Diffusion to fractal surfaces—II. Verification of theory

✍ Scribed by Tamás Pajkossy; Lajos Nyikos

• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 866 KB
• Volume: 34
• Category: Article
• ISSN: 0013-4686
• DOI: 10.1016/0013-4686(89)87082-3

✦ Synopsis

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 z-time-dependence instead of the conventional t -1/2 one with the exponent a being determined by the fractal dimension, D r , of the interface as a=(D,-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 Dr >2 (rough interface), and D,<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 a(D,) relationship was seen to prevail in each case .