Nonequilibrium fluctuation theory on pitting dissolution. I. Derivation of dissolution current equations

Abstract

Following the foregoing papers, in this paper, mathematical procedures to describe the time development of the unstable nonequilibrium fluctuations in pitting dissolution are presented: First, general equations depicting the time development of the amplitudes of the fluctuations are deduced, which are the same as those describing nucleation phenomena. Then, with the same definition as nucleation, the average values of the fluctuations are decided, and measurable pitting current is calculated. Actually, some analytical equations are derived for some characteristic parts of the current–time transient. As a result, after applying a constant potential step to the electrode, a slow relaxation current, which follows a double-layer charging current, is decided as the diffusion current of the fluctuations. This current gives the values of passive film coverage and average critical concentration fluctuation on the completely active surface. Moreover, from the minimum current attained by the diffusion current, the ratio of the average critical concentration fluctuation to the autocorrelation distance is determined. Finally, resultant pitting growth current arising from the unstable growth of the fluctuations is deduced as a function of supporting-electrolyte concentration and overpotential, which is attributed to the fact that the instability occurs from the electrostatic interaction of the solution particles in the double layer.