Nucleation in periodically driven electrochemical systems

We calculate both the exponent and the prefactor in the nucleation rate of a periodically driven system. Nucleation dynamics is described by the Fokke r-Planck equation for the probability distribution of the nuclei over their size. This distribution is found using the concept of the most probable (o ptimal) nucleation path. The results apply in a broad range of driving forc e amplitudes, from weak to moderately strong forces where the nucleation ra te is changed exponentially strongly, and also in the broad range of the dr iving frequencies, from low-frequency driving, where the system follows the force adiabatically, to high-frequency nonadiabatic driving. For strong dr iving forces, the time dependence of the nucleation rate changes from stron gly nonsinusoidal to a weak with the increasing frequency of driving. The r esponse of the nucleation rate to the driving force is described in terms o f logarithmic susceptibility (LS), which can be obtained from the optimal n ucleation path in the absence of the driving. LS is a smooth function of fr equency, and therefore even a driving force with comparatively high frequen cy can change the modulation rate exponentially strongly. LS and the Farada y current are calculated for simple models of electrochemical systems, wher e the ac driving is produced by modulation of the electrode potential. We a lso suggest how to find LS from measurements of the average nucleation rate . (C) 1999 American Institute of Physics. [S0021-9606(99)50121-9].