Basis of permeability/selectivity tradeoff relations in polymeric gas separation membranes

Gas separation properties of polymer membrane materials follow distinct tradeoff relations: more permeable polymers are generally less selective and vice versa. Robeson¹ identified the best combinations of permeability and selectivity for important binary gas pairs (O₂/N₂, CO₂/CH₄, H₂/N₂, etc.) and represented these permeability/selectivity combinations empirically as α_A/B = β_A/BP_A^-λAB, where P_A and P_B are the permeability coefficients of the more permeable and less permeable gases, respectively, α_A/B is selectivity (=P_A/P_B), and λ_A/B and β_A/B are empirical parameters. This report provides a fundamental theory for this observation. In the theory, λ_A/B depends only on gas size. β_A/B depends on λ_A/B, gas condensability, and one adjustable parameter.