Local composition fluctuations act as precursors for crystal nucleation in polydisperse hard spheres

Abstract

We revisit the effect of polydispersity on the crystal nucleation of hard spheres. Using event-driven molecular dynamics simulations, we obtain the nucleation rate as a function of the supersaturation for a range of polydispersities, and demonstrate that the nucleation rate of polydisperse hard spheres deviates from the trend of monodisperse hard spheres, even when mapped to the effective packing fraction. Furthermore, we show that nucleation tends to originate in regions with on average more larger-sized particles, indicating that such regions act as precursors for nucleation in systems of polydisperse hard spheres.

Figures (4)

• Figure 1: Nucleation rate as a function of (a) packing fraction and (b) effective packing fraction $\eta^\text{eff}=(\eta_F^0 / \eta_F)\eta$ for monodisperse and polydisperse hard spheres. The lines serve as guides to the eye, and indicate CNT-like fits (Eq. \ref{['eq:fitrate']}). The solid black symbols indicate the rates obtained via umbrella sampling and the open symbols indicate the rates reported by Wöhler & Schilling wohler2022hard. The nucleation rates are given in terms of the long-time diffusion time $\tau_D$.
• Figure 2: (a) Average and (b) standard deviation of the particle size inside the crystal nucleus as a function of time for a typical nucleation event (6% polydispersity at $\eta=0.562$). The black line indicates the nucleus size as a function of time. Note that the first $152.5\cdot10^3\tau$ of the simulation are not shown. In (c,d), we combine the data on all 100 nucleation events of the same system (6% polydispersity at $\eta=0.562$) and show (c) the average particle size versus the nucleus size and (d) the standard deviation of the particle size versus the nucleus size. The color gradient indicates the bin count.
• Figure 3: Average trends of the nucleus composition for (a,b) 4%, (c,d) 5%, and (e,f) 6% polydispersity. These average trends are obtained from density histograms such as depicted in Fig. \ref{['fig:compo']}c,d. The different colored lines indicate different packing fractions of the system. Symbols correspond to critical nuclei from US simulations, and dotted lines are the composition of the equilibrium crystal phase obtained from direct coexistence simulations, taken from Ref. castagnede2025freezing. Note that Ref. castagnede2025freezing did not provide data for $5\%$ polydispersity.
• Figure 4: Size distribution of the fluid region from which the nuclei originate for (a) 4%, (b) 5%, and (c) 6% polydispersity. The different colored lines indicate different packing fractions of the system, and the black line indicates the size distribution of the entire system. Assuming that the supersaturation has no significant effect on the distribution, the means of the distributions are (a) $1.0032\bar{\sigma}$, (b) $1.0053\bar{\sigma}$, and (c) $1.0071\bar{\sigma}$, and the widths (i.e. standard deviations) are (a) $0.0367\bar{\sigma}$, (b) $0.0444\bar{\sigma}$, and (c) $0.0505\bar{\sigma}$.