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 LHΩ which is summation of diffusion-kinetics (LH) and diffusion-ohmic (LΩ) coupling lengths. The current time response is therefore an interplay of LHΩ, diffusion length, three finite fractal lengths and fractal dimension (manifesting themselves at different times). At short time, diffusion length is smaller than LHΩ, current is proportionate to the ratio of real microscopic area and LHΩ. These phenomenological coupling delays and curtails the onset of the anomalous response. As diffusion length becomes greater than LHΩ, there is an emergence of intermediate anomalous region. However, limiting case of large LHΩ approximately constant current is seen, without dynamic roughness effects.