Bromate electroreduction from acidic solution at rotating disc electrode. Theory of steady-state convective-diffusion transport
Résumé
Theory of the steady-state electroreduction of bromate-anion at rotating disk electrode has been developed. Bulk solution contains high concentrations of bromate anion and a strong acid (which are non-electroactive at the electrode) as well as a tracer amount of bromine. The current passes owing to bromine which is reduced to bromide ion that participates further in the comproportionation reaction with bromate anion, with regeneration of bromine. This process has been described for the first time on the basis of convective diffusion transport equations for solute components, bromate and bromide ions as well as bromine, with taking into account the difference of their diffusion coefficients. Approximate analytical solutions for all concentration distributions have been derived. It has been demonstrated that the passage of the bromate process depends crucially on the value of the ratio of two characteristic lengths: individual diffusion-layer thicknesses determined for each transporting component by an interplay of the diffusion and convection mechanisms, and kinetic layer thickness where the comproportionation reaction takes place. For small values of their ratio, bromide ions cross the diffusion layer and react with bromate ions only in the bulk solution so that this process does not affect the electrode reaction and the current is very weak since it is related to reduction of bromine from the bulk solution. For moderate values of this parameter (if the ratio of these thicknesses is less than 6), a thin kinetic layer is formed deeply inside the diffusion layer where the comproportionation reaction is localized while bromide ions are absent in the outer part of the diffusion layer where bromate ions are transported from the bulk solution towards the kinetic layer and bromine is transferred in the opposite direction. Under such conditions, this bromine flux to the bulk solution makes insufficiently efficient the redox cycle formed by the electrode and comproportionation reactions, and the passing current remains relative weak. Finally, for large values of the key parameters (if the ratio of these layer thicknesses exceeds its critical value equal to 6), the redox cycle demonstrates its autocatalytic features, i.e. the reduction of bromate ions may lead to accumulation of enormous amounts of the redox couple components, bromine and bromide ion, near the electrode surface, thus resulting in a very strong current, comparable with (or even exceeding) the formally defined “diffusion-limited current for bromate anion”. Expressions for the concentration distributions inside the (thin) kinetic layer, as well as those for the maximal current density, derived within the framework of the convective-diffusion theory are in agreement with those found for the Generalized Nernst Layer model proposed by us earlier. On the contrary, there is a marked deviation of these results from those for the conventional Nernst layer model, i.e. this simplified approach is not applicable for quantitative description of the process, even though it provides its correct qualitative picture. For the outer part of the diffusional layer the newly derived concentration distributions are essentially different from predictions of both previous approaches.