Transient nucleation in H2O–H2SO4 mixtures: A stochastic approach

Abstract

Transient phenomena in the rate of nucleation are of importance in the interpretation of experimental data on nucleation in the H2SO4–H2O vapor system. Furthermore, fluctuations in the rate of nucleation can actually be measured. In view of these facts, a stochastic approach to the theory of nucleation is developed with eventual application to the H2SO4–H2O system. The central goal of the theory is the evaluation of the distribution of ’’first passage times,’’ for a nucleus, over the relevant free energy barrier. This distribution is calculated from the distribution of a ’’walker’’ on a lattice. However, the distribution of the walker is derived from a ’’master equation,’’ and for this purpose it is demonstrated that walks on lattices and master equations are, in this sense, ’’equivalent’’ even for a lattice which is not translationally invariant. Given the distribution of first passage times, it is possible to compute the transient rate of nucleation, as well as the distribution of fluctuations of the rate about some instantaneous mean. This theory is then applied to the H2SO4–H2O vapor system, and the results indicate that, under many typical experimental conditions, the time to reach the steady state may be quite long (hundreds or thousands of seconds), but that nevertheless, some nucleation should be observed in the laboratory time frame (in agreement with experiment). The character of nucleation as an ’’extreme event’’ is demonstrated by the appearance of a large band gap in the spectrum of relaxation times for the process.