Theory for admittance voltammetry of reversible two step electron transfer process with DC bias at rough and fractal electrodes

Abstract

We developed a phenomenological theory for DC-bias dependent electrochemical impedance response and admittance voltammetry of reversible two-step electron transfer (EE) process at randomly rough and fractal electrodes. The power spectrum of roughness is used to incorporate the statistical information of surface randomness. For the finite fractal model, statistical morphological parameters of roughness, viz., fractal dimension (DH), topothesy length (ℓτ) and lower cut-off length (ℓ), significantly influence the admittance response. The magnitude of admittance increases with an increase in the roughness of fractal electrode (e.g. increase in the value of DH or ℓτ or decrease in ℓ) for both the electron transfer steps. The magnitude of admittance with the variation of DC potential at fixed temporal frequency unravels the multi-electron transfer process. The two step electron transfer process has two characteristic peaks in their plot. The enhanced roughness of electrode increases the height of the admittance peaks and the regions around it (obtained at different fixed frequencies). Our theory is validated with experimental data for the ethyl viologen system at a moderately rough Pt electrode. Finally, our current methodology for admittance voltammetry has the dual advantage of impedance as well as of voltammetry.