Theory for anomalous response in cyclic staircase voltammetry: electrode roughness and unequal diffusivities

We develop a theory for cyclic staircase voltammetry (CSCV) of a reversible charge transfer process with unequal diffusivities on a randomly rough electrode. The roughness power spectrum based approach is developed and detailed analysis is performed for a finite fractal model. An elegant expression for the statistically averaged CSCV current is obtained in terms of single potential step current at a rough electrode. The extent of anomalous response due to finite fractal roughness is determined by scan rate. The characteristic peak current and peak to peak separation in CV are dependent on finite fractal features, namely, fractal dimension (D_H), topothesy length (ℓ_τ), and finest length scale of fractality (ℓ). Peak to peak separation is reduced while peak current is enhanced with increase in D_H and ℓ_τ and decrease in ℓ. The roughness induced anomalous regime often introduces errors in estimating diffusion coefficient from classical Randles–Sečvik equation. Our theory suggests that this error can be reduced using low scan rate regime data. Enhanced effects of roughness are seen in case of slowly diffusing electroactive species. Unequal diffusivities of redox species introduce shape asymmetry in CV of rough electrode. CV experiments have been carried out on Fc/Fc⁺ redox couple in room-temperature ionic liquid (BmimMF₄) medium. Effects of morphology of mechanically and chemically roughened gold electrode and unequal diffusivities of Fc/Fc⁺ redox species in BmimMF₄ are well captured by theoretical CV plots