NONEQUILIBRIUM FLUCTUATION THEORY IN ELECTROCHEMICAL NUCLEATION .1. DERIVATION OF NUCLEATION CURRENT EQUATIONS

摘要

In this paper, mathematical procedures to describe the time development of nonequilibrium fluctuations in nucleation are examined. General equations depicting the time development of amplitudes of the fluctuations are firstly deduced. Secondly, using the Rayleigh theorem, the rms values of the fluctuations are obtained, being defined as the average values. Finally, some analytical equations of the nucleation current are derived for the characteristic parts of current-time transient as follows: After applying a constant potential step to the electrode, the current attains a minimum state, which gives the ratio of the average critical concentration fluctuation to the autocorrelation distance. Then, the nucleation current arising from unstable growth of the fluctuations is derived as a function of supporting electrolyte concentration, depositing metal ion concentration and overpotential. This is attributed to the fact that the instability occurs from the electrostatic interaction between electrode surface and solution particles in electric double layer. As the growth progresses, the enhancement of diffusion process yields the change of rate-controlling step to the electron transfer process, so that the observed current approaches a maximum state composed of reaction current. After passing the maximum current, the increase of concentration overpotential leads to decrease of overall double-layer overpotential. The nucleation process regains diffusion control; it is concluded that at the final stage, the diffusion limiting current flows in the same manner as the Cottrel equation. (C) 1997 American Institute of Physics. [References: 18]