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Bomont JM, Pastore G, Costa D, Munaò G, Malescio G, Prestipino S. Arrested states in colloidal fluids with competing interactions: A static replica study. J Chem Phys 2024; 160:214504. [PMID: 38828820 DOI: 10.1063/5.0208117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2024] [Accepted: 05/13/2024] [Indexed: 06/05/2024] Open
Abstract
We present the first systematic application of the integral equation implementation of the replica method to the study of arrested states in fluids with microscopic competing interactions (short-range attractive and long-range repulsive, SALR), as exemplified by the prototype Lennard-Jones-Yukawa model. Using a wide set of potential parameters, we provide as many as 11 different phase diagrams on the density (ρ)-temperature (T) plane, embodying both the cluster-phase boundary, TC(ρ), and the locus below which arrest takes place, TD(ρ). We describe how the interplay between TC and TD-with the former falling on top of the other, or the other way around, depending on thermodynamic conditions and potential parameters-gives rise to a rich variety of non-ergodic states interspersed with ergodic ones, of which both the building blocks are clusters or single particles. In a few cases, we find that the TD locus does not extend all over the density range subtended by the TC envelope; under these conditions, the λ-line is within reach of the cluster fluid, with the ensuing possibility to develop ordered microphases. Whenever a comparison is possible, our predictions favorably agree with previous numerical results. Thereby, we demonstrate the reliability and effectiveness of our scheme to provide a unified theoretical framework for the study of arrested states in SALR fluids, irrespective of their nature.
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Affiliation(s)
- Jean-Marc Bomont
- Université de Lorraine, LCP-A2MC, UR 3469, 1 Bd. François Arago, Metz F-57078, France
| | - Giorgio Pastore
- Dipartimento di Fisica, Università degli Studi di Trieste, Strada Costiera 11, 34151 Grignano (Trieste), Italy
| | - Dino Costa
- 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
| | - 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
| | - Gianpietro Malescio
- 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
| | - Santi Prestipino
- 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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2
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Bomont JM, Likos CN, Hansen JP. Glass quantization of the Gaussian core model. Phys Rev E 2022; 105:024607. [PMID: 35291117 DOI: 10.1103/physreve.105.024607] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2021] [Accepted: 02/07/2022] [Indexed: 06/14/2023]
Abstract
We use the replica method to study the dynamical glass transition of the Gaussian core model, a system of ultrasoft repulsive spheres interacting via a Gaussian potential, focusing on low temperatures and low-to-moderate densities. At constant temperature, an amorphous glassy state is entered upon a first compression but this glass melts as the density is further increased. In addition to this reentrant transition, a second, smooth transition is discovered between a continuous and a discretized glass. The properties of the former are continuous functions of temperatures, whereas the latter exhibits a succession of stripes, characterized by discontinuous jumps of the glassiness parameters. The glass physics of ultrasoft particles is hence richer than that of impenetrable particles for reasons that can be attributed to the ability of the former to create and break out-of-equilibrium clusters of overlapping particles.
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Affiliation(s)
- Jean-Marc Bomont
- Université de Lorraine, LCP-A2MC, UR 3469, 1 Blvd. François Arago, Metz F-57078, France
| | - Christos N Likos
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Jean-Pierre Hansen
- PHENIX, Sorbonne Université, F-75005 Paris, France
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
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Lucco Castello F, Tolias P. Bridge functions of classical one-component plasmas. Phys Rev E 2022; 105:015208. [PMID: 35193199 DOI: 10.1103/physreve.105.015208] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Accepted: 01/10/2022] [Indexed: 06/14/2023]
Abstract
In a recent paper, Lucco Castello et al. [arXiv:2107.03537] performed systematic extractions of classical one-component plasma bridge functions from molecular dynamics simulations and provided an accurate parametrization that was incorporated in their isomorph-based empirically modified hypernetted chain approach for Yukawa one-component plasmas. Here the extraction technique and parametrization strategy are described in detail, while the deficiencies of earlier efforts are discussed. The structural and thermodynamic predictions of the updated version of the integral equation theory approach are compared with extensive available simulation results revealing a truly unprecedented level of accuracy in the entire dense liquid region of the Yukawa phase diagram.
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Affiliation(s)
- F Lucco Castello
- Space and Plasma Physics, Royal Institute of Technology, Stockholm SE-100 44, Sweden
| | - P Tolias
- Space and Plasma Physics, Royal Institute of Technology, Stockholm SE-100 44, Sweden
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Tolias P, Lucco Castello F, Dornheim T. Integral equation theory based dielectric scheme for strongly coupled electron liquids. J Chem Phys 2021; 155:134115. [PMID: 34625000 DOI: 10.1063/5.0065988] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In a recent paper, Lucco Castello et al. (arXiv:2107.03537) provided an accurate parameterization of classical one-component plasma bridge functions that was embedded in a novel dielectric scheme for strongly coupled electron liquids. Here, this approach is rigorously formulated, its set of equations is formally derived, and its numerical algorithm is scrutinized. A systematic comparison with available and new path integral Monte Carlo simulations reveals a rather unprecedented agreement especially in terms of the interaction energy and the long wavelength limit of the static local field correction.
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Affiliation(s)
- P Tolias
- Space and Plasma Physics-Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
| | - F Lucco Castello
- Space and Plasma Physics-Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
| | - T Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
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5
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Castello FL, Tolias P. Structure and thermodynamics of two-dimensional Yukawa liquids. Phys Rev E 2021; 103:063205. [PMID: 34271703 DOI: 10.1103/physreve.103.063205] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2021] [Accepted: 05/26/2021] [Indexed: 11/07/2022]
Abstract
The thermodynamic and structural properties of two-dimensional dense Yukawa liquids are studied with molecular dynamics simulations. The "exact" thermodynamic properties are simultaneously employed in an advanced scheme for the determination of an equation of state that shows an unprecedented level of accuracy for the internal energy, pressure, and isothermal compressibility. The "exact" structural properties are utilized to formulate a novel empirical correction to the hypernetted-chain approach that leads to a very high accuracy level in terms of static correlations and thermodynamics.
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Affiliation(s)
- F Lucco Castello
- Space and Plasma Physics, Royal Institute of Technology, Stockholm, SE-100 44, Sweden
| | - P Tolias
- Space and Plasma Physics, Royal Institute of Technology, Stockholm, SE-100 44, Sweden
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6
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Lucco Castello F, Tolias P, Dyre JC. Testing the isomorph invariance of the bridge functions of Yukawa one-component plasmas. J Chem Phys 2021; 154:034501. [PMID: 33499616 DOI: 10.1063/5.0036226] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It has been recently conjectured that bridge functions remain nearly invariant along phase diagram lines of constant excess entropy for the broad class of R-simple liquids. To test this hypothesis, the bridge functions of Yukawa systems are computed outside the correlation void with the Ornstein-Zernike inversion method employing structural input from ultra-accurate molecular dynamics simulations and inside the correlation void with the cavity distribution method employing structural input from ultra-long specially designed molecular dynamics simulations featuring a tagged particle pair. Yukawa bridge functions are revealed to be isomorph invariant to a very high degree. The observed invariance is not exact, however, since isomorphic deviations exceed the overall uncertainties.
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Affiliation(s)
- F Lucco Castello
- Space and Plasma Physics, Royal Institute of Technology, Stockholm SE-100 44, Sweden
| | - P Tolias
- Space and Plasma Physics, Royal Institute of Technology, Stockholm SE-100 44, Sweden
| | - J C Dyre
- Glass and Time, IMFUFA, Roskilde University, Roskilde DK-4000, Denmark
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Yagi T, Sato H. Density functional theory for molecular liquids based on interaction site model and self-consistent integral equations for site–site pair correlation functions. J Chem Phys 2020; 153:164102. [DOI: 10.1063/5.0022568] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tomoaki Yagi
- Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
| | - Hirofumi Sato
- Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-8520, Japan
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan
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Frusawa H. Free-energy functional of instantaneous correlation field in liquids: Field-theoretic derivation of the closures. Phys Rev E 2020; 102:012117. [PMID: 32795019 DOI: 10.1103/physreve.102.012117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2020] [Accepted: 06/18/2020] [Indexed: 06/11/2023]
Abstract
This paper presents a unified method for formulating a field-theoretic perturbation theory that encompasses the conventional liquid state theory. First, the free-energy functional of an instantaneous correlation field is obtained from the functional-integral representation of the grand potential. Next, we demonstrate that the instantaneous free-energy functional yields a closure relation between the correlation functions in the mean-field approximation. Notably, the obtained closure relation covers a variety of approximate closures introduced in the liquid state theory.
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Affiliation(s)
- Hiroshi Frusawa
- Laboratory of Statistical Physics, Kochi University of Technology, Tosa-Yamada, Kochi 782-8502, Japan
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Bomont JM, Costa D, Bretonnet JL. Local order and cluster formation in model fluids with competing interactions: a simulation and theoretical study. Phys Chem Chem Phys 2020; 22:5355-5365. [DOI: 10.1039/c9cp06710h] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
In SALR fluids, theory and simulation predict tiny morphological changes in the density profile occurring at the onset of clustering.
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Affiliation(s)
| | - Dino Costa
- Dipartimento di Scienze Matematiche e Informatiche
- Scienze Fisiche e Scienze della Terra
- Università degli Studi di Messina
- 98158 Messina
- Italy
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Bomont JM, Hansen JP, Pastore G. Revisiting the replica theory of the liquid to ideal glass transition. J Chem Phys 2019; 150:154504. [PMID: 31005075 DOI: 10.1063/1.5088811] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The replica theory of the "Random First Order Transition" (RFOT) from a supercooled liquid to an "ideal" glass of a system of "soft spheres" is revisited. Following the seminal work of Mézard and Parisi [J. Chem. Phys. 111, 1076 (1999)], the number m of weakly interacting replicas of the system is varied continuously from m = 2 to m < 1. Relevant order parameters and the free energy of the liquid and glass phases are calculated using the hypernetted chain (HNC) approximation for the pair correlation functions. The scenario observed for all m confirms the existence of two glass branches G1 and G2. The latter has the lowest free energy for all m > 1, while the former has a lower free energy for m < 1 but is shown to be unstable against spinodal decomposition for any nonzero value of the attractive inter-replica coupling. The critical temperature Tcr of the RFOT turns out to depend on m, which may be a by-product of the approximation inherent in the HNC closure. The RFOT is predicted to be weakly first order, characterized by a small jump in density between the coexisting liquid and G2 phases for all m > 1. Estimating Tcr in the limit m → 1 requires a proper extrapolation of high resolution HNC calculations. The present protocol explores the behavior of the free energy of the ideal glass phase below Tcr as a function of m.
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Affiliation(s)
- Jean-Marc Bomont
- Université de Lorraine, LCP-A2MC, EA 3469, 1 Blvd. François Arago, Metz F-57078, France
| | - Jean-Pierre Hansen
- Université Pierre et Marie Curie, UMR 8234 PHENIX, Paris, France and Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Giorgio Pastore
- Università di Trieste, Dipartimento di Fisica, Strada Costiera 11, 34151 Grignano, Trieste, Italy
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Bretonnet JL, Bomont JM, Costa D. A semianalytical “reverse” approach to link structure and microscopic interactions in two-Yukawa competing fluids. J Chem Phys 2018; 149:234907. [DOI: 10.1063/1.5047448] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Jean-Louis Bretonnet
- Université de Lorraine, LCP-A2MC, EA 3469, 1 Bd. François Arago, Metz F-57078, France
| | - Jean-Marc Bomont
- Université de Lorraine, LCP-A2MC, EA 3469, 1 Bd. François Arago, Metz F-57078, France
| | - Dino Costa
- 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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12
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Kohlbrecher J, Studer A. Transformation cycle between the spherically symmetric correlation function, projected correlation function and differential cross section as implemented inSASfit. J Appl Crystallogr 2017. [DOI: 10.1107/s1600576717011979] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
Spin-echo-based small-angle neutron scattering techniques like spin-echo SANS (SESANS) or spin-echo modulated SANS (SEMSANS) as well as dark-field (DF) imaging are directly sensitive to \tilde{G}(\delta), which is the projection of the scattering length density autocorrelation function \tilde{\gamma}(r). Here, a simplified transformation cycle relating the spherically symmetric correlation function \tilde{\gamma}(r), the projected correlation function \tilde{G}(\delta) and the macroscopic small-angle scattering cross section dΣ/dΩ is introduced. The suggested changes to the cycle make it easier to include size distribution on an absolute scale if the data from the different techniques are fitted simultaneously. As up to now only very few analytical expressions for the projected correlation function are known, a numerical transformation of known scattering functions into the projected correlation function in theSASfitsoftware package is supplied. Furthermore, a new analytical expression for the projected correlation function for polymers that can be described by the generalized Gaussian coil model is provided. For this polymer model, the Hankel transform used to calculate \tilde{G}(0) from the SANS signal is divergent for a certain parameter range describing a polymer in a good solvent and finite in the case of a poor solvent. It is therefore a suitable example of how the experimentally availableqrange can strongly influence the obtained results.
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Johnson JK, Henderson D, Labík S, Malijevský A. A comparison of the correlation functions of the Lennard–Jones fluid for the first-order Duh–Haymet–Henderson closure with molecular simulations. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1292011] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- J. Karl Johnson
- Department of Chemical & Petroleum Engineering, The University of Pittsburgh, Pittsburgh, PA, USA
| | - Douglas Henderson
- Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT, USA
| | - Stanislav Labík
- Department of Physical Chemistry, The University of Chemical Technology, Prague, Czech Republic
| | - Anatol Malijevský
- Department of Physical Chemistry, The University of Chemical Technology, Prague, Czech Republic
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Bomont JM, Costa D, Bretonnet JL. Tiny changes in local order identify the cluster formation threshold in model fluids with competing interactions. Phys Chem Chem Phys 2017; 19:15247-15255. [DOI: 10.1039/c7cp01811h] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
In two-Yukawa fluids, the increment of attraction causes a tiny reversal of trend in the local density, within specific ranges of interparticle distances. This event precisely signals the onset of a clustered state.
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Affiliation(s)
| | - Dino Costa
- Dipartimento di Scienze Matematiche e Informatiche
- Scienze Fisiche e Scienze della Terra
- Università degli Studi di Messina
- 98158 Messina
- Italy
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Ciach A, Hall CK, Kahl G, Lomba E. Fifty years of liquid state physics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:410301. [PMID: 27545863 DOI: 10.1088/0953-8984/28/41/410301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
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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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Cigala G, Costa D, Bomont JM, Caccamo C. Aggregate formation in a model fluid with microscopic piecewise-continuous competing interactions. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1078006] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- G. Cigala
- Dipartimento di Fisica e di Scienze della Terra, Università degli Studi di Messina Viale , Messina, Italy
| | - D. Costa
- Dipartimento di Fisica e di Scienze della Terra, Università degli Studi di Messina Viale , Messina, Italy
| | | | - C. Caccamo
- Dipartimento di Fisica e di Scienze della Terra, Università degli Studi di Messina Viale , Messina, Italy
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Bomont JM, Hansen JP, Pastore G. Hypernetted-chain investigation of the random first-order transition of a Lennard-Jones liquid to an ideal glass. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042316. [PMID: 26565249 DOI: 10.1103/physreve.92.042316] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2015] [Indexed: 06/05/2023]
Abstract
The structural and thermodynamic behavior of a deeply supercooled Lennard-Jones liquid, and its random first-order transition (RFOT) to an ideal glass is investigated, using a system of two weakly coupled replicas and the hypernetted chain integral equation for the pair structure of this symmetric binary system. A systematic search in the density-temperature plane points to the existence of two glass branches below a density-dependent threshold temperature. The branch of lower free energy exhibits a rapid growth of the structural overlap order parameter upon cooling and may be identified with the ideal glass phase conjectured by several authors for both spin and structural glasses. The RFOT, signaled by a sharp discontinuity of the order parameter, is predicted to be weakly first order from a thermodynamic viewpoint. The transition temperature T(cr) increases rapidly with density and approximately obeys a scaling relation valid for a reference system of particles interacting via a purely repulsive 1/r(18) potential.
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Affiliation(s)
- Jean-Marc Bomont
- Université de Lorraine, LCP-A2MC, EA 3469, 1 Boulevard François Arago, Metz F-57078, France
| | - Jean-Pierre Hansen
- Université Pierre et Marie Curie, UMR 8234 PHENIX, Paris, France
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Giorgio Pastore
- Università di Trieste, Dipartimento di Fisica, strada Costiera 11, 34151 Grignano (Trieste), Italy
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Bomont JM, Hansen JP, Pastore G. An investigation of the liquid to glass transition using integral equations for the pair structure of coupled replicae. J Chem Phys 2014; 141:174505. [DOI: 10.1063/1.4900774] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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20
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Jaiswal A, Bharadwaj AS, Singh Y. Communication: Integral equation theory for pair correlation functions in a crystal. J Chem Phys 2014; 140:211103. [DOI: 10.1063/1.4881420] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
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21
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Ramana ASV. Generalized coupling parameter expansion: Application to square well and Lennard-Jones fluids. J Chem Phys 2013; 139:044106. [DOI: 10.1063/1.4813797] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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Kast SM, Tomazic D. Communication: An exact bound on the bridge function in integral equation theories. J Chem Phys 2012; 137:171102. [DOI: 10.1063/1.4766465] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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23
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Bomont JM, Costa D. A theoretical study of structure and thermodynamics of fluids with long-range competing interactions exhibiting pattern formation. J Chem Phys 2012; 137:164901. [DOI: 10.1063/1.4759503] [Citation(s) in RCA: 20] [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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Costa D, Caccamo C, Bomont JM, Bretonnet JL. Theoretical description of cluster formation in two-Yukawa competing fluids. Mol Phys 2011. [DOI: 10.1080/00268976.2011.611480] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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25
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Bomont JM, Bretonnet JL, Costa D. Temperature study of cluster formation in two-Yukawa fluids. J Chem Phys 2010. [DOI: 10.1063/1.3418609] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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