Modeling Sorption of Water and Vanadium Cations by Ion-Exchange Membranes

We develop a macroscopic model for sorption of ions and solvent by ion-exchange membranes and use it to investigate how different membranes behave when exposed to electrolytes for vanadium flow batteries. The model combines a classical expression for the Gibbs free energy of a moderately concentrated electrolyte containing several ions with a term that describes elastic swelling of a polymer membrane. Parameters describing pairwise interactions between mobile ions and fixed membrane ions were fit to published experimental data and discussed in the context of the competition for sites in ion-exchange membranes. The model provides insights into why sorption of vanadium cations by Nafion is lower than predicted by Donnan theory and why switching to an anion-exchange membrane does not dramatically reduce vanadium sorption.