Influence of electrode roughness on DC biased admittance of quasi-reversible charge transfer with uncompensated solution resistance

Abstract

Abstract The theory is developed for the DC potential biased electrochemical impedance spectroscopy (EIS) of quasi-reversible charge transfer with uncompensated solution resistance developed for rough and fractal electrodes. Theory shows that the influence of the real and apparent kinetics is contained in DC bias dependent characteristic length called the diffusion-kinetics-ohmic coupling length (LQΩ). Theory characterizes fractal irregularities of an electrode through its power spectrum which is experimentally obtained from SEM or AFM recordings. EIS response of DC biased quasi-reversible systems is an interplay of phenomenological lengths, i.e., LQΩ, diffusion length (LD) and morphological characteristics (fractal dimension and lengths in roughness), manifesting themselves at different frequencies. High frequency regime, LD > LQΩ, electrode kinetics follows the Warburg response with the macroscopic area of the electrode. There is an emergence of anomalous intermediate region, LD ~ LQΩ, which is influenced by various fractal morphological characteristics. This regime has maximum in phase angle (ϕ > 450) as well as signature of the fractal roughness.