A perturbation theory of classical equilibrium fluids

Kang, Hong Seok; Lee, Choong-Sik; Ree, Taikyue; Ree, Francis H.

doi:10.1063/1.448762

Cited by 171 publications

(93 citation statements)

References 29 publications

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“…Concerning the first point, we use a modification of the procedure of Kang et al [11], namely: where λ = (a −3 fcc + r * −3 ) −1/3 ; a fcc = ( √ 2/(N/V )) 1/3 and r * corresponds to the minimum of the potential Φ(r). This choice for the density-dependent break-point λ has the advantage to give a continuously differentiable λ.…”

Section: The Configurational Free-energy F Confmentioning

confidence: 99%

Free-energy model for fluid helium at high density

Winisdoerffer

Chabrier

2005

Phys. Rev. E

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We present a semi-analytical free-energy model aimed at characterizing the thermodynamic properties of dense fluid helium, from the low-density atomic phase to the high-density fully ionized regime. The model is based on a free-energy minimization method and includes various different contributions representative of the correlations between atomic and ionic species and electrons. This model allows the computation of the thermodynamic properties of dense helium over an extended range of density and temperature and leads to the computation of the phase diagram of dense fluid helium, with its various temperature and pressure ionization contours. One of the predictions of the model is that pressure ionization occurs abruptly at ρ ∼ > 10 g cm −3 , i.e. P ∼ > 20 Mbar, from atomic helium He to fully ionized helium He 2+ , or at least to a strongly ionized state, without He + stage, except at high enough temperature for temperature ionization to become dominant. These predictions and this phase diagram provide a guide for future dynamical experiments or numerical first-principle calculations aimed at studying the properties of helium at very high density, in particular its metallization. Indeed, the characterization of the helium phase diagram bears important consequences for the thermodynamic, magnetic and transport properties of cool and dense astrophysical objects, among which the solar and the numerous recently discovered extrasolar giant planets.

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Section: The Configurational Free-energy F Confmentioning

confidence: 99%

Free-energy model for fluid helium at high density

Winisdoerffer

Chabrier

2005

Phys. Rev. E

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“…Furthermore, the determination of phase coexistence is a very sensitive test since it depends on getting both the absolute magnitude and the slope of the free energies correct. To put this in perspective, deviations are observed in Fig.1 between the calculated and simulated gas-liquid coexistence curve for the LJ system even though the liquid-state perturbation theory gives free energies which differ from simulation by less than 1% [16].…”

mentioning

confidence: 99%

“…In the following, we use the first order WCA perturbation theory [11,12,13,14] as modified by Ree et al [15,16,17] to calculate the free energy of the liquid phase. This theory is known to be very accurate for a wide class of potentials.…”

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confidence: 99%

Theoretical Evidence for a Dense Fluid Precursor to Crystallization

2006

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We present classical density functional theory calculations of the free energy landscape for fluids below their triple point as a function of density and crystallinity. We find that for both a model globular protein and for a simple atomic fluid modeled with a Lennard-Jones interaction, it is free-energetically easier to crystallize by passing through a metastable dense fluid in accord with the Ostwald rule of stages but in contrast to the alternative of ordering and densifying at once as assumed in the classical picture of crystallization.PACS numbers: 82.60. Nh,87.15.Nn,05.20.Jj Crystallization is an intricate process of fundamental importance in many areas of physics, chemistry and engineering. The classical picture of crystallization from supersaturated solutions goes back to Gibbs and consists of the spontaneous formation of crystalline clusters which then either grow or shrink depending on the relative importance of the free energy gain due to the lower bulk free energy of the crystal cluster and the free energy penalty due to the surface tension between the two phases. In this picture, the local density is the only order parameter: the crystalline cluster is (in general) denser than the fluid. In recent years, this picture has been called into question by simulation, theory and experiment for the particular and important case of the crystallization of globular proteins. ten Wolde and Frenkel (hereafter tWF) showed by means of simulation that the free energy landscape of protein crystal clusters as a function of the number of atoms in the cluster and the "crystallinity " favored paths leading from no clusters to clusters with low order to ordered clusters over paths moving from no clusters directly to ordered clusters [1]. This picture was confirmed by Talanquer and Oxtoby [2] and Shiryayev and Gunton[3] who showed using a parameterized van der Waals-type model of globular proteins that surface wetting did indeed lower the free energy of crystal clusters. More recently, the simple picture has also been challenged by novel experimental investigations. Vekilov and co-workers have shown that, prior to crystallization, protein solutions harbor metastable droplets of dense fluid and they have suggested that these droplets are necessary precursors of crystallization [4,5,6,7]. The picture that emerges is one of the formation of metastable droplets of dense fluid which then subsequently crystallize. In this paper, we show by means of classical density functional theory calculations that there is an intrinsic free-energy advantage in first densifying into a metastable densefluid state and then crystallizing rather than following the classical path which goes directly from gas to crystal. Furthermore, our calculations suggest that a similar advantage exists for fluids of small molecules, modeled here via the Lennard-Jones (LJ) interaction, thus indicating that this mechanism may underlie most crystallization processes.The starting point for our analysis is classical density functional theory (DFT) which is based...

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“…In this case effective isotropic single-site interaction models are often convenient. Highly accurate theories of the free energy of the single-site exp-6 potential have been proposed [17][18][19]. In the current work, we use a numerical fit to free energies of the exp-6 fluid calculated from Ross's theory [18] and expressed as a polynomial in suitable variables [19,20].…”

Section: Equation Of State Predictions Using Exp-6 Modelsmentioning

confidence: 99%

Application of the TraPPE Force Field to Predicting Isothermal Pressure–Volume Curves at High Pressures and High Temperatures

2007

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Knowledge of the thermophysical properties of materials at extreme pressure and temperature conditions is essential for improving our understanding of many planetary and detonation processes. Significant gaps in what is known about the behavior of materials at high density and high temperature exist, largely due to the limitations and dangers of performing experiments at the necessary extreme conditions. Modelling these systems through the use of equations of state and particle-based simulation methods significantly extends the range of pressures and temperatures that can be safely studied. The reliability of such calculations depends on the accuracy of the models used. Here we present an assessment of the united-atom version of the TraPPE (Transferable Potentials for Phase Equilibria) force field and single-site exp-6 representations for methane, methanol, oxygen, and ammonia at extreme conditions. As shown by Monte Carlo simulations in the isobaricisothermal ensemble, the TraPPE models, despite being parameterized to the vapor-liquid coexistence curve (i.e. relatively mild conditions), perform remarkably well in the high pressure/high temperature regime. The single-site exp-6 models can fit experimental data in the high pressure/temperature regime very well, but the parameters are less transferable to ambient conditions.

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A perturbation theory of classical equilibrium fluids

Cited by 171 publications

References 29 publications

Free-energy model for fluid helium at high density

Free-energy model for fluid helium at high density

Theoretical Evidence for a Dense Fluid Precursor to Crystallization

Application of the TraPPE Force Field to Predicting Isothermal Pressure–Volume Curves at High Pressures and High Temperatures

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