A stochastic analysis of the homogeneous nucleation of vapor condensation
Abstract
It is argued that condensational growth and evaporative decay of a molecular cluster are intrinsically stochastic processes, properly described by condensation and evaporation ''probability'' rates rather than ''number'' rates. This implies that the pretransitional evolution of a pure, supersaturated vapor should be mathematically described as a continuoustime/discretestate Markovian random walk. A ''master equation'' is derived for a simplified version of this random walk. It is shown to lead, on the one hand, to the approximate formulas of classical steadystate nucleation theory, and, on the other hand, to an exact (but complicated) formula for the probability distribution of the system nucleation time. An alternate ''pedestrian'' approach to random walks is then described, and is shown to lead to a simple, approximate way of calculating the average time to system nucleation. This calculation also provides additional insight into the relationship between the approximate results of classical steadystate nucleation theory and the exact results of the master equation treatment. Finally, the pedestrian approach is used to estimate the mean nucleation time for a cluster growth mechanism that is energetically more realistic than the commonly used cluster growth mechanism.
 Publication:

Journal of Chemical Physics
 Pub Date:
 January 1981
 DOI:
 10.1063/1.440825
 Bibcode:
 1981JChPh..74..661G