Practical thermodynamic quantities for aqueous vanadium- and iron-based flow batteries

A simple method for experimentally determining thermodynamic quantities for flow battery cell reactions is presented. Equilibrium cell potentials, temperature derivatives of cell potential (dE/dT), Gibbs free energies, and entropies are reported here for all-vanadium, iron–vanadium, and iron–chromium flow cells with state-of-the-art solution compositions. Proof is given that formal potentials and formal temperature coefficients can be used with modified forms of the Nernst Equation to quantify the thermodynamics of flow cell reactions as a function of state-of-charge. Such empirical quantities can be used in thermo-electrochemical models of flow batteries at the cell or system level. In most cases, the thermodynamic quantities measured here are significantly different from standard values reported and used previously in the literature. The data reported here are also useful in the selection of operating temperatures for flow battery systems. Because higher temperatures correspond to lower equilibrium cell potentials for the battery chemistries studied here, it can be beneficial to charge a cell at higher temperature and discharge at lower temperature. Proof-of-concept of improved voltage efficiency with the use of such non-isothermal cycling is given for the all-vanadium redox flow battery, and the effect is shown to be more pronounced at lower current densities.