Overestimation of heterogeneous rate constants of hexacyanoferrate at nanometer-sized ultramicroelectrodes

Standard rate constants of hexacyanoferrate (Fe(III)/Fe(II)) at nanometer-scaled ultramicroelectrodes were evaluated from a plot of half-wave potentials of the steady-state voltammograms against logarithms of radii of ultramicroelectrodes. The smaller is the radius, the more positively shifts the anodic voltammogram and the more negatively does the cathodic wave. The shift is ascribed to the increase in the current density, which alters the diffusion-control into the charge-transfer control. However, the amount of the shift was smaller than that predicted from the conventional theory for the kinetic mass transport at ultramicroelectrodes. Consequently, the standard rate constant was overestimated by three times. A possible reason of the smaller shift is a non-negligible length of the mean free path of the diffusing redox particle in comparison with the electrode size. A stochastic diffusion model is proposed, in which a particle walks by random distances of which average is of the order of the electrode diameter. Monte Carlo simulation for this model showed that the concentration profiles were more uniform than the conventional profile, and hence the overpotential is observed to be apparently smaller. (C) 2002 Elsevier Science B.V. All rights reserved.