A new grand canonical ensemble method to calculate first-order phase transitions

Tang, Yiping

doi:10.1063/1.3599048

Cited by 12 publications

(10 citation statements)

References 20 publications

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“…There are only a few recent works devoted to finding possible ways of solving this problem in the framework of grand canonical ensemble. Among them, there is a collective variables method [9] used by Yukhnovskii to completely integrate the grand partition function of a system of interacting particles in the phase-space of collective variables and, therefore, investigate its behavior in the vicinity of a critical point, or the method developed by Tang [10] where he combined the grand canonical ensemble with density functional to explain the occurrence of a first-order phase transition in homogeneous fluids.…”

Section: Introductionmentioning

confidence: 99%

Phase transition in a cell fluid model

Kozlovskii¹,

Dobush²

2017

Condens. Matter Phys.

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We propose a method of describing a phase transition in a cell fluid model with pair interaction potential that includes repulsive and attractive parts. An exact representation of the grand partition function of this model is obtained in the collective variables set. The behavior of the system at temperatures below and above the critical one is explored in the approximation of a mean-field type. An explicit analytic form of the equation of state which is applicable in a wide range of temperatures is derived, taking into account an equation between chemical potential and density. The coexistence curve, the surface of the equation of state and the phase diagram of the cell Morse fluid are plotted.

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Section: Introductionmentioning

confidence: 99%

Phase transition in a cell fluid model

Kozlovskii¹,

Dobush²

2017

Condens. Matter Phys.

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“…It is generally believed that grand canonical ensemble is fundamental to describe the phase behavior of system and it is better than canonical ensemble by accounting for density fluctuations. Thus, to make the transform much easier in practical calculation of phase equilibrium, we use the grand canonical ensemble method, 42 which can be simply represented by 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 The integral equation is formally reliable for the radial distribution function of oxygen−oxygen.…”

Section: Theory and Equationsmentioning

confidence: 99%

Thermodynamics of Ice Nucleation in Liquid Water

Wang

et al. 2015

J. Phys. Chem. B

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We present a density functional theory approach to investigate the thermodynamics of ice nucleation in supercooled water. Within the theoretical framework, the free-energy functional is constructed by the direct correlation function of oxygen-oxygen of the equilibrium water, and the function is derived from the reference interaction site model in consideration of the interactions of hydrogen-hydrogen, hydrogen-oxygen, and oxygen-oxygen. The equilibrium properties, including vapor-liquid and liquid-solid phase equilibria, local structure of hexagonal ice crystal, and interfacial structure and tension of water-ice are calculated in advance to examine the basis for the theory. The predicted phase equilibria and the water-ice surface tension are in good agreement with the experimental data. In particular, the critical nucleus radius and free-energy barrier during ice nucleation are predicted. The critical radius is similar to the simulation value, suggesting that the current theoretical approach is suitable in describing the thermodynamic properties of ice crystallization.

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“…After the determination of ρ m , n ( r ), the crystal–melt phase equilibrium can be calculated by the grand canonical method where F i (ρ) denotes the free-energy density after i th transforms, ρ is the average density of melt or crystal, t max corresponds to min(ρ max – ρ,ρ), and ρ max is the maximum of density allowed by the given free-energy functional. The chemical potential is related to the free-energy through μ = ∂ F (ρ)/∂ρ.…”

Section: Theory and Equationsmentioning

confidence: 99%

Theory of Crystals and Interfaces in Polyethylene and Isotactic Polypropylene

et al. 2016

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We present a three-dimensional density functional method to investigate the crystallization thermodynamics of polyethylene and isotactic polypropylene. Within the theoretical framework, the effects of excluded volume, dispersive attraction, chain connectivity, and conformation are integrated into the nonlocal free-energy functional. Under the condition of crystal–melt phase equilibrium, the crystal lattice parameters as a function of temperature are first determined through the restricted and full free-energy minimizations of crystal cell. The interfacial density profiles and interfacial tensions are then calculated via the restricted and full free-energy minimizations of interfaces. Accordingly, the free-energy barriers and critical sizes during the formation of crystal nuclei are predicted to evaluate the structures and properties of such crystallites. Some results are in good agreement with the available experimental data, indicating that the present theoretical approach could be a good candidate for understanding the molecular mechanism of polymer crystallization.

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A new grand canonical ensemble method to calculate first-order phase transitions

Cited by 12 publications

References 20 publications

Phase transition in a cell fluid model

Phase transition in a cell fluid model

Thermodynamics of Ice Nucleation in Liquid Water

Theory of Crystals and Interfaces in Polyethylene and Isotactic Polypropylene

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