1
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de With G. Melting Is Well-Known, but Is It Also Well-Understood? Chem Rev 2023; 123:13713-13795. [PMID: 37963286 PMCID: PMC10722469 DOI: 10.1021/acs.chemrev.3c00489] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Revised: 10/11/2023] [Accepted: 10/12/2023] [Indexed: 11/16/2023]
Abstract
Contrary to continuous phase transitions, where renormalization group theory provides a general framework, for discontinuous phase transitions such a framework seems to be absent. Although the thermodynamics of the latter type of transitions is well-known and requires input from two phases, for melting a variety of one-phase theories and models based on solids has been proposed, as a generally accepted theory for liquids is (yet) missing. Each theory or model deals with a specific mechanism using typically one of the various defects (vacancies, interstitials, dislocations, interstitialcies) present in solids. Furthermore, recognizing that surfaces are often present, one distinguishes between mechanical or bulk melting and thermodynamic or surface-mediated melting. After providing the necessary preliminaries, we discuss both types of melting in relation to the various defects. Thereafter we deal with the effect of pressure on the melting process, followed by a discussion along the line of type of materials. Subsequently, some other aspects and approaches are dealt with. An attempt to put melting in perspective concludes this review.
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Affiliation(s)
- Gijsbertus de With
- Laboratory of Physical Chemistry, Eindhoven University of Technology, Het Kranenveld 14, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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2
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Stones AE, Aarts DGAL. Measuring many-body distribution functions in fluids using test-particle insertion. J Chem Phys 2023; 159:194502. [PMID: 37975484 DOI: 10.1063/5.0172664] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2023] [Accepted: 10/19/2023] [Indexed: 11/19/2023] Open
Abstract
We derive a hierarchy of equations, which allow a general n-body distribution function to be measured by test-particle insertion of between 1 and n particles. We apply it to measure the pair and three-body distribution functions in a simple fluid using snapshots from Monte Carlo simulations in the grand canonical ensemble. The resulting distribution functions obtained from insertion methods are compared with the conventional distance-histogram method: the insertion approach is shown to overcome the drawbacks of the histogram method, offering enhanced structural resolution and a more straightforward normalization. At high particle densities, the insertion method starts breaking down, which can be delayed by utilizing the underlying hierarchical structure of the insertion method. Our method will be especially useful in characterizing the structure of inhomogeneous fluids and investigating closure approximations in liquid state theory.
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Affiliation(s)
- Adam Edward Stones
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom
| | - Dirk G A L Aarts
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom
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3
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Lucco Castello F, Tolias P. Theoretical Estimate of the Glass Transition Line of Yukawa One-Component Plasmas. Molecules 2021; 26:molecules26030669. [PMID: 33525346 PMCID: PMC7865523 DOI: 10.3390/molecules26030669] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Revised: 01/07/2021] [Accepted: 01/25/2021] [Indexed: 12/04/2022] Open
Abstract
The mode coupling theory of supercooled liquids is combined with advanced closures to the integral equation theory of liquids in order to estimate the glass transition line of Yukawa one-component plasmas from the unscreened Coulomb limit up to the strong screening regime. The present predictions constitute a major improvement over the current literature predictions. The calculations confirm the validity of an existing analytical parameterization of the glass transition line. It is verified that the glass transition line is an approximate isomorphic curve and the value of the corresponding reduced excess entropy is estimated. Capitalizing on the isomorphic nature of the glass transition line, two structural vitrification indicators are identified that allow a rough estimate of the glass transition point only through simple curve metrics of the static properties of supercooled liquids. The vitrification indicators are demonstrated to be quasi-universal by an investigation of hard sphere and inverse power law supercooled liquids. The straightforward extension of the present results to bi-Yukawa systems is also discussed.
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4
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Munaò G, Saija F. Monte Carlo simulation and integral equation study of Hertzian spheres in the low-temperature regime. J Chem Phys 2019; 151:134901. [PMID: 31594317 DOI: 10.1063/1.5121007] [Citation(s) in RCA: 5] [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 investigate the behavior of Hertzian spheres in the fluid phase and in proximity of the freezing threshold by using Monte Carlo (MC) simulations and integral equation theories, based on the Ornstein-Zernike (OZ) approach. The study is motivated by the importance of the Hertzian model in representing a large class of systems interacting via soft interactions, such as star polymers or microgels. Radial distribution functions, structure factors, and excess entropy clearly show the reentrant behavior typical of the Hertzian fluid, well caught by both MC simulations and OZ theory. Then, we make use of some phenomenological one-phase criteria for testing their reliability in detecting the freezing threshold. All criteria provide evidence of the fluid-solid transition with different degrees of accuracy. This suggests the possibility to adopt these empirical rules to provide a quick and reasonable estimate of the freezing transition in model potentials of wide interest for soft matter systems.
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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
| | - Franz Saija
- CNR-IPCF, Viale F. Stagno Alcontres 37, I-98158 Messina, Italy
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5
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Ruiz-Franco J, Zaccarelli E, Schöpe HJ, van Megen W. Coincidence of the freezing and the onset of caging in hard sphere and Lennard-Jones fluids. J Chem Phys 2019; 151:104501. [PMID: 31521083 DOI: 10.1063/1.5114720] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this article, we examine the collective particle dynamics, as expressed by the time correlation function of the longitudinal particle current density, of several different fluids in the vicinity of their freezing points/lines. We consider and compare results obtained by dynamic light scattering for a suspension of hard spheres and by molecular dynamics for fluids with hard sphere and Lennard-Jones interactions. The latter are performed along both an isotherm and an isochore. In all cases, we find a qualitative change in the collective dynamics, within the resolution of the data, when their respective freezing lines are crossed. We associate this change with the onset of caging. The new results for the Lennard-Jones fluid reported here confirm that the occurrence of caging, found previously for systems of hard spheres, is a more general feature that distinguishes a metastable fluid from one in thermodynamic equilibrium.
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Affiliation(s)
- J Ruiz-Franco
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy
| | - E Zaccarelli
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy
| | - H J Schöpe
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | - W van Megen
- Department of Applied Physics, Royal Melbourne Institute of Technology, Melbourne, Victoria 3000, Australia
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6
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Klumov BA, Ryltsev RE, Chtchelkatchev NM. Polytetrahedral structure and glass-forming ability of simulated Ni–Zr alloys. J Chem Phys 2018; 149:134501. [DOI: 10.1063/1.5041325] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Affiliation(s)
- B. A. Klumov
- Joint Institute for High Temperatures, Russian Academy of Sciences, 125412 Moscow, Russia
- L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 117940 Moscow, Russia
- Ural Federal University, 620002 Ekaterinburg, Russia
| | - R. E. Ryltsev
- L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 117940 Moscow, Russia
- Ural Federal University, 620002 Ekaterinburg, Russia
- Institute of Metallurgy, Ural Branch of Russian Academy of Sciences, 620016 Ekaterinburg, Russia
| | - N. M. Chtchelkatchev
- L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 117940 Moscow, Russia
- Ural Federal University, 620002 Ekaterinburg, Russia
- Institute of Metallurgy, Ural Branch of Russian Academy of Sciences, 620016 Ekaterinburg, Russia
- Moscow Institute of Physics and Technology, 141700 Moscow, Russia
- Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 108840, Moscow, Russia
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7
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Khrapak S, Klumov B, Couëdel L. Collective modes in simple melts: Transition from soft spheres to the hard sphere limit. Sci Rep 2017; 7:7985. [PMID: 28801556 PMCID: PMC5554265 DOI: 10.1038/s41598-017-08429-5] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2017] [Accepted: 07/11/2017] [Indexed: 12/02/2022] Open
Abstract
We study collective modes in a classical system of particles with repulsive inverse-power-law (IPL) interactions in the fluid phase, near the fluid-solid coexistence (IPL melts). The IPL exponent is varied from n = 10 to n = 100 to mimic the transition from moderately soft to hard-sphere-like interactions. We compare the longitudinal dispersion relations obtained using molecular dynamic (MD) simulations with those calculated using the quasi-crystalline approximation (QCA) and find that this simple theoretical approach becomes grossly inaccurate for \documentclass[12pt]{minimal}
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\begin{document}$$n\,\gtrsim 20$$\end{document}n≳20. Similarly, conventional expressions for high-frequency (instantaneous) elastic moduli, predicting their divergence as n increases, are meaningless in this regime. Relations of the longitudinal and transverse elastic velocities of the QCA model to the adiabatic sound velocity, measured in MD simulations, are discussed for the regime where QCA is applicable. Two potentially useful freezing indicators for classical particle systems with steep repulsive interactions are discussed.
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Affiliation(s)
- Sergey Khrapak
- Aix Marseille University, CNRS, PIIM, Marseille, France. .,Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), Oberpfaffenhofen, Germany. .,Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia.
| | - Boris Klumov
- Aix Marseille University, CNRS, PIIM, Marseille, France.,Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia.,L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, Russia.,Ural Federal University, Ekaterinburg, Russia
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8
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Dyre JC. Simple liquids' quasiuniversality and the hard-sphere paradigm. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:323001. [PMID: 27345623 DOI: 10.1088/0953-8984/28/32/323001] [Citation(s) in RCA: 72] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
This topical review discusses the quasiuniversality of simple liquids' structure and dynamics and two possible justifications of it. The traditional one is based on the van der Waals picture of liquids in which the hard-sphere system reflects the basic physics. An alternative explanation argues that all quasiuniversal liquids to a good approximation conform to the same equation of motion, referring to the exponentially repulsive pair-potential system as the basic reference system. The paper, which is aimed at non-experts, ends by listing a number of open problems in the field.
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Affiliation(s)
- Jeppe C Dyre
- "Glass and Time", IMFUFA, Department of Science and Environment, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
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9
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Ryltsev RE, Klumov BA, Chtchelkatchev NM, Shunyaev KY. Cooling rate dependence of simulated Cu64.5Zr35.5 metallic glass structure. J Chem Phys 2016; 145:034506. [DOI: 10.1063/1.4958631] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- R. E. Ryltsev
- Institute of Metallurgy, Ural Branch of Russian Academy of Sciences, 101 Amundsen Str., 620016 Ekaterinburg, Russia
- Ural Federal University, 19 Mira Str., 620002 Ekaterinburg, Russia
- L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 2 Kosygina Str., 119334 Moscow, Russia
| | - B. A. Klumov
- L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 2 Kosygina Str., 119334 Moscow, Russia
- Aix-Marseille-Université, CNRS, Laboratoire PIIM, UMR 7345, 13397 Marseille Cedex 20, France
- High Temperature Institute, Russian Academy of Sciences, 13/2 Izhorskaya Str., 125412 Moscow, Russia
| | - N. M. Chtchelkatchev
- Institute of Metallurgy, Ural Branch of Russian Academy of Sciences, 101 Amundsen Str., 620016 Ekaterinburg, Russia
- L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 2 Kosygina Str., 119334 Moscow, Russia
- Moscow Institute of Physics and Technology, 9 Institutskiy Per., Dolgoprudny, 141700 Moscow Region, Russia
- All-Russia Research Institute of Automatics, 22 Sushchevskaya, 127055 Moscow, Russia
| | - K. Yu. Shunyaev
- Institute of Metallurgy, Ural Branch of Russian Academy of Sciences, 101 Amundsen Str., 620016 Ekaterinburg, Russia
- Ural Federal University, 19 Mira Str., 620002 Ekaterinburg, Russia
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10
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Abstract
The location of the melting line (ML) of the Lennard-Jones (LJ) system and its associated physical properties are investigated using molecular dynamics computer simulation. The radial distribution function and the behavior of the repulsive and attractive parts of the potential energy indicate that the ML is not a single isomorph, but the isomorphic state evolves gradually with temperature, i.e., it is only "locally isomorphic." The state point dependence of the unitless isomorphic number, X̃, for a range of static and dynamical properties of the LJ system in the solid and fluid states, and for fluid argon, are also reported. The quantity X̃ typically varies most with state point in the vicinity of the triple point and approaches a plateau in the high density (temperature) limit along the ML.
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Affiliation(s)
- D M Heyes
- Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom
| | - A C Brańka
- Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland
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11
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Benjamin R, Horbach J. Crystal growth kinetics in Lennard-Jones and Weeks-Chandler-Andersen systems along the solid-liquid coexistence line. J Chem Phys 2015; 143:014702. [PMID: 26156487 DOI: 10.1063/1.4923340] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Kinetics of crystal-growth is investigated along the solid-liquid coexistence line for the (100), (110), and (111) orientations of the Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA) fcc crystal-liquid interface, using non-equilibrium molecular dynamics simulations. A slowing down of the growth kinetics along the coexistence line is observed, which is due to the decrease of the melting enthalpy with increasing coexistence temperature and pressure. Other quantities such as the melting pressure and liquid self-diffusion coefficient have a comparatively lesser impact on the kinetic growth coefficient. Growth kinetics of the LJ and WCA potentials become similar at large values of the melting temperature and pressure, when both resemble a purely repulsive soft-sphere potential. Classical models of crystallization from the melt are in reasonable qualitative agreement with our simulation data. Finally, several one-phase empirical melting/freezing rules are studied with respect to their validity along the coexistence line.
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Affiliation(s)
- Ronald Benjamin
- Institut für Theoretische Physik II, Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Jürgen Horbach
- Institut für Theoretische Physik II, Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
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12
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Tolias P, Ratynskaia S, de Angelis U. Soft mean spherical approximation for dusty plasma liquids: One-component Yukawa systems with plasma shielding. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:053101. [PMID: 25493891 DOI: 10.1103/physreve.90.053101] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2014] [Indexed: 06/04/2023]
Abstract
The structure and thermodynamics of strongly coupled dusty plasmas are investigated with the soft mean spherical approximation. This integral theory approach is analytically solvable for Yukawa pair interactions yielding a closed-form solution for the direct correlation function. The pair correlation function, the structure factor, and basic thermodynamic quantities are calculated for a wide range of parameters. Exact consistency between the "energy"-"virial" thermodynamic routes and approximate consistency between the "energy"-"compressibility" paths is demonstrated. Comparison with extensive molecular dynamics results is carried out and a remarkable agreement from the Coulomb limit to the strongly screened limit is revealed. The soft mean spherical approximation is concluded to be particularly well suited for the study of dusty plasma liquids, uniquely combining simplicity and accuracy.
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Affiliation(s)
- P Tolias
- Space and Plasma Physics, Royal Institute of Technology, Stockholm, SE-100 44, Sweden
| | - S Ratynskaia
- Space and Plasma Physics, Royal Institute of Technology, Stockholm, SE-100 44, Sweden
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13
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Gapinski J, Nägele G, Patkowski A. Freezing lines of colloidal Yukawa spheres. II. Local structure and characteristic lengths. J Chem Phys 2014; 141:124505. [DOI: 10.1063/1.4895965] [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)
- Jacek Gapinski
- Molecular Biophysics Division, Faculty of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
- NanoBioMedical Center, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
| | - Gerhard Nägele
- Institute of Complex Systems (ICS-3), Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Adam Patkowski
- Molecular Biophysics Division, Faculty of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
- NanoBioMedical Center, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
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14
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Pieprzyk S, Heyes DM, Brańka AC. Thermodynamic properties and entropy scaling law for diffusivity in soft spheres. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012106. [PMID: 25122250 DOI: 10.1103/physreve.90.012106] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2014] [Indexed: 06/03/2023]
Abstract
The purely repulsive soft-sphere system, where the interaction potential is inversely proportional to the pair separation raised to the power n, is considered. The Laplace transform technique is used to derive its thermodynamic properties in terms of the potential energy and its density derivative obtained from molecular dynamics simulations. The derived expressions provide an analytic framework with which to explore soft-sphere thermodynamics across the whole softness-density fluid domain. The trends in the isochoric and isobaric heat capacity, thermal expansion coefficient, isothermal and adiabatic bulk moduli, Grüneisen parameter, isothermal pressure, and the Joule-Thomson coefficient as a function of fluid density and potential softness are described using these formulas supplemented by the simulation-derived equation of state. At low densities a minimum in the isobaric heat capacity with density is found, which is a new feature for a purely repulsive pair interaction. The hard-sphere and n = 3 limits are obtained, and the low density limit specified analytically for any n is discussed. The softness dependence of calculated quantities indicates freezing criteria based on features of the radial distribution function or derived functions of it are not expected to be universal. A new and accurate formula linking the self-diffusion coefficient to the excess entropy for the entire fluid softness-density domain is proposed, which incorporates the kinetic theory solution for the low density limit and an entropy-dependent function in an exponential form. The thermodynamic properties (or their derivatives), structural quantities, and diffusion coefficient indicate that three regions specified by a convex, concave, and intermediate density dependence can be expected as a function of n, with a narrow transition region within the range 5 < n < 8.
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Affiliation(s)
- S Pieprzyk
- Institute of Molecular Physics, Polish Academy of Sciences, Mariana Smoluchowskiego 17, 60-179 Poznań, Poland
| | - D M Heyes
- Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom
| | - A C Brańka
- Institute of Molecular Physics, Polish Academy of Sciences, Mariana Smoluchowskiego 17, 60-179 Poznań, Poland
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15
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Heyes DM, Rickayzen G. Continuous distributions of charges: extensions of the one component plasma. J Chem Phys 2014; 140:024506. [PMID: 24437895 DOI: 10.1063/1.4858405] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
The electrostatic interaction between finite charge distributions, ρ(r), in a neutralizing background is considered as an extension of the one component plasma (OCP) model of point charges. A general form for the interaction potential is obtained which can be applied to molecular theories of many simple charged fluids and mixtures and to the molecular dynamics (MD) simulation of such systems. The formalism is applied to the study of a fluid of Gaussian charges in a neutralizing background by MD simulation and using hypernetted-chain integral equation theory. The treatment of these interactions is extended to a periodic system using a Fourier Transform formulation and, for a rapidly decaying charge distribution, an application of the Ewald method. The contributions of the self-energy and neutralizing background to the system's energy are explicitly included in the formulation. Calculations reveal differences in behavior from the OCP model when the Wigner-Seitz radius is of order and less than the Gaussian charge density decay length. For certain parameter values these systems can exhibit a multiple occupancy crystalline phase at high density which undergoes re-entrant melting at higher density. An exploration of the effects of the various length scales of the system on the equation of state and radial distribution function is made.
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Affiliation(s)
- D M Heyes
- School of Design, Engineering and Computing, Bournemouth University, Poole House, Talbot Campus, Poole, Dorset BH12 5BB, United Kingdom
| | - G Rickayzen
- School of Physical Sciences, University of Kent, Canterbury, Kent CT2 7NH, United Kingdom
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16
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Dyre JC. NVU perspective on simple liquids' quasiuniversality. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:022106. [PMID: 23496459 DOI: 10.1103/physreve.87.022106] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2012] [Indexed: 06/01/2023]
Abstract
The last half-century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids' reduced-coordinate constant-potential-energy hypersurfaces constitute a quasiuniversal family of compact Riemannian manifolds parametrized by a single number; from this follows the quasiuniversalities.
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Affiliation(s)
- Jeppe C Dyre
- DNRF Centre Glass and Time, IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark.
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17
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Khrapak SA, Klumov BA, Huber P, Molotkov VI, Lipaev AM, Naumkin VN, Ivlev AV, Thomas HM, Schwabe M, Morfill GE, Petrov OF, Fortov VE, Malentschenko Y, Volkov S. Fluid-solid phase transitions in three-dimensional complex plasmas under microgravity conditions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:066407. [PMID: 23005228 DOI: 10.1103/physreve.85.066407] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2012] [Indexed: 06/01/2023]
Abstract
Phase behavior of large three-dimensional (3D) complex plasma systems under microgravity conditions onboard the International Space Station is investigated. The neutral gas pressure is used as a control parameter to trigger phase changes. Detailed analysis of structural properties and evaluation of three different melting-freezing indicators reveal that complex plasmas can exhibit melting by increasing the gas pressure. Theoretical estimates of complex plasma parameters allow us to identify main factors responsible for the observed behavior. The location of phase states of the investigated systems on a relevant equilibrium phase diagram is estimated. Important differences between the melting process of 3D complex plasmas under microgravity conditions and that of flat 2D complex plasma crystals in ground based experiments are discussed.
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Affiliation(s)
- S A Khrapak
- Max-Planck-Institut für extraterrestrische Physik, D-85741 Garching, Germany
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18
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Khrapak SA, Saija F. Application of phenomenological freezing and melting indicators to the exp-6 and Gaussian core potentials. Mol Phys 2011. [DOI: 10.1080/00268976.2011.616544] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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19
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Khrapak SA, Klumov BA, Huber P, Molotkov VI, Lipaev AM, Naumkin VN, Thomas HM, Ivlev AV, Morfill GE, Petrov OF, Fortov VE, Malentschenko Y, Volkov S. Freezing and melting of 3D complex plasma structures under microgravity conditions driven by neutral gas pressure manipulation. PHYSICAL REVIEW LETTERS 2011; 106:205001. [PMID: 21668236 DOI: 10.1103/physrevlett.106.205001] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2010] [Indexed: 05/30/2023]
Abstract
Freezing and melting of large three-dimensional complex plasmas under microgravity conditions is investigated. The neutral gas pressure is used as a control parameter to trigger the phase changes: Complex plasma freezes (melts) by decreasing (increasing) the pressure. The evolution of complex plasma structural properties upon pressure variation is studied. Theoretical estimates allow us to identify the main factors responsible for the observed behavior.
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Affiliation(s)
- S A Khrapak
- Max-Planck-Institut für extraterrestrische Physik, D-85741 Garching, Germany
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20
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Cao QL, Wang WL, Li YD, Liu CS. Correlations among residual multiparticle entropy, local atomic-level pressure, free volume and the phase-ordering rule in several liquids. J Chem Phys 2011; 134:044508. [DOI: 10.1063/1.3524206] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Lee LL, Hara MC, Simon SJ, Ramos FS, Winkle AJ, Bomont JM. Crystallization limits of the two-term Yukawa potentials based on the entropy criterion. J Chem Phys 2010; 132:074505. [DOI: 10.1063/1.3308648] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Lloyd L Lee
- Department of Chemical and Materials Engineering, California State University, Pomona, California 91768, USA.
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Ahmed A, Sadus RJ. Phase diagram of the Weeks-Chandler-Andersen potential from very low to high temperatures and pressures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:061101. [PMID: 20365112 DOI: 10.1103/physreve.80.061101] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2009] [Indexed: 05/29/2023]
Abstract
A combination of two molecular simulation algorithms has been used to determine the solid-liquid coexistence of the Weeks-Chandler-Andersen (WCA) fluid from low temperatures up to very high temperatures. Values are reported for the coexistence pressure, temperature, energy, enthalpy change, and densities of both the liquid and solid phases. At very high temperatures, the coexistence pressure approaches the same 12th-power soft-sphere asymptote as the 12-6 Lennard-Jones potential. However, in contrast to the Lennard-Jones potential, which shows a discontinuity of pressure at low temperatures, the coexistence pressure of the WCA potential approaches the zero-temperature limit. Empirical relationships are determined to accurately reproduce the coexistence pressure and both solid and liquid phase densities from near zero temperature to very high temperatures. The simulation data are used to improve the accuracy of a WCA equation of state. The validity of common melting and freezing rules is tested.
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Affiliation(s)
- Alauddin Ahmed
- Centre for Molecular Simulation, Swinburne University of Technology, PO Box 218, Hawthorn, Victoria 3122, Australia
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Ahmed A, Sadus RJ. Solid-liquid equilibria and triple points of n-6 Lennard-Jones fluids. J Chem Phys 2009; 131:174504. [DOI: 10.1063/1.3253686] [Citation(s) in RCA: 74] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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24
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Angell CA, Clarke JHR, Woodcock LV. Interaction Potentials and Glass Formation: A Survey of Computer Experiments. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470142684.ch5] [Citation(s) in RCA: 151] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/09/2023]
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26
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Vogelsang R, Hoheisel C. Structure and dynamics of a supercritical fluid in comparison with a liquid. Mol Phys 2006. [DOI: 10.1080/00268978400103051] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Saija F, Prestipino S, Giaquinta PV. Evaluation of phenomenological one-phase criteria for the melting and freezing of softly repulsive particles. J Chem Phys 2006; 124:244504. [PMID: 16821986 DOI: 10.1063/1.2208357] [Citation(s) in RCA: 52] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We test the validity of some widely used phenomenological criteria for the localization of the fluid-solid transition thresholds against the phase diagrams of particles interacting through the exp-6, inverse-power-law, and Gaussian potentials. We find that one-phase rules give, on the whole, reliable estimates of freezing/melting points. The agreement is ordinarily better for a face-centered-cubic solid than for a body-centered-cubic crystal, even more so in the presence of a pressure-driven reentrant transition of the solid into a denser fluid phase, as found in the Gaussian-core model.
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Affiliation(s)
- Franz Saija
- Istituto per i Processi Chimico-Fisici del CNR, Sezione di Messina, Via La Farina 237, 98123 Messina, Italy.
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Charpentier I, Jakse N. Phase diagram of complex fluids using an efficient integral equation method. J Chem Phys 2005; 123:204910. [PMID: 16351320 DOI: 10.1063/1.2117010] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an adaptive technique for the determination of the phase diagram of fluids within the integral equation theory. It enables an efficient and accurate systematic mapping of the thermodynamic space in order to construct the binodal and spinodal lines. Results are obtained with the thermodynamically consistent integral equation proposed by Sarkisov [J. Chem. Phys. 114, 9496 (2001)] within the tangent linear technique that yields an exact differentiation of correlation functions. The generality of the numerical approach is assessed by determining both the liquid-vapor coexistence and the critical parameters of the generalized Lennard-Jones (n,6) potentials with varying repulsive part, including the hard-sphere limit.
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Affiliation(s)
- I Charpentier
- Laboratoire de Modélisation et Calcul, 51 rue des Mathématiques, BP 53, F-38041 Grenoble Cedex 9, France
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Zahn K, Maret G, Russ C, von Grünberg HH. Three-particle correlations in simple liquids. PHYSICAL REVIEW LETTERS 2003; 91:115502. [PMID: 14525436 DOI: 10.1103/physrevlett.91.115502] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2003] [Indexed: 05/24/2023]
Abstract
We use videomicroscopy to follow the phase-space trajectory of a two-dimensional colloidal model liquid and calculate three-point correlation functions from the measured particle configurations. Approaching the fluid-solid transition by increasing the strength of the pair-interaction potential, one observes the gradual formation of a crystal-like local order due to triplet correlations, while being still deep inside the fluid phase. Furthermore, we show that in a strongly interacting system the Born-Green equation can be satisfied only with the full triplet correlation function but not with three-body distribution functions obtained from superposing pair correlations (Kirkwood superposition approximation).
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Affiliation(s)
- K Zahn
- Fachbereich Physik, Universität Konstanz, PO Box 5560, 78457 Konstanz, Germany
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Affiliation(s)
- Shiqi Zhou
- Research Institute of Modern Statistical Mechanics, Zhuzhou Institute of Technology, Wenhua Road, Zhuzhou City 412008, P. R. China
| | - Xiaoqi Zhang
- Research Institute of Modern Statistical Mechanics, Zhuzhou Institute of Technology, Wenhua Road, Zhuzhou City 412008, P. R. China
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31
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Stillinger FH. Lattice sums and their phase diagram implications for the classical Lennard-Jones model. J Chem Phys 2001. [DOI: 10.1063/1.1394922] [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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Lewis JWE, Lovesey SW. Short-wavelength collective density excitations in monatomic liquids. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0022-3719/10/17/007] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Bengtzelius U, Gotze W, Sjolander A. Dynamics of supercooled liquids and the glass transition. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/17/33/005] [Citation(s) in RCA: 1016] [Impact Index Per Article: 42.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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34
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Sanyal S, Sood AK. Brownian dynamics simulation of dense binary colloidal mixtures. I. Structural evolution and dynamics. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:4154-4167. [PMID: 9963887 DOI: 10.1103/physreve.52.4154] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Agrawal R, Kofke DA. Thermodynamic and structural properties of model systems at solid-fluid coexistence. Mol Phys 1995. [DOI: 10.1080/00268979500100921] [Citation(s) in RCA: 214] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Agrawal R, Kofke DA. Thermodynamic and structural properties of model systems at solid-fluid coexistence. Mol Phys 1995. [DOI: 10.1080/00268979500100911] [Citation(s) in RCA: 145] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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37
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Hummer G, Soumpasis DM. Correlations and free energies in restricted primitive model descriptions of electrolytes. J Chem Phys 1993. [DOI: 10.1063/1.464600] [Citation(s) in RCA: 50] [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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Rosenberg RO, Thirumalai D. Order-disorder transition in colloidal suspensions. PHYSICAL REVIEW. A, GENERAL PHYSICS 1987; 36:5690-5700. [PMID: 9898859 DOI: 10.1103/physreva.36.5690] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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39
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Amar JG, Mountain RD. Molecular dynamics study of a supercooled soft‐sphere fluid. J Chem Phys 1987. [DOI: 10.1063/1.452122] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Broughton JQ, Gilmer GH. Molecular dynamics investigation of the crystal–fluid interface. I. Bulk properties. J Chem Phys 1983. [DOI: 10.1063/1.445633] [Citation(s) in RCA: 252] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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McNeil WJ, Madden WG, Haymet ADJ, Rice SA. Triplet correlation functions in the Lennard‐Jones fluid: Tests against molecular dynamics simulations. J Chem Phys 1983. [DOI: 10.1063/1.444514] [Citation(s) in RCA: 57] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- William J. McNeil
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755
| | - William G. Madden
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755
| | - A. D. J. Haymet
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138
| | - Stuart A. Rice
- The Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637
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Weber TA, Stillinger FH. GLASS TRANSITION IN THE GAUSSIAN CORE MODEL. Ann N Y Acad Sci 1981. [DOI: 10.1111/j.1749-6632.1981.tb55476.x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Co KU, Kozak JJ, Luks KD. Solutions of the Yvon–Born–Green and Kirkwood equations for hard spheres at very high densities. J Chem Phys 1977. [DOI: 10.1063/1.433980] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Rosenfeld Y, Thieberger R. Freezing structure criterion for hard core potentials. J Chem Phys 1975. [DOI: 10.1063/1.431216] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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