On the calculation of potential energy profile diagrams for processes in electrolytic metal deposition

Abstract

The calculation of potential energy and free energy profile diagrams for successive and alternative steps in electrolytic metal deposition is described with reference to two extreme models of the entity resulting from the initial transfer of the metal particle from the solution to the surface of the metal.Neutralization of the transferred ions to form adsorbed metal atoms is distinguished from ion-transfer processes in which the transferred entity maintains ionic character, with the appropriate number of stoichiometric electrons entering the metal lattice for each ion transferred.The elementary processes considered are: transfer of ions from the solution to different types of surface sites upon the metal; surface diffusion of adsorbed ions; successive, dehydration of the adsorbed ions in lattice building.The free energies of the transition states in successive steps in consecutive ion-transfer, surface-diffusion and lattice-building reactions are compared, and the probable rate-determining process in the over-all metal deposition reaction is deduced in the cases of Cu2+, Ni2+ and Ag+ ion deposition on to the respective metals. Uncertainties in the calculation are examined.The heat of activation (ΔH0≠) for transfer of ions from the solution to the metal surface depends upon the site to which transfer occurs, that to a planar site being significantly less than that to other sites (e.g., edges, kinks, etc.) Transfer to form completely non-polar neutral adatoms has prohibitively high values of ΔH0≠Direct deposition Of Cu2+ on to surface sites would be associated with a prohibitively high heat of activation. The path Cu2+ + eM → Cu+ followed by Cu+ + eM → (Cuadion++ eM) is associated with heats of activation significantly lower than that for direct Cu2+ deposition in a single two-electron step. The free energy diagrams are consistent with the existence of a rate-determining reduction mechanism found experimentally. Near the Cu/Cu2+ reversible potential the free energy barrier for adion surface diffusion can become the highest. This is consistent with the experimental behaviour under these conditions. With Ag+ ion deposition the ion-transfer step has the highest free energy barrier at high negative overpotentials, whilst near the reversible potential the barrier for surface diffusion can become the highest. The kinetic behaviour found experimentally with silver supports the theoretical conclusions.The low exchange current density for Ni2+ ion deposition is probably associated with the instability of the simple Ni+ ion in aqueous solutions.