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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] [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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Khanpour M. Variants of the optimised random phase approximation: from one direct correlation function to many different radial distribution functions. Mol Phys 2020. [DOI: 10.1080/00268976.2019.1678774] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Mehrdad Khanpour
- Department of Chemistry, Amol Branch, Islamic Azad University, Amol, Iran
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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] [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] [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. Convergence and low temperature adaptability analysis of the high temperature series expansion of the free energy. J Chem Phys 2014; 139:124111. [PMID: 24089754 DOI: 10.1063/1.4821762] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By appealing to the coupling parameter series expansion to calculate the first seven perturbation coefficients of the high temperature series expansion (HTSE) of the free energy, analysis of convergence and low temperature adaptability of the HTSE in calculating fluid thermodynamic properties is performed for the first time; the fluid thermodynamic properties considered include critical parameters, vapor-liquid coexistence curve, thermodynamic characteristic functions, chemical potential, pressure, and constant volume excess heat capacity. To proceed with the analysis, a well known square well model is used as sample; the well widths considered range over a wide interval, and the relevant temperatures amenable to simulation calculations (used as "exact" results to analyze the HTSE) can be both very high and very low. The main discoveries reached are summarized as follows: (1) The HTSE usually converges at the 4th-order truncation, but with decrease of the temperature considered, the lowest truncation order, which makes the HTSE to converge, tends to rise. As a conservative estimate, it is considered that the HTSE always converges for reduced temperature T* higher than 0.25, whereas for T* < 0.25 there appear signs indicating that the HTSE may diverge from the 7th-order truncation. (2) Within the temperature interval with T* ≥ 0.5, the HTSE converges approximately to the correct solution, and the HTSE can be reliably used to calculate the fluid thermodynamic properties, and within this temperature interval, the 4th-order truncation is enough; whereas for T* < 0.5, such as within the temperature interval with 0.275 ≤ T* ≤ 0.355, although the HTSE does converge, it does not converge to the correct solution, and the deviations between the HTSE calculations and MC simulations become an ever-prominent issue with the rising of the density, and the slopes of the thermodynamic properties over density are not satisfactorily represented. As a result, the HTSE is not suited for calculations for temperature interval T* < 0.5.
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Affiliation(s)
- Shiqi Zhou
- School of Physics and Electronics, Central South University, Changsha, Hunan 410083, China
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Khanpour M. A new analytical approximation for the second term in the thermodynamic perturbation theory of simple hard-core fluids. J Mol Liq 2014. [DOI: 10.1016/j.molliq.2013.11.025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Lafitte T, Apostolakou A, Avendaño C, Galindo A, Adjiman CS, Müller EA, Jackson G. Accurate statistical associating fluid theory for chain molecules formed from Mie segments. J Chem Phys 2013; 139:154504. [DOI: 10.1063/1.4819786] [Citation(s) in RCA: 304] [Impact Index Per Article: 27.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
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D’Agostino T, Solana JR, Emanuele A. Prediction of thermodynamic instabilities of protein solutions from simple protein–protein interactions. Chem Phys 2013. [DOI: 10.1016/j.chemphys.2013.01.041] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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9
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Ramana ASV. Generalized coupling parameter expansion: Application to square well and Lennard-Jones fluids. J Chem Phys 2013; 139:044106. [DOI: 10.1063/1.4813797] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [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] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chapela GA, del Río F, Alejandre J. Liquid-vapor phase diagram and surface properties in oppositely charged colloids represented by a mixture of attractive and repulsive Yukawa potentials. J Chem Phys 2013; 138:054507. [PMID: 23406133 DOI: 10.1063/1.4789915] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
The liquid-vapor phase diagrams of equal size diameter σ binary mixtures of screened potentials have been reported for several ranges of interaction using Monte Carlo simulation methods [J. B. Caballero, A. M. Puertas, A. Ferńandez-Barbero, F. J. de las Nieves, J. M. Romero-Enrique, and L. F. Rull, J. Chem. Phys. 124, 054909 (2006); A. Fortini, A.-P. Hynninen, and M. Dijkstra, J. Chem. Phys. 125, 094502 (2006)]. Both works report controversial results about the stability of the phase diagram with the inverse Debye screening length κ. Caballero found stability for values of κσ up to 20 while Fortini reported stability for κσ up to 20 while Fortini reported stability for κσ ≤ 4. In this work a spinodal decomposition process where the liquid and vapor phases coexist through an interface in a slab geometry is used to obtain the phase equilibrium and surface properties using a discontinuous molecular dynamics simulations for mixtures of equal size particles carrying opposite charge and interacting with a mixture of attractive and repulsive Yukawa potentials at different values of κσ. An crude estimation of the triple point temperatures is also reported. The isothermal-isobaric method was also used to determine the phase stability using one phase simulations. We found that liquid-vapor coexistence is stable for values of κσ > 20 and that the critical temperatures have a maximum value at around κσ = 10, in agreement with Caballero et al. calculations. There also exists a controversy about the liquid-vapor envelope stability of the pure component attractive Yukawa model which is also discussed in the text. In addition, details about the equivalence between continuous and discontinuous molecular dynamics simulations are given, in the Appendix, for Yukawa and Lennard-Jones potentials.
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Affiliation(s)
- Gustavo A Chapela
- Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 México D.F., México.
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González-Melchor M, Hernández-Cocoletzi G, López-Lemus J, Ortega-Rodríguez A, Orea P. Interfacial and coexistence properties of soft spheres with a short-range attractive Yukawa fluid: Molecular dynamics simulations. J Chem Phys 2012; 136:154702. [DOI: 10.1063/1.3703507] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
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Khanpour M. Comment on “Structure and thermodynamics of hard-core Yukawa fluids: Thermodynamic perturbation approaches” [J. Chem. Phys, 135, 034505 (2011)]. J Chem Phys 2012; 136:047101. [DOI: 10.1063/1.3678583] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Kim EY, Kim SC, Seong BS. Structure and thermodynamics of hard-core Yukawa fluids: thermodynamic perturbation approaches. J Chem Phys 2011; 135:034505. [PMID: 21787011 DOI: 10.1063/1.3610400] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The thermodynamic perturbation theories, which are based on the power series of a coupling constant (λ-expansion), have been proposed for studying the structural and thermodynamic properties of a hard-core Yukawa (HCY) fluid: one (A1-approximation) is the perturbation theory based on the hard-sphere repulsion as a reference system. The other (A2-approximation) is the perturbation theory based on the reference system which incorporates both the repulsive and short-range attractive interactions. The first-order mean-spherical approximation (FMSA) provided by Tang and Lu [J. Chem. Phys. 99, 9828 (1993)] has been employed for investigating the thermodynamic properties of a HCY fluid using the alternative method via the direct correlation function. The calculated results show that (i) the A1 and A2 approximations are in excellent agreements with previous computer simulation results in the literature and compare with the semi-empirical works of Shukla including the higher-order free energy terms, (ii) the A1 and A2 approximations are better than the FMSA and the mean-spherical approximation, (iii) the A2-approximation compares with the A1-approximation, even though the perturbation effect of an A2-approximation is much smaller than that of an A1-approximation, and that (iv) the FMSA study is particularly of advantage in providing the structure and thermodynamics in a simple and analytic manner.
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Affiliation(s)
- Eun-Young Kim
- Department of Physics, Kyungpook National University, Taegu 702-701, Korea
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Khanpour M. Perturbation theory of liquids for short-ranged hard-core potentials: structure and thermodynamics of short-ranged square-well fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:021203. [PMID: 21405836 DOI: 10.1103/physreve.83.021203] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2010] [Revised: 11/01/2010] [Indexed: 05/30/2023]
Abstract
A new method is devised to derive a thermodynamic perturbation theory that is suitable for short-ranged potentials. We have calculated structure and thermodynamic of short-ranged square-well potential with good agreement with computer simulation data even at low temperatures. We have also compared the results with other perturbation theories. It is found that the proposed theory gives better results when used to compute the structure and thermodynamic of short-ranged hard-core potentials.
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Affiliation(s)
- Mehrdad Khanpour
- Department of Chemistry, Islamic Azad University, Amol Branch, Amol, Iran.
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da Silva JN, Salcedo E, de Oliveira AB, Barbosa MC. Effects of the attractive interactions in the thermodynamic, dynamic, and structural anomalies of a two length scale potential. J Chem Phys 2010; 133:244506. [DOI: 10.1063/1.3511704] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Abstract
A local self-consistent Ornstein-Zernike (OZ) integral equation theory (IET) is proposed to provide a rapid route for obtaining thermodynamic and structural information for any thermodynamically stable or metastable state points in the bulk phase diagram without recourse to traditional thermodynamic integration, and extensive NVT-Monte Carlo simulations are performed on a recently proposed honeycomb potential in three dimensions to test the theory's reliability. The simulated quantities include radial distribution function (rdf) and excess internal energy, pressure, excess chemical potential, and excess Helmholtz free energy. It is demonstrated that (i) the theory reproduces the rdf very satisfactorily only if the bulk state does not enter deep into a two phases coexistence region; (ii) the excess internal energy is the only one of the four thermodynamic quantities investigated amenable to the most accurate prediction by the present theory, and the simulated pressure is somewhat overestimated by the theoretical calculations, but the deviation tends to vanish along with rising of the temperature; (iii) using the structural functions from the present local self-consistent OZ IET, a previously derived local expression, due to the present author, achieves even a higher accuracy in calculating for the excess chemical potential than the exact virial pressure formula for the pressure, and the resulting excess Helmholtz free energy is in surprisingly same with the simulation results due to offset of the errors. Based on the above observations, it is suggested that it may be a good procedure to integrate the theoretical excess internal energy along the isochors to get the excess Helmholtz free energy, which is then fitted to a polynomial to be used for calculation of all of other thermodynamic quantities in the framework of the OZ IET.
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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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Khanpour M. Perturbation theory based direct correlation function for fluids with hard core potentials. Mol Phys 2010. [DOI: 10.1080/00268976.2010.481641] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Barros de Oliveira A, Neves EB, Gavazzoni C, Paukowski JZ, Netz PA, Barbosa MC. Liquid crystal phase and waterlike anomalies in a core-softened shoulder-dumbbells system. J Chem Phys 2010; 132:164505. [DOI: 10.1063/1.3386384] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Orea P, Tapia-Medina C, Pini D, Reiner A. Thermodynamic properties of short-range attractive Yukawa fluid: Simulation and theory. J Chem Phys 2010; 132:114108. [DOI: 10.1063/1.3357352] [Citation(s) in RCA: 22] [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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Zhou S. A new scheme for perturbation contribution in density functional theory and application to solvation force and critical fluctuations. J Chem Phys 2009; 131:134702. [DOI: 10.1063/1.3242717] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
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Zhou S, Solana JR. Progress in the Perturbation Approach in Fluid and Fluid-Related Theories. Chem Rev 2009; 109:2829-58. [DOI: 10.1021/cr900094p] [Citation(s) in RCA: 61] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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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