Free Energy Barriers for Crystal Nucleation from Fluid Phases

Abstract

Monte Carlo simulations of crystal nuclei coexisting with the fluid phase in thermal equilibrium in finite volumes are presented and analyzed, for fluid densities from dense melts to the vapor. Generalizing the lever-rule for two-phase coexistence in the canonical ensemble to finite volume, "measurements" of the nucleus volume together with the pressure and chemical potential of the surrounding fluid allows to extract the surface free energy of the nucleus. Neither the knowledge of the (in general non-spherical) nucleus shape nor of the angle-dependent interface tension is required for this task. The feasibility of the approach is demonstrated for a variant of the Asakura-Oosawa model for colloid-polymer mixtures, which form face-centered cubic colloidal crystals. For a polymer to colloid size ratio of $0.15$, the colloid packing fraction in the fluid phase can be varied from melt values to zero by the variation of an effective attractive potential between the colloids. It is found that the approximation of spherical crystal nuclei often underestimates actual nucleation barriers significantly. Nucleation barriers are found to scale as $\Delta F^{\ast }=(4\pi /3{)}^{1/3}\bar{\gamma }(V^{\ast }{)}^{2/3}+const.$ with the nucleus volume $V^{\ast }$, and the effective surface tension $\bar{\gamma }$ that accounts implicitly for the nonspherical shape can be precisely estimated.

arXiv comment17 pages, 17 figures

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• Seeding Approach to nucleation in the NVT ensemble: the case of bubble cavitation in overstretched Lennard Jones fluids
• Interfacial free energy and Tolman length of curved liquid-solid interfaces from equilibrium studies
• Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension
• Equivalence between condensation and boiling in a Lennard Jones fluid
• Crystal nucleation along an entropic pathway: Teaching liquids how to transition
• Statistical mechanics of crystal nuclei of hard spheres