Fractal geometry of the surface potential in electrochemically deposited platinum and palladium films

Abstract

The surface potentials are distributed very nonuniformly in electrochemically deposited thin films of palladium and platinum, and it reflects the grain structure of their surface profile. The Hausdorf-Bezikovich space dimensions of the surface potentials in these films much exceed the topological dimension of their projections, which is indicative of their fractal geometry. It is found that the surfaces of platinum and palladium films differ both in the spread of magnitudes of the surface-potential nonuniformities and in the shape and character of their distribution. This substantially affects the way of formation (geometry) of their potential profile and the values of their fractal dimensions. In addition, the fractal geometry of the potential profile of these film surfaces leads to the fact that the total electric charge of their surfaces varies much slower-it is proportional to the change in their linear dimensions to power (4 − D f), where 2 < D f < 3, instead of being proportional to the square of the change in the linear dimensions of the areas under investigation as in the two-dimension case. As a result, it is shown that, for the accurate designing of devices with metal components of submicrometer and nanometer sizes on the basis of thin films of platinum and palladium, it is necessary to take into account their fractal geometry.