Theory for Anomalous Response in Cyclic Staircase Voltammetry: Electrode Roughness and Unequal Diffusivities

Abstract

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 ( τ ), and finest length scale of fractality ( ). Peak to peak separation is reduced while peak current is enhanced with increase in D H and τ and decrease in . The roughness induced anomalous regime often introduces errors in estimating diffusion coefficient from classical Randles−Secvik 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 (BmimMF 4 ) medium. Effects of morphology of mechanically and chemically roughened gold electrode and unequal diffusivities of Fc/Fc + redox species in BmimMF 4 are well captured by theoretical CV plots.

Semimicroscopic Theory for Underscreening-Induced Anomalous Migration–Diffusion Coupling

“…The concentration profile of the electroactive species satisfies the following diffusion equation in the bulk in the sinusoidal potential perturbation regime, where ω is the angular frequency and ι is . Utilizing the condition of flux balance with initial and bulk boundary conditions, viz., δ C i ( z , t = 0) = δ C i ( z → ∞, t = 0) = 0, concentrations of oxidized and reduced species OHP are related through the expression . The decoupled oxidized and reduced species representation of the Nernst equation at OHP is where f = F /RT ( F is Faraday constant).…”

Influence of Geometry on Thin Layer and Diffusion Processes at Carbon Electrodes

“…Carbon materials exhibit complex surface structures due to the type of carbon, its shape, the interfacial structures, and the surface functional groups. , Most studies have explored the effects of the surface chemical structures of carbon electrodes, aiming to promote electrocatalytic effects and adsorption. , Recently, more studies are addressing how three-dimensional geometric structure affects electrochemistry. − Kant et al developed the theory regarding random surface roughness of electrodes and demonstrated that the surface roughness or morphology can affect amperometry, , voltammetry, − and electrochemical impedance responses. , In particular, when the size of the geometric structure matches the thickness of the diffusion layer, the geometric structure confines the analyte within the rough surface, resulting in thin layer electrochemical behavior. , Thin layer electrochemistry affects the redox products observed; for example, under thin layer conditions, there are enhanced cyclization reactions of catecholamines. , The Compton group developed thin layer theory for several carbon geometric structures, including arrays , and porous structures. − Thin layer phenomena were observed in porous materials or in those with cavities for solution confinement, such as vertically aligned multiwall carbon nanotubes, carbon nanotube yarns, and carbon nanopipets. ,,− However, both diffusion and thin layer electrochemistry contribute to the electrode response, but results are often simplified to consider only one effect at a time. , Systematic experiments with simulations that explain the effects of various carbon electrode geometries would provide a comprehensive understanding of how surface structure affects the contributions of diffusion and thin layer processes to electrochemical behavior.…”

Differential Square-Wave Voltammetry

“…At solid electrodes differential pulse voltammetry can be even more analytically effective than SWV, due to the ability for providing lower background current by adjusting the ratio between the potential step and pulse duration . Parveen and Kant studied extensively the properties of arbitrary pulse voltammetries, − considering in particular the role of the solid electrode roughness and unequal diffusivity. On the other hand differential pulse voltammetry is inferior in providing mechanistic information on the electrode reaction compared to SWV.…”