The time lag in nucleation theory

Abstract

The time lag in transient nucleation is solved exactly for both the simple monomer approximation and the more complicated multipath kinetics with detailed balancing. It is shown that only initial and steady-state quantities are required for its calculation. The time lag within the continuum approximation is also considered. By evaluating the exact expression approximately, a simple functional form is obtained. The controversy over the ‘‘prefactor’’ in previous approximate time lags is resolved. It is shown that in general none of the approximate time lags are correct. The ‘‘relative time lag’’ is introduced. It is useful when detailed balance is not obeyed and also when the lower cutoff cluster size is not known precisely.