Experimental Validation of Roughness Power Spectrum-Based Theory of Anomalous Cottrell Response

Abstract

We experimentally validate theoretical relation between the roughness power spectrum (PS) and electrochemical current transient for a reversible charge transfer system under a single potential step. Roughness features at the electrochemically roughened electrode are characterized using standard measurements such as scanning electron microscopy (SEM), atomic force microscopy (AFM) and cyclic voltammetry (CV). The PS obtained from AFM shows composite finite fractal and nonfractal nature in roughness, whereas the PS from SEM shows only a finite fractal nature. AFM or SEM measurements provide knowledge of fractal dimension (DH) and two fractal cutoff lengths (landL). Topothesy length (lτ) or the related proportionality factor (μ≡lτ2DH−3) from PS data of AFM requires extrapolation of data for unit wavenumber, but this method usually provides unphysical values of μ. We provide a novel method to determine the topothesy of electrodes from CV measurements of electroactive area in conjunction with SEM or AFM measur...