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

In this paper, mathematical procedures to describe the time developmen t of nonequilibrium fluctuations in nucleation are examined. General e quations depicting the time development of amplitudes of the fluctuati ons 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, th e current attains a minimum state, which gives the ratio of the averag e critical concentration fluctuation to the autocorrelation distance. Then, the nucleation current arising from unstable growth of the fluct uations is derived as a function of supporting electrolyte concentrati on, depositing metal ion concentration and overpotential. This is attr ibuted to the fact that the instability occurs from the electrostatic interaction between electrode surface and solution particles in electr ic double layer. As the growth progresses, the enhancement of diffusio n process yields the change of rate-controlling step to the electron t ransfer process, so that the observed current approaches a maximum sta te composed of reaction current. After passing the maximum current, th e 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 limiti ng current flows in the same manner as the Cottrel equation. (C) 1997 American Institute of Physics.