Investigating the influence of diffusional coupling on mixture permeation across porous membranes

Abstract

A careful analysis of published experimental data on permeation of a variety of binary mixtures reveals that there are fundamentally two types of diffusional coupling effects that need to be recognized. The first type of coupling occurs when the less-mobile species slows down its more mobile partner by not vacating an adsorption site quick enough for its more mobile partner to occupy that position. Such slowing-down effects, also termed correlation effects, are quantified by the exchange coefficient D₁₂ in the Maxwell–Stefan (M–S) formulation. The parameter D₁/D₁₂, quantifying the degree of correlations, is strongly dependent on the pore size, topology and connectivity and reasonable estimates are provided by molecular dynamics (MD) simulations. In cage-type structures (e.g. CHA, DDR, LTA, and ZIF-8) in which adjacent cages are separated by narrow windows correlations are weak, and D₁/D₁₂ ≈ 0 is a good approximation. On the other hand correlations are particularly strong in structures consisting of one-dimensional channels (e.g. NiMOF-74), or intersecting channels (e.g. MFI) structures; in these cases the values of D₁/D₁₂ are in the range 1–5. A wide variety of experimental data on binary mixture permeation can be quantitatively modeled with the Maxwell–Stefan equations using data inputs based on unary permeation experiments, along with D₁/D₁₂ values suggested by MD. The second type of coupling occurs as a consequence of molecular clustering due to hydrogen bonding. Such clustering effects, commonly prevalent in alcohol/water pervaporation, can cause mutual slowing-down of partner molecules in the mixture. When molecular clustering occurs the Maxwell–Stefan diffusivity of a species in the mixture, D₁, cannot be identified with that obtained from unary permeation.