Halate electroreduction from acidic solution at rotating disk electrode: Theoretical study of the steady-state convective-migration-diffusion transport for comparable concentrations of halate ions and protons

Abstract

Theoretical analysis of electrochemically inactive halate-anion (XO3−, X = halogen) electroreduction at rotating disk electrode (RDE) under steady-state conditions via autocatalytic mediator cycle based on X2/X− redox couple in acidic aqueous medium has been performed in relation to prospects to use this reaction as cathodic process of high energy density flow batteries. For the first time, full set of coupled diffusion-migration-convection transport equations for the components of the system, including kinetic terms due to the comproportionation reaction between solute species, has been solved via numerical and analytical tools. All principal characteristics of the system have been found: distributions of concentrations of all components inside the diffusion layer as well as of induced electric field and of the chemical reaction rate, diffusion-layer thicknesses for all components as functions of the principal dimensionless parameters: passing current, J, ratios of the diffusion-limited currents for species H (protons) and A (XO3−), JHA, or for species C (X2) and A, JCA, ratio of the diffusion and kinetic layer thicknesses for species A, xdkA = zdA / zk, as well as ratios of the diffusion coefficients of components, DiA = Di / DA (i = other components). The strongest dimensionless current, Jmax, which can pass across the system, can also be calculated for any set of particular values of the dimensionless parameters: JHA, JCA, xdkA and DiA. General features of the dependence, Jmax vs. xdkA, have been analyzed for various values of JHA (i.e. of the ratio of their bulk-solution concentrations, Ho/Ao) while the value of JCA (and consequently of the concentrations' ratio, Co/Ao) is very small. It has been demonstrated that within the range of sufficiently low rotation frequencies the maximal dimensional current density, jmax, is comparable with the combined diffusion-limited current of species A (XO3−) and H (H+), even for extremely low bulk-solution concentration of catalytic species C (X2), Co, i.e. passing current can reach enormous values, despite the electrochemical inactivity of species A and H. This feature which is highly beneficial for the application of this reaction in power sources is a direct consequence of the autocatalytic character of the redox-mediator cycle based on reactions of species XO3−, X− and X2 in acidic medium.