Abstract
The metal electrodeposition through a colloidal crystal mask is simulated by using the multi-level approach. The space near the cathode surface is divided into several zones with different characteristics of transport processes. In each zone, 1D or 3D approximations may be used. In the zones of 1D type, the distributions of electroactive ion concentration and potential are calculated by the analytical equations; in the zones of 3D type, the numerical finite element method is used. The transport processes in the neighboring zones are conjugated by using the condition of equal currents through the boundary between these zones.
In this work, we develop the method of simulation of metal electrodeposition in the solution with an excess of supporting electrolyte: the migration transfer of all ions is taken into account and the electrode reaction governed by the equation of Butler-Volmer is considered. The developed mathematical model involves the Laplace equation for the concentration of electroactive ion, effective concentration of supporting electrolyte, and potential. It is shown that the model can be reduced to a single Laplace equation for the concentration of electroactive ion with the corresponding boundary conditions.
As a result of modeling, the distributions of electroactive ion concentration and cathodic current density are obtained for various instants of time (deposit of various thicknesses). The calculated dependences of current on the deposit thickness agree with the literature data. The relative amplitude of current oscillations, which is determined by the variation of relative pore area along the height of colloidal crystal, depends on the ratio of an average current density to the limiting current density: when an average current approaches the limiting one, the relative amplitude of current oscillations decreases.
