Nucleation time lag at nano-sizes

A rapidly convergent exact expression for the time lag (also, ‘induction time’) of transient nucleation obtained by Shneidman and Weinberg [J. Chem. Phys. 97 (1992) 3629] is used to evaluate the lag for clusters with up to 10⁸ monomers. Asymptotic approximations to the exact expression are further advanced to provide explicit elementary expressions for the time lag in the Turnbull-Fisher (TF) nucleation model in various domains of parameters. The difference between the TF time lag and the one of Zeldovich-Frenkel nucleation equation is examined in detail. Transient nucleation flux and the number of nuclei are also discussed, and analytical results appear to be in very good agreement with numerical solutions of the TF equations at large sizes, as reported by Granasy and James [J. Chem. Phys. 113 (2000) 9810].