One-dimensional model of steady-state discharge process in hydrogen-bromate flow battery

Abstract

Theoretical analysis has been developed for the reduction reaction of the non-electroactive bromate anion from its aqueous solution at a thin-layer porous electrode on the surface of a membrane transporting protons from anode under steady-state 1D conditions. The cathodic process is realized via a cycle composed of the reversible Br2 to 2 Br− transformation and of the irreversible (owing to high acidity of the solution) comproportionation reaction between bromate and bromide which regenerates bromine. Protons (assumed to be in great excess) are transported to the comproportionation-reaction (kinetic) layer near the electrode both via the membrane and from the bulk solution. As it has been demonstrated by calculations for the dependence of the local value of the maximal current density, jmax, on the local value of the diffusion layer thickness, zd, high values of the current density cannot be achieved for relatively thin diffusion layers. Contrary to intuitive expectations, for sufficiently thick diffusion layers the current density may reach extremely high values comparable with the diffusion-limited flux of bromate anions (if they could react at the electrode), even for a tracer amount of Br2 in the bulk solution. Such strong steady-state currents originate from the autocatalytic character of this redox-mediating cycle (EC″ mechanism) resulting in progressive accumulation of the components of the Br2/Br− mediating redox couple near the electrode surface. Relations between the fluxes of bromate and bromide anions, protons and bromine across the diffusion layer in solution as well as the flux of protons across the membrane have been established. Approximate analytical expressions for all characteristics of the system (concentration profiles, maximal current, etc.) have been derived for two regimes corresponding either to “weak currents” or to “thin kinetic layer”. The quantitative criterion for protons to be considered as being in great excess compared to bromate anions has been derived for both an ion-impermeable electrode/bromate solution cell (corresponding to the rotating-disk electrode system, RDE) and a proton-exchange membrane/porous electrode/bromate solution configuration.