Electron Transfer through a Modified Electrode with a Fractal Structure:  Cyclic Voltammetry and Chronoamperometry Responses

The problem of charge transfer by electron hopping through a volumic-modified electrode with a fractal structure was addressed, both in the case of chronoamperometry and linear sweep voltammetry. A behavior intermediate between that seen in classical diffusion and that of a thin layer was found. The currents in chronoamperometry and the peak currents in cyclic voltammetry both depend linearly on a bilogarithmic scale with, respectively, the time and the scan rate. The slopes of the curves in both cases depend on the fractal dimension, provided the spectral dimension remains constant. Plots are given in the case where the spectral dimension is equal to 4/3.