Theory for influence of uncompensated solution resistance on EIS of diffusion limited adsorption at rough electrode

Abstract

Theory is developed for the electrochemical impedance spectroscopy (EIS) of the diffusion-limited adsorption process coupled with reversible charge transfer at rough electrodes under the influence of ubiquitous uncompensated solution resistance. This study quantitatively relates the impedance response of rough electrode to its phenomenological components, viz., diffusion limited adsorption, reversible charge transfer and uncompensated solution resistance. The random roughness of electrode is expressed by the surface statistical property, i.e., power spectrum of roughness. The fractal nature of roughness is characterized in terms of fractal dimension, lower cut-off length and topothesy length. The high-frequency regime is controlled by the uncompensated solution resistance whereas the low-frequency regime is governed by the adsorption process. The magnitude of impedance as well as phase decreases with rise in adsorption isotherm (length) parameter. The intermediate frequency regime is controlled by the coupling of adsorption and uncompensated solution resistance with the diffusion process. The fractal roughness parameters has quantitative influence on the magnitude of impedance over whole frequency regime while the phase plot shows qualitative difference in the intermediate frequency regime. The governing length scales which controls the characteristic crossover frequencies are: diffusion length, adsorption-ohmic coupling length and topothesy length (or width of interface). The three emergent crossover frequencies are: (i) ohmic reduced inner crossover frequency (ii) adsorption roughness topothesy dependent pseudo-quasireversibility characteristic frequency (iii) outer crossover frequency. Synopsis: This study quantitatively relates the impedance response of rough electrode to its phenomenological components, viz., diffusion limited adsorption, reversible charge transfer and uncompensated solution resistance. The random roughness of electrode is expressed by the surface statistical property, i.e., power spectrum of roughness.