The Maxwell–Stefan description of mixture diffusion in nanoporous crystalline materials

Abstract

The efficacy of nanoporous crystalline materials in separation applications is often influenced to a significant extent by diffusion of guest molecules within the pores of the structural frameworks. The Maxwell–Stefan (M–S) equations provide a fundamental and convenient description of mixture diffusion. The M–S formulation highlights two separate factors that cause mixture diffusion to be intrinsically coupled: correlation effects and thermodynamic coupling. By careful and detailed analyses of a variety of published experimental data on (a) mixture permeation across nanoporous membranes, (b) transient uptake of mixtures within crystals and (c) transient breakthrough characteristics of fixed bed adsorbers, we identify conditions that require the use of M–S equations including both correlation effects and thermodynamic coupling. Situations are also identified in which either of the coupling effects can be ignored. Correlation effects cause slowing-down of more-mobile-less-strongly-adsorbed molecules by tardier-more-strongly-adsorbed-partner species; such slowing-down effects are often essential for modeling mixture permeation across nanoporous membranes. Overshoots in the transient uptake of the more mobile partners in single crystals are essentially the consequence of thermodynamic coupling, originating from sizable off-diagonal elements of thermodynamic correction factors Γ_ij. In the case of transient breakthrough of hexane isomers in a fixed bed of MFI zeolite, we show that thermodynamic coupling effects lead to a significant improvement in the separation performance.