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Lucco Castello F, Tolias P. Bridge functions of classical one-component plasmas. Phys Rev E 2022; 105:015208. [PMID: 35193199 DOI: 10.1103/physreve.105.015208] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Accepted: 01/10/2022] [Indexed: 06/14/2023]
Abstract
In a recent paper, Lucco Castello et al. [arXiv:2107.03537] performed systematic extractions of classical one-component plasma bridge functions from molecular dynamics simulations and provided an accurate parametrization that was incorporated in their isomorph-based empirically modified hypernetted chain approach for Yukawa one-component plasmas. Here the extraction technique and parametrization strategy are described in detail, while the deficiencies of earlier efforts are discussed. The structural and thermodynamic predictions of the updated version of the integral equation theory approach are compared with extensive available simulation results revealing a truly unprecedented level of accuracy in the entire dense liquid region of the Yukawa phase diagram.
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Affiliation(s)
- F Lucco Castello
- Space and Plasma Physics, Royal Institute of Technology, Stockholm SE-100 44, Sweden
| | - P Tolias
- Space and Plasma Physics, Royal Institute of Technology, Stockholm SE-100 44, Sweden
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2
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Lucco Castello F, Tolias P, Dyre JC. Testing the isomorph invariance of the bridge functions of Yukawa one-component plasmas. J Chem Phys 2021; 154:034501. [PMID: 33499616 DOI: 10.1063/5.0036226] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It has been recently conjectured that bridge functions remain nearly invariant along phase diagram lines of constant excess entropy for the broad class of R-simple liquids. To test this hypothesis, the bridge functions of Yukawa systems are computed outside the correlation void with the Ornstein-Zernike inversion method employing structural input from ultra-accurate molecular dynamics simulations and inside the correlation void with the cavity distribution method employing structural input from ultra-long specially designed molecular dynamics simulations featuring a tagged particle pair. Yukawa bridge functions are revealed to be isomorph invariant to a very high degree. The observed invariance is not exact, however, since isomorphic deviations exceed the overall uncertainties.
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Affiliation(s)
- F Lucco Castello
- Space and Plasma Physics, Royal Institute of Technology, Stockholm SE-100 44, Sweden
| | - P Tolias
- Space and Plasma Physics, Royal Institute of Technology, Stockholm SE-100 44, Sweden
| | - J C Dyre
- Glass and Time, IMFUFA, Roskilde University, Roskilde DK-4000, Denmark
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Stones AE, Dullens RPA, Aarts DGAL. Communication: Contact values of pair distribution functions in colloidal hard disks by test-particle insertion. J Chem Phys 2018; 148:241102. [PMID: 29960354 DOI: 10.1063/1.5038668] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
We apply Henderson's method for measuring the cavity distribution function y(r) [J. Henderson, Mol. Phys. 48, 389 (1983)] to obtain the pair distribution function at contact, g(σ+). In contrast to the conventional distance-histogram method, no approximate extrapolation to contact is required. The resulting equation of state from experiments and simulations of hard disks agrees well with the scaled particle theory prediction up to high fluid packing fractions. We also provide the first experimental measurement of y(r) inside the hard core, which will allow for a more complete comparison with theory. The method's flexibility is further illustrated by measuring the partial pair distribution functions of binary hard-disk mixtures in simulation. The equation for the contact values can be used to derive familiar results from statistical geometry.
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Affiliation(s)
- Adam Edward Stones
- Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Roel P A Dullens
- Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Dirk G A L Aarts
- Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, United Kingdom
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Belloni L. Exact molecular direct, cavity, and bridge functions in water system. J Chem Phys 2018; 147:164121. [PMID: 29096488 DOI: 10.1063/1.5001684] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
The exact molecular bridge function of the extended simple point charge model of liquid water at room temperature is extracted from Monte Carlo (MC) simulation data. The projections gμνmnl(r) onto rotational invariants of the highly directional pair distribution function g(r,Ω) are accumulated during simulation performed with N = 512 molecules (cubic box size L ≈ 25 Å). Making intensive use of anisotropic integral equation techniques, the molecular Ornstein-Zernike equation fed with the MC data available at short distances and completed beyond L/2 with the hypernetted chain closure valid at long distances is then inverted in order to derive on the whole r range the direct correlation function cμνmnl(r), the cavity function yμνmnl(r), the negative excess potential of mean force lnyμνmnl(r), and, finally, the holy grail in such liquid state theory, the bridge function bμνmnl(r) projections. For completeness, the short distance domain inside the soft core can be reached, thanks to the use of a specially designed anisotropic finite potential which replaces the true one between a single pair of molecules in the simulation. The final bridge function b(r,Ω) of bulk water presents strong, non-universal directional features and can now serve as a reference for approximated bridge functions or functionals in liquid physics of aqueous solvents and solutions.
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Affiliation(s)
- Luc Belloni
- LIONS, NIMBE, CEA, CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
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5
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Belloni L, Puibasset J. Finite-size corrections in simulation of dipolar fluids. J Chem Phys 2017; 147:224110. [DOI: 10.1063/1.5005912] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Luc Belloni
- LIONS, NIMBE, CEA, CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| | - Joël Puibasset
- ICMN, UMR 7374, CNRS et Université d’Orléans, 1B Rue de la Férollerie, 45071 Orléans Cedex, France
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Vyalov I, Chuev G, Georgi N. Solute-solvent cavity and bridge functions. I. Varying size of the solute. J Chem Phys 2014; 141:074505. [PMID: 25149799 DOI: 10.1063/1.4892876] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Affiliation(s)
- I Vyalov
- Max-Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig 04103, Germany
| | - G Chuev
- Max-Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig 04103, Germany
| | - N Georgi
- Max-Planck Institute for Mathematics in the Sciences, Inselstrasse 22, Leipzig 04103, Germany
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Wu L, Müller EA, Jackson G. Understanding and Describing the Liquid-Crystalline States of Polypeptide Solutions: A Coarse-Grained Model of PBLG in DMF. Macromolecules 2014. [DOI: 10.1021/ma401230x] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Liang Wu
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Erich A. Müller
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - George Jackson
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
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8
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Zhao S, Liu H, Ramirez R, Borgis D. Accurate evaluation of the angular-dependent direct correlation function of water. J Chem Phys 2013; 139:034503. [DOI: 10.1063/1.4813400] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
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9
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Wu L, Wensink H, Jackson G, Müller E. A generic equation of state for liquid crystalline phases of hard-oblate particles. Mol Phys 2012. [DOI: 10.1080/00268976.2011.649794] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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You XM, Vlasov AY, Anton L, Masters AJ. Isotropic and nematic phases of the hard spheroid fluid: a virial approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:061706. [PMID: 23005113 DOI: 10.1103/physreve.85.061706] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2012] [Indexed: 06/01/2023]
Abstract
We use a high level virial expansion to investigate the properties of the isotropic and nematic phases of the hard spheroid fluid. We use the Monte Carlo techniques described previously to calculate the virial coefficients up to seventh order and we represent the dependence of these coefficients on particle orientations via a spherical harmonic expansion. The expansion coefficients are determined using Lebedev quadrature which carries out the angular integration required exactly. For fairly spherical spheroids (1/3<a/b<3, where a and b are the semiaxes of the spheroid) the virial expansion appears to be convergent in both the isotropic and nematic phases up to high density. For more aspherical particles, the predictions varied in a more erratic fashion upon increasing the number of virials. The use of a finite angular basis set to represent the orientationally dependent virial coefficients could be a contributory cause to this.
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Affiliation(s)
- X-M You
- School of Chemical Engineering and Analytical Science, University of Manchester, Manchester M13 9PL, United Kingdom
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11
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Puibasset J, Belloni L. Bridge function for the dipolar fluid from simulation. J Chem Phys 2012; 136:154503. [DOI: 10.1063/1.4703899] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Dennison M, J. Masters A, L. Cheung D, P. Allen M. Calculation of direct correlation function for hard particles using a virial expansion. Mol Phys 2010. [DOI: 10.1080/00268970902784934] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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13
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Reich H, Schmidt M. Sedimentation equilibrium of colloidal platelets in an aligning magnetic field. J Chem Phys 2010; 132:144509. [DOI: 10.1063/1.3378264] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Singh RC, Singh BM, Ram J. The Percus-Yevick approximation for quadrupolar molecular fluids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:115101. [PMID: 21693907 DOI: 10.1088/0953-8984/21/11/115101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The Percus-Yevick integral equation theory has been solved to study the equilibrium and structural properties of quadrupolar Gay-Berne fluids. 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 l indices up to less than or equal to 6 have been considered. Molecules with length-to-breadth ratios 3.0 and 4.0 have been considered and results are reported for different densities, temperatures, and quadrupole moments. The values of pair correlation functions have been compared with the available computer simulation results.
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Affiliation(s)
- Ram Chandra Singh
- Department of Physics, Hindustan Institute of Technology, 32,34 Knowledge Park III, Greater Noida 201306, India
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Cheung DL, Anton L, Allen MP, Masters AJ, Phillips J, Schmidt M. Structure and stability of isotropic states of hard platelet fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:041201. [PMID: 18999406 DOI: 10.1103/physreve.78.041201] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2008] [Indexed: 05/27/2023]
Abstract
We study the thermodynamics and the pair structure of hard, infinitely thin, circular platelets in the isotropic phase. Monte Carlo simulation results indicate a rich spatial structure of the spherical expansion components of the direct correlation function, including nonmonotonical variation of some of the components with density. Integral equation theory is shown to reproduce the main features observed in simulations. The hypernetted chain closure, as well as its extended versions that include the bridge function up to second and third order in density, perform better than both the Percus-Yevick closure and Verlet bridge function approximation. Using a recent fundamental measure density functional theory, an analytic expression for the direct correlation function is obtained as the sum of the Mayer bond and a term proportional to the density and the intersection length of two platelets. This is shown to give a reasonable estimate of the structure found in simulations, but to fail to capture the nonmonotonic variation with density. We also carry out a density functional stability analysis of the isotropic phase with respect to nematic ordering and show that the limiting density is consistent with that where the Kerr coefficient vanishes. As a reference system, we compare to simulation results for hard oblate spheroids with small, but nonzero elongations, demonstrating that the case of vanishingly thin platelets is approached smoothly.
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Affiliation(s)
- David L Cheung
- Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom.
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Cheung DL, Anton L, Allen MP, Masters AJ. Structure of molecular liquids: hard rod-disk mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:011202. [PMID: 18351843 DOI: 10.1103/physreve.77.011202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2007] [Indexed: 05/26/2023]
Abstract
The structure of hard rod-disk mixtures is studied using Monte Carlo simulations and integral equation theory, for a range of densities in the isotropic phase. By extension of methods used in single component fluids, the pair correlation functions of the molecules are calculated and comparisons between simulation and integral equation theory, using a number of different closure relations, are made. Comparison is also made for thermodynamic data and phase behavior.
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Affiliation(s)
- David L Cheung
- Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom
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18
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Cheung DL, Anton L, Allen MP, Masters AJ. Structure of molecular liquids: closure relations for hard spheroids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:041201. [PMID: 17994971 DOI: 10.1103/physreve.76.041201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2007] [Indexed: 05/25/2023]
Abstract
We present the results of Monte Carlo simulations of hard spheroids of revolution of different elongations. Both prolate and oblate shapes are examined. A systematic study of the bridge function b(1,2), and direct comparison with the indirect correlation function gamma(1,2)=h(1,2)-c(1,2) at densities spanning the isotropic fluid range, allow us to evaluate the accuracy of various proposed closure relations for integral equations.
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Affiliation(s)
- David L Cheung
- Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom.
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Mishra P, Singh SL, Ram J, Singh Y. Pair correlation functions and a free energy functional for the nematic phase. J Chem Phys 2007; 127:044905. [PMID: 17672723 DOI: 10.1063/1.2752170] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
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 a 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(x1,x2) 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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Affiliation(s)
- Pankaj Mishra
- Department of Physics, Banaras Hindu University, Varanasi-221 005, India
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