Effect of uncompensated solution resistance on quasireversible charge transfer at rough and finite fractal electrode

Abstract

Theory for the influence of uncompensated solution resistance on quasi-reversible charge transfer at an arbitrary rough electrode is developed. Detailed model analysis is performed for a finite fractal power spectrum; characterized with fractal dimension, lowest, highest cutoff-length scales of roughness and topothesy length (width) of the interface. The composite effect of the real and apparent kinetics is contained in L_HΩ which is summation of diffusion-kinetics (L_H) and diffusion-ohmic (L_Ω) coupling lengths. The current time response is therefore an interplay of L_HΩ, diffusion length, three finite fractal lengths and fractal dimension (manifesting themselves at different times). At short time, diffusion length is smaller than L_HΩ, current is proportionate to the ratio of real microscopic area and L_HΩ. These phenomenological coupling delays and curtails the onset of the anomalous response. As diffusion length becomes greater than L_HΩ, there is an emergence of intermediate anomalous region. However, limiting case of large L_HΩ approximately constant current is seen, without dynamic roughness effects.