Classical Nucleation Theory and Tolman Equation in Cluster Thermodynamics: How Small Can They Truly Apply?

Classical nucleation theory and the Tolman equation are two fundamental theories in cluster thermodynamics. Despite their long-standing existence, the applicability of these theories remains questionable. Direct experimental validation is challenging due to the small size of the clusters involved. While theoretical approaches are often used as alternatives, the findings are frequently controversial. In this work, free energy calculations were performed across an unprecedentedly large size range using sophisticated techniques, including aggregation-volume-bias Monte Carlo, for two systems: Lennard-Jones and TIP4<i>P</i>/2005 water. The availability of bulk-phase properties for an infinitely large system (i.e., γ^∞) facilitates a direct comparison to these two theories. The simulation results provide strong support for the applicability of these theories to large clusters, down to those containing a few hundred particles. However, these theories break down for small clusters.