Analytical expressions for surface concentration distribution in a model electrochemical process with a preceding chemical reaction

The goal of this study is unraveling the specific features of non-stationary surface concentration distribution of electroactive and inactive species in a model electrochemical process with a preceding homogeneous first-order chemical reaction (CE mechanism). For this purpose, the exact analytical expressions for the non-stationary concentration distributions of electroactive and inactive species in the thin layer attached to a planar electrode are analyzed. The both cases of equal and unequal diffusion coefficients of species taking part in the preceding chemical reaction are considered. In the former case, the exact analytical expressions for the concentration distributions of electroactive and inactive species on a planar electrode are obtained. The peculiarities of the limiting cases of zero and infinite frequency of an applied alternating current for the both cases of equal and unequal diffusion coefficients of species are discussed. It is shown that there is a phase shift between AC and the surface concentration of species that changes under the action of this current. At low frequencies, the phase angle tends to p/2, whereas at high frequencies it decreases to p/4. The phase angle is the function of the two important measures, namely, the ratio of the Nernst diffusion layer thickness to the oscillation diffusion layer thickness, and the ratio of the Nernst diffusion layer thickness to the reaction layer one. It is shown that the phase angle depends on the diffusion coefficient of species in different manner for low and high values of the rate constants of the chemical reaction. At low values of these parameters, the phase angle shifts slightly to the range of high frequencies with an increase of diffusion coefficient. At the high rate constants, the phase angle decreases with frequency more slowly, and its dependence on diffusion coefficient is observed only at middle frequencies. The surface concentration of electroactive and inactive species decreases with an increase of frequency, but for the inactive species this process is faster than that for the electroactive species. The influence of the inactive species on the surface concentration of electroactive species decreases at high frequencies and at low rate constants of the preceding chemical reaction. The results obtained shed the light on complex dynamics at an electrode/electrolyte interface under non-stationary conditions.