DIFFUSION TO ROUGH INTERFACES - FINITE CHARGE-TRANSFER RATES

We develop a perturbation formalism for diffusion accompanying the fin ite charge transfer rates on an arbitrary rough electrode. Second-orde r perturbation expressions are obtained for the concentration, current density and measured current transients for an arbitrary surface prof ile electrode. Various results obtained by earlier workers in the area of complex interfacial geometry are generalized. The results reported earlier for diffusion-limited (Nemstian) charge transfer at an arbitr ary roughness about plane, sinusoidal, curvature expansion and realist ic random surface models are generalized for the case where the effect s 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-dim ensional arbitrary surface. In the random surface model (the gross geo metrical property of an electrochemically active rough surface) the su rface structure factor is related to the average electrochemical curre nt, the current density and the concentration. Under the short- and lo ng-time regimes, various morphological features of the rough electrode , i.e. roughness factor (related to excess area and slope due to rough ness), curvature, correlation length etc. are related to the (average) current transients. The expressions for inner and outer cross-over ti mes are obtained. Finally, the effect of surface roughness is studied for specific surface statistics, namely a Gaussian correlation functio n. It is shown how roughness and finite charge transfer rates affect t he overall quasi-reversible charge transfer current.