Decay of the diffusion controlled current of particles diffusing from an initially homogeneous medium to a completely absorbing fractal boundary was previously shown to exhibit t-α time-dependence instead of the conventional t- 1 2 one with the exponent α being determined by the fractal dimension, Df, of the interface as α =(Df-1)/2. In electrochemical terms this corresponds to a generalized Cottrell equation (or Warburg impedance) and can be used to describe the frequency dispersion caused by surface roughness effects. We verify the predicted behaviour for fractal surfaces with Df>2 (rough interface), and Df<2 (partially blocked surface or active islands on inactive support). In addition, the fractal decay kinetics is shown to be valid for both contiguous and non-contiguous surfaces. Computer simulation, a mathematical model, and direct experiments on well defined fractal electrodes are the tools for verifying the fractal decay law for the different surfaces. The predicted power law behaviour is observed, and the predicted α(Df) relationship was seen to prevail in each case.
ASJC Scopus subject areas
- Chemical Engineering(all)