A time-dependent approach to the kinetics of homogeneous nucleation

We present a time-dependent model for homogeneous nucleation and derive a time-dependent solution to the coupled growth-rate equations for molecular cluster concentrations. A correction to the monomer concentration growth-rate equation is applied, which accounts for the gain and loss of molecules by all cluster populations. The condensation rate used considers all embryos to be in motion, rather than assuming that only the monomers move. In order to allow for size-dependent variations in a cluster’s surface tension, the evaporation rate incorporates the revised parametrization of Laaksonen et al. [Phys. Rev. E 49, 5517 (1994)] of the homogeneous nucleation theory of Dillmann and Meier [J. Chem. Phys. 94 3872 (1991)]. Eigenvalue analysis illuminates how the steady-state is approached from the transient period and allows us to estimate the accuracy of a steady-state approximation. It is shown that the distributions of clusters predicted by this theory generate nucleation currents that are more accurate than those produced by other steady-state cluster distributions. More importantly, this model can be used to calculate the time-dependent cluster behavior for any nucleation model that has an expression for the change in Gibbs free energy. The theory agrees well with the experimental data of Miller et al. [J. Chem. Phys. 78, 3204 (1983)] and Viisanen et al. [J. Chem. Phys. 99 4680 (1993)], and with the theoretical predictions of Laaksonen et al.