General Theory for Pulse Voltammetric Techniques on Rough and Finite Fractal Electrodes for Reversible Redox System with Unequal Diffusivities

The prediction of voltammetric response from the microscopic information of the electrode surface morphology is an important problem of fourth generation electrochemistry which we have theoretically addressed here. We develop a theory for pulse based voltammetric response of reversible charge transfer process with unequal diffusivities on randomly rough electrode. The microscopic information of the electrode surface is incorporated into the response expression in the form of power spectrum of roughness. An elegant expression for the statistically averaged generalized pulse voltammetric current is obtained in terms of single potential step current at rough electrode from which, the explicit current expressions for differential pulse (DPV), staircase (SCV), cyclic staircase (CSCV) and square wave (SWV) voltammetries are obtained for random and finite fractal roughness electrode. The SCV and CSCV responses, as elaborately discussed in our previous work, here we have focused more on the explorations of DPV and SWV responses. In the presence of equal diffusion coefficients of the electroactive species, roughness induces enhancement in the peak heights with retention of peak position at the same potential for DPV as well as SWV. This points towards an enhanced sensitivity of these differential techniques at rough electrodes. In the presence of unequal diffusivities of redox species, SWV shows a distinguished signature of roughness due to variation in peak heights along with alteration in the position of the peaks. Square wave voltammetry on rough electrode shows an asymmetric suppression in the peak height of the anodic or cathodic sampled current plots due to unequal diffusivities which resembles the behavior of a chemically irreversible system.

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