Integral equation theory for uncharged liquids: The Lennard-Jones fluid and the bridge function

Duh, Der‐Ming; Haymet, A. D. J.

doi:10.1063/1.470724

Cited by 125 publications

(67 citation statements)

References 41 publications

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“…RDF g (2) LJ (r), which is needed as an input in (16) and (26), was calculated using OZ equation together with the closure relation suggested by Duh et al [17][18][19]. For the pressure P and chemical potential µ the standard thermodynamical relations…”

Section: Resultsmentioning

confidence: 99%

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Liquid-gas phase behavior of Stockmayer fluid with high dipolar moment

Kalyuzhnyi¹,

Protsykevitch²,

Cummings³

2007

Condens. Matter Phys.

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A multi-density version of the thermodynamic perturbation theory for associative fluids with central force associative potential is developed. The theory is used to describe the liquid-gas phase behavior of Stochmayer fluid with different values of the dipole moment ranging from low to high. Results of the theory are in a reasonable agreement with corresponding computer simulation results in a whole range of the dipole moment values studied. Contrary to previous computer simulation findings our calculations predict the occurrence of the liquid-gas phase coexistence for the soft-sphere dipole fluid model.

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Section: Resultsmentioning

confidence: 99%

“…This function was calculated using solution of the Ornstein-Zernike (OZ) equation supplemented by the closure conditions due to Duh et al [17][18][19].…”

Section: G (3)mentioning

confidence: 99%

Liquid-gas phase behavior of Stockmayer fluid with high dipolar moment

Kalyuzhnyi¹,

Protsykevitch²,

Cummings³

2007

Condens. Matter Phys.

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“…(15) (20) where Ĥ(k) and Ĉ(K) are the Fourier transform of Ĥ and C(r), respectively. For homonuclear diatomic fluids, the screened density and the renormalized intramolecular matrices ρ ̅ and Ŝ (k) are given by the following expressions: (21) η being the screened density whose approximation to first order 45 can be numerically approximated by the following expression: . In the latter formula, ρ represents the site density, L the bond length, and f is the Mayer function.…”

Section: B An Approximate Theory For Molecular Fluidsmentioning

confidence: 99%

“…This has encouraged refined approximations to overcome those difficulties. [15][16][17][18][19][20][21][22][23][24][25][26][27][28] Such is the case of hybrid theories which mix two of the approximations via a switching function. Further direct calculation of a series of bridge diagrams leads to considerable improvement in the results but dramatically increases the computational complexity.…”

Section: Introductionmentioning

confidence: 99%

Optimized theory for simple and molecular fluids

Marucho

Pettitt

2007

The Journal of Chemical Physics

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An optimized closure approximation for both simple and molecular fluids is presented. A smooth interpolation between Perkus-Yevick and hypernetted chain closures is optimized by minimizing the free energy self-consistently with respect to the interpolation parameter(s). The molecular version is derived from a refinement of the method for simple fluids. In doing so, a method is proposed which appropriately couples an optimized closure with the variant of the diagrammatically proper integral equation recently introduced by this laboratory [K. M. Dyer et al., J. Chem. Phys. 123, 204512 (2005)]. The simplicity of the expressions involved in this proposed theory has allowed the authors to obtain an analytic expression for the approximate excess chemical potential. This is shown to be an efficient tool to estimate, from first principles, the numerical value of the interpolation parameters defining the aforementioned closure. As a preliminary test, representative models for simple fluids and homonuclear diatomic Lennard-Jones fluids were analyzed, obtaining site-site correlation functions in excellent agreement with simulation data.

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“…We begin by evaluating the HNC solution ͓b͑r͒ =0͔ for h͑r͒ using the Picard iteration algorithm presented by Duh and Haymet. 33 The result is used to estimate b͑r͒ from its h-bond series expansion including only the b 2 term, which is evaluated by the Mayer-sampling technique using the HNC h͑r͒ interpolated from a table. This estimate of b͑r͒ is then used in another Duh-Haymet calculation of h͑r͒ via Eqs.…”

Section: Computational Detailsmentioning

confidence: 99%

Evaluation of bridge-function diagrams via Mayer-sampling Monte Carlo simulation

Kwak

Kofke

2005

The Journal of Chemical Physics

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We report coefficients of the h-bond expansion of the bridge function of the hard-sphere system up to order ρ4 (where ρ is the density in units of the hard-sphere diameter), which in the highest-order term includes 88 cluster diagrams with bonds representing the total correlation function h(r). Calculations are performed using the recently introduced Mayer-sampling method for evaluation of cluster integrals, and an iterative scheme is applied in which the h(r) used in the cluster integrals is determined by solution of the Ornstein–Zernike equation with a closure given by the calculated clusters. Calculations are performed for reduced densities from 0.1 to 0.9 in increments of 0.1. Comparison with molecular simulation data shows that the convergence is very slow for the density expansion of the bridge function calculated this way.

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Integral equation theory for uncharged liquids: The Lennard-Jones fluid and the bridge function

Cited by 125 publications

References 41 publications

Liquid-gas phase behavior of Stockmayer fluid with high dipolar moment

Liquid-gas phase behavior of Stockmayer fluid with high dipolar moment

Optimized theory for simple and molecular fluids

Evaluation of bridge-function diagrams via Mayer-sampling Monte Carlo simulation

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