Theory for influence of ohmic resistance and electrode roughness on admittance voltammetry of reversible E and EE reactions

Abstract

• Admittance voltammetric response for E and EE processes is influenced by roughness. • Random roughness is modeled through power spectrum of roughness. • Diffusion and uncompensated solution resistance are non-linearly coupled phenomena. • Characteristic peaks in admittance voltammetric response depend on finite fractal roughness. • Work emphasize on the enhanced sensitivity of this technique for E and EE processes. The theory is developed for the admittance voltammetry of reversible EE process under the influence of uncompensated solution resistance at random and fractally rough electrode. The theory accounts for the influence of random roughness through the power spectrum of roughness. The finite fractal model, with its three response controlling statistical parameters, viz. fractal dimension ( D H ), topothesy length ( ℓ τ ) or width of the interface and lower cut-off length ( ℓ ), is used to analyze the admittance voltammogram. DC biased admittance response of a rough electrode is determined by an interplay of morphological and phenomenological length scales. The characteristic phenomenological length scales of processes involved are diffusion length ( D / ω ) and DC bias dependent diffusion-ohmic coupling length ( L Ω ). These characteristic lengths significantly influence the potential dependent magnitude of admittance at a given temporal frequency or scan rate. The characteristic electron transfer admittance voltammetric peaks are significantly influenced by roughness in intermediate and high-frequency scans, i.e., ω > D/( L Ω 2 + ℓ τ 2 ). Similarly, at sufficiently low frequency, ω < D/( L Ω 2 + ℓ τ 2 ), the influence of roughness diminishes around the admittance peaks. The uncompensated solution resistance suppresses the height of admittance peaks and also alters the value of peak width at half peak height of both the electron transfer steps in moderately and strongly supported systems.