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Yuste SB, Santos A, de Haro ML. Structural and thermodynamic properties of fluids whose molecules interact via one-, two-, and three-step potentials. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.119890] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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2
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Akhouri BP, Solana JR. On the choice of the effective diameter in the high-temperature expansion for the Lennard–Jones fluid. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2028918] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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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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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Guérin H. First-order mean spherical approximation (FMSA) for the Buckingham Exp(αE, m) potential. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2020.112812] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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5
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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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Santos A, de Haro ML. Radial distribution function for hard spheres in fractal dimensions: A heuristic approximation. Phys Rev E 2016; 93:062126. [PMID: 27415227 DOI: 10.1103/physreve.93.062126] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2016] [Indexed: 06/06/2023]
Abstract
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension d (1≤d≤3) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for a fractal dimension [M. Heinen et al., Phys. Rev. Lett. 115, 097801 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.097801], a good agreement being observed.
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Affiliation(s)
- Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, Badajoz, E-06071, 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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Montes J, Robles M, López de Haro M. Equation of state and critical point behavior of hard-core double-Yukawa fluids. J Chem Phys 2016; 144:084503. [PMID: 26931708 DOI: 10.1063/1.4942199] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
A theoretical study on the equation of state and the critical point behavior of hard-core double-Yukawa fluids is presented. Thermodynamic perturbation theory, restricted to first order in the inverse temperature and having the hard-sphere fluid as the reference system, is used to derive a relatively simple analytical equation of state of hard-core multi-Yukawa fluids. Using such an equation of state, the compressibility factor and phase behavior of six representative hard-core double-Yukawa fluids are examined and compared with available simulation results. The effect of varying the parameters of the hard-core double-Yukawa intermolecular potential on the location of the critical point is also analyzed using different perspectives. The relevance of this analysis for fluids whose molecules interact with realistic potentials is also pointed out.
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Affiliation(s)
- J Montes
- Instituto de Energías Renovables, Universidad Nacional Autóinoma de México, Privada Xochicalco S/N 62580, Temixco, Morelos, Mexico
| | - M Robles
- Instituto de Energías Renovables, Universidad Nacional Autóinoma de México, Privada Xochicalco S/N 62580, Temixco, Morelos, Mexico
| | - M López de Haro
- Instituto de Energías Renovables, Universidad Nacional Autóinoma de México, Privada Xochicalco S/N 62580, Temixco, Morelos, Mexico
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Fantoni R, Santos A. Depletion force in the infinite-dilution limit in a solvent of nonadditive hard spheres. J Chem Phys 2014; 140:244513. [DOI: 10.1063/1.4884353] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Riccardo Fantoni
- Dipartimento di Scienze dei Materiali e Nanosistemi, Università Ca’ Foscari Venezia, Calle Larga S. Marta DD2137, I-30123 Venezia, Italy
| | - Andrés Santos
- Departamento de Física and Instituto de Computación Científica Avanzada de Extremadura (ICCAEx), Universidad de Extremadura, Badajoz E-06071, Spain
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Fantoni R, Santos A. Multicomponent fluid of nonadditive hard spheres near a wall. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:042102. [PMID: 23679368 DOI: 10.1103/physreve.87.042102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2013] [Revised: 03/20/2013] [Indexed: 06/02/2023]
Abstract
A recently proposed rational-function approximation [Phys. Rev. E 84, 041201 (2011)] for the structural properties of nonadditive hard spheres is applied to evaluate analytically (in Laplace space) the local density profiles of multicomponent nonadditive hard-sphere mixtures near a planar nonadditive hard wall. The theory is assessed by comparison with NVT Monte Carlo simulations of binary mixtures with a size ratio 1:3 in three possible scenarios: a mixture with either positive or negative nonadditivity near an additive wall, an additive mixture with a nonadditive wall, and a nonadditive mixture with a nonadditive wall. It is observed that, while the theory tends to underestimate the local densities at contact (especially in the case of the big spheres) it captures very well the initial decay of the densities with increasing separation from the wall and the subsequent oscillations.
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Affiliation(s)
- Riccardo Fantoni
- Dipartimento di Scienze dei Materiali e Nanosistemi, Università Ca' Foscari Venezia, Calle Larga S. Marta DD2137, I-30123 Venezia, Italy.
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Dubinin NÉ, Yuryev AA, Vatolin NA. Pseudopotential calculation of the structure and thermodynamics of liquid alkali metals with a square-well model as a reference system. J STRUCT CHEM+ 2012. [DOI: 10.1134/s0022476612030080] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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12
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Grest GS, Wang Q, Veld PI, Keffer DJ. Effective potentials between nanoparticles in suspension. J Chem Phys 2011; 134:144902. [DOI: 10.1063/1.3578181] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Wang Q, Keffer DJ, Nicholson DM, Thomas JB. Use of the Ornstein-Zernike Percus-Yevick equation to extract interaction potentials from pair correlation functions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:061204. [PMID: 20866409 DOI: 10.1103/physreve.81.061204] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2010] [Indexed: 05/29/2023]
Abstract
In this work, we test the ability of the Ornstein-Zernike equation in the Percus-Yevick approximation (OZPY) to generate interaction potentials from pair correlation functions (PCFs) of monatomic and diatomic Lennard-Jones fluids. The PCFs are generated by solving OZPY equation (monatomic fluid) and molecular-dynamics (MD) simulations (diatomic fluid). Since the interaction potentials are inputs in the OZPY method and the MD simulation, the extraction of the potential from the PCFs using OZPY is a test of self-consistency. This test is necessary if the procedure is to be used to generate coarse-grained (CG) potentials from PCFs. We find that the procedure is completely self-consistent for the monatomic fluid in the whole range of densities studied (reduced density up to 0.55, under reduced temperature of 2.0). In the diatomic case, we find that the procedure is generally self-consistent under both low and high densities, although there is a systematic deviation at high densities. The method is able to reproduce the two parameters (ε and σ) of the input Lennard-Jones potential model to within about 1%. This CG potential generating procedure can be straightforwardly extended to more complicated molecules.
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Affiliation(s)
- Qifei Wang
- Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA
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SASTRY SRIKANTH, TRUSKETT THOMASM, DEBENEDETTI PABLOG, TORQUATO SALVATORE, STILLINGER FRANKH. Free volume in the hard sphere liquid. Mol Phys 2009. [DOI: 10.1080/00268979809483161] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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16
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Scott PJ, Smith RW. Estimation of the solute diffusion coefficient of a dilute liquid alloy: static structure factor and isothermal compressibility estimates obtained using the rational function approximation of the radial distribution. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:335104. [PMID: 21828598 DOI: 10.1088/0953-8984/21/33/335104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
A simple method for estimating the mass diffusion coefficient of a dilute binary liquid alloy that sequentially uses experimental data for the static structure factor and isothermal susceptibility of the solvent is presented, as well as another using the static structure factor alone and a method using the isothermal susceptibility alone. A fourth method that simultaneously uses the static structure factor and isothermal susceptibility is also noted. Of significance is the fact that these methods do not require information about the interatomic potential. Stability with respect to weights in the optimization process employed has been established and is reported, as well as some indication of the upper limits on the applicable solute concentration. Comparisons are made with results from a high quality capillary experiment for Pb 1 wt% Au liquid alloy performed in microgravity, and with velocity autocorrelation estimates derived from molecular dynamics simulation. The results suggest that the capillary experiments are influenced by reverse diffusion of the solvent, and actually measure an average of the mass diffusion coefficients, D(ij), weighted by the equilibrium concentrations of the solvent, x(1), and solute, x(2), defined by [Formula: see text] The three methods are required to provide upper and lower estimates for the mixed solvent-solute diffusion coefficient, which is not directly accessible from the experimental data, and demonstrate agreement with the experiment via D(tot).
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Affiliation(s)
- Paul J Scott
- Department of Mechanical and Materials Engineering, Queen's University, Kingston, ON, K7L 3N6, Canada
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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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18
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Benyahia S. Validation Study of Two Continuum Granular Frictional Flow Theories. Ind Eng Chem Res 2008. [DOI: 10.1021/ie8003557] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sofiane Benyahia
- National Energy Technology Laboratory, Morgantown, West Virginia 26505
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Equations of State for Hard Spheres and Hard Disks. THEORY AND SIMULATION OF HARD-SPHERE FLUIDS AND RELATED SYSTEMS 2008. [DOI: 10.1007/978-3-540-78767-9_3] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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Rohrmann RD, Santos A. Structure of hard-hypersphere fluids in odd dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:051202. [PMID: 18233644 DOI: 10.1103/physreve.76.051202] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2007] [Indexed: 05/25/2023]
Abstract
The structural properties of single component fluids of hard hyperspheres in odd space dimensionalities d are studied with an analytical approximation method that generalizes the rational function approximation earlier introduced in the study of hard-sphere fluids [S. B. Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)]. The theory makes use of the exact form of the radial distribution function to first order in density and extends it to finite density by assuming a rational form for a function defined in Laplace space, the coefficients being determined by simple physical requirements. Fourier transform in terms of reverse Bessel polynomials constitute the mathematical framework of this approximation, from which an analytical expression for the static structure factor is obtained. In its most elementary form, the method recovers the solution of the Percus-Yevick closure to the Ornstein-Zernike equation for hyperspheres at odd dimensions. The present formalism allows one to go beyond by yielding solutions with thermodynamic consistency between the virial and compressibility routes to any desired equation of state. Excellent agreement with available computer simulation data at d=5 and d=7 is obtained.
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Affiliation(s)
- René D Rohrmann
- Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, 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] [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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López de Haro M, Santos A, Yuste SB. On the radial distribution function of a hard-sphere fluid. J Chem Phys 2006; 124:236102. [PMID: 16821959 DOI: 10.1063/1.2201699] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Zoetekouw B, van Roij R. Volume terms for charged colloids: a grand-canonical treatment. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:021403. [PMID: 16605335 DOI: 10.1103/physreve.73.021403] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2005] [Indexed: 05/08/2023]
Abstract
We present a study of thermodynamic properties of suspensions of charged colloids on the basis of linear Poisson-Boltzmann theory. We calculate the effective Hamiltonian of the colloids by integrating out the ionic degrees of freedom grand canonically. This procedure not only yields the well-known pairwise screened-Coulomb interaction between the colloids, but also additional volume terms that affect the phase behavior and the thermodynamic properties, such as the osmotic pressure. These calculations are greatly facilitated by the grand-canonical character of our treatment of the ions and allow for relatively fast computations compared to earlier studies in the canonical ensemble. Moreover, the present derivation of the volume terms are relatively simple, make a direct connection with Donnan equilibrium, yield an explicit expression for the effective screening constant, and allow for extensions to include, for instance, nonlinear effects.
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Affiliation(s)
- Bas Zoetekouw
- Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584CE Utrecht, The Netherlands
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25
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Siderius DW, Corti DS. Thermodynamically Consistent Adaptation of Scaled Particle Theory to an Arbitrary Hard-Sphere Equation of State. Ind Eng Chem Res 2006. [DOI: 10.1021/ie051038t] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Daniel W. Siderius
- School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-2100
| | - David S. Corti
- School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-2100
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26
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Heying M, Corti DS. Scaled Particle Theory Revisited: New Conditions and Improved Predictions of the Properties of the Hard Sphere Fluid. J Phys Chem B 2004. [DOI: 10.1021/jp040398b] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Affiliation(s)
- Michael Heying
- School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-2100
| | - David S. Corti
- School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-2100
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27
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Jiuxun S. Simple analytic equations of state for hard-core single and double Yukawa fluids and mixtures based on second-order Barker-Henderson perturbation theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:061503. [PMID: 14754208 DOI: 10.1103/physreve.68.061503] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2003] [Revised: 09/15/2003] [Indexed: 05/24/2023]
Abstract
A simple analytic expression with high precision for the radial distribution function of hard spheres is proposed. The form of the expression has been carefully selected to combine the well-known Camahan-Starling equation of state in it and satisfy the limit condition at low density, its simplicity and precision is superior to the well-known Percus-Yevick expression. The coefficients contained in the expression have been determined by fitting the Monte Carlo data for the first coordination shell, and by fitting both the Monte Carlo data and the numerical results of the Percus-Yevick expression for the second coordination shell. The expression has been applied to develop simple analytic equations of state for the hard-core single, double Yukawa fluids, and the hard-core Yukawa mixtures. The comparisons show that the agreement of our model with the computer simulation data is slightly better than the mean spherical approximation and other analytic models.
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Affiliation(s)
- Sun Jiuxun
- Department of Applied Physics, University of Electronic Science and Technology, Chengdu 610054, People's Republic of China
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28
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Largo J, Solana J. Theory and Computer Simulation of the First- and Second-order Perturbative Contributions to the Free Energy of Square-well Fluids. MOLECULAR SIMULATION 2003. [DOI: 10.1080/0892702031000117180] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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30
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Largo J, Solana JR. Generalized van der Waals theory for the thermodynamic properties of square-well fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 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] [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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31
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Gránásy L, Pusztai T. Diffuse interface analysis of crystal nucleation in hard-sphere liquid. J Chem Phys 2002. [DOI: 10.1063/1.1519862] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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Acedo L, Santos A. A square-well model for the structural and thermodynamic properties of simple colloidal systems. J Chem Phys 2001. [DOI: 10.1063/1.1384419] [Citation(s) in RCA: 33] [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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33
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Kaur C, Das SP. Heterogeneities in supercooled liquids: a density-functional study. PHYSICAL REVIEW LETTERS 2001; 86:2062-2065. [PMID: 11289855 DOI: 10.1103/physrevlett.86.2062] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2000] [Indexed: 05/23/2023]
Abstract
A metastable state, characterized by a low degree of mass localization, is identified using density-functional theory (DFT). This free energy minimum, located through the proper evaluation of competing terms in the free energy functional, is independent of the specific form of the DFT used. Computer simulation results on particle motion indicate that this heterogeneous state corresponds to the deeply supercooled state.
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Affiliation(s)
- C Kaur
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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Mulero A, Galán C, Cuadros F. Application of hard sphere equations of state to the Weeks–Chandler–Andersen reference system. J Chem Phys 1999. [DOI: 10.1063/1.479716] [Citation(s) in RCA: 14] [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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Santos A, Yuste SB, López de Haro M. Radial distribution functions for a multicomponent system of sticky hard spheres. J Chem Phys 1998. [DOI: 10.1063/1.477328] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Yuste SB, Santos A, López de Haro M. Structure of multi-component hard-sphere mixtures. J Chem Phys 1998. [DOI: 10.1063/1.475762] [Citation(s) in RCA: 49] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Robles M, López de Haro M, Santos A, Bravo Yuste S. Is there a glass transition for dense hard-sphere systems? J Chem Phys 1998. [DOI: 10.1063/1.475499] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Robles M, López de Haro M. On the contact values of the derivatives of the hard-sphere radial distribution function. J Chem Phys 1997. [DOI: 10.1063/1.474826] [Citation(s) in RCA: 17] [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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