Supersaturation rates and schedules: Nucleation kinetics from isothermal metastable zone widths

The metastability limit can be defined as the average supersaturation at which nucleation first occurs when the supersaturation steadily increases under isothermal conditions. We present a quasi-steady stochastic model for such experiments in terms of the nucleation free energy barrier at some reference supersaturation and in terms of a Damkohler number involving the kinetic prefactor, the observation volume, and the supersaturation schedule as a function of time. Classical nucleation theory provides a model for the dependence of the nucleation free energy barrier on the slowly increasing supersaturation. We derive the average critical supersaturation as a function of two dimensionless parameters and the type of supersaturation schedule. For slow supersaturation rates, the metastable zone width expression for one schedule collapses to earlier expressions from Volmer, Kashchiev, Verdoes, and van Rosmalen, which arose from alternative definitions of the metastability limit. Our findings show that isothermal metastable zone width experiments cannot be performed slowly enough to attain the limit where homogeneous nucleation occurs at the equilibrium boundary of the metastable zone. We also suggest a simple linear regression strategy to extract kinetic parameters for nucleation from isothermal metastability limit experiments.