Kinetic equations and fluctuations in electrochemical nucleation: Studies of many-body effects on diffusion-controlled particle growth on a substrate

Abstract

A new viewpoint on the kinetics of electrochemical nucleation of a new phase is presented by numerically solving the kinetic equations recently derived by one of the present authors (M.T.) to study the many-body effects on diffusion-controlled three-dimensional nucleus growth on a substrate. The static many-body (screening) effect is shown to cause the crossover of the growth exponent for the average nucleus radius from 1/2 to 1/6. Hence the electric current grows as t1/2 at short times and falls with t−1/2 at long times, according to the Cottrell equation. The dynamic many-body (correlation) effect is shown to give rise to a dispersion in the size of the nuclei and thus to cause appreciable corrections to the amplitudes for the radius and the current in the zero limit of volume fraction Q. The corrections go as Q1/2t1/3 and hence cause a large deviation of the average current from the Cottrell equation at long times. Nonthermal fluctuations around the mean motion generated by the correlation effect are also explicitly explored together with a comparison with thermal fluctuations existing at the beginning. A computer simulation is finally performed to confirm the validity of the kinetic equations. The theoretical results are shown to have excellent agreement with the simulation.