How Does Molecular Diameter Correlate with the Penetration Barrier of Small Gas Molecules on Porous Carbon-Based Monolayer Membranes?

Molecular diameter is an essential molecule-size descriptor that is widely used to understand, e.g., the gas separation preference of a permeable membrane. In this contribution, we have proposed two new molecular diameters calculated respectively by the circumscribed-cylinder method (Dn') and the group-separated method (Dn), and compared them with the already known kinetic diameter (Dk), averaged diameters (Dpa), and maximum diameters (Dpm and Dmm) in correlating with the penetration barriers of small gas molecules on a total of 14 porous carbon-based monolayer membranes (PCMMs). D1' and D2' give the best barrier-diameter correlations with average Pearson's correlation coefficients of 0.91 and 0.90, which are markedly larger than those (0.77, 0.76, 0.60, 0.48, 0.33, and 0.32) for D1, D2, Dk, Dpa, Dpm, and Dmm. Our results manifest that the choice of vdW radii set does not drastically change the barrier-diameter correlation. Our newly defined D1', D2', D1, and D2, especially D1' and D2', show universal applicability in predicting the relative permeability of small gas molecules on different PCMMs. The circumscribed-cylinder method proposed here is a facile approach that considers the molecule's directionality and can be applicable to larger molecules. The excellent linear correlation between Dn' and gas penetration barrier implies that the computationally less demanding molecular diameter Dn' can be an alternative to the penetration barrier in diagnosing the gas separation preference of the PCMMs.

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