Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension

Abstract

Combining three numerical methods (forward flux sampling, seeding of droplets, and finite-size droplets), we probe the crystallization of hard spheres over the full range from close to coexistence to the spinodal regime. We show that all three methods allow us to sample different regimes and agree perfectly in the ranges where they overlap. By combining the nucleation work calculated from forward flux sampling of small droplets and the nucleation theorem, we show how to compute the nucleation work spanning three orders of magnitude. Using a variation of the nucleation theorem, we show how to extract the pressure difference between the solid droplet and ambient liquid. Moreover, combining the nucleation work with the pressure difference allows us to calculate the interfacial tension of small droplets. Our results demonstrate that employing bulk quantities yields inaccurate results for the nucleation rate.

Classical nucleation theory for the crystallization kinetics in sheared liquids

“…Note that results for n = 80 are extracted from configurations generated by direct simulations. As already discussed extensively in our previous work [34], we observe a gradual increase of the density inside the solid droplet as its size grows. Profiles can be well modeled by the mean-field expression…”

“…The second term Φ(V s ) = ΓA is the excess interfacial free energy given as the product of the droplet surface A ∼ V 2/3 s and the interfacial tension Γ. In principle, Γ again depends on the droplet size [34]. The thermodynamic driving force for nucleation is the difference ∆P = P s − P l of pressure P s between the inside of the solid droplet and the ambient liquid pressure P l at the same liquid chemical potential, µ s = µ l .…”

The effect of hydrodynamics on the crystal nucleation of nearly hard spheres

“…In this ensemble, however, the stability of the seed is influenced by finite-size effects. 32 In fact, given a seed of size n, the critical density found with a system of N particles is higher as compared to the critical density we would obtain with an infinitely large system, which corresponds to the thermodynamic limit. This effect is due to the progressive depletion of colloidal particles in the supersaturated fluid phase which surround the nucleus, while the latter is increasing in size.…”

“…This technique is known as the seeding approach, 42,43 and it has been applied to study the nucleation barrier of nearly hard spheres with βε = 40. 32 In this section, we aim to understand the relevance of HIs on the nucleation process of a colloidal fluid at low supersaturation. To do so, we employ a seeding approach method and implement both the MD and the MD + SRD techniques to neglect or account for HIs in the model system, respectively.…”

“…28 Therefore, it has been questioned whether the softness of the interaction potentially might be the missing ingredient in numerical models to recover the experimental nucleation rates. A numerical investigation initiated by Kawasaki and Tanaka 29 and followed by Filion et al 30 and Richard and Speck, 31,32 has looked into this issue by simulating nearly hard particles interacting through the Weeks-Chandler-Andersen (WCA) potential. 33 The nucleation rate of this softer system is in good agreement with the earlier numerical results for hard spheres, 25,27 thus proving that introducing a small amount of softness does not influence the nucleation rate.…”