A surface-electrochemical basis for the direct logarithmic growth law for initial stages of extension of anodic oxide films formed at noble metals

Measurements on anodic surface oxidation of noble metals as a function of time and electrode potential show that the initial extension and subsequent thickening of such oxide films is directly logarithmic in time. A striking feature of this behavior is that the direct logarithmic extension law already applies to increase of coverage of Pt or Au electrodes with time well below the limit of formation of one monolayer of OH or O species on the metal surface. A direct logarithmic law of oxide film growth also applies to post-monolayer growth involving early stages of quasi-three-dimensional film formation. Eventually, as the oxide film thickens, the Mott–Cabrera ‘‘high-field’’ growth mechanism can apply. However, below the monolayer level of oxide film formation, electrochemisorption of two-dimensional (2D) structures of OH or O arises so that the Mott–Cabrera mechanism cannot be applicable to that situation. It is shown that the kinetic relation for direct electrodeposition of OH or O species onto available metal surface sites also cannot lead to a log law in time for extension of a 2D film. A new treatment, based on the changing surface-potential component of the electrode-solution potential difference, due to place exchange between metal atoms in the surface and electrosorbed OH or O species on the surface, is presented and shown to give rise to a direct log law for extension of the film in time. The relation derived has features in conformity with the experimentally demonstrated characteristics of submonolayer and early post-monolayer film extension.