General theory for pulse voltammetric techniques at rough electrodes: multistep reversible charge transfer mechanism

Abstract

Theoretical model is developed for the voltammetric response of multistep reversible charge transfer mechanism at rough electrode. This theory is applicable for arbitrary as well as random roughness profiles. An explicit mathematical expression relating the staircase (SCV), cyclic staircase (CSCV), differential pulse (DPV) and square wave (SWV) voltammetric response of finite fractal electrode to the statistical morphological characteristics is obtained. The fractal characteristics, viz. fractal dimension (D_H), lower length scale of fractality (ℓ) and topothesy length (ℓ_τ) are found to dominantly control the various voltammetric techniques responses of a multistep charge transfer mechanism. The heights of the voltammetric peaks corresponding to each charge transfer step is found to increase with increasing roughness. In CSCV, the anomalous intermediate scan rate window of Randles-Sevčik plots shifts with the number of charge transfer step. The peak current for the charge transfer step occurring at lower potential has an early onset of the influence of morphology, i.e., the anomalous regime window shifts at lower scan rates compared to those occurring at higher potential values. The differential techniques show roughness induced current enhancement for all the peaks without affecting the position of the peak potential. Thus, roughness helps to overcome the major drawback of low Faradaic current in these techniques and improves their application for chemical sensing purposes.