The Maxwell–Stefan description of mixture permeation across nanoporous graphene membranes

Abstract

There is increasing research interest on the use of two-dimensional (2D) nanoporous materials, such as graphenes and graphene oxides, in a variety of membrane separation applications. The membrane permeation selectivitites are governed by a variety of factors that include surface diffusion as an important constituent. The primary objective of this article is to present a Maxwell–Stefan (M–S) formulation for surface diffusion of binary (1, 2) mixtures on 2D nanoporous graphene surfaces. In the developed formulation, adsorbate–adsorbate interactions, either attractive or repulsive, are described by the quasi-chemical (QC) mean field approximation of Guggenheim. Such interactions have a direct influence on the occupancy dependencies of the M–S diffusivities, Ð1 and Ð2, that quantify molecule-surface “friction”. An essential feature of the M–S formulation is the inclusion of exchange coefficients, Ð12, that quantify correlation, or slowing-down effects for surface diffusion; the tardier-more-strongly-adsorbed species usually “slows down” the more-mobile-less-strongly-adsorbed species. Kinetic Monte Carlo (KMC) simulations on 2D square lattice of adsorption sites are used to quantify the the loading dependence of the M–S diffusivities, and also correlation effects. The usefulness of the developed model, combining QC and M–S approaches, is illustrated for CO2/CH4, CO2/H2, CO2/N2, and CH4/H2, mixture separations. For all four mixtures, the neglect of correlation effects leads to a severe underestimation of the membrane permeation selectivities that favor the more strongly adsorbed species.