Classical Theory of Nucleation Applied to Condensation of a Lennard-Jones Fluid

The classical nucleation theory (CNT) and its modified versions provide a convenient framework for describing the nucleation process under the capillary approximation. However, these models often predict nucleation rates that depart significantly from simulation results, even for a simple Lennard-Jones fluid. This large discrepancy is likely due to the inaccurate estimation of the driving force for nucleation, which most traditional models estimate within the ideal solution approximation. In this study, we address this issue by directly calculating the driving force for nucleation using equations of state (EOS) and integrating this approach into the calculation of nucleation rates within the framework of CNT and its modified model. We apply this method to examine the condensation of a Lennard-Jones fluid and compare the resulting nucleation rates with molecular dynamics (MD) simulation data. Our results demonstrate that at relatively low supersaturation, where the capillary approximation is reasonable, our thermodynamic models exhibit excellent agreement with MD results, significantly outperforming traditional models. At moderate and high supersaturation, our approach continues to show a reasonable agreement with MD results. Furthermore, when comparing the results obtained by using different EOS, we find that more precise EOS generally yield better agreement with MD data.