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 D-1, D-2, 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 D-1 ', D-2 ', D-1, and D-2, especially D-1 ' and D-2 ', 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 Dn ' can be an alternative to the penetration barrier in diagnosing the gas separation preference of the PCMMs.

Automated summary

In this study, two new molecular diameters, calculated using the circumscribed-cylinder method and the group-separated method, were proposed and compared with other existing diameter descriptors. The results showed that the newly defined diameters had strong correlations with the penetration barriers of gas molecules on porous carbon-based monolayer membranes. The circumscribed-cylinder method was found to be a simple yet effective approach for determining molecular diameter.