Mass Transport across Two-Dimensional Graphene Nanopores*

Mass transport across two-dimensional nanopores is very essential to the porous graphene and other atomically thin membranes for gas separation. Due to the contribution of gas adsorption and diffusion over the two-dimensional surfaces, mass transport across two-dimensional nanopores cannot be described only by the kinetic theory of gases. We identify the molecular transport routes through two-dimensional nanopores and propose two permeation mechanisms (direct versus surface) with establishing their theoretical descriptions. The contribution of surface mechanism is especially analyzed by considering the surface adsorption and diffusion. The combination of the linear pressure-dependent direct flux, governed by the kinetic motion of gas molecules, and the nonlinear pressure-dependent surface flux, caused by the Langmuir isothermal adsorption characteristics of gas molecules on the two-dimensional surfaces, results in an overall nonlinear pressure dependence of the gas permeation flux through two-dimensional nanopores. We also reveal the mechanisms of the selective molecular permeation through nanopores, from the aspects of molecular size and structure, pore structure and the gas-graphene interactions.