Maximum Current Density in the Reduction of the Bromate Anion on a Rotating Disk Electrode: Asymptotic Behavior at Large Thicknesses of the Diffusion Layer
Résumé
The reduction of the bromate anion on a rotating disk electrode (RDE) in a steady-state mode due to the catalytic cycle consisting of a reversible bromine/bromide redox pair and irreversible counter-proportionation reaction was studied theoretically. As the cycle is autocatalytic (EC″ mechanism: Electrochim. Acta, 2015, vol. 173, p. 779), at high volume concentrations of bromate the passing current can reach huge values limited by the ultimate diffusion current of bromate through the diffusion layer even at very low volume concentrations of bromine. In contrast to previous theoretical studies of this process, for numerical solution of the set of nonlinear equations with boundary conditions for concentrations we used the COMSOL Multiphysics program package, with which the solution can be found for both the galvanostatic mode (at a given current density) and the maximum current density. This allowed us to study the behavior of the maximum current density for the case of very high thickness of the diffusion layer and very high reaction rate constant. In this mode, the ratio of the maximum current to the limiting diffusion current of the reduction of the bromate anion to bromine was found to exceed not only intuitively anticipated unity, but also the “critical” value of 1.2, which formally corresponds to the limiting diffusion current of its reduction to the bromide anion (though the real end product is bromine), and this limiting value depends on the volume concentrations of both bromate and bromine.