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Amokrane S, Tchangnwa Nya F, Ndjaka JM. Glass transition in hard-core fluids and beyond, using an effective static structure in the mode coupling theory. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:17. [PMID: 28210959 DOI: 10.1140/epje/i2017-11506-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2016] [Accepted: 01/26/2017] [Indexed: 06/06/2023]
Abstract
The dynamical arrest in classical fluids is studied using a simple modification of the mode coupling theory (MCT) aimed at correcting its overestimation of the tendency to glass formation while preserving its overall structure. As in previous attempts, the modification is based on the idea of tempering the static pair correlations used as input. It is implemented in this work by computing the static structure at a different state point than the one used to solve the MCT equation for the intermediate scattering function, using the pure hard-sphere glass for calibration. The location of the glass transition predicted from this modification is found to agree with simulations data for a variety of systems --pure fluids and mixtures with either purely repulsive interaction potentials or ones with attractive contributions. Besides improving the predictions in the long-time limit, and so reducing the non-ergodicity domain, the same modification works as well for the time-dependent correlators.
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Affiliation(s)
- S Amokrane
- Physique des Liquides et Milieux Complexes, Faculté des Sciences et Technologie, Université Paris-Est (Créteil), 61 Av. du Général de Gaulle, 94010, Créteil Cedex, France.
| | - F Tchangnwa Nya
- Physique des Liquides et Milieux Complexes, Faculté des Sciences et Technologie, Université Paris-Est (Créteil), 61 Av. du Général de Gaulle, 94010, Créteil Cedex, France
- Département de Physique, Faculté des Sciences, Université de Maroua, BP 814, Maroua, Cameroon
| | - J M Ndjaka
- Département de Physique, Faculté des Sciences, Université de Yaoundé, I. B.P. 812, Yaoundé, Cameroon
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Frey S, Weysser F, Meyer H, Farago J, Fuchs M, Baschnagel J. Simulated glass-forming polymer melts: dynamic scattering functions, chain length effects, and mode-coupling theory analysis. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:97. [PMID: 25715952 DOI: 10.1140/epje/i2015-15011-x] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2014] [Revised: 01/09/2015] [Accepted: 01/28/2015] [Indexed: 06/04/2023]
Abstract
We present molecular-dynamics simulations for a fully flexible model of polymer melts with different chain length N ranging from short oligomers (N = 4) to values near the entanglement length (N = 64). For these systems we explore the structural relaxation of the supercooled melt near the critical temperature T c of mode-coupling theory (MCT). Coherent and incoherent scattering functions are analyzed in terms of the idealized MCT. For temperatures T > T c we provide evidence for the space-time factorization property of the β relaxation and for the time-temperature superposition principle (TTSP) of the α relaxation, and we also discuss deviations from these predictions for T ≈ T c. For T larger than the smallest temperature where the TTSP holds we perform a quantitative analysis of the dynamics with the asymptotic MCT predictions for the late β regime. Within MCT a key quantity, in addition to T c, is the exponent parameter λ. For the fully flexible polymer models studied we find that λ is independent of N and has a value (λ = 0.735 ) typical of simple glass-forming liquids. On the other hand, the critical temperature increases with chain length toward an asymptotic value T c (∞) . This increase can be described by T c (∞) - T c(N) ∼ 1/N and may be interpreted in terms of the N dependence of the monomer density ρ, if we assume that the MCT glass transition is ruled by a soft-sphere-like constant coupling parameter Γ c = ρ c T c (-1/4), where ρ c is the monomer density at T c. In addition, we also estimate T c from a Hansen-Verlet-like criterion and MCT calculations based on structural input from the simulation. For our polymer model both the Hansen-Verlet criterion and the MCT calculations suggest T c to decrease with increasing chain length, in contrast to the direct analysis of the simulation data.
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Affiliation(s)
- S Frey
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR 22, 23 rue du Loess, BP 84047, 67034, Strasbourg Cedex 2, France
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Kondrin MV, Gromnitskaya EL, Pronin AA, Lyapin AG, Brazhkin VV, Volkov AA. Dielectric spectroscopy and ultrasonic study of propylene carbonate under ultra-high pressures. J Chem Phys 2012; 137:084502. [DOI: 10.1063/1.4746022] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
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Abstract
We present evidence from computer simulation that the slowdown of relaxation of a standard Lennard-Jones glass-forming liquid and that of its reduction to a model with truncated pair potentials without attractive tails are quantitatively and qualitatively different in the viscous regime. The pair structure of the two models is however very similar. This finding, which appears to contradict the common view that the physics of dense liquids is dominated by the steep repulsive forces between atoms, is characterized in detail, and its consequences are explored. Beyond the role of attractive forces themselves, a key aspect in explaining the differences in the dynamical behavior of the two models is the truncation of the interaction potentials beyond a cutoff at typical interatomic distance. This leads us to question the ability of the jamming scenario to describe the physics of glass-forming liquids and polymers.
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Affiliation(s)
- Ludovic Berthier
- Laboratoire Charles Coulomb, UMR 5221, CNRS and Université Montpellier 2, Montpellier, France.
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Coslovich D. Locally preferred structures and many-body static correlations in viscous liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:051505. [PMID: 21728538 DOI: 10.1103/physreve.83.051505] [Citation(s) in RCA: 55] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2011] [Indexed: 05/31/2023]
Abstract
The influence of static correlations beyond the pair level on the dynamics of selected model glass formers is investigated. The pair structure, angular distribution functions, and statistics of Voronoi polyhedra of two well-known Lennard-Jones mixtures as well as of the corresponding Weeks-Chandler-Andersen variants, in which the attractive part of the potential is truncated, are compared. By means of the Voronoi construction, the atomic arrangements corresponding to the locally preferred structures of the models are identified. It is found that the growth of domains formed by interconnected locally preferred structures signals the onset of the slow-dynamics regime and allows the rationalization of the different dynamic behaviors of the models. At low temperature, the spatial extension of the structurally correlated domains, evaluated at fixed relaxation time, increases with the fragility of the models and is systematically reduced by truncating the attractions. In view of these results, proper inclusion of many-body static correlations in theories of the glass transition appears crucial for the description of the dynamics of fragile glass formers.
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Affiliation(s)
- Daniele Coslovich
- Laboratoire Charles Coulomb UMR 5221, Université Montpellier 2 and CNRS, Montpellier, France.
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Larsen RJ, Zukoski CF. Molecular Mixture as an Effective Single-Component System. J Phys Chem B 2011; 115:3981-91. [DOI: 10.1021/jp1120838] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ryan J. Larsen
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana−Champaign, 114 Roger Adams Laboratory, 600 South Mathews Avenue, Urbana, Illinois 61801, United States
| | - Charles F. Zukoski
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana−Champaign, 114 Roger Adams Laboratory, 600 South Mathews Avenue, Urbana, Illinois 61801, United States
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Berthier L, Tarjus G. Critical test of the mode-coupling theory of the glass transition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:031502. [PMID: 21230078 DOI: 10.1103/physreve.82.031502] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2010] [Revised: 07/06/2010] [Indexed: 05/30/2023]
Abstract
In its common implementation, the mode-coupling theory of the glass transition predicts the time evolution of the intermediate scattering functions in viscous liquids on the sole basis of the structural information encoded in two-point density correlations. We provide a critical test of this property and show that the theory fails to describe the strong differences of dynamical behavior seen in two model liquids characterized by very similar pair-correlation functions. Because we use "exact" static information provided by numerical simulations, our results are a direct indication that some important information about the dynamics of viscous liquids is not captured by pair correlations and is thus not described by the mode-coupling theory, even in the temperature regime where the theory is usually applied.
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Affiliation(s)
- Ludovic Berthier
- Laboratoire des Colloïdes, Verres et Nanomatériaux, Université Montpellier II and UMR 5587 CNRS, 34095 Montpellier, France
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Pronin AA, Kondrin MV, Lyapin AG, Brazhkin VV, Volkov AA, Lunkenheimer P, Loidl A. Glassy dynamics under superhigh pressure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:041503. [PMID: 20481727 DOI: 10.1103/physreve.81.041503] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2009] [Indexed: 05/29/2023]
Abstract
Nearly all glass-forming liquids feature, along with the structural alpha-relaxation process, a faster secondary process (beta relaxation), whose nature belongs to the great mysteries of glass physics. However, for some of these liquids, no well-pronounced secondary relaxation is observed. A prominent example is the archetypical glass-forming liquid glycerol. In the present work, by performing dielectric spectroscopy under superhigh pressures up to 6 GPa, we show that in glycerol a significant secondary relaxation peak appears in the dielectric loss at P>3 GPa. We identify this beta relaxation to be of Johari-Goldstein type and discuss its relation to the excess wing. We provide evidence for a smooth but significant increase in glass-transition temperature and fragility on increasing pressure.
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Affiliation(s)
- A A Pronin
- General Physics Institute, Russian Academy of Sciences, Vavilov Street 38, Moscow 119991, Russia
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Berthier L, Flenner E, Jacquin H, Szamel G. Scaling of the glassy dynamics of soft repulsive particles: a mode-coupling approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:031505. [PMID: 20365738 DOI: 10.1103/physreve.81.031505] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2009] [Indexed: 05/29/2023]
Abstract
We combine the hypernetted chain approximation of liquid state theory with the mode-coupling theory of the glass transition to analyze the structure and dynamics of soft spheres interacting via harmonic repulsion. We determine the locus of the fluid-glass dynamic transition in a temperature--volume fraction phase diagram. The zero-temperature (hard-sphere) glass transition influences the dynamics at finite temperatures in its vicinity. This directly implies a form of dynamic scaling for both the average relaxation time and dynamic susceptibilities quantifying dynamic heterogeneity. We discuss several qualitative disagreements between theory and existing simulations at equilibrium. Our theoretical results are, however, very similar to numerical results for the driven athermal dynamics of repulsive spheres, suggesting that "mean-field" mode-coupling approaches might be good starting points to describe these nonequilibrium dynamics.
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Affiliation(s)
- Ludovic Berthier
- Laboratoire des Colloïdes, Verres et Nanomatériaux, UMR CNRS 5587, Université Montpellier 2, 34095 Montpellier, France
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Xu N, Haxton TK, Liu AJ, Nagel SR. Equivalence of glass transition and colloidal glass transition in the hard-sphere limit. PHYSICAL REVIEW LETTERS 2009; 103:245701. [PMID: 20366210 DOI: 10.1103/physrevlett.103.245701] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2009] [Indexed: 05/29/2023]
Abstract
We show that the slowing of the dynamics in simulations of several model glass-forming liquids is equivalent to the hard-sphere glass transition in the low-pressure limit. In this limit, we find universal behavior of the relaxation time by collapsing molecular-dynamics data for all systems studied onto a single curve as a function of T/p, the ratio of the temperature to the pressure. At higher pressures, there are deviations from this universal behavior that depend on the interparticle potential, implying that additional physical processes must enter into the dynamics of glass formation.
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Affiliation(s)
- Ning Xu
- Department of Physics, The Chinese University of Hong Kong, Hong Kong, People's Republic of China
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Berthier L, Tarjus G. Nonperturbative effect of attractive forces in viscous liquids. PHYSICAL REVIEW LETTERS 2009; 103:170601. [PMID: 19905741 DOI: 10.1103/physrevlett.103.170601] [Citation(s) in RCA: 62] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2009] [Indexed: 05/28/2023]
Abstract
We study the role of the attractive intermolecular forces in the viscous regime of a simple glass-forming liquid by using computer simulations. To this end, we compare the structure and the dynamics of a standard Lennard-Jones glass-forming liquid model with and without the attractive tail of the interaction potentials. The viscous slowing down of the two systems is found to be quantitatively and qualitatively different over a broad density range, whereas the static pair correlations remain close. The common assumption that the behavior of dense nonassociated liquids is determined by the short-ranged repulsive part of the intermolecular potentials dramatically breaks down for the relaxation in the viscous liquid regime.
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Affiliation(s)
- Ludovic Berthier
- Laboratoire des Colloïdes, Verres et Nanomatériaux, Université Montpellier II and CNRS, 34095 Montpellier, France
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Brazhkin VV, Kanzaki M, Funakoshi KI, Katayama Y. Viscosity behavior spanning four orders of magnitude in As-S melts under high pressure. PHYSICAL REVIEW LETTERS 2009; 102:115901. [PMID: 19392217 DOI: 10.1103/physrevlett.102.115901] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2008] [Indexed: 05/27/2023]
Abstract
Under compression, the As-S liquids are subject to transformations, including polymerization and metallization. We have measured the viscosity of the As-S liquids under high pressures. As a result, large viscosity variations by 4-5 orders of magnitude have been revealed. The viscosity values of the As-S liquids are moderate in the molecular state, very high in the covalent state, and low in the metallic state. Therefore, predicting the viscosity behavior in other melts under pressure is possible, which is of considerable importance for the physics of glass transition, geophysics, and material science.
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Affiliation(s)
- V V Brazhkin
- Institute for High Pressure Physics RAS, 142190 Troitsk Moscow Region, Russia.
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