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Mutneja A, Karmakar S. Method to probe the pronounced growth of correlation lengths in active glass-forming liquids using an elongated probe. Phys Rev E 2023; 108:L022601. [PMID: 37723727 DOI: 10.1103/physreve.108.l022601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2022] [Accepted: 07/01/2023] [Indexed: 09/20/2023]
Abstract
The growth of correlation lengths in equilibrium glass-forming liquids near the glass transition is considered a critical finding in the quest to understand the physics of glass formation. These understandings helped us understand various dynamical phenomena observed in supercooled liquids. It is known that at least two different length scales exist; one is of thermodynamic origin, while the other is dynamical in nature. Recent observations of glassy dynamics in biological and synthetic systems where the external or internal driving source controls the dynamics, apart from the usual thermal noise, lead to the emergence of the field of active glassy matter. A question of whether the physics of glass formation in these active systems is also accompanied by growing dynamic and static lengths is indeed timely. In this article, we probe the growth of dynamic and static lengths in a model active glass system using rod-like elongated probe particles, an experimentally viable method. We show that the dynamic and static lengths in these nonequilibrium systems grow much more rapidly than their passive counterparts. We then offer an understanding of the violation of the Stokes-Einstein relation and Stokes-Einstein-Debye relation using these lengths via a scaling theory.
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Affiliation(s)
- Anoop Mutneja
- Tata Institute of Fundamental Research, 36/P, Gopanpally Village, Serilingampally Mandal,Ranga Reddy District, Hyderabad, Telangana 500107, India
| | - Smarajit Karmakar
- Tata Institute of Fundamental Research, 36/P, Gopanpally Village, Serilingampally Mandal,Ranga Reddy District, Hyderabad, Telangana 500107, India
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2
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Laudicina CCL, Luo C, Miyazaki K, Janssen LMC. Dynamical susceptibilities near ideal glass transitions. Phys Rev E 2022; 106:064136. [PMID: 36671198 DOI: 10.1103/physreve.106.064136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2022] [Accepted: 11/28/2022] [Indexed: 06/17/2023]
Abstract
Building on the recently derived inhomogeneous mode-coupling theory, we extend the generalized mode-coupling theory of supercooled liquids to inhomogeneous environments. This provides a first-principles-based, systematic, and rigorous way of deriving high-point dynamical susceptibilities from variations of the many-body dynamic structure factors with respect to their conjugate field. This framework allows for a fully microscopic possibility to probe for collective relaxation mechanisms in supercooled liquids near the mode-coupling glass transition. The behavior of these dynamical susceptibilities is then studied in the context of simplified self-consistent relaxation models.
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Affiliation(s)
- Corentin C L Laudicina
- Soft Matter & Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
| | - Chengjie Luo
- Soft Matter & Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
| | | | - Liesbeth M C Janssen
- Soft Matter & Biological Physics, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
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3
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Hong G, Zhou Y, Li J. Relaxation dynamics of vibrated dense granular media: Hysteresis and nonlocal effects. POWDER TECHNOL 2022. [DOI: 10.1016/j.powtec.2022.117847] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
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4
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Jin W, O'Hern CS, Radin C, Shattuck MD, Swinney HL. Homogeneous Crystallization in Cyclically Sheared Frictionless Grains. PHYSICAL REVIEW LETTERS 2020; 125:258003. [PMID: 33416399 DOI: 10.1103/physrevlett.125.258003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Accepted: 11/20/2020] [Indexed: 06/12/2023]
Abstract
Many experiments over the past half century have shown that, for a range of protocols, granular materials compact under pressure and repeated small disturbances. A recent experiment on cyclically sheared spherical grains showed significant compaction via homogeneous crystallization (Rietz et al., 2018). Here we present numerical simulations of frictionless, purely repulsive spheres undergoing cyclic simple shear via Newtonian dynamics with linear viscous drag at fixed vertical load. We show that for sufficiently small strain amplitudes, cyclic shear gives rise to homogeneous crystallization at a volume fraction ϕ=0.646±0.001. This result indicates that neither friction nor gravity is essential for homogeneous crystallization in driven granular media. Understanding how crystal formation is initiated within a homogeneous disordered state gives key insights into the old open problem of glass formation in fluids.
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Affiliation(s)
- Weiwei Jin
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Corey S O'Hern
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Charles Radin
- Department of Mathematics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Mark D Shattuck
- Benjamin Levich Institute and Physics Department, The City College of New York, New York, New York 10031, USA
| | - Harry L Swinney
- Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
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5
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Tapia-Ignacio C, Moctezuma RE, Donado F, Weeks ER. Brownian motion of ellipsoidal particles on a granular magnetic bath. Phys Rev E 2020; 102:022902. [PMID: 32942353 DOI: 10.1103/physreve.102.022902] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2019] [Accepted: 06/19/2020] [Indexed: 11/07/2022]
Abstract
We study the Brownian motion of ellipsoidal particles lying on an agitated granular bath composed of magnetic particles. We quantify the mobility of different floating ellipsoidal particles using the mean-square displacement and the mean-square angular displacement, and relate the diffusion coefficients to the bath particle motion. In terms of the particle major radius R, we find the translational diffusion coefficient scales roughly as 1/R^{2} and the rotational diffusion coefficient scales as roughly 1/R^{4}; this is consistent with the assumption that diffusion arises from random kicks of the bath particles underneath the floating particle. By varying the magnetic forcing, the bath particles' diffusivity changes by a factor of ten; over this range, the translational and rotational diffusion of the floating particles change by a factor of 50. However, the ratio of the two diffusion constants for the floating particles is forcing-independent. Unusual aspects of the floating particle motion include non-Gaussian statistics for their displacements.
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Affiliation(s)
- C Tapia-Ignacio
- Instituto de Ciencias Básicas e Ingeniería, Universidad Autónoma del Estado de Hidalgo, Mineral de la Reforma 42184, Hidalgo, México
| | - R E Moctezuma
- CONACYT-Instituto de Física "Manuel Sandoval Vallarta", Universidad Autónoma de San Luis Potosí, Alvaro Obregón 64, 78000 San Luis Potosí, S.L.P., México
| | - F Donado
- Instituto de Ciencias Básicas e Ingeniería, Universidad Autónoma del Estado de Hidalgo, Mineral de la Reforma 42184, Hidalgo, México
| | - Eric R Weeks
- Physics Department, Emory University, Atlanta, Georgia 30322, USA
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6
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Srivastava A, Karmakar S, Debnath A. Quantification of spatio-temporal scales of dynamical heterogeneity of water near lipid membranes above supercooling. SOFT MATTER 2019; 15:9805-9815. [PMID: 31746927 DOI: 10.1039/c9sm01725a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
A hydrated 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC) lipid membrane is investigated using an all atom molecular dynamics simulation at 308 K to determine the physical sources of universal slow relaxations of hydration layers and length-scale of the spatially heterogeneous dynamics. Continuously residing interface water (IW) molecules hydrogen bonded to different moieties of lipid heads in the membrane are identified. The non-Gaussian parameters of all classes of IW molecules show a cross-over from cage vibration to translational diffusion. A significant non-Gaussianity is observed for the IW molecules exhibiting large length correlations in translational van Hove functions. Two time-scales for the ballistic motions and hopping transitions are obtained from the self intermediate scattering functions of the IW molecules with an additional long relaxation, which disappears for bulk water. The long relaxation time-scales for the IW molecules obtained from the self intermediate scattering functions are in good accordance with the hydrogen bond relaxation time-scales irrespective of the nature of the chemical confinement and the confinement lifetime. Employing a block analysis approach, the length-scale of dynamical heterogeneities is captured from a transition from non-Gaussianity to Gaussianity in van Hove correlation functions of the IW molecules. The heterogeneity length-scale is comparable to the wave-length of the small and weak undulations of the membrane calculated by Fourier transforms of lipid tilts. This opens up a new avenue towards a possible correlation between heterogeneity length-scale and membrane curvature more significant for rippled membranes. Thus, our analyses provide a measure towards the spatio-temporal scale of dynamical heterogeneity of confined water near membranes.
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Affiliation(s)
- Abhinav Srivastava
- Department of Chemistry, Indian Institute of Technology Jodhpur, Jodhpur 342037, India.
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7
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Mandal S, Schrack L, Löwen H, Sperl M, Franosch T. Persistent Anti-Correlations in Brownian Dynamics Simulations of Dense Colloidal Suspensions Revealed by Noise Suppression. PHYSICAL REVIEW LETTERS 2019; 123:168001. [PMID: 31702351 DOI: 10.1103/physrevlett.123.168001] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2019] [Revised: 08/28/2019] [Indexed: 06/10/2023]
Abstract
Transport properties of a hard-sphere colloidal fluid are investigated by Brownian dynamics simulations. We implement a novel algorithm for the time-dependent velocity-autocorrelation function (VACF) essentially eliminating the noise of the bare random motion. The measured VACF reveals persistent anti-correlations manifested by a negative algebraic power-law tail t^{-5/2} at all densities. At small packing fractions the simulations fully agree with the analytic low-density prediction, yet the amplitude of the tail becomes dramatically suppressed as the packing fraction is increased. The mode-coupling theory of the glass transition provides a qualitative explanation for the strong variation in terms of the static compressibility as well as the slowing down of the structural relaxation.
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Affiliation(s)
- Suvendu Mandal
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Lukas Schrack
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Matthias Sperl
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt, 51170 Köln, Germany
- Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
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8
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Montes de Oca JM, Accordino SR, Appignanesi GA, Handle PH, Sciortino F. Size dependence of dynamic fluctuations in liquid and supercooled water. J Chem Phys 2019; 150:144505. [DOI: 10.1063/1.5085886] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joan Manuel Montes de Oca
- INQUISUR, Departamento de Química, Universidad Nacional del Sur (UNS)-CONICET, Avenida Alem 1253, 8000 Bahía Blanca, Argentina
| | - Sebastián R. Accordino
- INQUISUR, Departamento de Química, Universidad Nacional del Sur (UNS)-CONICET, Avenida Alem 1253, 8000 Bahía Blanca, Argentina
| | - Gustavo A. Appignanesi
- INQUISUR, Departamento de Química, Universidad Nacional del Sur (UNS)-CONICET, Avenida Alem 1253, 8000 Bahía Blanca, Argentina
| | - Philip H. Handle
- Department of Physical Chemistry, University of Innsbruck, Innrain 52c, A-6020 Innsbruck, Austria
| | - Francesco Sciortino
- Dipartimento di Fisica, Sapienza Universita’ di Roma, Piazzale A. Moro 5, Roma 00185, Italy
- CNR-ISC, c/o Sapienza, Piazzale A. Moro 5, Roma 00185, Italy
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9
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Bhowmik BP, Tah I, Karmakar S. Non-Gaussianity of the van Hove function and dynamic-heterogeneity length scale. Phys Rev E 2018; 98:022122. [PMID: 30253524 DOI: 10.1103/physreve.98.022122] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2018] [Indexed: 11/07/2022]
Abstract
Non-Gaussian nature of the probability distribution of particles' displacements in the supercooled temperature regime in glass-forming liquids are believed to be one of the major hallmarks of glass transition. It has already been established that this probability distribution, which is also known as the van Hove function, shows universal exponential tail. The origin of such an exponential tail in the distribution function is attributed to the hopping motion of particles observed in the supercooled regime. The non-Gaussian nature can also be explained if one assumes that the system has heterogeneous dynamics in space and time. Thus exponential tail is the manifestation of dynamic heterogeneity. In this work we directly show that non-Gaussianity of the distribution of particles' displacements occur over the dynamic heterogeneity length scale and the dynamical behavior course grained over this length scale becomes homogeneous. We study the non-Gaussianity of the van Hove function by systematically coarse graining at different length scales and extract the length scale of dynamic heterogeneity at which the shape of the van Hove function crosses over from non-Gaussian to Gaussian. The obtained dynamic heterogeneity scale is found to be in very good agreement with the scale obtained from other conventional methods.
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Affiliation(s)
- Bhanu Prasad Bhowmik
- Tata Institute of Fundamental Research, 36/P, Gopanpally Village, Serilingampally Mandal, Ranga Reddy District, Hyderabad, 500107 Telangana, India
| | - Indrajit Tah
- Tata Institute of Fundamental Research, 36/P, Gopanpally Village, Serilingampally Mandal, Ranga Reddy District, Hyderabad, 500107 Telangana, India
| | - Smarajit Karmakar
- Tata Institute of Fundamental Research, 36/P, Gopanpally Village, Serilingampally Mandal, Ranga Reddy District, Hyderabad, 500107 Telangana, India
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10
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Rodriguez Fris JA, Weeks ER, Sciortino F, Appignanesi GA. Spatiotemporal intermittency and localized dynamic fluctuations upon approaching the glass transition. Phys Rev E 2018; 97:060601. [PMID: 30011454 DOI: 10.1103/physreve.97.060601] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2018] [Indexed: 11/07/2022]
Abstract
We introduce a robust approach for characterizing spatially and temporally heterogeneous behavior within a system based on the evolution of dynamic fluctuations averaged over different space lengths and timescales. We apply it to investigate the dynamics in two canonical systems as the glass transition is approached: simulated Lennard-Jones liquids and experimental dense colloidal suspensions. In both cases the onset of glassiness is marked by spatially localized dynamic fluctuations originating in regions of correlated mobile particles. By removing the trivial system size dependence we show that the spatial heterogeneity of the dynamics extends to large length scales containing tens to hundreds of particles, corresponding to the timescale of maximally non-Gaussian dynamics.
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Affiliation(s)
- J Ariel Rodriguez Fris
- INQUISUR, Departamento de Química, Universidad Nacional del Sur (UNS)-CONICET, Avenida Alem 1253, 8000 Bahía Blanca, Argentina
| | - Eric R Weeks
- Physics Department, Emory University, Atlanta, Georgia 30322, USA
| | - Francesco Sciortino
- Dipartimento di Fisica, Sapienza Universita' di Roma, Piazzale A. Moro 5, Roma 00185, Italy.,CNR-ISC, c/o Sapienza, Piazzale A. Moro 5, Roma 00185, Italy
| | - Gustavo A Appignanesi
- INQUISUR, Departamento de Química, Universidad Nacional del Sur (UNS)-CONICET, Avenida Alem 1253, 8000 Bahía Blanca, Argentina
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11
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Chakrabarty S, Tah I, Karmakar S, Dasgupta C. Block Analysis for the Calculation of Dynamic and Static Length Scales in Glass-Forming Liquids. PHYSICAL REVIEW LETTERS 2017; 119:205502. [PMID: 29219342 DOI: 10.1103/physrevlett.119.205502] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2017] [Indexed: 05/17/2023]
Abstract
We present block analysis, an efficient method of performing finite-size scaling for obtaining the length scale of dynamic heterogeneity and the point-to-set length scale for generic glass-forming liquids. This method involves considering blocks of varying sizes embedded in a system of a fixed (large) size. The length scale associated with dynamic heterogeneity is obtained from a finite-size scaling analysis of the dependence of the four-point dynamic susceptibility on the block size. The block size dependence of the variance of the α relaxation time yields the static point-to-set length scale. The values of the obtained length scales agree quantitatively with those obtained from other conventional methods. This method provides an efficient experimental tool for studying the growth of length scales in systems such as colloidal glasses for which performing finite-size scaling by carrying out experiments for varying system sizes may not be feasible.
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Affiliation(s)
- Saurish Chakrabarty
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Shivakote, Hesaraghatta, Hubli, Bangalore, 560089, India
| | - Indrajit Tah
- Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Narisingi, Hyderabad 500075, India
| | - Smarajit Karmakar
- Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Narisingi, Hyderabad 500075, India
| | - Chandan Dasgupta
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
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12
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Avila KE, Castillo HE, Vollmayr-Lee K, Zippelius A. Slow and long-ranged dynamical heterogeneities in dissipative fluids. SOFT MATTER 2016; 12:5461-5474. [PMID: 27230572 DOI: 10.1039/c6sm00784h] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Here we focus on the most direct approach to study these heterogeneities: we identify clusters of slow particles and determine their size, Nc, and their radius of gyration, RG. We show that , providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, df, that is observed to increase with packing fraction ϕ. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., ϕ→ϕc. Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor S4(q,t) and the dynamical susceptibility χ4(t). S4(q,t) is shown to obey scaling in the full range of packing fractions, 0.6 ≤ϕ≤ 0.805, and to become increasingly long-ranged as ϕ→ϕc. Finite size scaling of χ4(t) provides a consistency check for the previously analyzed divergences of χ4(t) ∝ (ϕ-ϕc)(-γχ) and the correlation length ξ∝ (ϕ-ϕc)(-γξ). We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for ϕ→ϕc suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.
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Affiliation(s)
- Karina E Avila
- Institut für Theoretische Physik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
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13
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Vollmayr-Lee K, Gorman CH, Castillo HE. Universal scaling in the aging of the strong glass former SiO2. J Chem Phys 2016; 144:234510. [PMID: 27334182 DOI: 10.1063/1.4953911] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We show that the aging dynamics of a strong glass former displays a strikingly simple scaling behavior, connecting the average dynamics with its fluctuations, namely, the dynamical heterogeneities. We perform molecular dynamics simulations of SiO2 with van Beest-Kramer-van Santen interactions, quenching the system from high to low temperature, and study the evolution of the system as a function of the waiting time tw measured from the instant of the quench. We find that both the aging behavior of the dynamic susceptibility χ4 and the aging behavior of the probability distribution P(fs,r) of the local incoherent intermediate scattering function fs,r can be described by simple scaling forms in terms of the global incoherent intermediate scattering function C. The scaling forms are the same that have been found to describe the aging of several fragile glass formers and that, in the case of P(fs,r), have been also predicted theoretically. A thorough study of the length scales involved highlights the importance of intermediate length scales. We also analyze directly the scaling dependence on particle type and on wavevector q and find that both the average and the fluctuations of the slow aging dynamics are controlled by a unique aging clock, which is not only independent of the wavevector q, but is also the same for O and Si atoms.
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Affiliation(s)
- Katharina Vollmayr-Lee
- Department of Physics and Astronomy, Bucknell University, Lewisburg, Pennsylvania 17837, USA
| | - Christopher H Gorman
- Department of Mathematics, University of California, Santa Barbara, California 93106, USA
| | - Horacio E Castillo
- Department of Physics and Astronomy and Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, Ohio 45701, USA
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14
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Karmakar S, Dasgupta C, Sastry S. Length scales in glass-forming liquids and related systems: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:016601. [PMID: 26684508 DOI: 10.1088/0034-4885/79/1/016601] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The central problem in the study of glass-forming liquids and other glassy systems is the understanding of the complex structural relaxation and rapid growth of relaxation times seen on approaching the glass transition. A central conceptual question is whether one can identify one or more growing length scale(s) associated with this behavior. Given the diversity of molecular glass-formers and a vast body of experimental, computational and theoretical work addressing glassy behavior, a number of ideas and observations pertaining to growing length scales have been presented over the past few decades, but there is as yet no consensus view on this question. In this review, we will summarize the salient results and the state of our understanding of length scales associated with dynamical slow down. After a review of slow dynamics and the glass transition, pertinent theories of the glass transition will be summarized and a survey of ideas relating to length scales in glassy systems will be presented. A number of studies have focused on the emergence of preferred packing arrangements and discussed their role in glassy dynamics. More recently, a central object of attention has been the study of spatially correlated, heterogeneous dynamics and the associated length scale, studied in computer simulations and theoretical analysis such as inhomogeneous mode coupling theory. A number of static length scales have been proposed and studied recently, such as the mosaic length scale discussed in the random first-order transition theory and the related point-to-set correlation length. We will discuss these, elaborating on key results, along with a critical appraisal of the state of the art. Finally we will discuss length scales in driven soft matter, granular fluids and amorphous solids, and give a brief description of length scales in aging systems. Possible relations of these length scales with those in glass-forming liquids will be discussed.
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Affiliation(s)
- Smarajit Karmakar
- TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India
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15
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Flenner E, Szamel G. Fundamental differences between glassy dynamics in two and three dimensions. Nat Commun 2015; 6:7392. [PMID: 26067877 PMCID: PMC4490572 DOI: 10.1038/ncomms8392] [Citation(s) in RCA: 89] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2015] [Accepted: 05/04/2015] [Indexed: 11/09/2022] Open
Abstract
The two-dimensional freezing transition is very different from its three-dimensional counterpart. In contrast, the glass transition is usually assumed to have similar characteristics in two and three dimensions. Using computer simulations, here we show that glassy dynamics in supercooled two- and three-dimensional fluids are fundamentally different. Specifically, transient localization of particles on approaching the glass transition is absent in two dimensions, whereas it is very pronounced in three dimensions. Moreover, the temperature dependence of the relaxation time of orientational correlations is decoupled from that of the translational relaxation time in two dimensions but not in three dimensions. Last, the relationships between the characteristic size of dynamically heterogeneous regions and the relaxation time are very different in two and three dimensions. These results strongly suggest that the glass transition in two dimensions is different than in three dimensions. The existing glass transition theories show little dimensional dependence. Here Flenner et al. disprove this general consensus by finding that, for instance, the bond-orientational relaxation is decoupled from the translational relaxation in two dimensions, but not in three dimensions.
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Affiliation(s)
- Elijah Flenner
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
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