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

TL;DR

This paper introduces a theoretical framework for analyzing diffusive reaction rates on self-affine fractal surfaces, explaining experimental observations and challenging previous assumptions about the role of fractal dimension.

Contribution

The paper presents a new theoretical method based on limited scale power-law characterization to analyze diffusive flux on self-affine fractals, validated with experimental data.

Findings

The theory explains temporal scale invariance and deviations in current transients.

It challenges the idea that fractal dimension solely determines anomalous diffusion behavior.

The method enables scale-invariant roughness characterization.

Abstract

In this letter, a theoretical method for the analysis of diffusive flux/current to limited scale self-affine random fractals is presented and compared with experimentally measured electrochemical current for such roughness. The theory explains the several experimental findings of the temporal scale invariance as well as deviation from this of current transients in terms of three dominant fractal parameters for the limited-length scales of roughness. This theoretical method is based on limited scale power-law characterization of the interfacial roughness spectrum and the solution of diffusion equation under the diffusion-limited boundary conditions on rough interfaces. More broadly, these calculations challenges the earlier belief that the anomalous behavior is solely dependent on fractal dimension of roughness and highlight the potential to apply this equation for the scale invariant roughness determination. Finally, the validity of theoretical result is tested with extensive experimental data.