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Zhuravlyov V, Goree J, Elvati P, Violi A. Finite-size effects in the static structure factor S(k) and S(0) for a two-dimensional Yukawa liquid. Phys Rev E 2023; 108:035211. [PMID: 37849136 DOI: 10.1103/physreve.108.035211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2023] [Accepted: 08/29/2023] [Indexed: 10/19/2023]
Abstract
Finite-size effects in the static structure factor S(k) are analyzed for an amorphous substance. As the number of particles is reduced, S(0) increases greatly, up to an order of magnitude. Meanwhile, there is a decrease in the height of the first peak S_{peak}. These finite-size effects are modeled accurately by the Binder formula for S(0) and our empirical formula for S_{peak}. Procedures are suggested to correct for finite-size effects in S(k) data and in the hyperuniformity index H≡S(0)/S_{peak}. These principles generally apply to S(k) obtained from particle positions in noncrystalline substances. The amorphous substance we simulate is a two-dimensional liquid, with a soft Yukawa interaction modeling a dusty plasma experiment.
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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
| | - 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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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] [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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Dale JR, Sartor JD, Dennis RC, Corwin EI. Hyperuniform jammed sphere packings have anomalous material properties. Phys Rev E 2022; 106:024903. [PMID: 36109903 DOI: 10.1103/physreve.106.024903] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2022] [Accepted: 07/26/2022] [Indexed: 06/15/2023]
Abstract
A spatial distribution is hyperuniform if it has local density fluctuations that vanish in the limit of long length scales. Hyperuniformity is a well known property of both crystals and quasicrystals. Of recent interest, however, is disordered hyperuniformity: the presence of hyperuniform scaling without long-range configurational order. Jammed granular packings have been proposed as an example of disordered hyperuniformity, but recent numerical investigation has revealed that many jammed systems instead exhibit a complex set of distinct behaviors at long, emergent length scales. We use the Voronoi tessellation as a tool to define a set of rescaling transformations that can impose hyperuniformity on an arbitrary weighted point process, and show that these transformations can be used in simulations to iteratively generate hyperuniform, mechanically stable packings of athermal soft spheres. These hyperuniform jammed packings display atypical mechanical properties, particularly in the low-frequency phononic excitations, which exhibit an isolated band of highly collective modes and a band gap around zero frequency.
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Affiliation(s)
- Jack R Dale
- Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA
| | - James D Sartor
- Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA
| | - R Cameron Dennis
- Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA
| | - Eric I Corwin
- Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA
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Self-assembly in binary mixtures of spherical colloids. Adv Colloid Interface Sci 2022; 308:102748. [DOI: 10.1016/j.cis.2022.102748] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Revised: 06/16/2022] [Accepted: 07/29/2022] [Indexed: 11/18/2022]
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Yanagishima T, Russo J, Dullens RPA, Tanaka H. Towards Glasses with Permanent Stability. PHYSICAL REVIEW LETTERS 2021; 127:215501. [PMID: 34860078 DOI: 10.1103/physrevlett.127.215501] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2021] [Revised: 06/30/2021] [Accepted: 10/11/2021] [Indexed: 06/13/2023]
Abstract
Unlike crystals, glasses age or devitrify over time, reflecting their nonequilibrium nature. This lack of stability is a serious issue in many industrial applications. Here, we show by numerical simulations that the devitrification of quasi-hard-sphere glasses is prevented by suppressing volume-fraction inhomogeneities. A monodisperse glass known to devitrify with "avalanchelike" intermittent dynamics is subjected to small iterative adjustments to particle sizes to make the local volume fractions spatially uniform. We find that this entirely prevents structural relaxation and devitrification over aging time scales, even in the presence of crystallites. There is a dramatic homogenization in the number of load-bearing nearest neighbors each particle has, indicating that ultrastable glasses may be formed via "mechanical homogenization." Our finding provides a physical principle for glass stabilization and opens a novel route to the formation of mechanically stabilized glasses.
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Affiliation(s)
- Taiki Yanagishima
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QZ, United Kingdom
- Department of Physics, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan
| | - John Russo
- Department of Physics, Sapienza University of Rome, P. le Aldo Moro 5, 00185 Rome, Italy
| | - Roel P A Dullens
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QZ, United Kingdom
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
| | - Hajime Tanaka
- Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
- Research Center for Advanced Science and Technology, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
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Ma Z, Lomba E, Torquato S. Optimized Large Hyperuniform Binary Colloidal Suspensions in Two Dimensions. PHYSICAL REVIEW LETTERS 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] [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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Kim J, Torquato S. Methodology to construct large realizations of perfectly hyperuniform disordered packings. Phys Rev E 2019; 99:052141. [PMID: 31212467 DOI: 10.1103/physreve.99.052141] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2019] [Indexed: 01/26/2023]
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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