A study on the simulated diffusion-limited current transient of a self-affine fractal electrode based upon the scaling property

Abstract

The power law relation I( t)∝ t − α , α=( D f−1)/2 between current I and time t has been widely used to analyse current transient (chronoamperometric) behaviour during atomic/ionic diffusion towards the electrode with a fractal dimension D f, irrespective of whether the electrode has a self-similar fractal structure or at best a self-affine fractal structure. We show that the self-affine fractal dimension D f,sa (or Hurst exponent H) is not always the sufficient condition required for describing the atomic/ionic diffusion behaviour to the self-affine fractal electrode: the current transient exhibits a more negative power dependence of current on time before temporal outer cut-off of fractality with increasing morphological amplitude (roughness factor) of the self-affine fractal electrode, rather than a unique power dependence corresponding to D f,sa. It is particularly noted that the current transients from the electrodes with comparatively large amplitudes are roughly characterised by a two-stage power dependence before temporal outer cut-off of fractality. In the present work, a practical method has been suggested to interpret the anomalous current transient from the self-affine fractal electrodes with various amplitudes. This method includes the determination of the apparent self-similar scaling properties of the self-affine fractal structure by the triangulation method.