Theory of anomalous diffusive reaction rates on realistic self-affine fractals

Abstract

We developed a theoretical method based on limited scale power law form of the interfacial roughness power spectrum and the solution of diffusion equation under the diffusion-limited boundary conditions on rough interfaces. This theoretical method is useful for the analysis of diffusion-limited flux/current to limited scale self-affine random fractal interfaces and is compared with experimentally measured electrochemical current for nano- and micron scales of roughness. The new result explains experimental findings of the temporal scale invariance as well as deviation from this in transition, short, and long time regions. Our result show flux/current transients in terms of three dominant fractal morphological parameters, that is, fractal dimension, lower cutoff length scale of fractality, and topothesy, for the limited length scales of fractality. More broadly, these results are applicable for all time scales and roughness factors.