Solution of the Percus-Yevick equation for pair-correlation functions of molecular fluids

Ram, Jokhan; Singh, Ram Chandra; Singh, Yashwant

doi:10.1103/physreve.49.5117

Cited by 35 publications

(27 citation statements)

References 23 publications

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“…[3][4][5][6][7][8]. Along these directions, all G n0, Ј are real for the chosen Ј, by the symmetries (A5).…”

Section: Numerical Results For the Correlation Functionsmentioning

confidence: 99%

“…[3,4,21,22]) we will expand all orientation-dependent functions with respect to spherical harmonics Y ͑⍀͒, = ͑lm͒. 1 Consequently, we have for any functions f͑⍀͒ and F nn Ј ͑⍀ , ⍀Ј͒ their transforms and the corresponding inverse transformations,…”

Section: ͑14͒mentioning

confidence: 99%

“…For the iteration procedure it is convenient to use the -transform of the PY equation (33), 3 4 ͒f nn Ј , 1 2 ϫ͑g nn Ј , 3 4 − c nn Ј , 3 …”

Section: B Numerical Solution Of the Oz Equation Using The Py Approxmentioning

confidence: 99%

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Ornstein-Zernike equation and Percus-Yevick theory for molecular crystals

Ricker

Schilling

2004

Phys. Rev. E

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We derive the Ornstein-Zernike equation for molecular crystals of axially symmetric particles and apply the Percus-Yevick approximation. The one-particle orientational distribution function rho((1)) (Omega) has a nontrivial dependence on the orientation Omega, in contrast to a liquid, and is needed as an input. Despite some differences, the Ornstein-Zernike equation for molecular crystals has a similar structure as for liquids. We solve both equations numerically for hard ellipsoids of revolution on a simple cubic lattice. Compared to molecular liquids, the orientational correlators in direct and reciprocal space exhibit less structure. However, depending on the lengths a and b of the rotation axis and the perpendicular axes of the ellipsoids, respectively, different behavior is found. For oblate and prolate ellipsoids with b greater, similar 0.35 (in units of the lattice constant), damped oscillations in distinct directions of direct space occur for some of the orientational correlators. They manifest themselves in some of the correlators in reciprocal space as a maximum at the Brillouin zone edge, accompanied by a maximum at the zone center for other correlators. The oscillations indicate alternating orientational fluctuations, while the maxima at the zone center originate from ferrorotational fluctuations. For a less, similar 2.5 and b less, similar 0.35, the oscillations are weaker, leading to no marked maxima at the Brillouin zone edge. For a greater, similar 3.0 and b less, similar 0.35, no oscillations occur any longer. For many of the orientational correlators in reciprocal space, an increase of a at fixed b or vice versa leads to a divergence at the zone center q=0, consistent with the formation of ferrorotational long-range fluctuations, and for some oblate and prolate systems with b less, similar 1.0 a simultaneous tendency to divergence of few other correlators at the zone edge is observed. Comparison of the orientational correlators with those from Monte Carlo simulations shows satisfactory agreement. From these simulations we also obtain a phase boundary in the a-b plane for order-disorder transitions.

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“…[3][4][5][6][7][8]. Along these directions, all G n0, Ј are real for the chosen Ј, by the symmetries (A5).…”

Section: Numerical Results For the Correlation Functionsmentioning

confidence: 99%

Section: ͑14͒mentioning

confidence: 99%

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Ornstein-Zernike equation and Percus-Yevick theory for molecular crystals

Ricker

Schilling

2004

Phys. Rev. E

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“…The density-functional theory (DFT) has been clearly discussed several times in literature [24][25][26][27] and the essentials of the approach are well known. With more and more reliable approximations available, the DFT has been applied to different problems of increasing complexity [28].…”

Section: Density-functional Theory Of Freezingmentioning

confidence: 99%

An Integral Equation Approach to Orientational Phase Transitions in Quadrupolar Gay-Berne Fluid Using Density-Functional Theory

Singh¹

2009

AIP Conference Proceedings

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A comparison of density functional and integral equation theories vs Monte Carlo simulations for hard sphere associating fluids near a hard wall Abstract. The effects of quadrupole moments on the phase behaviour of isotropic-nematic transition are studied by using density functional theory for a system of molecules which interact via the Gay-Berne pair potential. The pair correlation functions of isotropic phase, which enter in the theory as input information, are found from the Percus-Yevick integral equation theory. The method used involves an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. All the terms of harmonic coefficients which involve / indices up to less than or equal to six have been considered. The dependence of the accuracy of the results on the number of terms taken in the basis set is explored for both fluids at different densities, temperatures and quadrupole moments. The results have been compared with the available computer simulation results.

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“…Well known approximations to the closure relation are the hypernetted-chain relation, the Percus-Yevick (PY) relation and the mean spherical approximation (MSA) [6]. These integral equation theories have been quite successful in describing the structure and thermodynamic properties of isotropic fluids [7][8][9][10][11]. However, their application to ordered phases which can be regarded as inhomogeneous, have so far been very limited [12][13][14][15], though no feature of the theory inherently prevents them from being used to describe the structure of ordered phases.…”

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confidence: 99%

Pair correlation functions and a free energy functional for the nematic phase

Mishra

Singh

Ram

et al. 2007

The Journal of Chemical Physics

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In this paper we have presented the calculation of pair correlation functions in a nematic phase for a model of spherical particles with the long-range anisotropic interaction from the mean spherical approximation(MSA) and the Percus-Yevick (PY) integral equation theories. The results found from the MSA theory have been compared with those found analytically by Holovko and Sokolovska (J. Mol. Liq. 82, 161(1999)). A free energy functional which involves both the symmetry conserving and symmetry broken parts of the direct pair correlation function has been used to study the properties of the nematic phase. We have also examined the possibility of constructing a free energy functional with the direct pair correlation function which includes only the principal order parameter of the ordered phase and found that the resulting functional gives results that are in good agreement with the original functional. The isotropic-nematic transition has been located using the grand thermodynamic potential. The PY theory has been found to give nematic phase with pair correlation function harmonic coefficients having all the desired features. In a nematic phase the harmonic coefficient of the total pair correlation function h(x 1 , x 2 ) connected with the correlations of the director transverse fluctuations should develop a long-range tail. This feature has been found in both the MSA and PY theories.

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Solution of the Percus-Yevick equation for pair-correlation functions of molecular fluids

Cited by 35 publications

References 23 publications

Ornstein-Zernike equation and Percus-Yevick theory for molecular crystals

Ornstein-Zernike equation and Percus-Yevick theory for molecular crystals

An Integral Equation Approach to Orientational Phase Transitions in Quadrupolar Gay-Berne Fluid Using Density-Functional Theory

Pair correlation functions and a free energy functional for the nematic phase

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