A review of anomalous diffusion phenomena at fractal interface for diffusion-controlled and non-diffusion-controlled transfer processes

Abstract

This article reviewed anomalous diffusion phenomena coupled with facile and sluggish charge-transfer reactions at fractal interface. Firstly, the generalised diffusion equation (GDE) involving a fractional derivative which describes diffusion towards and from fractal interface was briefly introduced. And then, anomalous diffusion coupled with facile charge-transfer reaction at fractal interface, i.e., diffusion-controlled transfer process across fractal interface, was mathematically examined by the generalised Cottrell, Sand, Randles-Sevcik and Warburg equations theoretically derived from the analytical solutions to the GDE under the semi-infinite boundary condition. Finally, in order to provide a guideline in analysing anomalous diffusion coupled with sluggish charge-transfer reaction at fractal interface, i.e., non-diffusion-controlled transfer process across fractal interface, this review covered the recent researches into the effect of surface roughness on non-diffusion-controlled transfer process within the intercalation electrodes.