Manning condensation in ion exchange membranes: A review on ion partitioning and diffusion models

The rational design of ion exchange membranes (IEMs) is becoming more pertinent as their usage becomes broader and as their staple applications (i.e., electrodialysis, flow batteries, and fuel cells) improve in commercial viability. Such efforts would be catalyzed by an improved fundamental understanding of ion transport in IEMs. This review discusses recent progress in modeling ion partitioning and diffusion in IEMs in an effort to relate IEM performance metrics to fundamental membrane properties over which researchers and membrane manufacturers possess direct and sometimes precise control. Central focus is given to the Donnan-Manning model for ion partitioning and the Manning-Meares model for ion diffusion in IEMs. These two frameworks, which are derived from Manning's counter-ion condensation theory for polyelectrolyte solutions, have been widely used within the IEM literature since their recent introduction. To explore this topic, the mathematical derivation of both models is revisited, followed by a survey of experimental and computational discussions of counter-ion condensation in IEMs. Alternative models which fulfill similar roles in predicting IEM transport properties are compared. This review concludes by highlighting the uniquely favorable positions of the Donnan-Manning and Manning-Meares models and discussing their prospects as leading predictors of IEM partitioning and diffusive properties.