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Mossa S, Bryk T, Ruocco G, Schirmacher W. Heterogeneous-elasticity theory of instantaneous normal modes in liquids. Sci Rep 2023; 13:21442. [PMID: 38052816 DOI: 10.1038/s41598-023-46248-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Accepted: 10/30/2023] [Indexed: 12/07/2023] Open
Abstract
Since decades, the concept of vibrational density of states in glasses has been mirrored in liquids by the instantaneous-normal-mode spectrum. In glasses instantaneous configurations are believed to be situated close to minima of the potential-energy hypersurface and all eigenvalues of the associated Hessian matrix are positive. In liquids this is no longer true, and modes corresponding to both positive and negative eigenvalues exist. The instantaneous-normal-mode spectrum has been numerically investigated in the past, and it has been demonstrated to bring important information on the liquid dynamics and transport properties. A systematic deeper theoretical understanding is now needed. Heterogeneous-elasticity theory has proven to be particularly successful in explaining many details of the low-frequency excitations in glasses, ranging from the thoroughly studied boson peak, to other anomalies related to the crossover between wave-like and random-matrix-like excitations. Here we present an extension of heterogeneous-elasticity theory to the liquid state, and show that the outcome of the theory agrees well to the results of extensive molecular-dynamics simulations of a model liquid at different temperatures. We find that the spectrum of eigenvalues [Formula: see text] has a sharp maximum close to (but not at) [Formula: see text], and decreases monotonically with [Formula: see text] on both its stable and unstable side. We show that the spectral shape strongly depends on temperature, being symmetric at high temperatures and becoming rather asymmetric at low temperatures, close to the dynamical critical temperature. Most importantly, we demonstrate that the theory naturally reproduces a surprising phenomenon, a zero-energy spectral singularity with a cusp-like character developing in the vibrational spectra upon cooling. This feature, known from a few previous numerical studies, has been generally overlooked in the past due to a misleading representation of the data. We provide a thorough analysis of this issue, based on both very accurate predictions of our theory, and computational studies of model liquid systems with extended size.
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Affiliation(s)
- Stefano Mossa
- CEA, IRIG-MEM-LSim, University Grenoble Alpes, 38054, Grenoble, France.
| | - Taras Bryk
- Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, Lviv, 79011, Ukraine
- Institute of Applied Mathematics and Fundamental Sciences, Lviv National Polytechnic University, Lviv, 79013, Ukraine
| | - Giancarlo Ruocco
- Center for Life Nano Science @Sapienza, Istituto Italiano di Tecnologia, 295 Viale Regina Elena, 00161, Roma, Italy.
- Dipartimento di Fisica, Universitá di Roma "La Sapienza", P.le Aldo Moro 5, 00185, Roma, Italy.
| | - Walter Schirmacher
- Center for Life Nano Science @Sapienza, Istituto Italiano di Tecnologia, 295 Viale Regina Elena, 00161, Roma, Italy
- Institut für Physik, Universität Mainz, Staudinger Weg 7, 55099, Mainz, Germany
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Chakraborty S, Krishnan VV, Ramola K, Karmakar S. Enhanced vibrational stability in glass droplets. PNAS NEXUS 2023; 2:pgad289. [PMID: 37746327 PMCID: PMC10516527 DOI: 10.1093/pnasnexus/pgad289] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/08/2023] [Accepted: 08/28/2023] [Indexed: 09/26/2023]
Abstract
We show through simulations of amorphous solids prepared in open-boundary conditions that they possess significantly fewer low-frequency vibrational modes compared to their periodic boundary counterparts. Specifically, using measurements of the vibrational density of states, we find that the D ( ω ) ∼ ω 4 law changes to D ( ω ) ∼ ω δ with δ ≈ 5 in two dimensions and δ ≈ 4.5 in three dimensions. Crucially, this enhanced stability is achieved when utilizing slow annealing protocols to generate solid configurations. We perform an anharmonic analysis of the minima corresponding to the lowest frequency modes in such open-boundary systems and discuss their correlation with the density of states. A study of various system sizes further reveals that small systems display a higher degree of localization in vibrations. Lastly, we confine open-boundary solids in order to introduce macroscopic stresses in the system, which are absent in the unconfined system and find that the D ( ω ) ∼ ω 4 behavior is recovered.
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Affiliation(s)
| | - Vishnu V Krishnan
- Tata Institute of Fundamental Research, Hyderabad, 500046 Telangana, India
| | - Kabir Ramola
- Tata Institute of Fundamental Research, Hyderabad, 500046 Telangana, India
| | - Smarajit Karmakar
- Tata Institute of Fundamental Research, Hyderabad, 500046 Telangana, India
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3
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Xu X, Douglas JF, Xu WS. Thermodynamic–Dynamic Interrelations in Glass-Forming Polymer Fluids. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01511] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Xiaolei Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Wen-Sheng Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
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4
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Modeling the instantaneous normal mode spectra of liquids as that of unstable elastic media. Proc Natl Acad Sci U S A 2022; 119:2119288119. [PMID: 35169078 PMCID: PMC8872781 DOI: 10.1073/pnas.2119288119] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 01/18/2022] [Indexed: 11/18/2022] Open
Abstract
We present a theory, based on an unstable elasticity model with thermally fluctuating elastic constants, which explains the salient features of the instantaneous normal mode (INM) spectrum of a numerically simulated liquid over a large range of temperatures. The INM spectrum of a liquid is obtained in a molecular dynamics (MD) simulation by considering the harmonic eigenvalue spectrum of the potential energy, taken at a given instant (snapshot). Because the INM spectrum records the curvatures of the fluctuating potential landscape of the liquid, an understanding of this spectrum may pave the way toward understanding the liquid to glass transformation process. We study the instantaneous normal mode (INM) spectrum of a simulated soft-sphere liquid at different equilibrium temperatures T. We find that the spectrum of eigenvalues ρ(λ) has a sharp maximum near (but not at) λ=0 and decreases monotonically with |λ| on both the stable and unstable sides of the spectrum. The spectral shape strongly depends on temperature. It is rather asymmetric at low temperatures (close to the dynamical critical temperature) and becomes symmetric at high temperatures. To explain these findings we present a mean-field theory for ρ(λ), which is based on a heterogeneous elasticity model, in which the local shear moduli exhibit spatial fluctuations, including negative values. We find good agreement between the simulation data and the model calculations, done with the help of the self-consistent Born approximation (SCBA), when we take the variance of the fluctuations to be proportional to the temperature T. More importantly, we find an empirical correlation of the positions of the maxima of ρ(λ) with the low-frequency exponent of the density of the vibrational modes of the glasses obtained by quenching to T=0 from the temperature T. We discuss the present findings in connection to the liquid to glass transformation and its precursor phenomena.
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5
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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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6
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Stariolo DA, Cugliandolo LF. Barriers, trapping times, and overlaps between local minima in the dynamics of the disordered Ising p-spin model. Phys Rev E 2020; 102:022126. [PMID: 32942488 DOI: 10.1103/physreve.102.022126] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2020] [Accepted: 07/28/2020] [Indexed: 11/07/2022]
Abstract
We study the low-temperature out-of-equilibrium Monte Carlo dynamics of the disordered Ising p-spin Model with p=3 and a small number of spin variables. We focus on sequences of configurations that are stable against single spin flips obtained by instantaneous gradient descent from persistent ones. We analyze the statistics of energy gaps, energy barriers, and trapping times on subsequences such that the overlap between consecutive configurations does not overcome a threshold. We compare our results to the predictions of various trap models finding the best agreement with the step model when the p-spin configurations are constrained to be uncorrelated.
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Affiliation(s)
- Daniel A Stariolo
- Universidade Federal Fluminense, Departamento de Física and National Institute of Science and Technology for Complex Systems, Av. Gal. Milton Tavares de Souza s/n, Campus da Praia Vermelha, 24210-346 Niterói, RJ, Brazil
| | - Leticia F Cugliandolo
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, UMR 7589 CNRS, Tour 13, 5ème Etage, 4 Place Jussieu, 75252 Paris 05, France.,Institut Universitaire de France, 1 rue Descartes, 75231 Paris Cedex 05, France
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7
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Bonfanti S, Kob W. Methods to locate saddle points in complex landscapes. J Chem Phys 2017; 147:204104. [DOI: 10.1063/1.5012271] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Affiliation(s)
- Silvia Bonfanti
- Dipartimento di Scienza ed Alta Tecnologia, Università dell’Insubria, Via Valleggio 11, 22100 Como, Italy
- Center for Complexity and Biosystems, Department of Physics, University of Milano, Via Celoria 16, 20133 Milano, Italy
- Laboratoire Charles Coulomb, Université de Montpellier and CNRS, UMR 5221, 34095 Montpellier, France
| | - Walter Kob
- Laboratoire Charles Coulomb, Université de Montpellier and CNRS, UMR 5221, 34095 Montpellier, France
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8
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Hinze G, Basché T, Vallée RAL. Single molecule probing of dynamics in supercooled polymers. Phys Chem Chem Phys 2011; 13:1813-8. [PMID: 21203637 DOI: 10.1039/c0cp01654c] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Fluorescence experiments with single BODIPY molecules embedded in a poly(methyl acrylate) matrix have been performed at various temperatures in the supercooled regime. By using pulsed excitation, fluorescence lifetime and linear dichroism time trajectories were accessible at the same time. Both observables have been analyzed without data binning. While the linear dichroism solely reflects single particle dynamics, the fluorescence lifetime observable depends on the molecular environment, so that the dynamics from the polymer host surrounding a chromophore contributes to this quantity. We observe that the lifetime correlation decays slightly faster than polarization correlation, indicating the occurrence of large angular reorientations. Additionally, dichroism time trajectories have been adducted to reveal directly the geometry of rotational dynamics. We identify small but also significantly larger rotational jumps being responsible for the overall molecular reorientation.
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Affiliation(s)
- G Hinze
- Department of Physical Chemistry, Johannes-Gutenberg University, 55099 Mainz, Germany
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9
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Andreozzi L, Faetti M, Giordano M, Zulli F. Length scales and dynamics in the reorientational relaxation of tracers in molecular and polymeric glass formers via electron spin resonance spectroscopy. J Phys Chem B 2010; 114:12833-9. [PMID: 20860386 DOI: 10.1021/jp106798c] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
It is widely accepted that a temperature region exists above the glass transition temperature, playing a fundamental role in the physics of polymers and glass formers. In this region, several dynamic crossovers have been experimentally and numerically revealed in the past years and the onset of glassy behavior is generally located, because of cooperative and heterogeneous features exhibited by the dynamics. In this Article, the rotational dynamics of two different stiff molecular spin probes dissolved in poly(propylene glycol) has been investigated by electron spin resonance spectroscopy in a wide temperature range. Decoupling phenomena between macroscopic and microscopic transport properties have been observed in the crossover region. A comparison with previous studies carried out with the same tracers dissolved in different polymers and glass formers strongly supports the idea that the observed crossover signals the onset of spatial correlations of dynamics on the length scale probed by the tracers.
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Affiliation(s)
- Laura Andreozzi
- Dipartimento di Fisica Enrico Fermi, Università di Pisa, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy
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10
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Papathanassiou AN, Sakellis I. Correlation of the scaling exponent γ of the diffusivity-density function in viscous liquids with their elastic properties. J Chem Phys 2010; 132:154503. [DOI: 10.1063/1.3382645] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Vallée RAL, Paul W, Binder K. Probe molecules in polymer melts near the glass transition: A molecular dynamics study of chain length effects. J Chem Phys 2010; 132:034901. [PMID: 20095750 DOI: 10.1063/1.3284780] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- R A L Vallée
- Centre de Recherche Paul Pascal (CNRS), 115 Avenue du Docteur Albert Schweitzer, 33600 Pessac, France
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12
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Coslovich D, Pastore G. Dynamics and energy landscape in a tetrahedral network glass-former: direct comparison with models of fragile liquids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:285107. [PMID: 21828513 DOI: 10.1088/0953-8984/21/28/285107] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We report molecular dynamics simulations for a new model of tetrahedral network glass-former, based on short-range spherical potentials. Despite the simplicity of the forcefield employed, our model reproduces some essential physical properties of silica, an archetypal network-forming material. Structural and dynamical properties, including dynamic heterogeneities and the nature of local rearrangements, are investigated in detail and a direct comparison with models of close-packed, fragile glass-formers is performed. The outcome of this comparison is rationalized in terms of the properties of the potential energy surface, focusing on the unstable modes of the stationary points. Our results indicate that the weak degree of dynamic heterogeneity observed in network glass-formers may be attributed to an excess of localized unstable modes, associated with elementary dynamical events such as bond breaking and reformation. In contrast, the more fragile Lennard-Jones mixtures are characterized by a larger fraction of extended unstable modes, which lead to a more cooperative and heterogeneous dynamics.
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Affiliation(s)
- D Coslovich
- Institut für Theoretische Physik and CMS, Technische Universität Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria
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13
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14
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Papathanassiou AN. Density scaling of the diffusion coefficient at various pressures in viscous liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:032501. [PMID: 19391997 DOI: 10.1103/physreve.79.032501] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2008] [Indexed: 05/27/2023]
Abstract
Fundamental thermodynamics and an earlier elastic solid-state point defect model [P. Varotsos and K. Alexopoulos, Phys. Rev. B 15, 4111 (1977); Phys. Rev. B 18, 2683 (1978)] are employed to formulate an analytical second-order polynomial function describing the density scaling of the diffusion coefficient in viscous liquids. The function parameters are merely determined by the scaling exponent, which is directly connected with the Grüneisen constant. Density scaling diffusion coefficient isotherms obtained at different pressures collapse on a unique master curve, in agreement with recent computer simulation results of Lennard-Jones viscous liquids [D. Coslovich and C. M. Roland, J. Phys. Chem. 112, 1329 (2008)].
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Affiliation(s)
- A N Papathanassiou
- Department of Physics, Solid State Physics Section, University of Athens, Panepistimiopolis, 157 84 Zografos, Greece.
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15
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Heuer A. Exploring the potential energy landscape of glass-forming systems: from inherent structures via metabasins to macroscopic transport. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2008; 20:373101. [PMID: 21694408 DOI: 10.1088/0953-8984/20/37/373101] [Citation(s) in RCA: 203] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
In this review a systematic analysis of the potential energy landscape (PEL) of glass-forming systems is presented. Starting from the thermodynamics, the route towards the dynamics is elucidated. A key step in this endeavor is the concept of metabasins. The relevant energy scales of the PEL can be characterized. Based on the simulation results for some glass-forming systems one can formulate a relevant model system (ideal Gaussian glass-former) which can be treated analytically. The macroscopic transport can be related to the microscopic hopping processes, using either the strong relation between energy (thermodynamics) and waiting times (dynamics) or, alternatively, the concepts of the continuous-time random walk. The relation to the geometric properties of the PEL is stressed. The emergence of length scales within the PEL approach as well as the nature of finite-size effects is discussed. Furthermore, the PEL view is compared to other approaches describing the glass transition.
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Affiliation(s)
- Andreas Heuer
- Institut für Physikalische Chemie, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Corrensstraße 30, Germany
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16
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Wang C, Stratt RM. Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: Geodesic pathways through the potential energy landscape. J Chem Phys 2007; 127:224504. [DOI: 10.1063/1.2801995] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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17
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Coslovich D, Pastore G. Understanding fragility in supercooled Lennard-Jones mixtures. II. Potential energy surface. J Chem Phys 2007; 127:124505. [PMID: 17902919 DOI: 10.1063/1.2773720] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The connection between isobaric fragility and the properties of high-order stationary points of the potential energy surface in different supercooled Lennard-Jones mixtures was investigated. The increase of effective activation energies upon supercooling appears to be driven by the increase of average potential energy barriers measured by the energy dependence of the fraction of unstable modes. Such an increase is sharper, the more fragile the mixture. Correlations between fragility and other properties of high-order stationary points, including the vibrational density of states and the localization features of unstable modes, are also discussed.
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Affiliation(s)
- D Coslovich
- Dipartimento di Fisica Teorica, Università di Trieste--Strada Costiera 11, 34100 Triesta, Italy
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18
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Vallée RAL, Paul W, Binder K. Single molecule probing of the glass transition phenomenon: Simulations of several types of probes. J Chem Phys 2007; 127:154903. [DOI: 10.1063/1.2794334] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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19
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Stariolo DA, Fabricius G. Fickian crossover and length scales from two point functions in supercooled liquids. J Chem Phys 2007; 125:64505. [PMID: 16942296 DOI: 10.1063/1.2221309] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Particle motion of a Lennard-Jones supercooled liquid near the glass transition is studied by molecular dynamics simulations. We analyze the wave vector dependence of relaxation times in the incoherent self-scattering function and show that at least three different regimes can be identified and its scaling properties determined. The transition from one regime to another happens at characteristic length scales. The length scale associated with the onset of Fickian diffusion corresponds to the maximum size of heterogeneities in the system, and the characteristic time scale is several times larger than the alpha relaxation time. A second crossover length scale is observed, which corresponds to the typical time and length of heterogeneities, in agreement with results from four point functions. The different regimes can be traced back to the behavior of the van Hove distribution of displacements, which shows a characteristic exponential regime in the heterogeneous region before the crossover to Gaussian diffusion and should be observable in experiments. Our results show that it is possible to obtain characteristic length scales of heterogeneities through the computation of two point functions at different times.
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Affiliation(s)
- Daniel A Stariolo
- Departamento de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre, Brazil.
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20
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Chamon C, Charbonneau P, Cugliandolo LF, Reichman DR, Sellitto M. Out-of-equilibrium dynamical fluctuations in glassy systems. J Chem Phys 2006; 121:10120-37. [PMID: 15549887 DOI: 10.1063/1.1809585] [Citation(s) in RCA: 57] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper we extend the earlier treatment of out-of-equilibrium mesoscopic fluctuations in glassy systems in several significant ways. First, via extensive simulations, we demonstrate that models of glassy behavior without quenched disorder display scalings of the probability of local two-time correlators that are qualitatively similar to that of models with short-ranged quenched interactions. The key ingredient for such scaling properties is shown to be the development of a criticallike dynamical correlation length, and not other microscopic details. This robust data collapse may be described in terms of a time-evolving "extreme value" distribution. We develop a theory to describe both the form and evolution of these distributions based on a effective sigma model approach.
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Affiliation(s)
- C Chamon
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA.
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21
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Kim J, Keyes T. On the mechanism of reorientational and structural relaxation in supercooled liquids: the role of border dynamics and cooperativity. J Chem Phys 2006; 121:4237-45. [PMID: 15332971 DOI: 10.1063/1.1776553] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Molecular dynamics simulation and analysis based upon the many-body potential energy landscape (PEL) are employed to characterize single molecule reorientation and structural relaxation, and their interrelation, in deeply supercooled liquid CS(2). The rotational mechanism changes from small-step Debye diffusion to sudden large angle reorientation (SLAR) as the temperature falls below the mode-coupling temperature T(c). The onset of SLAR is explained in terms of the PEL; it is an essential feature of low-T rotational dynamics, along with the related phenomena of dynamic heterogeneity and the bifurcation of slow and fast relaxation processes. A long trajectory in which the system is initially trapped in a low energy local minimum, and eventually escapes, is followed in detail, both on the PEL and in real space. During the trapped period, "return" dynamics occurs, always leading back to the trap. Structural relaxation is identified with irreversible escape to a new trap. These processes lead to weak and strong SLAR, respectively; strong SLAR is a clear signal of structural relaxation. Return dynamics involves small groups of two to four molecules, while a string-like structure composed of all the active groups participates in the escape. It is proposed that, rather than simple, nearly instantaneous, one-dimensional barrier crossings, relaxation involves activation of the system to the complex, multidimensional region on the borders of the basins of attraction of the minima for an extended period.
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Affiliation(s)
- Joohyun Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA
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22
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Cotterill RMJ, Madsen JU. The glass state: characterizing energy landscape features. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2006; 18:6507-6516. [PMID: 21690850 DOI: 10.1088/0953-8984/18/28/006] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We probed the topologies imposed on configuration hyperspace by the potential energy function-the shapes of the constant potential energy manifolds-for the glassy state of monatomic Lennard-Jones matter, by following trajectories of constant potential energy. A prominent characteristic of this model matter is well-defined regions of confinement (pockets) in configuration hyperspace. We found that there are constant potential energy hyperspace paths (tubes) between such pockets, applying even to paths linking glassy regions to crystalline regions of configuration hyperspace. Also, we found that glass and crystal pockets are interspersed. For monatomic Lennard-Jones matter at least, the transition from glass to crystal therefore does not have to involve the traversing of a potential energy barrier, as is usually assumed.
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Affiliation(s)
- Rodney M J Cotterill
- Quantum Protein Centre, Physics Institute, Building 309, Technical University of Denmark, 2800 Lyngby, Denmark
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23
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Moreno AJ, Saika-Voivod I, Zaccarelli E, La Nave E, Buldyrev SV, Tartaglia P, Sciortino F. Non-Gaussian energy landscape of a simple model for strong network-forming liquids: Accurate evaluation of the configurational entropy. J Chem Phys 2006; 124:204509. [PMID: 16774355 DOI: 10.1063/1.2196879] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a numerical study of the statistical properties of the potential energy landscape of a simple model for strong network-forming liquids. The model is a system of spherical particles interacting through a square-well potential, with an additional constraint that limits the maximum number of bonds Nmax per particle. Extensive simulations have been carried out as a function of temperature, packing fraction, and Nmax. The dynamics of this model are characterized by Arrhenius temperature dependence of the transport coefficients and by nearly exponential relaxation of dynamic correlators, i.e., features defining strong glass-forming liquids. This model has two important features: (i) Landscape basins can be associated with bonding patterns. (ii) The configurational volume of the basin can be evaluated in a formally exact way, and numerically with an arbitrary precision. These features allow us to evaluate the number of different topologies the bonding pattern can adopt. We find that the number of fully bonded configurations, i.e., configurations in which all particles are bonded to Nmax neighbors, is extensive, suggesting that the configurational entropy of the low temperature fluid is finite. We also evaluate the energy dependence of the configurational entropy close to the fully bonded state and show that it follows a logarithmic functional form, different from the quadratic dependence characterizing fragile liquids. We suggest that the presence of a discrete energy scale, provided by the particle bonds, and the intrinsic degeneracy of fully bonded disordered networks differentiates strong from fragile behavior.
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Affiliation(s)
- A J Moreno
- Dipartimento di Fisica, Università degli Studi di Roma La Sapienza, Piazzale Aldo Moro 2, I-00185 Roma, Italy.
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Angelani L, Ruocco G, Zamponi F. Relationship between phase transitions and topological changes in one-dimensional models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:016122. [PMID: 16090051 DOI: 10.1103/physreve.72.016122] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2005] [Revised: 05/24/2005] [Indexed: 05/03/2023]
Abstract
We address the question of the quantitative relationship between thermodynamic phase transitions and topological changes in the potential energy manifold analyzing two classes of one dimensional models, the Burkhardt solid-on-solid model and the Peyrard-Bishop model for DNA thermal denaturation, both in the confining and nonconfining version. These models, apparently, do not fit [M. Kastner, Phys. Rev. Lett. 93, 150601 (2004)] in the general idea that the phase transition is signaled by a topological discontinuity. We show that in both models the phase transition energy v(c) is actually noncoincident with, and always higher than, the energy v(theta) at which a topological change appears. However, applying a procedure already successfully employed in other cases as the mean field phi4 model, i.e., introducing a map M:v-->v(s) from levels of the energy hypersurface V to the level of the stationary points "visited" at temperature T, we find that M (v(c))=v(theta). This result enhances the relevance of the underlying stationary points in determining the thermodynamics of a system, and extends the validity of the topological approach to the study of phase transition to the elusive one-dimensional systems considered here.
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Affiliation(s)
- L Angelani
- Dipartimento di Fisica, Università di Roma La Sapienza, P.le A. Moro 2, 00185 Roma, Italy
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Andersen HC. Molecular dynamics studies of heterogeneous dynamics and dynamic crossover in supercooled atomic liquids. Proc Natl Acad Sci U S A 2005; 102:6686-91. [PMID: 15870201 PMCID: PMC1100779 DOI: 10.1073/pnas.0500946102] [Citation(s) in RCA: 95] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Supercooled liquids near the glass transition exhibit the phenomenon of heterogeneous relaxation; at any specific time, a nominally homogeneous equilibrium fluid undergoes dynamic fluctuations in its structure on a molecular distance scale with rates that are very different in different regions of the sample. Several theoretical and simulation studies have suggested a change in the nature of the dynamics of fluids as they are supercooled, leading to the concept of a dynamic crossover that is often associated with mode coupling theory. Here, we will review the use of molecular dynamics computer simulation methods to investigate heterogeneous dynamics and dynamic crossovers in models of atomic liquids.
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Affiliation(s)
- Hans C Andersen
- Department of Chemistry, Stanford University, Stanford, CA 94305, USA.
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Angelani L, Casetti L, Pettini M, Ruocco G, Zamponi F. Topology and phase transitions: from an exactly solvable model to a relation between topology and thermodynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:036152. [PMID: 15903538 DOI: 10.1103/physreve.71.036152] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2004] [Indexed: 05/02/2023]
Abstract
The elsewhere surmized topological origin of phase transitions is given here important evidence through the analytic study of an exactly solvable model for which both topology of submanifolds of configuration space and thermodynamics are worked out. The model is a mean-field one with a k-body interaction. It undergoes a second-order phase transition for k=2 and a first-order one for k >2 . This opens a perspective for the understanding of the deep origin of first and second-order phase transitions, respectively. In particular, a remarkable theoretical result consists of a mathematical characterization of first-order transitions. Moreover, we show that a "reduced" configuration space can be defined in terms of collective variables, such that the correspondence between phase transitions and topology changes becomes one-to-one, for this model. Finally, an unusual relationship is worked out between the microscopic description of a classical N -body system and its macroscopic thermodynamic behavior. This consists of a functional dependence of thermodynamic entropy upon the Morse indexes of the critical points (saddles) of the constant energy hypersurfaces of the microscopic 2N-dimensional phase space. Thus phase space (and configuration space) topology is directly related to thermodynamics.
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Affiliation(s)
- Luca Angelani
- Dipartimento di Fisica and INFM-CRS SMC, Università di Roma La Sapienza, Piazzale A. Moro 2, I-00185 Rome, Italy.
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27
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Junier I, Bertin E. Dynamic phase diagram of the number partitioning problem. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:066126. [PMID: 15697453 DOI: 10.1103/physreve.70.066126] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2004] [Indexed: 05/24/2023]
Abstract
We study the dynamic phase diagram of a spin model associated with the number partitioning problem, as a function of temperature and of the fraction K/N of spins allowed to flip simultaneously. The case K=1 reproduces the activated behavior of Bouchaud's trap model, whereas the opposite limit K=N can be mapped onto the entropic trap model proposed by Barrat and Mézard. In the intermediate case 1<<K<<N , the dynamics corresponds to a modified version of the Barrat and Mézard model, which includes a slow (rather than instantaneous) decorrelation at each step. A transition from an activated regime to an entropic one is observed at temperature T(g) /2 in agreement with recent work on this model. Ergodicity breaking occurs for T< T(g) /2 in the thermodynamic limit, if K/N-->0 . In this temperature range, the model exhibits a nontrivial fluctuation-dissipation relation leading for K<<N to a single effective temperature equal to T(g) /2 . These results give insights into the relevance and limitations of the picture proposed by simple trap models.
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Affiliation(s)
- Ivan Junier
- PMMH, ESPCI, 10 rue Vauquelin, F-75005 Paris, France
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Angelani L, De Michele C, Ruocco G, Sciortino F. Saddles and softness in simple model liquids. J Chem Phys 2004; 121:7533-4. [PMID: 15473830 DOI: 10.1063/1.1801011] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Mittal J, Shah P, Truskett TM. Using Energy Landscapes To Predict the Properties of Thin Films. J Phys Chem B 2004. [DOI: 10.1021/jp040402j] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jeetain Mittal
- Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712
| | - Pooja Shah
- Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712
| | - Thomas M. Truskett
- Department of Chemical Engineering and Institute for Theoretical Chemistry, The University of Texas at Austin, Austin, Texas 78712
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Garanin DA, Schilling R, Scala A. Saddle index properties, singular topology, and its relation to thermodynamic singularities for a phi4 mean-field model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:036125. [PMID: 15524605 DOI: 10.1103/physreve.70.036125] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2004] [Indexed: 05/24/2023]
Abstract
We investigate the potential energy surface of a phi(4) model with infinite range interactions. All stationary points can be uniquely characterized by three real numbers alpha(+) , alpha(0) , alpha(-) with alpha(+) + alpha(0) + alpha(-) =1 , provided that the interaction strength mu is smaller than a critical value. The saddle index n(s) is equal to alpha(0) and its distribution function has a maximum at n(max)(s) =1/3 . The density p (e) of stationary points with energy per particle e , as well as the Euler characteristic chi (e) , are singular at a critical energy e(c) (mu) , if the external field H is zero. However, e(c) (mu) not equal upsilon(c) (mu) , where upsilon(c) (mu) is the mean potential energy per particle at the thermodynamic phase transition point T(c) . This proves that previous claims that the topological and thermodynamic transition points coincide is not valid, in general. Both types of singularities disappear for H not equal 0 . The average saddle index n (s) as function of e decreases monotonically with e and vanishes at the ground state energy, only. In contrast, the saddle index n(s) as function of the average energy e ( n(s) ) is given by n(s) ( e ) =1+4 e (for H=0 ) that vanishes at e =-1/4> upsilon(0) , the ground state energy.
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Affiliation(s)
- D A Garanin
- Institut für Physik, Johannes-Gutenberg-Universität, D-55099 Mainz, Germany
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Shell MS, Debenedetti PG, Panagiotopoulos AZ. Saddles in the energy landscape: extensivity and thermodynamic formalism. PHYSICAL REVIEW LETTERS 2004; 92:035506. [PMID: 14753888 DOI: 10.1103/physrevlett.92.035506] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2003] [Indexed: 05/24/2023]
Abstract
We formally extend the energy landscape approach for the thermodynamics of liquids to account for saddle points. By considering the extensive nature of macroscopic potential energies, we derive the scaling behavior of saddles with system size, as well as several approximations for the properties of low-order saddles (i.e., those with only a few unstable directions). We then cast the canonical partition function in a saddle-explicit form and develop, for the first time, a rigorous energy landscape approach capable of reproducing trends observed in simulations, in particular, the temperature dependence of the energy and fractional order of sampled saddles.
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Affiliation(s)
- M Scott Shell
- Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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Berthier L, Garrahan JP. Real space origin of temperature crossovers in supercooled liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:041201. [PMID: 14682930 DOI: 10.1103/physreve.68.041201] [Citation(s) in RCA: 74] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2003] [Indexed: 05/24/2023]
Abstract
We show that the various crossovers between dynamical regimes observed in experiments and simulations of supercooled liquids can be explained in simple terms from the existence and statistical properties of dynamical heterogeneities. We confirm that dynamic heterogeneity is responsible for the slowing down of glass formers at temperatures well above the dynamic singularity Tc predicted by mode-coupling theory. Our results imply that activated processes govern the long-time dynamics even in the temperature regime where they are neglected by mode-coupling theory. We show that alternative interpretations based on topographic properties of the potential energy landscape are inefficient ways of describing simple physical features which are naturally accounted for within our approach. We show in particular that the reported links between mode coupling and landscape singularities do not exist.
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Affiliation(s)
- Ludovic Berthier
- Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
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Zamponi F, Angelani L, Cugliandolo LF, Kurchan J, Ruocco G. Dynamics and geometric properties of thek-trigonometric model. ACTA ACUST UNITED AC 2003. [DOI: 10.1088/0305-4470/36/32/303] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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