Evaluating gas permeance through graphene nanopores and porous 2D-membranes: A generalized approach

Abstract

Porous graphene and 2D-membranes are known for favorable nanofluidic properties, such as high gas permeability and selectivity, depending on energy barrier for the molecule translocated through the nanopore. Despite the immense demand for proper theoretical description of gas flow through nanopores, a formalism including the energy barrier and steric effects to translocation remains conspicuously absent. Here, using both analytical and first-principles calculations, we study the permeance properties of porous 2D membranes. In particular, we develop the general equation for the permeance (and selectivity) of gases through circular nanopores, including both energy barrier and additional steric effects. Our theory captures sensitivity to the pore size, yields easy estimates for permeance through nanopores of less regular shape, and corroborates experimental findings. For completeness of the analysis, we disclose the importance of the energy barrier against surface diffusion of the permeance and report that e.g. the energy barrier against surface diffusion of He (CH4) through a pore with effective size 0.55 nm is 32 meV (114 meV), which is four times larger than the barrier predicted by the classical force fields. Presented upgrades of the long-standing gas flow theory are critical for further development of nano-patterned 2D membranes, as needed for emergent gas separation and purification technology.

Keywords

• Knudsen’s theory
• Graphene
• Porous 2D-membranes
• Energy barrier
• Surface diffusion