Halate electroreduction via autocatalytic mechanism for rotating disk electrode configuration: Evolution of concentrations and current after large-amplitude potential step

Abstract Temporal evolution of the process of reduction of the electrochemically-inactive halate anion, XO3− (X is halogen), via autocatalytic redox mediator cycle based on the X2/X− couple, after a large-amplitude stepwise potential change has been studied theoretically for the first time via numerical and analytical methods. This analysis has been performed for identical values of the diffusion coefficients of the components. The description is based on solution of a set of coupled non-stationary transport equations for the rotating disk electrode (RDE) configuration which contain kinetic terms due to the comproportionation reaction between XO3− and X− anions inside the solution phase. Convection effects are taken into account either via the Levich terms in the transport equations (with the subsequent use of the Hale transformation), or within the framework of either the Nernst-Levich or the novel Nernst-Levich-Hale model, with comparison of their results for the current and for the concentration distributions. Complicated temporal variation of the passing current has been discovered, especially if the thickness of the steady-state diffusion layer exceeds strongly that of the weak-current kinetic layer. During the initial stage of the process the current is determined by discharge of X2 species diffusing from bulk solution towards the electrode surface, followed by diffusion of generated X− ions in the opposite direction while catalytic effects are negligible. Within this initial time range the current decreases according to the Cottrell equation for X2 species. Then, if the convection intensity is sufficiently weak, generation of excessive amounts of the X2 and X− species via autocatalytic redox cycle leads to the current increase according to the exponential law after its passage via a low-amplitude minimum. At the end of this intermediate stage of exponential growth the passing current can reach very high values which are comparable with the maximal steady-state current at the optimal intensity of convection controlled by the diffusion-limited transport of XO3− species into the reaction region from bulk solution. Then, after passing a maximum, the current decreases due to time-dependent expansion of the non-stationary diffusion layer for XO3− species, up to its approach to the corresponding steady-state value determined by the convection intensity, i.e. by the RDE frequency. More intensive solution's agitation reduces the duration of the temporal evolution via interruption of the above evolution in the vicinity of the corresponding steady-state limiting current, after current maximum for very weak convection, or within the range of the exponential increase of current for a higher rotation frequency, or even within the initial stage of the evolution if the agitation of solution is intensive. For any rotation frequency the varying current approaches finally its steady-state value. Evolution of the non-stationary concentration distributions has been analyzed for each characteristic time range within both the convective-diffusion and the Nernst-Levich descriptions.