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Mendoza-Méndez P, Peredo-Ortiz R, Lázaro-Lázaro E, Chávez-Paez M, Ruiz-Estrada H, Pacheco-Vázquez F, Medina-Noyola M, Elizondo-Aguilera LF. Structural relaxation, dynamical arrest, and aging in soft-sphere liquids. J Chem Phys 2022; 157:244504. [PMID: 36586975 DOI: 10.1063/5.0121224] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
We investigate the structural relaxation of a soft-sphere liquid quenched isochorically (ϕ = 0.7) and instantaneously to different temperatures Tf above and below the glass transition. For this, we combine extensive Brownian dynamics simulations and theoretical calculations based on the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory. The response of the liquid to a quench generally consists of a sub-linear increase of the α-relaxation time with system's age. Approaching the ideal glass-transition temperature from above (Tf > Ta), sub-aging appears as a transient process describing a broad equilibration crossover for quenches to nearly arrested states. This allows us to empirically determine an equilibration timescale teq(Tf) that becomes increasingly longer as Tf approaches Ta. For quenches inside the glass (Tf ≤ Ta), the growth rate of the structural relaxation time becomes progressively larger as Tf decreases and, unlike the equilibration scenario, τα remains evolving within the whole observation time-window. These features are consistently found in theory and simulations with remarkable semi-quantitative agreement and coincide with those revealed in a previous and complementary study [P. Mendoza-Méndez et al., Phys. Rev. 96, 022608 (2017)] that considered a sequence of quenches with fixed final temperature Tf = 0 but increasing ϕ toward the hard-sphere dynamical arrest volume fraction ϕHS a=0.582. The NE-SCGLE analysis, however, unveils various fundamental aspects of the glass transition, involving the abrupt passage from the ordinary equilibration scenario to the persistent aging effects that are characteristic of glass-forming liquids. The theory also explains that, within the time window of any experimental observation, this can only be observed as a continuous crossover.
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Affiliation(s)
- P Mendoza-Méndez
- Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, CP 72570 Puebla, Mexico
| | - R Peredo-Ortiz
- Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, CP 72570 Puebla, Mexico
| | - E Lázaro-Lázaro
- Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, CP 72570 Puebla, Mexico
| | - M Chávez-Paez
- Instituto de Física, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, Mexico
| | - H Ruiz-Estrada
- Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, CP 72570 Puebla, Mexico
| | - F Pacheco-Vázquez
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570 Puebla, Mexico
| | - M Medina-Noyola
- Instituto de Física, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, Mexico
| | - L F Elizondo-Aguilera
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570 Puebla, Mexico
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Mandal R, Sollich P. Shear-induced orientational ordering in an active glass former. Proc Natl Acad Sci U S A 2021; 118:e2101964118. [PMID: 34551973 PMCID: PMC8488658 DOI: 10.1073/pnas.2101964118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 08/12/2021] [Indexed: 11/18/2022] Open
Abstract
Dense assemblies of self-propelled particles that can form solid-like states also known as active or living glasses are abundant around us, covering a broad range of length scales and timescales: from the cytoplasm to tissues, from bacterial biofilms to vehicular traffic jams, and from Janus colloids to animal herds. Being structurally disordered as well as strongly out of equilibrium, these systems show fascinating dynamical and mechanical properties. Using extensive molecular dynamics simulation and a number of distinct dynamical and mechanical order parameters, we differentiate three dynamical steady states in a sheared model active glassy system: 1) a disordered state, 2) a propulsion-induced ordered state, and 3) a shear-induced ordered state. We supplement these observations with an analytical theory based on an effective single-particle Fokker-Planck description to rationalize the existence of the shear-induced orientational ordering behavior in an active glassy system without explicit aligning interactions of, for example, Vicsek type. This ordering phenomenon occurs in the large persistence time limit and is made possible only by the applied steady shear. Using a Fokker-Planck description with parameters that can be measured independently, we make testable predictions for the joint distribution of single-particle position and orientation. These predictions match well with the joint distribution measured from direct numerical simulation. Our results are of relevance for experiments exploring the rheological response of dense active colloids and jammed active granular matter systems.
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Affiliation(s)
- Rituparno Mandal
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37 077 Göttingen, Germany;
| | - Peter Sollich
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37 077 Göttingen, Germany
- Department of Mathematics, King's College London, London WC2R 2LS, United Kingdom
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3
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Mandal R, Sollich P. Multiple Types of Aging in Active Glasses. PHYSICAL REVIEW LETTERS 2020; 125:218001. [PMID: 33274976 DOI: 10.1103/physrevlett.125.218001] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2020] [Accepted: 10/20/2020] [Indexed: 06/12/2023]
Abstract
Recent experiments and simulations have revealed glassy features in, e.g., cytoplasm, living tissues and dense assemblies of self-propelled colloids. This leads to a fundamental question: how do these nonequilibrium (active) amorphous materials differ from conventional passive glasses, created by lowering temperature or increasing density? To address this we investigate the aging after a quench to an almost arrested state of a model active glass former, a Kob-Andersen glass in two dimensions. Each constituent particle is driven by a constant propulsion force whose direction diffuses over time. Using extensive molecular dynamics simulations we reveal rich aging behavior of this dense active matter system: short persistence times of the active forcing give effective thermal aging; in the opposite limit we find a two-step aging process with active athermal aging at short times and activity-driven aging at late times. We develop a dedicated simulation method that gives access to this longtime scaling regime for highly persistent active forces.
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Affiliation(s)
- Rituparno Mandal
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
| | - Peter Sollich
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
- Department of Mathematics, King's College London, London WC2R 2LS, United Kingdom
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4
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Kasting BJ, Beasley MS, Guiseppi-Elie A, Richert R, Ediger MD. Relationship between aged and vapor-deposited organic glasses: Secondary relaxations in methyl-m-toluate. J Chem Phys 2019; 151:144502. [DOI: 10.1063/1.5123305] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Affiliation(s)
- B. J. Kasting
- Department of Chemistry, University of Wisconsin – Madison, Madison, Wisconsin 53706, USA
| | - M. S. Beasley
- Department of Chemistry, University of Wisconsin – Madison, Madison, Wisconsin 53706, USA
| | - A. Guiseppi-Elie
- Department of Biomedical Engineering, Texas A&M University, College Station, Texas 77843, USA
| | - R. Richert
- Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287, USA
| | - M. D. Ediger
- Department of Chemistry, University of Wisconsin – Madison, Madison, Wisconsin 53706, USA
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Rodríguez-Tinoco C, Gonzalez-Silveira M, Ràfols-Ribé J, Vila-Costa A, Martinez-Garcia JC, Rodríguez-Viejo J. Surface-Bulk Interplay in Vapor-Deposited Glasses: Crossover Length and the Origin of Front Transformation. PHYSICAL REVIEW LETTERS 2019; 123:155501. [PMID: 31702315 DOI: 10.1103/physrevlett.123.155501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2019] [Revised: 07/24/2019] [Indexed: 06/10/2023]
Abstract
Thin film stable glasses transform into a liquid by a moving front that propagates from surfaces or interfaces with higher mobility. We use calorimetric data of vapor-deposited glasses of different thicknesses and stabilities to identify the role of glassy and liquid dynamics on the transformation process. By invoking the existence of an ultrathin intermediate layer whose transformation strongly depends on the properties of both the liquid and the glass, we show that the recovery to equilibrium is driven by the mismatch in the dynamics between glass and liquid. The lifetime of this intermediate layer associated with the moving front is the geometric mean between the bulk transformation time and the alpha relaxation time. Within this view, we explain the observed dependencies of the growth front velocity and the crossover length with both stability and temperature. Extrapolation of these results points towards ordinary thin film glasses transforming via a frontlike transformation mechanism if heated sufficiently fast, establishing a close connection between vapor-deposited and liquid-cooled glasses.
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Affiliation(s)
- Cristian Rodríguez-Tinoco
- Group of Nanomaterials and Microsystems, Physics Department, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
| | - Marta Gonzalez-Silveira
- Group of Nanomaterials and Microsystems, Physics Department, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
| | - Joan Ràfols-Ribé
- Group of Nanomaterials and Microsystems, Physics Department, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
| | - Ana Vila-Costa
- Group of Nanomaterials and Microsystems, Physics Department, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
| | - Julio Cesar Martinez-Garcia
- Group of Nanomaterials and Microsystems, Physics Department, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
| | - Javier Rodríguez-Viejo
- Group of Nanomaterials and Microsystems, Physics Department, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
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6
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Boettcher S, Robe DM, Sibani P. Aging is a log-Poisson process, not a renewal process. Phys Rev E 2018; 98:020602. [PMID: 30253586 DOI: 10.1103/physreve.98.020602] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2018] [Indexed: 06/08/2023]
Abstract
Aging is a ubiquitous relaxation dynamic in disordered materials. It ensues after a rapid quench from an equilibrium "fluid" state into a nonequilibrium, history-dependent jammed state. We propose a physically motivated description that contrasts sharply with a continuous-time random walk (CTRW) with broadly distributed trapping times commonly used to fit aging data. A renewal process such as CTRW proves irreconcilable with the log-Poisson statistic exhibited, for example, by jammed colloids as well as by disordered magnets. A log-Poisson process is characteristic of the intermittent and decelerating dynamics of jammed matter usually activated by record-breaking fluctuations ("quakes"). We show that such a record dynamics provides a universal model for aging, physically grounded in generic features of free-energy landscapes of disordered systems.
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Affiliation(s)
- Stefan Boettcher
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| | - Dominic M Robe
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| | - Paolo Sibani
- Institut for Fysik Kemi og Farmaci, Syddansk Universitet, DK-5230 Odense M, Denmark
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7
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Jenkinson T, Crowther P, Turci F, Royall CP. Weak temperature dependence of ageing of structural properties in atomistic model glassformers. J Chem Phys 2018; 147:054501. [PMID: 28789533 DOI: 10.1063/1.4994836] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Ageing phenomena are investigated from a structural perspective in two binary Lennard-Jones glassformers, the Kob-Andersen and Wahnström mixtures. In both, the geometric motif assumed by the glassformer upon supercooling, the locally favoured structure (LFS), has been established. The Kob-Andersen mixture forms bicapped square antiprisms; the Wahnström model forms icosahedra. Upon ageing, we find that the structural relaxation time has a time-dependence consistent with a power law. However, the LFS population and potential energy increase and decrease, respectively, in a logarithmic fashion. Remarkably, over the time scales investigated, which correspond to a factor of 104 change in relaxation times, the rate at which these quantities age appears almost independent of temperature. Only at temperatures far below the Vogel-Fulcher-Tamman temperature do the ageing dynamics slow.
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Affiliation(s)
- Thomas Jenkinson
- H. H. Wills Physics Laboratory, Tyndall Avenue, Bristol, United Kingdom
| | - Peter Crowther
- H. H. Wills Physics Laboratory, Tyndall Avenue, Bristol, United Kingdom
| | - Francesco Turci
- H. H. Wills Physics Laboratory, Tyndall Avenue, Bristol, United Kingdom
| | - C Patrick Royall
- H. H. Wills Physics Laboratory, Tyndall Avenue, Bristol, United Kingdom
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8
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Helfferich J, Brisch J, Meyer H, Benzerara O, Ziebert F, Farago J, Baschnagel J. Continuous-time random-walk approach to supercooled liquids: Self-part of the van Hove function and related quantities. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:71. [PMID: 29876655 DOI: 10.1140/epje/i2018-11680-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2018] [Accepted: 05/16/2018] [Indexed: 06/08/2023]
Abstract
From equilibrium molecular dynamics (MD) simulations of a bead-spring model for short-chain glass-forming polymer melts we calculate several quantities characterizing the single-monomer dynamics near the (extrapolated) critical temperature [Formula: see text] of mode-coupling theory: the mean-square displacement g0(t), the non-Gaussian parameter [Formula: see text] and the self-part of the van Hove function [Formula: see text] which measures the distribution of monomer displacements r in time t. We also determine these quantities from a continuous-time random walk (CTRW) approach. The CTRW is defined in terms of various probability distributions which we know from previous analysis. Utilizing these distributions the CTRW can be solved numerically and compared to the MD data with no adjustable parameter. The MD results reveal the heterogeneous and non-Gaussian single-particle dynamics of the supercooled melt near [Formula: see text]. In the time window of the early [Formula: see text] relaxation [Formula: see text] is large and [Formula: see text] is broad, reflecting the coexistence of monomer displacements that are much smaller ("slow particles") and much larger ("fast particles") than the average at time t, i.e. than [Formula: see text]. For large r the tail of [Formula: see text] is compatible with an exponential decay, as found for many glassy systems. The CTRW can reproduce the spatiotemporal dependence of [Formula: see text] at a qualitative to semiquantitative level. However, it is not quantitatively accurate in the studied temperature regime, although the agreement with the MD data improves upon cooling. In the early [Formula: see text] regime we also analyze the MD results for [Formula: see text] via the space-time factorization theorem predicted by ideal mode-coupling theory. While we find the factorization to be well satisfied for small r, both above and below [Formula: see text] , deviations occur for larger r comprising the tail of [Formula: see text]. The CTRW analysis suggests that single-particle "hops" are a contributing factor for these deviations.
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Affiliation(s)
- J Helfferich
- Institute of Nanotechnology, Karlsruhe Institute of Technology, D-76021, Karlsruhe, Germany
| | - J Brisch
- Université de Strasbourg, CNRS, ICS UPR22, F-67000, Strasbourg, France
| | - H Meyer
- Université de Strasbourg, CNRS, ICS UPR22, F-67000, Strasbourg, France
| | - O Benzerara
- Université de Strasbourg, CNRS, ICS UPR22, F-67000, Strasbourg, France
| | - F Ziebert
- Institute for Theoretical Physics, University of Heidelberg, D-69120, Heidelberg, Germany
| | - J Farago
- Université de Strasbourg, CNRS, ICS UPR22, F-67000, Strasbourg, France
| | - J Baschnagel
- Université de Strasbourg, CNRS, ICS UPR22, F-67000, Strasbourg, France.
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Ruta B, Pineda E, Evenson Z. Relaxation processes and physical aging in metallic glasses. JOURNAL OF PHYSICS: CONDENSED MATTER 2017; 29:503002. [PMID: 0 DOI: 10.1088/1361-648x/aa9964] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
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10
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Micoulaut M. Relaxation and physical aging in network glasses: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:066504. [PMID: 27213928 DOI: 10.1088/0034-4885/79/6/066504] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Recent progress in the description of glassy relaxation and aging are reviewed for the wide class of network-forming materials such as GeO2, Ge x Se1-x , silicates (SiO2-Na2O) or borates (B2O3-Li2O), all of which have an important usefulness in domestic, geological or optoelectronic applications. A brief introduction of the glass transition phenomenology is given, together with the salient features that are revealed both from theory and experiments. Standard experimental methods used for the characterization of the slowing down of the dynamics are reviewed. We then discuss the important role played by aspects of network topology and rigidity for the understanding of the relaxation of the glass transition, while also permitting analytical predictions of glass properties from simple and insightful models based on the network structure. We also emphasize the great utility of computer simulations which probe the dynamics at the molecular level, and permit the calculation of various structure-related functions in connection with glassy relaxation and the physics of aging which reveal the non-equilibrium nature of glasses. We discuss the notion of spatial variations of structure which leads to the concept of 'dynamic heterogeneities', and recent results in relation to this important topic for network glasses are also reviewed.
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Affiliation(s)
- Matthieu Micoulaut
- Paris Sorbonne Universités, LPTMC-UPMC, 4 place Jussieu, 75252 Paris cedex 05, France
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11
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Metzler R, Jeon JH, Cherstvy AG. Non-Brownian diffusion in lipid membranes: Experiments and simulations. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2016; 1858:2451-2467. [PMID: 26826272 DOI: 10.1016/j.bbamem.2016.01.022] [Citation(s) in RCA: 127] [Impact Index Per Article: 15.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2015] [Revised: 01/21/2016] [Accepted: 01/23/2016] [Indexed: 12/14/2022]
Abstract
The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane-binding particles. We discuss how membrane compartmentalisation and the particle-membrane binding energy may impact the dynamics and response of lipid membranes. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.
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Affiliation(s)
- R Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany; Department of Physics, Tampere University of Technology, 33101 Tampere, Finland.
| | - J-H Jeon
- Korea Institute for Advanced Study (KIAS), Seoul, Republic of Korea
| | - A G Cherstvy
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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12
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Raza Z, Alling B, Abrikosov IA. Computer simulations of glasses: the potential energy landscape. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:293201. [PMID: 26139691 DOI: 10.1088/0953-8984/27/29/293201] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We review the current state of research on glasses, discussing the theoretical background and computational models employed to describe them. This article focuses on the use of the potential energy landscape (PEL) paradigm to account for the phenomenology of glassy systems, and the way in which it can be applied in simulations and the interpretation of their results. This article provides a broad overview of the rich phenomenology of glasses, followed by a summary of the theoretical frameworks developed to describe this phenomonology. We discuss the background of the PEL in detail, the onerous task of how to generate computer models of glasses, various methods of analysing numerical simulations, and the literature on the most commonly used model systems. Finally, we tackle the problem of how to distinguish a good glass former from a good crystal former from an analysis of the PEL. In summarising the state of the potential energy landscape picture, we develop the foundations for new theoretical methods that allow the ab initio prediction of the glass-forming ability of new materials by analysis of the PEL.
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Affiliation(s)
- Zamaan Raza
- Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83, Linköping, Sweden
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13
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Seif A, Loscar ES, Grigera TS. Aging and crystallization in a lattice glass model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042302. [PMID: 25974486 DOI: 10.1103/physreve.91.042302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2014] [Indexed: 06/04/2023]
Abstract
We have studied the three-dimensional lattice glass of Pica Ciamarra et al. [Phys. Rev. E 67, 057105 (2003)], which has been shown to reproduce several features of the structural glass phenomenology, such as the cage effect, exponential increase of relaxation times, and aging. We show, using short-time dynamics, that the metastability limit is above the estimated Kauzmann temperature. We also find that in the region where the metastable liquid exists the aging exponent is lower than 0.5, indicating that equilibrium is reached relatively quickly. We conclude that the usefulness of this model to study the deeply supercooled regime is rather limited.
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Affiliation(s)
- Alejandro Seif
- Instituto de Investigaciones Fisicoqumicas Teóricas y Aplicadas (INIFTA) and Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, c.c. 16, suc. 4, B1904DPI La Plata, Argentina and CCT CONICET La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, La Plata, Argentina
| | - Ernesto S Loscar
- Instituto de Investigaciones Fisicoqumicas Teóricas y Aplicadas (INIFTA) and Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, c.c. 16, suc. 4, B1904DPI La Plata, Argentina and CCT CONICET La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, La Plata, Argentina
| | - Tomás S Grigera
- Instituto de Investigaciones Fisicoqumicas Teóricas y Aplicadas (INIFTA) and Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, c.c. 16, suc. 4, B1904DPI La Plata, Argentina and CCT CONICET La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, La Plata, Argentina
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14
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Helfferich J. Renewal events in glass-forming liquids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:32. [PMID: 25160488 DOI: 10.1140/epje/i2014-14073-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2014] [Revised: 07/16/2014] [Accepted: 07/29/2014] [Indexed: 06/03/2023]
Abstract
On cooling toward the glass transition temperature, glass-forming liquids display long periods of localized motion interrupted by fast "jumps" in the single-particle trajectories. Several theoretical models based on these single-particle jumps have been proposed, most prominently the continuous-time random walk (CTRW). The central assumption of the CTRW is that jumps are renewal events, i.e. that the internal clock of a particle can be reset upon a jump. In this paper, I present an easy-to-implement method to test whether jumps detected in a supercooled liquid or glass are renewal events or not. The test was applied to molecular dynamics simulations of a short-chain polymer melt, demonstrating that the jumps can in fact be treated as renewal events. The test further revealed that additional relaxation processes are present which are not accounted for in the CTRW picture, highlighting the limitations of this approach. The notion of renewal events in glass-forming systems could be a very important building block for the interpretation of aging and the glass transition. Furthermore, it could have practical implications for the study of non-equilibrium dynamics in glasses as well as mechanical rejuvenation.
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Affiliation(s)
- Julian Helfferich
- Theoretical Polymer Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104, Freiburg, Germany,
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15
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Ruta B, Baldi G, Chushkin Y, Rufflé B, Cristofolini L, Fontana A, Zanatta M, Nazzani F. Revealing the fast atomic motion of network glasses. Nat Commun 2014; 5:3939. [PMID: 24835825 DOI: 10.1038/ncomms4939] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2013] [Accepted: 04/23/2014] [Indexed: 01/29/2023] Open
Abstract
Still very little is known on the relaxation dynamics of glasses at the microscopic level due to the lack of experiments and theories. It is commonly believed that glasses are in a dynamical arrested state, with relaxation times too large to be observed on human time scales. Here we provide the experimental evidence that glasses display fast atomic rearrangements within a few minutes, even in the deep glassy state. Following the evolution of the structural relaxation in a sodium silicate glass, we find that this fast dynamics is accompanied by the absence of any detectable aging, suggesting a decoupling of the relaxation time and the viscosity in the glass. The relaxation time is strongly affected by the network structure with a marked increase at the mesoscopic scale associated with the ion-conducting pathways. Our results modify the conception of the glassy state and asks for a new microscopic theory.
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Affiliation(s)
- B Ruta
- ESRF - The European Synchroton, CS 40220, 38043 Grenoble Cedex 9, France
| | - G Baldi
- IMEM-CNR Institute, Parco Area delle Scienze, I-43124 Parma, Italy
| | - Y Chushkin
- ESRF - The European Synchroton, CS 40220, 38043 Grenoble Cedex 9, France
| | - B Rufflé
- 1] Université Montpellier 2, Laboratoire Charles Coulomb UMR 5221, F-34095 Montpellier, France [2] CNRS, Laboratoire Charles Coulomb UMR 5221, F-34095 Montpellier, France
| | - L Cristofolini
- Physics and Earth Sciences Department, Parma University, I-43124 Parma, Italy
| | - A Fontana
- Dipartimento di Fisica, Trento University, Povo, Trento I-38123, Italy
| | - M Zanatta
- Dipartimento di Fisica e Geologia, Universitá di Perugia, I-06123 Perugia, Italy
| | - F Nazzani
- Department of Physics, University of Fribourg, Chemin du Musée 3, 1700 Fribourg, Switzerland
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Helfferich J, Ziebert F, Frey S, Meyer H, Farago J, Blumen A, Baschnagel J. Continuous-time random-walk approach to supercooled liquids. II. Mean-square displacements in polymer melts. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042604. [PMID: 24827271 DOI: 10.1103/physreve.89.042604] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2013] [Indexed: 06/03/2023]
Abstract
The continuous-time random walk (CTRW) describes the single-particle dynamics as a series of jumps separated by random waiting times. This description is applied to analyze trajectories from molecular dynamics (MD) simulations of a supercooled polymer melt. Based on the algorithm presented by Helfferich et al. [Phys. Rev. E 89, 042603 (2014)], we detect jump events of the monomers. As a function of temperature and chain length, we examine key distributions of the CTRW: the jump-length distribution (JLD), the waiting-time distribution (WTD), and the persistence-time distribution (PTD), i.e., the distribution of waiting times for the first jump. For the equilibrium (polymer) liquid under consideration, we verify that the PTD is determined by the WTD. For the mean-square displacement (MSD) of a monomer, the results for the CTRW model are compared with the underlying MD data. The MD data exhibit two regimes of subdiffusive behavior, one for the early α process and another at later times due to chain connectivity. By contrast, the analytical solution of the CTRW yields diffusive behavior for the MSD at all times. Empirically, we can account for the effect of chain connectivity in Monte Carlo simulations of the CTRW. The results of these simulations are then in good agreement with the MD data in the connectivity-dominated regime, but not in the early α regime where they systematically underestimate the MSD from the MD.
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Affiliation(s)
- J Helfferich
- Physikalisches Institut, Albert-Ludwigs-Universität, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - F Ziebert
- Physikalisches Institut, Albert-Ludwigs-Universität, Hermann-Herder-Str. 3, 79104 Freiburg, Germany and Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France
| | - S Frey
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France
| | - H Meyer
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France
| | - J Farago
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France
| | - A Blumen
- Physikalisches Institut, Albert-Ludwigs-Universität, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - J Baschnagel
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France
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17
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Helfferich J, Ziebert F, Frey S, Meyer H, Farago J, Blumen A, Baschnagel J. Continuous-time random-walk approach to supercooled liquids. I. Different definitions of particle jumps and their consequences. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042603. [PMID: 24827270 DOI: 10.1103/physreve.89.042603] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2013] [Indexed: 06/03/2023]
Abstract
Single-particle trajectories in supercooled liquids display long periods of localization interrupted by "fast moves." This observation suggests a modeling by a continuous-time random walk (CTRW). We perform molecular dynamics simulations of equilibrated short-chain polymer melts near the critical temperature of mode-coupling theory Tc and extract "moves" from the monomer trajectories. We show that not all moves comply with the conditions of a CTRW. Strong forward-backward correlations are found in the supercooled state. A refinement procedure is suggested to exclude these moves from the analysis. We discuss the repercussions of the refinement on the jump-length and waiting-time distributions as well as on characteristic time scales, such as the average waiting time ("exchange time") and the average time for the first move ("persistence time"). The refinement modifies the temperature (T) dependence of these time scales. For instance, the average waiting time changes from an Arrhenius-type to a Vogel-Fulcher-type T dependence. We discuss this observation in the context of the bifurcation of the α process and (Johari) β process found in many glass-forming materials to occur near Tc. Our analysis lays the foundation for a study of the jump-length and waiting-time distributions, their temperature and chain-length dependencies, and the modeling of the monomer dynamics by a CTRW approach in the companion paper [J. Helfferich et al., Phys. Rev. E 89, 042604 (2014)].
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Affiliation(s)
- J Helfferich
- Physikalisches Institut, Albert-Ludwigs-Universität, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - F Ziebert
- Physikalisches Institut, Albert-Ludwigs-Universität, Hermann-Herder-Str. 3, 79104 Freiburg, Germany and Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France
| | - S Frey
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France
| | - H Meyer
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France
| | - J Farago
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France
| | - A Blumen
- Physikalisches Institut, Albert-Ludwigs-Universität, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
| | - J Baschnagel
- Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France
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Metzler R, Jeon JH, Cherstvy AG, Barkai E. Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking. Phys Chem Chem Phys 2014; 16:24128-64. [DOI: 10.1039/c4cp03465a] [Citation(s) in RCA: 1046] [Impact Index Per Article: 104.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
This Perspective summarises the properties of a variety of anomalous diffusion processes and provides the necessary tools to analyse and interpret recorded anomalous diffusion data.
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Affiliation(s)
- Ralf Metzler
- Institute of Physics and Astronomy
- University of Potsdam
- Potsdam-Golm, Germany
- Physics Department
- Tampere University of Technology
| | - Jae-Hyung Jeon
- Physics Department
- Tampere University of Technology
- Tampere, Finland
- Korean Institute for Advanced Study (KIAS)
- Seoul, Republic of Korea
| | - Andrey G. Cherstvy
- Institute of Physics and Astronomy
- University of Potsdam
- Potsdam-Golm, Germany
| | - Eli Barkai
- Physics Department and Institute of Nanotechnology and Advanced Materials
- Bar-Ilan University
- Ramat Gan, Israel
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