Theory of single potential step absorbance transient at an optically transparent rough and finite fractal electrode: EC′ mechanism

A theoretical model for single potential step absorbance transient has been developed for the pseudo first-order catalytic coupled mechanism (EC′) at a rough optically transparent electrode (OTE). A second-order perturbation theory is developed for an arbitrary surface roughness profile. Results are further extended for the ensemble averaged absorbance response on the random surface roughness model in term of the power-spectrum of roughness. A general result derived showing relation between the absorbance of pseudo first-order catalytic reaction and the absorbance of reversible charge transfer. The dependence of absorbance transient on morphological characteristics and homogeneous rate constant is highlighted. Our results show an enhancement in the absorbance-transients for the band limited self-affine fractal roughness of OTE and coupled kinetics of homogeneous reaction with a heterogeneous charge transfer step.