Peculiarities of the concentration distribution in the near-electrode layer in a course of homogeneous chemical reaction of the first order in a model electrocatalytic process under steady-state conditions

In this theoretical study, the model electrocatalytic process with potential-dependent adsorption/desorption of electroactive species on planar electrode surface and a preceding homogeneous chemical reaction of first order in the Nernst diffusion layer is investigated. The adsorption process is described by the Frumkin isotherm. The limiting stage of the process under consideration is a preceding homogeneous chemical reaction. The purpose of the work is to obtain and analyze the analytical expressions for the concentration distributions of species taking part of a homogeneous chemical reaction of first order with different diffusion coefficients. The case of stationary conditions is considered. The chosen model system belongs to the N-NDR type of system. The system’s voltammetric curve has the N-shaped form with the region of the negative differential resistance (NDR), where dynamic instabilities occur. An exact solution of a system of differential equations describing the concentration distribution in the Nernst diffusion layer was obtained. The dependencs of electrode surface stationary concentrations on the coverage by adsorbate q were obtained. The functions of concentration gradients of reactive species depending on a distance to electrode surface and the parameter q were analyzed. It was shown that the function of concentration distribution for electroactive species changes sharply on inner side of the Nernst diffusion layer. In contrast to this, the function of concentration distribution for non-electroactive species changes smoothly and reaches its greatest value on outer side of the Nernst diffusion layer. The curves of the dependencs of electrode surface stationary concentrations for electroactive and for non-electroactive species on the parameter q as well as the system’s voltammetric curve have N-shaped form. But in this case the maxima of the curves correspond to low values of q and their minima correspond to high values of q. The value of the concentration gradient of electroactive particles reaches its maximum value on inner side of the Nernst diffusion layer. In contrast to this, the concentration gradient of non-electroactive particles turns to zero in this area and reaches its maximum value on outer side of the Nernst diffusion layer. The obtained results can be applied for a better understanding of the non-linear behavior of non-equilibrium system.