Correlation of separation factor versus permeability for polymeric membranes

The separation of gases utilizing polymeric membranes has emerged into a commercially utilized unit operation. It has been recognized in the past decade that the separation factor for gas pairs varies inversely with the permeability of the more permeable gas of the specific pair. An analysis of the literature data for binary gas mixtures from the list of He, H2, O2, N2, CH4, and CO2 reveals an upper bound relationship for these mixtures. The upper bound can be represented by a log-log plot of αij (separation factor = Pi/Pj) versus Pi (where Pi = permeability of the more permeable gas). Above the linear upper bound on the log-log plot, virtually no values exist. The slope of this line (n) from the relationship Pi=kαnij can be related to the difference between the gas molecular diameters Δdji (djdi) where the gas molecular diameter chosen is the Lennard-Jones kinetic diameter. This relationship yields linearity for a plot of −1/n versus Δdji, and the line passes through (0,0) for the x–y plot thus providing further verification of this analysis. These results indicate that the diffusion coefficient governs the separating capabilities of polymers for these gas pairs. As the polymer molecular spacing becomes tighter the permeability decreases due to decreasing diffusion coefficients, but the separation characteristics are enhanced.