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

A large database of permeability values for common gases (He, H₂, O₂, N₂, CO₂ and CH₄) has been employed in the following correlation: P_j = k P_iⁿ where P_i and P_j are the permeabilities of gases i and j; the indices 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 nine orders of magnitude implying solution-diffusion behavior persists over the entire range of permeabilities 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∼(d_j/d_i)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 α_{i j}^nu where α_ij = P_i/P_j. The experimental values of n - 1 enable the determination of a new set of kinetic diameters showing excellent agreement between theory and experimental results. The value of 1/k was found to be virtually an exact fit with the relationship developed by Freeman in predicting the value of k_u for the upper bound relationship using the new set of kinetic diameters where the calculations 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 accuracy 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 O₂. 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.