Onsager coefficients for binary mixture diffusion in nanopores

Abstract

This paper presents a critical appraisal of current estimation methods for the Onsager coefficientsL₁₁, L₂₂, and L₁₂ for binary mixture diffusion inside nanopores using pure component diffusivity data inputs. The appraisal is based on extensive sets of molecular dynamics (MD) simulation data on L_ij for a variety of mixtures in zeolites (MFI, AFI, TON, FAU, CHA, DDR, MOR, and LTA), carbon nanotubes (CNTs: armchair and zig-zag configurations), titanosilicates (ETS-4), and metal–organic frameworks (IRMOF-1, CuBTC). The success of the L_ij predictions is crucially dependent on the estimates of the degree of correlations in molecular jumps for different guest–host combinations; these correlations are captured in Maxwell–Stefan approach by the exchange coefficients Ð _ij. Three limiting scenarios for correlation effects have been distinguished; for each of these scenarios appropriate expressions for the L_ij are presented. For CNTs, correlation effects are dominant and the interaction factor, defined by α ₁₂ = L₁₂ √ L₁₁L₁₂, is close to unity. For cage-type zeolites such as LTA, CHA, and DDR with narrow windows separating cages, correlation effects are often, but not always, negligibly small and the assumption of uncoupled diffusion, i.e., α ₁₂ =0, is a reasonable approximation provided the occupancies are not too high. In other cases such as zeolites with one-dimensional channel structures (AFI, TON), intersecting channels (MFI), cage-type zeolite with large windows (FAU), ETS-4, CuBTC, and in IRMOF-1, it is essential to have a reliable estimation of the Ð _ij; MD simulations underline the wide variety of factors that influence the Ð _ij. We also highlight two situations where estimations of the L_ij fail completely; in both cases the failure is caused due to segregated adsorption. In adsorption of CO₂–bearing mixtures in LTA and DDR zeolites, CO₂ is preferentially lodged at the narrow window regions and this hinders the diffusion of partner molecules between cages. The second situation arises in MOR zeolite that has one-dimensional channels connected to side pockets. Some molecules such as methane, get preferentially lodged in the side pockets and do not freely participate in the molecular thoroughfare. Current phenomenological models do not cater for segregation effects on mixturediffusion.