Ab Initio Energetic Barriers of Gas Permeation across Nanoporous Graphene

Realizing membranes of atomic thickness functioning reliably constitutes a giant leap forward for a plethora of applications where the efficient separation of fluid constituents at the molecular level is critical. Here, by employing density functional theory, we explore the energy landscape of typical gas molecules attempting permeation through graphene nanopores and determine the minimum energy permeation pathways, based on the precise knowledge of the related molecular level interactions. With this approach we investigate two basic permeation routes: direct permeation and surface-based transport. We find that for subnanometer pores, the diffusion barrier of direct and surface transport depends on the pore chemical functionalization, while the molecule pore permeation barrier is independent of the gas-pore approach due to the overlap of surface and direct diffusion paths over the pore center. The overall minimum energy permeation pathway of He, H₂, CO₂, and CH₄ molecules, across nanopores of different dimensions and chemical functionalization, defines the pore diameter (∼1.2 nm) below which effusion theory is inaccurate, as well as the critical pore diameter (∼0.8 nm) required to achieve positive permeation barriers driving molecular sieving. We determine that achieving positive permeation barriers required for high selectivity gas separation is inseparably combined with postpermeation desorption barriers due to attractive van der Waals interactions. The discovered permeation energetics are pore-molecule-specific and are incorporated into an analytical model extending existing theory. Our results provide a scientific background for rational pore design in graphene membranes, which can lead to gas separation at a commercially relevant performance level.