Effect of surface roughness on interfacial reaction–diffusion admittance

We develop a theory for the electrical admittance of a rough interface under diffusion-limited and partial diffusion-limited charge transfer conditions. The large and small-frequency expansion brings out the relationships between the various morphological features of the rough electrode i.e. area, curvature and width, and the average admittance. The diffusion-limited reaction admittance is determined on an approximately self-affine corrugated random surface fractal. We obtain exact results for the low roughness and the asymptotic results (in three frequency regions) for the arbitrary and large roughness surfaces. These results show an anomalous frequency dependence for the mean admittance and the mean excess admittance for the large and small roughness surfaces, respectively. The intermediate frequency behavior of the reaction admittance for small roughness interfaces has the following form: 〈Y〉∼(iω)1/2+const.(iω)3/2−H, where H is Hurstʹs exponent, for the large roughness interfaces it has same form as predicted earlier: 〈Y〉∼(iω)1−H/2. This non-universality and dependence of intermediate-frequency behavior on the strength of interfacial fractality has not been previously conceived. We also show the localization of the active zones in the presence of roughness. Finally, these results unravel the connection between the total reaction admittance and the crossover frequency to the roughness characteristics likes the fractal dimension, lower and upper fractal cutoff lengths, and the amplitude of the fluctuations of the fractal.