Diffusion toward Fractal Interfaces: Potentiostatic, Galvanostatic, and Linear Sweep Voltammetric Techniques

Diffusion to fractal electrodes has been investigated by three different techniques for the oxidation of ferrocyanide in a gel electrolyte: the current response to a potential step, the potential response to a current step, and the current response to a linearly increasing potential. The current density vs. time relationship under potentiostatic control, the transition time vs. current density under galvanostatic control, and the peak current density vs. sweep rate in a voltammetric experiment all followed power laws similar to those describing the experiments carried out with a planar electrode. The usual −0.5 exponent, however, became in the case of a fractal electrode of dimension . The experimental results were analyzed and described by solving a generalized diffusion equation involving a fractional derivative operator.