Theory of Multicomponent Phenomena in Cation-Exchange Membranes: Part III. Transport in Vanadium Redox-Flow-Battery Separators

Transport through vanadium redox-flow-battery membranes strongly influences cell performance. In this work, we use a multicomponent concentrated-solution model of transport and thermodynamics in phase-separated cation-exchange membranes, the most common separator type, to develop structure-performance relationships. The model incorporates species partitioning into the membrane, thermodynamic nonidealities, and Stefan-Maxwell-Onsager frictions between species. Molecular-thermodynamics and -transport theories parameterize the model. We validate the calculations against measured Coulombic and voltage efficiencies of a vanadium flow battery as a function of current density. Our model shows that species transport is the result of collective interactions between all species present in the system. The magnitude of coupling suggests that predictions made using dilute-solution theory for transport in these systems will be misleading in many situations. As a demonstration of the capabilities of the model, we predict cell performance, incorporating these interactions, as a function of electrolyte concentration and composition and membrane equivalent weight and backbone modulus. We find that electrolytes with high sulfuric acid concentrations provide the greatest cell performance (quantified by maximizing power density at a target energy efficiency). In the case of membrane properties, low equivalent-weight polymers perform better; at high equivalent weights, a low membrane modulus is preferred.