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Katts AM, Kulinskii VL. Parameters of the Liquid-Gas-State Triangle for Hard-Core Attractive Yukawa Fluids. J Phys Chem B 2023; 127:8468-8475. [PMID: 37729006 DOI: 10.1021/acs.jpcb.3c04310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/22/2023]
Abstract
We discuss the triangle of the liquid-gas concept within the fluid-lattice gas isomorphism approach and the Zeno-element, taking the hard-core Yukawa fluid (HCAYF) as an example. The applicability of such an isomorphism is demonstrated by the symmetrization of binodals with mapping onto the Ising model coexistence curve. We show that the parameters of the isomorphism transformation reflect the liquid-phase instability for hard-core Yukawa potential and its generalization. We also provide a simple mean-field estimate for the parameter z of the fluid-lattice gas transformation and use it to obtain the locus of the critical point.
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Affiliation(s)
- A M Katts
- Department for Theoretical Physics, Odessa National University, Dvoryanskaya 2, 65026 Odessa, Ukraine
| | - V L Kulinskii
- Department for Theoretical Physics, Odessa National University, Dvoryanskaya 2, 65026 Odessa, Ukraine
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2
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van Westen T, Hammer M, Hafskjold B, Aasen A, Gross J, Wilhelmsen Ø. Perturbation theories for fluids with short-ranged attractive forces: A case study of the Lennard-Jones spline fluid. J Chem Phys 2022; 156:104504. [DOI: 10.1063/5.0082690] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It is generally not straightforward to apply molecular-thermodynamic theories to fluids with short-ranged attractive forces between their constituent molecules (or particles). This especially applies to perturbation theories, which, for short-ranged attractive fluids, typically must be extended to high order or may not converge at all. Here, we show that a recent first-order perturbation theory, the uv-theory, holds promise for describing such fluids. As a case study, we apply the uv-theory to a fluid with pair interactions defined by the Lennard-Jones spline potential, which is a short-ranged version of the LJ potential that is known to provide a challenge for equation-of-state development. The results of the uv-theory are compared to those of third-order Barker–Henderson and fourth-order Weeks–Chandler–Andersen perturbation theories, which are implemented using Monte Carlo simulation results for the respective perturbation terms. Theoretical predictions are compared to an extensive dataset of molecular simulation results from this (and previous) work, including vapor–liquid equilibria, first- and second-order derivative properties, the critical region, and metastable states. The uv-theory proves superior for all properties examined. An especially accurate description of metastable vapor and liquid states is obtained, which might prove valuable for future applications of the equation-of-state model to inhomogeneous phases or nucleation processes. Although the uv-theory is analytic, it accurately describes molecular simulation results for both the critical point and the binodal up to at least 99% of the critical temperature. This suggests that the difficulties typically encountered in describing the vapor–liquid critical region are only to a small extent caused by non-analyticity.
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Affiliation(s)
- Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| | - Morten Hammer
- Department of Gas Technology, SINTEF Energy Research, NO-7465 Trondheim, Norway
| | - Bjørn Hafskjold
- Porelab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Ailo Aasen
- Department of Gas Technology, SINTEF Energy Research, NO-7465 Trondheim, Norway
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| | - Øivind Wilhelmsen
- Porelab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
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3
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Thermodynamic properties of hard-core attractive Yukawa fluids: Single-component monomers, binary mixtures and chains. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.116493] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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4
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Ramos F, Ramos A, Pellicane G, Lee LL. Construction of a composite-sphere model for molecules of tetrahedral symmetry. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1913254] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Franklin Ramos
- Department of Chemical & Materials Engineering, California State University, Pomona, CA, USA
| | - Ana Ramos
- Department of Chemical & Materials Engineering, California State University, Pomona, CA, USA
| | - Giuseppe Pellicane
- Dipartimento di Scienze Biomediche, Odontoiatriche e delle Immagini Morfologiche e Funzionali Università degli Studi di Messina, Messina, Italy
- CNR-IPCF, Messina, Italy
- School of Chemistry and Physics, University of Kwazulu-Natal, Pietermaritzburg, South Africa
- National Institute of Theoretical Physics (NIThEP), Pietermaritzburg, South Africa
| | - Lloyd L. Lee
- Department of Chemical & Materials Engineering, California State University, Pomona, CA, USA
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5
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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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Mkanya A, Pellicane G, Pini D, Caccamo C. Theory and computer simulation of hard-core Yukawa mixtures: thermodynamical, structural and phase coexistence properties. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:365102. [PMID: 28661404 DOI: 10.1088/1361-648x/aa7c8b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We report extensive calculations, based on the modified hypernetted chain (MHNC) theory, on the hierarchical reference theory (HRT), and on Monte Carlo simulations, of thermodynamical, structural and phase coexistence properties of symmetric binary hard-core Yukawa mixtures (HCYM) with attractive interactions at equal species concentration. The obtained results are throughout compared with those available in the literature for the same systems. It turns out that the MHNC predictions for thermodynamic and structural quantities are quite accurate in comparison with the MC data. The HRT is equally accurate for thermodynamics, and slightly less accurate for structure. Liquid-vapor (LV) and liquid-liquid (LL) consolute coexistence conditions as emerging from simulations, are also highly satisfactorily reproduced by both the MHNC and HRT for relatively long ranged potentials. When the potential range reduces, the MHNC faces problems in determining the LV binodal line; however, the LL consolute line and the critical end point (CEP) temperature and density turn out to be still satisfactorily predicted within this theory. The HRT also predicts with good accuracy the CEP position. The possibility of employing liquid state theories HCYM for the purpose of reliably determining phase equilibria in multicomponent colloidal fluids of current technological interest, is discussed.
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Affiliation(s)
- Anele Mkanya
- School of Chemistry and Physics, University of Kwazulu-Natal, Private Bag X01, Scottsville 3209, Pietermaritzburg, South Africa
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Pellicane G, Caccamo C. A thermodynamic self-consistent theory of asymmetric hard-core Yukawa mixtures. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:414009. [PMID: 27545096 DOI: 10.1088/0953-8984/28/41/414009] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We perform structural and thermodynamic calculations in the framework of the modified hypernetted chain (MHNC) integral equation closure to the Ornstein-Zernike equation for binary mixtures of size-different particles interacting with hard-core Yukawa pair potentials. We use the Percus-Yevick (PY) bridge functions of a binary mixture of hard-sphere (HSM) particles. The hard-sphere diameters of the PY bridge functions of the HSM system are adjusted so to achieve thermodynamic consistency between the virial and compressibility equations of state. We show the benefit of thermodynamic consistency by comparing the MHNC results with the available computer simulation data reported in the literature, and we demonstrate that the self-consistent thermodynamic theory provides a better reproduction of the simulation data over other microscopic theories.
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Affiliation(s)
- Giuseppe Pellicane
- School of Chemistry and Physics, University of Kwazulu-Natal, Private Bag X01, Scottsville 3209, Pietermaritzburg, South Africa. National Institute for Theoretical Physics (NITheP), KZN Node, Pietermaritzburg, South Africa
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Munaò G, Costa D, Caccamo C. Development of molecular closures for the reference interaction site model theory with application to square-well and Lennard-Jones homonuclear diatomics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:414007. [PMID: 27548461 DOI: 10.1088/0953-8984/28/41/414007] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Inspired by significant improvements obtained for the performances of the polymer reference interaction site model (PRISM) theory of the fluid phase when coupled with 'molecular closures' (Schweizer and Yethiraj 1993 J. Chem. Phys. 98 9053), we exploit a matrix generalization of this concept, suitable for the more general RISM framework. We report a preliminary test of the formalism, as applied to prototype square-well homonuclear diatomics. As for the structure, comparison with Monte Carlo shows that molecular closures are slightly more predictive than their 'atomic' counterparts, and thermodynamic properties are equally accurate. We also devise an application of molecular closures to models interacting via continuous, soft-core potentials, by using well established prescriptions in liquid state perturbation theories. In the case of Lennard-Jones dimers, our scheme definitely improves over the atomic one, providing semi-quantitative structural results, and quite good estimates of internal energy, pressure and phase coexistence. Our finding paves the way to a systematic employment of molecular closures within the RISM framework to be applied to more complex systems, such as molecules constituted by several non-equivalent interaction sites.
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Affiliation(s)
- Gianmarco Munaò
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
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Sohrabi Mahboub M, Farrokhpour H. Molecular thermodynamic modeling of ionic liquids using the perturbation-based linear Yukawa isotherm regularity. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:235101. [PMID: 27157142 DOI: 10.1088/0953-8984/28/23/235101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In this paper, we present the results of an extensive study on a novel approach to the molecular modeling of pure ionic liquids (ILs) that incorporates the perturbed thermodynamic linear Yukawa isotherm regularity (LYIR), which is derived based on an effective nearest neighboring pair attractive interaction of the Yukawa potential. The LYIR was used to model the densities of ILs up to high pressures (35 MPa) and in the temperature range 293.15 to 393.15 K. To use the LYIR for ILs, a simple molecular model was proposed to describe their molecular structure, in which they were considered as a liquid consisting of the ion pairs moving together in the fluid, and each ion pair was assumed to be a one-center spherical united atom. The ILs under consideration contained one of the IL cations [C2mim](+), [C4mim](+), [C7mim](+), [C8mim](+), [C3mpy](+), [C3mpip](+), [C3mpyr](+) or [C4mpyr](+), and one of the IL anions [BF4](-), [C(CN)3](-), [CF3SO4](-) or [NTf2](-). The reliability and physical significance of the parameters as well as the proposed molecular model were tested by calculating the densities of pure imidazolium-, pyridinium-, piperidinium- and pyrrolidimium-based ILs. The results showed that the LYIR can be used to predict and reproduce the density of ILs in good agreement with the experimental data. In addition, the LYIR enabled us to determine the physical quantities, such as an effective Yukawa screening length, λ eff, the product of the effective energy well depth and the effective coordination number, (ε eff/k)z eff, the contribution of the non-reference thermal pressure and also the influence of the anionic and cationic structure on the λ eff parameter. The standard deviation of the IL densities predicted in this work is lower than those calculated by the one other important equation of state reported in the literature.
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Affiliation(s)
- Mahdi Sohrabi Mahboub
- Department of Chemistry, Isfahan University of Technology, 84156-83111 Isfahan, Iran
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10
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da Costa VCP, Annunziata O. Unusual liquid-liquid phase transition in aqueous mixtures of a well-known dendrimer. Phys Chem Chem Phys 2015; 17:28818-29. [PMID: 26451401 DOI: 10.1039/c5cp04642d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Liquid-liquid phase separation (LLPS) has been extensively investigated for polymer and protein solutions due to its importance in mixture thermodynamics, separation science and self-assembly processes. However, to date, no experimental studies have been reported on LLPS of dendrimer solutions. Here, it is shown that LLPS of aqueous solutions containing a hydroxyl-functionalized poly(amido amine) dendrimer of fourth generation is induced in the presence of sodium sulfate. Both the LLPS temperature and salt-dendrimer partitioning between the two coexisting phases at constant temperature were measured. Interestingly, our experiments show that LLPS switches from being induced by cooling to being induced by heating as the salt concentration increases. The two coexisting phases also show opposite temperature response. Thus, this phase transition exhibits a simultaneous lower and upper critical solution temperature-type behavior. Dynamic light-scattering and dye-binding experiments indicate that no appreciable conformational change occurs as the salt concentration increases. To explain the observed phase behavior, a thermodynamic model based on two parameters was developed. The first parameter, which describes dendrimer-dendrimer interaction energy, was determined by isothermal titration calorimetry. The second parameter describes the salt salting-out strength. By varying the salting-out parameter, it is shown that the model achieves agreement not only with the location of the experimental binodal at 25 °C but also with the slope of this curve around the critical point. The proposed model also predicts that the unusual temperature behavior of this phase transition can be described as the net result of two thermodynamic factors with opposite temperature responses: salt thermodynamic non-ideality and salting-out strength.
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Affiliation(s)
- Viviana C P da Costa
- Department of Chemistry, Texas Christian University, Fort Worth, Texas 76129, USA.
| | - Onofrio Annunziata
- Department of Chemistry, Texas Christian University, Fort Worth, Texas 76129, USA.
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11
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Singh SK. Effect of surface-screening parameter of the Yukawa potential model on vapour–liquid phase coexistence and critical-point properties of confined Yukawa fluid. MOLECULAR SIMULATION 2015. [DOI: 10.1080/08927022.2015.1059431] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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12
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Heinen M, Allahyarov E, Löwen H. Highly asymmetric electrolytes in the primitive model: Hypernetted chain solution in arbitrary spatial dimensions. J Comput Chem 2013; 35:275-89. [DOI: 10.1002/jcc.23446] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2013] [Revised: 09/03/2013] [Accepted: 09/09/2013] [Indexed: 12/24/2022]
Affiliation(s)
- Marco Heinen
- Institut für Theoretische Physik II; Weiche Materie, Heinrich-Heine-Universität, Düsseldorf, 40225; Düsseldorf Germany
| | - Elshad Allahyarov
- Institut für Theoretische Physik II; Weiche Materie, Heinrich-Heine-Universität, Düsseldorf, 40225; Düsseldorf Germany
- Theoretical Department; Joint Institute for High Temperatures, Russian Academy of Sciences (IVTAN); 13/19 Izhorskaya street Moscow 125412 Russia
| | - Hartmut Löwen
- Institut für Theoretische Physik II; Weiche Materie, Heinrich-Heine-Universität, Düsseldorf, 40225; Düsseldorf Germany
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13
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Nikoofard H, Esmaili BA. Determination of the structure factor for the rare gas fluids based on the ORPA theory and LIR equation of state. Mol Phys 2013. [DOI: 10.1080/00268976.2012.760056] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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14
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Valadez-Pérez NE, Benavides AL, Schöll-Paschinger E, Castañeda-Priego R. Phase behavior of colloids and proteins in aqueous suspensions: Theory and computer simulations. J Chem Phys 2012; 137:084905. [PMID: 22938263 DOI: 10.1063/1.4747193] [Citation(s) in RCA: 69] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Affiliation(s)
- Néstor E Valadez-Pérez
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Lomas del Campestre, 37150 León, Guanajuato, Mexico
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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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17
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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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18
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Pini D, Parola A, Colombo J, Reatto L. An investigation of the SCOZA for narrow square-well potentials and in the sticky limit. Mol Phys 2011. [DOI: 10.1080/00268976.2011.558028] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Odriozola G, Bárcenas M, Orea P. Vapor–liquid surface tension of strong short-range Yukawa fluid. J Chem Phys 2011; 134:154702. [DOI: 10.1063/1.3578637] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
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Caillol JM, Verso FL, Schöll-Paschinger E, Weis JJ. Liquid–vapour transition of the long range Yukawa fluid. Mol Phys 2010. [DOI: 10.1080/00268970701420524] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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21
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Singh SK, Singh JK, Kwak SK, Deo G. Phase transition and crossover behavior of colloidal fluids under confinement. Chem Phys Lett 2010. [DOI: 10.1016/j.cplett.2010.06.005] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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22
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HØye J, Lee CL, Stell G. Self-consistent Ornstein–Zernike Approach to Polymer Fluids. MOLECULAR SIMULATION 2010. [DOI: 10.1080/0892702031000121789] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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El Mendoub EB, Wax JF, Jakse N. Evolution of the liquid-vapor coexistence of the hard-core Yukawa fluid as a function of the interaction range. J Chem Phys 2010; 132:164503. [DOI: 10.1063/1.3385894] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Santos A, Manzano G. Simple relationship between the virial-route hypernetted-chain and the compressibility-route Percus-Yevick values of the fourth virial coefficient. J Chem Phys 2010; 132:144508. [PMID: 20406002 DOI: 10.1063/1.3367206] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
As is well known, approximate integral equations for liquids, such as the hypernetted chain (HNC) and Percus-Yevick (PY) theories, are in general thermodynamically inconsistent in the sense that the macroscopic properties obtained from the spatial correlation functions depend on the route followed. In particular, the values of the fourth virial coefficient B(4) predicted by the HNC and PY approximations via the virial route differ from those obtained via the compressibility route. Despite this, it is shown in this paper that the value of B(4) obtained from the virial route in the HNC theory is exactly three halves the value obtained from the compressibility route in the PY theory, irrespective of the interaction potential (whether isotropic or not), the number of components, and the dimensionality of the system. This simple relationship is confirmed in one-component systems by analytical results for the one-dimensional penetrable-square-well model and the three-dimensional penetrable-sphere model, as well as by numerical results for the one-dimensional Lennard-Jones model, the one-dimensional Gaussian core model, and the three-dimensional square-well model.
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Affiliation(s)
- Andrés Santos
- Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain.
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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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Torres-Arenas J, Cervantes LA, Benavides AL, Chapela GA, del Río F. Discrete perturbation theory for the hard-core attractive and repulsive Yukawa potentials. J Chem Phys 2010; 132:034501. [DOI: 10.1063/1.3281416] [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
Affiliation(s)
- J Torres-Arenas
- División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, Colonia Lomas del Campestre, León, Guanajuato CP 37150, Mexico.
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27
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Singh JK. Surface tension and vapour–liquid phase coexistence of variable-range hard-core attractive Yukawa fluids. MOLECULAR SIMULATION 2009. [DOI: 10.1080/08927020902787796] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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28
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Zhou S. Theoretical Investigation about the Possible Consequence of Artificial Discontinuity in Pair Potential Function on Overall Phase Behavior. J Phys Chem B 2009; 113:8635-45. [DOI: 10.1021/jp9007637] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Shiqi Zhou
- School of Physics Science and Technology, Central South University, Changsha, Hunan, China 410083
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Ayadim A, Oettel M, Amokrane S. Optimum free energy in the reference functional approach for the integral equations theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:115103. [PMID: 21693909 DOI: 10.1088/0953-8984/21/11/115103] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We investigate the question of determining the bulk properties of liquids, required as input for practical applications of the density functional theory of inhomogeneous systems, using density functional theory itself. By considering the reference functional approach in the test particle limit, we derive an expression of the bulk free energy that is consistent with the closure of the Ornstein-Zernike equations in which the bridge functions are obtained from the reference system bridge functional. By examining the connection between the free energy functional and the formally exact bulk free energy, we obtain an improved expression of the corresponding non-local term in the standard reference hypernetted chain theory derived by Lado. In this way, we also clarify the meaning of the recently proposed criterion for determining the optimum hard-sphere diameter in the reference system. This leads to a theory in which the sole input is the reference system bridge functional both for the homogeneous system and the inhomogeneous one. The accuracy of this method is illustrated with the standard case of the Lennard-Jones fluid and with a Yukawa fluid with very short range attraction.
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Affiliation(s)
- A Ayadim
- Physique des Liquides et Milieux Complexes, Faculté des Sciences et Technologie, Université Paris Est (Créteil), 61 Avenue du Général de Gaulle, F-94010 Créteil Cedex, France
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Zhou S. How to make thermodynamic perturbation theory to be suitable for low temperature? J Chem Phys 2009; 130:054103. [DOI: 10.1063/1.3072795] [Citation(s) in RCA: 30] [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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31
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Zhou S. Reformulation of liquid perturbation theory for low temperatures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:011126. [PMID: 19257020 DOI: 10.1103/physreve.79.011126] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2008] [Revised: 10/03/2008] [Indexed: 05/27/2023]
Abstract
A perturbation strategy is proposed which allows liquid perturbation methodology to be applied to extremely low temperature situations for which the available liquid integral equation theory and traditional thermodynamic perturbation theory fail. The possibility of avoiding the low temperature problem of the thermodynamic perturbation theory not only is of relevance to the investigation of complex fluids, but also may be useful for reformulation of other liquid theories to achieve higher accuracy and avoid the respective low temperature problems.
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Affiliation(s)
- Shiqi Zhou
- State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan, China, 410083.
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32
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Farrokhpour H, Satarinezhad E. A new analytical perturbed equation of state for hard chain fluids with attractive potentials of variable range. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2008.02.002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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33
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Zhou S. Fifth-order thermodynamic perturbation theory of uniform and nonuniform fluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:041110. [PMID: 18517581 DOI: 10.1103/physreve.77.041110] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2007] [Indexed: 05/26/2023]
Abstract
A recently proposed numerical third-order thermodynamic perturbation theory (TPT) is extended to its fifth-order counterpart. Extensive performance evaluation based on several model potentials indicates that the fifth-order version is generally superior to both the third-order version and a well-known second-order macroscopic compressibility approximation TPT, and is at least comparable to an accurate self-consistent Ornstein-Zernike integral equation approximation (SCOZA) with regard to predictions of varying bulk thermodynamic properties. A bulk second-order direct correlation function (DCF) free of numerical solution of a bulk OZ integral equation, is proposed, which, in combination with the framework of classical density functional theory (DFT) and a thermodynamic consistency condition, extends the uniform fifth-order TPT to nonuniform case. Grand canonical ensemble Monte Carlo simulation is carried out to produce density profile of a core-softened fluid confined in a hard spherical cavity, the resultant density profile is employed to evaluate the performance of the present nonuniform fifth-order TPT and a recently proposed third +second-order perturbation DFT. It is found that the present nonuniform fifth-order TPT is generally more accurate than the third+second-order perturbation DFT. Additional advantages of the present nonuniform fifth-order TPT over the third +second-order perturbation DFT is discussed.
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Affiliation(s)
- Shiqi Zhou
- School of Physics Science and Technology, Central South University, Changsha, Hunan, China, 410083
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35
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Reiner A, Høye JS. Self-consistent Ornstein–Zernike approximation for the Yukawa fluid with improved direct correlation function. J Chem Phys 2008; 128:114507. [DOI: 10.1063/1.2894474] [Citation(s) in RCA: 14] [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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36
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Lu M, Bevan MA, Ford DM. Closure-based density functional theory applied to interfacial colloidal fluids. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2007; 23:12481-12488. [PMID: 17973405 DOI: 10.1021/la701723b] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
The behavior of dense colloidal fluids near surfaces can now be probed in great detail with experimental techniques like confocal microscopy. In fact, we are approaching a point where quantitative comparisons of experiment with particle-level theory, such as classical density functional theory (DFT), are appropriate. In a forward sense, we may use a known surface potential to predict a particle density distribution function from DFT; in an inverse sense, we may use an experimentally measured particle density distribution function to predict the underlying surface potential from DFT. In this paper, we tested the ability of the closure-based DFT of Zhou and Ruckenstein (J. Chem. Phys. 2000, 112, 8079-8082) to perform forward and inverse calculations on potential models commonly employed for colloidal particles and surfaces. To reduce sources of uncertainty in this initial study, Monte Carlo simulation results played the role of experimental data. The combination of Rogers-Young and modified-Verlet closures consistently performed well across the different potential models. For a reasonable range of choices of the density, temperature, and potential parameters, the inversion procedure yielded particle-surface potentials to an accuracy on the order of 0.1kT.
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Affiliation(s)
- Mingqing Lu
- Department of Chemical Engineering, Texas A&M University, College Station, TX 77843-3122, USA
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37
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Duda Y, Romero-Martínez A, Orea P. Phase diagram and surface tension of the hard-core attractive Yukawa model of variable range: Monte Carlo simulations. J Chem Phys 2007; 126:224510. [PMID: 17581066 DOI: 10.1063/1.2743623] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The liquid-vapor phase diagram and surface tension for hard-core Yukawa potential with 4<or=kappa<or=7 are calculated by applying canonical Monte Carlo simulation. The authors' new simulation results are more precise than those reported before, which allows them to affirm the accuracy of the previously reported self-consistent Ornstein-Zernike approximation calculations for kappa=5 and 7.
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Affiliation(s)
- Yurko Duda
- Programa de Ingeniería Molecular, Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, 07730 México D.F., México
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Santos A. Thermodynamic consistency between the energy and virial routes in the mean spherical approximation for soft potentials. J Chem Phys 2007; 126:116101. [PMID: 17381234 DOI: 10.1063/1.2712181] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andrés Santos
- Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain.
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39
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Zhou S. Improvement on macroscopic compressibility approximation and beyond. J Chem Phys 2006; 125:144518. [PMID: 17042620 DOI: 10.1063/1.2353834] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A numerical procedure is proposed to extend the thermodynamic perturbation expansion (TPE) to a higher order. It is shown that the present second order term is superior to that due to a macroscopic compressibility approximation (MCA), a local compressibility approximation, and a superposition approximation by Barker and Henderson [Rev. Mod. Phys. 48, 587 (1976)]. Extensive model calculation and comparison with simulation data available in literature and supplied in the present report indicate that the present third order TPE is superior to a previous second order TPE based on the MCA, two previous perturbation theories, which are respectively based on an analytical mean spherical approximation for an Ornstein-Zernike equation, and an assumed explicit functional form for the Laplace transform of radial distribution function multiplied by radial distance, and a recent generalized van der Waals theory. The present critical temperature for a hard core attractive Yukawa fluid of varying range is in very good agreement with that due to a hierarchical reference theory. The present third order TPE is computationally far more modest than the self-consistent integral equation theory, and therefore is a viable alternative to use of the latter.
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Affiliation(s)
- Shiqi Zhou
- Institute of Modern Statistical Mechanics, Hunan University of Technology, Wenhua Road, Zhuzhou 412008, People's Republic of China.
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40
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Fortini A, Hynninen AP, Dijkstra M. Gas-liquid phase separation in oppositely charged colloids: Stability and interfacial tension. J Chem Phys 2006; 125:094502. [PMID: 16965092 DOI: 10.1063/1.2335453] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study the phase behavior and the interfacial tension of the screened Coulomb (Yukawa) restricted primitive model (YRPM) of oppositely charged hard spheres with diameter sigma using Monte Carlo simulations. We determine the gas-liquid and gas-solid phase transitions using free energy calculations and grand-canonical Monte Carlo simulations for varying inverse Debye screening length kappa. We find that the gas-liquid phase separation is stable for kappasigma<or=4, and that the critical temperature decreases upon increasing the screening of the interaction (decreasing the range of the interaction). In addition, we determine the gas-liquid interfacial tension using grand-canonical Monte Carlo simulations. The interfacial tension decreases upon increasing the range of the interaction. In particular, we find that simple scaling can be used to relate the interfacial tension of the YRPM to that of the restricted primitive model, where particles interact with bare Coulomb interactions.
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Affiliation(s)
- Andrea Fortini
- Soft Condensed Matter, Utrecht University, Princetonplein 5, 3584CC Utrecht, The Netherlands.
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41
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Yasutomi M. A modified version of a self-consistent Ornstein-Zernike approximation for a fluid with a one-Yukawa pair potential. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2006; 18:7569-7577. [PMID: 21690870 DOI: 10.1088/0953-8984/18/32/006] [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
We present a modified version of a thermodynamically self-consistent Ornstein-Zernike approximation (SCOZA) for a fluid of spherical particles with a pair potential given by a hard core repulsion and a Yukawa tail [Formula: see text]. We take advantage of the known analytical properties of the solution of the Ornstein-Zernike equation for the case in which the direct correlation function outside the repulsive core is given by the multi-screened Coulomb plus power series (multi-SCPPS) tails [Formula: see text] and the radial distribution function g(r) satisfies the exact core condition g(r) = 0 for r<1. The SCOZA is known to provide very good overall thermodynamics and a remarkably accurate critical point and coexistence curve. However, the SCOZA presented so far for continuum fluids has the deficiency that the solution behaves singularly at a density ρ where the screening length z(1)(ρ) of the hard sphere fluid nearly coincides with the Yukawa-tail screening length z(2) (>3.8). This is by no means a rare case in the studies of real fluids and colloidal suspensions. We show that the deficiency is resolved in the modified version of the SCOZA with multi-SCPPS tails. As a demonstration, we present some numerical results for z(2) = 8.0.
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Affiliation(s)
- M Yasutomi
- Department of Physics and Earth Sciences, College of Science, University of the Ryukyus, Nishihara-Cho, Okinawa 903-0213, Japan
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42
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Mladek BM, Kahl G, Neumann M. Thermodynamically self-consistent liquid state theories for systems with bounded potentials. J Chem Phys 2006; 124:64503. [PMID: 16483216 DOI: 10.1063/1.2167646] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The mean spherical approximation (MSA) can be solved semianalytically for the Gaussian core model (GCM) and yields exactly the same expressions for the energy and the virial equations. Taking advantage of this semianalytical framework, we apply the concept of the self-consistent Ornstein-Zernike approximation (SCOZA) to the GCM: a state-dependent function K is introduced in the MSA closure relation which is determined to enforce thermodynamic consistency between the compressibility route and either the energy or virial route. Utilizing standard thermodynamic relations this leads to two differential equations for the function K that have to be solved numerically. Generalizing our concept we propose an integrodifferential-equation-based formulation of the SCOZA which, although requiring a fully numerical solution, has the advantage that it is no longer restricted to the availability of an analytic solution for a particular system. Rather it can be used for an arbitrary potential and even in combination with other closure relations, such as a modification of the hypernetted chain approximation.
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Affiliation(s)
- Bianca M Mladek
- Center for Computational Materials Science, Vienna University of Technology, Austria.
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43
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Wilson DS, Lee LL. Chemical potentials and phase equilibria of Lennard-Jones mixtures: a self-consistent integral equation approach. J Chem Phys 2005; 123:044512. [PMID: 16095374 DOI: 10.1063/1.1961399] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We explore the vapor-liquid phase behavior of binary mixtures of Lennard-Jones-type molecules where one component is supercritical, given the system temperature. We apply the self-consistency approach to the Ornstein-Zernike integral equations to obtain the correlation functions. The consistency checks include not only thermodynamic consistencies (pressure consistency and Gibbs-Duhem consistency), but also pointwise consistencies, such as the zero-separation theorems on the cavity functions. The consistencies are enforced via the bridge functions in the closure which contain adjustable parameters. The full solution requires the values of not only the monomer chemical potentials, but also the dimer chemical potentials present in the zero-separation theorems. These are evaluated by the direct chemical-potential formula [L. L. Lee, J. Chem. Phys. 97, 8606 (1992)] that does not require temperature nor density integration. In order to assess the integral equation accuracy, molecular-dynamics simulations are carried out alongside the states studied. The integral equation results compare well with simulation data. In phase calculations, it is important to have pressure consistency and valid chemical potentials, since the matching of phase boundaries requires the equality of the pressures and chemical potentials of both the liquid and vapor phases. The mixtures studied are methane-type and pentane-type molecules, both characterized by effective Lennard-Jones potentials. Calculations on one isotherm show that the integral equation approach yields valid answers as compared with the experimental data of Sage and Lacey. To study vapor-liquid phase behavior, it is necessary to use consistent theories; any inconsistencies, especially in pressure, will vitiate the phase boundary calculations.
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Affiliation(s)
- D Scott Wilson
- School of Chemical, Biological, and Materials Engineering, University of Oklahoma, Norman, Oklahoma 73072, USA
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44
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Cellai D, Cuevas H, Lawlor A, McCullagh GD, Dawson KA. Competition between short-ranged attraction and short-ranged repulsion in crowded configurational space: aA lattice model description. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:022401. [PMID: 15447526 DOI: 10.1103/physreve.70.022401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2004] [Indexed: 05/24/2023]
Abstract
We describe a simple nearest-neighbor Ising model that is capable of supporting a gas, liquid, and crystal, in characteristic relationship to each other. As the parameters of the model are varied, one obtains characteristic patterns of phase behavior reminiscent of continuum systems where the range of the interaction is varied. The model also possesses dynamical arrest, and although we have not studied it in detail, these "transitions" appear to have a reasonable relationship to the phases and their transitions.
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Affiliation(s)
- Davide Cellai
- Irish Centre for Colloids and Biomaterials, Department of Chemistry, University College Dublin, Belfield, Dublin 4, Ireland
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45
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Schöll-Paschinger E. Self-consistent Ornstein–Zernike approximation for the Sogami–Ise fluid. J Chem Phys 2004; 120:11698-711. [PMID: 15268206 DOI: 10.1063/1.1755192] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We generalize the self-consistent Ornstein-Zernike approximation (SCOZA) to a fluid of particles with a pair potential consisting of a hard-core repulsion and a linear combination of Sogami-Ise tails, w(r)=-epsilonsigma summation operator (nu)(K(nu)/r+L(nu)z(nu))e(-z(nu)(r-sigma)). The formulation and implementation of the SCOZA takes advantage of the availability of semianalytic results for such systems within the mean-spherical approximation. The predictions for the thermodynamics, the phase behavior and the critical point are compared with optimized random phase approximation results; further, the effect of thermodynamic consistency is investigated.
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Affiliation(s)
- Elisabeth Schöll-Paschinger
- Center for Computational Materials Science and Institut für Theoretische Physik TU Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria.
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46
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47
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Ben-Amotz D, Stell G. Analytical implementation and critical tests of fluid thermodynamic perturbation theory. J Chem Phys 2003. [DOI: 10.1063/1.1620995] [Citation(s) in RCA: 38] [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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48
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Costa D, Pellicane G, Caccamo C, Schöll-Paschinger E, Kahl G. Theoretical description of phase coexistence in model C60. ACTA ACUST UNITED AC 2003; 68:021104. [PMID: 14524950 DOI: 10.1103/physreve.68.021104] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2003] [Indexed: 11/07/2022]
Abstract
We have investigated the phase diagram of a pair interaction model of C60 fullerene [L. A. Girifalco, J. Phys. Chem. 96, 858 (1992)], in the framework provided by two integral equation theories of the liquid state, namely, the modified hypernetted chain (MHNC) implemented under a global thermodynamic consistency constraint, and the self-consistent Ornstein-Zernike approximation (SCOZA), and by a perturbation theory (PT) with various degrees of refinement, for the free energy of the solid phase. We present an extended assessment of such theories as set against a recent Monte Carlo study of the same model [D. Costa, G. Pellicane, C. Caccamo, and M. C. Abramo, J. Chem. Phys. 118, 304 (2003)]. We have compared the theoretical predictions with the corresponding simulation results for several thermodynamic properties such as the free energy, the pressure, and the internal energy. Then we have determined the phase diagram of the model, by using either the SCOZA, the MHNC, or the PT predictions for one of the coexisting phases, and the simulation data for the other phase, in order to separately ascertain the accuracy of each theory. It turns out that the overall appearance of the phase portrait is reproduced fairly well by all theories, with remarkable accuracy as for the melting line and the solid-vapor equilibrium. All theories show a more or less pronounced discrepancy with the simulated fluid-solid coexistence pressure, above the triple point. The MHNC and SCOZA results for the liquid-vapor coexistence, as well as for the corresponding critical points, are quite accurate; the SCOZA tends to underestimate the density corresponding to the freezing line. All results are discussed in terms of the basic assumptions underlying each theory. We have then selected the MHNC for the fluid and the first-order PT for the solid phase, as the most accurate tools to investigate the phase behavior of the model in terms of purely theoretical approaches. It emerges that the use of different procedures to characterize the fluid and the solid phases provides a semiquantitative reproduction of the thermodynamic properties of the C60 model at issue. The overall results appear as a robust benchmark for further theoretical investigations on higher order C(n>60) fullerenes, as well as on other fullerene-related materials, whose description can be based on a modelization similar to that adopted in this work.
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Affiliation(s)
- D Costa
- Istituto Nazionale per la Fisica della Materia (INFM) and Dipartimento di Fisica, Università di Messina, Contrada Papardo, Cassella Postale 50, 98166 Messina, Italy.
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Pini D, Tau M, Parola A, Reatto L. Phase diagram of symmetric binary mixtures at equimolar and nonequimolar concentrations: a systematic investigation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:046116. [PMID: 12786445 DOI: 10.1103/physreve.67.046116] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2002] [Indexed: 05/24/2023]
Abstract
We consider symmetric binary mixtures consisting of spherical particles with equal diameters interacting via a hard-core plus attractive tail potential with strengths epsilon(ij), i,j=1,2, such that epsilon(11)=epsilon(22)>epsilon(12). The phase diagram of the system at all densities and concentrations is investigated as a function of the unlike-to-like interaction ratio delta=epsilon(12)/epsilon(11) by means of the hierarchical reference theory. The results are related to those of previous investigations performed at equimolar concentration, as well as to the topology of the mean-field critical lines. As delta is increased in the interval 0<delta<1, we find first a regime where the phase diagram at equal species concentration displays a tricritical point, then one where both a tricritical and a liquid-vapor critical point are present. We did not find any clear evidence of the critical end point topology predicted by mean-field theory as delta approaches 1, at least up to delta=0.8, which is the largest value of delta investigated here. Particular attention was paid to the description of the critical-plus-tricritical point regime in the whole density-concentration plane. In this situation, the phase diagram shows, in a certain temperature interval, a coexistence region that encloses an island of homogeneous, one-phase fluid.
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Affiliation(s)
- D Pini
- Istituto Nazionale di Fisica della Materia and Dipartimento di Fisica, Università di Milano, Via Celoria 16, 20133 Milano, Italy
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50
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Caccamo C, Pellicane G. Microscopic theories of model macromolecular fluids and fullerenes: The role of thermodynamic consistency. J Chem Phys 2002. [DOI: 10.1063/1.1499482] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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