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.

17 pages, 17 figures

References in corpus (11)

• Accurate determination of crystal structures based on averaged local bond order parameters
• Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations
• In Search of Colloidal Hard Spheres
• A perspective on the interfacial properties of nanoscopic liquid drops
• Tension and stiffness of the hard sphere crystal-fluid interface
• Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives
• Crystal nucleation as the ordering of multiple order parameters
• Logarithmic Finite-Size Effects on Interfacial Free Energies: Phenomenological Theory and Monte Carlo Studies
• Finite size effects on liquid-solid phase coexistence and the estimation of crystal nucleation barriers
• Canonical free-energy barrier of particle and polymer cluster formation
• A fingerprint of surface-tension anisotropy in the free-energy cost of nucleation

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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
• Equivalence between condensation and boiling in a Lennard Jones fluid
• Statistical mechanics of crystal nuclei of hard spheres