Influence of Uncompensated Solution Resistance on Diffusion Limited Chronocoulometric Response at Rough Electrode

Abstract

Theory is developed for the charge transient under ohmic effect in reversible charge transfer process at disordered electrodes. Preliminary experimental results are also analyzed using this theory. Our results show that the deviation from Anson response is stemming from surface disorder and solution resistance. Detailed theoretical results are obtained and analyzed for fractal roughness with self-affine statistical properties. Expressions for concentration, charge density, and total charge have operator structure in Fourier transformed (deterministic) surface profile function. An elegant mathematical formula between the average charge transient and surface structure factor of roughness is obtained. Initial response is attributed to resistive effects of the electrolyte. The intermediate response is attributed to the interplay between various characteristics of the power spectrum and “ohmic equilibration layer thickness”. The theory marks that ohmic effects penetrate farther in time so much so to merge with time regimes which are outside the diffusion regimes giving nonideal behavior at electrode/electrolyte interface. Our results help with the quantitative understanding of generalized Anson response for Nernstian system affected by the uncompensated resistance at rough electrode/electrolyte interface.