An empirical correlation of gas permeability and permselectivity in polymers and its theoretical basis

A large database of permeability values for common gases (He, H-2, O-2, N-2, CO2 and CH4) has been employed in the following correlation: P-j = kP(i)(n) where P-i and P-j are the permeabilities of gases i and j; the indicating are chosen such that the value of n is >1.0. The plots of log P-i versus log P-j show linear behavior over nitrate orders of magnitude implying solution-diffusion behavior persists over the entire range of permeability existing in known dense polymeric materials. The scatter of data around the linear correlation for each gas pair was modest over the entire range of permeability. It was found that n correlates with the kinetic diameter of the specific gases of the pair by a relationship: n - 1 similar to(d(j)/d(j))(2)-1 in agreement with theory Correlations exist between n and k for the noted relationship and n(u) and k(u) of the upper bound relationship of P-i = k(u)alpha(nu)(ij) where alpha(ij) = P-i/P-j. The experimental values of n - 1 enable the determination of a new set up kinetic diameters showing excellent agreement between theory and experimental results. The value of was found to be virtually an exact fit with the relationship developed by Freeman in predicting for value of k(u) for the upper bound relationship using the new set of kinetic diameters where the calculation were constrained to minimize the error in (n - 1) = (d(j)/d(i))(2) - 1. The significance of these results includes a new set of kinetic diameters predicted by theory and agreeing with experimental data with accurate significantly improved over the zeolite determined diameters previously employed to correlate diffusion selectivity in polymers. One consequence of this analysis is that the kinetic diameter Of CO2 is virtually identical to that Of O-2. Additionally, the theoretical relationship developed by Freeman for the upper bound prediction is further verified by this analysis which correlates the average permeability for polymeric materials as compared to the few optimized polymer structures offering upper bound performance. (C) 2009 Elsevier B.V. All rights reserved.