1
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Chakraborty S, Ramola K. Long-range correlations in elastic moduli and local stresses at the unjamming transition. SOFT MATTER 2024. [PMID: 38860707 DOI: 10.1039/d4sm00328d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2024]
Abstract
We explore the behaviour of spatially heterogeneous elastic moduli as well as the correlations between local moduli in model solids with short-range repulsive potentials. We show through numerical simulations that local elastic moduli exhibit long-range correlations, similar to correlations in the local stresses. Specifically, the correlations in local shear moduli exhibit anisotropic behavior at large lengthscales characterized by pinch-point singularities in Fourier space, displaying a structural pattern akin to shear stress correlations. Focussing on two-dimensional jammed solids approaching the unjamming transition, we show that stress correlations exhibit universal properties, characterized by a quadratic p2 dependence of the correlations as the pressure p approaches zero, independent of the details of the model. In contrast, the modulus correlations exhibit a power-law dependence with different exponents depending on the specific interaction potential. Furthermore, we illustrate that while affine responses lack long-range correlations, the total modulus, which encompasses non-affine behavior, exhibits long-range correlations.
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Affiliation(s)
| | - Kabir Ramola
- Tata Institute of Fundamental Research, Hyderabad 500046, India.
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2
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Wang Q, Zhang LF, Zhou ZY, Yu HB. Predicting the pathways of string-like motions in metallic glasses via path-featurizing graph neural networks. SCIENCE ADVANCES 2024; 10:eadk2799. [PMID: 38781338 PMCID: PMC11114230 DOI: 10.1126/sciadv.adk2799] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2024] [Accepted: 04/16/2024] [Indexed: 05/25/2024]
Abstract
String-like motions (SLMs)-cooperative, "snake"-like movements of particles-are crucial for dynamics in diverse glass formers. Despite their ubiquity, questions persist: Do SLMs prefer specific paths? If so, can we predict these paths? Here, in Al-Sm glasses, our isoconfigurational ensemble simulations reveal that SLMs do follow certain paths. By designing a graph neural network (GNN) to featurize the environment around directional paths, we achieve a high-fidelity prediction of likely SLM pathways, solely based on the static structure. GNN gauges a structural measure to assess each path's propensity to engage in SLMs, akin to a "softness" metric, but for paths rather than for atoms. Our GNN interpretation reveals the critical role of the bottleneck zone along a path in steering SLMs. By monitoring "path softness," we elucidate that SLM-favored paths transit from fragmented to interconnected upon glass transition. Our findings reveal that, beyond atoms or clusters, glasses have another dimension of structural heterogeneity: "paths."
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Affiliation(s)
- Qi Wang
- Science and Technology on Surface Physics and Chemistry Laboratory, Mianyang, Sichuan 621908, China
| | - Long-Fei Zhang
- China Telecom Artificial Intelligence Technology Co. Ltd., Chengdu, Sichuan 430074, China
| | - Zhen-Ya Zhou
- School of Physics, Ningxia University, Yinchuan, Ningxia 750021, China
| | - Hai-Bin Yu
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
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3
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Murphy KA, Bassett DS. Information decomposition in complex systems via machine learning. Proc Natl Acad Sci U S A 2024; 121:e2312988121. [PMID: 38498714 PMCID: PMC10990158 DOI: 10.1073/pnas.2312988121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 01/30/2024] [Indexed: 03/20/2024] Open
Abstract
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of linking variation across scales of a system due to its independence of functional relationship between observables. However, characterizing the manner in which information is distributed across a set of observables is computationally challenging and generally infeasible beyond a handful of measurements. Here, we propose a practical and general methodology that uses machine learning to decompose the information contained in a set of measurements by jointly optimizing a lossy compression of each measurement. Guided by the distributed information bottleneck as a learning objective, the information decomposition identifies the variation in the measurements of the system state most relevant to specified macroscale behavior. We focus our analysis on two paradigmatic complex systems: a Boolean circuit and an amorphous material undergoing plastic deformation. In both examples, the large amount of entropy of the system state is decomposed, bit by bit, in terms of what is most related to macroscale behavior. The identification of meaningful variation in data, with the full generality brought by information theory, is made practical for studying the connection between micro- and macroscale structure in complex systems.
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Affiliation(s)
- Kieran A. Murphy
- Department of Bioengineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, PA19104
| | - Dani S. Bassett
- Department of Bioengineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, PA19104
- Department of Electrical & Systems Engineering, School of Engineering & Applied Science, University of Pennsylvania, Philadelphia, PA19104
- Department of Neurology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA19104
- Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA19104
- Department of Physics & Astronomy, College of Arts & Sciences, University of Pennsylvania, Philadelphia, PA19104
- The Santa Fe Institute, Santa Fe, NM87501
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4
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Du X, Weeks ER. Rearrangements during slow compression of a jammed two-dimensional emulsion. Phys Rev E 2024; 109:034605. [PMID: 38632734 DOI: 10.1103/physreve.109.034605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2023] [Accepted: 02/20/2024] [Indexed: 04/19/2024]
Abstract
As amorphous materials get jammed, both geometric and dynamic heterogeneity are observed. We investigate the correlation between the local geometric heterogeneity and local rearrangements in a slowly compressed bidisperse quasi-two-dimensional emulsion system. The compression is driven by evaporation of the continuous phase and causes the area packing fraction to increase from 0.88 to 0.99. We quantify the structural heterogeneity of the system using the radical Voronoi tessellation following the method of Rieser et al. [Phys. Rev. Lett. 116, 088001 (2016)]0031-900710.1103/PhysRevLett.116.088001. We define two structural quantities characterizing local structure, the first of which considers nearest neighbors and the second of which includes information from second-nearest neighbors. We find that droplets in heterogeneous local regions are more likely to have local rearrangements. These rearrangements are generally T1 events where two droplets converge toward a void, and two droplets move away from the void to make room for the converging droplets. Thus, the presence of the voids tends to orient the T1 events. The presence of a correlation between the structural quantities and the rearrangement dynamics remains qualitatively unchanged over the entire range of packing fractions observed.
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Affiliation(s)
- Xin Du
- Department of Physics and Astronomy, Widener University, Chester, Pennsylvania 19013, USA
| | - Eric R Weeks
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
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5
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Xu D, Zhang S, Tong H, Wang L, Xu N. Low-frequency vibrational density of states of ordinary and ultra-stable glasses. Nat Commun 2024; 15:1424. [PMID: 38365816 DOI: 10.1038/s41467-024-45671-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 02/01/2024] [Indexed: 02/18/2024] Open
Abstract
A remarkable feature of disordered solids distinct from crystals is the violation of the Debye scaling law of the low-frequency vibrational density of states. Because the low-frequency vibration is responsible for many properties of solids, it is crucial to elucidate it for disordered solids. Numerous recent studies have suggested power-law scalings of the low-frequency vibrational density of states, but the scaling exponent is currently under intensive debate. Here, by classifying disordered solids into stable and unstable ones, we find two distinct and robust scaling exponents for non-phononic modes at low frequencies. Using the competition of these two scalings, we clarify the variation of the scaling exponent and hence reconcile the debate. Via the study of both ordinary and ultra-stable glasses, our work reveals a comprehensive picture of the low-frequency vibration of disordered solids and sheds light on the low-frequency vibrational features of ultra-stable glasses on approaching the ideal glass.
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Affiliation(s)
- Ding Xu
- Hefei National Research Center for Physical Sciences at the Microscale and CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026, P. R. China
- Department of Physics, University of Science and Technology of China, Hefei, 230026, P. R. China
| | - Shiyun Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026, P. R. China
- Department of Physics, University of Science and Technology of China, Hefei, 230026, P. R. China
| | - Hua Tong
- Department of Physics, University of Science and Technology of China, Hefei, 230026, P. R. China
| | - Lijin Wang
- School of Physics and Optoelectronic Engineering, Information Materials and Intelligent Sensing Laboratory of Anhui Province, Anhui University, Hefei, 230601, P. R. China.
| | - Ning Xu
- Hefei National Research Center for Physical Sciences at the Microscale and CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026, P. R. China.
- Department of Physics, University of Science and Technology of China, Hefei, 230026, P. R. China.
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6
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Zhang H, Zhang Q, Liu F, Han Y. Anisotropic-Isotropic Transition of Cages at the Glass Transition. PHYSICAL REVIEW LETTERS 2024; 132:078201. [PMID: 38427876 DOI: 10.1103/physrevlett.132.078201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Revised: 09/03/2023] [Accepted: 01/12/2024] [Indexed: 03/03/2024]
Abstract
Characterizing the local structural evolution is an essential step in understanding the nature of glass transition. In this work, we probe the evolution of Voronoi cell geometry in simple glass models by simulations and colloid experiments, and find that the individual particle cages deform anisotropically in supercooled liquid and isotropically in glass. We introduce an anisotropy parameter k for each Voronoi cell, whose mean value exhibits a sharp change at the mode-coupling glass transition ϕ_{c}. Moreover, a power law of packing fraction ϕ∝q_{1}^{d} is discovered in the supercooled liquid regime with d>D, in contrast to d=D in the glass regime, where q_{1} is the first peak position of structure factor, and D is the space dimension. This power law is qualitatively explained by the change of k. The active motions in supercooled liquid are spatially correlated with long axes rather than short axes of Voronoi cells. In addition, the dynamic slowing down approaching the glass transition can be well characterized through a modified free-volume model based on k. These findings reveal that the structural parameter k is effective in identifying the structure-dynamics correlations and the glass transition in these systems.
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Affiliation(s)
- Huijun Zhang
- State Key Laboratory for Mechanical Behavior of Materials, Shaanxi International Research Center for Soft Matter, School of Materials Science and Engineering, Xi'an Jiaotong University, 710049, Xi'an, China
| | - Qi Zhang
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
| | - Feng Liu
- State Key Laboratory for Mechanical Behavior of Materials, Shaanxi International Research Center for Soft Matter, School of Materials Science and Engineering, Xi'an Jiaotong University, 710049, Xi'an, China
| | - Yilong Han
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
- Shenzhen Research Institute, The Hong Kong University of Science and Technology, Shenzhen, China
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7
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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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8
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Shimada M, Shiraishi K, Mizuno H, Ikeda A. Instantaneous normal modes of glass-forming liquids during the athermal relaxation process of the steepest descent algorithm. SOFT MATTER 2024; 20:1583-1602. [PMID: 38273794 DOI: 10.1039/d3sm01104f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/27/2024]
Abstract
Understanding glass formation by quenching remains a challenge in soft condensed matter physics. Recent numerical studies on steepest descent dynamics, which is one of the simplest models of quenching, revealed that quenched liquids undergo slow relaxation with a power law towards mechanical equilibrium and that the late stage of this process is governed by local rearrangements of particles. These advances motivate the detailed study of instantaneous normal modes during the relaxation process because the glassy dynamics is considered to be governed by stationary points of the potential energy landscape. Here, we performed a normal mode analysis of configurations during the steepest descent dynamics and found that the dynamics is driven by almost flat directions of the potential energy landscape at long times. These directions correspond to localized modes and we characterized them in terms of their statistics and structure using methods developed in the study of local minima of the potential energy landscape.
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Affiliation(s)
- Masanari Shimada
- Department of Physics, Toronto Metropolitan University, M5B 2K3, Toronto, Canada.
| | - Kumpei Shiraishi
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
| | - Hideyuki Mizuno
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
| | - Atsushi Ikeda
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
- Research Center for Complex Systems Biology, Universal Biology Institute, The University of Tokyo, Tokyo 153-8902, Japan
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9
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Gagnon YJ, Burton JC, Roth CB. Development of broad modulus profile upon polymer-polymer interface formation between immiscible glassy-rubbery domains. Proc Natl Acad Sci U S A 2024; 121:e2312533120. [PMID: 38147561 PMCID: PMC10769838 DOI: 10.1073/pnas.2312533120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2023] [Accepted: 11/01/2023] [Indexed: 12/28/2023] Open
Abstract
Interfaces of glassy materials such as thin films, blends, and composites create strong unidirectional gradients to the local heterogeneous dynamics that can be used to elucidate the length scales and mechanisms associated with the dynamic heterogeneity of glasses. We focus on bilayer films of two different polymers with very different glass transition temperatures ([Formula: see text]) where previous work has demonstrated a long-range (∼200 nm) profile in local [Formula: see text] is established between immiscible glassy and rubbery polymer domains when the polymer-polymer interface is formed to equilibrium. Here, we demonstrate that an equally long-ranged gradient in local modulus [Formula: see text] is established when the polymer-polymer interface ([Formula: see text]5 nm) is formed between domains of glassy polystyrene (PS) and rubbery poly(butadiene) (PB), consistent with previous reports of a broad [Formula: see text] profile in this system. A continuum physics model for the shear wave propagation caused by a quartz crystal microbalance across a PB/PS bilayer film is used to measure the viscoelastic properties of the bilayer during the evolution of the PB/PS interface showing the development of a broad gradient in local modulus [Formula: see text] spanning [Formula: see text]180 nm between the glassy and rubbery domains of PS and PB. We suggest these broad profiles in [Formula: see text] and [Formula: see text] arise from a coupling of the spectrum of vibrational modes across the polymer-polymer interface as a result of acoustic impedance matching of sound waves with [Formula: see text] nm during interface broadening that can then trigger density fluctuations in the neighboring domain.
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Affiliation(s)
| | | | - Connie B. Roth
- Department of Physics, Emory University, Atlanta, GA30322
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10
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Rottler J, Ruscher C, Sollich P. Thawed matrix method for computing local mechanical properties of amorphous solids. J Chem Phys 2023; 159:214501. [PMID: 38038209 DOI: 10.1063/5.0167877] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2023] [Accepted: 11/07/2023] [Indexed: 12/02/2023] Open
Abstract
We present a method for computing locally varying nonlinear mechanical properties in particle simulations of amorphous solids. Plastic rearrangements outside a probed region are suppressed by introducing an external field that directly penalizes large nonaffine displacements. With increasing strength of the field, plastic deformation can be localized. We characterize the distribution of local plastic yield stresses (residual local stresses to instability) with our approach and assess the correlation of their spatial maps with plastic activity in a model two-dimensional amorphous solid. Our approach reduces artifacts inherent in a previous method known as the "frozen matrix" approach that enforces fully affine deformation and improves the prediction of plastic rearrangements from structural information.
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Affiliation(s)
- Jörg Rottler
- Department of Physics and Astronomy and Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Céline Ruscher
- Department of Mechanical Engineering, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
| | - Peter Sollich
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
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11
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Dattani UA, Karmakar S, Chaudhuri P. Athermal quasistatic cavitation in amorphous solids: Effect of random pinning. J Chem Phys 2023; 159:204501. [PMID: 38010327 DOI: 10.1063/5.0171905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 10/19/2023] [Indexed: 11/29/2023] Open
Abstract
Amorphous solids are known to fail catastrophically via fracture, and cavitation at nano-metric scales is known to play a significant role in such a failure process. Micro-alloying via inclusions is often used as a means to increase the fracture toughness of amorphous solids. Modeling such inclusions as randomly pinned particles that only move affinely and do not participate in plastic relaxations, we study how the pinning influences the process of cavitation-driven fracture in an amorphous solid. Using extensive numerical simulations and probing in the athermal quasistatic limit, we show that just by pinning a very small fraction of particles, the tensile strength is increased, and also the cavitation is delayed. Furthermore, the cavitation that is expected to be spatially heterogeneous becomes spatially homogeneous by forming a large number of small cavities instead of a dominant cavity. The observed behavior is rationalized in terms of screening of plastic activity via the pinning centers, characterized by a screening length extracted from the plastic-eigenmodes.
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Affiliation(s)
- Umang A Dattani
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Anushakti Nagar, Mumbai 400094, India
| | - Smarajit Karmakar
- Tata Institute of Fundamental Research, 36/P, Gopanpally Village, Serilingampally Mandal, Ranga Reddy District, Hyderabad 500046, Telangana, India
| | - Pinaki Chaudhuri
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Anushakti Nagar, Mumbai 400094, India
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12
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Jiang Y, Sussman DM, Weeks ER. Effects of polydispersity on the plastic behaviors of dense two-dimensional granular systems under shear. Phys Rev E 2023; 108:054605. [PMID: 38115404 DOI: 10.1103/physreve.108.054605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2022] [Accepted: 10/17/2023] [Indexed: 12/21/2023]
Abstract
We study particle-scale motion in sheared highly polydisperse amorphous materials, in which the largest particles are as much as ten times the size of the smallest. We find strikingly different behavior from the more commonly studied amorphous systems with low polydispersity. In particular, an analysis of the nonaffine motion of particles reveals qualitative differences between large and small particles: The smaller particles have dramatically more nonaffine motion, which is induced by the presence of the large particles. We characterize how the nonaffine motion changes from the low- to high-polydispersity regimes. We further demonstrate a quantitative way to distinguish between "large" and "small" particles in systems with broad distributions of particle sizes. A macroscopic consequence of the nonaffine motion is a decrease in the energy dissipation rate for highly polydisperse samples, which is due both to a geometric consequence of the changing jamming conditions for higher polydispersity and to the changing character of nonaffine motion.
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Affiliation(s)
- Yonglun Jiang
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| | - Daniel M Sussman
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
| | - Eric R Weeks
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
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13
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Richard D, Kapteijns G, Lerner E. Detecting low-energy quasilocalized excitations in computer glasses. Phys Rev E 2023; 108:044124. [PMID: 37978582 DOI: 10.1103/physreve.108.044124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Accepted: 09/15/2023] [Indexed: 11/19/2023]
Abstract
Soft, quasilocalized excitations (QLEs) are known to generically emerge in a broad class of disordered solids and to govern many facets of the physics of glasses, from wave attenuation to plastic instabilities. In view of this key role of QLEs, shedding light upon several open questions in glass physics depends on the availability of computational tools that allow one to study QLEs' statistical mechanics. The latter is a formidable task since harmonic analyses are typically contaminated by hybridizations of QLEs with phononic excitations at low frequencies, obscuring a clear picture of QLEs' abundance, typical frequencies, and other important micromechanical properties. Here we present an efficient algorithm to detect the field of quasilocalized excitations in structural computer glasses. The algorithm introduced takes a computer-glass sample as input and outputs a library of QLEs embedded in that sample. We demonstrate the power of the algorithm by reporting the spectrum of glassy excitations in two-dimensional computer glasses featuring a huge range of mechanical stability, which is inaccessible using conventional harmonic analyses due to phonon hybridizations. Future applications are discussed.
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Affiliation(s)
- David Richard
- Univ. Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
| | - Geert Kapteijns
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Edan Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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14
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Lieou CKC, Egami T. Relevance of structural defects to the mechanism of mechanical deformation in metallic glasses. Sci Rep 2023; 13:15979. [PMID: 37749128 PMCID: PMC10520023 DOI: 10.1038/s41598-023-42685-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Accepted: 09/13/2023] [Indexed: 09/27/2023] Open
Abstract
It is known that deformation in disordered materials such as metallic glasses and supercooled liquids occurs via the cooperative rearrangement of atoms or constituent particles at dynamical heterogeneities, commonly regarded as point-like defects. We show via molecular-dynamics simulations that there is no apparent relationship between atomic rearrangements and the local atomic environment as measured by the atomic-level stresses, kinetic and potential energies, and the per-atom Voronoi volume. In addition, there is only a weak correlation between atomic rearrangements and the largest and smallest eigenvalues of the dynamical matrix. Our results confirm the transient nature of dynamical heterogeneities and suggest that the notion of defects may be less relevant than that of a propensity for rearrangement.
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Affiliation(s)
- Charles K C Lieou
- Department of Nuclear Engineering, University of Tennessee, Knoxville, TN, USA
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN, USA
| | - Takeshi Egami
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN, USA.
- Department of Physics and Astronomy, University of Tennessee, Knoxville, TN, USA.
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA.
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15
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Chakraborty S, Krishnan VV, Ramola K, Karmakar S. Enhanced vibrational stability in glass droplets. PNAS NEXUS 2023; 2:pgad289. [PMID: 37746327 PMCID: PMC10516527 DOI: 10.1093/pnasnexus/pgad289] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/08/2023] [Accepted: 08/28/2023] [Indexed: 09/26/2023]
Abstract
We show through simulations of amorphous solids prepared in open-boundary conditions that they possess significantly fewer low-frequency vibrational modes compared to their periodic boundary counterparts. Specifically, using measurements of the vibrational density of states, we find that the D ( ω ) ∼ ω 4 law changes to D ( ω ) ∼ ω δ with δ ≈ 5 in two dimensions and δ ≈ 4.5 in three dimensions. Crucially, this enhanced stability is achieved when utilizing slow annealing protocols to generate solid configurations. We perform an anharmonic analysis of the minima corresponding to the lowest frequency modes in such open-boundary systems and discuss their correlation with the density of states. A study of various system sizes further reveals that small systems display a higher degree of localization in vibrations. Lastly, we confine open-boundary solids in order to introduce macroscopic stresses in the system, which are absent in the unconfined system and find that the D ( ω ) ∼ ω 4 behavior is recovered.
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Affiliation(s)
| | - Vishnu V Krishnan
- Tata Institute of Fundamental Research, Hyderabad, 500046 Telangana, India
| | - Kabir Ramola
- Tata Institute of Fundamental Research, Hyderabad, 500046 Telangana, India
| | - Smarajit Karmakar
- Tata Institute of Fundamental Research, Hyderabad, 500046 Telangana, India
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16
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Zhang J, Wang D, Jin W, Xia A, Pashine N, Kramer-Bottiglio R, Shattuck MD, O'Hern CS. Designing the pressure-dependent shear modulus using tessellated granular metamaterials. Phys Rev E 2023; 108:034901. [PMID: 37849141 DOI: 10.1103/physreve.108.034901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 08/22/2023] [Indexed: 10/19/2023]
Abstract
Jammed packings of granular materials display complex mechanical response. For example, the ensemble-averaged shear modulus 〈G〉 increases as a power law in pressure p for static packings of soft spherical particles that can rearrange during compression. We seek to design granular materials with shear moduli that can either increase or decrease with pressure without particle rearrangements even in the large-system limit. To do this, we construct tessellated granular metamaterials by joining multiple particle-filled cells together. We focus on cells that contain a small number of bidisperse disks in two dimensions. We first study the mechanical properties of individual disk-filled cells with three types of boundaries: periodic boundary conditions (PBC), fixed-length walls (FXW), and flexible walls (FLW). Hypostatic jammed packings are found for cells with FLW, but not in cells with PBC and FXW, and they are stabilized by quartic modes of the dynamical matrix. The shear modulus of a single cell depends linearly on p. We find that the slope of the shear modulus with pressure λ_{c}<0 for all packings in single cells with PBC where the number of particles per cell N≥6. In contrast, single cells with FXW and FLW can possess λ_{c}>0, as well as λ_{c}<0, for N≤16. We show that we can force the mechanical properties of multicell granular metamaterials to possess those of single cells by constraining the end points of the outer walls and enforcing an affine shear response. These studies demonstrate that tessellated granular metamaterials provide a platform for the design of soft materials with specified mechanical properties.
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Affiliation(s)
- Jerry Zhang
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Dong Wang
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Weiwei Jin
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Annie Xia
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Nidhi Pashine
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Rebecca Kramer-Bottiglio
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Mark D Shattuck
- Benjamin Levich Institute and Physics Department, The City College of New York, New York, New York 10031, USA
| | - Corey S O'Hern
- Department of Mechanical Engineering & 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
- Integrated Graduate Program in Physical and Engineering Biology, Yale University, New Haven, Connecticut 06520, USA
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17
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Wu ZW, Chen Y, Wang WH, Kob W, Xu L. Topology of vibrational modes predicts plastic events in glasses. Nat Commun 2023; 14:2955. [PMID: 37225717 DOI: 10.1038/s41467-023-38547-w] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Accepted: 05/02/2023] [Indexed: 05/26/2023] Open
Abstract
The plastic deformation of crystalline materials can be understood by considering their structural defects such as disclinations and dislocations. Although also glasses are solids, their structure resembles closely the one of a liquid and hence the concept of structural defects becomes ill-defined. As a consequence it is very challenging to rationalize on a microscopic level the mechanical properties of glasses close to the yielding point and to relate plastic events to structural properties. Here we investigate the topological characteristics of the eigenvector field of the vibrational excitations of a two-dimensional glass model, notably the geometric arrangement of the topological defects as a function of vibrational frequency. We find that if the system is subjected to a quasistatic shear, the location of the resulting plastic events correlate strongly with the topological defects that have a negative charge. Our results provide thus a direct link between the structure of glasses prior their deformation and the plastic events during deformation.
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Affiliation(s)
- Zhen Wei Wu
- Institute of Nonequilibrium Systems, School of Systems Science, Beijing Normal University, 100875, Beijing, China.
- International Center for Quantum Materials, School of Physics, Peking University, Beijing, 100871, China.
| | - Yixiao Chen
- Yuanpei College, Peking University, 100871, Beijing, China
| | - Wei-Hua Wang
- Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Walter Kob
- Department of Physics, University of Montpellier and CNRS, 34095, Montpellier, France.
| | - Limei Xu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing, 100871, China.
- Collaborative Innovation Center of Quantum Matter, Beijing, 100871, China.
- Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University, Beijing, 100871, China.
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18
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Ishima D, Saitoh K, Otsuki M, Hayakawa H. Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime. Phys Rev E 2023; 107:054902. [PMID: 37328994 DOI: 10.1103/physreve.107.054902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Accepted: 03/23/2023] [Indexed: 06/18/2023]
Abstract
Using the Jacobian matrix, we obtain a theoretical expression of rigidity and the density of states of two-dimensional amorphous solids consisting of frictional grains in the linear response to an infinitesimal strain, in which we ignore the dynamical friction caused by the slip processes of contact points. The theoretical rigidity agrees with that obtained by molecular dynamics simulations. We confirm that the rigidity is smoothly connected to the value in the frictionless limit. We find that there are two modes in the density of states for sufficiently small k_{T}/k_{N}, which is the ratio of the tangential to normal stiffness. Rotational modes exist at low frequencies or small eigenvalues, whereas translational modes exist at high frequencies or large eigenvalues. The location of the rotational band shifts to the high-frequency region with an increase in k_{T}/k_{N} and becomes indistinguishable from the translational band for large k_{T}/k_{N}.
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Affiliation(s)
- Daisuke Ishima
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Kuniyasu Saitoh
- Department of Physics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan
| | - Michio Otsuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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19
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Zhang S, Jin W, Wang D, Xu D, Zhang J, Shattuck MD, O'Hern CS. Local and global measures of the shear moduli of jammed disk packings. Phys Rev E 2023; 107:054903. [PMID: 37329065 DOI: 10.1103/physreve.107.054903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2023] [Accepted: 05/05/2023] [Indexed: 06/18/2023]
Abstract
Strain-controlled isotropic compression gives rise to jammed packings of repulsive, frictionless disks with either positive or negative global shear moduli. We carry out computational studies to understand the contributions of the negative shear moduli to the mechanical response of jammed disk packings. We first decompose the ensemble-averaged, global shear modulus as 〈G〉=(1-F_{-})〈G_{+}〉+F_{-}〈G_{-}〉, where F_{-} is the fraction of jammed packings with negative shear moduli and 〈G_{+}〉 and 〈G_{-}〉 are the average values from packings with positive and negative moduli, respectively. We show that 〈G_{+}〉 and 〈|G_{-}|〉 obey different power-law scaling relations above and below pN^{2}∼1. For pN^{2}>1, both 〈G_{+}〉N and 〈|G_{-}|〉N∼(pN^{2})^{β}, where β∼0.5 for repulsive linear spring interactions. Despite this, 〈G〉N∼(pN^{2})^{β^{'}} with β^{'}≳0.5 due to the contributions from packings with negative shear moduli. We show further that the probability distribution of global shear moduli P(G) collapses at fixed pN^{2} and different values of p and N. We calculate analytically that P(G) is a Γ distribution in the pN^{2}≪1 limit. As pN^{2} increases, the skewness of P(G) decreases and P(G) becomes a skew-normal distribution with negative skewness in the pN^{2}≫1 limit. We also partition jammed disk packings into subsystems using Delaunay triangulation of the disk centers to calculate local shear moduli. We show that the local shear moduli defined from groups of adjacent triangles can be negative even when G>0. The spatial correlation function of local shear moduli C(r[over ⃗]) displays weak correlations for pn_{sub}^{2}<10^{-2}, where n_{sub} is the number of particles within each subsystem. However, C(r[over ⃗]) begins to develop long-ranged spatial correlations with fourfold angular symmetry for pn_{sub}^{2}≳10^{-2}.
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Affiliation(s)
- Shiyun Zhang
- Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Weiwei Jin
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Dong Wang
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Ding Xu
- Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jerry Zhang
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Mark D Shattuck
- Benjamin Levich Institute and Physics Department, The City College of New York, New York, New York 10031, 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
- Graduate Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut 06520, USA
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20
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Ishima D, Saitoh K, Otsuki M, Hayakawa H. Eigenvalue analysis of stress-strain curve of two-dimensional amorphous solids of dispersed frictional grains with finite shear strain. Phys Rev E 2023; 107:034904. [PMID: 37073050 DOI: 10.1103/physreve.107.034904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2022] [Accepted: 03/05/2023] [Indexed: 04/20/2023]
Abstract
The stress-strain curve of two-dimensional frictional dispersed grains interacting with a harmonic potential without considering the dynamical slip under a finite strain is determined by using eigenvalue analysis of the Hessian matrix. After the configuration of grains is obtained, the stress-strain curve based on the eigenvalue analysis is in almost perfect agreement with that obtained by the simulation, even if there are plastic deformations caused by stress avalanches. Unlike the naive expectation, the eigenvalues in our model do not indicate any precursors to the stress-drop events.
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Affiliation(s)
- Daisuke Ishima
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Kuniyasu Saitoh
- Department of Physics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan
| | - Michio Otsuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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21
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Gao Y, Yang C, Ding G, Dai LH, Jiang MQ. Structural rejuvenation of a well-aged metallic glass. FUNDAMENTAL RESEARCH 2022. [DOI: 10.1016/j.fmre.2022.12.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
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22
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Shimada M, Oyama N. Gas-liquid phase separation at zero temperature: mechanical interpretation and implications for gelation. SOFT MATTER 2022; 18:8406-8417. [PMID: 36285640 DOI: 10.1039/d2sm00628f] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
The relationship between glasses and gels has been intensely debated for decades; however, the transition between these two phases remains elusive. To investigate a gel formation process in the zero-temperature limit and its relation to the glass phase, we conducted numerical experiments on athermal quasistatic decompression. During decompression, the system experiences a cavitation event similar to phase separation and this is a gelation process at zero temperature. A normal mode analysis revealed that the phase separation is signaled by the vanishing of the lowest eigenenergy, similar to plastic events of glasses under shear. One primary difference from the shear-induced plasticity is that the vanishing mode experiences a qualitative change in its spatial energy distribution at the phase separation point. These findings enable us to define the glass-gel phase boundary based on mechanics.
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Affiliation(s)
- Masanari Shimada
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
- Department of Physics, Toronto Metropolitan University, M5B 2K3, Toronto, Canada.
| | - Norihiro Oyama
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
- Mathematics for Advanced Materials-OIL, AIST, Sendai 980-8577, Japan
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23
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Shiraishi K, Hara Y, Mizuno H. Low-frequency vibrational states in ideal glasses with random pinning. Phys Rev E 2022; 106:054611. [PMID: 36559418 DOI: 10.1103/physreve.106.054611] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2022] [Accepted: 11/01/2022] [Indexed: 06/17/2023]
Abstract
Glasses exhibit spatially localized vibrations in the low-frequency regime. These localized modes emerge below the boson peak frequency ω_{BP}, and their vibrational densities of state follow g(ω)∝ω^{4} (ω is frequency). Here, we attempt to address how the localized vibrations behave through the ideal glass transition. To do this, we employ a random pinning method, which enables us to study the thermodynamic glass transition. We find that the localized vibrations survive even in equilibrium glass states. Remarkably, the localized vibrations still maintain the properties of appearance below ω_{BP} and g(ω)∝ω^{4}. Our results provide important insight into the material properties of ideal glasses.
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Affiliation(s)
- Kumpei Shiraishi
- Graduate School of Arts and Sciences, University of Tokyo, Komaba, Tokyo 153-8902, Japan
| | - Yusuke Hara
- Graduate School of Arts and Sciences, University of Tokyo, Komaba, Tokyo 153-8902, Japan
| | - Hideyuki Mizuno
- Graduate School of Arts and Sciences, University of Tokyo, Komaba, Tokyo 153-8902, Japan
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24
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Sartor JD, Corwin EI. Predicting Defects in Soft Sphere Packings near Jamming Using the Force Network Ensemble. PHYSICAL REVIEW LETTERS 2022; 129:188001. [PMID: 36374695 DOI: 10.1103/physrevlett.129.188001] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2021] [Accepted: 09/23/2022] [Indexed: 06/16/2023]
Abstract
Amorphous systems of soft particles above jamming have more contacts than are needed to achieve mechanical equilibrium. The force network of a granular system with a fixed contact network is thus underdetermined and can be characterized as a random instantiation within the space of the force network ensemble. In this Letter, we show that defect contacts that are not necessary for stability of the system can be uniquely identified by examining the boundaries of this space of allowed force networks. We further show that, for simulations in the near jamming limit, this identification is nearly always correct and that defect contacts are broken under decompression of the system.
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Affiliation(s)
- James D Sartor
- Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA
| | - Eric I Corwin
- Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA
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25
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Keim NC, Medina D. Mechanical annealing and memories in a disordered solid. SCIENCE ADVANCES 2022; 8:eabo1614. [PMID: 36197976 PMCID: PMC9534499 DOI: 10.1126/sciadv.abo1614] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Accepted: 08/18/2022] [Indexed: 06/16/2023]
Abstract
Shearing a disordered or amorphous solid for many cycles with a constant strain amplitude can anneal it, relaxing a sample to a steady state that encodes a memory of that amplitude. This steady state also features a remarkable stability to amplitude variations that allows one to read the memory. Here, we shed light on both annealing and memory by considering how to mechanically anneal a sample to have as little memory content as possible. In experiments, we show that a "ring-down" protocol reaches a comparable steady state but with no discernible memories and minimal structural anisotropy. We introduce a method to characterize the population of rearrangements within a sample and show how it connects with the response to amplitude variation and the size of annealing steps. These techniques can be generalized to other forms of glassy matter and a wide array of disordered solids, especially those that yield by flowing homogeneously.
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Affiliation(s)
- Nathan C. Keim
- Department of Physics, Pennsylvania State University, University Park, PA 16802, USA
- Department of Physics, California Polytechnic State University, San Luis Obispo, CA 93407, USA
| | - Dani Medina
- Department of Physics, California Polytechnic State University, San Luis Obispo, CA 93407, USA
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26
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Wang L, Fu L, Nie Y. Density of states below the first sound mode in 3D glasses. J Chem Phys 2022; 157:074502. [DOI: 10.1063/5.0102081] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
Glasses feature universally low-frequency excess vibrational modes beyond Debye prediction, which could help rationalize, e.g., the glasses’ unusual temperature dependence of thermal properties compared to crystalline solids. The way the density of states of these low-frequency excess modes D( ω) depends on the frequency ω has been debated for decades. Recent simulation studies of 3D glasses suggest that D( ω) scales universally with ω4 in a low-frequency regime below the first sound mode. However, no simulation study has ever probed as low frequencies as possible to test directly whether this quartic law could work all the way to extremely low frequencies. Here, we calculated D( ω) below the first sound mode in 3D glasses over a wide range of frequencies. We find D( ω) scales with ω β with β < 4 at very low frequencies examined, while the ω4 law works only in a limited intermediate-frequency regime in some glasses. Moreover, our further analysis suggests our observation does not depend on glass models or glass stabilities examined. The ω4 law of D( ω) below the first sound mode is dominant in current simulation studies of 3D glasses, and our direct observation of the breakdown of the quartic law at very low frequencies thus leaves an open but important question that may attract more future numerical and theoretical studies.
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Affiliation(s)
- Lijin Wang
- School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, China
| | - Licun Fu
- School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, China
| | - Yunhuan Nie
- Beijing Computational Science Research Center, Beijing 100193, China
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27
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28
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Correlation of plastic events with local structure in jammed packings across spatial dimensions. Proc Natl Acad Sci U S A 2022; 119:e2119006119. [PMID: 35412897 PMCID: PMC9169794 DOI: 10.1073/pnas.2119006119] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
SignificanceMean-field theories, exact in the limit of infinite spatial dimensions, succeed in describing many features of glasses and amorphous solids in low dimensions, leading to considerable effort to understand how behavior evolves with dimension. Until now, all evidence has supported a picture in which "localized physics," responsible for deviations from mean-field behavior in low dimensions, fades away with rising dimension. Our work shows that rearrangements, in which particles change relative positions leading to fluid-like response, reveal a different picture of dimensional cross-over. We find that rearrangements, which are localized in two- and three-dimensional systems and correlated with local structure, remain just as correlated with local structure up to five dimensions, suggesting that local structure is important even in high dimensions.
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29
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szulc A, Mungan M, Regev I. Cooperative effects driving the multi-periodic dynamics of cyclically sheared amorphous solids. J Chem Phys 2022; 156:164506. [DOI: 10.1063/5.0087164] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
When subject to cyclic forcing, amorphous solids can reach periodic, repetitive states, where the system behaves plastically, but the particles return to their initial positions after one or more forcing cycles, where the latter response is called multi-periodic. It is known that plasticity in amorphous materials is mediated by local rearrangements called ``soft spots' or ``shear transformation zones'.Experiments and simulations indicate that soft spots can be modeled as hysteretic two-state entities interacting via quadrupolar displacement fields generated when they switch states and that these interactions can give rise to multi-periodic behavior. However, how interactions facilitate multi-periodicity is unknown. Here we show, using a model of random interacting two-state systems and molecular dynamics simulations, that multi-periodicity arises from oscillations in the magnitudes of the switching field of soft spots which cause soft spots to be active during some forcing cycles and idle during others. We demonstrate that these oscillations result from cooperative effects facilitated by the frustrated interactions between the soft spots. The presence of such mechanisms has implications for manipulating memory in frustrated hysteretic systems.
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Affiliation(s)
- asaf szulc
- Department of Physics, Ben-Gurion University of the Negev, Israel
| | - Muhittin Mungan
- Rheinische Friedrich Wilhelms Universität Bonn Institute of Applied Mathematics, Germany
| | - Ido Regev
- Solar energy and environmental physics, Ben-Gurion University of the Negev - Sede Boqer Campus, Israel
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30
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Sharma M, Nandi MK, Bhattacharyya SM. Identifying structural signature of dynamical heterogeneity via the local softness parameter. Phys Rev E 2022; 105:044604. [PMID: 35590668 DOI: 10.1103/physreve.105.044604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Accepted: 03/25/2022] [Indexed: 06/15/2023]
Abstract
In this work we study the relationship between the softness of a mean-field caging potential and dynamics at the local level. We first describe the local softness, which shows a distribution, thus identifying structural heterogeneity. We show that the lifetime of the softness parameter is connected to the lifetime of the well-known cage structure in supercooled liquids. Finally, our theory predicts that the local softness and the local dynamics is causal below the onset temperature where there is a decoupling between the short and long time dynamics, thus allowing a static description of the cage. With the decrease in temperature, the correlation between structure and dynamics increases. The study shows that at lower temperatures, the structural heterogeneity increases, and since the structure becomes a better predictor of the dynamics, it leads to an increase in the dynamical heterogeneity. We also find that the softness of a hard, immobile region evolves with time and becomes soft and eventually mobile due to the rearrangements in the neighborhood, confirming the well-known facilitation effect.
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Affiliation(s)
- Mohit Sharma
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune-411008, India
| | - Manoj Kumar Nandi
- Department of Engineering, University of Campania "Luigi Vanvitelli" 81031 Aversa (Caserta), Italy
| | - Sarika Maitra Bhattacharyya
- Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune-411008, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
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31
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Jiang M, Dai L. 非晶态固体力学. CHINESE SCIENCE BULLETIN-CHINESE 2022. [DOI: 10.1360/tb-2022-0181] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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32
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Stanifer E, Manning ML. Avalanche dynamics in sheared athermal particle packings occurs via localized bursts predicted by unstable linear response. SOFT MATTER 2022; 18:2394-2406. [PMID: 35266483 DOI: 10.1039/d1sm01451j] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Under applied shear strain, granular and amorphous materials deform via particle rearrangements, which can be small and localized or organized into system-spanning avalanches. While the statistical properties of avalanches under quasi-static shear are well-studied, the dynamics during avalanches is not. In numerical simulations of sheared soft spheres, we find that avalanches can be decomposed into bursts of localized deformations, which we identify using an extension of persistent homology methods. We also study the linear response of unstable systems during an avalanche, demonstrating that eigenvalue dynamics are highly complex during such events, and that the most unstable eigenvector is a poor predictor of avalanche dynamics. Instead, we modify existing tools that identify localized excitations in stable systems, and apply them to these unstable systems with non-positive definite Hessians, quantifying the evolution of such excitations during avalanches. We find that bursts of localized deformations in the avalanche almost always occur at localized excitations identified using the linear spectrum. These new tools will provide an improved framework for validating and extending mesoscale elastoplastic models that are commonly used to explain avalanche statistics in glasses and granular matter.
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Affiliation(s)
- Ethan Stanifer
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - M Lisa Manning
- Department of Physics and BioInspired Institute, Syracuse University, Syracuse, New York 13244, USA.
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33
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Yang E, Riggleman RA. Role of Local Structure in the Enhanced Dynamics of Deformed Glasses. PHYSICAL REVIEW LETTERS 2022; 128:097801. [PMID: 35302792 DOI: 10.1103/physrevlett.128.097801] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2021] [Revised: 11/18/2021] [Accepted: 02/09/2022] [Indexed: 06/14/2023]
Abstract
External stress can accelerate molecular mobility of amorphous solids by several orders of magnitude. The changes in mobility are commonly interpreted through the Eyring model, which invokes an empirical activation volume. Here, we analyze constant-stress molecular dynamics simulations and propose a structure-dependent Eyring model, connecting activation volume to a machine-learned field, softness. We show that stress has a heterogeneous effect on the mobility that depends on local structure through softness. The barrier impeding relaxation reduces more for well-packed particles, which explains the narrower distribution of relaxation time observed under stress.
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Affiliation(s)
- Entao Yang
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Robert A Riggleman
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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34
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Luding S, Taghizadeh K, Cheng C, Kondic L. Understanding slow compression and decompression of frictionless soft granular matter by network analysis. SOFT MATTER 2022; 18:1868-1884. [PMID: 35171180 DOI: 10.1039/d1sm01689j] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We consider dense granular systems in three spatial dimensions exposed to slow compression and decompression, below, during, above and well above jamming. The evolution of granular systems under slow deformation is non-trivial and involves smooth, continuous, reversible (de)compression periods, interrupted by fast, discontinuous, irreversible transition events. These events are often, but not always, associated with rearrangements of particles and of the contact network. How many particles are involved in these transitions between two states can range from few to almost all in the system. An analysis of the force network that is built on top of the contact network is carried out using the tools of persistent homology. Results involve the observation that kinetic energy is correlated with the intensity of rearrangements, while the evolution of global mechanical measures, such as pressure, is strongly correlated with the evolution of the topological measures quantifying loops in the force network. Surprisingly, some transitions are clearly detected by persistent homology even though motion/rearrangement of particles is much weaker, i.e., much harder to detect or, in some cases, not observed at all.
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Affiliation(s)
- Stefan Luding
- MSM, TFE-ET, MESA+, University of Twente, PO Box 217, 7500AE Enschede, The Netherlands.
| | - Kianoosh Taghizadeh
- MSM, TFE-ET, MESA+, University of Twente, PO Box 217, 7500AE Enschede, The Netherlands.
- Institute of Applied Mechanics (CE), SC SimTech, University of Stuttgart, Germany
| | - Chao Cheng
- Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
| | - Lou Kondic
- Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA
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35
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Giannini JA, Stanifer EM, Manning ML. Searching for structural predictors of plasticity in dense active packings. SOFT MATTER 2022; 18:1540-1553. [PMID: 35107478 DOI: 10.1039/d1sm01675j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In amorphous solids subject to shear or thermal excitation, so-called structural indicators have been developed that predict locations of future plasticity or particle rearrangements. An open question is whether similar tools can be used in dense active materials, but a challenge is that under most circumstances, active systems do not possess well-defined solid reference configurations. We develop a computational model for a dense active crowd attracted to a point of interest, which does permit a mechanically stable reference state in the limit of infinitely persistent motion. Previous work on a similar system suggested that the collective motion of crowds could be predicted by inverting a matrix of time-averaged two-particle correlation functions. Seeking a first-principles understanding of this result, we demonstrate that this active matter system maps directly onto a granular packing in the presence of an external potential, and extend an existing structural indicator based on linear response to predict plasticity in the presence of noisy dynamics. We find that the strong pressure gradient necessitated by the directed activity, as well as a self-generated free boundary, strongly impact the linear response of the system. In low-pressure regions the linear-response-based indicator is predictive, but it does not work well in the high-pressure interior of our active packings. Our findings motivate and inform future work that could better formulate structure-dynamics predictions in systems with strong pressure gradients.
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Affiliation(s)
- Julia A Giannini
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA.
- BioInspired Institute, Syracuse University, Syracuse, New York 13244, USA
| | - Ethan M Stanifer
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - M Lisa Manning
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA.
- BioInspired Institute, Syracuse University, Syracuse, New York 13244, USA
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36
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Mitra S, Marín-Aguilar S, Sastry S, Smallenburg F, Foffi G. Correlation between plastic rearrangements and local structure in a cyclically driven glass. J Chem Phys 2022; 156:074503. [DOI: 10.1063/5.0077851] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | | | - Srikanth Sastry
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, India
| | | | - Giuseppe Foffi
- Laboratoire de Physique des Solides, Laboratoire de Physique des Solides, France
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37
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Zhai C, Albayrak N, Engqvist J, Hall SA, Wright J, Majkut M, Herbold EB, Hurley RC. Quantifying local rearrangements in three-dimensional granular materials: Rearrangement measures, correlations, and relationship to stresses. Phys Rev E 2022; 105:014904. [PMID: 35193203 DOI: 10.1103/physreve.105.014904] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Accepted: 01/04/2022] [Indexed: 06/14/2023]
Abstract
Quantifying the ways in which local particle rearrangements contribute to macroscopic plasticity is one of the fundamental pursuits of granular mechanics and soft matter physics. Here we examine local rearrangements that occur naturally during the deformation of three samples of 3D granular materials subjected to distinct boundary conditions by employing in situ x-ray measurements of particle-resolved structure and stress. We focus on five distinct rearrangement measures, their statistics, interrelationships, contributions to macroscopic deformation, repeatability, and dependence on local structure and stress. Our most significant findings are that local rearrangements (1) are correlated on a scale of three to four particle diameters, (2) exhibit volumetric strain-shear strain and nonaffine displacement-rotation coupling, (3) exhibit correlations that suggest either rearrangement repeatability or that rearrangements span multiple steps of incremental sample strain, and (4) show little dependence on local stress but correlate with quantities describing local structure, such as porosity. Our results are presented in the context of relevant plasticity theories and are consistent with recent findings suggesting that local structure may play at least as important of a role as local stress in determining the nature of local rearrangements.
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Affiliation(s)
- Chongpu Zhai
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an, China and Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Nahuel Albayrak
- Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Jonas Engqvist
- Division for Solid Mechanics, Lund University, Lund 22100, Sweden
| | | | | | | | - Eric B Herbold
- Atmospheric, Earth, & Energy Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Ryan C Hurley
- Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA and Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, Maryland 21218, USA
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38
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Mizuno H, Hachiya M, Ikeda A. Structural, mechanical, and vibrational properties of particulate physical gels. J Chem Phys 2021; 155:234502. [PMID: 34937359 DOI: 10.1063/5.0072863] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Our lives are surrounded by a rich assortment of disordered materials. In particular, glasses are well known as dense, amorphous materials, whereas gels exist in low-density, disordered states. Recent progress has provided a significant step forward in understanding the material properties of glasses, such as mechanical, vibrational, and transport properties. In contrast, our understanding of particulate physical gels is still highly limited. Here, using molecular dynamics simulations, we study a simple model of particulate physical gels, the Lennard-Jones (LJ) gels, and provide a comprehensive understanding of their structural, mechanical, and vibrational properties, all of which are markedly different from those of LJ glasses. First, the LJ gels show sparse, heterogeneous structures, and the length scale ξs of the structures grows as the density is lowered. Second, the LJ gels are extremely soft, with both shear G and bulk K moduli being orders of magnitude smaller than those of LJ glasses. Third, many low-frequency vibrational modes are excited, which form a characteristic plateau with the onset frequency ω* in the vibrational density of states. Structural, mechanical, and vibrational properties, characterized by ξs, G, K, and ω*, respectively, show power-law scaling behaviors with the density, which establishes a close relationship between them. Throughout this work, we also reveal that LJ gels are multiscale, solid-state materials: (i) homogeneous elastic bodies at long lengths, (ii) heterogeneous elastic bodies with fractal structures at intermediate lengths, and (iii) amorphous structural bodies at short lengths.
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Affiliation(s)
- Hideyuki Mizuno
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
| | - Makoto Hachiya
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
| | - Atsushi Ikeda
- Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan
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39
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Wang L, Szamel G, Flenner E. Low-Frequency Excess Vibrational Modes in Two-Dimensional Glasses. PHYSICAL REVIEW LETTERS 2021; 127:248001. [PMID: 34951818 DOI: 10.1103/physrevlett.127.248001] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Accepted: 11/09/2021] [Indexed: 06/14/2023]
Abstract
Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding of the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency ω as ω^{4} in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows D_{exc}(ω)∼ω^{2} up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of D_{exc}(ω) correlates with the stability dependence of low-frequency sound attenuation. However, we also find that, in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode, there are excess modes with a system size independent density of states that scales as ω^{3}.
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Affiliation(s)
- Lijin Wang
- School of Physics and Optoelectronics Engineering, Information Materials and Intelligent Sensing Laboratory of Anhui Province, Anhui University, Hefei 230601, People's Republic of China
| | - Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Elijah Flenner
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
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40
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Wang X, Zhang H, Douglas JF. The initiation of shear band formation in deformed metallic glasses from soft localized domains. J Chem Phys 2021; 155:204504. [PMID: 34852471 DOI: 10.1063/5.0069729] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It has long been thought that shear band (SB) formation in amorphous solids initiates from relatively "soft" regions in the material in which large-scale non-affine deformations become localized. The test of this hypothesis requires an effective means of identifying "soft" regions and their evolution as the material is deformed to varying degrees, where the metric of "softness" must also account for the effect of temperature on local material stiffness. We show that the mean square atomic displacement on a caging timescale ⟨u2⟩, the "Debye-Waller factor," provides a useful method for estimating the shear modulus of the entire material and, by extension, the material stiffness at an atomic scale. Based on this "softness" metrology, we observe that SB formation indeed occurs through the strain-induced formation of localized soft regions in our deformed metallic glass free-standing films. Unexpectedly, the critical strain condition for SB formation occurs when the softness (⟨u2⟩) distribution within the emerging soft regions approaches that of the interfacial region in its undeformed state, initiating an instability with similarities to the transition to turbulence. Correspondingly, no SBs arise when the material is so thin that the entire material can be approximately described as being "interfacial" in nature. We also quantify relaxation in the glass and the nature and origin of highly non-Gaussian particle displacements in the dynamically heterogeneous SB regions at times longer than the caging time.
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Affiliation(s)
- Xinyi Wang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 1H9, Canada
| | - Hao Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 1H9, Canada
| | - Jack F Douglas
- Material Measurement Laboratory, Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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41
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Lerner E, Bouchbinder E. Low-energy quasilocalized excitations in structural glasses. J Chem Phys 2021; 155:200901. [PMID: 34852497 DOI: 10.1063/5.0069477] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
Glassy solids exhibit a wide variety of generic thermomechanical properties, ranging from universal anomalous specific heat at cryogenic temperatures to nonlinear plastic yielding and failure under external driving forces, which qualitatively differ from their crystalline counterparts. For a long time, it has been believed that many of these properties are intimately related to nonphononic, low-energy quasilocalized excitations (QLEs) in glasses. Indeed, recent computer simulations have conclusively revealed that the self-organization of glasses during vitrification upon cooling from a melt leads to the emergence of such QLEs. In this Perspective, we review developments over the past three decades toward understanding the emergence of QLEs in structural glasses and the degree of universality in their statistical and structural properties. We discuss the challenges and difficulties that hindered progress in achieving these goals and review the frameworks put forward to overcome them. We conclude with an outlook on future research directions and open questions.
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Affiliation(s)
- Edan Lerner
- 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
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42
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Mahajan S, Ciamarra MP. Unifying Description of the Vibrational Anomalies of Amorphous Materials. PHYSICAL REVIEW LETTERS 2021; 127:215504. [PMID: 34860101 DOI: 10.1103/physrevlett.127.215504] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2021] [Revised: 08/19/2021] [Accepted: 10/08/2021] [Indexed: 06/13/2023]
Abstract
The vibrational density of states D(ω) of solids controls their thermal and transport properties. In crystals, the low-frequency modes are extended phonons distributed in frequency according to Debye's law, D(ω)∝ω^{2}. In amorphous solids, phonons are damped, and at low frequency D(ω) comprises extended modes in excess over Debye's prediction, leading to the so-called boson peak in D(ω)/ω^{2} at ω_{bp}, and quasilocalized ones. Here we show that boson peak and phonon attenuation in the Rayleigh scattering regime are related, as suggested by correlated fluctuating elasticity theory, and that amorphous materials can be described as homogeneous isotropic elastic media punctuated by quasilocalized modes acting as elastic heterogeneities. Our numerical results resolve the conflict between theoretical approaches attributing amorphous solids' vibrational anomalies to elastic disorder and localized defects.
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Affiliation(s)
- Shivam Mahajan
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371
| | - Massimo Pica Ciamarra
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371
- CNRS@CREATE LTD, 1 Create Way, #08-01 CREATE Tower, Singapore 138602
- CNR-SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126, Napoli, Italy
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43
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Giannini JA, Richard D, Manning ML, Lerner E. Bond-space operator disentangles quasilocalized and phononic modes in structural glasses. Phys Rev E 2021; 104:044905. [PMID: 34781437 DOI: 10.1103/physreve.104.044905] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2021] [Accepted: 09/20/2021] [Indexed: 11/07/2022]
Abstract
The origin of several emergent mechanical and dynamical properties of structural glasses is often attributed to populations of localized structural instabilities, coined quasilocalized modes (QLMs). Under a restricted set of circumstances, glassy QLMs can be revealed by analyzing computer glasses' vibrational spectra in the harmonic approximation. However, this analysis has limitations due to system-size effects and hybridization processes with low-energy phononic excitations (plane waves) that are omnipresent in elastic solids. Here we overcome these limitations by exploring the spectrum of a linear operator defined on the space of particle interactions (bonds) in a disordered material. We find that this bond-force-response operator offers a different interpretation of QLMs in glasses and cleanly recovers some of their important statistical and structural features. The analysis presented here reveals the dependence of the number density (per frequency) and spatial extent of QLMs on material preparation protocol (annealing). Finally, we discuss future research directions and possible extensions of this work.
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Affiliation(s)
- Julia A Giannini
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA.,BioInspired Institute, Syracuse University, Syracuse, New York 13244, USA
| | - David Richard
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA.,Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, Netherlands
| | - M Lisa Manning
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA.,BioInspired Institute, Syracuse University, Syracuse, New York 13244, USA
| | - Edan Lerner
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, Netherlands
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44
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Arceri F, Corwin EI, Hagh VF. Marginal stability in memory training of jammed solids. Phys Rev E 2021; 104:044907. [PMID: 34781479 DOI: 10.1103/physreve.104.044907] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 09/29/2021] [Indexed: 11/07/2022]
Abstract
Memory encoding by cyclic shear is a reliable process to store information in jammed solids, yet its underlying mechanism and its connection to the amorphous structure are not fully understood. When a jammed sphere packing is repeatedly sheared with cycles of the same strain amplitude, it optimizes its mechanical response to the cyclic driving and stores a memory of it. We study memory by cyclic shear training as a function of the underlying stability of the amorphous structure in marginally stable and highly stable packings, the latter produced by minimizing the potential energy using both positional and radial degrees of freedom. We find that jammed solids need to be marginally stable in order to store a memory by cyclic shear. In particular, highly stable packings store memories only after overcoming brittle yielding and the cyclic shear training takes place in the shear band, a region which we show to be marginally stable.
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Affiliation(s)
- Francesco Arceri
- Department of Physics, University of Oregon, Eugene, Oregon 97403, USA
| | - Eric I Corwin
- Department of Physics, University of Oregon, Eugene, Oregon 97403, USA
| | - Varda F Hagh
- Department of Physics, University of Oregon, Eugene, Oregon 97403, USA.,James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
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45
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Jin W, Datye A, Schwarz UD, Shattuck MD, O'Hern CS. Using delaunay triangularization to characterize non-affine displacement fields during athermal, quasistatic deformation of amorphous solids. SOFT MATTER 2021; 17:8612-8623. [PMID: 34545381 DOI: 10.1039/d1sm00898f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We investigate the non-affine displacement fields that occur in two-dimensional Lennard-Jones models of metallic glasses subjected to athermal, quasistatic simple shear (AQS). During AQS, the shear stress versus strain displays continuous quasi-elastic segments punctuated by rapid drops in shear stress, which correspond to atomic rearrangement events. We capture all information concerning the atomic motion during the quasi-elastic segments and shear stress drops by performing Delaunay triangularizations and tracking the deformation gradient tensor Fα associated with each triangle α. To understand the spatio-temporal evolution of the displacement fields during shear stress drops, we calculate Fα along minimal energy paths from the mechanically stable configuration immediately before to that after the stress drop. We find that quadrupolar displacement fields form and dissipate both during the quasi-elastic segments and shear stress drops. We then perform local perturbations (rotation, dilation, simple and pure shear) to single triangles and measure the resulting displacement fields. We find that local pure shear deformations of single triangles give rise to mostly quadrupolar displacement fields, and thus pure shear strain is the primary type of local strain that is activated by bulk, athermal quasistatic simple shear. Other local perturbations, e.g. rotations, dilations, and simple shear of single triangles, give rise to vortex-like and dipolar displacement fields that are not frequently activated by bulk AQS. These results provide fundamental insights into the non-affine atomic motion that occurs in driven, glassy materials.
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Affiliation(s)
- Weiwei Jin
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Amit Datye
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Udo D Schwarz
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA
| | - Mark D Shattuck
- Benjamin Levich Institute and Physics Department, The City College of New York, New York, New York 10031, 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
- Graduate Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut 06520, USA.
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46
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Fan H, Fan Z, Liu X, Lu Z, Ma E. Atomic vibration as an indicator of the propensity for configurational rearrangements in metallic glasses. MATERIALS HORIZONS 2021; 8:2359-2372. [PMID: 34870291 DOI: 10.1039/d1mh00491c] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
In a metallic glass (MG), the propensity for atomic rearrangements varies spatially from location to location in the amorphous solid, making the prediction of their likelihood a major challenge. One can attack this problem from the "structure controls properties" standpoint. But all the current structure-centric parameters are mostly based on local atomic packing information limited to short-range order, hence falling short in reliably forecasting how the local region would respond to external stimuli (e.g., temperature and/or stress). Alternatively, one can use indicators informed by physical properties to bridge the static structure on the one hand, and the response of the local configuration on the other. A sub-group of such physics-informed quantities consists of atomic vibration parameters, which will be singled out as the focus of this article. Here we use the Cu64Zr36 alloy to systematically demonstrate the following two points, all using a single model MG. First, we show in a comprehensive manner the interrelation among common vibrational parameters characterizing the atomic vibrational amplitude and frequency, including the atomic mean square displacement, flexibility volume, participation fraction in the low-frequency vibrational modes and boson peak intensity. Second, we demonstrate that these vibrational parameters fare much better than purely static structural parameters based on local geometrical packing in providing correlation with the propensity for local configurational transitions. These vibrational parameters also share a correlation length similar to that in structural rearrangements induced by external stimuli. This success, however, also poses a challenge, as it remains to be elucidated as to why short-time dynamical (vibrational) behavior at the bottom of the energy basin can be exploited to project the height of the energy barrier for cross-basin activities and in turn the propensity for locally collective atomic rearrangements.
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Affiliation(s)
- Huiyang Fan
- State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, 100083, China.
- Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
| | - Zhao Fan
- Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
| | - Xiongjun Liu
- State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, 100083, China.
| | - Zhaoping Lu
- State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, 100083, China.
| | - En Ma
- Center for Alloy Innovation and Design (CAID), State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an 710049, China.
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47
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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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48
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Ma X, Mishra CK, Habdas P, Yodh AG. Structural and short-time vibrational properties of colloidal glasses and supercooled liquids in the vicinity of the re-entrant glass transition. J Chem Phys 2021; 155:074902. [PMID: 34418931 DOI: 10.1063/5.0059084] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
We investigate the short-time vibrational properties and structure of two-dimensional, bidisperse, colloidal glasses and supercooled liquids in the vicinity of the re-entrant glass transition, as a function of interparticle depletion attraction strength. The long-time spatiotemporal dynamics of the samples are measured to be non-monotonic, confirming that the suspensions evolve from repulsive glass to supercooled liquid to attractive glass with increasing depletion attraction. Here, we search for vibrational signatures of the re-entrant behavior in the short-time spatiotemporal dynamics, i.e., dynamics associated with particle motion inside its nearest-neighbor cage. Interestingly, we observe that the anharmonicity of these in-cage vibrations varies non-monotonically with increasing attraction strength, consistent with the non-monotonic long-time structural relaxation dynamics of the re-entrant glass. We also extract effective spring constants between neighboring particles; we find that spring stiffness involving small particles also varies non-monotonically with increasing attraction strength, while stiffness between large particles increases monotonically. Last, from study of depletion-dependent local structure and vibration participation fractions, we gain microscopic insight into the particle-size-dependent contributions to short-time vibrational modes in the glass and supercooled liquid states.
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Affiliation(s)
- Xiaoguang Ma
- Center for Complex Flows and Soft Matter Research, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
| | - Chandan K Mishra
- Discipline of Physics, Indian Institute of Technology (IIT) Gandhinagar Palaj, Gandhinagar, Gujarat 382355, India
| | - P Habdas
- Department of Physics, Saint Joseph's University, Philadelphia, Pennsylvania 19131, USA
| | - A G Yodh
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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Oyama N, Mizuno H, Ikeda A. Unified view of avalanche criticality in sheared glasses. Phys Rev E 2021; 104:015002. [PMID: 34412287 DOI: 10.1103/physreve.104.015002] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2020] [Accepted: 06/14/2021] [Indexed: 11/07/2022]
Abstract
Plastic events in sheared glasses are considered an example of so-called avalanches, whose sizes obey a power-law probability distribution with the avalanche critical exponent τ. Although the so-called mean-field depinning (MFD) theory predicts a universal value of this exponent, τ_{MFD}=1.5, such a simplification is now known to connote qualitative disagreement with realistic systems. Numerically and experimentally, different values of τ have been reported depending on the literature. Moreover, in the elastic regime, it has been noted that the critical exponent can be different from that in the steady state, and even criticality itself is a matter of debate. Because these confusingly varying results have been reported under different setups, our knowledge of avalanche criticality in sheared glasses is greatly limited. To gain a unified understanding, in this work, we conduct a comprehensive numerical investigation of avalanches in Lennard-Jones glasses under athermal quasistatic shear. In particular, by excluding the ambiguity and arbitrariness that has crept into the conventional measurement schemes, we achieve high-precision measurement and demonstrate that the exponent τ in the steady state follows the prediction of MFD theory, τ_{MFD}=1.5. Our results also suggest that there are two qualitatively different avalanche events. This binariness leads to the nonuniversal behavior of the avalanche size distribution and is likely to be the cause of the varying values of τ reported thus far. To investigate the dependence of criticality and universality on applied shear, we further study the statistics of avalanches in the elastic regime and the ensemble of the first avalanche event in different samples, which provide information about the unperturbed system. We show that while the unperturbed system is indeed off-critical, criticality gradually develops as shear is applied. The degree of criticality is encoded in the fractal dimension of the avalanches, which starts from zero in the off-critical unperturbed state and saturates in the steady state. Moreover, the critical exponent τ is consistent with the prediction of the MFD τ_{MFD} universally, regardless of the amount of applied shear, once the system becomes critical.
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Affiliation(s)
- Norihiro Oyama
- Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Tokyo 153-8902, Japan.,Mathematics for Advanced Materials-OIL, AIST, Sendai 980-8577, Japan
| | - Hideyuki Mizuno
- Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Tokyo 153-8902, Japan
| | - Atsushi Ikeda
- Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Tokyo 153-8902, Japan.,Research Center for Complex Systems Biology, Universal Biology Institute, The University of Tokyo, Komaba, Tokyo 153-8902, Japan
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Keim NC, Paulsen JD. Multiperiodic orbits from interacting soft spots in cyclically sheared amorphous solids. SCIENCE ADVANCES 2021; 7:7/33/eabg7685. [PMID: 34380623 PMCID: PMC8357233 DOI: 10.1126/sciadv.abg7685] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2021] [Accepted: 06/03/2021] [Indexed: 05/06/2023]
Abstract
When an amorphous solid is deformed cyclically, it may reach a steady state in which the paths of constituent particles trace out closed loops that repeat in each driving cycle. A remarkable variant has been noticed in simulations where the period of particle motions is a multiple of the period of driving, but the reasons for this behavior have remained unclear. Motivated by mesoscopic features of displacement fields in experiments on jammed solids, we propose and analyze a simple model of interacting soft spots-locations where particles rearrange under stress and that resemble two-level systems with hysteresis. We show that multiperiodic behavior can arise among just three or more soft spots that interact with each other, but in all cases it requires frustrated interactions, illuminating this otherwise elusive type of interaction. We suggest directions for seeking this signature of frustration in experiments and for achieving it in designed systems.
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Affiliation(s)
- Nathan C Keim
- Department of Physics, Pennsylvania State University, University Park, PA 16802, USA.
- Department of Physics, California Polytechnic State University, San Luis Obispo, CA 93407, USA
| | - Joseph D Paulsen
- Department of Physics, Syracuse University, Syracuse, NY 13244, USA.
- BioInspired Syracuse: Institute for Material and Living Systems, Syracuse University, Syracuse, NY 13244, USA
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