Defining Physical Clusters in Nucleation Theory from the N-Particle Distribution Function

In this paper we propose a refined definition of a cluster to be used in a theory for the rate of homogeneous nucleation. It contains n particles in a volume v (n/v cluster). Starting from the N-particle distribution function, we define the free energy of an n/v cluster interacting with its vapor. The expression obtained for the free energy is the same as that obtained previously using a different approach. However, the method of derivation proposed in this paper has the advantage of clarifying the nature of any approximation involved in obtaining this expression. We also discuss methods for evaluating this free energy using Monte Carlo simulation.