Nonclassical Nucleation Pathways in Liquid Condensation Revealed by Simulation and Theory

Abstract

Using state-of-the-art rare-event sampling simulations, we precisely characterize the nucleation of liquid droplets from a supersaturated Lennard-Jones gas and uncover a key physical feature: critical clusters nucleate with a density that differs substantially from that of the macroscopic equilibrium liquid. Our atomistic simulations also reveal a nonclassical nucleation pathway showing simultaneous growth and densification in liquid condensation. We then exploit these insights to develop a two-variable nucleation theory, in which the cluster density is allowed to vary. Our accessible model based on the capillary approximation is able to quantitatively retrieve the numerical results in nucleation rate and critical cluster properties over a large range of supersaturation. Remarkably, the two-variable model successfully captures the observed nucleation pathway. The effectiveness of this integrated numerical and theoretical framework demonstrates that the cluster density is a decisive variable in nucleation, highlighting the limitations of the single-variable description while offering a robust foundation for its refinement.

Figures (4)

• Figure 1: (a) Snapshots of critical clusters from our simulations and evolution of the (b) radius and (c) density of critical cluster against initial density at temperature $T=0.8\epsilon/k_\mathrm{B}$. The first three snapshots are from seeding simulations, and the last two are from steering + aimless shooting simulations. Our seeding and aimless shooting MD simulation results are represented by blue squares and circles, respectively, with error bars indicating standard deviations. Predictions from our two-variable nucleation theory, CNT, and the SGA diffuse-interface model are represented by red solid lines, yellow dotted lines, and black dashed lines, respectively.
• Figure 2: Evolution of the steady-state nucleation rate against initial density at $T=0.8\epsilon/k_\mathrm{B}$. Our brute-force simulation results are represented by blue up triangles. Results from Diemand et al.Diemand_JCP2013 are represented by green down triangles. Predictions from our two-variable nucleation theory and CNT are represented by a red solid line and a yellow dotted line, respectively. Predictions from our two-variable nucleation theory incorporated with Tolman correction of $\delta=0.05\sigma$ and $\delta=0.1\sigma$ are represented by the pink and violet thinner solid lines, respectively.
• Figure 3: Evolution of the critical work of formation against initial density at $T=0.8\epsilon/k_\mathrm{B}$. Predictions from our two-variable nucleation theory, CNT, and the SGA diffuse-interface model are represented by a red solid line, a yellow dotted line, and a black dashed line, respectively.
• Figure 4: Contour plot of the work of formation overlaid with growth trajectories of critical clusters from simulations at $T=0.8\epsilon/k_\mathrm{B}$ and $\rho_0=0.03\sigma^{-3}$. The work of formation is computed using our two-variable nucleation theory (without Tolman correction), with the saddle point marked by a red hexagram. The red dashed line and blue dotted line indicate the predicted nucleation flux direction and steepest decent direction at the saddle point, respectively. Growth trajectories from four independent simulations are represented by colored crosses, with corresponding mean values shown as dots. Error bars denote standard deviations. $(R,\rho)$ coordinates from theory and simulation are normalized by their corresponding critical values.