Fundamental measure density functional theory studies on the freezing of binary hard-sphere and Lennard-Jones mixtures

Abstract. We review theoretical and simulational approaches to the description of equilibrium bulk crystal and interface properties as well as to the nonequilibrium processes of homogeneous and heterogeneous crystal nucleation for the simple model systems of hard spheres and Lennard-Jones particles. For the equilibrium properties of bulk and interfaces, density functional theories employing fundamental measure functionals prove to be a precise and versatile tool, as exemplified with a closer analysis of the hard sphere crystal-liquid interface. A detailed understanding of the dynamic process of nucleation in these model systems nevertheless still relies on simulational approaches. We review bulk nucleation and nucleation at structured walls and examine in closer detail the influence of walls with variable strength on nucleation in the Lennard-Jones fluid. We find that a planar crystalline substrate induces the growth of a crystalline film for a large range of lattice spacings and interaction potentials. Only a strongly incommensurate substrate and a very weakly attractive substrate potential lead to crystal growth with a non-zero contact angle.

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“…The phase diagram of binary hard spheres has been investigated in Ref. [6], again finding good agreement with simulations.…”

Section: Density Functional Theorysupporting

confidence: 54%

Solid phase properties and crystallization in simple model systems

Turci

Schilling

Yamani

et al. 2014

Eur. Phys. J. Spec. Top.

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“…17 Combined with the DFT for solids [18][19][20][21] this method allows us to calculate free energies of solid mixtures with realistic interaction potentials and, hence, to study the phase behaviors of realistic molecular mixtures. An application to the freezing of LJ mixtures 22 has been successful as the obtained spindle-and azeotropic-type solid-liquid phase diagrams of LJ mixtures are in good agreement with the corresponding ones from simulations.…”

Section: Introductionsupporting

confidence: 52%

“…30 To calculate the free energies of liquid and solid phases using the WCA perturbation theory, the potentials ij ͑r͒ are separated into a short-range, purely repulsive reference part ij ͑ref͒ ͑r͒ and a perturbative part ij ͑pert͒ ͑r͒; the reference system is mapped onto an effective HS system with a set of temperature-dependent HS diameters ͕d ij ͖ ͓with d 11 Ͻ d 22 and d 12 = ͑d 11 + d 22 ͒ / 2͔ prescribed by the WCA criteria for mixtures. 16,22,31 Using Eq. ͑3͒ the resulting expression for the total Helmholtz free energy is…”

Section: ͑4͒mentioning

confidence: 99%

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Phase diagrams of binary alloys calculated from a density functional theory

Warshavsky

Song

2009

Phys. Rev. B

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Phase behaviors of binary alloys with an embedded atom model potential are investigated using the thermodynamic perturbation theory. The free energies of the liquid and solid phases are computed using the fundamental measure density functional theory and accurate approximations to the hard-sphere mixture correlation functions. The method is applied to calculate the Au-Cu alloy phase diagram. To improve the accuracy of the computed phase diagram, we developed a systematic approach to optimize the model potential of Au-Cu by adjusting the melting temperature of the pure Au to its experimental one. With such an optimized potential the computed Au-Cu alloy phase diagram is in good agreement with the experimental one for the whole composition range. Disciplines Chemistry CommentsThis article is from Physical Review B 79 (2009): 015101, doi:10.1103/PhysRevB.79.014101. Posted with permission.Phase behaviors of binary alloys with an embedded atom model potential are investigated using the thermodynamic perturbation theory. The free energies of the liquid and solid phases are computed using the fundamental measure density functional theory and accurate approximations to the hard-sphere mixture correlation functions. The method is applied to calculate the Au-Cu alloy phase diagram. To improve the accuracy of the computed phase diagram, we developed a systematic approach to optimize the model potential of Au-Cu by adjusting the melting temperature of the pure Au to its experimental one. With such an optimized potential the computed Au-Cu alloy phase diagram is in good agreement with the experimental one for the whole composition range.

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“…The crystal of a binary hard-sphere mixture with size ratios between σ s /σ b = 0.95 and 0.85 was recently studied within FMT using a Gaussian parameterization for the density profiles [69]. The size ratios considered are chosen with a reference system for interacting systems in mind.…”

Section: Properties Of the Crystalmentioning

confidence: 99%

Fundamental measure theory for hard-sphere mixtures: a review

Roth¹

2010

J. Phys.: Condens. Matter

557

756

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Hard-sphere systems are one of the fundamental model systems of statistical physics and represent an important reference system for molecular or colloidal systems with soft repulsive or attractive interactions in addition to hard-core repulsion at short distances. Density functional theory for classical systems, as one of the core theoretical approaches of statistical physics of fluids and solids, has to be able to treat such an important system successfully and accurately. Fundamental measure theory is up to date the most successful and most accurate density functional theory for hard-sphere mixtures. Since its introduction fundamental measure theory has been applied to many problems, tested against computer simulations, and further developed in many respects. The literature on fundamental measure theory is already large and is growing fast. This review aims to provide a starting point for readers new to fundamental measure theory and an overview of important developments.

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Fundamental measure density functional theory studies on the freezing of binary hard-sphere and Lennard-Jones mixtures

Cited by 18 publications

References 40 publications

Solid phase properties and crystallization in simple model systems

Solid phase properties and crystallization in simple model systems

Phase diagrams of binary alloys calculated from a density functional theory

Fundamental measure theory for hard-sphere mixtures: a review

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