Theory of absorbance transients of an optically transparent rough electrode

Theory for the potentiostatic absorbance transient for a species generated at the rough electrode/electrolyte interface is developed. Absorbance transients are strongly affected by electrode geometries, particularly the effect of electrode roughness which is the least understood area, is dealt here. A general operator structure between concentration, surface absorbance density, absorbance transients and arbitrary roughness profile of electrode is emphasized. The statistically averaged absorbance transients is obtained by ensemble averaging over all possible surface roughness configurations. An elegant mathematical formula between the average spectroelectrochemical absorbance transient and surface structure factor or power spectrum of roughness is obtained. This formula is used to obtain an explicit equation for the absorbance on an approximately self-affine (or realistic) fractal and nonfractal electrode. Our results are also applicable to chronocoulometric response as its directly related to chronoabsorptometric response. Limiting behavior in short time, is attributed to the electrode roughness factor and surface curvatures. Limiting behavior in long time is like a smooth electrode response but the transition region is attributed to the mean square width of roughness. In the intermediate time, the absorbance has anomalous power law behavior which is attributed to the diffusion length weighted spatial frequency features of roughness and becomes almost time independent for large roughness electrodes. Finally, this theory provides a quantitative description of the role of roughness on potential step transmission chronoabsorptometry and chronocoulometric measurements, therefore opening up the way to explore and understand various anomalies in their response