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 (D_n^′) and the group-separated method (D_n), and compared them with the already known kinetic diameter (D_k), averaged diameters (D_pa), and maximum diameters (D_pm and D_mm) 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, D_k, D_pa, D_pm, and D_mm. 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 D_n^′ and gas penetration barrier implies that the computationally less demanding molecular diameter D_n^′ can be an alternative to the penetration barrier in diagnosing the gas separation preference of the PCMMs.