51
|
Karmakar S, Dasgupta C, Sastry S. Short-Time Beta Relaxation in Glass-Forming Liquids Is Cooperative in Nature. PHYSICAL REVIEW LETTERS 2016; 116:085701. [PMID: 26967425 DOI: 10.1103/physrevlett.116.085701] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2015] [Indexed: 05/17/2023]
Abstract
Temporal relaxation of density fluctuations in supercooled liquids near the glass transition occurs in multiple steps. Using molecular dynamics simulations for three model glass-forming liquids, we show that the short-time β relaxation is cooperative in nature. Using finite-size scaling analysis, we extract a growing length scale associated with beta relaxation from the observed dependence of the beta relaxation time on the system size. We find, in qualitative agreement with the prediction of the inhomogeneous mode coupling theory, that the temperature dependence of this length scale is the same as that of the length scale that describes the spatial heterogeneity of local dynamics in the long-time α-relaxation regime.
Collapse
Affiliation(s)
- Smarajit Karmakar
- Centre for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India
| | - Chandan Dasgupta
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
| | - Srikanth Sastry
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
| |
Collapse
|
52
|
Shen H, Tan P, Xu L. Probing the Role of Mobility in the Collective Motion of Nonequilibrium Systems. PHYSICAL REVIEW LETTERS 2016; 116:048302. [PMID: 26871359 DOI: 10.1103/physrevlett.116.048302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2015] [Indexed: 06/05/2023]
Abstract
By systematically varying the mobility of self-propelled particles in a 2D lattice, we experimentally study the influence of particle mobility on system's collective motion. Our system is intrinsically nonequilibrium due to the lack of energy equipartition. By constructing the covariance matrix of spatial fluctuations and solving for its eigenmodes, we obtain the collective motions of the system with various magnitudes. Interestingly, our structurally ordered nonequilibrium system exhibits properties almost identical to disordered glassy systems under thermal equilibrium: the modes with large overall motions are spatially correlated and quasilocalized while the modes with small collective motions are highly localized, resembling the low- and high-frequency modes in glass. More surprisingly, a peak similar to the boson peak forms in our nonequilibrium system as the number of mobile particles increases, revealing the possible origin of the boson peak from a dynamic aspect. We further illustrate that the spatially correlated large-movement modes can be produced by the cooperation of highly active particles above a threshold fraction, while the localized small-movement modes can be created by adding individual inactive particles. Our study clarifies the role of mobility in collective motions, and further suggests a promising possibility of extending the powerful mode analysis approach to nonequilibrium systems.
Collapse
Affiliation(s)
- Hongchuan Shen
- Department of Physics, The Chinese University of Hong Kong, Hong Kong, China
| | - Peng Tan
- Department of Physics, The Chinese University of Hong Kong, Hong Kong, China
- Department of Physics, State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
| | - Lei Xu
- Department of Physics, The Chinese University of Hong Kong, Hong Kong, China
| |
Collapse
|
53
|
Karmakar S, Dasgupta C, Sastry S. Length scales in glass-forming liquids and related systems: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:016601. [PMID: 26684508 DOI: 10.1088/0034-4885/79/1/016601] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The central problem in the study of glass-forming liquids and other glassy systems is the understanding of the complex structural relaxation and rapid growth of relaxation times seen on approaching the glass transition. A central conceptual question is whether one can identify one or more growing length scale(s) associated with this behavior. Given the diversity of molecular glass-formers and a vast body of experimental, computational and theoretical work addressing glassy behavior, a number of ideas and observations pertaining to growing length scales have been presented over the past few decades, but there is as yet no consensus view on this question. In this review, we will summarize the salient results and the state of our understanding of length scales associated with dynamical slow down. After a review of slow dynamics and the glass transition, pertinent theories of the glass transition will be summarized and a survey of ideas relating to length scales in glassy systems will be presented. A number of studies have focused on the emergence of preferred packing arrangements and discussed their role in glassy dynamics. More recently, a central object of attention has been the study of spatially correlated, heterogeneous dynamics and the associated length scale, studied in computer simulations and theoretical analysis such as inhomogeneous mode coupling theory. A number of static length scales have been proposed and studied recently, such as the mosaic length scale discussed in the random first-order transition theory and the related point-to-set correlation length. We will discuss these, elaborating on key results, along with a critical appraisal of the state of the art. Finally we will discuss length scales in driven soft matter, granular fluids and amorphous solids, and give a brief description of length scales in aging systems. Possible relations of these length scales with those in glass-forming liquids will be discussed.
Collapse
Affiliation(s)
- Smarajit Karmakar
- TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India
| | | | | |
Collapse
|
54
|
Abstract
We report an analytical study of the vibrational spectrum of the simplest model of jamming, the soft perceptron. We identify two distinct classes of soft modes. The first kind of modes are related to isostaticity and appear only in the close vicinity of the jamming transition. The second kind of modes instead are present everywhere in the glass phase and are related to the hierarchical structure of the potential energy landscape. Our results highlight the universality of the spectrum of normal modes in disordered systems, and open the way toward a detailed analytical understanding of the vibrational spectrum of low-temperature glasses.
Collapse
|
55
|
Tong H, Tan P, Xu N. From Crystals to Disordered Crystals: A Hidden Order-Disorder Transition. Sci Rep 2015; 5:15378. [PMID: 26483326 PMCID: PMC4613360 DOI: 10.1038/srep15378] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2015] [Accepted: 09/24/2015] [Indexed: 11/09/2022] Open
Abstract
To distinguish between order and disorder is of fundamental importance to understanding solids. It becomes more significant with recent observations that solids with high structural order can behave like disordered solids, while properties of disordered solids can approach crystals under certain circumstance. It is then imperative to understand when and how disorder takes effect to deviate the properties of a solid from crystals and what the correct factors are to control the behaviours of solids. Here we answer these questions by reporting the finding of a hidden order-disorder transition from crystals to disordered crystals for static packings of frictionless spheres. While the geometric indicators are mostly blind to the transition, disordered crystals already exhibit properties apart from crystals. The transition approaches the close packing of hard spheres, giving rise to the singularity of the close packing point. We evidence that both the transition and properties of disordered crystals are jointly determined by the structural order and density. Near the transition, the elastic moduli and coordination number of disordered crystals show particular pressure dependence distinct from known behaviours of both crystals and jammed solids. The discovery of the transition therefore reveals some unknown aspects of solids.
Collapse
Affiliation(s)
- Hua Tong
- 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
| | - Peng Tan
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, 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
| |
Collapse
|
56
|
Schindler M, Maggs AC. Cavity averages for hard spheres in the presence of polydispersity and incomplete data. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2015; 38:97. [PMID: 26359237 DOI: 10.1140/epje/i2015-15097-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2015] [Revised: 07/30/2015] [Accepted: 07/31/2015] [Indexed: 06/05/2023]
Abstract
We develop a cavity-based method which allows to extract thermodynamic properties from position information in hard-sphere/disk systems. So far, there are available-volume and free-volume methods. We add a third one, which we call available volume after take-out, and which is shown to be mathematically equivalent to the others. In applications, where data sets are finite, all three methods show limitations, and they do this in different parameter ranges. We illustrate the principal equivalence and the limitations on data from molecular dynamics: In particular, we test robustness against missing data. We have in mind experimental limitations where there is a small polydispersity, say 4% in the particle radii, but individual radii cannot be determined. We observe that, depending on the used method, the errors in such a situation are easily 100% for the pressure and 10kT for the chemical potentials. Our work is meant as guideline to the experimentalists for choosing the right one of the three methods, in order to keep the outcome of experimental data analysis meaningful.
Collapse
Affiliation(s)
- Michael Schindler
- UMR Gulliver 7083 CNRS, ESPCI ParisTech, PSL Research University, 10 rue Vauquelin, 75005, Paris, France.
| | - A C Maggs
- UMR Gulliver 7083 CNRS, ESPCI ParisTech, PSL Research University, 10 rue Vauquelin, 75005, Paris, France
| |
Collapse
|
57
|
Yan L, Wyart M. Adaptive elastic networks as models of supercooled liquids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022310. [PMID: 26382409 DOI: 10.1103/physreve.92.022310] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2015] [Indexed: 06/05/2023]
Abstract
The thermodynamics and dynamics of supercooled liquids correlate with their elasticity. In particular for covalent networks, the jump of specific heat is small and the liquid is strong near the threshold valence where the network acquires rigidity. By contrast, the jump of specific heat and the fragility are large away from this threshold valence. In a previous work [Proc. Natl. Acad. Sci. USA 110, 6307 (2013)], we could explain these behaviors by introducing a model of supercooled liquids in which local rearrangements interact via elasticity. However, in that model the disorder characterizing elasticity was frozen, whereas it is itself a dynamic variable in supercooled liquids. Here we study numerically and theoretically adaptive elastic network models where polydisperse springs can move on a lattice, thus allowing for the geometry of the elastic network to fluctuate and evolve with temperature. We show numerically that our previous results on the relationship between structure and thermodynamics hold in these models. We introduce an approximation where redundant constraints (highly coordinated regions where the frustration is large) are treated as an ideal gas, leading to analytical predictions that are accurate in the range of parameters relevant for real materials. Overall, these results lead to a description of supercooled liquids, in which the distance to the rigidity transition controls the number of directions in phase space that cost energy and the specific heat.
Collapse
Affiliation(s)
- Le Yan
- Center for Soft Matter Research, Department of Physics, New York University 4 Washington Place, New York, 10003, New York, USA
| | - Matthieu Wyart
- Institute of Theoretical Physics, EPFL, CH-1015 Lausanne, Switzerland
| |
Collapse
|
58
|
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
| |
Collapse
|
59
|
Spatiotemporal chaotic unjamming and jamming in granular avalanches. Sci Rep 2015; 5:8128. [PMID: 25634753 PMCID: PMC4311237 DOI: 10.1038/srep08128] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2014] [Accepted: 01/07/2015] [Indexed: 11/17/2022] Open
Abstract
We have investigated the spatiotemporal chaotic dynamics of unjamming and jamming of particles in a model experiment – a rotating drum partially filled with bidisperse disks to create avalanches. The magnitudes of the first Lyapunov vector δu(t) and velocity v(t) of particles are directly measured for the first time to yield insights into their spatial correlation Cδu,v, which is on statistical average slightly larger near the unjamming than the value near the jamming transition. These results are consistent with the recent work of Banigan et al (Nature Phys. 2013), and it is for the first time to validate their theoretical models in a real scenario. v(t) shows rich dynamics: it grows exponentially for unstable particles and keeps increasing despite stochastic interactions; after the maximum, it decays with large fluctuations. Hence the spatiotemporal chaotic dynamics of avalanche particles are entangled, causing temporal correlations of macroscopic quantities of the system. We propose a simple model for these observations.
Collapse
|
60
|
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.
Collapse
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
| |
Collapse
|
61
|
Paillusson F. Devising a protocol-related statistical mechanics framework for granular materials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012204. [PMID: 25679616 DOI: 10.1103/physreve.91.012204] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2014] [Indexed: 06/04/2023]
Abstract
Devising a statistical mechanics framework for jammed granular materials is a challenging task as those systems do not share some important properties required to characterize them with statistical thermodynamics tools. In a recent paper [Asenjo et al. Phys. Rev. Lett. 112, 098002 (2014)], a new definition of a granular entropy, which puts the protocol used to generate the packings at its roots, has been proposed. Following up these results, it is shown that the protocol used in Asenjo et al. can be recast as a canonical ensemble with a particular value of the temperature. Signature of gaussianity for large system sizes strongly suggests an asymptotic equivalence with a corresponding microcanonical ensemble where jammed states with certain basin volumes are sampled uniformly. We argue that this microcanonical ensemble is not Edwards's microcanonical ensemble and generalize this argument to other protocols.
Collapse
Affiliation(s)
- Fabien Paillusson
- Departament de fisica fonamental, Universitat de Barcelona, 1 Marti i Franques, 08028, Barcelona, Spain
| |
Collapse
|
62
|
Hasan A, Maloney CE. Inferring elastic properties of an fcc crystal from displacement correlations: subspace projection and statistical artifacts. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062309. [PMID: 25615095 DOI: 10.1103/physreve.90.062309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2014] [Indexed: 06/04/2023]
Abstract
We compute the effective dispersion and vibrational density of states (DOS) of two-dimensional subregions of three-dimensional face-centered-cubic crystals using both a direct projection-inversion technique and a Monte Carlo simulation based on a common underlying Hamiltonian. We study both a (111) and (100) plane. We show that for any given direction of wave vector, both (111) and (100) show an anomalous ω(2)∼q regime at low q where ω(2) is the energy associated with the given mode and q is its wave number. The ω(2)∼q scaling should be expected to give rise to an anomalous DOS, D(ω), at low ω: D(ω)∼ω(3) rather than the conventional Debye result: D(ω)∼ω(2). The DOS for (100) looks to be consistent with D(ω)∼ω(3), while (111) shows something closer to the conventional Debye result at the smallest frequencies. In addition to the direct projection-inversion calculation, we perform Monte Carlo simulations to study the effects of finite sampling statistics. We show that finite sampling artifacts act as an effective disorder and bias D(ω), giving a behavior closer to D(ω)∼ω(2) than D(ω)∼ω(3). These results should have an important impact on the interpretation of recent studies of colloidal solids where the two-point displacement correlations can be obtained directly in real-space via microscopy.
Collapse
Affiliation(s)
- A Hasan
- Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA
| | - C E Maloney
- Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA
| |
Collapse
|
63
|
Lohr MA, Still T, Ganti R, Gratale MD, Davidson ZS, Aptowicz KB, Goodrich CP, Sussman DM, Yodh AG. Vibrational and structural signatures of the crossover between dense glassy and sparse gel-like attractive colloidal packings. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062305. [PMID: 25615091 DOI: 10.1103/physreve.90.062305] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2014] [Indexed: 06/04/2023]
Abstract
We investigate the vibrational modes of quasi-two-dimensional disordered colloidal packings of hard colloidal spheres with short-range attractions as a function of packing fraction. Certain properties of the vibrational density of states (vDOS) are shown to correlate with the density and structure of the samples (i.e., in sparsely versus densely packed samples). Specifically, a crossover from dense glassy to sparse gel-like states is suggested by an excess of phonon modes at low frequency and by a variation in the slope of the vDOS with frequency at low frequency. This change in phonon mode distribution is demonstrated to arise largely from localized vibrations that involve individual and/or small clusters of particles with few local bonds. Conventional order parameters and void statistics did not exhibit obvious gel-glass signatures as a function of volume fraction. These mode behaviors and accompanying structural insights offer a potentially new set of indicators for identification of glass-gel transitions and for assignment of gel-like versus glass-like character to a disordered solid material.
Collapse
Affiliation(s)
- Matthew A Lohr
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Tim Still
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Raman Ganti
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Matthew D Gratale
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Zoey S Davidson
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Kevin B Aptowicz
- Department of Physics, West Chester University, West Chester, Pennsylvania 19383, USA
| | - Carl P Goodrich
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Daniel M Sussman
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - A G Yodh
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| |
Collapse
|
64
|
Force distribution affects vibrational properties in hard-sphere glasses. Proc Natl Acad Sci U S A 2014; 111:17054-9. [PMID: 25406326 DOI: 10.1073/pnas.1415298111] [Citation(s) in RCA: 93] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We theoretically and numerically study the elastic properties of hard-sphere glasses and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero temperature, we argue that the presence of certain pairs of particles interacting with a small force f soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting P(f) ~ f(θ(e)), the force distribution of such pairs and ϕ(c) the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale ω*, rising up to it as D(ω) ~ ω(2+a), and decaying above ω* as D(ω) ~ ω(-a) where a = (1 - θ(e))/(3 + θ(e)) and ω is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with ⟨δR²⟩ ~ 1/μ ~ (ϕ(c) - ϕ)(κ), where κ = 2 - 2/(3 + θ(e)), and (iii) continuum elasticity breaks down on a scale ℓ(c) ~ 1/√(δz) ~ (ϕ(c) - ϕ)(-b), where b = (1 + θ(e))/(6 + 2θ(e)) and δz = z - 2d, where z is the coordination and d the spatial dimension. We numerically test (i) and provide data supporting that θ(e) ≈ 0.41 in our bidisperse system, independently of system preparation in two and three dimensions, leading to κ ≈ 1.41, a ≈ 0.17, and b ≈ 0.21. Our results for the mean-square displacement are consistent with a recent exact replica computation for d = ∞, whereas some observations differ, as rationalized by the present approach.
Collapse
|
65
|
DeGiuli E, Laversanne-Finot A, Düring G, Lerner E, Wyart M. Effects of coordination and pressure on sound attenuation, boson peak and elasticity in amorphous solids. SOFT MATTER 2014; 10:5628-5644. [PMID: 24981002 DOI: 10.1039/c4sm00561a] [Citation(s) in RCA: 105] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Connectedness and applied stress strongly affect elasticity in solids. In various amorphous materials, mechanical stability can be lost either by reducing connectedness or by increasing pressure. We present an effective medium theory of elasticity that extends previous approaches by incorporating the effect of compression, of amplitude e, allowing one to describe quantitative features of sound propagation, transport, the boson peak, and elastic moduli near the elastic instability occurring at a compression ec. The theory disentangles several frequencies characterizing the vibrational spectrum: the onset frequency where strongly-scattered modes appear in the vibrational spectrum, the pressure-independent frequency ω* where the density of states displays a plateau, the boson peak frequency ωBP found to scale as , and the Ioffe-Regel frequency ωIR where scattering length and wavelength become equal. We predict that sound attenuation crosses over from ω(4) to ω(2) behaviour at ω0, consistent with observations in glasses. We predict that a frequency-dependent length scale ls(ω) and speed of sound ν(ω) characterize vibrational modes, and could be extracted from scattering data. One key result is the prediction of a flat diffusivity above ω0, in agreement with previously unexplained observations. We find that the shear modulus does not vanish at the elastic instability, but drops by a factor of 2. We check our predictions in packings of soft particles and study the case of covalent networks and silica, for which we predict ωIR ≈ ωBP. Overall, our approach unifies sound attenuation, transport and length scales entering elasticity in a single framework where disorder is not the main parameter controlling the boson peak, in agreement with observations. This framework leads to a phase diagram where various glasses can be placed, connecting microscopic structure to vibrational properties.
Collapse
Affiliation(s)
- Eric DeGiuli
- Center for Soft Matter Research, New York University, 4 Washington Place, New York, NY 10003, USA.
| | | | | | | | | |
Collapse
|
66
|
Goodrich CP, Liu AJ, Nagel SR. Contact nonlinearities and linear response in jammed particulate packings. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022201. [PMID: 25215727 DOI: 10.1103/physreve.90.022201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2014] [Indexed: 06/03/2023]
Abstract
Packings of frictionless athermal particles that interact only when they overlap experience a jamming transition as a function of packing density. Such packings provide the foundation for the theory of jamming. This theory rests on the observation that, despite the multitude of disordered configurations, the mechanical response to linear order depends only on the distance to the transition. We investigate the validity and utility of such measurements that invoke the harmonic approximation and show that, despite particles coming in and out of contact, there is a well-defined linear regime in the thermodynamic limit.
Collapse
Affiliation(s)
- Carl P Goodrich
- Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Andrea J Liu
- Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Sidney R Nagel
- James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| |
Collapse
|
67
|
Lerner E, DeGiuli E, Düring G, Wyart M. Breakdown of continuum elasticity in amorphous solids. SOFT MATTER 2014; 10:5085-5092. [PMID: 24905568 DOI: 10.1039/c4sm00311j] [Citation(s) in RCA: 67] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We show numerically that the response of simple amorphous solids (elastic networks and particle packings) to a local force dipole is characterized by a lengthscale lc that diverges as unjamming is approached as lc ∼ (z - 2d)(-1/2), where z ≥ 2d is the mean coordination, and d is the spatial dimension, at odds with previous numerical claims. We also show how the magnitude of the lengthscale lc is amplified by the presence of internal stresses in the disordered solid. Our data suggests a divergence of lc ∼ (pc - p)(-1/4) with proximity to a critical internal stress pc at which soft elastic modes become unstable.
Collapse
Affiliation(s)
- Edan Lerner
- New York University, Center for Soft Matter Research, 4 Washington Place, New York, NY 10003, USA.
| | | | | | | |
Collapse
|
68
|
Hu Y, Johnson DL, Valenza JJ, Santibanez F, Makse HA. Stress-dependent normal-mode frequencies from the effective mass of granular matter. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062202. [PMID: 25019765 DOI: 10.1103/physreve.89.062202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2014] [Indexed: 06/03/2023]
Abstract
A zero-temperature critical point has been invoked to control the anomalous behavior of granular matter as it approaches jamming or mechanical arrest. Criticality manifests itself in an anomalous spectrum of low-frequency normal modes and scaling behavior near the jamming transition. The critical point may explain the peculiar mechanical properties of dissimilar systems such as glasses and granular materials. Here we study the critical scenario via an experimental measurement of the normal modes frequencies of granular matter under stress from a pole decomposition analysis of the effective mass. We extract a complex-valued characteristic frequency which displays scaling |ω (σ)| ∼ σΩ' with vanishing stress σ for a variety of granular systems. The critical exponent is smaller than that predicted by mean-field theory opening new challenges to explain the exponent for frictional and dissipative granular matter. Our results shed light on the anomalous behavior of stress-dependent acoustics and attenuation in granular materials near the jamming transition.
Collapse
Affiliation(s)
- Yanqing Hu
- Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA
| | - David L Johnson
- Schlumberger-Doll Research, One Hampshire, Cambridge, Massachusetts 02139, USA
| | - John J Valenza
- Schlumberger-Doll Research, One Hampshire, Cambridge, Massachusetts 02139, USA
| | - Francisco Santibanez
- Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA and Departamento de Física, Universidad de Santiago de Chile, Av. Ecuador 3493, Santiago, Chile
| | - Hernán A Makse
- Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA
| |
Collapse
|
69
|
Bertrand T, Schreck CF, O'Hern CS, Shattuck MD. Hypocoordinated solids in particulate media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062203. [PMID: 25019766 DOI: 10.1103/physreve.89.062203] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2013] [Indexed: 06/03/2023]
Abstract
We propose a "phase diagram" for particulate systems with purely repulsive contact forces, such as granular media and colloids. We characterize two classes of behavior as a function of the input kinetic energy per degree of freedom T_{0} and packing fraction deviation from jamming onset Δϕ=ϕ-ϕ_{J} using simulations of frictionless disks. Isocoordinated solids (ICS) exist above jamming; they possess an average contact number equal to the isostatic value z_{iso}. ICS display "strict" harmonic response, where the density of vibrational modes from the Fourier transform of the velocity autocorrelation function is a set of sharp peaks at eigenfrequencies ω_{k}{d} of the dynamical matrix. In contrast, hypocoordinated solids (HCS) occur above and below jamming and possess fluctuating networks of interparticle contacts but do not undergo cage-breaking particle rearrangements. The density of vibrational frequencies for the HCS is not a collection of sharp peaks at ω_{k}{d}, but it does possess a common form over a range of Δϕ and T_{0}.
Collapse
Affiliation(s)
- Thibault Bertrand
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA and Center for Research on Interface Structures and Phenomena, Yale University, New Haven, Connecticut 06520, USA
| | - Carl F Schreck
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA and Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA
| | - Corey S O'Hern
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA and Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA and Department of Applied Physics, Yale University, New Haven, Connecticut 06520-8120, USA and Center for Research on Interface Structures and Phenomena, Yale University, New Haven, Connecticut 06520, USA
| | - Mark D Shattuck
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA and Benjamin Levich Institute and Physics Department, The City College of the City University of New York, New York, New York 10031, USA
| |
Collapse
|
70
|
Basu A, Xu Y, Still T, Arratia PE, Zhang Z, Nordstrom KN, Rieser JM, Gollub JP, Durian DJ, Yodh AG. Rheology of soft colloids across the onset of rigidity: scaling behavior, thermal, and non-thermal responses. SOFT MATTER 2014; 10:3027-35. [PMID: 24695615 DOI: 10.1039/c3sm52454j] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
We study the rheological behavior of colloidal suspensions composed of soft sub-micron-size hydrogel particles across the liquid-solid transition. The measured stress and strain-rate data, when normalized by thermal stress and time scales, suggest our systems reside in a regime wherein thermal effects are important. In a different vein, critical point scaling predictions for the jamming transition, typical in athermal systems, are tested. Near dynamic arrest, the suspensions exhibit scaling exponents similar to those reported in Nordstrom et al., Phys. Rev. Lett., 2010, 105, 175701. The observation suggests that our system exhibits a glass transition near the onset of rigidity, but it also exhibits a jamming-like scaling further from the transition point. These observations are thought-provoking in light of recent theoretical and simulation findings, which show that suspension rheology across the full range of microgel particle experiments can exhibit both thermal and athermal mechanisms.
Collapse
Affiliation(s)
- Anindita Basu
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA.
| | | | | | | | | | | | | | | | | | | |
Collapse
|
71
|
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.
Collapse
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
| | | | | | | | | | | |
Collapse
|
72
|
Hydrodynamics selects the pathway for displacive transformations in DNA-linked colloidal crystallites. Proc Natl Acad Sci U S A 2014; 111:4803-8. [PMID: 24639545 DOI: 10.1073/pnas.1318012111] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The degree to which DNA-linked particle crystals, particularly those composed of micrometer-scale colloids, are able to dynamically evolve or whether they are kinetically arrested after formation remains poorly understood. Here, we study a recently observed displacive transformation in colloidal binary superlattice crystals, whereby a body-centered cubic to face-centered cubic transformation is found to proceed spontaneously under some annealing conditions. Using a comprehensive suite of computer simulation tools, we develop a framework for analyzing the many displacive transformation pathways corresponding to distinct, but energetically degenerate, random hexagonal close-packed end states. Due to the short-ranged, spherically symmetric nature of the particle interactions the pathways are all barrierless, suggesting that all end states should be equally likely. Instead, we find that hydrodynamic correlations between particles result in anisotropic mobility along the various possible displacive pathways, strongly selecting for pathways that lead to the fcc-CuAu-I configuration, explaining recent experimental observations. This finding may provide clues for discovering new approaches for controlling structure in this emerging class of materials.
Collapse
|
73
|
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.
Collapse
Affiliation(s)
- C Coulais
- SPHYNX/SPEC, CEA-Saclay, URA 2464 CNRS, 91 191 Gif-sur-Yvette, France
| | | | | |
Collapse
|
74
|
Still T, Goodrich CP, Chen K, Yunker PJ, Schoenholz S, Liu AJ, Yodh AG. Phonon dispersion and elastic moduli of two-dimensional disordered colloidal packings of soft particles with frictional interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012301. [PMID: 24580221 DOI: 10.1103/physreve.89.012301] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2013] [Indexed: 06/03/2023]
Abstract
Particle tracking and displacement covariance matrix techniques are employed to investigate the phonon dispersion relations of two-dimensional colloidal glasses composed of soft, thermoresponsive microgel particles whose temperature-sensitive size permits in situ variation of particle packing fraction. Bulk, B, and shear, G, moduli of the colloidal glasses are extracted from the dispersion relations as a function of packing fraction, and variation of the ratio G/B with packing fraction is found to agree quantitatively with predictions for jammed packings of frictional soft particles. In addition, G and B individually agree with numerical predictions for frictional particles. This remarkable level of agreement enabled us to extract an energy scale for the interparticle interaction from the individual elastic constants and to derive an approximate estimate for the interparticle friction coefficient.
Collapse
Affiliation(s)
- Tim Still
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA and Complex Assemblies of Soft Matter, CNRS-Rhodia-UPenn UMI 3254, Bristol, Pennsylvania 19007, USA
| | - Carl P Goodrich
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Ke Chen
- Beijing National Laboratory for Condensed Matter Physics and Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Peter J Yunker
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Samuel Schoenholz
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Andrea J Liu
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - A G Yodh
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| |
Collapse
|
75
|
Shiba H, Kawasaki T. Spatiotemporal heterogeneity of local free volumes in highly supercooled liquid. J Chem Phys 2013; 139:184502. [PMID: 24320279 DOI: 10.1063/1.4829442] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We discuss the spatiotemporal behavior of local density and its relation to dynamical heterogeneity in a highly supercooled liquid by using molecular dynamics simulations of a binary mixture with different particle sizes in two dimensions. To trace voids heterogeneously existing with lower local densities, which move along with the structural relaxation, we employ the minimum local density for each particle in a time window whose width is set along with the structural relaxation time. Particles subject to free volumes correspond well to the configuration rearranging region of dynamical heterogeneity. While the correlation length for dynamical heterogeneity grows with temperature decrease, no growth in the correlation length of heterogeneity in the minimum local density distribution takes place. A comparison of these results with those of normal mode analysis reveals that superpositions of lower-frequency soft modes extending over the free volumes exhibit spatial correlation with the broken bonds. This observation suggests a possibility that long-ranged vibration modes facilitate the interactions between fragile regions represented by free volumes, to induce dynamical correlations at a large scale.
Collapse
Affiliation(s)
- Hayato Shiba
- Institute for Solid State Physics, University of Tokyo, Chiba 277-8581, Japan
| | | |
Collapse
|
76
|
Schreck CF, Hoy RS, Shattuck MD, O'Hern CS. Particle-scale reversibility in athermal particulate media below jamming. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052205. [PMID: 24329257 DOI: 10.1103/physreve.88.052205] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2013] [Revised: 11/04/2013] [Indexed: 06/03/2023]
Abstract
We perform numerical simulations of repulsive, frictionless athermal disks in two and three spatial dimensions undergoing cyclic quasistatic simple shear to investigate particle-scale reversible motion. We identify three classes of steady-state dynamics as a function of packing fraction φ and maximum strain amplitude per cycle γ(max). Point-reversible states, where particles do not collide and exactly retrace their intracycle trajectories, occur at low φ and γ(max). Particles in loop-reversible states undergo numerous collisions and execute complex trajectories but return to their initial positions at the end of each cycle. For sufficiently large φ and γ(max), systems display irreversible dynamics with nonzero self-diffusion. Loop-reversible dynamics enables the reliable preparation of configurations with specified structural and mechanical properties over a broad range of φ.
Collapse
Affiliation(s)
- Carl F Schreck
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA and Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA
| | - Robert S Hoy
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
| | - Mark D Shattuck
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA and Benjamin Levich Institute and Physics Department, The City College of the City University of New York, New York, New York 10031, USA
| | - Corey S O'Hern
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA and Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA and Department of Applied Physics, Yale University, New Haven, Connecticut 06520-8120, USA
| |
Collapse
|
77
|
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.
Collapse
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
| |
Collapse
|
78
|
Chen K, Still T, Schoenholz S, Aptowicz KB, Schindler M, Maggs AC, Liu AJ, Yodh AG. Phonons in two-dimensional soft colloidal crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022315. [PMID: 24032840 DOI: 10.1103/physreve.88.022315] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2012] [Revised: 05/08/2013] [Indexed: 06/02/2023]
Abstract
The vibrational modes of pristine and polycrystalline monolayer colloidal crystals composed of thermosensitive microgel particles are measured using video microscopy and covariance matrix analysis. At low frequencies, the Debye relation for two-dimensional harmonic crystals is observed in both crystal types; at higher frequencies, evidence for van Hove singularities in the phonon density of states is significantly smeared out by experimental noise and measurement statistics. The effects of these errors are analyzed using numerical simulations. We introduce methods to correct for these limitations, which can be applied to disordered systems as well as crystalline ones, and we show that application of the error correction procedure to the experimental data leads to more pronounced van Hove singularities in the pristine crystal. Finally, quasilocalized low-frequency modes in polycrystalline two-dimensional colloidal crystals are identified and demonstrated to correlate with structural defects such as dislocations, suggesting that quasilocalized low-frequency phonon modes may be used to identify local regions vulnerable to rearrangements in crystalline as well as amorphous solids.
Collapse
Affiliation(s)
- Ke Chen
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA and Beijing National Laboratory for Condensed Matter Physics and Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | | | | | | | | | | | | | | |
Collapse
|
79
|
Gratale MD, Yunker PJ, Chen K, Still T, Aptowicz KB, Yodh AG. Phonons in two-dimensional colloidal crystals with bond-strength disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:052301. [PMID: 23767534 DOI: 10.1103/physreve.87.052301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2013] [Revised: 04/02/2013] [Indexed: 06/02/2023]
Abstract
We study phonon modes in two-dimensional colloidal crystals composed of soft microgel particles with hard polystyrene particle dopants distributed randomly on the triangular lattice. This experimental approach produces close-packed lattices of spheres with random bond strength disorder, i.e., the effective springs coupling nearest neighbors are very stiff, very soft, or of intermediate stiffness. Particle tracking video microscopy and covariance matrix techniques are then employed to derive the phonon modes of the corresponding "shadow" crystals with bond strength disorder as a function of increasing dopant concentration. At low frequencies, hard and soft particles participate equally in the phonon modes, and the samples exhibit Debye-like density of states behavior characteristic of crystals. For mid- and high-frequency phonons, the relative participation of hard versus soft particles in each mode is found to vary systematically with dopant concentration. Additionally, a few localized modes, primarily associated with hard particle motions, are found at the highest frequencies.
Collapse
Affiliation(s)
- Matthew D Gratale
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | | | | | | | | | | |
Collapse
|
80
|
Bhattacharya R, Basu J. Microscopic dynamics of nanoparticle monolayers at air–water interface. J Colloid Interface Sci 2013; 396:69-74. [DOI: 10.1016/j.jcis.2013.01.003] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2012] [Revised: 12/01/2012] [Accepted: 01/02/2013] [Indexed: 10/27/2022]
|
81
|
Why glass elasticity affects the thermodynamics and fragility of supercooled liquids. Proc Natl Acad Sci U S A 2013; 110:6307-12. [PMID: 23576746 DOI: 10.1073/pnas.1300534110] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Supercooled liquids are characterized by their fragility: The slowing down of the dynamics under cooling is more sudden and the jump of specific heat at the glass transition is generally larger in fragile liquids than in strong ones. Despite the importance of this quantity in classifying liquids, explaining what aspects of the microscopic structure controls fragility remains a challenge. Surprisingly, experiments indicate that the linear elasticity of the glass--a purely local property of the free energy landscape--is a good predictor of fragility. In particular, materials presenting a large excess of soft elastic modes, the so-called boson peak, are strong. This is also the case for network liquids near the rigidity percolation, known to affect elasticity. Here we introduce a model of the glass transition based on the assumption that particles can organize locally into distinct configurations that are coupled spatially via elasticity. The model captures the mentioned observations connecting elasticity and fragility. We find that materials presenting an abundance of soft elastic modes have little elastic frustration: Energy is insensitive to most directions in phase space, leading to a small jump of specific heat. In this framework strong liquids turn out to lie the closest to a critical point associated with a rigidity or jamming transition, and their thermodynamic properties are related to the problem of number partitioning and to Hopfield nets in the limit of small memory.
Collapse
|
82
|
Kawasaki T, Onuki A. Dynamics of thermal vibrational motions and stringlike jump motions in three-dimensional glass-forming liquids. J Chem Phys 2013; 138:12A514. [DOI: 10.1063/1.4770337] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
83
|
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
|
84
|
Yunker PJ, Zhang Z, Gratale M, Chen K, Yodh AG. Relationship between neighbor number and vibrational spectra in disordered colloidal clusters with attractive interactions. J Chem Phys 2013; 138:12A525. [DOI: 10.1063/1.4774076] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
85
|
Hocky GM, Reichman DR. A small subset of normal modes mimics the properties of dynamical heterogeneity in a model supercooled liquid. J Chem Phys 2013; 138:12A537. [DOI: 10.1063/1.4790799] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
86
|
Klix CL, Ebert F, Weysser F, Fuchs M, Maret G, Keim P. Glass elasticity from particle trajectories. PHYSICAL REVIEW LETTERS 2012; 109:178301. [PMID: 23215226 DOI: 10.1103/physrevlett.109.178301] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2011] [Indexed: 06/01/2023]
Abstract
Using positional data from video microscopy of a two-dimensional colloidal system and from simulations of hard disks, we determine the wave-vector-dependent elastic dispersion relations in glass. The emergence of rigidity based on the existence of a well defined displacement field in amorphous solids is demonstrated. Continuum elastic theory is recovered in the limit of long wavelengths which provides the glass elastic shear and bulk modulus as a function of temperature. The onset of a finite static shear modulus upon cooling marks the fluid-glass transition in an intuitive and unique way.
Collapse
|
87
|
Shiba H, Kawasaki T, Onuki A. Relationship between bond-breakage correlations and four-point correlations in heterogeneous glassy dynamics: configuration changes and vibration modes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:041504. [PMID: 23214588 DOI: 10.1103/physreve.86.041504] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2012] [Indexed: 06/01/2023]
Abstract
We investigate the dynamic heterogeneities of glassy particle systems in the theoretical schemes of bond breakage and four-point correlation functions. In the bond-breakage scheme, we introduce the structure factor S(b)(q,t) and the susceptibility χ(b)(t) to detect the spatial correlations of configuration changes. Here χ(b)(t) attains a maximum at t=t(b)(max) as a function of time t, where the fraction of the particles with broken bonds φ(b)(t) is about 1/2. In the four-point scheme, treating the structure factor S(4)(q,t) and the susceptibility χ(4)(t), we detect superpositions of the heterogeneity of bond breakage and that of thermal low-frequency vibration modes. While the former grows slowly, the latter emerges quickly to exhibit complex space-time behavior. In two dimensions, the vibration modes extending over the system yield significant contributions to the four-point correlations, which depend on the system size logarithmically. A maximum of χ(4)(t) is attained at t=t(4)(max), where these two contributions become of the same order. As a result, t(4)(max) is considerably shorter than t(b)(max).
Collapse
Affiliation(s)
- Hayato Shiba
- Institute for Solid State Physics, University of Tokyo, Chiba 277-8581, Japan
| | | | | |
Collapse
|
88
|
Hunter GL, Weeks ER. The physics of the colloidal glass transition. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:066501. [PMID: 22790649 DOI: 10.1088/0034-4885/75/6/066501] [Citation(s) in RCA: 334] [Impact Index Per Article: 27.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
As one increases the concentration of a colloidal suspension, the system exhibits a dramatic increase in viscosity. Beyond a certain concentration, the system is said to be a colloidal glass; structurally, the system resembles a liquid, yet motions within the suspension are slow enough that it can be considered essentially frozen. For several decades, colloids have served as a valuable model system for understanding the glass transition in molecular systems. The spatial and temporal scales involved allow these systems to be studied by a wide variety of experimental techniques. The focus of this review is the current state of understanding of the colloidal glass transition, with an emphasis on experimental observations. A brief introduction is given to important experimental techniques used to study the glass transition in colloids. We describe features of colloidal systems near and in glassy states, including increases in viscosity and relaxation times, dynamical heterogeneity and ageing, among others. We also compare and contrast the glass transition in colloids to that in molecular liquids. Other glassy systems are briefly discussed, as well as recently developed synthesis techniques that will keep these systems rich with interesting physics for years to come.
Collapse
Affiliation(s)
- Gary L Hunter
- Department of Physics, Emory University, Math and Science Center 400 Dowman Dr., N201 Atlanta, GA 30322, USA
| | | |
Collapse
|
89
|
Valenza J, Johnson DL. Normal-mode spectrum of finite-sized granular systems: The effects of fluid viscosity at the grain contacts. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041302. [PMID: 22680464 DOI: 10.1103/physreve.85.041302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2011] [Revised: 11/17/2011] [Indexed: 06/01/2023]
Abstract
We investigate the effects of adsorbed films on the attenuative properties of loose granular media occupying a finite-sized rigid container that is open at the top. We measure the effective mass, M[over ̃](ω), of loose tungsten particles prepared under two different sets of conditions: (i) We lightly coat tungsten grains with a fixed volume fraction of silicone oil (polydimethylsiloxane, PDMS), where the liquid viscosity is varied for individual realizations, and (ii) in the other set of experiments we vary the humidity. On a theoretical level, we are able to decompose the effective mass into a sum over the contributions from each of the normal modes of the granular medium. Our results indicate that increasing either the PDMS viscosity or the humidity, as the case may be, markedly increases the damping rate of each normal mode relevant to our measurements. However, there is appreciable damping even in the absence of any macroscopic film. With a notable exception in the case of the highest humidity in the humidity-controlled experiments, all the relevant modes are weakly damped in the sense of a microscopic theory based on damped contact forces between rigid particles.
Collapse
Affiliation(s)
- John Valenza
- Schlumberger-Doll Research, One Hampshire Street, Cambridge, Massachusetts 02139, USA
| | | |
Collapse
|
90
|
Tan P, Xu N, Schofield AB, Xu L. Understanding the low-frequency quasilocalized modes in disordered colloidal systems. PHYSICAL REVIEW LETTERS 2012; 108:095501. [PMID: 22463646 DOI: 10.1103/physrevlett.108.095501] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2011] [Revised: 01/09/2012] [Indexed: 05/31/2023]
Abstract
In disordered colloidal systems, we experimentally measure the normal modes with the covariance matrix method and clarify the origin of low-frequency quasilocalization at the single-particle level. We observe important features from both jamming and glass simulations: There is a plateau in the density of states [D(ω)] which is suppressed upon compression, as predicted by jamming; within the same systems, we also find that the low-frequency quasilocalization originates from the large vibrations of defective structures coupled with transverse excitations, consistent with a recent glass simulation. The coexistence of these features demonstrates an experimental link between jamming and glass. Extensive simulations further show that such a structural origin of quasilocalization is universally valid for various temperatures and volume fractions.
Collapse
Affiliation(s)
- Peng Tan
- Department of Physics, The Chinese University of Hong Kong, Hong Kong, People's Republic of China
| | | | | | | |
Collapse
|
91
|
|
92
|
Zanatta M, Baldi G, Caponi S, Fontana A, Petrillo C, Rossi F, Sacchetti F. Debye to non-Debye scaling of the Boson peak dynamics: Critical behavior and local disorder in vitreous germania. J Chem Phys 2011; 135:174506. [DOI: 10.1063/1.3656697] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
93
|
Divalent cation-dependent formation of electrostatic PIP2 clusters in lipid monolayers. Biophys J 2011; 101:2178-84. [PMID: 22067156 DOI: 10.1016/j.bpj.2011.09.039] [Citation(s) in RCA: 70] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2011] [Revised: 08/30/2011] [Accepted: 09/19/2011] [Indexed: 11/22/2022] Open
Abstract
Polyphosphoinositides are among the most highly charged molecules in the cell membrane, and the most common polyphosphoinositide, phosphatidylinositol-4,5-bisphosphate (PIP(2)), is involved in many mechanical and biochemical processes in the cell membrane. Divalent cations such as calcium can cause clustering of the polyanionic PIP(2), but the origin and strength of the effective attractions leading to clustering has been unclear. In addition, the question of whether the ion-mediated attractions could be strong enough to alter the mechanical properties of the membrane, to our knowledge, has not been addressed. We study phase separation in mixed monolayers of neutral and highly negatively charged lipids, induced by the addition of divalent positively charged counterions, both experimentally and numerically. We find good agreement between experiments on mixtures of PIP(2) and 1-stearoyl-2-oleoyl phosphatidylcholine and simulations of a simplified model in which only the essential electrostatic interactions are retained. In addition, we find numerically that under certain conditions the effective attractions can rigidify the resulting clusters. Our results support an interpretation of PIP(2) clustering as governed primarily by electrostatic interactions. At physiological pH, the simulations suggest that the effective attractions are strong enough to give nearly pure clusters of PIP(2) even at small overall concentrations of PIP(2).
Collapse
|
94
|
Ghosh A, Chikkadi V, Schall P, Bonn D. Connecting structural relaxation with the low frequency modes in a hard-sphere colloidal glass. PHYSICAL REVIEW LETTERS 2011; 107:188303. [PMID: 22107681 DOI: 10.1103/physrevlett.107.188303] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2011] [Indexed: 05/31/2023]
Abstract
Structural relaxation in hard-sphere colloidal glasses has been studied using confocal microscopy. The motion of individual particles is followed over long time scales to detect the rearranging regions in the system. We have used normal mode analysis to understand the origin of the rearranging regions. The low-frequency modes, obtained over short time scales, show strong spatial correlation with the rearrangements that happen on long time scales.
Collapse
Affiliation(s)
- Antina Ghosh
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.
| | | | | | | |
Collapse
|
95
|
Richter C, Schmiedeberg M, Stark H. A colloidal model system with tunable disorder: solid-fluid transition and discontinuities in the limit of zero disorder. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2011; 34:107. [PMID: 21979839 DOI: 10.1140/epje/i2011-11107-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2011] [Accepted: 08/24/2011] [Indexed: 05/31/2023]
Abstract
We study a colloidal model system where disorder can be continuously tuned from no disorder--corresponding to a system that can crystallize--to large disorder where geometrical frustration occurs. The model system consists of colloidal particles with screened electrostatic repulsion. They can only move on single lines which are parallel and equidistant to each other. We introduce disorder by modulating the particle line density. The system exhibits a solid-to-fluid transition which we study by the structure factor and the temporal evolution of the mean-square distance of nearest neighbors on neighboring lines. A determining feature is the occurrence of discontinuities when disorder is tuned to zero. We observe that the peak height of the pair correlation function in the solid phase does not extrapolate to the value of the perfect crystal. Similarly, the mean interaction energy and the screening length at which the solid-fluid transition occurs seem to be discontinuous when the limit of zero disorder is approached.
Collapse
Affiliation(s)
- C Richter
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | | | | |
Collapse
|
96
|
Schindler M, Maggs AC. Anisotropic elasticity in confocal studies of colloidal crystals. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2011; 34:115. [PMID: 22042209 DOI: 10.1140/epje/i2011-11115-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2011] [Accepted: 09/12/2011] [Indexed: 05/31/2023]
Abstract
We consider the theory of fluctuations of a colloidal solid observed in a confocal slice. For a cubic crystal we study the evolution of the projected elastic properties as a function of the anisotropy of the crystal using numerical methods based on the fast Fourier transform. In certain situations of high symmetry we find exact analytic results for the projected fluctuations.
Collapse
Affiliation(s)
- M Schindler
- Laboratoire PCT, UMR Gulliver CNRS-ESPCI 7083, 10 rue Vauquelin, 75231 Paris Cedex 05, France.
| | | |
Collapse
|
97
|
Chen K, Manning ML, Yunker PJ, Ellenbroek WG, Zhang Z, Liu AJ, Yodh AG. Measurement of correlations between low-frequency vibrational modes and particle rearrangements in quasi-two-dimensional colloidal glasses. PHYSICAL REVIEW LETTERS 2011; 107:108301. [PMID: 21981536 DOI: 10.1103/physrevlett.107.108301] [Citation(s) in RCA: 73] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2011] [Indexed: 05/31/2023]
Abstract
We investigate correlations between low-frequency vibrational modes and rearrangements in two-dimensional colloidal glasses composed of thermosensitive microgel particles, which readily permit variation of the sample packing fraction. At each packing fraction, the particle displacement covariance matrix is measured and used to extract the vibrational spectrum of the "shadow" colloidal glass (i.e., the particle network with the same geometry and interactions as the sample colloid but absent damping). Rearrangements are induced by successive, small reductions in the packing fraction. The experimental results suggest that low-frequency quasilocalized phonon modes in colloidal glasses, i.e., modes that present low energy barriers for system rearrangements, are spatially correlated with rearrangements in this thermal system.
Collapse
Affiliation(s)
- Ke Chen
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | | | | | | | | | | | | |
Collapse
|
98
|
Schreck CF, Bertrand T, O'Hern CS, Shattuck MD. Repulsive contact interactions make jammed particulate systems inherently nonharmonic. PHYSICAL REVIEW LETTERS 2011; 107:078301. [PMID: 21902435 DOI: 10.1103/physrevlett.107.078301] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2010] [Revised: 07/12/2011] [Indexed: 05/31/2023]
Abstract
Many jammed particulate systems, such as granular and colloidal materials, interact via repulsive contact forces. We find that these systems possess no harmonic regime in the large system limit (N→∞) for all compressions Δϕ studied, and at jamming onset Δϕ→0 for all N. We perform fixed energy simulations following perturbations with amplitude δ along eigendirections of the dynamical matrix. The fluctuations abruptly spread to all modes for δ≈δ(c) (where a single contact breaks) in contrast to linear and weakly nonlinear behavior. For δ > δ(c), all discrete modes disappear into a continuous frequency band. <δ(c)> scales with 1/N and Δϕ, which limits harmonic behavior to only overcompressed systems. The density of vibrational modes deviates strongly from that predicted from the dynamical matrix when the system enters the nonharmonic regime, which significantly affects its mechanical and transport properties.
Collapse
Affiliation(s)
- Carl F Schreck
- Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA
| | | | | | | |
Collapse
|
99
|
Nordstrom KN, Gollub JP, Durian DJ. Dynamical heterogeneity in soft-particle suspensions under shear. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:021403. [PMID: 21928990 DOI: 10.1103/physreve.84.021403] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2011] [Indexed: 05/31/2023]
Abstract
We present experimental measurements of dynamical heterogeneities in a dense system of microgel spheres, sheared at different rates and at different packing fractions in a microfluidic channel, and visualized with high-speed digital video microscopy. A four-point dynamic susceptibility is deduced from video correlations, and is found to exhibit a peak that grows in height and shifts to longer times as the jamming transition is approached from two different directions. In particular, the time for particle-size root-mean square relative displacements is found to scale as τ*∼(γΔφ4)(-1), where γ is the strain rate and Δφ = |φ - φ(c)| is the distance from the random close-packing volume fraction. The typical number of particles in a dynamical heterogeneity is deduced from the susceptibility peak height and found to scale as n*∼(γΔφ4)(-0.3). Exponent uncertainties are less than ten percent. We emphasize that the same power-law behavior is found at packing fractions above and below φ(c). Thus our results considerably extend a previous observation of n*∼γ(-0.3) for granular heap flow at fixed packing below φ(c). Furthermore, the implied result n*∼(τ*)(0.3) compares well with the expectation from mode-coupling theory and with prior observations for driven granular systems.
Collapse
Affiliation(s)
- K N Nordstrom
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA
| | | | | |
Collapse
|
100
|
Order by disorder in the antiferromagnetic Ising model on an elastic triangular lattice. Proc Natl Acad Sci U S A 2011; 108:11804-9. [PMID: 21730164 DOI: 10.1073/pnas.1014915108] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Geometrically frustrated materials have a ground-state degeneracy that may be lifted by subtle effects, such as higher-order interactions causing small energetic preferences for ordered structures. Alternatively, ordering may result from entropic differences between configurations in an effect termed order by disorder. Motivated by recent experiments in a frustrated colloidal system in which ordering is suspected to result from entropy, we consider in this paper the antiferromagnetic Ising model on a deformable triangular lattice. We calculate the displacements exactly at the microscopic level and, contrary to previous studies, find a partially disordered ground state of randomly zigzagging stripes. Each such configuration is deformed differently and thus has a unique phonon spectrum with distinct entropy, lifting the degeneracy at finite temperature. Nonetheless, due to the free-energy barriers between the ground-state configurations, the system falls into a disordered glassy state.
Collapse
|