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Kurita R, Tamura Y, Tani M. Formations of force network and softening of amorphous elastic materials from a coarsen-grained particle model. Sci Rep 2024; 14:8888. [PMID: 38632271 PMCID: PMC11024121 DOI: 10.1038/s41598-024-59498-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2023] [Accepted: 04/11/2024] [Indexed: 04/19/2024] Open
Abstract
Amorphous materials, such as granular substances, glasses, emulsions, foams, and cells, play significant roles in various aspects of daily life, serving as building materials, plastics, food products, and agricultural items. Understanding the mechanical response of these materials to external forces is crucial for comprehending their deformation, toughness, and stiffness. Despite the recognition of the formation of force networks within amorphous materials, the mechanisms behind their formation and their impact on macroscopic physical properties remain elusive. In this study, we employ a coarse-grained particle model to investigate the mechanical response, wherein local physical properties are integrated into the softness of the particles. Our findings reveal the emergence of a chain-like force distribution, which correlates with the planar distribution of softness and heterogeneous density variations. Additionally, we observe that the amorphous material undergoes softening due to the heterogeneous distribution of softness, a phenomenon explicable through a simple theoretical framework. Moreover, we demonstrate that the ambiguity regarding the size ratio of the blob to the force network can be adjusted by the amplitude of planar fluctuations in softness, underscoring the robustness of the coarse-grained particle model.
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Affiliation(s)
- Rei Kurita
- Department of Physics, Tokyo Metropolitan University, 1-1 Minamioosawa, Hachiouji-shi, Tokyo, 192-0397, Japan.
| | - Yuto Tamura
- Department of Physics, Tokyo Metropolitan University, 1-1 Minamioosawa, Hachiouji-shi, Tokyo, 192-0397, Japan
| | - Marie Tani
- Department of Physics, Tokyo Metropolitan University, 1-1 Minamioosawa, Hachiouji-shi, Tokyo, 192-0397, Japan
- Department of Physics, Kyoto University, Kitashirakawa-Oiwake-Cho, Sakyo-ku, Kyoto, 606-8502, Japan
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2
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Zhuang H, Chen D, Liu L, Keeney D, Zhang G, Jiao Y. Vibrational properties of disordered stealthy hyperuniform 1D atomic chains. J Phys Condens Matter 2024; 36:285703. [PMID: 38579735 DOI: 10.1088/1361-648x/ad3b5c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2024] [Accepted: 04/05/2024] [Indexed: 04/07/2024]
Abstract
Disorder hyperuniformity is a recently discovered exotic state of many-body systems that possess a hidden order in between that of a perfect crystal and a completely disordered system. Recently, this novel disordered state has been observed in a number of quantum materials including amorphous 2D graphene and silica, which are endowed with unexpected electronic transport properties. Here, we numerically investigate 1D atomic chain models, including perfect crystalline, disordered stealthy hyperuniform (SHU) as well as randomly perturbed atom packing configurations to obtain a quantitative understanding of how the unique SHU disorder affects the vibrational properties of these low-dimensional materials. We find that the disordered SHU chains possess lower cohesive energies compared to the randomly perturbed chains, implying their potential reliability in experiments. Our inverse partition ratio (IPR) calculations indicate that the SHU chains can support fully delocalized states just like perfect crystalline chains over a wide range of frequencies, i.e.ω∈(0,100)cm-1, suggesting superior phonon transport behaviors within these frequencies, which was traditionally considered impossible in disordered systems. Interestingly, we observe the emergence of a group of highly localized states associated withω∼200cm-1, which is characterized by a significant peak in the IPR and a peak in phonon density of states at the corresponding frequency, and is potentially useful for decoupling electron and phonon degrees of freedom. These unique properties of disordered SHU chains have implications in the design and engineering of novel quantum materials for thermal and phononic applications.
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Affiliation(s)
- Houlong Zhuang
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85287, United States of America
| | - Duyu Chen
- Materials Research Laboratory, University of California, Santa Barbara, CA 93106, United States of America
| | - Lei Liu
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85287, United States of America
| | - David Keeney
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85287, United States of America
| | - Ge Zhang
- Department of Physics, City University of Hong Kong, Hong Kong Special Administrative Region of China, People's Republic of China
| | - Yang Jiao
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85287, United States of America
- Department of Physics, Arizona State University, Tempe, AZ 85287, United States of America
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3
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Maher CE, Jiao Y, Torquato S. Hyperuniformity of maximally random jammed packings of hyperspheres across spatial dimensions. Phys Rev E 2023; 108:064602. [PMID: 38243527 DOI: 10.1103/physreve.108.064602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2023] [Accepted: 11/16/2023] [Indexed: 01/21/2024]
Abstract
The maximally random jammed (MRJ) state is the most random (i.e., disordered) configuration of strictly jammed (mechanically rigid) nonoverlapping objects. MRJ packings are hyperuniform, meaning their long-wavelength density fluctuations are anomalously suppressed compared to typical disordered systems, i.e., their structure factors S(k) tend to zero as the wave number |k| tends to zero. Here we show that generating high-quality strictly jammed states for Euclidean space dimensions d=3,4, and 5 is of paramount importance in ensuring hyperuniformity and extracting precise values of the hyperuniformity exponent α>0 for MRJ states, defined by the power-law behavior of S(k)∼|k|^{α} in the limit |k|→0. Moreover, we show that for fixed d it is more difficult to ensure jamming as the particle number N increases, which results in packings that are nonhyperuniform. Free-volume theory arguments suggest that the ideal MRJ state does not contain rattlers, which act as defects in numerically generated packings. As d increases, we find that the fraction of rattlers decreases substantially. Our analysis of the largest truly jammed packings suggests that the ideal MRJ packings for all dimensions d≥3 are hyperuniform with α=d-2, implying the packings become more hyperuniform as d increases. The differences in α between MRJ packings and the recently proposed Manna-class random close packed (RCP) states, which were reported to have α=0.25 in d=3 and be nonhyperuniform (α=0) for d=4 and d=5, demonstrate the vivid distinctions between the large-scale structure of RCP and MRJ states in these dimensions. Our paper clarifies the importance of the link between true jamming and hyperuniformity and motivates the development of an algorithm to produce rattler-free three-dimensional MRJ packings.
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Affiliation(s)
| | - Yang Jiao
- Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
| | - Salvatore Torquato
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544, USA
- Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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4
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Shi W, Keeney D, Chen D, Jiao Y, Torquato S. Computational design of anisotropic stealthy hyperuniform composites with engineered directional scattering properties. Phys Rev E 2023; 108:045306. [PMID: 37978628 DOI: 10.1103/physreve.108.045306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Accepted: 09/18/2023] [Indexed: 11/19/2023]
Abstract
Disordered hyperuniform materials are an emerging class of exotic amorphous states of matter that endow them with singular physical properties, including large isotropic photonic band gaps, superior resistance to fracture, and nearly optimal electrical and thermal transport properties, to name but a few. Here we generalize the Fourier-space-based numerical construction procedure for designing and generating digital realizations of isotropic disordered hyperuniform two-phase heterogeneous materials (i.e., composites) developed by Chen and Torquato [Acta Mater. 142, 152 (2018)1359-645410.1016/j.actamat.2017.09.053] to anisotropic microstructures with targeted spectral densities. Our generalized construction procedure explicitly incorporates the vector-dependent spectral density function χ[over ̃]_{_{V}}(k) of arbitrary form that is realizable. We demonstrate the utility of the procedure by generating a wide spectrum of anisotropic stealthy hyperuniform microstructures with χ[over ̃]_{_{V}}(k)=0 for k∈Ω, i.e., complete suppression of scattering in an "exclusion" region Ω around the origin in Fourier space. We show how different exclusion-region shapes with various discrete symmetries, including circular-disk, elliptical-disk, square, rectangular, butterfly-shaped, and lemniscate-shaped regions of varying size, affect the resulting statistically anisotropic microstructures as a function of the phase volume fraction. The latter two cases of Ω lead to directionally hyperuniform composites, which are stealthy hyperuniform only along certain directions and are nonhyperuniform along others. We find that while the circular-disk exclusion regions give rise to isotropic hyperuniform composite microstructures, the directional hyperuniform behaviors imposed by the shape asymmetry (or anisotropy) of certain exclusion regions give rise to distinct anisotropic structures and degree of uniformity in the distribution of the phases on intermediate and large length scales along different directions. Moreover, while the anisotropic exclusion regions impose strong constraints on the global symmetry of the resulting media, they can still possess structures at a local level that are nearly isotropic. Both the isotropic and anisotropic hyperuniform microstructures associated with the elliptical-disk, square, and rectangular Ω possess phase-inversion symmetry over certain range of volume fractions and a percolation threshold ϕ_{c}≈0.5. On the other hand, the directionally hyperuniform microstructures associated with the butterfly-shaped and lemniscate-shaped Ω do not possess phase-inversion symmetry and percolate along certain directions at much lower volume fractions. We also apply our general procedure to construct stealthy nonhyperuniform systems. Our construction algorithm enables one to control the statistical anisotropy of composite microstructures via the shape, size, and symmetries of Ω, which is crucial to engineering directional optical, transport, and mechanical properties of two-phase composite media.
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Affiliation(s)
- Wenlong Shi
- Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - David Keeney
- Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - Duyu Chen
- Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
| | - Yang Jiao
- Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
| | - Salvatore Torquato
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Princeton Institute of Materials, Princeton University, Princeton, New Jersey 08544, USA
- Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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5
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Zhuravlyov V, Goree J, Douglas JF, Elvati P, Violi A. Comparison of the static structure factor at long wavelengths for a dusty plasma liquid and other liquids. Phys Rev E 2022; 106:055212. [PMID: 36559416 DOI: 10.1103/physreve.106.055212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2021] [Accepted: 10/23/2022] [Indexed: 06/17/2023]
Abstract
Especially small values of the static structure factor S(k) at long wavelengths, i.e., small k, were obtained in an analysis of experimental data, for a two-dimensional dusty plasma in its liquid state. For comparison, an analysis of S(k) data was carried out for many previously published experiments with other liquids. The latter analysis indicates that the magnitude of S(k) at small k is typically in a range 0.02-0.13. In contrast, the corresponding value for a dusty plasma liquid was found to be as small as 0.0139. Another basic finding for the dusty plasma liquid is that S(k) at small k generally increases with temperature, with its lowest value, noted above, occurring near the melting point. Simulations were carried out for the dusty plasma liquid, and their results are generally consistent with the experiment. Since a dusty plasma has a soft interparticle interaction, our findings support earlier theoretical suggestions that a useful design strategy for creating materials having exceptionally low values of S(0), so-called hyperuniform materials, is the use of a condensed material composed of particles that interact softly at their periphery.
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Affiliation(s)
- Vitaliy Zhuravlyov
- Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242, USA
| | - J Goree
- Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242, USA
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Paolo Elvati
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Angela Violi
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
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6
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Chehadi Z, Bouabdellaoui M, Modaresialam M, Bottein T, Salvalaglio M, Bollani M, Grosso D, Abbarchi M. Scalable Disordered Hyperuniform Architectures via Nanoimprint Lithography of Metal Oxides. ACS Appl Mater Interfaces 2021; 13:37761-37774. [PMID: 34320811 DOI: 10.1021/acsami.1c05779] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Fabrication and scaling of disordered hyperuniform materials remain hampered by the difficulties in controlling the spontaneous phenomena leading to this novel kind of exotic arrangement of objects. Here, we demonstrate a hybrid top-down/bottom-up approach based on sol-gel dip-coating and nanoimprint lithography for the faithful reproduction of disordered hyperuniform metasurfaces in metal oxides. Nano- to microstructures made of silica and titania can be directly printed over several cm2 on glass and on silicon substrates. First, we describe the polymer mold fabrication starting from a hard master obtained via spontaneous solid-state dewetting of SiGe and Ge thin layers on SiO2. Then, we assess the effective disordered hyperuniform character of master and replica and the role of the thickness of the sol-gel layer on the metal oxide replicas and on the presence of a residual layer underneath. Finally, as a potential application, we show the antireflective character of titania structures on silicon. Our results are relevant for the realistic implementation over large scales of disordered hyperuniform nano- and microarchitectures made of metal oxides, thus opening their exploitation in the framework of wet chemical assembly.
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Affiliation(s)
- Zeinab Chehadi
- Aix Marseille Univ, Université de Toulon, CNRS, IM2NP, Marseille, France
| | | | | | - Thomas Bottein
- Aix Marseille Univ, Université de Toulon, CNRS, IM2NP, Marseille, France
| | - Marco Salvalaglio
- Institute of Scientific Computing, TU Dresden, 01062 Dresden, Germany
- Dresden Center for Computational Materials Science (DCMS), TU Dresden, 01062 Dresden, Germany
| | - Monica Bollani
- Laboratory for Nanostructure Epitaxy and Spintronics on Silicon, Istituto di Fotonica e Nanotecnologie-Consiglio Nazionale delle Ricerche, Via Anzani 42, 22100 Como, Italy
| | - David Grosso
- Aix Marseille Univ, Université de Toulon, CNRS, IM2NP, Marseille, France
| | - Marco Abbarchi
- Aix Marseille Univ, Université de Toulon, CNRS, IM2NP, Marseille, France
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7
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Chieco AT, Durian DJ. Quantifying the long-range structure of foams and other cellular patterns with hyperuniformity disorder length spectroscopy. Phys Rev E 2021; 103:062609. [PMID: 34271712 DOI: 10.1103/physreve.103.062609] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2020] [Accepted: 05/21/2021] [Indexed: 11/07/2022]
Abstract
We investigate the local and long-range structure of several space-filling cellular patterns: bubbles in a quasi-two-dimensional foam, and Voronoi constructions made around points that are uncorrelated (Poisson patterns), low discrepancy (Halton patterns), and displaced from a lattice by Gaussian noise (Einstein patterns). We study local structure with distributions of quantities including cell areas and side numbers. The former is the widest for the bubbles making foams the most locally disordered, while the latter show no major differences between the cellular patterns. To study long-range structure, we begin by representing the cellular systems as patterns of points, both unweighted and weighted by cell area. For this, foams are represented by their bubble centroids and the Voronoi constructions are represented by the centroids as well as the points from which they are created. Long-range structure is then quantified in two ways: by the spectral density, and by a real-space analog where the variance of density fluctuations for a set of measuring windows of diameter D is made more intuitive by conversion to the distance h(D) from the window boundary where these fluctuations effectively occur. The unweighted bubble centroids have h(D) that collapses for the different ages of the foam with random Poissonian fluctuations at long distances. The area-weighted bubble centroids and area-weighted Voronoi points all have constant h(D)=h_{e} for large D; the bubble centroids have the smallest value h_{e}=0.084sqrt[〈a〉], meaning they are the most uniform. Area-weighted Voronoi centroids exhibit collapse of h(D) to the same constant h_{e}=0.084sqrt[〈a〉] as for the bubble centroids. A similar analysis is performed on the edges of the cells and the spectra of h(D) for the foam edges show h(D)∼D^{1-ε} where ε=0.30±0.15.
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Affiliation(s)
- A T Chieco
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA
| | - D J Durian
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA
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8
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Affiliation(s)
- Eric Zhonghang Qu
- Division of Natural and Applied Sciences, Duke Kunshan University, Kunshan, Jiangsu 215300, China
| | - Andrew Matthew Jimenez
- Department of Chemical Engineering, Columbia University, New York, New York 10027, United States
| | - Sanat K. Kumar
- Department of Chemical Engineering, Columbia University, New York, New York 10027, United States
| | - Kai Zhang
- Division of Natural and Applied Sciences, Duke Kunshan University, Kunshan, Jiangsu 215300, China
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9
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Chen D, Zheng Y, Liu L, Zhang G, Chen M, Jiao Y, Zhuang H. Stone-Wales defects preserve hyperuniformity in amorphous two-dimensional networks. Proc Natl Acad Sci U S A 2021; 118:e2016862118. [PMID: 33431681 DOI: 10.1073/pnas.2016862118] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Disordered hyperuniformity (DHU) is a recently discovered novel state of many-body systems that possesses vanishing normalized infinite-wavelength density fluctuations similar to a perfect crystal and an amorphous structure like a liquid or glass. Here, we discover a hyperuniformity-preserving topological transformation in two-dimensional (2D) network structures that involves continuous introduction of Stone-Wales (SW) defects. Specifically, the static structure factor [Formula: see text] of the resulting defected networks possesses the scaling [Formula: see text] for small wave number k, where [Formula: see text] monotonically decreases as the SW defect concentration p increases, reaches [Formula: see text] at [Formula: see text], and remains almost flat beyond this p. Our findings have important implications for amorphous 2D materials since the SW defects are well known to capture the salient feature of disorder in these materials. Verified by recently synthesized single-layer amorphous graphene, our network models reveal unique electronic transport mechanisms and mechanical behaviors associated with distinct classes of disorder in 2D materials.
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10
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Sánchez JA, Rumi G, Maldonado RC, Bolecek NRC, Puig J, Pedrazzini P, Nieva G, Dolz MI, Konczykowski M, van der Beek CJ, Kolton AB, Fasano Y. Non-Gaussian tail in the force distribution: a hallmark of correlated disorder in the host media of elastic objects. Sci Rep 2020; 10:19452. [PMID: 33173105 DOI: 10.1038/s41598-020-76529-w] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2020] [Accepted: 10/09/2020] [Indexed: 11/11/2022] Open
Abstract
Inferring the nature of disorder in the media where elastic objects are nucleated is of crucial importance for many applications but remains a challenging basic-science problem. Here we propose a method to discern whether weak-point or strong-correlated disorder dominates based on characterizing the distribution of the interaction forces between objects mapped in large fields-of-view. We illustrate our proposal with the case-study system of vortex structures nucleated in type-II superconductors with different pinning landscapes. Interaction force distributions are computed from individual vortex positions imaged in thousands-vortices fields-of-view in a two-orders-of-magnitude-wide vortex-density range. Vortex structures nucleated in point-disordered media present Gaussian distributions of the interaction force components. In contrast, if the media have dilute and randomly-distributed correlated disorder, these distributions present non-Gaussian algebraically-decaying tails for large force magnitudes. We propose that detecting this deviation from the Gaussian behavior is a fingerprint of strong disorder, in our case originated from a dilute distribution of correlated pinning centers.
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11
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Klochko L, Baschnagel J, Wittmer JP, Benzerara O, Ruscher C, Semenov AN. Composition fluctuations in polydisperse liquids: Glasslike effects well above the glass transition. Phys Rev E 2020; 102:042611. [PMID: 33212658 DOI: 10.1103/physreve.102.042611] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2020] [Accepted: 09/24/2020] [Indexed: 06/11/2023]
Abstract
We study a two-dimensional glass-forming system of slightly polydisperse (LJ) particles using molecular dynamics simulations and demonstrate that in the liquid regime (well above the vitrification temperature) this model shows a number of features typical of the glass transition: (i) the relation between compressibility and structure factor S(q) is strongly violated; (ii) the dynamical structure factor S(q,t) at low q shows a two-step relaxation; (iii) the time-dependent heat capacity c_{v}(t) shows a long-time power-law tail. We show that these phenomena can be rationalized with the idea of composition fluctuations and provide a quantitative theory for the effects (i) and (ii). It implies that such effects must be inherent in all polydisperse colloidal models, including binary LJ mixtures.
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Affiliation(s)
- L Klochko
- Institut Charles Sadron, CNRS-UPR 22, Université de Strasbourg, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France
| | - J Baschnagel
- Institut Charles Sadron, CNRS-UPR 22, Université de Strasbourg, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France
| | - J P Wittmer
- Institut Charles Sadron, CNRS-UPR 22, Université de Strasbourg, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France
| | - O Benzerara
- Institut Charles Sadron, CNRS-UPR 22, Université de Strasbourg, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France
| | - C Ruscher
- Institut Charles Sadron, CNRS-UPR 22, Université de Strasbourg, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France
| | - A N Semenov
- Institut Charles Sadron, CNRS-UPR 22, Université de Strasbourg, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France
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12
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Ma Z, Lomba E, Torquato S. Optimized Large Hyperuniform Binary Colloidal Suspensions in Two Dimensions. Phys Rev Lett 2020; 125:068002. [PMID: 32845658 DOI: 10.1103/physrevlett.125.068002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2020] [Accepted: 07/15/2020] [Indexed: 06/11/2023]
Abstract
The creation of disordered hyperuniform materials with extraordinary optical properties (e.g., large complete photonic band gaps) requires a capacity to synthesize large samples that are effectively hyperuniform down to the nanoscale. Motivated by this challenge, we propose a feasible equilibrium fabrication protocol using binary paramagnetic colloidal particles confined in a 2D plane. The strong and long-ranged dipolar interaction induced by a tunable magnetic field is free from screening effects that attenuate long-ranged electrostatic interactions in charged colloidal systems. Specifically, we numerically find a family of optimal size ratios that makes the two-phase system effectively hyperuniform. We show that hyperuniformity is a general consequence of low isothermal compressibilities, which makes our protocol suitable to treat more general systems with other long-ranged interactions, dimensionalities, and/or polydispersity. Our methodology paves the way to synthesize large photonic hyperuniform materials that function in the visible to infrared range and hence may accelerate the discovery of novel photonic materials.
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Affiliation(s)
- Zheng Ma
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Enrique Lomba
- Instituto de Química Física Rocasolano, CSIC, Calle Serrano 119, E-28006 Madrid, Spain
| | - Salvatore Torquato
- Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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13
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Zheng Y, Liu L, Nan H, Shen ZX, Zhang G, Chen D, He L, Xu W, Chen M, Jiao Y, Zhuang H. Disordered hyperuniformity in two-dimensional amorphous silica. Sci Adv 2020; 6:eaba0826. [PMID: 32494625 PMCID: PMC7164937 DOI: 10.1126/sciadv.aba0826] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Accepted: 01/17/2020] [Indexed: 06/11/2023]
Abstract
Disordered hyperuniformity (DHU) is a recently proposed new state of matter, which has been observed in a variety of classical and quantum many-body systems. DHU systems are characterized by vanishing infinite-wavelength normalized density fluctuations and are endowed with unique novel physical properties. Here, we report the discovery of disordered hyperuniformity in atomic-scale two-dimensional materials, i.e., amorphous silica composed of a single layer of atoms, based on spectral-density analysis of high-resolution transmission electron microscopy images. Moreover, we show via large-scale density functional theory calculations that DHU leads to almost complete closure of the electronic bandgap compared to the crystalline counterpart, making the material effectively a metal. This is in contrast to the conventional wisdom that disorder generally diminishes electronic transport and is due to the unique electron wave localization induced by the topological defects in the DHU state.
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Affiliation(s)
- Yu Zheng
- Department of Physics, Arizona State University,Tempe, AZ 85287, USA
| | - Lei Liu
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85287, USA
| | - Hanqing Nan
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85287, USA
| | - Zhen-Xiong Shen
- Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China
| | - Ge Zhang
- Department of Physics, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Duyu Chen
- Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Lixin He
- Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China
| | - Wenxiang Xu
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85287, USA
- College of Mechanics and Materials, Hohai University, Nanjing 211100, P.R. China
| | - Mohan Chen
- CAPT, HEDPS, College of Engineering, Peking University 100871, P.R. China
| | - Yang Jiao
- Department of Physics, Arizona State University,Tempe, AZ 85287, USA
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85287, USA
| | - Houlong Zhuang
- Department of Physics, Arizona State University,Tempe, AZ 85287, USA
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85287, USA
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14
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Abstract
Disordered hyperuniform packings (or dispersions) are unusual amorphous two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations at infinitely long-wavelengths, compared to ordinary disordered materials. While there has been growing interest in such singular states of amorphous matter, a major obstacle has been an inability to produce large samples that are perfectly hyperuniform due to practical limitations of conventional numerical and experimental methods. To overcome these limitations, we introduce a general theoretical methodology to construct perfectly hyperuniform packings in d-dimensional Euclidean space R^{d}. Specifically, beginning with an initial general tessellation of space by disjoint cells that meets a "bounded-cell" condition, hard particles of general shape are placed inside each cell such that the local-cell particle packing fractions are identical to the global packing fraction. We prove that the constructed packings with a polydispersity in size are perfectly hyperuniform in the infinite-sample-size limit, regardless of particle shapes, positions, and numbers per cell. We use this theoretical formulation to devise an efficient and tunable algorithm to generate extremely large realizations of such packings. We employ two distinct initial tessellations: Voronoi as well as sphere tessellations. Beginning with Voronoi tessellations, we show that our algorithm can remarkably convert extremely large nonhyperuniform packings into hyperuniform ones in R^{2} and R^{3}. Implementing our theoretical methodology on sphere tessellations, we establish the hyperuniformity of the classical Hashin-Shtrikman multiscale coated-spheres structures, which are known to be two-phase media microstructures that possess optimal effective transport and elastic properties. A consequence of our work is a rigorous demonstration that packings that have identical tessellations can either be nonhyperuniform or hyperuniform by simply tuning local characteristics. It is noteworthy that our computationally designed hyperuniform two-phase systems can easily be fabricated via state-of-the-art methods, such as 2D photolithographic and 3D printing technologies. In addition, the tunability of our methodology offers a route for the discovery of novel disordered hyperuniform two-phase materials.
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Affiliation(s)
- Jaeuk Kim
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Salvatore Torquato
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.,Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.,Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA.,Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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15
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Klatt MA, Lovrić J, Chen D, Kapfer SC, Schaller FM, Schönhöfer PWA, Gardiner BS, Smith AS, Schröder-Turk GE, Torquato S. Universal hidden order in amorphous cellular geometries. Nat Commun 2019; 10:811. [PMID: 30778054 PMCID: PMC6379405 DOI: 10.1038/s41467-019-08360-5] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2018] [Accepted: 01/03/2019] [Indexed: 12/04/2022] Open
Abstract
Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile space are preferred. We employ Lloyd’s centroidal Voronoi diagram algorithm to solve this problem and find that it converges to disordered states associated with deep local minima. These states are universal in the sense that their structure factors are characterised by a complete independence of a wide class of initial conditions they evolved from. They moreover exhibit an anomalous suppression of long-wavelength density fluctuations and quickly become effectively hyperuniform. Our findings warrant the search for novel amorphous hyperuniform phases and cellular materials with unique physical properties. Disordered hyperuniformity implies a hidden order on length scales that can be found in various amorphous materials. Klatt et al. analyse the evolution of random point patterns using Llyod’s algorithm and show that they converge to an effectively hyperuniform state regardless of the initial conditions.
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Affiliation(s)
- Michael A Klatt
- Institute of Stochastics, Karlsruhe Institute of Technology (KIT), Englerstr. 2, 76131, Karlsruhe, Germany.,Department of Physics, Princeton University, Princeton, NJ, 08544, USA
| | - Jakov Lovrić
- Division of Physical Chemistry, Ruđer Bošković Institute, Bijenička 54, 10 000 Zagreb, Croatia.,School of Engineering and Information Technology, Murdoch University, 90 South St, Murdoch, WA, 6150, Australia.,PULS Group, Department of Physics and Interdisciplinary Center for Nanostructured Films, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 3, 91058 Erlangen, Germany
| | - Duyu Chen
- Department of Chemistry, Princeton University, Princeton, NJ, 08544, USA
| | - Sebastian C Kapfer
- Institut für Theoretische Physik I, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058, Erlangen, Germany
| | - Fabian M Schaller
- Institute of Stochastics, Karlsruhe Institute of Technology (KIT), Englerstr. 2, 76131, Karlsruhe, Germany.,Institut für Theoretische Physik I, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058, Erlangen, Germany
| | - Philipp W A Schönhöfer
- School of Engineering and Information Technology, Murdoch University, 90 South St, Murdoch, WA, 6150, Australia.,Institut für Theoretische Physik I, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058, Erlangen, Germany
| | - Bruce S Gardiner
- School of Engineering and Information Technology, Murdoch University, 90 South St, Murdoch, WA, 6150, Australia.,School of Computer Science and Software Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia
| | - Ana-Sunčana Smith
- Division of Physical Chemistry, Ruđer Bošković Institute, Bijenička 54, 10 000 Zagreb, Croatia.,PULS Group, Department of Physics and Interdisciplinary Center for Nanostructured Films, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstraße 3, 91058 Erlangen, Germany
| | - Gerd E Schröder-Turk
- School of Engineering and Information Technology, Murdoch University, 90 South St, Murdoch, WA, 6150, Australia.,Institut für Theoretische Physik I, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058, Erlangen, Germany.,Department of Applied Mathematics, Research School of Physical Sciences and Engineering, The Australian National University, Canberra, ACT, 0200, Australia
| | - Salvatore Torquato
- Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544, USA.
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16
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Middlemas TM, Stillinger FH, Torquato S. Hyperuniformity order metric of Barlow packings. Phys Rev E 2019; 99:022111. [PMID: 30934256 DOI: 10.1103/physreve.99.022111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2018] [Indexed: 06/09/2023]
Abstract
The concept of hyperuniformity has been a useful tool in the study of density fluctuations at large length scales in systems ranging across the natural and mathematical sciences. One can rank a large class of hyperuniform systems by their ability to suppress long-range density fluctuations through the use of a hyperuniformity order metric Λ[over ¯]. We apply this order metric to the Barlow packings, which are the infinitely degenerate densest packings of identical rigid spheres that are distinguished by their stacking geometries and include the commonly known fcc lattice and hcp crystal. The "stealthy stacking" theorem implies that these packings are all stealthy hyperuniform, a strong type of hyperuniformity, which involves the suppression of scattering up to a wave vector K. We describe the geometry of three classes of Barlow packings, two disordered classes and small-period packings. In addition, we compute a lower bound on K for all Barlow packings. We compute Λ[over ¯] for the aforementioned three classes of Barlow packings and find that, to a very good approximation, it is linear in the fraction of fcc-like clusters, taking values between those of least-ordered hcp and most-ordered fcc. This implies that the value of Λ[over ¯] of all Barlow packings is primarily controlled by the local cluster geometry. These results highlight the special nature of anisotropic stacking disorder, which provides impetus for future research on the development of anisotropic order metrics and hyperuniformity properties.
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Affiliation(s)
- T M Middlemas
- Department of Chemistry, Princeton University, New Jersey 08544, USA
| | - F H Stillinger
- Department of Chemistry, Princeton University, New Jersey 08544, USA
| | - S Torquato
- Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, New Jersey 08544, USA
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17
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Hexner D, Liu AJ, Nagel SR. Two Diverging Length Scales in the Structure of Jammed Packings. Phys Rev Lett 2018; 121:115501. [PMID: 30265103 DOI: 10.1103/physrevlett.121.115501] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2017] [Revised: 06/11/2018] [Indexed: 06/08/2023]
Abstract
At densities higher than the jamming transition for athermal, frictionless repulsive spheres we find two distinct length scales, both of which diverge as a power law as the transition is approached. The first, ξ_{Z}, is associated with the two-point correlation function for the number of contacts on two particles as a function of the particle separation. The second, ξ_{f}, is associated with contact-number fluctuations in subsystems of different sizes. On scales below ξ_{f}, the fluctuations are highly suppressed, similar to the phenomenon of hyperuniformity usually associated with density fluctuations. The exponents for the divergence of ξ_{Z} and ξ_{f} are different and appear to be different in two and three dimensions.
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Affiliation(s)
- Daniel Hexner
- The James Franck Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA and Department of Physics and Astronomy, The University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Andrea J Liu
- Department of Physics and Astronomy, The University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Sidney R Nagel
- The James Franck and Enrico Fermi Institutes and Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA
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18
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Leahy BD, Lin NY, Cohen I. Quantitative light microscopy of dense suspensions: Colloid science at the next decimal place. Curr Opin Colloid Interface Sci 2018. [DOI: 10.1016/j.cocis.2018.03.002] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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19
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DiStasio RA, Zhang G, Stillinger FH, Torquato S. Rational design of stealthy hyperuniform two-phase media with tunable order. Phys Rev E 2018; 97:023311. [PMID: 29548140 DOI: 10.1103/physreve.97.023311] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2017] [Indexed: 06/08/2023]
Abstract
Disordered stealthy hyperuniform materials are exotic amorphous states of matter that have attracted recent attention because of their novel structural characteristics (hidden order at large length scales) and physical properties, including desirable photonic and transport properties. It is therefore useful to devise algorithms that enable one to design a wide class of such amorphous configurations at will. In this paper, we present several algorithms enabling the systematic identification and generation of discrete (digitized) stealthy hyperuniform patterns with a tunable degree of order, paving the way towards the rational design of disordered materials endowed with novel thermodynamic and physical properties. To quantify the degree of order or disorder of the stealthy systems, we utilize the discrete version of the τ order metric, which accounts for the underlying spatial correlations that exist across all relevant length scales in a given digitized two-phase (or, equivalently, a two-spin state) system of interest. Our results impinge on a myriad of fields, ranging from physics, materials science and engineering, visual perception, and information theory to modern data science.
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Affiliation(s)
- Robert A DiStasio
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Ge Zhang
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - Frank H Stillinger
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - Salvatore Torquato
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
- Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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20
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Klatt MA, Torquato S. Characterization of maximally random jammed sphere packings. III. Transport and electromagnetic properties via correlation functions. Phys Rev E 2018; 97:012118. [PMID: 29448326 DOI: 10.1103/physreve.97.012118] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2017] [Indexed: 06/08/2023]
Abstract
In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral functions, hole probabilities, and local density fluctuations. From the remarkable structural features of the MRJ packings, especially its disordered hyperuniformity, exceptional physical properties can be expected. Here we employ these structural descriptors to estimate effective transport and electromagnetic properties via rigorous bounds, exact expansions, and accurate analytical approximation formulas. These property formulas include interfacial bounds as well as universal scaling laws for the mean survival time and the fluid permeability. We also estimate the principal relaxation time associated with Brownian motion among perfectly absorbing traps. For the propagation of electromagnetic waves in the long-wavelength limit, we show that a dispersion of dielectric MRJ spheres within a matrix of another dielectric material forms, to a very good approximation, a dissipationless disordered and isotropic two-phase medium for any phase dielectric contrast ratio. We compare the effective properties of the MRJ sphere packings to those of overlapping spheres, equilibrium hard-sphere packings, and lattices of hard spheres. Moreover, we generalize results to micro- and macroscopically anisotropic packings of spheroids with tensorial effective properties. The analytic bounds predict the qualitative trend in the physical properties associated with these structures, which provides guidance to more time-consuming simulations and experiments. They especially provide impetus for experiments to design materials with unique bulk properties resulting from hyperuniformity, including structural-color and color-sensing applications.
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Affiliation(s)
- Michael A Klatt
- Institute of Stochastics, Department of Mathematics, Karlsruhe Institute of Technology, Englerstraße 2, 76131 Karlsruhe, Germany
| | - Salvatore Torquato
- Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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21
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Ricouvier J, Pierrat R, Carminati R, Tabeling P, Yazhgur P. Optimizing Hyperuniformity in Self-Assembled Bidisperse Emulsions. Phys Rev Lett 2017; 119:208001. [PMID: 29219379 DOI: 10.1103/physrevlett.119.208001] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2017] [Indexed: 06/07/2023]
Abstract
We study long range density fluctuations (hyperuniformity) in two-dimensional jammed packings of bidisperse droplets. Taking advantage of microfluidics, we systematically span a large range of size and concentration ratios of the two droplet populations. We identify various defects increasing long range density fluctuations mainly due to organization of local particle environment. By choosing an appropriate bidispersity, we fabricate materials with a high level of hyperuniformity. Interesting transparency properties of these optimized materials are established based on numerical simulations.
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Affiliation(s)
- Joshua Ricouvier
- ESPCI Paris, PSL Research University, CNRS, IPGG, MMN, 6 rue Jean Calvin, F-75005 Paris, France
| | - Romain Pierrat
- ESPCI Paris, PSL Research University, CNRS, Institut Langevin, 1 rue Jussieu, F-75005 Paris, France
| | - Rémi Carminati
- ESPCI Paris, PSL Research University, CNRS, Institut Langevin, 1 rue Jussieu, F-75005 Paris, France
| | - Patrick Tabeling
- ESPCI Paris, PSL Research University, CNRS, IPGG, MMN, 6 rue Jean Calvin, F-75005 Paris, France
| | - Pavel Yazhgur
- ESPCI Paris, PSL Research University, CNRS, IPGG, MMN, 6 rue Jean Calvin, F-75005 Paris, France
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22
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Abstract
A hyperuniform random heterogeneous material is one in which the local volume fraction fluctuations in an observation window decay faster than the reciprocal window volume as the window size increases. Recent studies show that this class of materials are endowed with superior physical properties such as large isotropic photonic band gaps and optimal transport properties. Here we employ a stochastic optimization procedure to systematically generate realizations of hyperuniform heterogeneous materials with controllable short-range order, which is partially quantified using the two-point correlation function S_{2}(r) associated with the phase of interest. Specifically, our procedure generalizes the widely used Yeong-Torquato reconstruction procedure by including an additional constraint for hyperuniformity, i.e., the volume integral of the autocovariance function χ(r)=S_{2}(r)-ϕ^{2} over the whole space is zero. In addition, we only require the reconstructed S_{2} to match the target function up to a certain cutoff distance γ, in order to give the system sufficient degrees of freedom to satisfy the hyperuniform condition. By systematically increasing the γ value for a given S_{2}, one can produce a spectrum of hyperuniform heterogeneous materials with varying degrees of partial short-range order compatible with the specified S_{2}. The mechanical performance including both elastic and brittle fracture behaviors of the generated hyperuniform materials is analyzed using a volume-compensated lattice-particle method. For the purpose of comparison, the corresponding nonhyperuniform materials with the same short-range order (i.e., with S_{2} constrained up to the same γ value) are also constructed and their mechanical performance is analyzed. Here we consider two specific S_{2} including the positive exponential decay function and the correlation function associated with an equilibrium hard-sphere system. For the constructed systems associated with these two specific functions, we find that although the hyperuniform materials are softer than their nonhyperuniform counterparts, the former generally possess a significantly higher brittle fracture strength than the latter. This superior mechanical behavior is attributed to the lower degree of stress concentration in the material resulting from the hyperuniform microstructure, which is crucial to crack initiation and propagation.
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Affiliation(s)
- Yaopengxiao Xu
- Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - Shaohua Chen
- Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - Pei-En Chen
- Mechanical Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - Wenxiang Xu
- Institute of Soft Matter Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 211100, People's Republic of China
| | - Yang Jiao
- Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA
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23
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Abstract
We introduce the concept of a "hyperuniformity disorder length" h that controls the variance of volume fraction fluctuations for randomly placed windows of fixed size. In particular, fluctuations are determined by the average number of particles within a distance h from the boundary of the window. We first compute special expectations and bounds in d dimensions, and then illustrate the range of behavior of h versus window size L by analyzing several different types of simulated two-dimensional pixel patterns-where particle positions are stored as a binary digital image in which pixels have value zero if empty and one if they contain a particle. The first are random binomial patterns, where pixels are randomly flipped from zero to one with probability equal to area fraction. These have long-ranged density fluctuations, and simulations confirm the exact result h=L/2. Next we consider vacancy patterns, where a fraction f of particles on a lattice are randomly removed. These also display long-range density fluctuations, but with h=(L/2)(f/d) for small f, and h=L/2 for f→1. And finally, for a hyperuniform system with no long-range density fluctuations, we consider "Einstein patterns," where each particle is independently displaced from a lattice site by a Gaussian-distributed amount. For these, at large L,h approaches a constant equal to about half the root-mean-square displacement in each dimension. Then we turn to gray-scale pixel patterns that represent simulated arrangements of polydisperse particles, where the volume of a particle is encoded in the value of its central pixel. And we discuss the continuum limit of point patterns, where pixel size vanishes. In general, we thus propose to quantify particle configurations not just by the scaling of the density fluctuation spectrum but rather by the real-space spectrum of h(L) versus L. We call this approach "hyperuniformity disorder length spectroscopy".
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Affiliation(s)
- A T Chieco
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA
| | - R Dreyfus
- Complex Assemblies of Soft Matter, CNRS-Solvay-UPenn UMI 3254, Bristol, Pennsylvania 19007-3624, USA
| | - D J Durian
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA
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24
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Abstract
The concept of a hyperuniformity disorder length h was recently introduced for analyzing volume fraction fluctuations for a set of measuring windows [Chieco et al., Phys. Rev. E 96, 032909 (2017).PLEEE81539-375510.1103/PhysRevE.96.032909]. This length permits a direct connection to the nature of disorder in the spatial configuration of the particles and provides a way to diagnose the degree of hyperuniformity in terms of the scaling of h and its value in comparison with established bounds. Here, this approach is generalized for extended particles, which are larger than the image resolution and can lie partially inside and partially outside the measuring windows. The starting point is an expression for the relative volume fraction variance in terms of four distinct volumes: that of the particle, the measuring window, the mean-squared overlap between particle and region, and the region over which particles have nonzero overlap with the measuring window. After establishing limiting behaviors for the relative variance, computational methods are developed for both continuum and pixelated particles. Exact results are presented for particles of special shape and for measuring windows of special shape, for which the equations are tractable. Comparison is made for other particle shapes, using simulated Poisson patterns. And the effects of polydispersity and image errors are discussed. For small measuring windows, both particle shape and spatial arrangement affect the form of the variance. For large regions, the variance scaling depends only on arrangement but particle shape sets the numerical proportionality. The combined understanding permit the measured variance to be translated to the spectrum of hyperuniformity lengths versus region size, as the quantifier of spatial arrangement. This program is demonstrated for a system of nonoverlapping particles at a series of increasing packing fractions as well as for an Einstein pattern of particles with several different extended shapes.
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Affiliation(s)
- D J Durian
- Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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25
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Abstract
We numerically analyze the density field of three-dimensional randomly jammed packings of monodisperse soft frictionless spherical particles, paying special attention to fluctuations occurring at large length scales. We study in detail the two-point static structure factor at low wave vectors in Fourier space. We also analyze the nature of the density field in real space by studying the large-distance behavior of the two-point pair correlation function, of density fluctuations in subsystems of increasing sizes, and of the direct correlation function. We show that such real space analysis can be greatly improved by introducing a coarse-grained density field to disentangle genuine large-scale correlations from purely local effects. Our results confirm that both Fourier and real space signatures of vanishing density fluctuations at large scale are absent, indicating that randomly jammed packings are not hyperuniform. In addition, we establish that the pair correlation function displays a surprisingly complex structure at large distances, which is however not compatible with the long-range negative correlation of hyperuniform systems but fully compatible with an analytic form for the structure factor. This implies that the direct correlation function is short ranged, as we also demonstrate directly. Our results reveal that density fluctuations in jammed packings do not follow the behavior expected for random hyperuniform materials, but display instead a more complex behavior.
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Affiliation(s)
- Atsushi Ikeda
- Graduate School of Arts and Sciences, University of Tokyo, Komaba, Tokyo 153-8902, Japan
| | - Ludovic Berthier
- Laboratoire Charles Coulomb, UMR 5221, Centre National de la Recherche Scientifique and Université de Montpellier, 34095 Montpellier, France
| | - Giorgio Parisi
- Dipartimento di Fisica, Università Degli Studi di Roma La Sapienza, Nanotec, Consiglio Nazionale delle Ricerche, UOS Rome, Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Piazzale A. Moro 2, 00185 Rome, Italy
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26
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Zhang G, Stillinger FH, Torquato S. Transport, geometrical, and topological properties of stealthy disordered hyperuniform two-phase systems. J Chem Phys 2016; 145:244109. [DOI: 10.1063/1.4972862] [Citation(s) in RCA: 43] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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27
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Zhang G, Stillinger FH, Torquato S. The Perfect Glass Paradigm: Disordered Hyperuniform Glasses Down to Absolute Zero. Sci Rep 2016; 6:36963. [PMID: 27892452 PMCID: PMC5125002 DOI: 10.1038/srep36963] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2016] [Accepted: 10/24/2016] [Indexed: 01/06/2023] Open
Abstract
Rapid cooling of liquids below a certain temperature range can result in a transition to glassy states. The traditional understanding of glasses includes their thermodynamic metastability with respect to crystals. However, here we present specific examples of interactions that eliminate the possibilities of crystalline and quasicrystalline phases, while creating mechanically stable amorphous glasses down to absolute zero temperature. We show that this can be accomplished by introducing a new ideal state of matter called a "perfect glass". A perfect glass represents a soft-interaction analog of the maximally random jammed (MRJ) packings of hard particles. These latter states can be regarded as the epitome of a glass since they are out of equilibrium, maximally disordered, hyperuniform, mechanically rigid with infinite bulk and shear moduli, and can never crystallize due to configuration-space trapping. Our model perfect glass utilizes two-, three-, and four-body soft interactions while simultaneously retaining the salient attributes of the MRJ state. These models constitute a theoretical proof of concept for perfect glasses and broaden our fundamental understanding of glass physics. A novel feature of equilibrium systems of identical particles interacting with the perfect-glass potential at positive temperature is that they have a non-relativistic speed of sound that is infinite.
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Affiliation(s)
- G. Zhang
- Department of Chemistry, Princeton University, Princeton, 08540, USA
| | - F. H. Stillinger
- Department of Chemistry, Princeton University, Princeton, 08540, USA
| | - S. Torquato
- Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, 08540, USA
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28
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Abstract
Disordered hyperuniform many-body systems are distinguishable states of matter that lie between a crystal and liquid: they are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks. These systems play a vital role in a number of fundamental and applied problems: glass formation, jamming, rigidity, photonic and electronic band structure, localization of waves and excitations, self-organization, fluid dynamics, quantum systems, and pure mathematics. Much of what we know theoretically about disordered hyperuniform states of matter involves many-particle systems. In this paper, we derive new rigorous criteria that disordered hyperuniform two-phase heterogeneous materials must obey and explore their consequences. Two-phase heterogeneous media are ubiquitous; examples include composites and porous media, biological media, foams, polymer blends, granular media, cellular solids, and colloids. We begin by obtaining some results that apply to hyperuniform two-phase media in which one phase is a sphere packing in d-dimensional Euclidean space [Formula: see text]. Among other results, we rigorously establish the requirements for packings of spheres of different sizes to be 'multihyperuniform'. We then consider hyperuniformity for general two-phase media in [Formula: see text]. Here we apply realizability conditions for an autocovariance function and its associated spectral density of a two-phase medium, and then incorporate hyperuniformity as a constraint in order to derive new conditions. We show that some functional forms can immediately be eliminated from consideration and identify other forms that are allowable. Specific examples and counterexamples are described. Contact is made with well-known microstructural models (e.g. overlapping spheres and checkerboards) as well as irregular phase-separation and Turing-type patterns. We also ascertain a family of autocovariance functions (or spectral densities) that are realizable by disordered hyperuniform two-phase media in any space dimension, and present select explicit constructions of realizations. These studies provide insight into the nature of disordered hyperuniformity in the context of heterogeneous materials and have implications for the design of such novel amorphous materials.
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Affiliation(s)
- Salvatore Torquato
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA. Department of Physics, Princeton University, Princeton, NJ 08544, USA. Princeton Institute for the Science and Technology of Materials, Princeton, NJ 08544, USA. Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA
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29
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Abstract
Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystal and liquid: They are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks. These exotic states of matter play a vital role in a number of problems across the physical, mathematical as well as biological sciences and, because they are endowed with novel physical properties, have technological importance. Given the fundamental as well as practical importance of disordered hyperuniform systems elucidated thus far, it is natural to explore the generalizations of the hyperuniformity notion and its consequences. In this paper, we substantially broaden the hyperuniformity concept along four different directions. This includes generalizations to treat fluctuations in the interfacial area (one of the Minkowski functionals) in heterogeneous media and surface-area driven evolving microstructures, random scalar fields, divergence-free random vector fields, and statistically anisotropic many-particle systems and two-phase media. In all cases, the relevant mathematical underpinnings are formulated and illustrative calculations are provided. Interfacial-area fluctuations play a major role in characterizing the microstructure of two-phase systems (e.g., fluid-saturated porous media), physical properties that intimately depend on the geometry of the interface, and evolving two-phase microstructures that depend on interfacial energies (e.g., spinodal decomposition). In the instances of random vector fields and statistically anisotropic structures, we show that the standard definition of hyperuniformity must be generalized such that it accounts for the dependence of the relevant spectral functions on the direction in which the origin in Fourier space is approached (nonanalyticities at the origin). Using this analysis, we place some well-known energy spectra from the theory of isotropic turbulence in the context of this generalization of hyperuniformity. Among other results, we show that there exist many-particle ground-state configurations in which directional hyperuniformity imparts exotic anisotropic physical properties (e.g., elastic, optical, and acoustic characteristics) to these states of matter. Such tunability could have technological relevance for manipulating light and sound waves in ways heretofore not thought possible. We show that disordered many-particle systems that respond to external fields (e.g., magnetic and electric fields) are a natural class of materials to look for directional hyperuniformity. The generalizations of hyperuniformity introduced here provide theoreticians and experimentalists new avenues to understand a very broad range of phenomena across a variety of fields through the hyperuniformity "lens."
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Affiliation(s)
- Salvatore Torquato
- Department of Chemistry, Department of Physics, Princeton Center for Theoretical Science, Program of Applied and Computational Mathematics, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
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Klatt MA, Torquato S. Characterization of maximally random jammed sphere packings. II. Correlation functions and density fluctuations. Phys Rev E 2016; 94:022152. [PMID: 27627291 DOI: 10.1103/physreve.94.022152] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2016] [Indexed: 06/06/2023]
Abstract
In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales. In the present paper, we determine a variety of different correlation functions that arise in rigorous expressions for the effective physical properties of MRJ sphere packings and compare them to the corresponding statistical descriptors for overlapping spheres and equilibrium hard-sphere systems. Such structural descriptors arise in rigorous bounds and formulas for effective transport properties, diffusion and reactions constants, elastic moduli, and electromagnetic characteristics. First, we calculate the two-point, surface-void, and surface-surface correlation functions, for which we derive explicit analytical formulas for finite hard-sphere packings. We show analytically how the contact Dirac delta function contribution to the pair correlation function g_{2}(r) for MRJ packings translates into distinct functional behaviors of these two-point correlation functions that do not arise in the other two models examined here. Then we show how the spectral density distinguishes the MRJ packings from the other disordered systems in that the spectral density vanishes in the limit of infinite wavelengths; i.e., these packings are hyperuniform, which means that density fluctuations on large length scales are anomalously suppressed. Moreover, for all model systems, we study and compute exclusion probabilities and pore size distributions, as well as local density fluctuations. We conjecture that for general disordered hard-sphere packings, a central limit theorem holds for the number of points within an spherical observation window. Our analysis links problems of interest in material science, chemistry, physics, and mathematics. In the third paper of this series, we will evaluate bounds and estimates of a host of different physical properties of the MRJ sphere packings that are based on the structural characteristics analyzed in this paper.
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Affiliation(s)
- Michael A Klatt
- Karlsruhe Institute of Technology (KIT), Institute of Stochastics, Englerstraße 2, 76131 Karlsruhe, Germany
| | - Salvatore Torquato
- Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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Abstract
Hyperuniformity characterizes a state of matter that is poised at a critical point at which density or volume-fraction fluctuations are anomalously suppressed at infinite wavelengths. Recently, much attention has been given to the link between strict jamming (mechanical rigidity) and (effective or exact) hyperuniformity in frictionless hard-particle packings. However, in doing so, one must necessarily study very large packings in order to access the long-ranged behavior and to ensure that the packings are truly jammed. We modify the rigorous linear programming method of Donev et al. [J. Comput. Phys. 197, 139 (2004)JCTPAH0021-999110.1016/j.jcp.2003.11.022] in order to test for jamming in putatively collectively and strictly jammed packings of hard disks in two dimensions. We show that this rigorous jamming test is superior to standard ways to ascertain jamming, including the so-called "pressure-leak" test. We find that various standard packing protocols struggle to reliably create packings that are jammed for even modest system sizes of N≈10^{3} bidisperse disks in two dimensions; importantly, these packings have a high reduced pressure that persists over extended amounts of time, meaning that they appear to be jammed by conventional tests, though rigorous jamming tests reveal that they are not. We present evidence that suggests that deviations from hyperuniformity in putative maximally random jammed (MRJ) packings can in part be explained by a shortcoming of the numerical protocols to generate exactly jammed configurations as a result of a type of "critical slowing down" as the packing's collective rearrangements in configuration space become locally confined by high-dimensional "bottlenecks" from which escape is a rare event. Additionally, various protocols are able to produce packings exhibiting hyperuniformity to different extents, but this is because certain protocols are better able to approach exactly jammed configurations. Nonetheless, while one should not generally expect exact hyperuniformity for disordered packings with rattlers, we find that when jamming is ensured, our packings are very nearly hyperuniform, and deviations from hyperuniformity correlate with an inability to ensure jamming, suggesting that strict jamming and hyperuniformity are indeed linked. This raises the possibility that the ideal MRJ packings have no rattlers. Our work provides the impetus for the development of packing algorithms that produce large disordered strictly jammed packings that are rattler free, which is an outstanding, challenging task.
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Affiliation(s)
- Steven Atkinson
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Ge Zhang
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - Adam B Hopkins
- Uniformity Labs, 1600 Adams Drive, Suite 104, Menlo Park, California 94025, USA
| | - Salvatore Torquato
- Department of Chemistry, Department of Physics, Princeton Center for Theoretical Science, Program of Applied and Computational Mathematics, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
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Kurita R. Experimental study of the relationship between local particle-size distributions and local ordering in random close packing. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 92:062305. [PMID: 26764690 DOI: 10.1103/physreve.92.062305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2015] [Indexed: 06/05/2023]
Abstract
We experimentally study the structural properties of a sediment of size distributed colloids. By determining each particle size using a size estimation algorithm, we are able to investigate the relationship between local environment and local ordering. Our results show that ordered environments of particles tend to generate where the local particle-size distribution is within 5%. In addition, we show that particles whose size is close to the average size have 12 coordinate neighbors, which matches the coordination number of the fcc and hcp crystals. On the other hand, bcc structures are observed around larger particles. Our results represent experiments to show a size dependence of the specific ordering in colloidal systems.
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Affiliation(s)
- Rei Kurita
- Department of Physics, Tokyo Metropolitan University, Tokyo 192-0397, Japan
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Zito G, Rusciano G, Pesce G, Malafronte A, Di Girolamo R, Ausanio G, Vecchione A, Sasso A. Nanoscale engineering of two-dimensional disordered hyperuniform block-copolymer assemblies. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 92:050601. [PMID: 26651630 DOI: 10.1103/physreve.92.050601] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2015] [Indexed: 06/05/2023]
Abstract
Disordered hyperuniform (DH) media have been recognized as a new state of disordered matter that broadens our vision of material engineering. Here, long-range correlated disordered two-dimensional patterns are fabricated by self-assembling of spherical diblock-copolymer (BCP) micelles. Control of the self-assembling parameters leads to the formation of DH patterns of micelles that can host nanoscale material inclusions, therefore providing an effective strategy for fabricating multimaterial DH structures at molecular scale. Centroidal patterns are accurately determined by virtue of BCP micelles loaded with metal nanoparticles. Our analysis reveals the signature of nearly ideal DH BCP assemblies in the local density fluctuation and a dominant linear scaling in the local number fluctuation.
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Affiliation(s)
- Gianluigi Zito
- Università degli Studi di Napoli Federico II, via Cintia I-80126 Napoli, Italy
| | - Giulia Rusciano
- Università degli Studi di Napoli Federico II, via Cintia I-80126 Napoli, Italy
| | - Giuseppe Pesce
- Università degli Studi di Napoli Federico II, via Cintia I-80126 Napoli, Italy
| | - Anna Malafronte
- Università degli Studi di Napoli Federico II, via Cintia I-80126 Napoli, Italy
| | - Rocco Di Girolamo
- Università degli Studi di Napoli Federico II, via Cintia I-80126 Napoli, Italy
| | - Giovanni Ausanio
- Università degli Studi di Napoli Federico II, via Cintia I-80126 Napoli, Italy
- Consiglio Nazionale delle Ricerche-SPIN, via Cintia I-80126 Napoli, Italy
| | - Antonio Vecchione
- Università degli Studi di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (Sa), Italy
- Consiglio Nazionale delle Ricerche-SPIN U.O.S Salerno, via Giovanni Paolo II 132, 84084 Fisciano (Sa), Italy
| | - Antonio Sasso
- Università degli Studi di Napoli Federico II, via Cintia I-80126 Napoli, Italy
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Zhang G, Stillinger FH, Torquato S. Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 92:022119. [PMID: 26382356 DOI: 10.1103/physreve.92.022119] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2015] [Indexed: 06/05/2023]
Abstract
Systems of particles interacting with "stealthy" pair potentials have been shown to possess infinitely degenerate disordered hyperuniform classical ground states with novel physical properties. Previous attempts to sample the infinitely degenerate ground states used energy minimization techniques, introducing algorithmic dependence that is artificial in nature. Recently, an ensemble theory of stealthy hyperuniform ground states was formulated to predict the structure and thermodynamics that was shown to be in excellent agreement with corresponding computer simulation results in the canonical ensemble (in the zero-temperature limit). In this paper, we provide details and justifications of the simulation procedure, which involves performing molecular dynamics simulations at sufficiently low temperatures and minimizing the energy of the snapshots for both the high-density disordered regime, where the theory applies, as well as lower densities. We also use numerical simulations to extend our study to the lower-density regime. We report results for the pair correlation functions, structure factors, and Voronoi cell statistics. In the high-density regime, we verify the theoretical ansatz that stealthy disordered ground states behave like "pseudo" disordered equilibrium hard-sphere systems in Fourier space. The pair statistics obey certain exact integral conditions with very high accuracy. These results show that as the density decreases from the high-density limit, the disordered ground states in the canonical ensemble are characterized by an increasing degree of short-range order and eventually the system undergoes a phase transition to crystalline ground states. In the crystalline regime (low densities), there exist aperiodic structures that are part of the ground-state manifold but yet are not entropically favored. We also provide numerical evidence suggesting that different forms of stealthy pair potentials produce the same ground-state ensemble in the zero-temperature limit. Our techniques may be applied to sample the zero-temperature limit of the canonical ensemble of other potentials with highly degenerate ground states.
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Affiliation(s)
- G Zhang
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - F H Stillinger
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - S Torquato
- Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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Ikeda A, Berthier L. Thermal fluctuations, mechanical response, and hyperuniformity in jammed solids. Phys Rev E Stat Nonlin Soft Matter Phys 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] [What about the content of this article? (0)] [Affiliation(s)] [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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Dreyfus R, Xu Y, Still T, Hough LA, Yodh AG, Torquato S. Diagnosing hyperuniformity in two-dimensional, disordered, jammed packings of soft spheres. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 91:012302. [PMID: 25679618 DOI: 10.1103/physreve.91.012302] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2014] [Indexed: 06/04/2023]
Abstract
Hyperuniformity characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. However, the task of determining whether or not an image of an experimental system is hyperuniform is experimentally challenging due to finite-resolution, noise, and sample-size effects that influence characterization measurements. Here we explore these issues, employing video optical microscopy to study hyperuniformity phenomena in disordered two-dimensional jammed packings of soft spheres. Using a combination of experiment and simulation we characterize the possible adverse effects of particle polydispersity, image noise, and finite-size effects on the assignment of hyperuniformity, and we develop a methodology that permits improved diagnosis of hyperuniformity from real-space measurements. The key to this improvement is a simple packing reconstruction algorithm that incorporates particle polydispersity to minimize the free volume. In addition, simulations show that hyperuniformity in finite-sized samples can be ascertained more accurately in direct space than in reciprocal space. Finally, our experimental colloidal packings of soft polymeric spheres are shown to be effectively hyperuniform.
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Affiliation(s)
- Remi Dreyfus
- Complex Assemblies of Soft Matter, CNRS-Rhodia-UPenn UMI 3254, Bristol, Pennsylvania 19007-3624, USA
| | - Ye Xu
- Complex Assemblies of Soft Matter, CNRS-Rhodia-UPenn UMI 3254, Bristol, Pennsylvania 19007-3624, USA and Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA
| | - Tim Still
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA
| | - L A Hough
- Complex Assemblies of Soft Matter, CNRS-Rhodia-UPenn UMI 3254, Bristol, Pennsylvania 19007-3624, USA
| | - A G Yodh
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA
| | - Salvatore Torquato
- Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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Hopkins AB, Stillinger FH, Torquato S. Disordered strictly jammed binary sphere packings attain an anomalously large range of densities. Phys Rev E Stat Nonlin Soft Matter Phys 2013; 88:022205. [PMID: 24032826 DOI: 10.1103/physreve.88.022205] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2013] [Indexed: 06/02/2023]
Abstract
Previous attempts to simulate disordered binary sphere packings have been limited in producing mechanically stable, isostatic packings across a broad spectrum of packing fractions. Here we report that disordered strictly jammed binary packings (packings that remain mechanically stable under general shear deformations and compressions) can be produced with an anomalously large range of average packing fractions 0.634≤φ≤0.829 for small to large sphere radius ratios α restricted to α≥0.100. Surprisingly, this range of average packing fractions is obtained for packings containing a subset of spheres (called the backbone) that are exactly strictly jammed, exactly isostatic, and also generated from random initial conditions. Additionally, the average packing fractions of these packings at certain α and small sphere relative number concentrations x approach those of the corresponding densest known ordered packings. These findings suggest for entropic reasons that these high-density disordered packings should be good glass formers and that they may be easy to prepare experimentally. We also identify an unusual feature of the packing fraction of jammed backbones (packings with rattlers excluded). The backbone packing fraction is about 0.624 over the majority of the α-x plane, even when large numbers of small spheres are present in the backbone. Over the (relatively small) area of the α-x plane where the backbone is not roughly constant, we find that backbone packing fractions range from about 0.606 to 0.829, with the volume of rattler spheres comprising between 1.6% and 26.9% of total sphere volume. To generate isostatic strictly jammed packings, we use an implementation of the Torquato-Jiao sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010)], which is an efficient producer of inherent structures (mechanically stable configurations at the local maxima in the density landscape). The identification and explicit construction of binary packings with such high packing fractions could have important practical implications for granular composites where density is critical both to material properties and fabrication cost, including for solid propellants, concrete, and ceramics. The densities and structures of jammed binary packings at various α and x are also relevant to the formation of a glass phase in multicomponent metallic systems.
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Affiliation(s)
- Adam B Hopkins
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
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Kurita R, Ruffner DB, Weeks ER. Measuring the size of individual particles from three-dimensional imaging experiments. Nat Commun 2012; 3:1127. [DOI: 10.1038/ncomms2114] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2012] [Accepted: 09/04/2012] [Indexed: 12/21/2022] Open
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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.
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Affiliation(s)
- Gary L Hunter
- Department of Physics, Emory University, Math and Science Center 400 Dowman Dr., N201 Atlanta, GA 30322, USA
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Jiao Y, Torquato S. Maximally random jammed packings of Platonic solids: hyperuniform long-range correlations and isostaticity. Phys Rev E Stat Nonlin Soft Matter Phys 2011; 84:041309. [PMID: 22181137 DOI: 10.1103/physreve.84.041309] [Citation(s) in RCA: 80] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2011] [Indexed: 05/31/2023]
Abstract
We generate maximally random jammed (MRJ) packings of the four nontiling Platonic solids (tetrahedra, octahedra, dodecahedra, and icosahedra) using the adaptive-shrinking-cell method [S. Torquato and Y. Jiao, Phys. Rev. E 80, 041104 (2009)]. Such packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The MRJ packing fractions for tetrahedra, octahedra, dodecahedra, and icosahedra are, respectively, 0.763±0.005, 0.697±0.005, 0.716±0.002, and 0.707±0.002. We find that as the number of facets of the particles increases, the translational order in the packings increases while the orientational order decreases. Moreover, we show that the MRJ packings are hyperuniform (i.e., their infinite-wavelength local-number-density fluctuations vanish) and possess quasi-long-range pair correlations that decay asymptotically with scaling r(-4). This provides further evidence that hyperuniform quasi-long-range correlations are a universal feature of MRJ packings of frictionless particles of general shape. However, unlike MRJ packings of ellipsoids, superballs, and superellipsoids, which are hypostatic, MRJ packings of the nontiling Platonic solids are isostatic. We provide a rationale for the organizing principle that the MRJ packing fractions for nonspherical particles with sufficiently small asphericities exceed the corresponding value for spheres (∼0.64). We also discuss how the shape and symmetry of a polyhedron particle affects its MRJ packing fraction.
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Affiliation(s)
- Yang Jiao
- Princeton Institute of the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
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