Vanadium Transport through Cation and Anion Exchange Membranes

Transport of redox active molecules across the separator in a flow battery represents an important source of inefficiency and electrolyte-imbalance-induced capacity fade [1]. This transport can occur by diffusion, migration, and convection, with driving forces that change as cells are charged and discharged. The negative electrolyte in a vanadium redox flow battery, for example, contains V 2+ and V 3+ in proportions that depend on state of charge, but these species are absent from the positive side, leading to ever present concentration driving forces for diffusion across the separator. Migration alternately enhances and diminishes crossover since the electric field in the membrane orients in opposite directions during charge and discharge. Finally, hydraulic and osmotic pressure differences between the positive and negative electrolytes cause solvent flow that carries redox ions. Rigorous theoretical treatment of transport across membranes in flow batteries with concentrated-solution theory is complicated by the large number of species. For example, Nafion in a vanadium redox flow battery may contain: V 2+ , V 3+ , VO 2+ , VO 2 + , H + , HSO 4 - , SO 4 2- , H 2 O, and fixed SO 3 - anions (8). The number of multicomponent diffusion coefficients required to characterize a systems is , where n is the number of species present (after accounting for species coupled by rapid chemical equilibrium). The n multicomponent diffusion coefficients define one conductivity, transference numbers or ratios, , and diffusion coefficients of neutral combinations of species. The experimental and theoretical complexities associated with the multicomponent framework when many species are present motivates exploration of the applicability of the simpler, but less generally valid dilute-solution framework. In particular, we seek to understand how well do the relationships between diffusion coefficients, transference numbers, and conductivity predicted by dilute solution theory hold in practical membranes exposed to application-relevant electrolyte solutions? Do transference numbers predicted from conductivity and permeability measurements agree with independently measured values? Figure 1 shows measured transference numbers for the four vanadium ions relevant to flow batteries in N211 and N212 as blue and red squares, respectively. The measurements were made using a cell with three membranes and four flow compartments [2, 3]. Good agreement between the two data sets is apparent.