Review The Maxwell–Stefan description of mixture diffusion in nanoporous crystalline materials Rajamani Krishna ⇑ Van’t Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands article info Article history: Received 24 July 2013 Received in revised form 21 October 2013 Accepted 29 October 2013 Available online 7 November 2013 Keywords: Mixture diffusion Correlation effects Thermodynamic coupling Fixed bed adsorbers Membrane permeation abstract The efficacy of nanoporous crystalline materials in separation applications is often influenced to a signif- icant 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: cor- relation 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 break- through characteristics of fixed bed adsorbers, we identify conditions that require the use of M–S equa- tions 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, originat- ing from sizable off-diagonal elements of thermodynamic correction factors C 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. Ó 2013 Elsevier Inc. All rights reserved. Contents 1. Introduction .......................................................................................................... 30 2. Correlation effects in binary mixture permeation across membranes ............................................................ 33 3. Overshoot phenomena in transient membrane permeation .................................................................... 36 4. Overshoot phenomena in transient mixture uptake in crystals ................................................................. 37 5. Intra-crystalline diffusion influences on transient breakthrough in fixed bed adsorbers ............................................. 37 6. Transient breakthrough of alkane isomers in MFI packed bed .................................................................. 44 7. Conclusions ........................................................................................................... 47 Acknowledgement ..................................................................................................... 48 Appendix A. Supplementary data ......................................................................................... 48 References ........................................................................................................... 48 1. Introduction Ordered crystalline nanoporous materials such as zeolites (crystalline aluminosilicates), metal–organic frameworks (MOFs), zeolitic imidazolate frameworks (ZIFs), covalent organic frame- works (COFs), and porous aromatic frameworks (PAFs) offer con- siderable potential for a wide variety of separations. The technologies used in such separations are either fixed bed adsorp- tion units (examples listed in Table 1), or membrane permeation devices (examples are listed in Table 2). The separation perfor- mance is dictated by a combination of adsorption and diffusion 1387-1811/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.micromeso.2013.10.026 ⇑ Tel.: +31 20 6270990; fax: +31 20 5255604. E-mail address: r.krishna@uva.nl Microporous and Mesoporous Materials 185 (2014) 30–50 Contents lists available at ScienceDirect Microporous and Mesoporous Materials journal homepage: www.elsevier.com/locate/micromeso