gas j is larger than that of gas i. This empirical trend is likely a consequence of larger gas molecules having less access than smaller molecules to sorption sites as the polymer packing density increases and free volume decreases. The diffusion data permit determination of a diffusivity upper bound, which is modestly different from the permeability-based upper bound relationship. The diffusion data analysis allows a determination of a new set of gas diameters more appropriate for gas diffusion in polymers than prior correlations.