Novel procedure towards approximate analytical description of bromate-anion reduction at rotating disk electrode under steady-state transport conditions

Theoretical description of the BrO3− anion reduction from aqueous acidic solution at RDE under steady-state conditions requires to solve a set of ordinary differential transport-kinetic equations for the concentrations of the components of this system (BrO3−, Br−, Br2, H+) supplemented with boundary conditions at the electrode surface and in the bulk solution. Its approximate solution in the form of analytical expressions (“A0 approximation”) was derived for the first time in our previous paper (Electrochim. Acta, 2015, 173, 779) within the framework of the Nernst layer model, protons being in excess compared to another principal component, bromate anion, in the presence of very low amount of Br2 in the bulk solution. Later an analogous analysis was performed for the Generalized Nernst Layer model and for convective-diffusion transport equations. This consideration was also extended for systems where BrO3− component was in excess compared to protons. Numerical integration of the same set of transport equations for these models confirmed a good, or even excellent, applicability of these approximate analytical results for a wide range of the system's parameters, in particular of the ratio of the diffusion (zd) and kinetic (zk) layer thicknesses, xdk = zd/zk. On the contrary, significant deviation of solutions provided by the F0 approximation from the numerical ones has recently been revealed for very large values of this parameter, xdk, (well above 10) and strong current passage. This study proposes a novel method (called “AA approximation”) for derivation of different approximate analytical solution of this set of equations (tested within the framework of the Nernst layer model). Its results have turned out to be in a very good agreement with numerical results within a much wider range of the system's parameters, in particular for very large values of the principal parameter, xdk, and any value of the passing current.