Interrelation between cluster formation time, cluster growth probability, and nucleation rate

Approximate expressions are derived for the mean time tau for formation of a cluster of n molecules in nucleation of single-component phases. The derivation elucidates the interrelation between tau, the cluster growth probability P, and the stationary nucleation rate. The extraction of both tau(n) and P(n) data from individual cluster growth curves obtained in experiments or simulations is discussed. It is shown that the analysis of tau(n) data allows a model-independent determination of the nucleus size, the Zeldovich factor, the stationary nucleation rate, the frequency with which molecules are attached to the nucleus, and the difference between the works to form the nucleus and the smallest "cluster" of one molecule.