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Pieprzyk S, Yuste SB, Santos A, de Haro ML, Brańka AC. Structural properties of additive binary hard-sphere mixtures. III. Direct correlation functions. Phys Rev E 2021; 104:054142. [PMID: 34942716 DOI: 10.1103/physreve.104.054142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2021] [Accepted: 11/17/2021] [Indexed: 11/07/2022]
Abstract
An analysis of the direct correlation functions c_{ij}(r) of binary additive hard-sphere mixtures of diameters σ_{s} and σ_{b} (where the subscripts s and b refer to the "small" and "big" spheres, respectively), as obtained with the rational-function approximation method and the WM scheme introduced in previous work [S. Pieprzyk et al., Phys. Rev. E 101, 012117 (2020)2470-004510.1103/PhysRevE.101.012117], is performed. The results indicate that the functions c_{ss}(r<σ_{s}) and c_{bb}(r<σ_{b}) in both approaches are monotonic and can be well represented by a low-order polynomial, while the function c_{sb}(r<1/2(σ_{b}+σ_{s})) is not monotonic and exhibits a well-defined minimum near r=1/2(σ_{b}-σ_{s}), whose properties are studied in detail. Additionally, we show that the second derivative c_{sb}^{''}(r) presents a jump discontinuity at r=1/2(σ_{b}-σ_{s}) whose magnitude satisfies the same relationship with the contact values of the radial distribution function as in the Percus-Yevick theory.
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Affiliation(s)
- Sławomir Pieprzyk
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
| | - Santos B Yuste
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, Badajoz, E-06006, Spain
| | - Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, Badajoz, E-06006, Spain
| | - Mariano López de Haro
- Instituto de Energías Renovables, Universidad Nacional Autónoma de México (U.N.A.M.), Temixco, Morelos 62580, Mexico
| | - Arkadiusz C Brańka
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
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Pieprzyk S, Yuste SB, Santos A, de Haro ML, Brańka AC. Structural properties of additive binary hard-sphere mixtures. II. Asymptotic behavior and structural crossovers. Phys Rev E 2021; 104:024128. [PMID: 34525547 DOI: 10.1103/physreve.104.024128] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2021] [Accepted: 08/02/2021] [Indexed: 11/07/2022]
Abstract
The structural properties of additive binary hard-sphere mixtures are addressed as a follow-up of a previous paper [S. Pieprzyk et al., Phys. Rev. E 101, 012117 (2020)]2470-004510.1103/PhysRevE.101.012117. The so-called rational-function approximation method and an approach combining accurate molecular dynamics simulation data, the pole structure representation of the total correlation functions, and the Ornstein-Zernike equation are considered. The density, composition, and size-ratio dependencies of the leading poles of the Fourier transforms of the total correlation functions h_{ij}(r) of such mixtures are presented, those poles accounting for the asymptotic decay of h_{ij}(r) for large r. Structural crossovers, in which the asymptotic wavelength of the oscillations of the total correlation functions changes discontinuously, are investigated. The behavior of the structural crossover lines as the size ratio and densities of the two species are changed is also discussed.
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Affiliation(s)
- Sławomir Pieprzyk
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
| | - Santos B Yuste
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, Badajoz E-06006, Spain
| | - Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, Badajoz E-06006, Spain
| | - Mariano López de Haro
- Instituto de Energías Renovables, Universidad Nacional Autónoma de México (U.N.A.M.), Temixco, Morelos 62580, Mexico
| | - Arkadiusz C Brańka
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
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Santos A, Yuste SB, López de Haro M. Structural and thermodynamic properties of hard-sphere fluids. J Chem Phys 2020; 153:120901. [PMID: 33003724 DOI: 10.1063/5.0023903] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
This Perspective article provides an overview of some of our analytical approaches to the computation of the structural and thermodynamic properties of single-component and multicomponent hard-sphere fluids. For the structural properties, they yield a thermodynamically consistent formulation, thus improving and extending the known analytical results of the Percus-Yevick theory. Approximate expressions linking the equation of state of the single-component fluid to the one of the multicomponent mixtures are also discussed.
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Affiliation(s)
- Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, Badajoz E-06006, Spain
| | - Santos B Yuste
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, Badajoz E-06006, Spain
| | - Mariano López de Haro
- Instituto de Energías Renovables, Universidad Nacional Autónoma de México (U.N.A.M.), Temixco, Morelos 62580, Mexico
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Zhou Y, Mei B, Schweizer KS. Integral equation theory of thermodynamics, pair structure, and growing static length scale in metastable hard sphere and Weeks-Chandler-Andersen fluids. Phys Rev E 2020; 101:042121. [PMID: 32422713 DOI: 10.1103/physreve.101.042121] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2020] [Accepted: 03/24/2020] [Indexed: 06/11/2023]
Abstract
We employ the Ornstein-Zernike integral equation theory with the Percus-Yevick (PY) and modified-Verlet (MV) closures to study the equilibrium structural and thermodynamic properties of metastable monodisperse hard sphere and continuous repulsion Weeks-Chandler-Andersen (WCA) fluids under density and temperature conditions where the system is strongly overcompressed or supercooled, respectively. The theoretical results are compared to crystal-avoiding simulations of these dense monodisperse model one-component fluids. The equation of state (EOS) and dimensionless compressibility are computed using both the virial and compressibility routes. For hard spheres, the MV-based virial route EOS and dimensionless compressibility are in very good agreement with simulation for all packing fractions, much better than the PY analogs. The corresponding MV-based predictions for the static structure factor are also very good. The amplitude of density fluctuations on the local cage scale and in the long wavelength limit, and three technically different measures of the density correlation length, are studied with both closures. All five properties grow in a roughly exponential manner with density in the metastable regime up to packing fractions of 58% with no sign of saturation. The MV-based results are in good agreement with our crystal-avoiding simulations. Interestingly, the density dependences of long and short wavelength quantities are closely related. The MV-based theory is also quite accurate for the thermodynamics and structure of supercooled monodisperse WCA fluids. Overall our findings are also relevant as critical input to microscopic theories that relate the equilibrium pair correlation function or static structure factor to dynamical constraints, barriers, and activated relaxation in glass-forming liquids.
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Affiliation(s)
- Yuxing Zhou
- Department of Material Science and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Baicheng Mei
- Department of Material Science and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Kenneth S Schweizer
- Department of Material Science and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Department of Chemistry and Department of Chemical & Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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Coquand O, Sperl M. Temperature expansions in the square-shoulder fluid. I. The Wiener–Hopf function. J Chem Phys 2020; 152:124112. [DOI: 10.1063/1.5142661] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Affiliation(s)
- O. Coquand
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany
| | - M. Sperl
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany
- Institut für Theoretische Physik, Universität zu Köln, 50937 Köln, Germany
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Pieprzyk S, Brańka AC, Yuste SB, Santos A, de Haro ML. Structural properties of additive binary hard-sphere mixtures. Phys Rev E 2020; 101:012117. [PMID: 32069599 DOI: 10.1103/physreve.101.012117] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2019] [Indexed: 11/07/2022]
Abstract
An approach to obtain the structural properties of additive binary hard-sphere mixtures is presented. Such an approach, which is a nontrivial generalization of the one recently used for monocomponent hard-sphere fluids [S. Pieprzyk, A. C. Brańka, and D. M. Heyes, Phys. Rev. E 95, 062104 (2017)2470-004510.1103/PhysRevE.95.062104], combines accurate molecular-dynamics simulation data, the pole structure representation of the total correlation functions, and the Ornstein-Zernike equation. A comparison of the direct correlation functions obtained with the present scheme with those derived from theoretical results stemming from the Percus-Yevick (PY) closure and the so-called rational-function approximation (RFA) is performed. The density dependence of the leading poles of the Fourier transforms of the total correlation functions and the decay of the pair correlation functions of the mixtures are also addressed and compared to the predictions of the two theoretical approximations. A very good overall agreement between the results of the present scheme and those of the RFA is found, thus suggesting that the latter (which is an improvement over the PY approximation) can safely be used to predict reasonably well the long-range behavior, including the structural crossover, of the correlation functions of additive binary hard-sphere mixtures.
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Affiliation(s)
- S Pieprzyk
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
| | - A C Brańka
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
| | - S B Yuste
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, Badajoz E-06006, Spain
| | - A Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, Badajoz E-06006, Spain
| | - M López de Haro
- Instituto de Energías Renovables, Universidad Nacional Autónoma de México (U.N.A.M.), Temixco, Morelos 62580, Mexico
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de Haro ML, Rodríguez-Rivas Á, Yuste SB, Santos A. Structural properties of the Jagla fluid. Phys Rev E 2018; 98:012138. [PMID: 30110748 DOI: 10.1103/physreve.98.012138] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2018] [Indexed: 06/08/2023]
Abstract
The structural properties of the Jagla fluid are studied by Monte Carlo (MC) simulations, numerical solutions of integral equation theories, and the (semi-analytical) rational-function approximation (RFA) method. In the latter case, the results are obtained from the assumption (supported by our MC simulations) that the Jagla potential and a potential with a hard core plus an appropriate piecewise constant function lead to practically the same cavity function. The predictions obtained for the radial distribution function, g(r), from this approach are compared against MC simulations and integral equations for the Jagla model, and also for the limiting cases of the triangle-well potential and the ramp potential, with a general good agreement. The analytical form of the RFA in Laplace space allows us to describe the asymptotic behavior of g(r) in a clean way and compare it with MC simulations for representative states with oscillatory or monotonic decay. The RFA predictions for the Fisher-Widom and Widom lines of the Jagla fluid are obtained.
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Affiliation(s)
- Mariano López de Haro
- Instituto de Energías Renovables, Universidad Nacional Autónoma de México (U.N.A.M.), Temixco, Morelos 62580, Mexico
| | - Álvaro Rodríguez-Rivas
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, Badajoz E-06006, Spain
| | - Santos B Yuste
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, Badajoz E-06006, Spain
| | - Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, Badajoz E-06006, Spain
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