Freezing of a Lennard-Jones Fluid: From Nucleation to Spinodal Regime

Using molecular dynamics, we investigate the crystal nucleation in a Lennard-Jones fluid as a function of the degree of supercooling. At moderate supercooling, a nucleation picture applies, while for deeper quenches, the phenomenon progressively acquires a spinodal character. We show that in the nucleation regime, the freezing is a two-step process. The formation of the critical nucleus is indeed preceded by the abrupt formation of a precritical crystallite from a density fluctuation in the fluid. In contrast, as the degree of supercooling is increased, crystallization proceeds in a more continuous and collective fashion and becomes more spatially diffuse, indicating that the liquid is unstable and crystallizes by a spinodal mechanism.

Figure 1

Comparison between the work of formation $\Delta G$ of nuclei of size $n$ as predicted by CNT (dashed line) and using in Eq. (1) the values of $S$ computed by the ellipsoidal approximation along the reactive trajectories (dots with error bars). For a given $n$, different values of $S$ are possible. The corresponding values of $\Delta G$ computed from Eq. (1) are averaged and their root mean square deviations reported in the picture. The values $\Delta \mu =0.262\mathrm{kJ}/\mathrm{mol}$ [7] and $\gamma =\gamma (111)=0.0307\mathrm{kJ}/\mathrm{mol}/{\AA }^2$ [18] have been used. The transition state ensemble, identified by the CPA on the MD trajectory, is delimited by the vertical lines.

Figure 2

The number of solid-like particles in the largest cluster (dashed line) and the average coordination between solid-like particles ($c_{ss}$, solid line) at $T/T_{\mathrm{melt}}=0.8$.

Figure 3

The free energy barriers as computed from MTD runs at different temperatures (circles) are compared to the work of formation of the critical nuclei and as predicted within our extended CNT model (crosses with dashed error bars). A linear fit to the MTD data is also shown.

Figure 4

For $T/T_{\mathrm{melt}}=0.8$, a snapshot of a critical nucleus is shown. For $T/T_{\mathrm{melt}}=0.7$ and 0.65, we have chosen a representative frame along the spontaneous crystallization trajectories. Colored spheres represent particles with a solid-like environment. Different colors indicate different aggregates with solid-like character. For clarity, the liquid-like particles are not shown.