1
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Jin J, Voth GA. Understanding dynamics in coarse-grained models. IV. Connection of fine-grained and coarse-grained dynamics with the Stokes-Einstein and Stokes-Einstein-Debye relations. J Chem Phys 2024; 161:034114. [PMID: 39012809 DOI: 10.1063/5.0212973] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2024] [Accepted: 06/28/2024] [Indexed: 07/18/2024] Open
Abstract
Applying an excess entropy scaling formalism to the coarse-grained (CG) dynamics of liquids, we discovered that missing rotational motions during the CG process are responsible for artificially accelerated CG dynamics. In the context of the dynamic representability between the fine-grained (FG) and CG dynamics, this work introduces the well-known Stokes-Einstein and Stokes-Einstein-Debye relations to unravel the rotational dynamics underlying FG trajectories, thereby allowing for an indirect evaluation of the effective rotations based only on the translational information at the reduced CG resolution. Since the representability issue in CG modeling limits a direct evaluation of the shear stress appearing in the Stokes-Einstein and Stokes-Einstein-Debye relations, we introduce a translational relaxation time as a proxy to employ these relations, and we demonstrate that these relations hold for the ambient conditions studied in our series of work. Additional theoretical links to our previous work are also established. First, we demonstrate that the effective hard sphere radius determined by the classical perturbation theory can approximate the complex hydrodynamic radius value reasonably well. Furthermore, we present a simple derivation of an excess entropy scaling relationship for viscosity by estimating the elliptical integral of molecules. In turn, since the translational and rotational motions at the FG level are correlated to each other, we conclude that the "entropy-free" CG diffusion only depends on the shape of the reference molecule. Our results and analyses impart an alternative way of recovering the FG diffusion from the CG description by coupling the translational and rotational motions at the hydrodynamic level.
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Affiliation(s)
- Jaehyeok Jin
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, Institute for Biophysical Dynamics, and James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
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2
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Clark JA, Douglas JF. Do Specific Ion Effects on Collective Relaxation Arise from Perturbation of Hydrogen-Bonding Network Structure? J Phys Chem B 2024; 128:6362-6375. [PMID: 38912895 PMCID: PMC11229691 DOI: 10.1021/acs.jpcb.4c02638] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2024] [Revised: 06/07/2024] [Accepted: 06/10/2024] [Indexed: 06/25/2024]
Abstract
The change in the transport properties (i.e., water diffusivity, shear viscosity, etc.) when adding salts to water has been used to classify ions as either being chaotropic or kosmotropic, a terminology based on the presumption that this phenomenon arises from respective breakdown or enhancement of the hydrogen-bonding network structure. Recent quasi-elastic neutron scattering measurements of the collective structural relaxation time, τC, in aqueous salt solutions were interpreted as confirming this proposed origin of ion effects on the dynamics of water. However, we find similar changes in τC in the same salt solutions based on molecular dynamics (MD) simulations using a coarse-grained water model in which no hydrogen bonding exists, challenging this conventional interpretation of mobility change resulting from the addition of salts to water. A thorough understanding of specific ion effects should be useful in diverse material manufacturing and biomedical applications, where these effects are prevalent, but poorly understood.
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Affiliation(s)
- Jennifer A. Clark
- Materials Science and Engineering
Division, Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Jack F. Douglas
- Materials Science and Engineering
Division, Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
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3
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Khrapak SA. Shoving model and the glass transition in one-component plasma. J Chem Phys 2024; 160:166101. [PMID: 38661202 DOI: 10.1063/5.0207393] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2024] [Accepted: 04/10/2024] [Indexed: 04/26/2024] Open
Abstract
A modified shoving model is applied to estimate the location of the glass transition in a one-component plasma. The estimated value of the coupling parameter Γ ≃ 570 at the glass transition is compared with other predictions available in the literature.
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Affiliation(s)
- S A Khrapak
- Joint Institute for High Temperatures, Russian Academy of Sciences, 125412 Moscow, Russia
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4
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Dyre JC. Solid-that-Flows Picture of Glass-Forming Liquids. J Phys Chem Lett 2024; 15:1603-1617. [PMID: 38306474 PMCID: PMC10875679 DOI: 10.1021/acs.jpclett.3c03308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2023] [Revised: 01/12/2024] [Accepted: 01/17/2024] [Indexed: 02/04/2024]
Abstract
This perspective article reviews arguments that glass-forming liquids are different from those of standard liquid-state theory, which typically have a viscosity in the mPa·s range and relaxation times on the order of picoseconds. These numbers grow dramatically and become 1012 - 1015 times larger for liquids cooled toward the glass transition. This translates into a qualitative difference, and below the "solidity length" which is roughly one micron at the glass transition, a glass-forming liquid behaves much like a solid. Recent numerical evidence for the solidity of ultraviscous liquids is reviewed, and experimental consequences are discussed in relation to dynamic heterogeneity, frequency-dependent linear-response functions, and the temperature dependence of the average relaxation time.
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Affiliation(s)
- Jeppe C Dyre
- "Glass and Time", IMFUFA, Dept. of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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5
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Song L, Gao Y, Zou P, Xu W, Gao M, Zhang Y, Huo J, Li F, Qiao J, Wang LM, Wang JQ. Detecting the exponential relaxation spectrum in glasses by high-precision nanocalorimetry. Proc Natl Acad Sci U S A 2023; 120:e2302776120. [PMID: 37155861 PMCID: PMC10193961 DOI: 10.1073/pnas.2302776120] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2023] [Accepted: 04/16/2023] [Indexed: 05/10/2023] Open
Abstract
Nonexponential relaxations are universal characteristics for glassy materials. There is a well-known hypothesis that nonexponential relaxation peaks are composed of a series of exponential events, which have not been verified. In this Letter, we discover the exponential relaxation events during the recovery process using a high-precision nanocalorimetry, which are universal for metallic glasses and organic glasses. The relaxation peaks can be well fitted by the exponential Debye function with a single activation energy. The activation energy covers a broad range from α relaxation to β relaxation and even the fast γ/β' relaxation. We obtain the complete spectrum of the exponential relaxation peaks over a wide temperature range from 0.63Tg to 1.03Tg, which provides solid evidence that nonexponential relaxation peaks can be decomposed into exponential relaxation units. Furthermore, the contribution of different relaxation modes in the nonequilibrium enthalpy space is measured. These results open a door for developing the thermodynamics of nonequilibrium physics and for precisely modulating the properties of glasses by controlling the relaxation modes.
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Affiliation(s)
- Lijian Song
- Key Laboratory of Magnetic Materials and Devices, and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo315201, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing100049, China
| | - Yurong Gao
- Key Laboratory of Magnetic Materials and Devices, and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo315201, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing100049, China
| | - Peng Zou
- Key Laboratory of Magnetic Materials and Devices, and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo315201, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing100049, China
| | - Wei Xu
- Key Laboratory of Magnetic Materials and Devices, and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo315201, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing100049, China
| | - Meng Gao
- Key Laboratory of Magnetic Materials and Devices, and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo315201, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing100049, China
| | - Yan Zhang
- Key Laboratory of Magnetic Materials and Devices, and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo315201, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing100049, China
| | - Juntao Huo
- Key Laboratory of Magnetic Materials and Devices, and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo315201, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing100049, China
| | - Fushan S. Li
- School of Materials Science and Engineering, Zhengzhou University, Zhengzhou450001, China
| | - Jichao C. Qiao
- School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xian710072, China
| | - Li-Min Wang
- State Key Laboratory of Metastable Materials Science and Technology, and College of Materials Science and Engineering, Yanshan University, Qinhuangdao, Hebei066004, China
| | - Jun-Qiang Wang
- Key Laboratory of Magnetic Materials and Devices, and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo315201, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing100049, China
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6
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Novikov VN, Sokolov AP. Temperature Dependence of Structural Relaxation in Glass-Forming Liquids and Polymers. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1101. [PMID: 36010765 PMCID: PMC9407199 DOI: 10.3390/e24081101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Revised: 08/05/2022] [Accepted: 08/07/2022] [Indexed: 06/15/2023]
Abstract
Understanding the microscopic mechanism of the transition of glass remains one of the most challenging topics in Condensed Matter Physics. What controls the sharp slowing down of molecular motion upon approaching the glass transition temperature Tg, whether there is an underlying thermodynamic transition at some finite temperature below Tg, what the role of cooperativity and heterogeneity are, and many other questions continue to be topics of active discussions. This review focuses on the mechanisms that control the steepness of the temperature dependence of structural relaxation (fragility) in glass-forming liquids. We present a brief overview of the basic theoretical models and their experimental tests, analyzing their predictions for fragility and emphasizing the successes and failures of the models. Special attention is focused on the connection of fast dynamics on picosecond time scales to the behavior of structural relaxation on much longer time scales. A separate section discusses the specific case of polymeric glass-forming liquids, which usually have extremely high fragility. We emphasize the apparent difference between the glass transitions in polymers and small molecules. We also discuss the possible role of quantum effects in the glass transition of light molecules and highlight the recent discovery of the unusually low fragility of water. At the end, we formulate the major challenges and questions remaining in this field.
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Affiliation(s)
- Vladimir N. Novikov
- Institute of Automation and Electrometry, Russian Academy of Sciences, 630090 Novosibirsk, Russia
| | - Alexei P. Sokolov
- Department of Chemistry and Joint Institute for Neutron Sciences, University of Tennessee, Knoxville, TN 37996, USA
- Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
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7
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Thermodynamics of Point Defects in Solids and Relation with the Bulk Properties: Recent Results. CRYSTALS 2022. [DOI: 10.3390/cryst12050686] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
For several decades, the crucial question has arisen as to whether there exists any direct interconnection between the thermodynamic parameters of point defects in solids with the bulk properties of the solid under investigation. To answer this important question, an interrelation of the defect Gibbs energy gi in solids with bulk properties has been proposed almost half a century ago. Considering that gi corresponds to an isobaric and isothermal process, this interrelation states that, for different processes (defect formation, self-diffusion activation, and heterodiffusion), gi is proportional to the isothermal bulk modulus B and the mean volume per atom Ω, termed cBΩ model. Here, we review several challenging applications of this interrelation that appeared during the last decade (2011–2021), including high pressure diamond anvil measurements, high Tc superconductors, nuclear fuels, and materials for micro-electronics devices, applications of usefulness in Geophysics and Seismology, a problem of major technological interest, search for compositions of better target properties in Cu-Co-Si alloys via machine learning as well as two independent studies on the physical origin of this interrelation that has been further strengthened during the last few years.
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8
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Heyes DM, Dini D. Intrinsic viscuit probability distribution functions for transport coefficients of liquids and solids. J Chem Phys 2022; 156:124501. [DOI: 10.1063/5.0083228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A reformulation of the Green–Kubo expressions for the transport coefficients of liquids in terms of a probability distribution function (PDF) of short trajectory contributions, which were named “viscuits,” has been explored in a number of recent publications. The viscuit PDF, P, is asymmetric on the two sides of the distribution. It is shown here using equilibrium 3D and 2D molecular dynamics simulations that the viscuit PDF of a range of simple molecular single component and mixture liquid and solid systems can be expressed in terms of the same intrinsic PDF ( P0), which is derived from P with the viscuit normalized by the standard deviation separately on each side of the distribution. P0 is symmetric between the two sides and can be represented for not very small viscuit values by the same gamma distribution formulated in terms of a single disposable parameter. P0 tends to an exponential in the large viscuit wings. Scattergrams of the viscuits and their associated single trajectory correlation functions are shown to distinguish effectively between liquids, solids, and glassy systems. The so-called viscuit square root method for obtaining the transport coefficients is shown to be a useful probe of small and statistically zero self-diffusion coefficients of molecules in the liquid and solid states, respectively. The results of this work suggest that the transport coefficients have a common underlying physical origin, reflecting at a coarse-grained level the traversal statistics of the system through its high-dimensioned potential energy landscape.
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Affiliation(s)
- D. M. Heyes
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - D. Dini
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
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9
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Makarov AS, Afonin GV, Aronin AS, Kobelev NP, Khonik VA. Thermodynamic approach for the understanding of the kinetics of heat effects induced by structural relaxation of metallic glasses. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:125701. [PMID: 34942612 DOI: 10.1088/1361-648x/ac4628] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2021] [Accepted: 12/23/2021] [Indexed: 06/14/2023]
Abstract
We present a novel approach to the understanding of heat effects induced by structural relaxation of metallic glasses. The key idea consists in the application of a general thermodynamic equation for the entropy change due to the evolution of a non-equilibrium part of a complex system. This non-equilibrium part is considered as a defect subsystem of glass and its evolution is governed by local thermoactivated rearrangements with a Gibbs free energy barrier proportional to the high-frequency shear modulus. The only assumption on the nature of the defects is that they should provide a reduction of the shear modulus-a diaelastic effect. This approach allows to determine glass entropy change upon relaxation. On this basis, the kinetics of the heat effects controlled by defect-induced structural relaxation is calculated. A very good agreement between the calculation and specially performed calorimetric and shear modulus measurements on three metallic glasses is found.
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Affiliation(s)
- A S Makarov
- Department of General Physics, State Pedagogical University, Lenin St. 86, Voronezh 394043, Russia
| | - G V Afonin
- Department of General Physics, State Pedagogical University, Lenin St. 86, Voronezh 394043, Russia
| | - A S Aronin
- Department of General Physics, State Pedagogical University, Lenin St. 86, Voronezh 394043, Russia
- Institute of Solid State Physics RAS, Moscow district, Chernogolovka 142432, Russia
| | - N P Kobelev
- Institute of Solid State Physics RAS, Moscow district, Chernogolovka 142432, Russia
| | - V A Khonik
- Department of General Physics, State Pedagogical University, Lenin St. 86, Voronezh 394043, Russia
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10
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Zhang W, Starr FW, Douglas JF. Activation free energy gradient controls interfacial mobility gradient in thin polymer films. J Chem Phys 2021; 155:174901. [PMID: 34742183 DOI: 10.1063/5.0064866] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
We examine the mobility gradient in the interfacial region of substrate-supported polymer films using molecular dynamics simulations and interpret these gradients within the string model of glass-formation. No large gradients in the extent of collective motion exist in these simulated films, and an analysis of the mobility gradient on a layer-by-layer basis indicates that the string model provides a quantitative description of the relaxation time gradient. Consequently, the string model indicates that the interfacial mobility gradient derives mainly from a gradient in the high-temperature activation enthalpy ΔH0 and entropy ΔS0 as a function of depth z, an effect that exists even in the high-temperature Arrhenius relaxation regime far above the glass transition temperature. To gain insight into the interfacial mobility gradient, we examined various material properties suggested previously to influence ΔH0 in condensed materials, including density, potential and cohesive energy density, and a local measure of stiffness or u2(z)-3/2, where u2(z) is the average mean squared particle displacement at a caging time (on the order of a ps). We find that changes in local stiffness best correlate with changes in ΔH0(z) and that ΔS0(z) also contributes significantly to the interfacial mobility gradient, so it must not be neglected.
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Affiliation(s)
- Wengang Zhang
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Francis W Starr
- Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
| | - Jack F Douglas
- Materials Science and Engineering Division, Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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11
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Kapteijns G, Richard D, Bouchbinder E, Schrøder TB, Dyre JC, Lerner E. Does mesoscopic elasticity control viscous slowing down in glassforming liquids? J Chem Phys 2021; 155:074502. [PMID: 34418936 DOI: 10.1063/5.0051193] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The dramatic slowing down of relaxation dynamics of liquids approaching the glass transition remains a highly debated problem, where the crux of the puzzle resides in the elusive increase in the activation barrier ΔE(T) with decreasing temperature T. A class of theoretical frameworks-known as elastic models-attribute this temperature dependence to the variations of the liquid's macroscopic elasticity, quantified by the high-frequency shear modulus G∞(T). While elastic models find some support in a number of experimental studies, these models do not take into account the spatial structures, length scales, and heterogeneity associated with structural relaxation in supercooled liquids. Here, we propose and test the possibility that viscous slowing down is controlled by a mesoscopic elastic stiffness κ(T), defined as the characteristic stiffness of response fields to local dipole forces in the liquid's underlying inherent structures. First, we show that κ(T)-which is intimately related to the energy and length scales characterizing quasilocalized, nonphononic excitations in glasses-increases more strongly with decreasing T than the macroscopic inherent structure shear modulus G(T) [the glass counterpart of liquids' G∞(T)] in several computer liquids. Second, we show that the simple relation ΔE(T) ∝ κ(T) holds remarkably well for some computer liquids, suggesting a direct connection between the liquid's underlying mesoscopic elasticity and enthalpic energy barriers. On the other hand, we show that for other computer liquids, the above relation fails. Finally, we provide strong evidence that what distinguishes computer liquids in which the ΔE(T) ∝ κ(T) relation holds from those in which it does not is that the latter feature highly fragmented/granular potential energy landscapes, where many sub-basins separated by low activation barriers exist. Under such conditions, it appears that the sub-basins do not properly represent the landscape properties relevant for structural relaxation.
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Affiliation(s)
- Geert Kapteijns
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - David Richard
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Eran Bouchbinder
- Chemical and Biological Physics Department, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Thomas B Schrøder
- "Glass and Time," IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Jeppe C Dyre
- "Glass and Time," IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Edan Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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12
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Khrapak S, Kryuchkov NP, Mistryukova LA, Yurchenko SO. From soft- to hard-sphere fluids: Crossover evidenced by high-frequency elastic moduli. Phys Rev E 2021; 103:052117. [PMID: 34134345 DOI: 10.1103/physreve.103.052117] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2020] [Accepted: 04/27/2021] [Indexed: 06/12/2023]
Abstract
The conventional (Zwanzig-Mountain) expressions for instantaneous elastic moduli of simple fluids predict their divergence as the limit of hard-sphere (HS) interaction is approached. However, elastic moduli of a true HS fluid are finite. Here we demonstrate that this paradox reveals the soft-to-hard-sphere crossover in fluid excitations and thermodynamics. With extensive in silico study of fluids with repulsive power-law interactions (∝r^{-n}), we locate the crossover at n≃10-20 and develop a simple and accurate model for the HS regime. The results open prospects to deal with the elasticity and related phenomena in various systems, from simple fluids to melts and glasses.
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Affiliation(s)
- Sergey Khrapak
- Joint Institute for High Temperatures, Russian Academy of Sciences, 125412 Moscow, Russia
- Bauman Moscow State Technical University, 105005 Moscow, Russia
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 82234 Weßling, Germany
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13
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Douglas JF, Xu WS. Equation of State and Entropy Theory Approach to Thermodynamic Scaling in Polymeric Glass-Forming Liquids. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00075] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- 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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14
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Evertz S, Schneider JM. Effect of the Free Volume on the Electronic Structure of Cu 70Zr 30 Metallic Glasses. MATERIALS 2020; 13:ma13214911. [PMID: 33142904 PMCID: PMC7672583 DOI: 10.3390/ma13214911] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/28/2020] [Revised: 10/26/2020] [Accepted: 10/29/2020] [Indexed: 01/27/2023]
Abstract
While it is accepted that the plastic behavior of metallic glasses is affected by their free volume content, the effect on chemical bonding has not been investigated systematically. According to electronic structure analysis, the overall bond strength is not significantly affected by the free volume content. However, with an increasing free volume content, the average coordination number decreases. Furthermore, the volume fraction of regions containing atoms with a lower coordination number increases. As the local bonding character changes from bonding to anti-bonding with a decreasing coordination number, bonding is weakened in the volume fraction of a lower coordination number. During deformation, the number of strong, short-distance bonds decreases more for free volume-containing samples than for samples without free volume, resulting in additional bond weakening. Therefore, we show that the introduction of free volume causes the formation of volume fractions of a lower coordination number, resulting in weaker bonding, and propose that this is the electronic structure origin of the enhanced plastic behavior reported for glasses containing free volume.
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15
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Khrapak SA. Sound Velocities of Lennard-Jones Systems Near the Liquid-Solid Phase Transition. Molecules 2020; 25:E3498. [PMID: 32752011 PMCID: PMC7435481 DOI: 10.3390/molecules25153498] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Revised: 07/27/2020] [Accepted: 07/29/2020] [Indexed: 11/30/2022] Open
Abstract
Longitudinal and transverse sound velocities of Lennard-Jones systems are calculated at the liquid-solid coexistence using the additivity principle. The results are shown to agree well with the "exact" values obtained from their relations to excess energy and pressure. Some consequences, in particular in the context of the Lindemann's melting rule and Stokes-Einstein relation between the self-diffusion and viscosity coefficients, are discussed. Comparison with available experimental data on the sound velocities of solid argon at melting conditions is provided.
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Affiliation(s)
- Sergey A. Khrapak
- Institute for Materials Physics in Space, German Aerospace Center (DLR), 82234 Wessling, Germany;
- Department of Physics, Bauman Moscow State Technical University, 105005 Moscow, Russia
- Joint Institute for High Temperatures, Russian Academy of Sciences, 125412 Moscow, Russia
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16
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Heyes DM, Dini D, Smith ER. Single trajectory transport coefficients and the energy landscape by molecular dynamics simulations. J Chem Phys 2020; 152:194504. [PMID: 33687256 DOI: 10.1063/5.0005600] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Green-Kubo (GK) method is widely used to calculate the transport coefficients of model liquids by Molecular Dynamics (MD) simulation. A reformulation of GK was proposed by Heyes et al. [J. Chem. Phys. 150, 174504 (2019)], which expressed the shear viscosity in terms of a probability distribution function (PDF) of "single trajectory (ST) viscosities," called "viscuits." This approach is extended here to the bulk viscosity, thermal conductivity, and diffusion coefficient. The PDFs of the four STs expressed in terms of their standard deviations (calculated separately for the positive and negative sides) are shown by MD to be statistically the same for the Lennard-Jones fluid. This PDF can be represented well by a sum of exponentials and is independent of system size and state point in the equilibrium fluid regime. The PDF is not well reproduced by a stochastic model. The PDF is statistically the same as that derived from the potential energy, u, and other thermodynamic quantities, indicating that the transport coefficients are determined quantitatively by and follow closely the time evolution of the underlying energy landscape. The PDFs of out-of-equilibrium supercooled high density states are quite different from those of the equilibrium states.
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Affiliation(s)
- D M Heyes
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - D Dini
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - E R Smith
- Department of Mechanical and Aerospace Engineering, Brunel University London, Uxbridge, Middlesex UB8 3PH, United Kingdom
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17
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Zykova VA, Adichtchev SV, Novikov VN, Surovtsev NV. Second-order-derivative analysis of structural relaxation time in the elastic model of glass-forming liquids. Phys Rev E 2020; 101:052610. [PMID: 32575277 DOI: 10.1103/physreve.101.052610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2019] [Accepted: 04/23/2020] [Indexed: 06/11/2023]
Abstract
Recently it was shown [V. N. Novikov and A. P. Sokolov, Phys. Rev. E 92, 062304 (2015)10.1103/PhysRevE.92.062304] that the second derivative with respect to inverse temperature of the structural relaxation time in some supercooled molecular liquids has a sharp maximum. It marks the point at which the apparent activation energy begins to saturate with decreasing temperature. The elastic model of glass-forming liquids expresses the temperature dependence of the structural relaxation time through that of the shear modulus. In this paper, we test whether this model is able to predict the maximum of the second derivative. We confirm its presence in the elastic model by analyzing the temperature dependence of the Brillouin light scattering in salol. This is a very subtle feature of the temperature dependence, which is greatly enhanced when taking derivatives. Its presence in the Brillouin data provides strong support to the elastic model of glass-forming liquids.
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Affiliation(s)
- V A Zykova
- Institute of Automation and Electrometry, Russian Academy of Sciences, Novosibirsk, 630090, Russia
| | - S V Adichtchev
- Institute of Automation and Electrometry, Russian Academy of Sciences, Novosibirsk, 630090, Russia
| | - V N Novikov
- Institute of Automation and Electrometry, Russian Academy of Sciences, Novosibirsk, 630090, Russia
| | - N V Surovtsev
- Institute of Automation and Electrometry, Russian Academy of Sciences, Novosibirsk, 630090, Russia
- Novosibirsk State University, Novosibirsk, 630090, Russia
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18
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Paschoal VH, Ribeiro MCC. Pseudo-Optical Modes in Room-Temperature Ionic Liquids. J Phys Chem B 2020; 124:2661-2667. [DOI: 10.1021/acs.jpcb.0c00890] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Vitor H. Paschoal
- Laboratório de Espectroscopia Molecular, Departamento de Química Fundamental, Instituto de Química, Universidade de São Paulo, Av. Prof. Lineu Prestes 748, 05508-000, São Paulo, SP, Brazil
| | - Mauro C. C. Ribeiro
- Laboratório de Espectroscopia Molecular, Departamento de Química Fundamental, Instituto de Química, Universidade de São Paulo, Av. Prof. Lineu Prestes 748, 05508-000, São Paulo, SP, Brazil
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19
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Abstract
A new analysis of elastic properties of dense hard-sphere (HS) fluids is presented, based on the expressions derived by Miller [J. Chem. Phys. 50, 2733 (1969)JCPSA60021-960610.1063/1.1671437]. Important consequences for HS fluids in terms of sound waves propagation, Poisson's ratio, Stokes-Einstein relation, and generalized Cauchy identity are explored. Conventional expressions for high-frequency elastic moduli for simple systems with continuous and differentiable interatomic interaction potentials are known to diverge when approaching the HS repulsive limit. The origin of this divergence is identified here. It is demonstrated that these conventional expressions are only applicable for sufficiently soft interactions and should not be applied to HS systems. The reported results can be of interest in the context of statistical physics, physics of fluids, soft condensed matter, and granular materials.
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Affiliation(s)
- Sergey Khrapak
- Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 82234 Weßling, Germany and Joint Institute for High Temperatures, Russian Academy of Sciences, 125412 Moscow, Russia
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20
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Chung JY, Douglas JF, Stafford CM. A wrinkling-based method for investigating glassy polymer film relaxation as a function of film thickness and temperature. J Chem Phys 2018; 147:154902. [PMID: 29055329 DOI: 10.1063/1.5006949] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
We investigate the relaxation dynamics of thin polymer films at temperatures below the bulk glass transition Tg by first compressing polystyrene films supported on a polydimethylsiloxane substrate to create wrinkling patterns and then observing the slow relaxation of the wrinkled films back to their final equilibrium flat state by small angle light scattering. As with recent relaxation measurements on thin glassy films reported by Fakhraai and co-workers, we find the relaxation time of our wrinkled films to be strongly dependent on film thickness below an onset thickness on the order of 100 nm. By varying the temperature between room temperature and Tg (≈100 °C), we find that the relaxation time follows an Arrhenius-type temperature dependence to a good approximation at all film thicknesses investigated, where both the activation energy and the relaxation time pre-factor depend appreciably on film thickness. The wrinkling relaxation curves tend to cross at a common temperature somewhat below Tg, indicating an entropy-enthalpy compensation relation between the activation free energy parameters. This compensation effect has also been observed recently in simulated supported polymer films in the high temperature Arrhenius relaxation regime rather than the glassy state. In addition, we find that the film stress relaxation function, as well as the height of the wrinkle ridges, follows a stretched exponential time dependence and the short-time effective Young's modulus derived from our modeling decreases sigmoidally with increasing temperature-both characteristic features of glassy materials. The relatively facile nature of the wrinkling-based measurements in comparison to other film relaxation measurements makes our method attractive for practical materials development, as well as fundamental studies of glass formation.
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Affiliation(s)
- Jun Young Chung
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Christopher M Stafford
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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21
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Heyes DM, Dini D, Smith ER. Incremental viscosity by non-equilibrium molecular dynamics and the Eyring model. J Chem Phys 2018; 148:194506. [DOI: 10.1063/1.5027681] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- D. M. Heyes
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - D. Dini
- Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
| | - E. R. Smith
- Department of Civil Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, United Kingdom
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22
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Guillaud E, Joly L, de Ligny D, Merabia S. Assessment of elastic models in supercooled water: A molecular dynamics study with the TIP4P/2005f force field. J Chem Phys 2017; 147:014504. [DOI: 10.1063/1.4991372] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Emmanuel Guillaud
- Institut Lumière Matière, CNRS, Université de Lyon, Université Claude Bernard Lyon 1, 69622 Villeurbanne, France
- Department of Materials Science, Institute of Glass and Ceramics, University of Erlangen-Nürnberg, Martensstrasse 5, 91058 Erlangen, Germany
| | - Laurent Joly
- Institut Lumière Matière, CNRS, Université de Lyon, Université Claude Bernard Lyon 1, 69622 Villeurbanne, France
| | - Dominique de Ligny
- Department of Materials Science, Institute of Glass and Ceramics, University of Erlangen-Nürnberg, Martensstrasse 5, 91058 Erlangen, Germany
| | - Samy Merabia
- Institut Lumière Matière, CNRS, Université de Lyon, Université Claude Bernard Lyon 1, 69622 Villeurbanne, France
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23
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Bernini S, Puosi F, Leporini D. Thermodynamic scaling of relaxation: insights from anharmonic elasticity. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:135101. [PMID: 28102828 DOI: 10.1088/1361-648x/aa5a7e] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Using molecular dynamics simulations of a molecular liquid, we investigate the thermodynamic scaling (TS) of the structural relaxation time [Formula: see text] in terms of the quantity [Formula: see text], where T and ρ are the temperature and density, respectively. The liquid does not exhibit strong virial-energy correlations. We propose a method for evaluating both the characteristic exponent [Formula: see text] and the TS master curve that uses experimentally accessible quantities that characterise the anharmonic elasticity and does not use details about the microscopic interactions. In particular, we express the TS characteristic exponent [Formula: see text] in terms of the lattice Grüneisen parameter [Formula: see text] and the isochoric anharmonicity [Formula: see text]. An analytic expression of the TS master curve of [Formula: see text] with [Formula: see text] as the key adjustable parameter is found. The comparison with the experimental TS master curves and the isochoric fragilities of 34 glassformers is satisfying. In a few cases, where thermodynamic data are available, we test (i) the predicted characteristic exponent [Formula: see text] and (ii) the isochoric anharmonicity [Formula: see text], as drawn by the best fit of the TS of the structural relaxation, against the available thermodynamic data. A linear relation between the isochoric fragility and the isochoric anharmonicity [Formula: see text] is found and compared favourably with the results of experiments with no adjustable parameters. A relation between the increase of the isochoric vibrational heat capacity due to anharmonicity and the isochoric fragility is derived.
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Affiliation(s)
- S Bernini
- Dipartimento di Fisica 'Enrico Fermi', Università di Pisa, Largo B Pontecorvo 3, I-56127 Pisa, Italy. Present address: Jawaharlal Nehru Center for Advanced Scientific Research, Theoretical Sciences Unit, Jakkur Campus, Bengaluru 560064, India
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24
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Bernini S, Leporini D. Cage effect in supercooled molecular liquids: Local anisotropies and collective solid-like response. J Chem Phys 2016; 144:144505. [DOI: 10.1063/1.4945756] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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25
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Liu W, Zhang L. Thermoforming mechanism of precision glass moulding. APPLIED OPTICS 2015; 54:6841-6849. [PMID: 26368100 DOI: 10.1364/ao.54.006841] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Precision glass moulding (PGM) enables the production of an aspherical lens and irregular optical products in a single step, but its product quality depends highly on the control of both material properties and process parameters. This paper investigates the thermoforming mechanism of a glass lens in PGM. To precisely describe the material behavior in PGM, a modulus-based constitutive model was framed and integrated with the finite element analysis. This model can be parameterized conveniently by an impulse excitation technique. Key processing parameters that influence the final profile and residual stresses of a lens were identified with the aid of dimensional analysis. The study found that the cooling stage above the glass transition temperature can bring about large geometry deviations of a lens. The residual stresses in a lens depend mainly on the temperature history in the supercooled liquid region caused by the variability and heterogeneity of thermal expansion. However, the stresses can be reduced effectively by decreasing the cooling rate from moulding temperature to glass transition temperature.
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26
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Fuereder I, Ilg P. Influence of inherent structure shear stress of supercooled liquids on their shear moduli. J Chem Phys 2015; 142:144505. [DOI: 10.1063/1.4917042] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Affiliation(s)
- Ingo Fuereder
- Department of Materials, ETH Zurich, Vladimir-Prelog-Weg 1-5/10, CH-8093 Zurich, Switzerland
| | - Patrick Ilg
- Department of Materials, ETH Zurich, Vladimir-Prelog-Weg 1-5/10, CH-8093 Zurich, Switzerland
- School of Mathematical and Physical Sciences, University of Reading, Reading RG6 6AX, United Kingdom
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27
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Bernini S, Puosi F, Leporini D. Weak links between fast mobility and local structure in molecular and atomic liquids. J Chem Phys 2015; 142:124504. [PMID: 25833593 DOI: 10.1063/1.4916047] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate by molecular-dynamics simulations, the fast mobility-the rattling amplitude of the particles temporarily trapped by the cage of the neighbors-in mildly supercooled states of dense molecular (linear trimers) and atomic (binary mixtures) liquids. The mixture particles interact by the Lennard-Jones potential. The non-bonded particles of the molecular system are coupled by the more general Mie potential with variable repulsive and attractive exponents in a range which is a characteristic of small n-alkanes and n-alcohols. Possible links between the fast mobility and the geometry of the cage (size and shape) are searched. The correlations on a per-particle basis are rather weak. Instead, if one groups either the particles in fast-mobility subsets or the cages in geometric subsets, the increase of the fast mobility with both the size and the asphericity of the cage is revealed. The observed correlations are weak and differ in states with equal relaxation time. Local forces between a tagged particle and the first-neighbour shell do not correlate with the fast mobility in the molecular liquid. It is concluded that the cage geometry alone is unable to provide a microscopic interpretation of the known, universal link between the fast mobility and the slow structural relaxation. We suggest that the particle fast dynamics is affected by regions beyond the first neighbours, thus supporting the presence of collective, extended fast modes.
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Affiliation(s)
- S Bernini
- Dipartimento di Fisica "Enrico Fermi," Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy
| | - F Puosi
- Laboratoire de Physique de l'École Normale Supérieure de Lyon, UMR CNRS 5672, 46 allée d'Italie, 69007 Lyon, France
| | - D Leporini
- Dipartimento di Fisica "Enrico Fermi," Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy
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28
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Lemaître A. Structural relaxation is a scale-free process. PHYSICAL REVIEW LETTERS 2014; 113:245702. [PMID: 25541780 DOI: 10.1103/physrevlett.113.245702] [Citation(s) in RCA: 67] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2014] [Indexed: 06/04/2023]
Abstract
We show that in deeply supercooled liquids, structural relaxation proceeds via the accumulation of Eshelby events, i.e. local rearrangements that create long-ranged and anisotropic stresses in the surrounding medium. Such events must be characterized using tensorial observables and we construct an analytical framework to probe their correlations using local stress data. By analyzing numerical simulations, we then demonstrate that events are power-law correlated in space, with a time-dependent amplitude which peaks at the alpha relaxation time τ(α). This effect, which becomes stronger near the glass transition, results from the increasingly important role of local stress fluctuations in facilitating relaxation events. Our finding precludes the existence of any length scale beyond which the relaxation process decorrelates.
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Affiliation(s)
- Anaël Lemaître
- Université Paris-Est, Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTAR, 2 allée Képler, F-77420 Marne-la-Valle, France
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29
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Abstract
Recent developments show that many liquids and solids have an approximate "hidden" scale invariance that implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics in properly reduced units are invariant to a good approximation. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. Liquids and solids with isomorphs include most or all van der Waals bonded systems and metals, as well as weakly ionic or dipolar systems. On the other hand, systems with directional bonding (hydrogen bonds or covalent bonds) or strong Coulomb forces generally do not exhibit hidden scale invariance. The article reviews the theory behind this picture of condensed matter and the evidence for it coming from computer simulations and experiments.
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Affiliation(s)
- Jeppe C Dyre
- DNRF Center "Glass and Time", IMFUFA, Department of Sciences, Roskilde University , P.O. Box 260, DK-4000 Roskilde, Denmark
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30
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Mirigian S, Schweizer KS. Elastically cooperative activated barrier hopping theory of relaxation in viscous fluids. I. General formulation and application to hard sphere fluids. J Chem Phys 2014; 140:194506. [DOI: 10.1063/1.4874842] [Citation(s) in RCA: 119] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
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31
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Rabochiy P, Wolynes PG, Lubchenko V. Microscopically based calculations of the free energy barrier and dynamic length scale in supercooled liquids: the comparative role of configurational entropy and elasticity. J Phys Chem B 2013; 117:15204-19. [PMID: 24195747 DOI: 10.1021/jp409502k] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
We compute the temperature-dependent barrier for α-relaxations in several liquids, without adjustable parameters, using experimentally determined elastic, structural, and calorimetric data. We employ the random first order transition (RFOT) theory, in which relaxation occurs via activated reconfigurations between distinct, aperiodic minima of the free energy. Two different approximations for the mismatch penalty between the distinct aperiodic states are compared, one due to Xia and Wolynes (Proc. Natl. Acad. Sci. U. S. A. 2000, 97, 2990), which scales universally with temperature as for hard spheres, and one due to Rabochiy and Lubchenko (J. Chem. Phys. 2013, 138, 12A534), which employs measured elastic and structural data for individual substances. The agreement between the predictions and experiment is satisfactory, given the uncertainty in the measured experimental inputs. The explicitly computed barriers are used to calculate the glass transition temperature for each substance--a kinetic quantity--from the static input data alone. The temperature dependence of both the elastic and structural constants enters the temperature dependence of the barrier over an extended range to a degree that varies from substance to substance. The lowering of the configurational entropy, however, seems to be the dominant contributor to the barrier increase near the laboratory glass transition, consistent with previous experimental tests of the RFOT theory using the XW approximation. In addition, we compute the temperature dependence of the dynamical correlation length, also without using adjustable parameters. These agree well with experimental estimates obtained using the Berthier et al. (Science 2005, 310, 1797) procedure. Finally, we find the temperature dependence of the complexity of a rearranging region is consistent with the picture based on the RFOT theory but is in conflict with the assumptions of the Adam-Gibbs and "shoving" scenarios for the viscous slowing down in supercooled liquids.
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Affiliation(s)
- Pyotr Rabochiy
- Department of Chemistry, University of Houston , Houston, Texas 77204-5003, United States
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32
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Syutkin VM. Relation between the activation energy of oxygen diffusion and the instantaneous shear modulus in propylene carbonate near the glass transition temperature. J Chem Phys 2013; 139:114506. [PMID: 24070296 DOI: 10.1063/1.4821752] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
We discuss the transport of small gas molecules in organic glassy matrices using oxygen diffusion in propylene carbonate as an example. The jumps of a penetrant from one interstitial cavity to another require energy to expand the channel between cavities to the size of the penetrant. It has been established that at temperatures below and slightly above the glass transition temperature, the activation energy of oxygen diffusion, E, is related to the instantaneous shear modulus G∞ of propylene carbonate via the equation E = V × G∞, where V is the temperature-independent parameter that characterizes the volume of the channel. Consequently, the E value is the work necessary for elastic deformation of the surrounding matrix to expand the channel available for oxygen diffusion.
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Affiliation(s)
- V M Syutkin
- Institute of Chemical Kinetics and Combustion, Novosibirsk 630090, Russian Federation
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33
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Shi Z, Debenedetti PG, Stillinger FH. Relaxation processes in liquids: variations on a theme by Stokes and Einstein. J Chem Phys 2013; 138:12A526. [PMID: 23556777 DOI: 10.1063/1.4775741] [Citation(s) in RCA: 80] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
We investigate numerically the temperature and density dependence of the Stokes-Einstein ratio, Dη∕T, and of two commonly-used variants thereof, Dτ and Dτ∕T, where D is a diffusivity, η the shear viscosity, and τ a structural relaxation time. We consider a family of atomic binary mixtures with systematically-softened repulsive interactions, and the Lewis-Wahnström model of ortho-terphenyl (OTP). The three quantities grow significantly as the temperature decreases in the supercooled regime, a well-known phenomenon. At higher temperatures, Dτ exhibits negative violations of Stokes-Einstein behavior, i.e., decrease upon cooling, for the atomic systems, though not for OTP. We consider two choices for the relaxation time, one based on the decay of the self-intermediate scattering function, and the other on the integral of the stress autocorrelation function. The instantaneous shear modulus exhibits appreciable temperature dependence for the two classes of systems investigated here. Our results suggest that commonly-invoked assumptions, such as τ ∼ η and τ ∼ η∕T, should be critically evaluated across a wide spectrum of systems and thermodynamic conditions. We find the Stokes-Einstein ratio, Dη∕T, to be constant across a broad range of temperatures and densities for the two classes of systems investigated here.
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Affiliation(s)
- Zane Shi
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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34
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Galvão AM, Di Paolo RE, Maçanita AL, Naqvi KR. Model for conformational relaxation of flexible conjugated polymers: application to p-phenylenevinylene trimers in nonpolar solvents. Chemphyschem 2013; 14:583-90. [PMID: 23364935 DOI: 10.1002/cphc.201200869] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2012] [Indexed: 11/08/2022]
Abstract
Photoexcitation of flexible conjugated polymers is invariably followed by a fast conformational/torsional relaxation towards a configuration favouring coplanarity of the conjugated segments. In general, the experimental relaxation rate constant (k(CR)) depends on the solvent viscosity (η) and temperature (T), and is not proportional to T/η. A theory capable of explaining the observed dependence of k(CR) on T and η over a wide range of these variables is not available. This gap is filled here by presenting a stochastic model that includes the participation of the oligomer side chain in storing and dissipating the stresses induced by photoexcitation. The model is able to account for the softening of solute-solvent interactions and its predictions are found to be in excellent agreement with the observed relaxation rate constants of a series of substituted p-phenylenevinylene trimers [ChemPhysChem 2009, 10, 448-454] on T, η and the size of the side-chains.
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Affiliation(s)
- Adelino M Galvão
- Centro de Química Estrutural, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais s/n, 1049-001 Lisbon, Portugal.
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35
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Dyre JC. NVU perspective on simple liquids' quasiuniversality. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:022106. [PMID: 23496459 DOI: 10.1103/physreve.87.022106] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2012] [Indexed: 06/01/2023]
Abstract
The last half-century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids' reduced-coordinate constant-potential-energy hypersurfaces constitute a quasiuniversal family of compact Riemannian manifolds parametrized by a single number; from this follows the quasiuniversalities.
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Affiliation(s)
- Jeppe C Dyre
- DNRF Centre Glass and Time, IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark.
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36
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Sen S. Entropic vs. elastic models of fragility of glass-forming liquids: two sides of the same coin? J Chem Phys 2012; 137:164505. [PMID: 23126728 DOI: 10.1063/1.4759155] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
Abstract
The two most influential atomistic models that have been proposed in the literature to explain the temperature dependent activation energy of viscous flow of a glass-forming liquid, i.e., its fragility, are the configurational entropy model of Adam and Gibbs [J. Chem. Phys. 43, 139 (1965)] and the elastic "shoving" model of Dyre et al. [J. Non-Cryst. Solids 352, 4635 (2006)]. Here we demonstrate a qualitative equivalence between these two models starting from the well-established general relationships between the interatomic potentials, elastic constants, structural rearrangement, and entropy in amorphous materials. The unification of these two models provides important predictions that are consistent with experimental observations and shed new light into the problem of glass transition.
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Affiliation(s)
- Sabyasachi Sen
- Division of Materials Science, University of California at Davis, Davis, California 95616, USA
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37
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Affiliation(s)
- M. D. Ediger
- Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Peter Harrowell
- School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia
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