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González HI, Cinacchi G. Dense Disordered Jammed Packings of Hard Spherocylinders with a Low Aspect Ratio: A Characterization of Their Structure. J Phys Chem B 2023; 127:6814-6824. [PMID: 37478840 PMCID: PMC10405222 DOI: 10.1021/acs.jpcb.3c03195] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Revised: 06/27/2023] [Indexed: 07/23/2023]
Abstract
This work numerically investigates dense disordered (maximally random) jammed packings of hard spherocylinders of cylinder length L and diameter D by focusing on L/D ∈ [0,2]. It is within this interval that one expects that the packing fraction of these dense disordered jammed packings ϕMRJ hsc attains a maximum. This work confirms the form of the graph ϕMRJ hsc versus L/D: here, comparably to certain previous investigations, it is found that the maximal ϕMRJ hsc = 0.721 ± 0.001 occurs at L/D = 0.45 ± 0.05. Furthermore, this work meticulously characterizes the structure of these dense disordered jammed packings via the special pair-correlation function of the interparticle distance scaled by the contact distance and the ensuing analysis of the statistics of the hard spherocylinders in contact: here, distinctly from all previous investigations, it is found that the dense disordered jammed packings of hard spherocylinders with 0.45 ≲ L/D ≤ 2 are isostatic.
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Affiliation(s)
- Hugo Imaz González
- Departamento
de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Ciudad Universitaria
de Cantoblanco, E-28049 Madrid, España
| | - Giorgio Cinacchi
- Departamento
de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Ciudad Universitaria
de Cantoblanco, E-28049 Madrid, España
- Instituto
de Física de la Materia Condensada (IFIMAC), Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, E-28049 Madrid, España
- Instituto
de Ciencias de Materiales “Nicolás Cabrera”, Universidad Autónoma de Madrid, Ciudad Universitaria
de Cantoblanco, E-28049 Madrid, España
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2
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Varma VA, Malhotra I, Babu SB. Enhancement in the diffusivity of Brownian spheroids in the presence of spheres. Phys Rev E 2022; 106:014602. [PMID: 35974557 DOI: 10.1103/physreve.106.014602] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2021] [Accepted: 06/13/2022] [Indexed: 06/15/2023]
Abstract
In the present paper, we have extended the simulation technique Brownian cluster dynamics (BCD) to analyze the dynamics of the binary mixture of hard ellipsoids and spheres. The shape dependent diffusional properties have been incorporated into BCD using Perrin's factor and compared with analytical results of a one-component ellipsoidal system. We have investigated pathways to enhance the diffusivity of spheroids in the binary mixture by manipulating the phase behavior of the system through varying the fraction of spheres in the binary mixture. We show that at low volume fraction the spherical particles have a higher diffusion coefficient than the ellipsoids due to the higher friction coefficient. However, at a higher volume fraction, we show that the diffusion coefficient of the ellipsoids increases irrespective of the aspect ratio due to the anisotropic shape.
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Affiliation(s)
- Vikki Anand Varma
- Out of Equilibrium Group, Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016, India
| | - Isha Malhotra
- Out of Equilibrium Group, Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016, India
| | - Sujin B Babu
- Out of Equilibrium Group, Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016, India
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3
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Marienhagen P, Wagner J. Equation of state of hard lenses: A combined virial series and simulation approach. Phys Rev E 2022; 106:014101. [PMID: 35974553 DOI: 10.1103/physreve.106.014101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Accepted: 05/23/2022] [Indexed: 06/15/2023]
Abstract
We provide highly accurate equation-of-state data for the isotropic phase of hard lenses obtained by means of cluster Monte Carlo simulations. This data is analyzed using a virial approach considering coefficients up to the order eight and Carnahan-Starling type closure relations for the virial series. The comparison with previously investigated systems consisting of hard, oblate ellipsoids of revolution allows insights into the detailed influence of the particle geometry. We propose a generalized Carnahan-Starling approach as a heuristic equation of state for the isotropic phase of hard lenses that in first approximation shows the same dependence on the excess part of the excluded volume as identified for oblate, hard lenses of revolution.
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Affiliation(s)
| | - Joachim Wagner
- Institut für Chemie, Universität Rostock, 18051 Rostock, Germany
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4
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Marienhagen P, Wagner J. Reexamining equations of state of oblate hard ellipsoids of revolution: Numerical simulation utilizing a cluster Monte Carlo algorithm and comparison to virial theory. Phys Rev E 2022; 105:014125. [PMID: 35193301 DOI: 10.1103/physreve.105.014125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Accepted: 01/05/2022] [Indexed: 06/14/2023]
Abstract
We provide highly accurate equation-of-state data determined by means of cluster Monte Carlo simulations for the isotropic phase of oblate hard ellipsoids of revolution. Both equation-of-state data and phase boundaries of the isotropic phase are obtained from relatively large ensembles with typically 1000 particles. The comparison of simulation data with a virial approach gives evidence for the importance of high-order so-far-unknown virial coefficients and therewith many-particle interactions in dense, isotropic systems of anisotropic particles. While a virial approach with a rescaled Carnahan-Starling correction for the unknown, higher-order virial coefficients reproduces the simulation data of moderately anisotropic particles with high accuracy, we suggest for highly anisotropic shapes a simple, heuristic equation of state as a suitable approach.
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Affiliation(s)
| | - Joachim Wagner
- Institut für Chemie, Universität Rostock, 18059 Rostock, Germany
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5
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Marienhagen P, Hellmann R, Wagner J. Calculation of third to eighth virial coefficients of hard lenses and hard, oblate ellipsoids of revolution employing an efficient algorithm. Phys Rev E 2021; 104:015308. [PMID: 34412361 DOI: 10.1103/physreve.104.015308] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2021] [Accepted: 06/25/2021] [Indexed: 11/07/2022]
Abstract
We provide third to eighth virial coefficients of oblate, hard ellipsoids of revolution and hard lenses in dependence on their aspect ratio ν. Employing an algorithm optimized for hard anisotropic shapes, highly accurate data are accessible with comparatively small numerical effort. For both geometries, reduced virial coefficients B[over ̃]_{i}(ν)=B_{i}(ν)/B_{2}^{i-1}(ν) are in first approximation proportional to the inverse excess contribution α^{-1} of their excluded volume. The latter quantity is directly accessible from second virial coefficients and analytically known for convex bodies.
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Affiliation(s)
- Philipp Marienhagen
- Institut für Chemie, Universität Rostock, Albert-Einstein-Straße 3a, 18059 Rostock, Germany
| | - Robert Hellmann
- Institut für Thermodynamik, Helmut-Schmidt-Universität/Universität der Bundeswehr Hamburg, 22043 Hamburg, Germany
| | - Joachim Wagner
- Institut für Chemie, Universität Rostock, Albert-Einstein-Straße 3a, 18059 Rostock, Germany
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6
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Basurto E, Gurin P, Varga S, Odriozola G. Anisotropy-independent packing of confined hard ellipses. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.115896] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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7
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Roller J, Laganapan A, Meijer JM, Fuchs M, Zumbusch A. Observation of liquid glass in suspensions of ellipsoidal colloids. Proc Natl Acad Sci U S A 2021; 118:e2018072118. [PMID: 33397813 PMCID: PMC7826331 DOI: 10.1073/pnas.2018072118] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
Abstract
Despite the omnipresence of colloidal suspensions, little is known about the influence of colloid shape on phase transformations, especially in nonequilibrium. To date, real-space imaging results at high concentrations have been limited to systems composed of spherical colloids. In most natural and technical systems, however, particles are nonspherical, and their structural dynamics are determined by translational and rotational degrees of freedom. Using confocal microscopy of fluorescently labeled core-shell particles, we reveal that suspensions of ellipsoidal colloids form an unexpected state of matter, a liquid glass in which rotations are frozen while translations remain fluid. Image analysis unveils hitherto unknown nematic precursors as characteristic structural elements of this state. The mutual obstruction of these ramified clusters prevents liquid crystalline order. Our results give insight into the interplay between local structures and phase transformations. This helps to guide applications such as self-assembly of colloidal superstructures and also gives evidence of the importance of shape on the glass transition in general.
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Affiliation(s)
- Jörg Roller
- Department of Chemistry, University of Konstanz, 78464 Konstanz, Germany
| | - Aleena Laganapan
- Department of Physics, University of Konstanz, 78464 Konstanz, Germany
| | - Janne-Mieke Meijer
- Department of Physics, University of Konstanz, 78464 Konstanz, Germany
- Institute of Physics, University of Amsterdam, 1098 XH Amsterdam, The Netherlands
| | - Matthias Fuchs
- Department of Physics, University of Konstanz, 78464 Konstanz, Germany;
| | - Andreas Zumbusch
- Department of Chemistry, University of Konstanz, 78464 Konstanz, Germany;
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8
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Liu L, Li S. Uniform shape elongation effects on the random packings of uniaxially variable superellipsoids. POWDER TECHNOL 2020. [DOI: 10.1016/j.powtec.2020.08.017] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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9
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Jin W, Chan HK, Zhong Z. Shape-Anisotropy-Induced Ordered Packings in Cylindrical Confinement. PHYSICAL REVIEW LETTERS 2020; 124:248002. [PMID: 32639829 DOI: 10.1103/physrevlett.124.248002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2019] [Revised: 04/29/2020] [Accepted: 05/26/2020] [Indexed: 06/11/2023]
Abstract
Densest possible packings of identical spheroids in cylindrical confinement have been obtained through Monte Carlo simulations. By varying the shape anisotropy of spheroids and also the cylinder-to-spheroid size ratio, a variety of densest possible crystalline structures have been discovered, including achiral structures with specific orientations of particles and chiral helical structures with rotating orientations of particles. Our findings reveal a transition between confinement-induced chiral ordering and shape-anisotropy-induced orientational ordering and would serve as a guide for the fabrication of crystalline wires using anisotropic particles.
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Affiliation(s)
- Weiwei Jin
- School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
| | - Ho-Kei Chan
- School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
| | - Zheng Zhong
- School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
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10
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Roller J, Geiger JD, Voggenreiter M, Meijer JM, Zumbusch A. Formation of nematic order in 3D systems of hard colloidal ellipsoids. SOFT MATTER 2020; 16:1021-1028. [PMID: 31854439 DOI: 10.1039/c9sm01926j] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Suspensions of hard ellipsoidal particles exhibit complex phase behavior as shown by theoretical predictions and simulations of phase diagrams. Here, we report quantitative confocal microscopy experiments of hard prolate colloidal ellipsoids with different aspect ratio a/b. We studied different volume fractions φ of ellipsoids in density and refractive index matched suspensions. Large 3D sample volumes were investigated and the positions as well as the orientations of all ellipsoids were extracted by image analysis routines. By evaluating the translational and orientational order in the system we determined the presence of isotropic and nematic phases. For ellipsoids with a/b = 2.0 we found that isotropic phases form at all φ, while ellipsoids with a/b = 7.0 formed nematic phases at high φ, as expected from theory and simulations. For a/b = 3.5 and a/b = 4.1, however, we observed the absence of long-range orientational order even at φ where nematic phases are expected. We show that local orientational order formed with the emergence of nematic precursors for a/b = 3.5 and short-ranged nematic domains for a/b = 4.1. Our results provide novel insight into the phase behavior and orientational order of ellipsoids with different aspect ratios.
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Affiliation(s)
- Jörg Roller
- Department of Chemistry, University of Konstanz, Universitätsstrasse 10, Konstanz, Germany.
| | - John David Geiger
- Department of Chemistry, University of Konstanz, Universitätsstrasse 10, Konstanz, Germany.
| | - Markus Voggenreiter
- Department of Chemistry, University of Konstanz, Universitätsstrasse 10, Konstanz, Germany.
| | - Janne-Mieke Meijer
- Department of Physics, University of Konstanz, Universitätsstrasse 10, Konstanz, Germany and University of Amsterdam, Science Park 904, Amsterdam, The Netherlands
| | - Andreas Zumbusch
- Department of Chemistry, University of Konstanz, Universitätsstrasse 10, Konstanz, Germany.
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11
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Cinacchi G, Torquato S. Hard convex lens-shaped particles: Characterization of dense disordered packings. Phys Rev E 2020; 100:062902. [PMID: 31962401 DOI: 10.1103/physreve.100.062902] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2019] [Indexed: 11/07/2022]
Abstract
Among the family of hard convex lens-shaped particles (lenses), the one with aspect ratio equal to 2/3 is "optimal" in the sense that the maximally random jammed (MRJ) packings of such lenses achieve the highest packing fraction ϕ_{MRJ}≃0.73 [G. Cinacchi and S. Torquato, Soft Matter 14, 8205 (2018)1744-683X10.1039/C8SM01519H]. This value is only a few percent lower than ϕ_{DKP}=0.76210⋯, the packing fraction of the corresponding densest-known crystalline (degenerate) packings [G. Cinacchi and S. Torquato, J. Chem. Phys. 143, 224506 (2015)JCPSA60021-960610.1063/1.4936938]. By exploiting the appreciably reduced propensity that a system of such optimal lenses has to positionally and orientationally order, disordered packings of them are progressively generated by a Monte Carlo method-based procedure from the dilute equilibrium isotropic fluid phase to the dense nonequilibrium MRJ state. This allows us to closely monitor how the (micro)structure of these packings changes in the process of formation of the MRJ state. The gradual changes undergone by the many structural descriptors calculated here can coherently and consistently be traced back to the gradual increase in contacts between the hard particles until the isostatic mean value of ten contact neighbors per lens is reached at the effectively hyperuniform MRJ state. Compared to the MRJ state of hard spheres, the MRJ state of such optimal lenses is denser (less porous), more disordered, and rattler-free. This set of characteristics makes them good glass formers. It is possible that this conclusion may also hold for other hard convex uniaxial particles with a correspondingly similar aspect ratio, be they oblate or prolate, and that, by using suitable biaxial variants of them, that set of characteristics might further improve.
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Affiliation(s)
- Giorgio Cinacchi
- Departamento de Física Teórica de la Materia Condensada, Instituto de Física de la Materia Condensada (IFIMAC), Instituto de Ciencias de Materiales "Nicolás Cabrera," Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, E-28049 Madrid, Spain
| | - Salvatore Torquato
- Department of Chemistry and Department of Physics, Institute for the Science and Technology of Materials, Program for Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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12
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Stradner A, Schurtenberger P. Potential and limits of a colloid approach to protein solutions. SOFT MATTER 2020; 16:307-323. [PMID: 31830196 DOI: 10.1039/c9sm01953g] [Citation(s) in RCA: 43] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
Looking at globular proteins with the eyes of a colloid scientist has a long tradition, in fact a significant part of the early colloid literature was focused on protein solutions. However, it has also been recognized that proteins are much more complex than the typical hard sphere-like synthetic model colloids. Proteins are not perfect spheres, their interaction potentials are in general not isotropic, and using theories developed for such particles are thus clearly inadequate in many cases. In this perspective article, we now take a closer look at the field. In particular, we reflect on the fact that modern colloid science has been undergoing a tremendous development, where a multitude of novel systems have been developed in the lab and in silico. During the last decade we have seen a rapidly increasing number of reports on the synthesis of anisotropic, patchy and/or responsive synthetic colloids, that start to resemble their complex biological counterparts. This experimental development is also reflected in a corresponding theoretical and simulation effort. The experimental and theoretical toolbox of colloid science has thus rapidly expanded, and there is obviously an enormous potential for an application of these new concepts to protein solutions, which has already been realized and harvested in recent years. In this perspective article we make an attempt to critically discuss the exploitation of colloid science concepts to better understand protein solutions. We not only consider classical applications such as the attempt to understand and predict solution stability and phase behaviour, but also discuss new challenges related to the dynamics, flow behaviour and liquid-solid transitions found in concentrated or crowded protein solutions. It not only aims to provide an overview on the progress in experimental and theoretical (bio)colloid science, but also discusses current shortcomings in our ability to correctly reproduce and predict the structural and dynamic properties of protein solutions based on such a colloid approach.
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Affiliation(s)
- Anna Stradner
- Division of Physical Chemistry, Department of Chemistry, Lund University, PO Box 124, SE-221 00 Lund, Sweden.
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13
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Cui D, MacLeod JM, Rosei F. Planar Anchoring of C 70 Liquid Crystals Using a Covalent Organic Framework Template. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2019; 15:e1903294. [PMID: 31513362 DOI: 10.1002/smll.201903294] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2019] [Revised: 08/12/2019] [Indexed: 06/10/2023]
Abstract
The surface-induced anchoring effect is a well-developed technique to control the growth of liquid crystals (LCs). Nevertheless, a defined nanometer-scale template has never been used to induce the anchored growth of LCs with molecular building units. Scanning tunneling microscopy results at the solid/liquid interface reveal that a 2D covalent organic framework (COF-1) can offer an anchoring effect to template C70 molecules into forming several LC mesophases, which cannot be obtained under other conditions. Through comparison with the C60 system, a stepwise breakdown in ordering of C70 LC is observed. The process is described in terms of the effects of molecular anisotropy on the epitaxial growth of molecular crystals. The results suggest that using a surface-confined template to anchor the initial layer of LC molecules can be a modular and potentially broadly applicable approach for organizing molecular mesogens into LCs.
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Affiliation(s)
- Daling Cui
- Centre Énergie, Matériaux et Télécommunications, Institut National de la Recherche Scientifique, 1650 Boulevard Lionel-Boulet, Varennes, Québec, J3 × 1S2, Canada
| | - Jennifer M MacLeod
- Centre Énergie, Matériaux et Télécommunications, Institut National de la Recherche Scientifique, 1650 Boulevard Lionel-Boulet, Varennes, Québec, J3 × 1S2, Canada
- School of Chemistry Physics and Mechanical Engineering, Queensland University of Technology, Brisbane, 4000, QLD, Australia
| | - Federico Rosei
- Centre Énergie, Matériaux et Télécommunications, Institut National de la Recherche Scientifique, 1650 Boulevard Lionel-Boulet, Varennes, Québec, J3 × 1S2, Canada
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14
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D'Urso C, Celebre G, Cinacchi G. Phase behavior of hard C_{2h}-symmetric particle systems. Phys Rev E 2019; 100:012709. [PMID: 31499787 DOI: 10.1103/physreve.100.012709] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2019] [Indexed: 06/10/2023]
Abstract
Using Monte Carlo numerical simulation, this work sketches the phase diagram of systems of certain hard C_{2h}-symmetric particles, formed by gluing two aligned and displaced hard spherocylinders with a cylindrical-length-to-diameter ratio realistically, if viewed not only from the lyotropic colloidal liquid-crystal side but also from the thermotropic low-molecular-mass liquid-crystal side, equal to 5, as a function of the displacement. Several distinctive phases are observed, such as a nonperiodic smectic-B-like phase, a nonperiodic smectic-H-like phase, a smectic-C phase, and a short-layer-spacing uniaxial smectic-A phase but no biaxial nematic phase.
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Affiliation(s)
- Christian D'Urso
- Dipartimento di Chimica e Tecnologie Chimiche, Università della Calabria, via P. Bucci, I-87036 Arcavacata di Rende (CS), Italy
| | - Giorgio Celebre
- Dipartimento di Chimica e Tecnologie Chimiche, Università della Calabria, via P. Bucci, I-87036 Arcavacata di Rende (CS), Italy
| | - Giorgio Cinacchi
- Departamento de Física Teórica de la Materia Condensada, Instituto de Física de la Materia Condensada (IFIMAC), Instituto de Ciencias de Materiales "Nicolás Cabrera," Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, E-28049 Madrid, Spain
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15
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Cinacchi G, Torquato S. Hard convex lens-shaped particles: metastable, glassy and jammed states. SOFT MATTER 2018; 14:8205-8218. [PMID: 30283973 DOI: 10.1039/c8sm01519h] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We generate and study dense positionally and/or orientationally disordered, including jammed, monodisperse packings of hard convex lens-shaped particles (lenses). Relatively dense isotropic fluid configurations of lenses of various aspect ratios are slowly compressed via a Monte Carlo method based procedure. Under this compression protocol, while 'flat' lenses form a nematic fluid phase (where particles are positionally disordered but orientationally ordered) and 'globular' lenses form a plastic solid phase (where particles are positionally ordered but orientationally disordered), 'intermediate', neither 'flat' nor 'globular', lenses do not form either mesophase. In general, a crystal solid phase (where particles are both positionally and orientationally ordered) does not spontaneously form during lengthy numerical simulation runs. In correspondence to those volume fractions at which a transition to the crystal solid phase would occur in equilibrium, a 'downturn' is observed in the inverse compressibility factor versus volume fraction curve beyond which this curve behaves essentially linearly. This allows us to estimate the volume fraction at jamming of the dense non-crystalline packings so generated. These packings are nematic for 'flat' lenses and plastic for 'globular' lenses, while they are robustly isotropic for 'intermediate' lenses, as confirmed by the calculation of the τ order metric, among other quantities. The structure factors S(k) of the corresponding jammed states tend to zero as the wavenumber k goes to zero, indicating they are effectively hyperuniform (i.e., their infinite-wavelength density fluctuations are anomalously suppressed). Among all possible lens shapes, 'intermediate' lenses with aspect ratio around 2/3 are special because they are those that reach the highest volume fractions at jamming while being positionally and orientationally disordered and these volume fractions are as high as those reached by nematic jammed states of 'flat' lenses and plastic jammed states of 'globular' lenses. All of their attributes, taken together, make such 'intermediate' lens packings particularly good glass-forming materials.
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Affiliation(s)
- Giorgio Cinacchi
- Departamento de Física Teórica de la Materia Condensada, Instituto de Física de la Materia Condensada (IFIMAC), Instituto de Ciencias de Materiales "Nicolás Cabrera", Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, E-28049 Madrid, Spain.
| | - Salvatore Torquato
- Department of Chemistry, Department of Physics, Institute for the Science and Technology of Materials, Program for Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA.
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16
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Liu L, Yu Z, Jin W, Yuan Y, Li S. Uniform and decoupled shape effects on the maximally dense random packings of hard superellipsoids. POWDER TECHNOL 2018. [DOI: 10.1016/j.powtec.2018.06.033] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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17
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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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18
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Bautista-Carbajal G, Gurin P, Varga S, Odriozola G. Phase diagram of hard squares in slit confinement. Sci Rep 2018; 8:8886. [PMID: 29891959 PMCID: PMC5995855 DOI: 10.1038/s41598-018-26922-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2018] [Accepted: 05/21/2018] [Indexed: 12/02/2022] Open
Abstract
This work shows a complete phase diagram of hard squares of side length σ in slit confinement for H < 4.5, H being the wall to wall distance measured in σ units, including the maximal packing fraction limit. The phase diagram exhibits a transition between a single-row parallel 1-\documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{\square }}$$\end{document}□ structures (two parallel rows) for 2 < H < Hc(3) (Hc(n) = n − 1 + \documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{{\bf{2}}{\boldsymbol{n}}-{\bf{1}}}$$\end{document}2n−1/n is the critical wall-to-wall distance for a (n − 1)-\documentclass[12pt]{minimal}
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\begin{document}$${\diamond }$$\end{document}◇ transition and where n-\documentclass[12pt]{minimal}
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\begin{document}$${\diamond }$$\end{document}◇ represents a structure formed by tilted rectangles, each one clustering n stacked squares), and a triple point for Ht \documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{\simeq }}$$\end{document}≃ 2.005. In this triple point there coexists the 1-\documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{\square }}$$\end{document}□, 2-\documentclass[12pt]{minimal}
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\begin{document}$$\hat{\diamond }$$\end{document}◇ˆ structures. For regions Hc(3) < H < Hc(4) and Hc(4) < H < Hc(5), very similar pictures arise. There is a (n − 1)-\documentclass[12pt]{minimal}
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\begin{document}$${\diamond }$$\end{document}◇ strong transition for Hc(n) < H < n, followed by a softer (n − 1)-\documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{\square }}$$\end{document}□ transition for n < H < Hc(n + 1). Again, at H \documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{\gtrsim }}$$\end{document}≳ n there appears a triple point, involving the (n − 1)-\documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{\square }}$$\end{document}□, n-\documentclass[12pt]{minimal}
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\begin{document}$${\diamond }$$\end{document}◇ structures. The similarities found for n = 2, 3 and 4 lead us to propose a tentative phase diagram for Hc(n) < H < Hc(n + 1) (n ∈ \documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{{\mathbb{N}}}}$$\end{document}ℕ, n > 2), where structures (n − 1)-\documentclass[12pt]{minimal}
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\begin{document}$${\boldsymbol{\square }}$$\end{document}□, n-\documentclass[12pt]{minimal}
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\begin{document}$${\diamond }$$\end{document}◇ fill the phase diagram. Simulation and Onsager theory results are qualitatively consistent.
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Affiliation(s)
- Gustavo Bautista-Carbajal
- Academia de Matemáticas, Universidad Autónoma de la Ciudad de México, 07160, México, Distrito Federal, Mexico
| | - Péter Gurin
- Institute of Physics and Mechatronics, University of Pannonia, P.O. Box 158, Veszprém, H-8201, Hungary
| | - Szabolcs Varga
- Institute of Physics and Mechatronics, University of Pannonia, P.O. Box 158, Veszprém, H-8201, Hungary
| | - Gerardo Odriozola
- Área de Física de Procesos Irreversibles, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo 180, 02200, CD, México, Mexico.
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19
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Heymans S, Schilling T. Elastic properties of the nematic phase in hard ellipsoids of short aspect ratio. Phys Rev E 2017; 96:022708. [PMID: 28950529 DOI: 10.1103/physreve.96.022708] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2017] [Indexed: 06/07/2023]
Abstract
We present a Monte Carlo simulation study of suspensions of hard ellipsoids of revolution. Based on the spatial fluctuations of the orientational order, we have computed the Frank elastic constants for prolate and oblate ellipsoids and compared them to the affine transformation model. The affine transformation model predicts the right order of magnitude of the twist and bend constant but not of the splay constant. In addition, we report the observation of a stable nematic phase at an aspect ratio as low as 2.5.
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Affiliation(s)
- S Heymans
- Université du Luxembourg, Theory of Soft Condensed Matter, Physics and Materials Sciences Research Unit, L-1511 Luxembourg, Luxembourg
| | - T Schilling
- Institute of Physics, University of Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
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20
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Jin W, Jiao Y, Liu L, Yuan Y, Li S. Dense crystalline packings of ellipsoids. Phys Rev E 2017; 95:033003. [PMID: 28415357 DOI: 10.1103/physreve.95.033003] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2016] [Indexed: 11/07/2022]
Abstract
An ellipsoid, the simplest nonspherical shape, has been extensively used as a model for elongated building blocks for a wide spectrum of molecular, colloidal, and granular systems. Yet the densest packing of congruent hard ellipsoids, which is intimately related to the high-density phase of many condensed matter systems, is still an open problem. We discover an unusual family of dense crystalline packings of self-dual ellipsoids (ratios of the semiaxes α:sqrt[α]:1), containing 24 particles with a quasi-square-triangular (SQ-TR) tiling arrangement in the fundamental cell. The associated packing density ϕ exceeds that of the densest known SM2 crystal [ A. Donev et al., Phys. Rev. Lett. 92, 255506 (2004)10.1103/PhysRevLett.92.255506] for aspect ratios α in (1.365, 1.5625), attaining a maximal ϕ≈0.75806... at α=93/64. We show that the SQ-TR phase derived from these dense packings is thermodynamically stable at high densities over the aforementioned α range and report a phase diagram for self-dual ellipsoids. The discovery of the SQ-TR crystal suggests organizing principles for nonspherical particles and self-assembly of colloidal systems.
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Affiliation(s)
- Weiwei Jin
- Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China
| | - Yang Jiao
- Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - Lufeng Liu
- Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China
| | - Ye Yuan
- Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China
| | - Shuixiang Li
- Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China
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21
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Gurin P, Odriozola G, Varga S. Critical behavior of hard squares in strong confinement. Phys Rev E 2017; 95:042610. [PMID: 28505711 DOI: 10.1103/physreve.95.042610] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2017] [Indexed: 06/07/2023]
Abstract
We examine the phase behavior of a quasi-one-dimensional system of hard squares with side-length σ, where the particles are confined between two parallel walls and only nearest-neighbor interactions occur. As in our previous work [Gurin, Varga, and Odriozola, Phys. Rev. E 94, 050603 (2016)]2470-004510.1103/PhysRevE.94.050603, the transfer operator method is used, but here we impose a restricted orientation and position approximation to yield an analytic description of the physical properties. This allows us to study the parallel fluid-like to zigzag solid-like structural transition, where the compressibility and heat capacity peaks sharpen and get higher as H→H_{c}=2sqrt[2]-1≈1.8284 and p→p_{c}=∞. Here H is the width of the channel measured in σ units and p is the pressure. We have found that this structural change becomes critical at the (p_{c},H_{c}) point. The obtained critical exponents belong to the universality class of the one-dimensional Ising model. We believe this behavior holds for the unrestricted orientational and positional case.
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Affiliation(s)
- Péter Gurin
- Institute of Physics and Mechatronics, University of Pannonia, P.O. Box 158, Veszprém H-8201, Hungary
| | - Gerardo Odriozola
- Area de Física de Procesos Irreversibles, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo 180, 02200 CD México, Mexico
| | - Szabolcs Varga
- Institute of Physics and Mechatronics, University of Pannonia, P.O. Box 158, Veszprém H-8201, Hungary
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22
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Martchenko I, Crassous JJ, Mihut AM, Bialik E, Hirt AM, Rufier C, Menzel A, Dietsch H, Linse P, Schurtenberger P. Anisotropic magnetic particles in a magnetic field. SOFT MATTER 2016; 12:8755-8767. [PMID: 27722439 PMCID: PMC5123642 DOI: 10.1039/c6sm01411a] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
We characterize the structural properties of magnetic ellipsoidal hematite colloids with an aspect ratio ρ ≈ 2.3 using a combination of small-angle X-ray scattering and computer simulations. The evolution of the phase diagram with packing fraction ϕ and the strength of an applied magnetic field B is described, and the coupling between orientational order of magnetic ellipsoids and the bulk magnetic behavior of their suspension addressed. We establish quantitative structural criteria for the different phase and arrest transitions and map distinct isotropic, polarized non-nematic, and nematic phases over an extended range in the ϕ-B coordinates. We show that upon a rotational arrest of the ellipsoids around ϕ = 0.59, the bulk magnetic behavior of their suspension switches from superparamagnetic to ordered weakly ferromagnetic. If densely packed and arrested, these magnetic particles thus provide persisting remanent magnetization of the suspension. By exploring structural and magnetic properties together, we extend the often used colloid-atom analogy to the case of magnetic spins.
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Affiliation(s)
- Ilya Martchenko
- Division of Physical Chemistry, Department of Chemistry, Lund University, Lund, Sweden. and Adolphe Merkle Institute and Fribourg Center for Nanomaterials, University of Fribourg, Fribourg, Switzerland
| | - Jérôme J Crassous
- Division of Physical Chemistry, Department of Chemistry, Lund University, Lund, Sweden.
| | - Adriana M Mihut
- Division of Physical Chemistry, Department of Chemistry, Lund University, Lund, Sweden.
| | - Erik Bialik
- Division of Physical Chemistry, Department of Chemistry, Lund University, Lund, Sweden.
| | - Ann M Hirt
- Institut fur Geophysik, ETH Zurich, Zurich, Switzerland
| | - Chantal Rufier
- Adolphe Merkle Institute and Fribourg Center for Nanomaterials, University of Fribourg, Fribourg, Switzerland
| | - Andreas Menzel
- Swiss Light Source, Paul Scherrer Institute, Villigen, Switzerland
| | - Hervé Dietsch
- Adolphe Merkle Institute and Fribourg Center for Nanomaterials, University of Fribourg, Fribourg, Switzerland
| | - Per Linse
- Division of Physical Chemistry, Department of Chemistry, Lund University, Lund, Sweden.
| | - Peter Schurtenberger
- Division of Physical Chemistry, Department of Chemistry, Lund University, Lund, Sweden.
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23
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Varga S, Martínez-Ratón Y, Velasco E, Bautista-Carbajal G, Odriozola G. Effect of orientational restriction on monolayers of hard ellipsoids. Phys Chem Chem Phys 2016; 18:4547-56. [PMID: 26796794 DOI: 10.1039/c5cp05702g] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The effect of out-of-plane orientational freedom on the orientational ordering properties of a monolayer of hard ellipsoids is studied using the Parsons-Lee scaling approach and replica exchange Monte Carlo computer simulation. Prolate and oblate ellipsoids exhibit very different ordering properties, namely, the axes of revolution of prolate particles tend to lean out, while those of oblate ones prefer to lean into the confining plane. The driving mechanism of this is that the particles try to maximize the available free area on the confining surface, which can be achieved by minimizing the cross section areas of the particles with the plane. In the lack of out-of-plane orientational freedom the monolayer of prolate particles is identical to a two-dimensional hard ellipse system, which undergoes an isotropic-nematic ordering transition with increasing density. With gradually switching on the out-of-plane orientational freedom the prolate particles lean out from the confining plane and destabilisation of the in-plane isotropic-nematic phase transition is observed. The system of oblate particles behaves oppositely to that of prolates. It corresponds to a two-dimensional system of hard disks in the lack of out-of-plane freedom, while it behaves similar to that of hard ellipses in the freely rotating case. Solid phases can be realised by lower surface coverage due to the out-of-plane orientation freedom for both oblate and prolate shapes.
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Affiliation(s)
- Szabolcs Varga
- Institute of Physics and Mechatronics, University of Pannonia, PO Box 158, Veszprém, H-8201 Hungary
| | - Yuri Martínez-Ratón
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911, Leganés, Madrid, Spain
| | - Enrique Velasco
- Departamento de Física Teórica de la Materia Condensada and Instituto de Ciencia de Materiales Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Gustavo Bautista-Carbajal
- Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, 09340, México, Distrito Federal, Mexico and Academia de Matemáticas, Universidad Autónoma de la Ciudad de México, 07160, México, D. F., Mexico
| | - Gerardo Odriozola
- Area de Física de Procesos Irreversibles, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo 180, 02200 México, D. F., Mexico.
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24
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Cinacchi G, Torquato S. Hard convex lens-shaped particles: Densest-known packings and phase behavior. J Chem Phys 2015; 143:224506. [DOI: 10.1063/1.4936938] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Giorgio Cinacchi
- Departamento de Física Teórica de la Materia Condensada, Instituto de Física de la Materia Condensada (IFIMAC), Instituto de Ciencias de Materiales “Nicolás Cabrera,” Universidad Autónoma de Madrid, Campus de Cantoblanco, E-28049 Madrid, Spain
| | - Salvatore Torquato
- Department of Chemistry, Department of Physics, Institute for the Science and Technology of Materials, Program for Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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25
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Xu WS, Duan X, Sun ZY, An LJ. Glass formation in a mixture of hard disks and hard ellipses. J Chem Phys 2015; 142:224506. [DOI: 10.1063/1.4922379] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Wen-Sheng Xu
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Xiaozheng Duan
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Zhao-Yan Sun
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Li-Jia An
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
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26
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Abstract
Spheroellipsoids are truncated ellipsoids with spherical end caps. If gradients are assumed to change smoothly at the junction of body and cap, the truncation height z0 determines the geometry uniquely. The resulting model particle has only two shape parameters, namely, the aspect ratio c/a of the basic ellipsoid and the cutoff z0/a. These two parameters can be tuned to yield a continuous transformation between a pure ellipsoid and a spherocylinder. Since parallel hard spherocylinders display a nematic-smectic A phase transition, while ellipsoids do not, the influence of the particle shape on the possibility of a smectic phase may be investigated. A density functional analysis is used to detect the dividing line, in the (c/a, z0/a) plane, between the presence and absence of the N-S transition. Since spheroellipsoids may be useful as generic model particles for anisotropic molecules, we provide a computationally efficient overlap criterion for a pair in a general, non-parallel configuration.
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Affiliation(s)
- Franz J Vesely
- Computational Physics Group, Faculty of Physics, University of Vienna, Sensengasse 8, A-1090 Vienna, Austria
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27
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Dorosz S, Shegokar N, Schilling T, Oettel M. Strong effect of weak charging in suspensions of anisotropic colloids. SOFT MATTER 2014; 10:4717-4724. [PMID: 24851924 DOI: 10.1039/c4sm00612g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Suspensions of hard colloidal particles frequently serve as model systems in studies on fundamental aspects of phase transitions. But often colloidal particles that are considered as "hard" are in fact weakly charged. If the colloids are spherical, weak charging has only a weak effect on the structural properties of the suspension, which can be easily corrected for. However, this does not hold for anisotropic particles. We introduce a model for the interaction potential between charged ellipsoids of revolution (spheroids) based on the Derjaguin approximation of Debye-Hückel theory and present a computer simulation study on aspects of the system's structural properties and phase behaviour. In line with previous experimental observations, we find that even a weak surface charge has a strong impact on the correlation functions. A likewise strong impact is seen on the phase behaviour, in particular, we find stable cubatic order in suspensions of oblate ellipsoids.
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Affiliation(s)
- Sven Dorosz
- Université du Luxembourg, Theory of Soft Condensed Matter, L-1511 Luxembourg, Luxembourg.
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28
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Bautista-Carbajal G, Odriozola G. Phase diagram of two-dimensional hard ellipses. J Chem Phys 2014; 140:204502. [DOI: 10.1063/1.4878411] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [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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Chen D, Jiao Y, Torquato S. Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra. J Phys Chem B 2014; 118:7981-92. [DOI: 10.1021/jp5010133] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Duyu Chen
- Department
of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
- Physical
Science in Oncology Center, Princeton University, Princeton, New Jersey 08544, United States
| | - Yang Jiao
- Materials
Science and Engineering, Arizona State University, Tempe, Arizona 85287, United States
| | - Salvatore Torquato
- Department
of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
- Physical
Science in Oncology Center, Princeton University, Princeton, New Jersey 08544, United States
- Department
of Physics, Princeton University, Princeton, New Jersey 08544, United States
- Program
in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, United States
- Princeton
Institute of the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, United States
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30
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Varga S, Meneses-Júarez E, Odriozola G. Empty liquid phase of colloidal ellipsoids: The role of shape and interaction anisotropy. J Chem Phys 2014; 140:134905. [DOI: 10.1063/1.4869938] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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