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 us. 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 -(d-1)/2 in the case of a fractal electrode of dimension d. The experimental results were analyzed and described by solving a generalized diffusion equation involving a fractional derivative operator.