1
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Winer M, Baldwin CL, Barney R, Galitski V, Swingle B. Glass transition of quantum hard spheres in high dimensions. Phys Rev E 2024; 109:044112. [PMID: 38755820 DOI: 10.1103/physreve.109.044112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2023] [Accepted: 03/12/2024] [Indexed: 05/18/2024]
Abstract
We study the equilibrium thermodynamics of quantum hard spheres in the infinite-dimensional limit, determining the boundary between liquid and glass phases in the temperature-density plane by means of the Franz-Parisi potential. We find that as the temperature decreases from high values, the effective radius of the spheres is enhanced by a multiple of the thermal de Broglie wavelength, thus increasing the effective filling fraction and decreasing the critical density for the glass phase. Numerical calculations show that the critical density continues to decrease monotonically as the temperature decreases further, suggesting that the system will form a glass at sufficiently low temperatures for any density. The methods used in this paper can be extended to more general potentials, and also to other transitions such as the Kauzman/Replica Symmetry Breaking (RSB) transition, the Gardner transition, and potentially even jamming.
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Affiliation(s)
- Michael Winer
- Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Christopher L Baldwin
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Richard Barney
- Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Victor Galitski
- Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Brian Swingle
- Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA
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2
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Jadrich RB, Lindquist BA, Truskett TM. Treating random sequential addition via the replica method. J Chem Phys 2022; 157:084116. [DOI: 10.1063/5.0096276] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
While many physical processes are non-equilibrium in nature, the theory and modeling of such phenomena lag behind theoretical treatments of equilibrium systems. The diversity of powerful theoretical tools available to describe equilibrium systems has inspired strategies that map non-equilibrium systems onto equivalent equilibrium analogs so that interrogation with standard statistical mechanical approaches is possible. In this work, we revisit the mapping from the non-equilibrium random sequential addition process onto an equilibrium multi-component mixture via the replica method, allowing for theoretical predictions of non-equilibrium structural quantities. We validate the above approach by comparing the theoretical predictions to numerical simulations of random sequential addition.
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Affiliation(s)
| | | | - Thomas M. Truskett
- McKetta Department of Chemical Engineering, University of Texas at Austin, United States of America
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3
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Lawson-Keister E, Manning ML. Jamming and arrest of cell motion in biological tissues. Curr Opin Cell Biol 2021; 72:146-155. [PMID: 34461581 DOI: 10.1016/j.ceb.2021.07.011] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Revised: 07/07/2021] [Accepted: 07/28/2021] [Indexed: 12/29/2022]
Abstract
Collective cell motility is crucial to many biological processes including morphogenesis, wound healing, and cancer invasion. Recently, the biology and biophysics communities have begun to use the term 'cell jamming' to describe the collective arrest of cell motion in tissues. Although this term is widely used, the underlying mechanisms are varied. In this review, we highlight three independent mechanisms that can potentially drive arrest of cell motion - crowding, tension-driven rigidity, and reduction of fluctuations - and propose a framework that connects all three. Because multiple mechanisms may be operating simultaneously, this emphasizes that experiments should strive to identify which mechanism dominates in a given situation. We also discuss how specific cell-scale and molecular-scale biological processes, such as cell-cell and cell-substrate interactions, control aspects of these underlying physical mechanisms.
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Affiliation(s)
| | - M Lisa Manning
- Department of Physics and BioInspired Institute, Syracuse University, Syracuse, NY 13244, USA.
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4
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George G, Klochko L, Semenov AN, Baschnagel J, Wittmer JP. Ensemble fluctuations matter for variances of macroscopic variables. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:13. [PMID: 33683484 DOI: 10.1140/epje/s10189-020-00004-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2020] [Accepted: 12/14/2020] [Indexed: 06/12/2023]
Abstract
Extending recent work on stress fluctuations in complex fluids and amorphous solids we describe in general terms the ensemble average [Formula: see text] and the standard deviation [Formula: see text] of the variance [Formula: see text] of time series [Formula: see text] of a stochastic process x(t) measured over a finite sampling time [Formula: see text]. Assuming a stationary, Gaussian and ergodic process, [Formula: see text] is given by a functional [Formula: see text] of the autocorrelation function h(t). [Formula: see text] is shown to become large and similar to [Formula: see text] if [Formula: see text] corresponds to a fast relaxation process. Albeit [Formula: see text] does not hold in general for non-ergodic systems, the deviations for common systems with many microstates are merely finite-size corrections. Various issues are illustrated for shear-stress fluctuations in simple coarse-grained model systems.
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Affiliation(s)
- G George
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034, Strasbourg Cedex, France
| | - L Klochko
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034, Strasbourg Cedex, France
| | - A N Semenov
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034, Strasbourg Cedex, France
| | - J Baschnagel
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034, Strasbourg Cedex, France
| | - J P Wittmer
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034, Strasbourg Cedex, France.
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5
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Levashov VA, Ryltsev RE, Chtchelkatchev NM. Structure of the simple harmonic-repulsive system in liquid and glassy states studied by the triple correlation function. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:025403. [PMID: 33063696 DOI: 10.1088/1361-648x/abb516] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
An efficient description of the structures of liquids and, in particular, the structural changes that happen with liquids on supercooling remains to be a challenge. The systems composed of soft particles are especially interesting in this context because they often demonstrate non-trivial local orders that do not allow to introduce the concept of the nearest-neighbor shell. For this reason, the use of some methods, developed for the structure analysis of atomic liquids, is questionable for the soft-particle systems. Here we report about our investigations of the structure of the simple harmonic-repulsive liquid in 3D using the triple correlation function (TCF), i.e., the method that does not rely on the nearest neighbor concept. The liquid is considered at reduced pressure (P = 1.8) at which it exhibits remarkable stability against crystallization on cooling. It is demonstrated that the TCF allows addressing the development of the orientational correlations in the structures that do not allow drawing definite conclusions from the studies of the bond-orientational order parameters. Our results demonstrate that the orientational correlations, if measured by the heights of the peaks in the TCF, significantly increase on cooling. This rise in the orientational ordering is not captured properly by the Kirkwood's superposition approximation. Detailed considerations of the peaks' shapes in the TCF suggest the existence of a link between the orientational ordering and the slowdown of the system's dynamics. Our findings support the view that the development of the orientational correlations in liquids may play a significant role in the liquids' dynamics and that the considerations of the pair distribution function may not be sufficient to understand intuitively all the structural changes that happen with liquids on supercooling. In general, our results demonstrate that the considerations of the TCF are useful in the discussions of the liquid's structures beyond the pair density function and interpreting the results obtained with the bond-orientational order parameters.
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Affiliation(s)
- V A Levashov
- Technological Design Institute of Scientific Instrument Engineering, 630055, Novosibirsk, Russia
- Vereshchagin Institute for High Pressure Physics, Russian Academy of Sciences, 108840, Troitsk, Moscow, Russia
| | - R E Ryltsev
- Vereshchagin Institute for High Pressure Physics, Russian Academy of Sciences, 108840, Troitsk, Moscow, Russia
- Institute of Metallurgy, UB RAS, 620016, 101 Amundsen str., Ekaterinburg, Russia
- Ural Federal University, 620002, 19 Mira str,, Ekaterinburg, Russia
| | - N M Chtchelkatchev
- Vereshchagin Institute for High Pressure Physics, Russian Academy of Sciences, 108840, Troitsk, Moscow, Russia
- Ural Federal University, 620002, 19 Mira str,, Ekaterinburg, Russia
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6
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Artiaco C, Baldan P, Parisi G. Exploratory study of the glassy landscape near jamming. Phys Rev E 2020; 101:052605. [PMID: 32575205 DOI: 10.1103/physreve.101.052605] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2019] [Accepted: 04/01/2020] [Indexed: 06/11/2023]
Abstract
We present a study of the landscape structure of hard and soft spheres as a function of the packing fraction and of the energy. We find that, on approaching the jamming transition, the number of different configurations available to the system increases steeply and a hierarchical organization of the landscape emerges. We use the knowledge of the structure of the landscape to predict the values of thermodynamic observables on the edge of the transition.
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Affiliation(s)
- Claudia Artiaco
- SISSA and INFN, Via Bonomea 265, 34136 Trieste, Italy
- Abdus Salam ICTP, Strada Costiera 11, 34151 Trieste, Italy
| | - Paolo Baldan
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
| | - Giorgio Parisi
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
- Nanotec-CNR, UOS Rome, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
- INFN, Sezione di Roma 1, Piazzale Aldo Moro 2, 00185 Roma, Italy
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7
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Dennis RC, Corwin EI. Jamming Energy Landscape is Hierarchical and Ultrametric. PHYSICAL REVIEW LETTERS 2020; 124:078002. [PMID: 32142348 DOI: 10.1103/physrevlett.124.078002] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2019] [Accepted: 01/22/2020] [Indexed: 06/10/2023]
Abstract
The free energy landscape of mean-field marginal glasses is ultrametric. We demonstrate that this feature persists in finite three-dimensional systems that are out of equilibrium by finding sets of minima, which are nearby in configuration space. By calculating the distance between these nearby minima, we produce a small region of the distance metric. This metric exhibits a clear hierarchical structure and shows the signature of an ultrametric space. That such a hierarchy exists for the jamming energy landscape provides direct evidence for the existence of a marginal phase along the zero temperature jamming line.
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Affiliation(s)
- R C Dennis
- Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA
| | - E I Corwin
- Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA
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8
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Levashov VA, Ryltsev R, Chtchelkatchev N. Anomalous behavior and structure of a liquid of particles interacting through the harmonic-repulsive pair potential near the crystallization transition. SOFT MATTER 2019; 15:8840-8854. [PMID: 31613306 DOI: 10.1039/c9sm01475f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
A characteristic property of many soft matter systems is an ultrasoft effective interaction between their structural units. This softness often leads to complex behavior. In particular, ultrasoft systems under pressure demonstrate polymorphism of complex crystal and quasicrystal structures. Therefore, it is of interest to investigate how different can be the structure of the fluid state in such systems at different pressures. Here we address this issue for a model liquid composed of particles interacting through the harmonic-repulsive pair potential. This system can form different crystal structures as the liquid is cooled. We find that, at certain pressures, the liquid exhibits unusual properties, such as a negative thermal expansion coefficient. Besides, the volume and the potential energy of the system can increase during crystallization. At certain pressures, the system demonstrates high stability against crystallization and it is hardly possible to crystallize it on the timescales of the simulations. To address the liquid's structure at high pressures, we consider the scaled pair distribution function (PDF) and the bond-orientational order (BOO) parameters. The marked change happening with the PDF, as pressure increases, is the splitting of the first peak which is caused by the appearance of non-negligible interactions with the second neighbors and the following rearrangement of the structure. Our findings suggest that non-trivial effects, usually explained by different interactions at different spatial scales, can also be observed in one-component systems with simple one-length-scale ultrasoft repulsive interactions.
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Affiliation(s)
- Valentin A Levashov
- Technological Design Institute of Scientific Instrument Engineering, 630055, Novosibirsk, Russia. and Institute for High Pressure Physics, Russian Academy of Sciences, 108840, Moscow (Troitsk), Russia
| | - Roman Ryltsev
- Institute for High Pressure Physics, Russian Academy of Sciences, 108840, Moscow (Troitsk), Russia and Institute of Metallurgy, UB RAS, 101 Amundsen str., 620016, Ekaterinburg, Russia and Ural Federal University, 19 Mira str., 620002, Ekaterinburg, Russia
| | - Nikolay Chtchelkatchev
- Institute for High Pressure Physics, Russian Academy of Sciences, 108840, Moscow (Troitsk), Russia and Ural Federal University, 19 Mira str., 620002, Ekaterinburg, Russia and Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, Moscow Region 141700, Russia
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9
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Abstract
We present the experimental studies of highly strained soft bidisperse granular systems made of hyperelastic and plastic particles. We explore the behavior of granular matter deep in the jammed state from local field measurement from the grain scale to the global scale. By means of a dedicated digital image correlation code and an accurate image recording method, we measure for each compression step the evolution of the particle geometries and their right Cauchy-Green strain tensor fields. We analyze the evolution of the usual macroscopic observables (stress, packing fraction, coordination, fraction of nonrattlers, etc.) along the compression process through the jamming point and far beyond. Analyzing the evolution of the local strain statistics, we evidence a crossover in the material behavior deep in the jammed state for both sorts of particles. We show that this crossover is due to a competition between material compression, dilation, and shear, so its position depends on the particle material. We argue that the strain field is a reliable observable to describe the evolution of a granular system through the jamming transition and deep in the dense packing state whatever the material behavior.
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Affiliation(s)
- Thi-Lo Vu
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, Montpellier 34000, France
| | - Jonathan Barés
- Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, Montpellier 34000, France
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10
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Berthier L, Flenner E, Szamel G. Glassy dynamics in dense systems of active particles. J Chem Phys 2019; 150:200901. [DOI: 10.1063/1.5093240] [Citation(s) in RCA: 58] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Affiliation(s)
- Ludovic Berthier
- Laboratoire Charles Coulomb, UMR 5221 CNRS, Université Montpellier, Montpellier, France
| | - Elijah Flenner
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
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11
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Parisi G, Pollack YG, Procaccia I, Rainone C, Singh M. Robustness of mean field theory for hard sphere models. Phys Rev E 2018; 97:063003. [PMID: 30011468 DOI: 10.1103/physreve.97.063003] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2017] [Indexed: 11/07/2022]
Abstract
In very recent work the mean field theory of the jamming transition in infinite-dimensional hard sphere models was presented. Surprisingly, this theory predicts quantitatively the numerically determined characteristics of jamming in two and three dimensions. This is a rare and unusual finding. Here we argue that this agreement is nongeneric: only for hard sphere models does it happen that sufficiently close to the jamming density (at any temperature) the effective interactions are binary, in agreement with mean field theory, justifying the truncation of many-body interactions (which is the exact protocol in infinite dimensions). Any softening of the bare hard sphere interactions results in many-body effective interactions that are not mean field at any density, making the d=∞ results not applicable.
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Affiliation(s)
- Giorgio Parisi
- Dipartimento di Fisica, Sapienza Università di Roma, INFN, Sezione di Roma I,IPFC CNR, Piazzale Aldo Moro 2, I-00185 Roma, Italy
| | - Yoav G Pollack
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Itamar Procaccia
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel.,Niels Bohr International Academy, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
| | - Corrado Rainone
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Murari Singh
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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12
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Ikeda H, Zamponi F, Ikeda A. Mean field theory of the swap Monte Carlo algorithm. J Chem Phys 2017; 147:234506. [DOI: 10.1063/1.5009116] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Harukuni Ikeda
- Department of Physics, Nagoya University, Nagoya, Japan
- IPhT, CEA/DSM-CNRS/URA 2306, CEA Saclay, F-91191 Gif-sur-Yvette Cedex, France
- Laboratoire de Physique Théorique, Ecole Normale Supérieure, PSL Research University, Sorbonne Universités, UPMC Université Paris 06, CNRS, 75005 Paris, France
| | - Francesco Zamponi
- Laboratoire de Physique Théorique, Ecole Normale Supérieure, PSL Research University, Sorbonne Universités, UPMC Université Paris 06, CNRS, 75005 Paris, France
| | - Atsushi Ikeda
- Graduate School of Arts and Sciences, University of Tokyo, Tokyo, Japan
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13
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Baranau V, Tallarek U. Another resolution of the configurational entropy paradox as applied to hard spheres. J Chem Phys 2017; 147:224503. [DOI: 10.1063/1.4999483] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Affiliation(s)
- Vasili Baranau
- Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse 4, 35032 Marburg, Germany
| | - Ulrich Tallarek
- Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse 4, 35032 Marburg, Germany
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14
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Abstract
The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomenological explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law.
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15
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Levashov VA. Crystalline structures of particles interacting through the harmonic-repulsive pair potential. J Chem Phys 2017; 147:114503. [DOI: 10.1063/1.5002536] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
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16
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Wittmer JP, Kriuchevskyi I, Cavallo A, Xu H, Baschnagel J. Shear-stress fluctuations in self-assembled transient elastic networks. Phys Rev E 2016; 93:062611. [PMID: 27415324 DOI: 10.1103/physreve.93.062611] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2016] [Indexed: 06/06/2023]
Abstract
Focusing on shear-stress fluctuations, we investigate numerically a simple generic model for self-assembled transient networks formed by repulsive beads reversibly bridged by ideal springs. With Δt being the sampling time and t_{☆}(f)∼1/f the Maxwell relaxation time (set by the spring recombination frequency f), the dimensionless parameter Δx=Δt/t_{☆}(f) is systematically scanned from the liquid limit (Δx≫1) to the solid limit (Δx≪1) where the network topology is quenched and an ensemble average over m-independent configurations is required. Generalizing previous work on permanent networks, it is shown that the shear-stress relaxation modulus G(t) may be efficiently determined for all Δx using the simple-average expression G(t)=μ_{A}-h(t) with μ_{A}=G(0) characterizing the canonical-affine shear transformation of the system at t=0 and h(t) the (rescaled) mean-square displacement of the instantaneous shear stress as a function of time t. This relation is compared to the standard expression G(t)=c[over ̃](t) using the (rescaled) shear-stress autocorrelation function c[over ̃](t). Lower bounds for the m configurations required by both relations are given.
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Affiliation(s)
- J P Wittmer
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France
| | - I Kriuchevskyi
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France
| | - A Cavallo
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France
| | - H Xu
- LCP-A2MC, Institut Jean Barriol, Université de Lorraine & CNRS, 1 bd Arago, 57078 Metz Cedex 03, France
| | - J Baschnagel
- Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034 Strasbourg Cedex, France
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17
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Baranau V, Zhao SC, Scheel M, Tallarek U, Schröter M. Upper bound on the Edwards entropy in frictional monodisperse hard-sphere packings. SOFT MATTER 2016; 12:3991-4006. [PMID: 27020114 DOI: 10.1039/c6sm00567e] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We extend the Widom particle insertion method [B. Widom, J. Chem. Phys., 1963, 39, 2808-2812] to determine an upper bound sub on the Edwards entropy in frictional hard-sphere packings. sub corresponds to the logarithm of the number of mechanically stable configurations for a given volume fraction and boundary conditions. To accomplish this, we extend the method for estimating the particle insertion probability through the pore-size distribution in frictionless packings [V. Baranau, et al., Soft Matter, 2013, 9, 3361-3372] to the case of frictional particles. We use computer-generated and experimentally obtained three-dimensional sphere packings with volume fractions φ in the range 0.551-0.65. We find that sub has a maximum in the vicinity of the Random Loose Packing Limit φRLP = 0.55 and decreases then monotonically with increasing φ to reach a minimum at φ = 0.65. Further on, sub does not distinguish between real mechanical stability and packings in close proximity to mechanical stable configurations. The probability to find a given number of contacts for a particle inserted in a large enough pore does not depend on φ, but it decreases strongly with the contact number.
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Affiliation(s)
- Vasili Baranau
- Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse 4, D-35032 Marburg, Germany.
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18
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Mangeat M, Zamponi F. Quantitative approximation schemes for glasses. Phys Rev E 2016; 93:012609. [PMID: 26871124 DOI: 10.1103/physreve.93.012609] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2015] [Indexed: 06/05/2023]
Abstract
By means of a systematic expansion around the infinite-dimensional solution, we obtain an approximation scheme to compute properties of glasses in low dimensions. The resulting equations take as input the thermodynamic and structural properties of the equilibrium liquid, and from this they allow one to compute properties of the glass. They are therefore similar in spirit to the Mode Coupling approximation scheme. Our scheme becomes exact, by construction, in dimension d→∞, and it can be improved systematically by adding more terms in the expansion.
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Affiliation(s)
- Matthieu Mangeat
- LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75005 Paris, France
- Master ICFP, Département de Physique, Ecole Normale Supérieure, 24 Rue Lhomond,75005 Paris, France
| | - Francesco Zamponi
- LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75005 Paris, France
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19
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Ikeda A, Berthier L. Thermal fluctuations, mechanical response, and hyperuniformity in jammed solids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012309. [PMID: 26274164 DOI: 10.1103/physreve.92.012309] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2015] [Indexed: 06/04/2023]
Abstract
Jamming is a geometric phase transition occurring in dense particle systems in the absence of temperature. We use computer simulations to analyze the effect of thermal fluctuations on several signatures of the transition. We show that scaling laws for bulk and shear moduli only become relevant when thermal fluctuations are extremely small, and propose their relative ratio as a quantitative signature of jamming criticality. Despite the nonequilibrium nature of the transition, we find that thermally induced fluctuations and mechanical responses obey equilibrium fluctuation-dissipation relations near jamming, provided the appropriate fluctuating component of the particle displacements is analyzed. This shows that mechanical moduli can be directly measured from particle positions in mechanically unperturbed packings, and suggests that the definition of a "nonequilibrium index" is unnecessary for amorphous materials. We find that fluctuations of particle displacements are spatially correlated, and define a transverse and a longitudinal correlation length scale which both diverge as the jamming transition is approached. We analyze the frozen component of density fluctuations and find that it displays signatures of nearly hyperuniform behavior at large length scales. This demonstrates that hyperuniformity in jammed packings is unrelated to a vanishing compressibility and explains why it appears remarkably robust against temperature and density variations. Differently from jamming criticality, obstacles preventing the observation of hyperuniformity in colloidal systems do not originate from thermal fluctuations.
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Affiliation(s)
- Atsushi Ikeda
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto, Japan
| | - Ludovic Berthier
- Laboratoire Charles Coulomb, UMR 5221 CNRS-Université de Montpellier, Montpellier, France
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20
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DeGiuli E, Lerner E, Wyart M. Theory of the jamming transition at finite temperature. J Chem Phys 2015; 142:164503. [DOI: 10.1063/1.4918737] [Citation(s) in RCA: 48] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- E. DeGiuli
- Center for Soft Matter Research, New York University, 4 Washington Place, New York, New York 10003, USA
| | - E. Lerner
- Center for Soft Matter Research, New York University, 4 Washington Place, New York, New York 10003, USA
- Institute for Theoretical Physics, Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - M. Wyart
- Center for Soft Matter Research, New York University, 4 Washington Place, New York, New York 10003, USA
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21
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Saitoh K, Magnanimo V, Luding S. A master equation for the probability distribution functions of forces in soft particle packings. SOFT MATTER 2015; 11:1253-1258. [PMID: 25521712 DOI: 10.1039/c4sm02452d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We study the microscopic response of force-chain networks in jammed soft particles to quasi-static isotropic (de)compressions by molecular dynamics simulations. We show that not only contacts but also interparticle gaps between the nearest neighbors must be considered for the stochastic evolution of the probability distribution functions (PDFs) of forces, where the mutual exchange of contacts and interparticle gaps, i.e. opening and closing contacts, are also crucial to the incremental system behavior. By numerically determining the transition rates for all changes of contacts and gaps, we formulate a Master equation for the PDFs of forces, where the insight one gets from the transition rates is striking: the mean change of forces reflects non-affine system responses, while their fluctuations obey uncorrelated Gaussian statistics. In contrast, interparticle gaps react mostly affine in average, but imply multi-scale correlations according to a much wider stable distribution function.
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Affiliation(s)
- Kuniyasu Saitoh
- Faculty of Engineering Technology, MESA+, University of Twente, Drienerlolaan 5, 7522 NB, Enschede, The Netherlands.
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22
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Wang X, Zheng W, Wang L, Xu N. Disordered solids without well-defined transverse phonons: the nature of hard-sphere glasses. PHYSICAL REVIEW LETTERS 2015; 114:035502. [PMID: 25659006 DOI: 10.1103/physrevlett.114.035502] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2014] [Indexed: 06/04/2023]
Abstract
We probe the Ioffe-Regel limits of glasses with repulsions near the zero-temperature jamming transition by calculating the dynamical structure factors. The Ioffe-Regel limit (frequency) is reached when the phonon wavelength is comparable to the mean free path, beyond which phonons are no longer well defined. At zero temperature, the transverse Ioffe-Regel frequency vanishes at the jamming transition with a diverging length, but the longitudinal one does not, which excludes the existence of a diverging length associated with the longitudinal excitations. At low temperatures, the transverse and longitudinal Ioffe-Regel frequencies approach zero at the jamminglike transition and glass transition, respectively. As a consequence, glasses between the glass transition and the jamminglike transition, which are hard-sphere glasses in the low temperature limit, can only carry well-defined longitudinal phonons and have an opposite pressure dependence of the ratio of the shear modulus to the bulk modulus from glasses beyond the jamminglike transition.
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Affiliation(s)
- Xipeng Wang
- CAS Key Laboratory of Soft Matter Chemistry, Hefei National Laboratory for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Wen Zheng
- CAS Key Laboratory of Soft Matter Chemistry, Hefei National Laboratory for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Lijin Wang
- CAS Key Laboratory of Soft Matter Chemistry, Hefei National Laboratory for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Ning Xu
- CAS Key Laboratory of Soft Matter Chemistry, Hefei National Laboratory for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
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23
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Rainone C, Urbani P, Yoshino H, Zamponi F. Following the evolution of hard sphere glasses in infinite dimensions under external perturbations: compression and shear strain. PHYSICAL REVIEW LETTERS 2015; 114:015701. [PMID: 25615481 DOI: 10.1103/physrevlett.114.015701] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2014] [Indexed: 06/04/2023]
Abstract
We consider the adiabatic evolution of glassy states under external perturbations. The formalism we use is very general. Here we use it for infinite-dimensional hard spheres where an exact analysis is possible. We consider perturbations of the boundary, i.e., compression or (volume preserving) shear strain, and we compute the response of glassy states to such perturbations: pressure and shear stress. We find that both quantities overshoot before the glass state becomes unstable at a spinodal point where it melts into a liquid (or yields). We also estimate the yield stress of the glass. Finally, we study the stability of the glass basins towards breaking into sub-basins, corresponding to a Gardner transition. We find that close to the dynamical transition, glasses undergo a Gardner transition after an infinitesimal perturbation.
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Affiliation(s)
- Corrado Rainone
- LPT, Ecole Normale Supérieure, CNRS UMR 8549, 24 Rue Lhomond, 75005 Paris, France and Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy
| | | | - Hajime Yoshino
- Cybermedia Center, Osaka University, Toyonaka, Osaka 560-0043, Japan and Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
| | - Francesco Zamponi
- LPT, Ecole Normale Supérieure, CNRS UMR 8549, 24 Rue Lhomond, 75005 Paris, France
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24
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Ouyang W, Sun B, Sun Z, Xu S. Structural and dynamical anomalies of soft particles interacting through harmonic repulsions. Phys Chem Chem Phys 2015; 17:5734-42. [DOI: 10.1039/c4cp05402d] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Molecular dynamics (MD) simulations are carried out to investigate the structural and dynamical anomalies in the core-softened fluid with harmonic repulsions.
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Affiliation(s)
- Wenze Ouyang
- Key Laboratory of Microgravity (National Microgravity Laboratory)
- Institute of Mechanics
- Chinese Academy of Sciences
- Beijing 100190
- People's Republic of China
| | - Bin Sun
- School of Materials and Chemical Engineering
- Zhongyuan University of Technology
- Zhengzhou 450007
- People's Republic of China
| | - Zhiwei Sun
- Key Laboratory of Microgravity (National Microgravity Laboratory)
- Institute of Mechanics
- Chinese Academy of Sciences
- Beijing 100190
- People's Republic of China
| | - Shenghua Xu
- Key Laboratory of Microgravity (National Microgravity Laboratory)
- Institute of Mechanics
- Chinese Academy of Sciences
- Beijing 100190
- People's Republic of China
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25
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Coulais C, Seguin A, Dauchot O. Shear modulus and dilatancy softening in granular packings above jamming. PHYSICAL REVIEW LETTERS 2014; 113:198001. [PMID: 25415925 DOI: 10.1103/physrevlett.113.198001] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2014] [Indexed: 06/04/2023]
Abstract
We investigate experimentally the mechanical response to shear of a monolayer of bidisperse frictional grains across the jamming transition. We inflate an intruder inside the packing and use photoelasticity and tracking techniques to measure the induced shear strain and stresses at the grain scale. We quantify experimentally the constitutive relations for strain amplitudes as low as 10(-3) and for a range of packing fractions within 2% variation around the jamming transition. At the transition strong nonlinear effects set in: both the shear modulus and the dilatancy shear soften at small strain until a critical strain is reached where effective linearity is recovered. The scaling of the critical strain and the associated critical stresses on the distance to jamming are extracted. We check that the constitutive laws, together with mechanical equilibrium, correctly predict to the observed stress and strain profiles. These profiles exhibit a spatial crossover between an effective linear regime close to the inflater and the truly nonlinear regime away from it. The crossover length diverges at the jamming transition.
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Affiliation(s)
- C Coulais
- SPHYNX/SPEC, CEA-Saclay, URA 2464 CNRS, 91191 Gif-sur-Yvette, France and Université Paris-Sud, CNRS, Lab FAST, Bat 502, Campus Université, Orsay F-91405, France and Huygens-Kamerlingh Onnes Lab, Universiteit Leiden, P.O. box 9504, 2300 RA Leiden, Netherlands
| | - A Seguin
- SPHYNX/SPEC, CEA-Saclay, URA 2464 CNRS, 91191 Gif-sur-Yvette, France and Université Paris-Sud, CNRS, Lab FAST, Bat 502, Campus Université, Orsay F-91405, France
| | - O Dauchot
- EC2M, ESPCI-ParisTech, UMR Gulliver 7083 CNRS, 75005 Paris, France
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26
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Bo L, Mari R, Song C, Makse HA. Cavity method for force transmission in jammed disordered packings of hard particles. SOFT MATTER 2014; 10:7379-7392. [PMID: 25082504 DOI: 10.1039/c4sm00667d] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The force distribution of jammed disordered packings has always been considered a central object in the physics of granular materials. However, many of its features are poorly understood. In particular, analytic relations to other key macroscopic properties of jammed matter, such as the contact network and its coordination number, are still lacking. Here we develop a mean-field theory for this problem, based on the consideration of the contact network as a random graph where the force transmission becomes a constraint satisfaction problem. We can thus use the cavity method developed in the past few decades within the statistical physics of spin glasses and hard computer science problems. This method allows us to compute the force distribution P(f) for random packings of hard particles of any shape, with or without friction. We find a new signature of jamming in the small force behavior P(f) ∼ f(θ), whose exponent has attracted recent active interest: we find a finite value for P(f = 0), along with θ = 0. Furthermore, we relate the force distribution to a lower bound of the average coordination number z[combining macron](μ) of jammed packings of frictional spheres with coefficient μ. This bridges the gap between the two known isostatic limits z[combining macron]c (μ = 0) = 2D (in dimension D) and z[combining macron]c(μ → ∞) = D + 1 by extending the naive Maxwell's counting argument to frictional spheres. The theoretical framework describes different types of systems, such as non-spherical objects in arbitrary dimensions, providing a common mean-field scenario to investigate force transmission, contact networks and coordination numbers of jammed disordered packings.
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Affiliation(s)
- Lin Bo
- Levich Institute and Physics Department, City College of New York, New York, NY 10031, USA
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27
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Yoshino H, Zamponi F. Shear modulus of glasses: results from the full replica-symmetry-breaking solution. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022302. [PMID: 25215733 DOI: 10.1103/physreve.90.022302] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2014] [Indexed: 06/03/2023]
Abstract
We compute the shear modulus of amorphous hard and soft spheres, using the exact solution in infinite spatial dimensions that has been developed recently. We characterize the behavior of this observable in the whole phase diagram, and in particular around the glass and jamming transitions. Our results are consistent with other theoretical approaches, which are unified within this general picture, and they are also consistent with numerical and experimental results. Furthermore, we discuss some properties of the out-of-equilibrium dynamics after a deep quench close to the jamming transition, and we show that a combined measure of the shear modulus and of the mean square displacement allows one to probe experimentally the complex structure of phase space predicted by the full replica-symmetry-breaking solution.
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Affiliation(s)
- Hajime Yoshino
- Department of Earth and Space Science, Faculty of Science, Osaka University, Toyonaka 560-0043, Japan and Cybermedia Center, Osaka University, Toyonaka, Osaka 560-0043, Japan
| | - Francesco Zamponi
- LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75005 Paris, France
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28
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Yunker PJ, Chen K, Gratale MD, Lohr MA, Still T, Yodh AG. Physics in ordered and disordered colloidal matter composed of poly(N-isopropylacrylamide) microgel particles. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2014; 77:056601. [PMID: 24801604 DOI: 10.1088/0034-4885/77/5/056601] [Citation(s) in RCA: 108] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
This review collects and describes experiments that employ colloidal suspensions to probe physics in ordered and disordered solids and related complex fluids. The unifying feature of this body of work is its clever usage of poly(N-isopropylacrylamide) (PNIPAM) microgel particles. These temperature-sensitive colloidal particles provide experimenters with a 'knob' for in situ control of particle size, particle interaction and particle packing fraction that, in turn, influence the structural and dynamical behavior of the complex fluids and solids. A brief summary of PNIPAM particle synthesis and properties is given, followed by a synopsis of current activity in the field. The latter discussion describes a variety of soft matter investigations including those that explore formation and melting of crystals and clusters, and those that probe structure, rearrangement and rheology of disordered (jammed/glassy) and partially ordered matter. The review, therefore, provides a snapshot of a broad range of physics phenomenology which benefits from the unique properties of responsive microgel particles.
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Affiliation(s)
- Peter J Yunker
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA. School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
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29
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Sun B, Sun Z, Ouyang W, Xu S. Structural ordering and glass forming of soft spherical particles with harmonic repulsions. J Chem Phys 2014; 140:134904. [DOI: 10.1063/1.4869833] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
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30
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Coulais C, Behringer RP, Dauchot O. How the ideal jamming point illuminates the world of granular media. SOFT MATTER 2014; 10:1519-1536. [PMID: 24651534 DOI: 10.1039/c3sm51231b] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The zero temperature properties of frictionless soft spheres near the jamming point have been extensively studied both numerically and theoretically; these studies provide a reliable base for the interpretation of experiments. However, recent work by Ikeda et al. showed that, in a parameter space of the temperature and packing fraction, experiments to date on colloids have been rather far from the theoretical scaling regime. An important question is then whether theoretical results concerning point-J are applicable to any physical/experimental system, including granular media, which we consider here. On the surface, such a-thermal, frictional systems might appear even further from the idealized case of thermal soft spheres. In this work we address this question via experiments on shaken granular materials near jamming. We have systematically investigated such systems over a number of years using hard metallic grains. The important feature of the present work is the use of much softer grains, cut from photoelastic materials, making it possible to determine forces at the grain scale, the details of the contact networks and the motion of individual grains. Using this new type of particle, we first show that the contact network exhibits remarkable dynamics. We find strong heterogeneities, which are maximum at the packing fraction ϕ*, distinct from and smaller than the packing fraction ϕ(†), where the average number of contacts per particle, z, starts to increase. In the limit of zero mechanical excitation, these two packing fractions converge at point J. We also determine dynamics on time scales ranging from a small fraction of the shaking cycle to thousands of cycles. We can then map the observed system behavior onto results from simulations of ideal thermal soft spheres. Our results indicate that the ideal jamming point indeed illuminates the world of granular media.
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Affiliation(s)
- C Coulais
- SPHYNX/SPEC, CEA-Saclay, URA 2464 CNRS, 91 191 Gif-sur-Yvette, France
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31
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Milz L, Schmiedeberg M. Connecting the random organization transition and jamming within a unifying model system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062308. [PMID: 24483445 DOI: 10.1103/physreve.88.062308] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2013] [Indexed: 06/03/2023]
Abstract
While the random organization transition describes the change from reversible to irreversible dynamics in a nonequilibrium system, the athermal jamming transition at zero shear rate occurs when particles can no longer avoid overlaps. Despite the obvious differences between these two transitions, we show that they both occur within the same model packing problem. In this unifying model system the particles are first randomly distributed and then displaced in each step if they overlap. For random displacements we obtain a random organization transition, while jamming occurs in the case of deterministic shifts. We also analyze the critical behavior of random organization. Our results show that random organization and jamming are opposite limits of random sphere packings, and we expect that various equilibrium and nonequilibrium transitions can be formulated as related intermediate packing problems.
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Affiliation(s)
- Lars Milz
- Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany and Institut für Theoretische Physik 2: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40204 Düsseldorf, Germany
| | - Michael Schmiedeberg
- Institut für Theoretische Physik 2: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40204 Düsseldorf, Germany and Fachbereich 4: Physik, Universität Osnabrück, D-49076 Osnabrück, Germany
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32
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Ikeda A, Berthier L. Yield stress in amorphous solids: a mode-coupling-theory analysis. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052305. [PMID: 24329262 DOI: 10.1103/physreve.88.052305] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2013] [Revised: 09/02/2013] [Indexed: 06/03/2023]
Abstract
The yield stress is a defining feature of amorphous materials which is difficult to analyze theoretically, because it stems from the strongly nonlinear response of an arrested solid to an applied deformation. Mode-coupling theory predicts the flow curves of materials undergoing a glass transition and thus offers predictions for the yield stress of amorphous solids. We use this approach to analyze several classes of disordered solids, using simple models of hard-sphere glasses, soft glasses, and metallic glasses for which the mode-coupling predictions can be directly compared to the outcome of numerical measurements. The theory correctly describes the emergence of a yield stress of entropic nature in hard-sphere glasses, and its rapid growth as density approaches random close packing at qualitative level. By contrast, the emergence of solid behavior in soft and metallic glasses, which originates from direct particle interactions is not well described by the theory. We show that similar shortcomings arise in the description of the caging dynamics of the glass phase at rest. We discuss the range of applicability of mode-coupling theory to understand the yield stress and nonlinear rheology of amorphous materials.
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Affiliation(s)
- Atsushi Ikeda
- Laboratoire Charles Coulomb, UMR 5221, CNRS and Université Montpellier 2, Montpellier, France
| | - Ludovic Berthier
- Laboratoire Charles Coulomb, UMR 5221, CNRS and Université Montpellier 2, Montpellier, France
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33
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Jadrich R, Schweizer KS. Equilibrium theory of the hard sphere fluid and glasses in the metastable regime up to jamming. II. Structure and application to hopping dynamics. J Chem Phys 2013; 139:054502. [DOI: 10.1063/1.4816276] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
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34
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Jadrich R, Schweizer KS. Equilibrium theory of the hard sphere fluid and glasses in the metastable regime up to jamming. I. Thermodynamics. J Chem Phys 2013; 139:054501. [DOI: 10.1063/1.4816275] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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35
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Kurchan J, Parisi G, Urbani P, Zamponi F. Exact Theory of Dense Amorphous Hard Spheres in High Dimension. II. The High Density Regime and the Gardner Transition. J Phys Chem B 2013; 117:12979-94. [DOI: 10.1021/jp402235d] [Citation(s) in RCA: 112] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jorge Kurchan
- LPS, École Normale Supérieure,
UMR 8550 CNRS, 24 Rue Lhomond, 75005 Paris, France
| | - Giorgio Parisi
- Dipartimento di Fisica, Universitá
di Roma “La Sapienza”, P.le Aldo Moro 2, I-00185 Roma, Italy
- INFN, Sezione di Roma I, IPFC - CNR, P.le A. Moro 2, I-00185
Roma, Italy
| | - Pierfrancesco Urbani
- Dipartimento di Fisica, Universitá
di Roma “La Sapienza”, P.le Aldo Moro 2, I-00185 Roma, Italy
- Laboratoire de
Physique Théorique et Modèles Statistiques, CNRS et
Université Paris-Sud 11, UMR8626, Bât. 100, 91405 Orsay
Cedex, France
| | - Francesco Zamponi
- LPT, École
Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75005 Paris, France
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36
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Schmiedeberg M. Multiple reentrant glass transitions of soft spheres at high densities: monotonicity of the curves of constant relaxation time in jamming phase diagrams depending on temperature over pressure and pressure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:052310. [PMID: 23767543 DOI: 10.1103/physreve.87.052310] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2013] [Indexed: 06/02/2023]
Abstract
By using molecular-dynamics simulations, we determine the jamming phase diagrams at high densities for a bidisperse mixture of soft spheres that interact according to repulsive power-law pair potentials. We observe that the relaxation time varies nonmonotonically as a function of density at constant temperature. Therefore, the jamming phase diagrams contain multiple reentrant glass transitions if temperature and density are used as control parameters. However, if we consider a new formulation of the jamming phase diagrams where temperature over pressure and pressure are employed as control parameters, no nonmonotonic behavior is observed.
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Affiliation(s)
- Michael Schmiedeberg
- Institut für Theoretische Physik 2: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40204 Düsseldorf, Germany
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37
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Zaccone A, Terentjev EM. Disorder-assisted melting and the glass transition in amorphous solids. PHYSICAL REVIEW LETTERS 2013; 110:178002. [PMID: 23679782 DOI: 10.1103/physrevlett.110.178002] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2012] [Indexed: 05/12/2023]
Abstract
The mechanical response of solids depends on temperature, because the way atoms and molecules respond collectively to deformation is affected at various levels by thermal motion. This is a fundamental problem of solid state science and plays a crucial role in materials science. In glasses, the vanishing of shear rigidity upon increasing temperature is the reverse process of the glass transition. It remains poorly understood due to the disorder leading to nontrivial (nonaffine) components in the atomic displacements. Our theory explains the basic mechanism of the melting transition of amorphous (disordered) solids in terms of the lattice energy lost to this nonaffine motion, compared to which thermal vibrations turn out to play only a negligible role. The theory is in good agreement with classic data on melting of amorphous polymers (for which no alternative theory can be found in the literature) and offers new opportunities in materials science.
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Affiliation(s)
- Alessio Zaccone
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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38
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Ashwin SS, Zaeifi Yamchi M, Bowles RK. Inherent structure landscape connection between liquids, granular materials, and the jamming phase diagram. PHYSICAL REVIEW LETTERS 2013; 110:145701. [PMID: 25167008 DOI: 10.1103/physrevlett.110.145701] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2010] [Revised: 01/24/2013] [Indexed: 06/03/2023]
Abstract
We provide a comprehensive picture of the jamming phase diagram by connecting the athermal, granular ensemble of jammed states and the equilibrium fluid through the inherent structure paradigm for a system of hard disks confined to a narrow channel. The J line is shown to be divided into packings that are either accessible or inaccessible from the equilibrium fluid. The J point itself is found to occur at the transition between these two sets of packings and is located at the maximum of the inherent structure distribution. We also present a general thermodynamic argument that suggests the density of the states at the maximum of the configurational entropy represents a lower bound on the J-point density in hard sphere systems. Finally, we show that the granular system, modeled using the Edwards ensemble, and the fluid sample the same set of thermodynamically accessible states over the full range of thermodynamic state points, but only occupy the same set of inherent structures, under the same thermodynamic conditions, at two points, corresponding to zero and infinite pressures, where they sample the J-point states and the most dense packing, respectively.
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Affiliation(s)
- S S Ashwin
- Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5C9, Canada and Department of Mechanical Engineering and Material Science and Department of Physics, Yale University, New Haven, Connecticut 06511, USA
| | - Mahdi Zaeifi Yamchi
- Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5C9, Canada
| | - Richard K Bowles
- Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5C9, Canada
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39
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Ikeda A, Berthier L, Biroli G. Dynamic criticality at the jamming transition. J Chem Phys 2013; 138:12A507. [DOI: 10.1063/1.4769251] [Citation(s) in RCA: 90] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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40
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Charbonneau P, Corwin EI, Parisi G, Zamponi F. Universal microstructure and mechanical stability of jammed packings. PHYSICAL REVIEW LETTERS 2012; 109:205501. [PMID: 23215504 DOI: 10.1103/physrevlett.109.205501] [Citation(s) in RCA: 83] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2012] [Indexed: 06/01/2023]
Abstract
The mechanical properties of jammed packings depend sensitively on their detailed local structure. Here we provide a complete characterization of the pair correlation close to contact and of the force distribution of jammed frictionless spheres. In particular we discover a set of new scaling relations that connect the behavior of particles bearing small forces and those bearing no force but that are almost in contact. By performing systematic investigations for spatial dimensions d=3-10, in a wide density range and using different preparation protocols, we show that these scalings are indeed universal. We therefore establish clear milestones for the emergence of a complete microscopic theory of jamming. This description is also crucial for high-precision force experiments in granular systems.
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Otsuki M, Hayakawa H. Critical scaling of a jammed system after a quench of temperature. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:031505. [PMID: 23030921 DOI: 10.1103/physreve.86.031505] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2011] [Revised: 07/21/2012] [Indexed: 06/01/2023]
Abstract
Critical behavior of soft repulsive particles after quench of temperature near the jamming transition is numerically investigated. It is found that the plateau of the mean-square displacement of tracer particles and the pressure satisfy critical scaling laws. The critical density for the jamming transition depends on the protocol to prepare the system, while the values of the critical exponents which are consistent with the prediction of a phenomenology are independent of the protocol.
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Affiliation(s)
- Michio Otsuki
- Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 229-8558, Japan
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Ikeda A, Berthier L, Sollich P. Unified study of glass and jamming rheology in soft particle systems. PHYSICAL REVIEW LETTERS 2012; 109:018301. [PMID: 23031135 DOI: 10.1103/physrevlett.109.018301] [Citation(s) in RCA: 142] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2012] [Indexed: 06/01/2023]
Abstract
We explore numerically the shear rheology of soft repulsive particles at large volume fraction. The interplay between viscous dissipation and thermal motion results in multiple rheological regimes encompassing Newtonian, shear-thinning, and yield stress regimes near the "colloidal" glass transition when thermal fluctuations are important, crossing over to qualitatively similar regimes near the "jamming" transition when dissipation dominates. In the crossover regime, glass and jamming sectors coexist and give complex flow curves. Although glass and jamming limits are characterized by similar macroscopic flow curves, we show that they occur over distinct time and stress scales and correspond to distinct microscopic dynamics. We propose a simple rheological model describing the glass-to-jamming crossover in the flow curves, and discuss the experimental implications of our results.
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Affiliation(s)
- Atsushi Ikeda
- Laboratoire Charles Coulomb, UMR 5221 CNRS and Université Montpellier 2, Montpellier, France
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Ashwin SS, Blawzdziewicz J, O'Hern CS, Shattuck MD. Calculations of the structure of basin volumes for mechanically stable packings. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:061307. [PMID: 23005086 DOI: 10.1103/physreve.85.061307] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2011] [Revised: 04/04/2012] [Indexed: 06/01/2023]
Abstract
Experimental and computational model systems composed of frictionless particles in a fixed geometry have a finite number of distinct mechanically stable (MS) packings. The frequency of occurrence for each MS packing is highly variable and depends strongly on preparation protocol. Despite intense work, it is extremely difficult to predict a priori the MS packing probabilities. We describe a novel computational method for calculating the volume and other geometrical properties of the "basin of attraction" for each MS packing. The basin of attraction for an MS packing contains all initial conditions in configuration space that map to that MS packing using a given preparation protocol. We find that the basin is a highly complex structure. For a compressive-quench-from-zero-density protocol, we show the existence of a small core volume of the basin around each MS packing for which all points map to that MS packing. However, in contrast to previous studies for supercooled liquids, glasses, and over-compressed jammed systems, we find that the MS packing probabilities are very weakly correlated with this core volume. Instead, MS packing probabilities obtained from compression protocols that use initially dilute configurations and do not allow particle overlaps (i.e., those relevant to granular media) are determined by complex geometric features of the basin of attraction that are distant from the MS packing. In particular, we find that the shape of the average basin profile function S(l), which gives the probability for a point on a hyperspherical shell a distance l from a given MS packing to map back to that packing, can be described by a Γ distribution with a peak that increases as the system size increases and as the quench rate decreases. We find a simple model which predicts S(l) for the extreme cases of very slow and fast quench rates.
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Affiliation(s)
- S S Ashwin
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520-8286, USA
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