A kinetic approach to nucleation in condensed systems

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Abstract
A recently published theory for homogeneous nucleation in dilute systems (Katz and Wiedersich 1977), which clearly distinguishes between the thermodynamic and kinetic quantities involved, is generalized so as to include condensed systems. We show that in these systems the nuclei are structural fluctuations and present a topological procedure for their identification. An expression for the steady-state nucleation rate is then derived from the growth and decay rates of these nuclei. The departure rate of atoms leaving a nucleus is calculated from the nucleus size distribution in an equilibrium system at the same temperature by assuming that the effect of a change in concentration or pressure is to change the departure rate by the same factor for nuclei of all sizes. The driving force for nucleation is shown to be the ratio of the impingement rates modified by a factor related to the velocity of the phase boundary in macroscopic samples (instead of the free-energy difference between the nuclei and the mother phase). All the quantities in the final expression thus obtained are, in principle, obtainable from experiment (for solutions of any concentration and for melts up to a limited degree of undercooling). It is shown that the usual expression for the rate of nucleation can be derived from the one presented here by using conventional expressions for the nucleus size distribution and the phase-boundary velocity.

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