ИСТИНА

Solutions containing complexes of metal ions with negatively charged ligands are widely used for electrodeposition of metals and alloys [1]. The mass-transfer processes in the solutions with complexes involve homogeneous chemical reactions and fluxes of ligands induced by the reduction of complexes. This allows one to raise considerably the efficiency of electrochemical processes by realizing electro- and autocatalysis and the exaltation effect. It is known that electro-migration can increase significantly the limiting current density in the case of electroreduction of cations from the solutions containing complexes, and under certain conditions, the limiting current is absent [2]. Theoretical analysis of mass transfer under the conditions of complex formation is commonly performed using simplified mathematical models (the approximation of Nernst diffusion layer, the condition of equilibrium of complex formation reaction, equality of diffusion coefficients of all components). As a result, approximate analytical solutions are obtained for some specific cases [3]. Frequently, the assumptions used in the simplified mathematical; models are not fulfilled: the diffusion coefficients of ions differ essentially; the convective transfer of the components is realized along with the electro-diffusion one; reaction of complex formation is nonequilibrium, which can have a pronounced effect on the regularities of mass transfer under the conditions of complex formation. Therefore, it is important to study the effect of hydrodynamic conditions, transport properties, and the rate of homogeneous chemical reaction on the transport processes under the conditions of complex formation. This can be performed only using the numerical methods [4]. In this work, the effect of complex formation on the mass transfer during the metal electrodeposition on a rotating disk electrode from the solution containing three types of ions (metal cation, cationic complex and non-electroactive anion) is studied theoretically. The dimensionless Nernst-Planck equations in the approximation of solution electroneutrality, which take into account the electro-diffusion and convective transfer of all types of ions and the homogeneous reaction of complex formation, are used as the mathematical model. The Butler-Volmer equations are used to take into account the kinetics of electrochemical reactions. In contrast to the known works, the approximations of the Nernst layer, equality of diffusion coefficients of all types of ions, and the equilibrium of complex formation reaction were not used. As a result of numerical solution, the distributions of concentration, potential, and the rate of complex formation reaction are obtained at various parameters of the system under consideration. It is shown that the constants of equilibrium and rate of complex formation reaction, as well as the ratio between the diffusion coefficients of complex cation and anion, have the strongest effect on the mass transfer.