Nonclassical condensation pathways revealed by the multivariable theory of nucleation
We extend classical nucleation theory (CNT) by explicitly incorporating the multidimensional nature of nucleation and the coupled roles of kinetics and thermodynamics. Specifically, we treat the cluster density as an independent variable, within both sharp-interface and diffuse-interface descriptions. The kinetics are governed by dynamical density functional theory. Applied to liquid condensation in the Lennard-Jones system, our two-variable (size--density) and three-variable (size--interface width--density) models reveal nonclassical nucleation mechanism. At low supersaturation, both models recover the classical picture, in which clusters nucleate and grow at the equilibrium liquid density. As supersaturation increases, a nonclassical behavior emerges: the critical cluster density decreases, and the nucleation pathway involves concomitant evolution in cluster size, density, and, within the diffuse-interface description, interfacial width. Our model with diffuse interface reveals a rapid increase in interfacial diffuseness at high supersaturation. Near the spinodal limit, both models predict the critical cluster with diverging sizes, densities approaching that of the metastable initial phase, and vanishing work of formation, which provides a smooth connection between nucleation and spinodal decomposition. Comparison with molecular dynamics simulations demonstrates that both models substantially outperform CNT. However, the weak non-monotonic dependence of the critical cluster density observed at very low supersaturation is captured only by diffuse-interface models. Overall, our findings indicate that CNT should be applied only in the low-supersaturation regime, and our work provides a robust foundation for its refinement beyond this limit.