Revisiting the experimental and theoretical upper bounds of light pure gas selectivity–permeability for polymeric membranes

Robeson [L.M. Robeson, J. Membr. Sci. 62 (1991) 165–185] described “upper bounds” correlating the pure gas selectivity with the permeability of the faster gas, PA. The exponential dependence of the selectivity–permeability trade off, −1/n  , according to the relationship αA/B=PA/PB=k−1/nPA1/n, was shown to be a function of the difference in the kinetic diameter of the gas pairs, ΔA/B = dB − dA. Robeson recently revisited the upper bounds [L.M. Robeson, J. Membr. Sci. Available online 22 April 2008], adding two new gas pairs, CO2/N2 and N2/CH4 and, with only minor changes to the slopes of the upper bounds, confirmed the relationship between −1/n and ΔA/B. Significant changes were reported for the front factor k  . Freeman [B.D. Freeman, Macromolecules, 32(1999) 375–380] developed a theoretical model which describes these upper bounds as a function of a reduced kinetic diameter, λA/B=(dB/dA)2−1 and αA/B=βA/BPA−λA/B. The theoretical model opened the possibility of setting upper bounds for gas pairs for which experimental upper bounds were not reported. Despite quantitative predictions of both −1/n and k−1/n (or βA/B) calculated values of αA/B compared poorly with Robeson's upper bounds for many of the gas pairs. This work revisits Robeson's findings as well as those of Freeman and seeks to improve the predictive accuracy of Freeman's model. Robeson had noted that the low precision of many of the kinetic gas diameters could have contributed to the scatter in his correlation of −1/n and ΔA/B. Considering this hypothesis, the gas diameters were re-estimated using the Error in the Variable Method (EVM) with the regression criterion based on the predicted selectivity at three permeabilites compared to Robeson's upper bounds. Very small changes to the gas diameters, typically <0.09 Å, made a significant improvement in the overall accuracy of the predicted selectivity and the correlation of λA/B = −1/n. Freeman's f value, a constant in the ED correlation as a function of the gas collision diameter, was revised from 12,600 to 16,909 cal mol−1 (52.7 to 70.7 KJ mol−1). Recent predictions of the theoretical upper bound are reviewed and corrections proposed based on Freeman's model and parameters for the gas pairs: N2/CH4 and CO2/N2.