Theory of double potential step chronoamperometry at rough electrodes: reversible redox reaction and Ohmic effects

Abstract

Theory is developed for the DPSC (double potential step chronoamperometry) response for finite fractal and nonfractal electrode roughness with and without uncompensated solution resistance. Mathematical equation for the statistically averaged current transient and its relation to surface structure factor of random roughness is highlighted for reversible charge transfer. Result shows the enhancement of current transient upto outer crossover time for the rough electrode. Current response after application of each potential steps can show upto three regimes, i.e. short, intermediate and long time regimes. In short time, when diffusion layer thickness is small, current response is controlled by the roughness factor. Crossover between short and intermediate time regimes is controlled by diffusion layer thickness scaled with mean square surface curvature. Current behavior in long time (after outer crossover time), when diffusion layer thickness is large compared to width of roughness, becomes identical to smooth electrode. Crossover between intermediate and long time regimes is controlled by mean square width scaled with diffusion layer thickness. For fractal roughness, current has anomalous power law behavior (in intermediate time regime) while for nonfractal roughness current shows crossover between two regimes. Increase in the ratio of reverse and forward current is usually understood as kinetic complications but here we show that this can also emerge out of electrode roughness. Uncompensated solution resistance correction is also included in our theory to account for realistic experimental conditions. Finally, results are compared with the experimental data of a reversible system in viscous medium.