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Skye RS, Teich EG, Dshemuchadse J. Tuning assembly structures of hard shapes in confinement via interface curvature. SOFT MATTER 2022; 18:6782-6790. [PMID: 35876270 DOI: 10.1039/d2sm00545j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Assembly in confinement is a problem of great interest in colloidal structure design, plasmonics, photonics, and industrial packaging. Along with the range of design choices provided by particle shape and attraction or repulsion, confined systems add an additional layer of complexity through the interactions between particles and the container holding them. The range of possible behaviors produced by these systems remains largely unexplored, yet has profound consequences on the resultant assembled structure. Here, we address this problem by exploring how the assembly of hard tetrahedral particles is affected by a spherical container. We simulate particle assemblies in containers holding 4 to 10 000 particles and analyze the range of resultant structures. We find that the presence of a curved wall causes organization into distinct concentric shells in containers holding up to thousands of particles. In addition, we see that wall curvature affects structural motifs in systems as large as 10 000 particles, promoting local environments that maximally conform to the wall and providing a seed for the propagation of these motifs into the interior of the container. Through this work, we show how confining interfaces can be used to promote the assembly of structures markedly distinct from those seen in the more commonly studied bulk systems.
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Affiliation(s)
- Rachael S Skye
- Department of Materials Science and Engineering, Cornell University, USA.
| | - Erin G Teich
- Department of Bioengineering, University of Pennsylvania, USA
| | - Julia Dshemuchadse
- Department of Materials Science and Engineering, Cornell University, USA.
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2
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Zarif M, Spiteri RJ, Bowles RK. Inherent structure landscape of hard spheres confined to narrow cylindrical channels. Phys Rev E 2021; 104:064602. [PMID: 35030837 DOI: 10.1103/physreve.104.064602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2021] [Accepted: 11/10/2021] [Indexed: 06/14/2023]
Abstract
The inherent structure landscape for a system of hard spheres confined to a hard cylindrical channel, such that spheres can only contact their first and second neighbors, is studied using an analytical model that extends previous results [Phys. Rev. Lett. 115, 025702 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.025702] to provide a comprehensive picture of jammed packings over a range of packing densities. In the model, a packing is described as an arrangement of k helical sections, separated by defects, that have alternating helical twist directions and where all spheres satisfy local jamming constraints. The structure of each helical section is determined by a single helical twist angle, and a jammed packing is obtained by minimizing the length of the channel per particle with respect to the k helical section angles. An analysis of a small system of N=20 spheres shows that the basins on the inherent structure landscape associated with these helical arrangements split into a number of distinct jammed states separated by low barriers giving rise to a degree of hierarchical organization. The model accurately predicts the geometric properties of packings generated using the Lubachevsky and Stillinger compression scheme (N=10^{4}) and provides insight into the nature of the probability distribution of helical section lengths.
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Affiliation(s)
- Mahdi Zarif
- Department of Physical and Computational Chemistry, Shahid Beheshti University, Tehran 19839-9411, Iran
| | - Raymond J Spiteri
- Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5C9, Canada
| | - Richard K Bowles
- Department of Chemistry, University of Saskatchewan, SK, S7N 5C9, Canada
- Centre for Quantum Topology and its Applications (quanTA), University of Saskatchewan, SK S7N 5E6, Canada
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3
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Koshoji R, Ozaki T. Densest ternary sphere packings. Phys Rev E 2021; 104:024101. [PMID: 34525636 DOI: 10.1103/physreve.104.024101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 07/08/2021] [Indexed: 11/07/2022]
Abstract
We present our exhaustive exploration of the densest ternary sphere packings (DTSPs) for 45 radius ratios and 237 kinds of compositions, which is a packing problem of three kinds of hard spheres with different radii, under periodic boundary conditions by a random structure searching method. To efficiently explore DTSPs we further develop the searching method based on the piling-up and iterative balance methods [Koshoji et al., Phys. Rev. E 103, 023307 (2021)2470-004510.1103/PhysRevE.103.023307]. The unbiased exploration identifies diverse 38 putative DTSPs appearing on phase diagrams in which 37 DTSPs of them are discovered in the study. The structural trend of DTSPs changes depending especially on the radius of small spheres. In case that the radius of small spheres is relatively small, structures of many DTSPs can be understood as derivatives of densest binary sphere packings (DBSPs), while characteristic structures specific to the ternary system emerge as the radius of small spheres becomes larger. In addition to DTSPs, we reveal a lot of semi-DTSPs (SDTSPs) which are obtained by excluding DBSPs in the calculation of phase diagram, and investigate the correspondence of DTSPs and SDTSPs with real crystals based on the space group, showing a considerable correspondence of SDTSPs having high symmetries with real crystals including Cu_{2}GaSr and ThCr_{2}Si_{2} structures. Our study suggests that the diverse structures of DBSPs, DTSPs, and SDTSPs can be effectively used as structural prototypes for searching complex crystal structures.
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Affiliation(s)
- Ryotaro Koshoji
- Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan
| | - Taisuke Ozaki
- Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan
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4
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Mahynski NA, Shen VK. Symmetry-derived structure directing agents for two-dimensional crystals of arbitrary colloids. SOFT MATTER 2021; 17:7853-7866. [PMID: 34382053 PMCID: PMC9793339 DOI: 10.1039/d1sm00875g] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We derive properties of self-assembling rings which can template the organization of an arbitrary colloid into any periodic symmetry in two Euclidean dimensions. By viewing this as a tiling problem, we illustrate how the shape and chemical patterning of these rings are derivable, and are explicitly reflected by the symmetry group's orbifold symbol. We performed molecular dynamics simulations to observe their self-assembly and found 5 different characteristics which could be easily rationalized on the basis of this symbol. These include systems which undergo chiral phase separation, are addressably complex, exhibit self-limiting growth into clusters, form ordered "rods" in only one-dimension akin to a smectic phase, and those from symmetry groups which are pluripotent and allow one to select rings which exhibit different behaviors. We discuss how the curvature of the ring's edges plays an integral role in achieving correct self-assembly, and illustrate how to obtain these shapes. This provides a method for patterning colloidal systems at interfaces without explicitly programming this information onto the colloid itself.
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Affiliation(s)
- Nathan A Mahynski
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, USA.
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5
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Koshoji R, Kawamura M, Fukuda M, Ozaki T. Diverse densest binary sphere packings and phase diagram. Phys Rev E 2021; 103:023307. [PMID: 33736079 DOI: 10.1103/physreve.103.023307] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2020] [Accepted: 01/26/2021] [Indexed: 01/10/2023]
Abstract
We revisit the densest binary sphere packings (DBSPs) under periodic boundary conditions and present an updated phase diagram, including newly found 12 putative densest structures over the x-α plane, where x is the relative concentration and α is the radius ratio of the small and large spheres. To efficiently explore the DBSPs, we develop an unbiased random search approach based on both the piling-up method to generate initial structures in an unbiased way and the iterative balance method to optimize the volume of a unit cell while keeping the overlap of hard spheres minimized. With those two methods, we have discovered 12 putative DBSPs and thereby the phase diagram is updated, while our results are consistent with those of a previous study [Hopkins et al., Phys. Rev. E 85, 021130 (2012)]PLEEE81539-375510.1103/PhysRevE.85.021130 with a small correction for the case of 12 or fewer spheres in the unit cell. Five of the discovered 12 DBSPs are identified in the small radius range of 0.42≤α≤0.50, where several structures are competitive to each other with respect to packing fraction. Through the exhaustive search, diverse dense packings are discovered and, accordingly, we find that packing structures achieve high packing fractions by introducing distortion and/or combining a few local dense structural units. Furthermore, we investigate the correspondence of the DBSPs with crystals based on the space group. The result shows that many structural units in real crystals, e.g., LaH_{10} and SrGe_{2-δ} being high-pressure phases, can be understood as DBSPs. The correspondence implies that the densest sphere packings can be used effectively as structural prototypes for searching complex crystal structures, especially for high-pressure phases.
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Affiliation(s)
- Ryotaro Koshoji
- Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan
| | - Mitsuaki Kawamura
- Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan
| | - Masahiro Fukuda
- Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan
| | - Taisuke Ozaki
- Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan
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6
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Kagan CR, Bassett LC, Murray CB, Thompson SM. Colloidal Quantum Dots as Platforms for Quantum Information Science. Chem Rev 2020; 121:3186-3233. [DOI: 10.1021/acs.chemrev.0c00831] [Citation(s) in RCA: 49] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
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7
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Ren S, Sun Y, Zhang F, Travesset A, Wang CZ, Ho KM. Phase Diagram and Structure Map of Binary Nanoparticle Superlattices from a Lennard-Jones Model. ACS NANO 2020; 14:6795-6802. [PMID: 32479719 DOI: 10.1021/acsnano.0c00250] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
A first-principles prediction of the binary nanoparticle phase diagram assembled by solvent evaporation has eluded theoretical approaches. In this paper, we show that a binary system interacting through the Lennard-Jones (LJ) potential contains all experimental phases in which nanoparticles are effectively described as quasi hard spheres. We report a phase diagram consisting of 53 equilibrium phases, whose stability is quite insensitive to the microscopic details of the potentials, thus giving rise to some type of universality. Furthermore, we show that binary lattices may be understood as consisting of certain particle clusters, i.e., motifs, that provide a generalization of the four conventional Frank-Kasper polyhedral units. Our results show that metastable phases share the very same motifs as equilibrium phases. We discuss the connection with packing models, phase diagrams with repulsive potentials, and the prediction of likely experimental superlattices.
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Affiliation(s)
- Shang Ren
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, United States
- Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011, United States
| | - Yang Sun
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, United States
- Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011, United States
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, United States
| | - Feng Zhang
- Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011, United States
| | - Alex Travesset
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, United States
- Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011, United States
| | - Cai-Zhuang Wang
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, United States
- Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011, United States
| | - Kai-Ming Ho
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, United States
- Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011, United States
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8
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Shu Y, Kono Y, Ohira I, Li Q, Hrubiak R, Park C, Kenney-Benson C, Wang Y, Shen G. Observation of 9-Fold Coordinated Amorphous TiO 2 at High Pressure. J Phys Chem Lett 2020; 11:374-379. [PMID: 31867974 DOI: 10.1021/acs.jpclett.9b03378] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Knowledge of the structure in amorphous dioxides is important in many fields of science and engineering. Here we report new experimental results of high-pressure polyamorphism in amorphous TiO2 (a-TiO2). Our data show that the Ti coordination number (CN) increases from 7.2 ± 0.3 at ∼16 GPa to 8.8 ± 0.3 at ∼70 GPa and finally reaches a plateau at 8.9 ± 0.3 at ≲86 GPa. The evolution of the structural changes under pressure is rationalized by the ratio (γ) of the ionic radius of Ti to that of O. It appears that the CN ≈ 9 plateau correlates with the two 9-fold coordinated polymorphs (cotunnite, Fe2P) with different γ values. This CN-γ relationship is compared with those of a-SiO2 and a-GeO2, displaying remarkably consistent behavior between CN and γ. The unified CN-γ relationship may be generally used to predict the compression behavior of amorphous AO2 compounds under extreme conditions.
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Affiliation(s)
- Yu Shu
- High Pressure Collaborative Access Team, X-ray Science Division , Argonne National Laboratory , Argonne , Illinois 60439 , United States
| | - Yoshio Kono
- Geophysical Laboratory , Carnegie Institution of Washington , Argonne , Illinois 60439 , United States
| | - Itaru Ohira
- Geophysical Laboratory , Carnegie Institution of Washington , Argonne , Illinois 60439 , United States
| | - Quanjun Li
- State Key Laboratory of Superhard Materials , Jilin University , Changchun 130012 , China
| | - Rostislav Hrubiak
- High Pressure Collaborative Access Team, X-ray Science Division , Argonne National Laboratory , Argonne , Illinois 60439 , United States
| | - Changyong Park
- High Pressure Collaborative Access Team, X-ray Science Division , Argonne National Laboratory , Argonne , Illinois 60439 , United States
| | - Curtis Kenney-Benson
- High Pressure Collaborative Access Team, X-ray Science Division , Argonne National Laboratory , Argonne , Illinois 60439 , United States
| | - Yanbin Wang
- Center for Advanced Radiation Sources , The University of Chicago , Chicago , Illinois 60637 , United States
| | - Guoyin Shen
- High Pressure Collaborative Access Team, X-ray Science Division , Argonne National Laboratory , Argonne , Illinois 60439 , United States
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9
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LaCour RA, Adorf CS, Dshemuchadse J, Glotzer SC. Influence of Softness on the Stability of Binary Colloidal Crystals. ACS NANO 2019; 13:13829-13842. [PMID: 31692332 DOI: 10.1021/acsnano.9b04274] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Mixtures of two types of nanoparticles can self-assemble into a wide variety of binary colloidal crystals (also called binary nanoparticle superlattices), which are interesting for their structural diversity and potential applications. Although so-called packing models-which usually treat the particles as "hard" with only excluded volume interactions-seem to explain many reported dense crystalline phases, these models often fail to predict the right structure. Here, we examine the role of soft repulsive interparticle interactions on binary colloidal crystals comprising two sizes of spherical particles; such "softness" can arise due to ligand shells or screened electrostatics. We determine the ground state phase diagram of binary systems of particles interacting with an additive inverse power law potential using a basin hopping algorithm to calculate the enthalpy of an extremely large pool of candidate structures. We find that a surprisingly small amount of softness can destabilize dense packings in favor of less densely packed structures, which provides further evidence that considerations beyond packing are necessary for describing many of the observed phases of binary colloidal crystals. Importantly, we find that several of the phases stabilized by softness, which are characterized by relatively few interparticle contacts and a tendency for local icosahedral order, are more likely to be observed experimentally than those predicted by packing models. We also report a previously unknown dense AB4 phase and conduct free energy calculations to examine how the stability of several crystals will vary with temperature. Our results further our understanding of why particular binary colloidal crystals form and will be useful as a reference for experimentalists working with softly repulsive colloids.
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10
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Mahynski NA, Pretti E, Shen VK, Mittal J. Using symmetry to elucidate the importance of stoichiometry in colloidal crystal assembly. Nat Commun 2019; 10:2028. [PMID: 31048700 PMCID: PMC6497718 DOI: 10.1038/s41467-019-10031-4] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2018] [Accepted: 04/09/2019] [Indexed: 01/05/2023] Open
Abstract
We demonstrate a method based on symmetry to predict the structure of self-assembling, multicomponent colloidal mixtures. This method allows us to feasibly enumerate candidate structures from all symmetry groups and is many orders of magnitude more computationally efficient than combinatorial enumeration of these candidates. In turn, this permits us to compute ground-state phase diagrams for multicomponent systems. While tuning the interparticle potentials to produce potentially complex interactions represents the conventional route to designing exotic lattices, we use this scheme to demonstrate that simple potentials can also give rise to such structures which are thermodynamically stable at moderate to low temperatures. Furthermore, for a model two-dimensional colloidal system, we illustrate that lattices forming a complete set of 2-, 3-, 4-, and 6-fold rotational symmetries can be rationally designed from certain systems by tuning the mixture composition alone, demonstrating that stoichiometric control can be a tool as powerful as directly tuning the interparticle potentials themselves.
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Affiliation(s)
- Nathan A Mahynski
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, 20899-8320, USA.
| | - Evan Pretti
- Department of Chemical and Biomolecular Engineering, Lehigh University, 111 Research Drive, Bethlehem, PA, 18015-4791, USA
| | - Vincent K Shen
- Chemical Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, 20899-8320, USA
| | - Jeetain Mittal
- Department of Chemical and Biomolecular Engineering, Lehigh University, 111 Research Drive, Bethlehem, PA, 18015-4791, USA.
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11
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Pedersen UR. Statistics of small length scale density fluctuations in supercooled viscous liquids. J Chem Phys 2019; 150:094505. [PMID: 30849876 DOI: 10.1063/1.5080277] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Many successful theories of liquids near the melting temperature assume that small length scale density fluctuations follow Gaussian statistics. This paper presents a numerical investigation of density fluctuations in the supercooled viscous regime using an enhanced sampling method. Five model systems are investigated: the single component Lennard-Jones liquid, the Kob-Andersen binary mixture, the Wahnström binary mixture, the Lewis-Wahnström model of ortho-terphenyl, and the TIP4P/Ice model of water. The results show that the Gaussian approximation persists to a good degree into the supercooled viscous regime; however, it is less accurate at low temperatures. The analysis suggests that non-Gaussian fluctuations are related to crystalline configurations. Implications for theories of the glass transition are discussed.
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Affiliation(s)
- Ulf R Pedersen
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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12
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Abstract
Particle assembly and co-assembly have been research frontiers in chemistry and material science in the past few decades. To achieve a large variety of intricate structures and functional materials, remarkable progress has been made in particle assembly principles and strategies. Essentially, particle assembly is driven by intrinsic interparticle interactions or the external control. In this article, we focus on binary or ternary particle co-assembly and review the principles and feasible strategies. These advances have led to new disciplines of microfabrication technology and material engineering. Although significant achievement on particle-based structures has been made, it is still challenging to fully develop general and facile strategies to precisely control the one-dimensional (1D) co-assembly. This article reviews the recent development on multicomponent particle co-assembly, which significantly increases structural complexity and functional diversity. In particular, we highlight the advances in the particle co-assembly of well-ordered 1D binary superstructures by liquid soft confinement. Finally, prospective outlook for future trends in this field is proposed.
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Affiliation(s)
- Dan Guo
- Department Key Laboratory of Green Printing, Institute of Chemistry, Chinese Academy of Sciences, Beijing, 100190, P. R. China.,Engineering Research Center of Nanomaterials for Green, Printing Technology, Beijing National Laboratory for Molecular Sciences, Beijing, 100190, P. R. China.,Department of Chemistry, University of Chinese Academy of Sciences, Beijing, 100049, P. R. China
| | - Yanlin Song
- Department Key Laboratory of Green Printing, Institute of Chemistry, Chinese Academy of Sciences, Beijing, 100190, P. R. China.,Engineering Research Center of Nanomaterials for Green, Printing Technology, Beijing National Laboratory for Molecular Sciences, Beijing, 100190, P. R. China
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13
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Torquato S. Perspective: Basic understanding of condensed phases of matter via packing models. J Chem Phys 2018; 149:020901. [DOI: 10.1063/1.5036657] [Citation(s) in RCA: 73] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- S. Torquato
- Department of Chemistry, Department of Physics, Princeton Center for Theoretical Science, 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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14
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van der Meer B, Lathouwers E, Smallenburg F, Filion L. Diffusion and interactions of interstitials in hard-sphere interstitial solid solutions. J Chem Phys 2017; 147:234903. [DOI: 10.1063/1.5003905] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Berend van der Meer
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Emma Lathouwers
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Frank Smallenburg
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Laura Filion
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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15
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Schella A, Weis S, Schröter M. Charging changes contact composition in binary sphere packings. Phys Rev E 2017; 95:062903. [PMID: 28709334 DOI: 10.1103/physreve.95.062903] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2017] [Indexed: 11/07/2022]
Abstract
Equal volume mixtures of small and large polytetrafluorethylene spheres are shaken in an atmosphere of controlled humidity which allows one to also control their tribocharging. We find that the contact numbers are charge dependent: As the charge density of the beads increases, the number of same-type contacts decreases and the number of opposite-type contacts increases. This change is not caused by a global segregation of the sample. Hence, tribocharging can be a way to tune the local composition of a granular material.
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Affiliation(s)
- André Schella
- Max Planck Institute for Dynamics and Self-Organization Göttingen, 37077 Göttingen, Germany
| | - Simon Weis
- Institute of Theoretical Physics I, University Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
| | - Matthias Schröter
- Max Planck Institute for Dynamics and Self-Organization Göttingen, 37077 Göttingen, Germany.,Institute for Multiscale Simulation, Friedrich-Alexander University, 91052 Erlangen, Germany
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16
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van der Meer B, Dijkstra M, Filion L. Diffusion and interactions of point defects in hard-sphere crystals. J Chem Phys 2017; 146:244905. [DOI: 10.1063/1.4990416] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Berend van der Meer
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Laura Filion
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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17
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Douglass I, Mayger H, Hudson T, Harrowell P. The stabilization of tubular crystals in mixtures of spherical particles. SOFT MATTER 2017; 13:1344-1351. [PMID: 28106204 DOI: 10.1039/c6sm02636b] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Novel crystal structures in binary atomic mixtures arise when the attractive well is wide enough to allow double occupancy by small particles. The resulting crystals consist of ordered packings of self assembled linear structures comprised of a cylindrical tube of large particles enclosing a close packed core of small particles that corresponds to a stacking of overlapping icosahedra. We show that the stability of these structures depends on two essential features of the spherically symmetric pairwise interactions: (i) a radius ratio between 0.414 and 0.588, and (ii) a width w of the attractive well in the interaction between unlike particles that satisfies w > σSS where σSS is the diameter of the small particle.
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Affiliation(s)
- Ian Douglass
- School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia.
| | - Helen Mayger
- School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia.
| | - Toby Hudson
- School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia.
| | - Peter Harrowell
- School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia.
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18
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Kuroda Y, Shimbo Y, Sakamoto Y, Wada H, Kuroda K. A Mesoporous Superlattice Consisting of Alternately Stacking Interstitial Nanospace within Binary Silica Colloidal Crystals. Angew Chem Int Ed Engl 2016. [DOI: 10.1002/ange.201605027] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Yoshiyuki Kuroda
- Waseda Institute for Advanced Study; Waseda University; 1-6-1 Nishiwaseda Shinjuku-ku Tokyo 169-8050 Japan
| | - Yosuke Shimbo
- Department of Applied Chemistry; Waseda University; 3-4-1 Okubo Shinjuku-ku Tokyo 169-8555 Japan
| | - Yasuhiro Sakamoto
- PRESTO, Japan, Science and Technology Agency (JST); 4-1-8 Honcho Kawaguchi Saitama 332-0012 Japan
- Department of Physics; Osaka University; 1-1 Machikaneyamacho Toyonaka-shi Osaka 560-0043 Japan
| | - Hiroaki Wada
- Department of Applied Chemistry; Waseda University; 3-4-1 Okubo Shinjuku-ku Tokyo 169-8555 Japan
| | - Kazuyuki Kuroda
- Department of Applied Chemistry; Waseda University; 3-4-1 Okubo Shinjuku-ku Tokyo 169-8555 Japan
- Kagami Memorial Research Institute for Science and Technology; Waseda University; 2-8-26 Nishiwaseda Shinjuku-ku Tokyo 169-0051 Japan
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19
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Boles MA, Engel M, Talapin DV. Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials. Chem Rev 2016; 116:11220-89. [PMID: 27552640 DOI: 10.1021/acs.chemrev.6b00196] [Citation(s) in RCA: 1043] [Impact Index Per Article: 130.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Chemical methods developed over the past two decades enable preparation of colloidal nanocrystals with uniform size and shape. These Brownian objects readily order into superlattices. Recently, the range of accessible inorganic cores and tunable surface chemistries dramatically increased, expanding the set of nanocrystal arrangements experimentally attainable. In this review, we discuss efforts to create next-generation materials via bottom-up organization of nanocrystals with preprogrammed functionality and self-assembly instructions. This process is often driven by both interparticle interactions and the influence of the assembly environment. The introduction provides the reader with a practical overview of nanocrystal synthesis, self-assembly, and superlattice characterization. We then summarize the theory of nanocrystal interactions and examine fundamental principles governing nanocrystal self-assembly from hard and soft particle perspectives borrowed from the comparatively established fields of micrometer colloids and block copolymer assembly. We outline the extensive catalog of superlattices prepared to date using hydrocarbon-capped nanocrystals with spherical, polyhedral, rod, plate, and branched inorganic core shapes, as well as those obtained by mixing combinations thereof. We also provide an overview of structural defects in nanocrystal superlattices. We then explore the unique possibilities offered by leveraging nontraditional surface chemistries and assembly environments to control superlattice structure and produce nonbulk assemblies. We end with a discussion of the unique optical, magnetic, electronic, and catalytic properties of ordered nanocrystal superlattices, and the coming advances required to make use of this new class of solids.
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Affiliation(s)
- Michael A Boles
- Department of Chemistry and James Franck Institute, University of Chicago , Chicago, Illinois 60637, United States
| | - Michael Engel
- Institute for Multiscale Simulation, Friedrich-Alexander University Erlangen-Nürnberg , 91052 Erlangen, Germany.,Department of Chemical Engineering, University of Michigan , Ann Arbor, Michigan 48109, United States
| | - Dmitri V Talapin
- Department of Chemistry and James Franck Institute, University of Chicago , Chicago, Illinois 60637, United States.,Center for Nanoscale Materials, Argonne National Lab , Argonne, Illinois 60439, United States
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20
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Kuroda Y, Shimbo Y, Sakamoto Y, Wada H, Kuroda K. A Mesoporous Superlattice Consisting of Alternately Stacking Interstitial Nanospace within Binary Silica Colloidal Crystals. Angew Chem Int Ed Engl 2016; 55:10702-6. [DOI: 10.1002/anie.201605027] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2016] [Indexed: 11/10/2022]
Affiliation(s)
- Yoshiyuki Kuroda
- Waseda Institute for Advanced Study; Waseda University; 1-6-1 Nishiwaseda Shinjuku-ku Tokyo 169-8050 Japan
| | - Yosuke Shimbo
- Department of Applied Chemistry; Waseda University; 3-4-1 Okubo Shinjuku-ku Tokyo 169-8555 Japan
| | - Yasuhiro Sakamoto
- PRESTO, Japan, Science and Technology Agency (JST); 4-1-8 Honcho Kawaguchi Saitama 332-0012 Japan
- Department of Physics; Osaka University; 1-1 Machikaneyamacho Toyonaka-shi Osaka 560-0043 Japan
| | - Hiroaki Wada
- Department of Applied Chemistry; Waseda University; 3-4-1 Okubo Shinjuku-ku Tokyo 169-8555 Japan
| | - Kazuyuki Kuroda
- Department of Applied Chemistry; Waseda University; 3-4-1 Okubo Shinjuku-ku Tokyo 169-8555 Japan
- Kagami Memorial Research Institute for Science and Technology; Waseda University; 2-8-26 Nishiwaseda Shinjuku-ku Tokyo 169-0051 Japan
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21
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Fu L, Steinhardt W, Zhao H, Socolar JES, Charbonneau P. Hard sphere packings within cylinders. SOFT MATTER 2016; 12:2505-2514. [PMID: 26843132 DOI: 10.1039/c5sm02875b] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Arrangements of identical hard spheres confined to a cylinder with hard walls have been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest configurations, called close packings, of hard spheres of diameter σ in a cylinder of diameter D is a purely geometric problem that grows increasingly complex as D/σ increases, and little is thus known about the regime for D > 2.873σ. In this work, we extend the identification of close packings up to D = 4.00σ by adapting Torquato-Jiao's adaptive-shrinking-cell formulation and sequential-linear-programming (SLP) technique. We identify 17 new structures, almost all of them chiral. Beyond D ≈ 2.85σ, most of the structures consist of an outer shell and an inner core that compete for being close packed. In some cases, the shell adopts its own maximum density configuration, and the stacking of core spheres within it is quasiperiodic. In other cases, an interplay between the two components is observed, which may result in simple periodic structures. In yet other cases, the very distinction between the core and shell vanishes, resulting in more exotic packing geometries, including some that are three-dimensional extensions of structures obtained from packing hard disks in a circle.
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Affiliation(s)
- Lin Fu
- Department of Chemistry, Duke University, Durham, NC 27708, USA.
| | | | - Hao Zhao
- Department of Chemistry, Duke University, Durham, NC 27708, USA.
| | | | - Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, NC 27708, USA. and Department of Physics, Duke University, Durham, NC 27708, USA
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22
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Horst N, Travesset A. Prediction of binary nanoparticle superlattices from soft potentials. J Chem Phys 2016; 144:014502. [DOI: 10.1063/1.4939238] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nathan Horst
- Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011, USA
| | - Alex Travesset
- Department of Physics and Astronomy, Ames Laboratory and Iowa State University, Ames, Iowa 50011, USA
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Tian J, Xu Y, Jiao Y, Torquato S. A Geometric-Structure Theory for Maximally Random Jammed Packings. Sci Rep 2015; 5:16722. [PMID: 26568437 PMCID: PMC4644945 DOI: 10.1038/srep16722] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2015] [Accepted: 10/19/2015] [Indexed: 01/10/2023] Open
Abstract
Maximally random jammed (MRJ) particle packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The prediction of the MRJ packing density ϕMRJ, among other packing properties of frictionless particles, still poses many theoretical challenges, even for congruent spheres or disks. Using the geometric-structure approach, we derive for the first time a highly accurate formula for MRJ densities for a very wide class of two-dimensional frictionless packings, namely, binary convex superdisks, with shapes that continuously interpolate between circles and squares. By incorporating specific attributes of MRJ states and a novel organizing principle, our formula yields predictions of ϕMRJ that are in excellent agreement with corresponding computer-simulation estimates in almost the entire α-x plane with semi-axis ratio α and small-particle relative number concentration x. Importantly, in the monodisperse circle limit, the predicted ϕMRJ = 0.834 agrees very well with the very recently numerically discovered MRJ density of 0.827, which distinguishes it from high-density "random-close packing" polycrystalline states and hence provides a stringent test on the theory. Similarly, for non-circular monodisperse superdisks, we predict MRJ states with densities that are appreciably smaller than is conventionally thought to be achievable by standard packing protocols.
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Affiliation(s)
- Jianxiang Tian
- Department of Physics, Qufu Normal University, Qufu 273165, China.,Department of Physics, Dalian University of Technology, Dalian 116024, China
| | - Yaopengxiao Xu
- Materials Science and Engineering, Arizona State University, Tempe Arizona 85287, USA
| | - Yang Jiao
- Materials Science and Engineering, 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.,Program in Applied and Computational Mathematics, Princeton University, Princeton New Jersey 08544, USA
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24
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Zhang K, Dice B, Liu Y, Schroers J, Shattuck MD, O’Hern CS. On the origin of multi-component bulk metallic glasses: Atomic size mismatches and de-mixing. J Chem Phys 2015; 143:054501. [DOI: 10.1063/1.4927560] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kai Zhang
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
- Center for Research on Interface Structures and Phenomena, Yale University, New Haven, Connecticut 06520, USA
| | - Bradley Dice
- Center for Research on Interface Structures and Phenomena, Yale University, New Haven, Connecticut 06520, USA
- William Jewell College, Liberty, Missouri 64068, USA
| | - Yanhui Liu
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
- Center for Research on Interface Structures and Phenomena, Yale University, New Haven, Connecticut 06520, USA
| | - Jan Schroers
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
- Center for Research on Interface Structures and Phenomena, Yale University, New Haven, Connecticut 06520, USA
| | - Mark D. Shattuck
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
- Department of Physics and Benjamin Levich Institute, The City College of the City University of New York, New York, New York 10031, USA
| | - Corey S. O’Hern
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
- Center for Research on Interface Structures and Phenomena, Yale University, New Haven, Connecticut 06520, USA
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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25
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Abstract
The solid-phase diagram of binary systems consisting of particles of diameter σA = σ and σB = γσ (γ ≤ 1) interacting with an inverse p = 12 power law is investigated as a paradigm of a soft potential. In addition to the diameter ratio γ that characterizes hard-sphere models, the phase diagram is a function of an additional parameter that controls the relative interaction strength between the different particle types. Phase diagrams are determined from extremes of thermodynamic functions by considering 15 candidate lattices. In general, it is shown that the phase diagram of a soft repulsive potential leads to the morphological diversity observed in experiments with binary nanoparticles, thus providing a general framework to understand their phase diagrams. Particular emphasis is given to the two most successful crystallization strategies so far: evaporation of solvent from nanoparticles with grafted hydrocarbon ligands and DNA programmable self-assembly.
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26
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Ronceray P, Harrowell P. Favoured local structures in liquids and solids: a 3D lattice model. SOFT MATTER 2015; 11:3322-3331. [PMID: 25773665 DOI: 10.1039/c5sm00312a] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We investigate the connection between the geometry of Favoured Local Structures (FLS) in liquids and the associated liquid and solid properties. We introduce a lattice spin model - the FLS model on a face-centered cubic lattice - where this geometry can be arbitrarily chosen among a discrete set of 115 possible FLS. We find crystalline groundstates for all choices of a single FLS. Sampling all possible FLS's, we identify the following trends: (i) low symmetry FLS's produce larger crystal unit cells but not necessarily higher energy groundstates, (ii) chiral FLS's exhibit peculiarly poor packing properties, (iii) accumulation of FLS's in supercooled liquids is linked to large crystal unit cells, and (iv) low symmetry FLS's tend to find metastable structures on cooling.
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Affiliation(s)
- Pierre Ronceray
- Laboratoire de Physique Théorique et Modèles Statistiques, Univ. Paris-Sud, Bât. 100, 91405 Orsay Cedex, France.
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27
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Dijkstra M. Entropy-Driven Phase Transitions in Colloids: From spheres to anisotropic particles. ADVANCES IN CHEMICAL PHYSICS 2014. [DOI: 10.1002/9781118949702.ch2] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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28
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Charbonneau B, Charbonneau P, Tarjus G. Geometrical frustration and static correlations in hard-sphere glass formers. J Chem Phys 2013; 138:12A515. [DOI: 10.1063/1.4770498] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Ben-Simon A, Eshet H, Rabani E. On the phase behavior of binary mixtures of nanoparticles. ACS NANO 2013; 7:978-986. [PMID: 23281700 DOI: 10.1021/nn302712h] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The assembly of mixtures of nanoparticles with different properties into a binary nanoparticle superlattice (BNSL) provides a route to fabricate novel classes of materials with properties emerging from the choice of the building blocks. The common theoretical approach based on the hard-spheres model predicts crystallization of only a few metastable binary superstructures (NaCl, AlB₂ or the AB₁₃). Recently [Shevchenko, E. V.; Talapin, D. V.; O'Brien, S.; Murray, C. B. Nature 2006; 439, 55.)], it has been demonstrated that with the use of a combination of semiconducting, metallic, and magnetic nanoparticles, a variety of novel BNSL structures were formed, where at least 10 were low density structures that have not been previously reported. While some of the structures can be explained by the addition of electrostatic interactions, it is clear that at the nanometer scale one needs to consider other influences, such as van der Waals forces, steric effects, etc. Motivated by those experiments, we study, using Monte Carlo simulations, the phase behavior of binary mixtures of nanoparticles interacting via a combination of hard-core electrostatics and van der Waals forces. We include a tuning parameter that can be used to balance between electrostatic and dispersion interactions and study the phase behavior as a function of the different charges and size ratios of the nanoparticles. The results indicate that at the nanoscale, both electrostatic and dispersion interactions are necessary to explain the experimental observed BNSL structures.
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Affiliation(s)
- Avi Ben-Simon
- School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
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30
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Xu X, Cui Z, Qi J, Liu X. Fabrication of Ag/CPs composite material, an effective strategy to improve the photocatalytic performance of coordination polymers under visible irradiation. Dalton Trans 2013; 42:13546-53. [DOI: 10.1039/c3dt51178b] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
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31
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Elias NT, Hudson TS. Structural search for dense packing of concave and convex shapes in two dimensions. ACTA ACUST UNITED AC 2012. [DOI: 10.1088/1742-6596/402/1/012005] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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32
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Dennison M, Milinković K, Dijkstra M. Phase diagram of hard snowman-shaped particles. J Chem Phys 2012; 137:044507. [DOI: 10.1063/1.4737621] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Hopkins AB, Stillinger FH, Torquato S. Densest binary sphere packings. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021130. [PMID: 22463175 DOI: 10.1103/physreve.85.021130] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2011] [Indexed: 05/31/2023]
Abstract
The densest binary sphere packings in the α-x plane of small to large sphere radius ratio α and small sphere relative concentration x have historically been very difficult to determine. Previous research had led to the prediction that these packings were composed of a few known "alloy" phases including, for example, the AlB(2) (hexagonal ω), HgBr(2), and AuTe(2) structures, and to XY(n) structures composed of close-packed large spheres with small spheres (in a number ratio of n to 1) in the interstices, e.g., the NaCl packing for n=1. However, utilizing an implementation of the Torquato-Jiao sphere-packing algorithm [Torquato and Jiao, Phys. Rev. E 82, 061302 (2010)], we have discovered that many more structures appear in the densest packings. For example, while all previously known densest structures were composed of spheres in small to large number ratios of one to one, two to one, and very recently three to one, we have identified densest structures with number ratios of seven to three and five to two. In a recent work [Hopkins et al., Phys. Rev. Lett. 107, 125501 (2011)], we summarized these findings. In this work, we present the structures of the densest-known packings and provide details about their characteristics. Our findings demonstrate that a broad array of different densest mechanically stable structures consisting of only two types of components can form without any consideration of attractive or anisotropic interactions. In addition, the structures that we have identified may correspond to currently unidentified stable phases of certain binary atomic and molecular systems, particularly at high temperatures and pressures.
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Affiliation(s)
- Adam B Hopkins
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
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34
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Charbonneau B, Charbonneau P, Tarjus G. Geometrical frustration and static correlations in a simple glass former. PHYSICAL REVIEW LETTERS 2012; 108:035701. [PMID: 22400759 DOI: 10.1103/physrevlett.108.035701] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2011] [Indexed: 05/31/2023]
Abstract
We study the geometrical frustration scenario of glass formation for simple hard-sphere models. We find that the dual picture in terms of defects brings little insight and no theoretical simplification for the understanding of the slowing down of relaxation, because of the strong frustration characterizing these systems. The possibility of a growing static length is furthermore found to be physically irrelevant in the regime that is accessible to computer simulations.
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Affiliation(s)
- Benoit Charbonneau
- Mathematics Department, St. Jerome's University in the University of Waterloo, Waterloo, Ontario, Canada
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35
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Widmer-Cooper A, Harrowell P. Structural phases in non-additive soft-disk mixtures: Glasses, substitutional order, and random tilings. J Chem Phys 2011; 135:224515. [DOI: 10.1063/1.3666010] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Hopkins AB, Jiao Y, Stillinger FH, Torquato S. Phase diagram and structural diversity of the densest binary sphere packings. PHYSICAL REVIEW LETTERS 2011; 107:125501. [PMID: 22026775 DOI: 10.1103/physrevlett.107.125501] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2011] [Indexed: 05/31/2023]
Abstract
The densest binary sphere packings have historically been very difficult to determine. The only rigorously known packings in the α-x plane of sphere radius ratio α and relative concentration x are at the Kepler limit α=1, where packings are monodisperse. Utilizing an implementation of the Torquato-Jiao sphere-packing algorithm [S. Torquato and Y. Jiao, Phys. Rev. E 82, 061302 (2010)], we present the most comprehensive determination to date of the phase diagram in (α,x) for the densest binary sphere packings. Unexpectedly, we find many distinct new densest packings.
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Affiliation(s)
- Adam B Hopkins
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
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37
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Hudson TS, Harrowell P. Structural searches using isopointal sets as generators: densest packings for binary hard sphere mixtures. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:194103. [PMID: 21525553 DOI: 10.1088/0953-8984/23/19/194103] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Algorithms to search for crystal structures that optimize some extensive property (energy, volume, etc) typically make use of random particle reorganizations in the context of one or more numerical techniques such as simulated annealing, genetic algorithms or biased random walks, applied to the coordinates of every particle in the unit cell, together with the cell angles and lengths. In this paper we describe the restriction of such searches to predefined isopointal sets, breaking the problem into countable sub-problems which exploit crystal symmetries to reduce the dimensionality of the search space. Applying this method to the search for maximally packed mixtures of hard spheres of two sizes, we demonstrate that the densest packed structures can be identified by searches within a couple of isopointal sets. For the A(2)B system, the densest known packings over the entire tested range 0.2 < r(A)/r(B) < 2.5, including some improvements on previous optima, can all be identified by searches within a single isopointal set. In the case of the AB composition, searches of two isopointal sets generate the densest packed structures over the radius ratio range 0.2 < r(A)/r(B) < 5.0.
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Affiliation(s)
- Toby S Hudson
- School of Chemistry, University of Sydney, NSW 2006, Australia
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38
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Ni† R, Smallenburg† F, Filion L, Dijkstra M. Crystal nucleation in binary hard-sphere mixtures: the effect of order parameter on the cluster composition. Mol Phys 2011. [DOI: 10.1080/00268976.2011.554333] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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39
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Affiliation(s)
- Anđela Šarić
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Behnaz Bozorgui
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
| | - Angelo Cacciuto
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
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40
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Filion L, Marechal M, van Oorschot B, Pelt D, Smallenburg F, Dijkstra M. Efficient method for predicting crystal structures at finite temperature: variable box shape simulations. PHYSICAL REVIEW LETTERS 2009; 103:188302. [PMID: 19905838 DOI: 10.1103/physrevlett.103.188302] [Citation(s) in RCA: 93] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2009] [Indexed: 05/12/2023]
Abstract
We present an efficient and robust method based on Monte Carlo simulations for predicting crystal structures at finite temperature. We apply this method, which is surprisingly easy to implement, to a variety of systems, demonstrating its effectiveness for hard, attractive, and anisotropic interactions, binary mixtures, semi-long-range soft interactions, and truly long-range interactions where the truly long-range interactions are treated using Ewald sums. In the case of binary hard-sphere mixtures, star polymers, and binary Lennard-Jones mixtures, the crystal structures predicted by this algorithm are consistent with literature, providing confidence in the method. Finally, we predict new crystal structures for hard asymmetric dumbbell particles, bowl-like particles and hard oblate cylinders and present the phase diagram for the oblate cylinders based on full free energy calculations.
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Affiliation(s)
- Laura Filion
- Soft Condensed Matter, Debye Institute for NanoMaterials Science, Utrecht University, Princetonplein 5, The Netherlands
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41
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Filion L, Dijkstra M. Prediction of binary hard-sphere crystal structures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:046714. [PMID: 19518387 DOI: 10.1103/physreve.79.046714] [Citation(s) in RCA: 100] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2008] [Revised: 02/25/2009] [Indexed: 05/27/2023]
Abstract
We present a method based on a combination of a genetic algorithm and Monte Carlo simulations to predict close-packed crystal structures in hard-core systems. We employ this method to predict the binary crystal structures in a mixture of large and small hard spheres with various stoichiometries and diameter ratios between 0.4 and 0.84. In addition to known binary hard-sphere crystal structures similar to NaCl and AlB2, we predict additional crystal structures with the symmetry of CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se, and various structures for which an atomic analog was not found. In order to determine the crystal structures at infinite pressures, we calculate the maximum packing density as a function of size ratio for the crystal structures predicted by our GA using a simulated annealing approach.
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Affiliation(s)
- Laura Filion
- Soft Condensed Matter, Debye Institute for NanoMaterials Science, Utrecht University, 3584 CC Utrecht, The Netherlands
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