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Zhou S, Solana JR. Integral equation theories for fluid with very short-range screened Coulomb plus power series interactions. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2157344] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- S. Zhou
- School of Physics and Electronics, Central South University, Changsha, People’s Republic of China
| | - J. R. Solana
- Departamento de Física Aplicada, Universidad de Cantabria Santander, España
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Affiliation(s)
- B. P. Akhouri
- Department of Physics, Suraj Singh Memorial College, Ranchi, Jharkhand, India
| | - J. R. Solana
- Department of Applied Physics, University of Cantabria, Santander, Spain
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Akhouri BP, Solana JR. Monte Carlo simulation and theoretical calculation of the thermodynamic properties of binary hard-core Lennard-Jones fluid mixtures. Molecular Simulation 2020. [DOI: 10.1080/08927022.2020.1806264] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- B. P. Akhouri
- Department of Physics, Birsa College, Khunti, Jharkhand, India
| | - J. R. Solana
- Department of Applied Physics, University of Cantabria, Santander, Spain
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Affiliation(s)
| | - J. R. Solana
- Department of Applied Physics, University of Cantabria, Santander, Spain
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Solana JR, Akhouri BP. The role of higher-order terms in perturbation approaches to the monomer and bonding contributions in a SAFT-type equation of state for square-well chain fluids. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1444802] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- J. R. Solana
- Departamento de Física Aplicada, Universidad de Cantabria, Santander, Spain
| | - B. P. Akhouri
- Department of Physics, Birsa College, Khunti, Jharkhand, India
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Zhou S, Solana JR. Thermodynamic properties of fluids with Lennard–Jones–Gauss potential from computer simulation and the coupling parameter series expansion. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1406162] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- S. Zhou
- School of Physics and Electronics, Central South University, Changsha, Hunan, China
| | - J. R. Solana
- Departamento De Física Aplicada, Universidad de Cantabria, Santander, Spain
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Largo J, Solana JR. Thermodynamic properties of a hard-core Lennard-Jones fluid from computer simulation and the coupling parameter series expansion. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1154618] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- J. Largo
- Departamento de Física Aplicada, Universidad de Cantabria, Santander, Spain
| | - J. R. Solana
- Departamento de Física Aplicada, Universidad de Cantabria, Santander, Spain
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Zhou S, Solana JR. Excellence of numerical differentiation method in calculating the coefficients of high temperature series expansion of the free energy and convergence problem of the expansion. J Chem Phys 2015; 141:244506. [PMID: 25554166 DOI: 10.1063/1.4904881] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, it is shown that the numerical differentiation method in performing the coupling parameter series expansion [S. Zhou, J. Chem. Phys. 125, 144518 (2006); AIP Adv. 1, 040703 (2011)] excels at calculating the coefficients ai of hard sphere high temperature series expansion (HS-HTSE) of the free energy. Both canonical ensemble and isothermal-isobaric ensemble Monte Carlo simulations for fluid interacting through a hard sphere attractive Yukawa (HSAY) potential with extremely short ranges and at very low temperatures are performed, and the resulting two sets of data of thermodynamic properties are in excellent agreement with each other, and well qualified to be used for assessing convergence of the HS-HTSE for the HSAY fluid. Results of valuation are that (i) by referring to the results of a hard sphere square well fluid [S. Zhou, J. Chem. Phys. 139, 124111 (2013)], it is found that existence of partial sum limit of the high temperature series expansion series and consistency between the limit value and the true solution depend on both the potential shapes and temperatures considered. (ii) For the extremely short range HSAY potential, the HS-HTSE coefficients ai falls rapidly with the order i, and the HS-HTSE converges from fourth order; however, it does not converge exactly to the true solution at reduced temperatures lower than 0.5, wherein difference between the partial sum limit of the HS-HTSE series and the simulation result tends to become more evident. Something worth mentioning is that before the convergence order is reached, the preceding truncation is always improved by the succeeding one, and the fourth- and higher-order truncations give the most dependable and qualitatively always correct thermodynamic results for the HSAY fluid even at low reduced temperatures to 0.25.
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Affiliation(s)
- S Zhou
- School of Physics and Electronics, Central South University, Changsha, Hunan 410083, China
| | - J R Solana
- Departamento de Física Aplicada, Universidad de Cantabria, 39005 Santander, Spain
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Zhou S, Solana JR. The First Three Coefficients in the High Temperature Series Expansion of Free Energy for Simple Potential Models with Hard-Sphere Cores and Continuous Tails. J Phys Chem B 2013; 117:9305-13. [DOI: 10.1021/jp405406f] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Shiqi Zhou
- School of Physics and Electronics, Central South University, Changsha, Hunan, 410083, People’s
Republic of China
| | - J. R. Solana
- Departamento
de Física Aplicada, Universidad de Cantabria, 39005 Santander, España
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Zhou S, Solana JR. Publisher's Note: “Monte Carlo and theoretical calculations of the first four perturbation coefficients in the high temperature series expansion of the free energy for discrete and core-softened potential models” [J. Chem. Phys. 138, 244115 (2013)]. J Chem Phys 2013. [DOI: 10.1063/1.4816674] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Zhou S, Solana JR. Monte Carlo and theoretical calculations of the first four perturbation coefficients in the high temperature series expansion of the free energy for discrete and core-softened potential models. J Chem Phys 2013; 138:244115. [DOI: 10.1063/1.4811285] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Affiliation(s)
- Shiqi Zhou
- State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, China.
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Zhou S, Solana JR. Comprehensive investigation about the second order term of thermodynamic perturbation expansion. J Chem Phys 2009; 131:134106. [DOI: 10.1063/1.3242801] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Affiliation(s)
- Shiqi Zhou
- State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, China, and School of Physics Science and Technology, Central South University, Changsha, Hunan 410083, China
| | - J. R. Solana
- Applied Physics Department, University of Cantabria, 39005 Santander, Spain
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Zhou S, Solana JR. Third-order thermodynamic perturbation theory for effective potentials that model complex fluids. Phys Rev E Stat Nonlin Soft Matter Phys 2008; 78:021503. [PMID: 18850837 DOI: 10.1103/physreve.78.021503] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2008] [Revised: 06/23/2008] [Indexed: 05/26/2023]
Abstract
We have performed Monte Carlo simulations to obtain the thermodynamic properties of fluids with two kinds of hard-core plus attractive-tail or oscillatory potentials. One of them is the square-well potential with small well width. The other is a model potential with oscillatory and decaying tail. Both model potentials are suitable for modeling the effective potential arising in complex fluids and fluid mixtures with extremely-large-size asymmetry, as is the case of the solvent-induced depletion interactions in colloidal dispersions. For the former potential, the compressibility factor, the excess energy, the constant-volume excess heat capacity, and the chemical potential have been obtained. For the second model potential only the first two of these quantities have been obtained. The simulations cover the whole density range for the fluid phase and several temperatures. These simulation data have been used to test the performance of a third-order thermodynamic perturbation theory (TPT) recently developed by one of us [S. Zhou, Phys. Rev. E 74, 031119 (2006)] as compared with the well-known second-order TPT based on the macroscopic compressibility approximation due to Barker and Henderson. It is found that the first of these theories provides much better accuracy than the second one for all thermodynamic properties analyzed for the two effective potential models.
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Affiliation(s)
- Shiqi Zhou
- School of Physics Science and Technology, Central South University, Changsha, Hunan, 410083, China.
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Díez A, Largo J, Solana JR. Thermodynamic properties of model solids with short-ranged potentials from Monte Carlo simulations and perturbation theory. J Phys Chem B 2007; 111:10194-201. [PMID: 17683133 DOI: 10.1021/jp072059z] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Monte Carlo simulations have been performed to determine the excess energy and the equation of state of fcc solids with Sutherland potentials for wide ranges of temperatures, densities, and effective potential ranges. The same quantities have been determined within a perturbative scheme by means of two procedures: (i) Monte Carlo simulations performed on the reference hard-sphere system and (ii) second-order Barker-Henderson perturbation theory. The aim was twofold: on the one hand, to test the capability of the "exact" MC-perturbation theory of reproducing the direct MC simulations and, on the other hand, the reliability of the Barker-Henderson perturbation theory, as compared with direct MC simulations and MC-perturbation theory, to determine the thermodynamic properties of these solids depending on temperature, density, and potential range. We have found that the simulation data for the excess energy obtained from the two procedures are in close agreement with each other. For the equation of state, the results from the MC-perturbation procedure also agree well with the direct MC simulations except for very low temperatures and extremely short-ranged potentials. Regarding the Barker-Henderson perturbation theory, we have found that in general the second-order approximation does not provide significant improvement over the first-order one.
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Affiliation(s)
- A Díez
- Departamento de Física Aplicada, Universidad de Cantabria, E-39005 Santander, Spain
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Díez A, Largo J, Solana JR. Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory. J Chem Phys 2006; 125:074509. [PMID: 16942353 DOI: 10.1063/1.2217944] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.
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Affiliation(s)
- A Díez
- Departamento de Física Aplicada, Universidad de Cantabria, E-39005 Santander, Spain
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Abstract
We have performed extensive Monte Carlo simulations in the canonical (NVT) ensemble of the pair correlation function for square-well fluids with well widths lambda-1 ranging from 0.1 to 1.0, in units of the diameter sigma of the particles. For each one of these widths, several densities rho and temperatures T in the ranges 0.1< or =rhosigma(3)< or =0.8 and T(c)(lambda) less or approximately T less or approximately 3T(c)(lambda), where T(c)(lambda) is the critical temperature, have been considered. The simulation data are used to examine the performance of two analytical theories in predicting the structure of these fluids: the perturbation theory proposed by Tang and Lu [Y. Tang and B. C.-Y. Lu, J. Chem. Phys. 100, 3079 (1994); 100, 6665 (1994)] and the nonperturbative model proposed by two of us [S. B. Yuste and A. Santos, J. Chem. Phys. 101 2355 (1994)]. It is observed that both theories complement each other, as the latter theory works well for short ranges and/or moderate densities, while the former theory works for long ranges and high densities.
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Affiliation(s)
- J Largo
- Departamento de Física Aplicada, Universidad de Cantabria, E-39005 Santander, Spain.
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Largo J, Maeso MJ, Solana JR, Vega C, MacDowell LG. Bonded hard-sphere theory and computer simulation of the equation of state of linear fused–hard-sphere fluids. J Chem Phys 2003. [DOI: 10.1063/1.1615964] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Barrio C, Solana JR. Contact pair correlation functions of binary mixtures of additive hard spheres from the virial expansion. J Chem Phys 2003. [DOI: 10.1063/1.1591718] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
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Largo J, Solana JR. Generalized van der Waals theory for the thermodynamic properties of square-well fluids. Phys Rev E Stat Nonlin Soft Matter Phys 2003; 67:066112. [PMID: 16241309 DOI: 10.1103/physreve.67.066112] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2003] [Indexed: 05/04/2023]
Abstract
A theory previously developed for the coordination number of square-well fluids is used within the context of a generalized van der Waals theory to obtain the compressibility factor and the internal energy of these fluids. Results are compared with computer simulations for several densities, temperatures, and potential widths, which are also reported.
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Affiliation(s)
- J Largo
- Departamento de Física Aplicada, Universidad de Cantabria, Santander, Spain
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Barrio C, Solana JR. Erratum: “Contact pair correlation functions and equation of state for additive hard disk fluid mixtures” [J. Chem. Phys. 115, 7123 (2001)]. J Chem Phys 2002. [DOI: 10.1063/1.1487372] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Barrio C, Solana JR. Theory and computer simulation for the equation of state of additive hard-disk fluid mixtures. Phys Rev E Stat Nonlin Soft Matter Phys 2001; 63:011201. [PMID: 11304240 DOI: 10.1103/physreve.63.011201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2000] [Indexed: 05/23/2023]
Abstract
A procedure previously developed by the authors to obtain the equation of state for a mixture of additive hard spheres on the basis of a pure fluid equation of state is applied here to a binary mixture of additive hard disks in two dimensions. The equation of state depends on two parameters which are determined from the second and third virial coefficients for the mixture, which are known exactly. Results are compared with Monte Carlo calculations which are also reported. The agreement between theory and simulation is very good. For the fourth and fifth virial coefficients of the mixture, the equation of state gives results which are also in close agreement with exact numerical values reported in the literature.
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Affiliation(s)
- C Barrio
- Departamento de Física Aplicada, Universidad de Cantabria, 39005 Santander, Spain
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Maeso MJ, Solana JR. Equation of state for hard convex body fluids from the equation of state of the hard sphere fluid. J Chem Phys 1994. [DOI: 10.1063/1.466404] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Maeso MJ, Solana JR. Instabilities in the equations of state of hard‐disk and hard‐sphere fluids from the virial expansions. J Chem Phys 1993. [DOI: 10.1063/1.465779] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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