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. Robeson(1) identified the best combinations of permeability and selectivity for important binary gas pairs (O-2/N-2, CO2/CH4, H-2/N-2, etc.) and represented these permeability/selectivity combinations empirically as alpha(A/B) = beta(A/B)P(A)(-lambda A/B), where P-A and P-B are the permeability coefficients of the more permeable and less permeable gases, respectively, alpha(A/B) is selectivity (=P-A/P-B), and lambda(A/B) and beta(A/B) are empirical parameters. This report provides a fundamental theory for this observation. In the theory, lambda(A/B) depends only on gas size. beta(A/B) depends on lambda(A/B), gas condensability, and one adjustable parameter.