A study on ionic diffusion towards self-affine fractal electrode by cyclic voltammetry and atomic force microscopy

Ionic diffusion towards a self-affine fractal electrode was investigated experimentally using both cyclic voltammetry and atomic force microscopy (AFM). For this purpose, three kinds of self-affine fractal Pt film electrodes were first prepared by dc sputtering of Pt on such substrate materials with different roughnesses as polished Al2O3, etched Ni and unpolished Al2O3. Then, the surface morphologies of the electrode specimens were examined by using AFM and cyclic voltammograms (CVs) were measured on the electrode specimens in a 30 wt.% glycerol+70 wt.% (0.01 M K4[Fe(CN)6]+0.5 M Na2SO4) solution at various scan rates. Finally, the fractal dimensions of the electrode surfaces were determined from analyses of AFM images and the power relation between peak current and scan rate in the CVs. All the fractal dimensions determined from the CVs were much smaller than the self-affine fractal dimensions determined by the perimeter–area method. Assuming that the self-affine fractal surface can have a self-similar scaling property, the apparent self-similar fractal dimensions of the self-affine fractal electrodes were determined by a triangulation method. These values agreed well with the fractal dimensions determined from the CVs. From the above results, it is concluded that ionic diffusion towards a self-affine fractal electrode should be described in terms of the apparent self-similar fractal dimension rather than the self-affine fractal dimension.