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Almodóvar A, Galla T, López C. Extinction and coexistence in a binary mixture of proliferating motile disks. Phys Rev E 2024; 109:064140. [PMID: 39021032 DOI: 10.1103/physreve.109.064140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2024] [Accepted: 05/16/2024] [Indexed: 07/20/2024]
Abstract
A binary mixture of two-different-size proliferating motile disks is studied. As growth is space limited, we focus on the conditions such that there is a coexistence of both large and small disks, or dominance of the larger disks. The study involves systematically varying some system parameters, such as diffusivities, growth rates, and self-propulsion velocities. In particular, we demonstrate that diffusing faster confers a competitive advantage, so that larger disks can in the long time coexist or even dominate the smaller ones. In the case of self-propelled disks, a coexistence regime is induced by the activity where the two types of disks show the same spatial distribution: both particles are phase separated or both are homogeneously distributed in the whole system.
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2
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Li YW, Yao Y, Ciamarra MP. Two-Dimensional Melting of Two- and Three-Component Mixtures. PHYSICAL REVIEW LETTERS 2023; 130:258202. [PMID: 37418714 DOI: 10.1103/physrevlett.130.258202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2023] [Revised: 05/16/2023] [Accepted: 06/01/2023] [Indexed: 07/09/2023]
Abstract
We elucidate the interplay between diverse two-dimensional melting pathways and establish solid-hexatic and hexatic-liquid transition criteria via the numerical simulations of the melting transition of two- and three-component mixtures of hard polygons and disks. We show that a mixture's melting pathway may differ from its components and demonstrate eutectic mixtures that crystallize at a higher density than their pure components. Comparing the melting scenario of many two- and three-component mixtures, we establish universal melting criteria: the solid and hexatic phases become unstable as the density of topological defects, respectively, overcomes ρ_{d,s}≃0.046 and ρ_{d,h}≃0.123.
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Affiliation(s)
- Yan-Wei Li
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Yugui Yao
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Massimo Pica Ciamarra
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore; CNR-SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy; and CNRS@CREATE LTD, 1 Create Way, #08-01 CREATE Tower, Singapore 138602, Singapore
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3
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Gupta M, Chaudhuri P, Bec J, Ray SS. Turbulent route to two-dimensional soft crystals. Phys Rev E 2022; 106:L062601. [PMID: 36671119 DOI: 10.1103/physreve.106.l062601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2019] [Accepted: 11/09/2022] [Indexed: 06/17/2023]
Abstract
We investigate the effect of a two-dimensional, incompressible, turbulent flow on soft granular particles and show the emergence of a crystalline phase due to the interplay of Stokesian drag and short-range interparticle interactions. We quantify this phase through the bond order parameter and local density fluctuations and find a sharp transition between the crystalline and noncrystalline phases as a function of the Stokes number. Furthermore, the nature of preferential concentration, characterized by the correlation dimension, is significantly different from that of particle-laden flows in the absence of repulsive potentials.
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Affiliation(s)
- Mohit Gupta
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Pinaki Chaudhuri
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India
| | - Jérémie Bec
- Université Côte d'Azur, Inria, CNRS, Cemef, 06902 Sophia-Antipolis, France
- MINES ParisTech, PSL Research University, CNRS, CEMEF, 06904 Sophia-Antipolis, France
| | - Samriddhi Sankar Ray
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
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4
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McCray ARC, Li Y, Basnet R, Pandey K, Hu J, Phelan DP, Ma X, Petford-Long AK, Phatak C. Thermal Hysteresis and Ordering Behavior of Magnetic Skyrmion Lattices. NANO LETTERS 2022; 22:7804-7810. [PMID: 36129969 DOI: 10.1021/acs.nanolett.2c02275] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The physics of phase transitions in two-dimensional (2D) systems underpins research in diverse fields including statistical mechanics, nanomagnetism, and soft condensed matter. However, many aspects of 2D phase transitions are still not well understood, including the effects of interparticle potential, polydispersity, and particle shape. Magnetic skyrmions are chiral spin-structure quasi-particles that form two-dimensional lattices. Here, we show, by real-space imaging using in situ cryo-Lorentz transmission electron microscopy coupled with machine learning image analysis, the ordering behavior of Néel skyrmion lattices in van der Waals Fe3GeTe2. We demonstrate a distinct change in the skyrmion size distribution during field-cooling, which leads to a loss of lattice order and an evolution of the skyrmion liquid phase. Remarkably, the lattice order is restored during field heating and demonstrates a thermal hysteresis. This behavior is explained by the skyrmion energy landscape and demonstrates the potential to control the lattice order in 2D phase transitions.
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Affiliation(s)
- Arthur R C McCray
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
- Applied Physics Program, Northwestern University, Evanston, Illinois 60208, United States
| | - Yue Li
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Rabindra Basnet
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, United States
| | - Krishna Pandey
- Materials Science and Engineering Program, University of Arkansas, Fayetteville, Arkansas 72701, United States
| | - Jin Hu
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, United States
- Materials Science and Engineering Program, University of Arkansas, Fayetteville, Arkansas 72701, United States
| | - Daniel P Phelan
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Xuedan Ma
- Center for Nanoscale Materials, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Amanda K Petford-Long
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Charudatta Phatak
- Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States
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5
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Self-assembly in binary mixtures of spherical colloids. Adv Colloid Interface Sci 2022; 308:102748. [DOI: 10.1016/j.cis.2022.102748] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Revised: 06/16/2022] [Accepted: 07/29/2022] [Indexed: 11/18/2022]
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6
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Downs JG, Smith ND, Mandadapu KK, Garrahan JP, Smith MI. Topographic Control of Order in Quasi-2D Granular Phase Transitions. PHYSICAL REVIEW LETTERS 2021; 127:268002. [PMID: 35029468 DOI: 10.1103/physrevlett.127.268002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2021] [Accepted: 10/21/2021] [Indexed: 06/14/2023]
Abstract
We experimentally investigate the nature of 2D phase transitions in a quasi-2D granular fluid. Using a surface decorated with periodically spaced dimples we observe interfacial tension between coexisting granular liquid and crystal phases. Measurements of the orientational and translational order parameters and associated susceptibilities indicate that the surface topography alters the order of the phase transition from a two-step continuous one to a first-order liquid-solid one. The interplay of boundary inelasticity and geometry, either order promoting or inhibiting, controls whether it is the granular crystal or the granular fluid which makes contact with the edge. This order induced wetting has important consequences, determining how coexisting phases separate spatially.
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Affiliation(s)
- J G Downs
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
| | - N D Smith
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
| | - K K Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - J P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
| | - M I Smith
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
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7
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Guo WC, Ai BQ, He L. Data-driven criterion for the solid-liquid transition of two-dimensional self-propelled colloidal particles far from equilibrium. Phys Rev E 2021; 104:044611. [PMID: 34781493 DOI: 10.1103/physreve.104.044611] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2021] [Accepted: 10/13/2021] [Indexed: 11/07/2022]
Abstract
We establish an explicit data-driven criterion for identifying the solid-liquid transition of two-dimensional self-propelled colloidal particles in the far from equilibrium parameter regime, where the transition points predicted by different conventional empirical criteria for melting and freezing diverge. This is achieved by applying a hybrid machine learning approach that combines unsupervised learning with supervised learning to analyze a huge amount of the system's configurations in the nonequilibrium parameter regime on an equal footing. Furthermore, we establish a generic data-driven evaluation function, according to which the performance of different empirical criteria can be systematically evaluated and improved. In particular, by applying this evaluation function, we identify a new nonequilibrium threshold value for the long-time diffusion coefficient, based on which the predictions of the corresponding empirical criterion are greatly improved in the far from equilibrium parameter regime. These data-driven approaches provide a generic tool for investigating phase transitions in complex systems where conventional empirical ones face difficulties.
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Affiliation(s)
- Wei-Chen Guo
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China and Guangdong-Hong Kong Joint Laboratory of Quantum Matter, South China Normal University, Guangzhou 510006, China
| | - Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China and Guangdong-Hong Kong Joint Laboratory of Quantum Matter, South China Normal University, Guangzhou 510006, China
| | - Liang He
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China and Guangdong-Hong Kong Joint Laboratory of Quantum Matter, South China Normal University, Guangzhou 510006, China
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8
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Suda K, Suematsu A, Akiyama R. Lateral depletion effect on two-dimensional ordering of bacteriorhodopsins in a lipid bilayer: A theoretical study based on a binary hard-disk model. J Chem Phys 2021; 154:204904. [PMID: 34241177 DOI: 10.1063/5.0044399] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The 2D ordering of bacteriorhodopsins in a lipid bilayer was studied using a binary hard-disk model. The phase diagrams were calculated taking into account the lateral depletion effects. The critical concentrations of the protein ordering for monomers and trimers were obtained from the phase diagrams. The critical concentration ratio agreed well with the experiment when the repulsive core interaction between the depletants, namely, lipids, was taken into account. The results suggest that the depletion effect plays an important role in the association behaviors of transmembrane proteins.
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Affiliation(s)
- Keiju Suda
- Department of Chemistry, Graduate School of Science, Kyushu University, Fukuoka 819-0395, Japan
| | - Ayumi Suematsu
- Faculty of Science and Engineering, Kyushu Sangyo University, Fukuoka 813-8503, Japan
| | - Ryo Akiyama
- Department of Chemistry, Graduate School of Science, Kyushu University, Fukuoka 819-0395, Japan
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Guo J, Nie Y, Xu N. Signatures of continuous hexatic-liquid transition in two-dimensional melting. SOFT MATTER 2021; 17:3397-3403. [PMID: 33645612 DOI: 10.1039/d0sm02199g] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Recent studies have shown that the melting of two-dimensional crystals can be either continuous or discontinuous, relying on multiple parameters such as particle stiffness, density, and particle size dispersity. However, what determines the continuity or discontinuity of the two-dimensional melting remains elusive. Here we study the two-dimensional melting of binary mixtures of soft-core particles. The two particle species are different in either particle size or particle stiffness. Starting with the mono-component systems which exhibit discontinuous hexatic-liquid transition, we gradually increase the particle size or stiffness dispersity and find that the hexatic-liquid coexistent region shrinks and eventually vanishes above a critical dispersity. Therefore, the growth of disorder caused by the particle size or stiffness dispersity leads to the discontinuous-continuous transition of the two-dimensional melting. We further find that as long as the melting is continuous the defect concentrations on the boundary between hexatic and liquid phases remain almost constant, accompanied by an almost constant correlation length. These characteristic defect concentrations and correlation length are universal and independent of particle interactions, temperature, and type of particle dispersity, which act as signatures of the continuous two-dimensional melting.
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Affiliation(s)
- Jialing Guo
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Microscale Magnetic Resonance and Department of Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
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10
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Li YW, Ciamarra MP. Phase behavior of Lennard-Jones particles in two dimensions. Phys Rev E 2020; 102:062101. [PMID: 33466090 DOI: 10.1103/physreve.102.062101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2020] [Accepted: 11/04/2020] [Indexed: 06/12/2023]
Abstract
The phase diagram of the prototypical two-dimensional Lennard-Jones (LJ) system, while extensively investigated, is still debated. In particular, there are controversial results in the literature with regard to the existence of the hexatic phase and the melting scenario. Here we study the phase behavior of two-dimensional range-limited LJ particles via large-scale numerical simulations. We demonstrate that at a high temperature, when the attraction in the potential plays a minor role, melting occurs via a continuous solid-hexatic transition followed by a first-order hexatic-fluid transition. The hexatic phase occurs in a density range that vanishes as the temperature decreases so that at low-temperature melting occurs via a first-order liquid-solid transition. The temperature where the hexatic phase disappears is well above the liquid-gas critical temperature. The evolution of the density of topological defects confirms this scenario.
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Affiliation(s)
- Yan-Wei Li
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Massimo Pica Ciamarra
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- CNR-SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126, Napoli, Italy
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11
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Sampedro Ruiz P, Ni R. Effect of particle size distribution on polydisperse hard disks. J Chem Phys 2020; 153:174501. [PMID: 33167632 DOI: 10.1063/5.0026910] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using Monte Carlo simulations, we systematically investigate the effect of particle size distribution on the phase behavior of polydisperse hard disks. Compared with the commonly used Gaussian-like polydisperse hard disks [P. Sampedro Ruiz, Q.-l. Lei, and R. Ni, Commun. Phys. 2, 70 (2019)], we find that the phase behavior of polydisperse hard-disk systems with lognormal and triangle distributions is significantly different. In polydisperse hard-disk systems of lognormal distributions, although the phase diagram appears similar to that of Gaussian-like polydisperse hard disks, the re-entrant melting of the hexatic or solid phase cannot be observed in sedimentation experiments. For polydisperse hard-disk systems of triangle distributions, the phase behavior is qualitatively different from the Gaussian-like and lognormal distributions, and we cannot reach any system of true polydispersity larger than 0.06, which is due to the special shape of the triangle distribution. Our results suggest that the exact particle size distribution is of primary importance in determining the phase behavior of polydisperse hard disks, and we do not have a universal phase diagram for different polydisperse hard-disk systems.
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Affiliation(s)
- Pablo Sampedro Ruiz
- School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, 637459, Singapore
| | - Ran Ni
- School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, 637459, Singapore
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12
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Mizani S, Gurin P, Aliabadi R, Salehi H, Varga S. Demixing and tetratic ordering in some binary mixtures of hard superellipses. J Chem Phys 2020; 153:034501. [PMID: 32716200 DOI: 10.1063/5.0009705] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Abstract
We examine the fluid phase behavior of binary mixtures of hard superellipses using the scaled particle theory. The superellipse is a general two-dimensional convex object that can be tuned between the elliptical and rectangular shapes continuously at a given aspect ratio. We find that the shape of the particle affects strongly the stability of isotropic, nematic, and tetratic phases in the mixture even if the side lengths of both species are fixed. While the isotropic-isotropic demixing transition can be ruled out using the scaled particle theory, the first order isotropic-nematic and the nematic-nematic demixing transition can be stabilized with strong fractionation between the components. It is observed that the demixing tendency is strongest in small rectangle-large ellipse mixtures. Interestingly, it is possible to stabilize the tetratic order at lower densities in the mixture of hard squares and rectangles where the long rectangles form a nematic phase, while the squares stay in the tetratic order.
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Affiliation(s)
- Sakine Mizani
- Department of Physics, Faculty of Science, Shahid Chamran University of Ahvaz, Ahvaz, Iran
| | - Péter Gurin
- Institute of Physics and Mechatronics, University of Pannonia, P.O. Box 158, Veszprém H-8201, Hungary
| | - Roohollah Aliabadi
- Department of Physics, Faculty of Science, Fasa University, 74617-81189 Fasa, Iran
| | - Hamdollah Salehi
- Department of Physics, Faculty of Science, Shahid Chamran University of Ahvaz, Ahvaz, Iran
| | - Szabolcs Varga
- Institute of Physics and Mechatronics, University of Pannonia, P.O. Box 158, Veszprém H-8201, Hungary
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H A, Chaudhuri P. Dense hard disk ordering: influence of bidispersity and quenched disorder. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:414001. [PMID: 32521523 DOI: 10.1088/1361-648x/ab9b52] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2019] [Accepted: 06/10/2020] [Indexed: 06/11/2023]
Abstract
Using Monte Carlo simulations, the impact on structural ordering in two-dimensional systems via the interplay of size bidispersity and quenched disorder in the form of an externally applied spatially random potential, is studied for a system of hard disks. By scanning across a wide range of dense packing fractions, size ratios and roughness of the applied potential, the phase diagram is constructed, which demonstrates that both quenched and size disorders shift the onset of translational order to higher packings, while maintaining the presence of the intermediate hexatic phase. At larger disorder strengths, the signatures of structural order are absent within the range of investigated packing fractions. Further, the dynamics with increasing potential strength is analysed for the mono-component system to obtain a spatio-temporal description of the melting process. Finally, the influence of the externally rough field on the Mermin-Wagner fluctuations, characteristic to two-dimensional systems, is investigated.
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Affiliation(s)
- Arjun H
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai-600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Pinaki Chaudhuri
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai-600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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14
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Connecting glass-forming ability of binary mixtures of soft particles to equilibrium melting temperatures. Nat Commun 2020; 11:3198. [PMID: 32581262 PMCID: PMC7314759 DOI: 10.1038/s41467-020-16986-z] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2019] [Accepted: 06/05/2020] [Indexed: 11/29/2022] Open
Abstract
The glass-forming ability is an important material property for manufacturing glasses and understanding the long-standing glass transition problem. Because of the nonequilibrium nature, it is difficult to develop the theory for it. Here we report that the glass-forming ability of binary mixtures of soft particles is related to the equilibrium melting temperatures. Due to the distinction in particle size or stiffness, the two components in a mixture effectively feel different melting temperatures, leading to a melting temperature gap. By varying the particle size, stiffness, and composition over a wide range of pressures, we establish a comprehensive picture for the glass-forming ability, based on our finding of the direct link between the glass-forming ability and the melting temperature gap. Our study reveals and explains the pressure and interaction dependence of the glass-forming ability of model glass-formers, and suggests strategies to optimize the glass-forming ability via the manipulation of particle interactions. Glass-forming ability is an important parameter for manufacturing glassy materials, but it remains challenging to be characterized due to its nonequilibrium nature. Nie et al. provide a solution by linking it to the pressure dependence of melting temperature of constituent components in binary mixtures.
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15
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Li YW, Ciamarra MP. Attraction Tames Two-Dimensional Melting: From Continuous to Discontinuous Transitions. PHYSICAL REVIEW LETTERS 2020; 124:218002. [PMID: 32530644 DOI: 10.1103/physrevlett.124.218002] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2020] [Accepted: 05/07/2020] [Indexed: 06/11/2023]
Abstract
Two-dimensional systems may admit a hexatic phase and hexatic-liquid transitions of different natures. The determination of their phase diagrams proved challenging, and indeed, those of hard disks, hard regular polygons, and inverse power-law potentials have only recently been clarified. In this context, the role of attractive forces is currently speculative, despite their prevalence at both the molecular and colloidal scale. Here, we demonstrate, via numerical simulations, that attraction promotes a discontinuous melting scenario with no hexatic phase. At high-temperature, Lennard-Jones particles and attractive polygons follow the shape-dominated melting scenario observed in hard disks and hard polygons, respectively. Conversely, all systems melt via a first-order transition with no hexatic phase at low temperature, where attractive forces dominate. The intermediate temperature melting scenario is shape dependent. Our results suggest that, in colloidal experiments, the tunability of the strength of the attractive forces allows for the observation of different melting scenarios in the same system.
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Affiliation(s)
- Yan-Wei Li
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Massimo Pica Ciamarra
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- CNR-SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy
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16
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H A, Chaudhuri P. Glass forming liquids in a quenched random potential. SOFT MATTER 2020; 16:3574-3585. [PMID: 32222740 DOI: 10.1039/c9sm01729a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The response of a model two-dimensional colloidal glass former to an externally imposed spatially random potential, which acts as a quenched disorder, is investigated using numerical simulations, motivated by recent experiments and also mean field predictions. The external potential induces the onset of the glassy dynamics at increasingly smaller field roughness, with increasing packing fraction of the particulate assembly, and the existence of aging processes within the glassy regime is also observed. Furthermore, along the axis of increasing field roughness, the dynamical slowdown is not correlated to the hexatic order within the supercooled regime.
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Affiliation(s)
- Arjun H
- The Institute of Mathematical Sciences, Taramani, Chennai-600113, India
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17
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Bolmatov D, Zav'yalov D, Carrillo JM, Katsaras J. Fractal boundaries underpin the 2D melting of biomimetic rafts. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2020; 1862:183249. [PMID: 32147353 DOI: 10.1016/j.bbamem.2020.183249] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2019] [Revised: 02/07/2020] [Accepted: 02/10/2020] [Indexed: 02/05/2023]
Affiliation(s)
- Dima Bolmatov
- Large Scale Structures Group, Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States; Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, United States.
| | | | - Jan-Michael Carrillo
- Center for Nanophase Materials Sciences and Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States
| | - John Katsaras
- Large Scale Structures Group, Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States; Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, United States.
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18
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Li YW, Ciamarra MP. Accurate determination of the translational correlation function of two-dimensional solids. Phys Rev E 2019; 100:062606. [PMID: 31962434 DOI: 10.1103/physreve.100.062606] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2019] [Indexed: 06/10/2023]
Abstract
The identification of the different phases of a two-dimensional (2D) system, which might be solid, hexatic, or liquid, requires the accurate determination of the correlation function of the translational and bond-orientational order parameters. According to the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory, in the solid phase the translational correlation function decays algebraically, as a consequence of the Mermin-Wagner long-wavelength fluctuations. However, recent results have shown an exponential-like decay. By revisiting different definitions of the translational correlation function commonly used in the literature, here we clarify that the observed exponential-like decay in the solid phase results from an inaccurate determination of the symmetry axis of the solid; the expected power-law behavior is recovered when the symmetry axis is properly identified. We show that, contrary to the common assumption, the symmetry axis of a 2D solid is not fixed by the direction of its global bond-orientational parameter, and we introduce an approach allowing one to determine the symmetry axis from a real space analysis of the sample.
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Affiliation(s)
- Yan-Wei Li
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Massimo Pica Ciamarra
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- CNR-SPIN, Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126, Napoli, Italy
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Hajibabaei A, Kim KS. First-order and continuous melting transitions in two-dimensional Lennard-Jones systems and repulsive disks. Phys Rev E 2019; 99:022145. [PMID: 30934337 DOI: 10.1103/physreve.99.022145] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2017] [Indexed: 06/09/2023]
Abstract
In two-dimensional Lennard-Jones (LJ) systems, a small interval of melting-mode switching occurs below which the melting occurs by first-order phase transitions in lieu of the melting scenario proposed by Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY). The extrapolated upper bound for phase coexistence is at density ρ∼0.893 and temperature T∼1.1, both in reduced LJ units. The two-stage KTHNY scenario is restored at higher temperatures, and the isothermal melting scenario is universal. The solid-hexatic and hexatic-liquid transitions in KTHNY theory, even so continuous, are distinct from typical continuous phase transitions in that instead of scale-free fluctuations, they are characterized by unbinding of topological defects, resulting in a special form of divergence of the correlation length: ξ≈exp(b|T-T_{c}|^{-ν}). Here such a divergence is firmly established for a two-dimensional melting phenomenon, providing a conclusive proof of the KTHNY melting. We explicitly confirm that this high-temperature melting behavior of the LJ system is consistent with the melting behavior of the r^{-12} potential and that melting of the r^{-n} potential is KTHNY-like for n≤12 but melting of the r^{-64} potential is first order; similar to hard disks. Therefore we suggest that the melting scenario of these repulsive potentials becomes hard-disk-like for an exponent in the range 12<n<64.
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Affiliation(s)
- Amir Hajibabaei
- Center for Superfunctional Materials, Department of Chemistry and Department of Physics, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Korea
| | - Kwang S Kim
- Center for Superfunctional Materials, Department of Chemistry and Department of Physics, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Korea
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Guo Z, Kindt JT. Partitioning of Size-Mismatched Impurities to Grain Boundaries in 2d Solid Hard-Sphere Monolayers. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2018; 34:12947-12956. [PMID: 30296104 DOI: 10.1021/acs.langmuir.8b02633] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Computational studies have been carried out to investigate the equilibrium partitioning of size-mismatched impurities between the bulk solid and grain boundary (GB) environments in 2d hard-sphere monolayers. The solvent repacking Monte Carlo method and a new variation were used to exchange varying numbers and types of particles under conditions of fixed particle fugacities, allowing efficient sampling of impurity particle distributions even within the bulk solid. Measurements of GB stiffness depression arising from the impurities were made via the capillary fluctuation method and found to agree with calculations based on the Gibbs adsorption isotherm, providing a test of the internal consistency of the results. The dependence of the excess concentration at the GB on factors, including impurity size (diameter ratios λ = 0.5-4 times the majority host particle diameter), impurity concentration, grain misorientation angle, and packing pressure, was studied. In general, the affinity of impurity particles for GB increased with the difference between their size and the host particles, and varied with grain misorientation angle with a dependence reflecting the excess free area at the GB. Impurities with λ = 4 were exceptions to both these trends, due to their ability to substitute efficiently for six-coordinate host particles within the bulk and for five-coordinate host particles at dislocations in the grain boundaries. Comparison with results from an experimental study of mixed colloidal monolayers raises questions about how kinetic effects during grain coarsening might produce less impurity segregation to the GB than equilibrium exchange.
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Affiliation(s)
- Ziwei Guo
- Department of Chemistry , Emory University , 201 Dowman Drive , Atlanta , Georgia 30322 , United States
| | - James T Kindt
- Department of Chemistry , Emory University , 201 Dowman Drive , Atlanta , Georgia 30322 , United States
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Royall CP, Turci F, Tatsumi S, Russo J, Robinson J. The race to the bottom: approaching the ideal glass? JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:363001. [PMID: 29972145 DOI: 10.1088/1361-648x/aad10a] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Key to resolving the scientific challenge of the glass transition is to understand the origin of the massive increase in viscosity of liquids cooled below their melting temperature (avoiding crystallisation). A number of competing and often mutually exclusive theoretical approaches have been advanced to describe this phenomenon. Some posit a bona fide thermodynamic phase to an 'ideal glass', an amorphous state with exceptionally low entropy. Other approaches are built around the concept of the glass transition as a primarily dynamic phenomenon. These fundamentally different interpretations give equally good descriptions of the data available, so it is hard to determine which-if any-is correct. Recently however this situation has begun to change. A consensus has emerged that one powerful means to resolve this longstanding question is to approach the putative thermodynamic transition sufficiently closely, and a number of techniques have emerged to meet this challenge. Here we review the results of some of these new techniques and discuss the implications for the existence-or otherwise-of the thermodynamic transition to an ideal glass.
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Affiliation(s)
- C Patrick Royall
- HH Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom. School of Chemistry, University of Bristol, Cantock Close, Bristol, BS8 1TS, United Kingdom. Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol, BS8 1FD, United Kingdom
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22
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Thorneywork AL, Schnyder SK, Aarts DGAL, Horbach J, Roth R, Dullens RPA. Structure factors in a two-dimensional binary colloidal hard sphere system. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1492745] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Alice L. Thorneywork
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford, UK
- Cavendish Laboratory, University of Cambridge, Cambridge, UK
| | - Simon K. Schnyder
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto, Japan
| | - Dirk G. A. L. Aarts
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford, UK
| | - Jürgen Horbach
- Institut für Theoretische Physik II, Heinrich-Heine Universität Düsseldorf, Düsseldorf, Germany
| | - Roland Roth
- Institut für Theoretische Physik, Universität Tübingen, Tübingen, Germany
| | - Roel P. A. Dullens
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford, UK
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Lin SC, Oettel M. Phase diagrams and crystal-fluid surface tensions in additive and nonadditive two-dimensional binary hard-disk mixtures. Phys Rev E 2018; 98:012608. [PMID: 30110806 DOI: 10.1103/physreve.98.012608] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2018] [Indexed: 06/08/2023]
Abstract
Using density functionals from fundamental measure theory, phase diagrams and crystal-fluid surface tensions in additive and nonadditive (Asakura-Oosawa model) two-dimensional binary hard-disk mixtures are determined for the whole range of size ratios q=smalldiameter/largediameter, assuming random disorder (lattice points or interstitial occupied by large or small disks at random) in the crystal phase. The fluid-crystal transitions are first order due to the assumption of a periodic unit cell in the density-functional calculations. Qualitatively, the shape of the phase diagrams is similar to the case of three-dimensional hard-sphere mixtures. For the nonadditive case, a broadening of the fluid-crystal coexistence region is found for small q, whereas for large q a vapor-fluid transition intervenes. In the additive case, we find a sequence of spindle-type, azeotropic, and eutectic phase diagrams upon lowering q from 1 to 0.6. The transition from azeotropic to eutectic is different from the three-dimensional case. Surface tensions in general become smaller (up to a factor 2) upon addition of a second species and they are rather small. The minimization of the functionals proceeds without restrictions and optimized graphics card routines are used.
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Affiliation(s)
- Shang-Chun Lin
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
| | - Martin Oettel
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
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Kryuchkov NP, Yurchenko SO, Fomin YD, Tsiok EN, Ryzhov VN. Complex crystalline structures in a two-dimensional core-softened system. SOFT MATTER 2018; 14:2152-2162. [PMID: 29488995 DOI: 10.1039/c7sm02429k] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
A transition from a square to a hexagonal lattice is studied in a 2D system of particles interacting via a core-softened potential. Due to the presence of two length scales of repulsion, different local configurations with four, five, and six neighbors are possible, leading to the formation of complex crystals. The previously proposed interpolation method is generalized to calculate pair correlations in crystals whose unit cell consists of more than one particle. The high efficiency of the method is illustrated using a snub square lattice as a representative example. Molecular dynamics simulations show that the snub square lattice is broken upon heating, generating a high-density quasicrystalline phase with 12-fold symmetry (HD12 phase). A simple theoretical model is proposed to explain the physical mechanism responsible for this phenomenon: with an increase in the density (from square to hexagonal phases), the concentrations of different local configurations randomly realized through a plane tiling change, which minimizes the energy of the system. The calculated phase diagram in the intermediate density range justifies the existence of the HD12 phase and demonstrates a cascade of first-order transitions "square - HD12 - hexagonal" solid phases with increasing density. The results allow us to better understand the physical mechanisms responsible for the formation of quasicrystals, and, therefore, should be of interest for broad community in materials science and soft matter.
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Affiliation(s)
- Nikita P Kryuchkov
- Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, 105005 Moscow, Russia.
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