Synthetic polymeric membranes typically exhibit a trade-off between permeability and selectivity that underpins their performance in separation processes. This trade-off is often contextualized for binary separations across membrane materials by plotting permeability as a function of selectivity (defined as the ratio of permeabilities). The best-performing membranes are observed to fall on or near a line termed the upper bound, more commonly known as the Robeson upper bound, named after Robeson’s empirical line drawn in 1991.
While early analyses were applied to gas-phase membrane separations, a quantitative description of this trade-off for polyelectrolyte membranes in aqueous separations is critical, especially given their prevalence in electrochemical devices such as electrolyzers, redox flow batteries and fuel cells. Now, Kitto and Kamcev propose an analytical model to describe the ionic conductivity/selectivity trade-off in ion-exchange membranes. The theoretical framework consists of the Donnan–Manning and Meares–Manning models to describe ion transport in the membranes, uncovering key parameters such as the maximum charge density, water volume fraction and reduced linear charge density. The authors further propose a simplified, linearized analytical expression for the upper bound that is validated against data from 40 commercial membranes and compares favorably with the full analytical model.
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