An Aggregation-Volume-Bias Monte Carlo Investigation on the Condensation of a Lennard-Jones Vapor below the Triple Point and Crystal Nucleation in Cluster Systems:  An In-Depth Evaluation of the Classical Nucleation Theory

Abstract

The aggregation-volume-bias Monte Carlo based simulation technique, which has led to our recent success in vapor-liquid nucleation research, was extended to the study of crystal nucleation processes. In contrast to conventional bulk-phase techniques, this method deals with crystal nucleation events in cluster systems. This approach was applied to the crystal nucleation of Lennard-Jonesium under a wide range of undercooling conditions from 35% to 13% below the triple point. It was found that crystal nucleation in these model clusters proceeds initially via a vapor-liquid like aggregation followed by the formation of crystals inside the aggregates. The separation of these two stages of nucleation is distinct except at deeper undercooling conditions where the crystal nucleation barrier was found to diminish. The simulation results obtained for these two nucleation steps are separately compared to the classical nucleation theory (CNT). For the vapor-liquid nucleation step, the CNT was shown to provide a reasonable description of the critical cluster size but overestimate the barrier heights, consistent with previous simulation studies. On the contrary, for the crystal nucleation step, nearly perfect agreement with the barrier heights was found between the simulations and the CNT. For the critical cluster size, the comparison is more difficult as the simulation data were found to be sensitive to the definition of the solid cluster, but a stringent criterion and lower undercooling conditions generally lead to results closer with the CNT. Additional simulations at undercooling conditions of 40% or above indicate a nearly barrierless transition from the liquid to crystalline-like structure for sufficiently large clusters, which leads to further departure of the barrier height predicted by the CNT from the simulation data for the aggregation step. This is consistent with the latest experimental results on argon that show an unusually large underestimation of the nucleation rate by the CNT toward deep undercooling conditions.

The non-classical nucleation of crystals: microscopic mechanisms and applications to molecular crystals, ice and calcium carbonate

“…This is the surface analogue of the situation found by Chen et al 103 and by van Meel et al 66 where the rate limiting step for crystallisation was nucleation of an intermediate liquid phase.…”

“…If the crystal does surface melt then ∆F * l should be the lowest nucleation barrier. This is the case for the Lennard-Jones model, where the crystalline nucleus forms in the bulk of droplets, away from the interface 66,103 .…”

“…Both Chen et al 103 and van Meel et al 66 used computer simulations of the Lennard-Jones model just below its triple point to study crystallisation from the dilute vapour. As expected from the above arguments, it is clear that there are conditions where homogeneous nucleation proceeds via two steps: nucleation of the liquid, followed by nucleation of the crystal in liquid droplets.…”

Self-assembly of amphiphilic peanut-shaped nanoparticles

“…4. Here a bilayer and a micelle merge before the former grows at the expense of the latter.Finally, we note that cluster formation by 'peanuts' whose hydrophilic lobes are of vanishing size proceeds via 'two-step' crystallization [46][47][48][49]: first, dense amorphous blobs nucleate from vapor; second, crystalline order nucleates within these blobs (not shown). We observed a similar dynamics (not shown) for crystal-forming peanuts (see Fig.…”

Molecular dynamics simulations of nucleation from vapor to solid composed of Lennard-Jones molecules

“…38 and 39) and was confirmed by MC simulations for clusters larger than a certain threshold size. 22,31,45,46,48,49 These results suggest that the SP model is inapplicable, at least, when the critical cluster is larger than the threshold size.…”