Diffusion to rough interfaces: finite charge transfer rates

We develop a perturbation formalism for diffusion accompanying the finite charge transfer rates on an arbitrary rough electrode. Second-order perturbation expressions are obtained for the concentration, current density and measured current transients for an arbitrary surface profile electrode. Various results obtained by earlier workers in the area of complex interfacial geometry are generalized. The results reported earlier for diffusion-limited (Nernstian) charge transfer at an arbitrary roughness about plane, sinusoidal, curvature expansion and realistic random surface models are generalized for the case where the effects of finite rates of charge transfer are incorporated. The problems of the screened electrostatic potential of the electric double layer for the one-dimensional arbitrary roughness are generalized for a two-dimensional arbitrary surface. In the random surface model (the gross geometrical property of an electrochemically active rough surface) the surface structure factor is related to the average electrochemical current, the current density and the concentration. Under the short- and long-time regimes, various morphological features of the rough electrode, i.e. roughness factor (related to excess area and slope due to roughness), curvature, correlation length etc. are related to the (average) current transients. The expressions for inner and outer cross-over times are obtained. Finally, the effect of surface roughness is studied for specific surface statistics, namely a Gaussian correlation function. It is shown how roughness and finite charge transfer rates affect the overall quasi-reversible charge transfer current.