Equilibrium and steady-state distributions of vapour clusters in nucleation theory

The relationship between equilibrium properties in nucleation theory and cluster partition functions is explored. A new approach to relating the partition function for a cluster with boundaries fixed in space to that required in nucleation theory, which includes arrangements omitted by other approaches, is described. Fluctuations about equilibrium in cluster size and energy are discussed. The usual way of obtaining the steady-state nucleation rate does not take account of possible differences in cluster energy distributions between equilibrium and steady state. A Fokker-Planck equation for the cluster distribution in size and energy is derived and an analytical approach to obtaining the steady nucleation flux from it is presented. In cases where the vapour molecule's latent heat of vaporization is much greater than its heat capacity, this approach gives the same values as those predicted by a simpler analytical formula derived previously. In other cases, the simpler formula underestimates the flux, although only by modest factors. Extensions of this treatment are discussed.