1
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Fayen E, Filion L, Foffi G, Smallenburg F. Quasicrystal of Binary Hard Spheres on a Plane Stabilized by Configurational Entropy. PHYSICAL REVIEW LETTERS 2024; 132:048202. [PMID: 38335332 DOI: 10.1103/physrevlett.132.048202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Revised: 09/08/2023] [Accepted: 01/03/2024] [Indexed: 02/12/2024]
Abstract
Because of their aperiodic nature, quasicrystals are one of the least understood phases in statistical physics. One significant complication they present in comparison to their periodic counterparts is the fact that any quasicrystal can be realized as an exponentially large number of different tilings, resulting in a significant contribution to the quasicrystal entropy. Here, we use free-energy calculations to demonstrate that it is this configurational entropy which stabilizes a dodecagonal quasicrystal in a binary mixture of hard spheres on a plane. Our calculations also allow us to quantitatively confirm that in this system all tiling realizations are essentially equally likely, with free-energy differences less than 0.0001k_{B}T per particle-an observation that could be related to the observation of only random tilings in soft-matter quasicrystals. Owing to the simplicity of the model and its available counterparts in colloidal experiments, we believe that this system is an excellent candidate to achieve the long-awaited quasicrystal self-assembly on the micron scale.
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Affiliation(s)
- Etienne Fayen
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Laura Filion
- Soft Condensed Matter, Debye Institute of Nanomaterials Science, Utrecht University, Utrecht, Netherlands
| | - Giuseppe Foffi
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Frank Smallenburg
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
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2
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Ruzzi V, Baglioni J, Piazza R. Optothermal crystallization of hard spheres in an effective bidimensional geometry. J Chem Phys 2023; 159:154904. [PMID: 37850694 DOI: 10.1063/5.0169221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 10/01/2023] [Indexed: 10/19/2023] Open
Abstract
Using colloids effectively confined in two dimensions by a cell with a thickness comparable to the particle size, we investigate the nucleation and growth of crystallites induced by locally heating the solvent with a near-infrared laser beam. The particles, which are "thermophilic," move towards the laser spot solely because of thermophoresis with no convection effects, forming dense clusters whose structure is monitored using two order parameters that gauge the local density and the orientational ordering. We find that ordering takes place when the cluster reaches an average surface density that is still below the upper equilibrium limit for the fluid phase of hard disks, meaning that we do not detect any sign of a proper "two-stage" nucleation from a glass or a polymorphic crystal structure. The crystal obtained at late growth stage displays a remarkable uniformity with a negligible amount of defects, arguably because the incoming particles diffuse, bounce, and displace other particles before settling at the crystal interface. This "fluidization" of the outer crystal edge may resemble the surface enhanced mobility giving rise to ultra-stable glasses by physical vapor deposition.
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Affiliation(s)
- Vincenzo Ruzzi
- Department of Chemistry, Materials Science, and Chemical Engineering (CMIC) "Giulio Natta," Politecnico di Milano, Edificio 6, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Jacopo Baglioni
- Department of Chemistry, Materials Science, and Chemical Engineering (CMIC) "Giulio Natta," Politecnico di Milano, Edificio 6, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Roberto Piazza
- Department of Chemistry, Materials Science, and Chemical Engineering (CMIC) "Giulio Natta," Politecnico di Milano, Edificio 6, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
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3
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Škvára J, Nezbeda I, Urbic T. Supercooled water in two dimensions: Structure and thermodynamics of the Mercedes-Benz model. J Mol Liq 2023; 386:122445. [PMID: 37435361 PMCID: PMC10331298 DOI: 10.1016/j.molliq.2023.122445] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/13/2023]
Abstract
The two-dimensional Mercedes-Benz model of water has been studied by molecular simulations over a wide range of thermodynamic conditions as an attempt to locate the supercooled region where a liquid-liquid separation and, potentially, also other structures may occur. Both the correlation functions and a number of local structure factors have been used to identify different structural arrangements. These include, in addition to the hexatic phase, also the hexagon, pentagon, and quadruplet arrangements. All these structures result from the competition between the hydrogen bonding and Lennard-Jones interactions and their effect at different temperatures and pressures. Based on the obtained results, an attempt is made to sketch a (rather complex) phase diagram of the model.
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Affiliation(s)
- Jiří Škvára
- Institute of Chemical Process Fundamentals, Czech Acad. Sci., 16502 Prague, Czech Republic
- Faculty of Science, J. E. Purkinje University, 40096 Ústí nad Labem, Czech Republic
| | - Ivo Nezbeda
- Faculty of Science, J. E. Purkinje University, 40096 Ústí nad Labem, Czech Republic
| | - Tomaz Urbic
- University of Ljubljana, Faculty of Chemistry and Chemical Technology, Večna pot 113, SI-1000 Ljubljana, Slovenia
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4
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Shi XQ, Cheng F, Chaté H. Extreme Spontaneous Deformations of Active Crystals. PHYSICAL REVIEW LETTERS 2023; 131:108301. [PMID: 37739375 DOI: 10.1103/physrevlett.131.108301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Accepted: 06/16/2023] [Indexed: 09/24/2023]
Abstract
We demonstrate that two-dimensional crystals made of active particles can experience extremely large spontaneous deformations without melting. Using particles mostly interacting via pairwise repulsive forces, we show that such active crystals maintain long-range bond order and algebraically decaying positional order, but with an exponent η not limited by the 1/3 bound given by the (equilibrium) KTHNY theory. We rationalize our findings using linear elastic theory and show the existence of two well-defined effective temperatures quantifying respectively large-scale deformations and bond-order fluctuations. The root of these phenomena lies in the sole time-persistence of the intrinsic axes of particles, and they should thus be observed in many different situations.
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Affiliation(s)
- Xia-Qing Shi
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China
| | - Fu Cheng
- Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China
| | - Hugues Chaté
- Service de Physique de l'Etat Condensé, CEA, CNRS Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Computational Science Research Center, Beijing 100094, China
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5
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Nishikawa Y, Krauth W, Maggs AC. Liquid-hexatic transition for soft disks. Phys Rev E 2023; 108:024103. [PMID: 37723788 DOI: 10.1103/physreve.108.024103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 06/28/2023] [Indexed: 09/20/2023]
Abstract
We study the liquid-hexatic transition of soft disks with massively parallel simulations and determine the equation of state as a function of system size. For systems with interactions decaying as the inverse mth power of the separation, the liquid-hexatic phase transition is continuous for m=12 and m=8, while it is of first order for m=24. The critical power m for the transition between continuous and first-order behavior is larger than previously reported. The continuous transition for m=12 implies that the two-dimensional Lennard-Jones model has a continuous liquid-hexatic transition at high temperatures. We also study the Weeks-Chandler-Andersen model and find a continuous transition at high temperatures that is consistent with the soft-disk case for m=12. Pressure data as well as our implementation are available from an open-source repository.
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Affiliation(s)
- Yoshihiko Nishikawa
- Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
| | - Werner Krauth
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris Cité, 75005 Paris, France
| | - A C Maggs
- CNRS UMR7083, ESPCI Paris, Université PSL, 10 rue Vauquelin, 75005 Paris, France
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6
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Eriçok OB, Mason JK. Geometric conjecture about phase transitions. Phys Rev E 2023; 107:064107. [PMID: 37464600 DOI: 10.1103/physreve.107.064107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2022] [Accepted: 05/05/2023] [Indexed: 07/20/2023]
Abstract
As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests that the existence of a phase transition could perhaps be inferred from changes to the topology of the accessible part of the configuration space. This paper instead suggests that such a topological change is often associated with a dramatic change in the configuration space geometry, and that the geometric change is the actual driver of the phase transition. More precisely, a geometric change that brings about a discontinuity in the mixing time required for an initial probability distribution on the configuration space to reach the steady state is conjectured to be related to the onset of a phase transition in the thermodynamic limit. This conjecture is tested by evaluating the diffusion diameter and ε-mixing time of the configuration spaces of hard-disk and hard-sphere systems of increasing size. Explicit geometries are constructed for the configuration spaces of these systems and numerical evidence suggests that a discontinuity in the ε-mixing time coincides with the solid-fluid phase transition in the thermodynamic limit.
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Affiliation(s)
- O B Eriçok
- Materials Science and Engineering, University of California, Davis, California 95616, USA
| | - J K Mason
- Materials Science and Engineering, University of California, Davis, California 95616, USA
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7
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Roberts RC, Palmer JC, Conrad JC. Long-Wavelength Fluctuations in Quasi-2D Supercooled Liquids. J Phys Chem B 2023; 127:961-969. [PMID: 36656297 DOI: 10.1021/acs.jpcb.2c07417] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
We use molecular simulation to characterize the dynamics of supercooled liquids confined in quasi-2D slit geometries. Similar to bulk supercooled liquids, the confined systems exhibit subdiffusive dynamics on intermediate time scales arising from particle localization inside their neighbor cages, followed by an eventual crossover to diffusive behavior as cage rearrangement occurs. The quasi-2D confined liquids also exhibit signatures of long-wavelength fluctuations (LWFs) in the lateral directions parallel to the confining walls, reminiscent of the collective displacements observed in 2D but not 3D systems. The magnitude of the LWFs increases with the lateral dimensions of systems with the same particle volume fraction and confinement length scale, consistent with the logarithmic scaling predicted for 2D Mermin-Wagner fluctuations. The amplitude of the fluctuations is a nonmonotonic function of the confinement length scale because of a competition between caging and strengthening LWFs upon approaching the 2D limit. Our findings suggest that LWFs may play an important role in understanding the behavior of confined supercooled liquids due to their prevalence over a surprisingly broad range of particle densities and confinement length scales.
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Affiliation(s)
- Ryan C Roberts
- Department of Chemical and Biomolecular Engineering, University of Houston, Houston, Texas77204-4004, United States
| | - Jeremy C Palmer
- Department of Chemical and Biomolecular Engineering, University of Houston, Houston, Texas77204-4004, United States
| | - Jacinta C Conrad
- Department of Chemical and Biomolecular Engineering, University of Houston, Houston, Texas77204-4004, United States
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8
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Li B, Nishikawa Y, Höllmer P, Carillo L, Maggs AC, Krauth W. Hard-disk pressure computations-a historic perspective. J Chem Phys 2022; 157:234111. [PMID: 36550024 DOI: 10.1063/5.0126437] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
We discuss pressure computations for the hard-disk model performed since 1953 and compare them to the results that we obtain with a powerful event-chain Monte Carlo and a massively parallel Metropolis algorithm. Like other simple models in the sciences, such as the Drosophila model of biology, the hard-disk model has needed monumental efforts to be understood. In particular, we argue that the difficulty of estimating the pressure has not been fully realized in the decades-long controversy over the hard-disk phase-transition scenario. We present the physics of the hard-disk model, the definition of the pressure and its unbiased estimators, several of which are new. We further treat different sampling algorithms and crucial criteria for bounding mixing times in the absence of analytical predictions. Our definite results for the pressure, for up to one million disks, may serve as benchmarks for future sampling algorithms. A synopsis of hard-disk pressure data as well as different versions of the sampling algorithms and pressure estimators are made available in an open-source repository.
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Affiliation(s)
- Botao Li
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris Cité, Paris, France
| | - Yoshihiko Nishikawa
- Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
| | - Philipp Höllmer
- Physikalisches Institut and Bethe Center for Theoretical Physics, University of Bonn, Nussallee 12, 53115 Bonn, Germany
| | - Louis Carillo
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris Cité, Paris, France
| | - A C Maggs
- CNRS Gulliver, ESPCI Paris, Université PSL, 10 rue Vauquelin, 75005 Paris, France
| | - Werner Krauth
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris Cité, Paris, France
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9
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Hendley RS, Zhang L, Bevan MA. Design rules for 2D field mediated assembly of different shaped colloids into diverse microstructures. SOFT MATTER 2022; 18:9273-9282. [PMID: 36445724 DOI: 10.1039/d2sm01078j] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Assembling different shaped particles into ordered microstructures is an open challenge in creating multifunctional particle-based materials and devices. Here, we report the two-dimensional (2D) AC electric field mediated assembly of different shaped colloidal particles into amorphous, liquid crystalline, and crystalline microstructures. Particle shapes investigated include disks, ellipses, squares, and rectangles, which show how systematic variations in anisotropy and corner curvature determine the number and type of resulting microstructures. AC electric fields induce dipolar interactions to control particle positional and orientational order. Microstructural states are determined via particle tracking to compute order parameters, which agree with computer simulations and show how particle packing and dipolar interactions together produce each structure. Results demonstrate how choice of particle shape and field conditions enable kinetically viable routes to assemble nematic, tetratic, and smectic liquid crystal structures as well as crystals with stretched 4- and 6-fold symmetry. Results show it is possible to assemble all corresponding hard particle phases, but also show how dipolar interactions influence and produce additional microstructures. Our findings provide design rules for the assembly of diverse microstructures of different shaped particles in AC electric fields, which could enable scalable and reconfigurable particle-based materials, displays, and printing technologies.
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Affiliation(s)
- Rachel S Hendley
- Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Lechuan Zhang
- Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Michael A Bevan
- Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
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10
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Lima EO, Pereira PCN, Apolinario SWS. Local orderings in the melting process of a square crystal and in the resulting liquid. Phys Rev E 2022; 106:054106. [PMID: 36559510 DOI: 10.1103/physreve.106.054106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2022] [Accepted: 10/12/2022] [Indexed: 06/17/2023]
Abstract
Using Brownian dynamics simulations we investigate the melting processes of a square crystalline lattice of colloidal particles interacting via an isotropic potential, which comprises both a hard-core repulsion and an additional softened square-well potential. For temperatures slightly lower than the transition one, we found a proliferation of small liquid clusters surrounded by the square lattice. These clusters are not static, quite the opposite, they have an intense dynamics and are continuously formed and destroyed over time. However, no unbound topological defects are observed. At the transition temperature, one of these liquid clusters starts to grow, until the entire system becomes in the liquid phase, then, characterizing a first-order phase transition. The tetratic intermediate phase, as given by the KTHNY theory, was not observed. Moreover, the liquid phase exhibits a considerable number of crystalline clusters having square and triangular orderings, which remain present even when increasing temperature by an order of magnitude. As the temperature increases, structural changes within the liquid phase are analyzed by evaluating the number and sizes of the square and triangular clusters. A transition of the dominant clusters is observed.
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Affiliation(s)
- E O Lima
- Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil
| | - P C N Pereira
- Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil
| | - S W S Apolinario
- Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil
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11
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Jaleel AAA, Mandal D, Thomas JE, Rajesh R. Freezing phase transition in hard-core lattice gases on the triangular lattice with exclusion up to seventh next-nearest neighbor. Phys Rev E 2022; 106:044136. [PMID: 36397521 DOI: 10.1103/physreve.106.044136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2022] [Accepted: 08/05/2022] [Indexed: 06/16/2023]
Abstract
Hard-core lattice-gas models are minimal models to study entropy-driven phase transitions. In the k-nearest-neighbor lattice gas, a particle excludes all sites up to the kth next-nearest neighbors from being occupied by another particle. As k increases from one, it extrapolates from nearest-neighbor exclusion to the hard-sphere gas. In this paper we study the model on the triangular lattice for k≤7 using a flat histogram algorithm that includes cluster moves. Earlier studies focused on k≤3. We show that for 4≤k≤7, the system undergoes a single phase transition from a low-density fluid phase to a high-density sublattice-ordered phase. Using partition function zeros and nonconvexity properties of the entropy, we show that the transitions are discontinuous. The critical chemical potential, coexistence densities, and critical pressure are determined accurately.
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Affiliation(s)
- Asweel Ahmed A Jaleel
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
- Department of Physics, Sadakathullah Appa College, Tirunelveli, Tamil Nadu 627011, India
| | - Dipanjan Mandal
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Jetin E Thomas
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - R Rajesh
- 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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12
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Gaiduk EA, Fomin YD, Tsiok EN, Ryzhov VN. Anomalous behavior of a two-dimensional Hertzian disk system. Phys Rev E 2022; 106:024602. [PMID: 36110004 DOI: 10.1103/physreve.106.024602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Accepted: 07/18/2022] [Indexed: 06/15/2023]
Abstract
The anomalous behavior of a two-dimensional system of Hertzian disks with exponent α=7/2 has been studied using the method of molecular dynamics. The phase diagram of this system is the melting line of a triangular crystal with several maxima and minima. Waterlike density and diffusion anomalies have been found in the reentrant melting regions. Noteworthy, a density anomaly has been observed not only in the liquid and hexatic but also in the solid phase. The calculations of the phonon spectra of longitudinal and transverse modes have yielded negative dependence of the frequency of transverse modes on density along all directions in the regions with a density anomaly. This indicates an association of the density anomaly with transverse oscillations of the crystal lattice. The regions of density and diffusion anomalies have been drawn on the phase diagram. It has been found that the stability regions of anomalous diffusion extend to temperatures well above the maximum melting point T=0.0058 of the triangular crystal.
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Affiliation(s)
- Eu A Gaiduk
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse, 14, Troitsk, Moscow, 108840 Russia
| | - Yu D Fomin
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse, 14, Troitsk, Moscow, 108840 Russia
| | - E N Tsiok
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse, 14, Troitsk, Moscow, 108840 Russia
| | - V N Ryzhov
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse, 14, Troitsk, Moscow, 108840 Russia
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13
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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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14
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Martin SC, Hansen-Goos H, Roth R, Laird BB. Inside and out: surface thermodynamics from positive to negative curvature. J Chem Phys 2022; 157:054702. [DOI: 10.1063/5.0099295] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
To explore the curvature dependence of solid-fluid interfacial thermodynamics, we calculate, using Grand Canonical Monte Carlo simulation, the surface free energy γ for a 2-d hard-disk fluid confined in a circular hard container of radius R as a function of the bulk packing fraction η and wall curvature C = −1/ R. (The curvature is negative because the surface is concave) Combining this with our previous data [J. Phys. Chem. B, 124, 7938 (2020)] for the positive curvature case (a hard-disk fluid at a circular wall, C = +1/ R), we obtain a full picture of surface thermodynamics in this system over the full range of positive and negative wall curvatures. Our results show that γ is linear in C with a slope that is the same for both positive and negative wall curvatures, with deviations seen only at high negative curvatures (strong confinement) and high density. This observation indicates that the surface thermodynamics of this system is consistent with the predictions of so-called Morphometric Thermodynamics at both positive and negative curvatures. In addition, we show that classical Density Functional Theory and a generalized scaled particle theory can be constructed that give excellent agreement with the simulation data over most of the range of curvatures and densities. For extremely high curvatures, where only one or two disks can occupy the container at maximum packing, it is possible to calculate γ exactly. In this limit the simulations and DFT calculations are in remarkable agreement with the exact results.
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Affiliation(s)
| | | | - Roland Roth
- University of Tübingen Department of Physics, Germany
| | - Brian B. Laird
- Chemistry, University of Kansas, United States of America
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15
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Abutbul D, Podolsky D. Topological Order in an Antiferromagnetic Tetratic Phase. PHYSICAL REVIEW LETTERS 2022; 128:255501. [PMID: 35802454 DOI: 10.1103/physrevlett.128.255501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2021] [Revised: 04/11/2022] [Accepted: 06/02/2022] [Indexed: 06/15/2023]
Abstract
We study lattice melting in two-dimensional systems of spinful particles that interact antiferromagnetically. We argue that, for strong spin interactions, single lattice dislocations are forbidden by magnetic frustration. This leads to a melting scenario in which a tetratic phase, containing free dislocation pairs and bound disclinations, separates the solid from the liquid. We demonstrate this phase numerically in a system of hard spheres confined between parallel plates, where spins are represented by the heights of the spheres. In the tetratic phase, the spins are shown to be as antiferromagnetically ordered as allowed by their spatial configuration.
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16
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Tsiok EN, Fomin YD, Gaiduk EA, Tareyeva EE, Ryzhov VN, Libet PA, Dmitryuk NA, Kryuchkov NP, Yurchenko SO. The role of attraction in the phase diagrams and melting scenarios of generalized 2D Lennard-Jones systems. J Chem Phys 2022; 156:114703. [DOI: 10.1063/5.0075479] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Monolayer and two-dimensional (2D) systems exhibit rich phase behavior, compared with 3D systems, in particular, due to the hexatic phase playing a central role in melting scenarios. The attraction range is known to affect critical gas–liquid behavior (liquid–liquid in protein and colloidal systems), but the effect of attraction on melting in 2D systems remains unstudied systematically. Here, we have revealed how the attraction range affects the phase diagrams and melting scenarios in a 2D system. Using molecular dynamics simulations, we have considered the generalized Lennard-Jones system with a fixed repulsion branch and different power indices of attraction from long-range dipolar to short-range sticky-sphere-like. A drop in the attraction range has been found to reduce the temperature of the gas–liquid critical point, bringing it closer to the gas–liquid–solid triple point. At high temperatures, attraction does not affect the melting scenario that proceeds through the cascade of solid–hexatic (Berezinskii–Kosterlitz–Thouless) and hexatic–liquid (first-order) phase transitions. In the case of dipolar attraction, we have observed two triple points inherent in a 2D system: hexatic–liquid–gas and crystal–hexatic–gas, the temperature of the crystal–hexatic–gas triple point is below the hexatic–liquid–gas triple point. This observation may have far-reaching consequences for future studies, since phase diagrams determine possible routes of self-assembly in molecular, protein, and colloidal systems, whereas the attraction range can be adjusted with complex solvents and external electric or magnetic fields. The results obtained may be widely used in condensed matter, chemical physics, materials science, and soft matter.
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Affiliation(s)
- Elena N. Tsiok
- Institute of High Pressure Physics RAS, Kaluzhskoe Shosse, 14, Troitsk, Moscow 108840, Russia
| | - Yuri D. Fomin
- Institute of High Pressure Physics RAS, Kaluzhskoe Shosse, 14, Troitsk, Moscow 108840, Russia
| | - Eugene A. Gaiduk
- Institute of High Pressure Physics RAS, Kaluzhskoe Shosse, 14, Troitsk, Moscow 108840, Russia
| | - Elena E. Tareyeva
- Institute of High Pressure Physics RAS, Kaluzhskoe Shosse, 14, Troitsk, Moscow 108840, Russia
| | - Valentin N. Ryzhov
- Institute of High Pressure Physics RAS, Kaluzhskoe Shosse, 14, Troitsk, Moscow 108840, Russia
| | - Pavel A. Libet
- Institute of High Pressure Physics RAS, Kaluzhskoe Shosse, 14, Troitsk, Moscow 108840, Russia
- Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, 105005 Moscow, Russia
| | - Nikita A. Dmitryuk
- Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, 105005 Moscow, Russia
| | - Nikita P. Kryuchkov
- Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, 105005 Moscow, Russia
| | - Stanislav O. Yurchenko
- Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, 105005 Moscow, Russia
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17
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Smallenburg F. Efficient event-driven simulations of hard spheres. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:22. [PMID: 35274181 DOI: 10.1140/epje/s10189-022-00180-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 02/24/2022] [Indexed: 06/14/2023]
Abstract
Hard spheres are arguably one of the most fundamental model systems in soft matter physics, and hence a common topic of simulation studies. Event-driven simulation methods provide an efficient method for studying the phase behavior and dynamics of hard spheres under a wide range of different conditions. Here, we examine the impact of several optimization strategies for speeding up event-driven molecular dynamics of hard spheres and present a light-weight simulation code that outperforms existing simulation codes over a large range of system sizes and packing fractions. The presented differences in simulation speed, typically a factor of five to ten, save significantly on both CPU time and energy consumption and may be a crucial factor for studying slow processes such as crystal nucleation and glassy dynamics.
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Affiliation(s)
- Frank Smallenburg
- Laboratoire de Physique des Solides, CNRS, Université Paris-Saclay, 91405, Orsay, France
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18
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Torres-Díaz I, Hendley RS, Mishra A, Yeh AJ, Bevan MA. Hard superellipse phases: particle shape anisotropy & curvature. SOFT MATTER 2022; 18:1319-1330. [PMID: 35072684 DOI: 10.1039/d1sm01523k] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We report computer simulations of two-dimensional convex hard superellipse particle phases vs. particle shape parameters including aspect ratio, corner curvature, and sidewall curvature. Shapes investigated include disks, ellipses, squares, rectangles, and rhombuses, as well as shapes with non-uniform curvature including rounded squares, rounded rectangles, and rounded rhombuses. Using measures of orientational order, order parameters, and a novel stretched bond orientational order parameter, we systematically identify particle shape properties that determine liquid crystal and crystalline phases including their coarse boundaries and symmetry. We observe phases including isotropic, nematic, tetratic, plastic crystals, square crystals, and hexagonal crystals (including stretched variants). Our results catalog known benchmark shapes, but include new shapes that also interpolate between known shapes. Our results indicate design rules for particle shapes that determine two-dimensional liquid, liquid crystalline, and crystalline microstructures that can be realized via particle assembly.
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Affiliation(s)
- Isaac Torres-Díaz
- Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Rachel S Hendley
- Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Akhilesh Mishra
- Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Alex J Yeh
- Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Michael A Bevan
- Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA.
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19
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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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20
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Martínez-Ratón Y, Velasco E. Failure of standard density functional theory to describe the phase behavior of a fluid of hard right isosceles triangles. Phys Rev E 2021; 104:054132. [PMID: 34942749 DOI: 10.1103/physreve.104.054132] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Accepted: 11/01/2021] [Indexed: 11/07/2022]
Abstract
A fluid of hard right isosceles triangles was studied using an extension of scaled-particle density-functional theory which includes the exact third virial coefficient. We show that the only orientationally ordered stable liquid-crystal phase predicted by the theory is the uniaxial nematic phase, in agreement with the second-order virial theory. By contrast, Monte Carlo simulations predict exotic liquid-crystal phases exhibiting tetratic and octatic correlations, with orientational distribution functions having four and eight equivalent peaks, respectively. This demonstrates the failure of the standard density-functional theory based on two- and three-body correlations to describe high-symmetry orientational phases in two-dimensional hard right-triangle fluids, and it points to the necessity to reformulate the theory to take into account high-order body correlations and ultimately particle self-assembling and clustering effects. This avenue may represent a great challenge for future research, and we discuss some fundamental ideas to construct a modified version of density-functional theory to account for these clustering effects.
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Affiliation(s)
- 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, Instituto de Física de la Materia Condensada (IFIMAC) and Instituto de Ciencia de Materiales Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049, Madrid, Spain
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21
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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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22
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Jaleel AAA, Mandal D, Rajesh R. Hard core lattice gas with third next-nearest neighbor exclusion on triangular lattice: One or two phase transitions? J Chem Phys 2021; 155:224101. [PMID: 34911313 DOI: 10.1063/5.0066098] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
We obtain the phase diagram of the hard core lattice gas with third nearest neighbor exclusion on the triangular lattice using Monte Carlo simulations that are based on a rejection-free flat histogram algorithm. In a recent paper [Darjani et al., J. Chem. Phys. 151, 104702 (2019)], it was claimed that the lattice gas with third nearest neighbor exclusion undergoes two phase transitions with increasing density with the phase at intermediate densities exhibiting hexatic order with continuously varying exponents. Although a hexatic phase is expected when the exclusion range is large, it has not been seen earlier in hard core lattice gases with short range exclusion. In this paper, by numerically determining the entropies for all densities, we show that there is only a single phase transition in the system between a low-density fluid phase and a high density ordered sublattice phase and that a hexatic phase is absent. The transition is shown to be first order in nature, and the critical parameters are determined accurately.
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Affiliation(s)
- Asweel Ahmed A Jaleel
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
| | - Dipanjan Mandal
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
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23
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Kawak P, Banks DS, Tree DR. Semiflexible oligomers crystallize via a cooperative phase transition. J Chem Phys 2021; 155:214902. [PMID: 34879681 DOI: 10.1063/5.0067788] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Semicrystalline polymers are ubiquitous, yet despite their fundamental and industrial importance, the theory of homogeneous nucleation from a melt remains a subject of debate. A key component of the controversy is that polymer crystallization is a non-equilibrium process, making it difficult to distinguish between effects that are purely kinetic and those that arise from the underlying thermodynamics. Due to computational cost constraints, simulations of polymer crystallization typically employ non-equilibrium molecular dynamics techniques with large degrees of undercooling that further exacerbate the coupling between thermodynamics and kinetics. In a departure from this approach, in this study, we isolate the near-equilibrium nucleation behavior of a simple model of a melt of short, semiflexible oligomers. We employ several Monte Carlo methods and compute a phase diagram in the temperature-density plane along with two-dimensional free energy landscapes (FELs) that characterize the nucleation behavior. The phase diagram shows the existence of ordered nematic and crystalline phases in addition to the disordered melt phase. The minimum free energy path in the FEL for the melt-crystal transition shows a cooperative transition, where nematic order and monomer positional order move in tandem as the system crystallizes. This near-equilibrium phase transition mechanism broadly agrees with recent evidence that polymer stiffness plays an important role in crystallization but differs in the specifics of the mechanism from several recent theories. We conclude that the computation of multidimensional FELs for models that are larger and more fine-grained will be important for evaluating and refining theories of homogeneous nucleation for polymer crystallization.
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Affiliation(s)
- Pierre Kawak
- Department of Chemical Engineering, Brigham Young University, Provo, Utah 84602, USA
| | - Dakota S Banks
- Department of Chemical Engineering, Brigham Young University, Provo, Utah 84602, USA
| | - Douglas R Tree
- Department of Chemical Engineering, Brigham Young University, Provo, Utah 84602, USA
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24
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James M, Suchla DA, Dunkel J, Wilczek M. Emergence and melting of active vortex crystals. Nat Commun 2021; 12:5630. [PMID: 34561437 PMCID: PMC8463610 DOI: 10.1038/s41467-021-25545-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2020] [Accepted: 08/18/2021] [Indexed: 11/09/2022] Open
Abstract
Melting of two-dimensional (2D) equilibrium crystals is a complex phenomenon characterized by the sequential loss of positional and orientational order. In contrast to passive systems, active crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Currently, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using a generalized Toner-Tu theory. Performing extensive hydrodynamic simulations, we find rich transition scenarios. On small domains, we identify a hysteretic transition as well as a transition featuring temporal coexistence of active vortex lattices and active turbulence, both of which can be controlled by self-propulsion and active stresses. On large domains, an active vortex crystal with solid order forms within the parameter range corresponding to active vortex lattices. The melting of this crystal proceeds through an intermediate hexatic phase. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts.
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Affiliation(s)
- Martin James
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany
| | - Dominik Anton Suchla
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany.,Faculty of Physics, University of Göttingen, Göttingen, Germany
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Michael Wilczek
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany. .,Faculty of Physics, University of Göttingen, Göttingen, Germany.
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25
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Charbonneau P, Gish CM, Hoy RS, Morse PK. Thermodynamic stability of hard sphere crystals in dimensions 3 through 10. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:101. [PMID: 34370117 DOI: 10.1140/epje/s10189-021-00104-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Accepted: 07/13/2021] [Indexed: 06/13/2023]
Abstract
Although much is known about the metastable liquid branch of hard spheres-from low dimension d up to [Formula: see text]-its crystal counterpart remains largely unexplored for [Formula: see text]. In particular, it is unclear whether the crystal phase is thermodynamically stable in high dimensions and thus whether a mean-field theory of crystals can ever be exact. In order to determine the stability range of hard sphere crystals, their equation of state is here estimated from numerical simulations, and fluid-crystal coexistence conditions are determined using a generalized Frenkel-Ladd scheme to compute absolute crystal free energies. The results show that the crystal phase is stable at least up to [Formula: see text], and the dimensional trends suggest that crystal stability likely persists well beyond that point.
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Affiliation(s)
- Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, NC, 27708, USA
- Department of Physics, Duke University, Durham, NC, 27708, USA
| | - Caitlin M Gish
- Department of Physics, University of South Florida, Tampa, FL, 33620, USA
| | - Robert S Hoy
- Department of Physics, University of South Florida, Tampa, FL, 33620, USA
| | - Peter K Morse
- Department of Chemistry, Duke University, Durham, NC, 27708, USA.
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26
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Tsiok EN, Fomin YD, Gaiduk EA, Ryzhov VN. Structural transition in two-dimensional Hertzian spheres in the presence of random pinning. Phys Rev E 2021; 103:062612. [PMID: 34271643 DOI: 10.1103/physreve.103.062612] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2021] [Accepted: 06/03/2021] [Indexed: 11/07/2022]
Abstract
Using molecular dynamics simulation we have investigated the influence of random pinning on the phase diagram and melting scenarios of a two-dimensional system with the Hertz potential for α=5/2. It has been shown that random pinning can cardinally change the mechanism of first-order transition between the different crystalline phases (triangular and square) by virtue of generating hexatic and tetratic phases: a triangular crystal to hexatic transition is of the continuous Berezinskii-Kosterlitz-Thouless (BKT) type, a hexatic to tetratic transition is of first order, and finally, there is a continuous BKT-type transition from tetratic to the square crystal.
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Affiliation(s)
- E N Tsiok
- Institute of High Pressure Physics RAS, Kaluzhskoe shosse, 14, Troitsk, 108840 Moscow, Russia
| | - Yu D Fomin
- Institute of High Pressure Physics RAS, Kaluzhskoe shosse, 14, Troitsk, 108840 Moscow, Russia
| | - E A Gaiduk
- Institute of High Pressure Physics RAS, Kaluzhskoe shosse, 14, Troitsk, 108840 Moscow, Russia
| | - V N Ryzhov
- Institute of High Pressure Physics RAS, Kaluzhskoe shosse, 14, Troitsk, 108840 Moscow, Russia
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27
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Klement M, Lee S, Anderson JA, Engel M. Newtonian Event-Chain Monte Carlo and Collision Prediction with Polyhedral Particles. J Chem Theory Comput 2021; 17:4686-4696. [PMID: 34255505 DOI: 10.1021/acs.jctc.1c00311] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Polyhedral nanocrystals are building blocks for nanostructured materials that find applications in catalysis and plasmonics. Synthesis efforts and self-assembly experiments have been assisted by computer simulations that predict phase equilibria. Most current simulations employ Monte Carlo methods, which generate stochastic dynamics. Collective and correlated configuration updates are alternatives that promise higher computational efficiency and generate trajectories with realistic dynamics. One such alternative involves event-chain updates and has recently been proposed for spherical particles. In this contribution, we develop and apply event-chain Monte Carlo for hard convex polyhedra. Our simulation makes use of an improved computational geometry algorithm XenoSweep, which predicts sweep collision in a particularly simple way. We implement Newtonian event chains in the open-source general-purpose particle simulation toolkit HOOMD-blue for serial and parallel simulation. The speedup over state-of-the-art Monte Carlo is between a factor of 10 for nearly spherical polyhedra and a factor of 2 for highly aspherical polyhedra. Finally, we validate the Newtonian event-chain algorithm by applying it to a current research problem, the multistep nucleation of two classes of hard polyhedra.
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Affiliation(s)
- Marco Klement
- Institute for Multiscale Simulation, IZNF, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen 91058, Germany
| | - Sangmin Lee
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States.,Department of Biochemistry, University of Washington, Seattle, Washington 98195, United States
| | - Joshua A Anderson
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Michael Engel
- Institute for Multiscale Simulation, IZNF, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen 91058, Germany
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28
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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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29
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Wan D, Glotzer SC. Unexpected Dependence of Photonic Band Gap Size on Randomness in Self-Assembled Colloidal Crystals. PHYSICAL REVIEW LETTERS 2021; 126:208002. [PMID: 34110222 DOI: 10.1103/physrevlett.126.208002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2020] [Revised: 03/07/2021] [Accepted: 04/21/2021] [Indexed: 06/12/2023]
Abstract
Using computer simulations, we explore how thermal noise-induced randomness in a self-assembled photonic crystal affects its photonic band gaps (PBGs). We consider a two-dimensional photonic crystal composed of a self-assembled array of parallel dielectric hard rods of infinite length with circular or square cross section. We find that PBGs can exist over a large range of intermediate packing densities and the largest band gap does not always appear at the highest packing density studied. Remarkably, for rods with square cross section at intermediate packing densities, the transverse magnetic (TM) band gap of the self-assembled (i.e., thermal) system can be larger than that of identical rods arranged in a perfect square lattice. By considering hollow rods, we find the band gap of transverse electric modes can be substantially increased while that of TM modes show no obvious improvement over solid rods. Our study suggests that particle shape and internal structure can be used to engineer the PBG of a self-assembled system despite the positional and orientational randomness arising from thermal noise.
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Affiliation(s)
- Duanduan Wan
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
- School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Sharon C Glotzer
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Materials Science and Engineering and Biointerfaces Institute, University of Michigan, Ann Arbor, Michigan 48109, USA
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30
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Liu (刘洪勤) H. Global equation of state and the phase transitions of the hard disc system. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1905897] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Hongqin Liu (刘洪勤)
- Integrated High Performance Computing Branch, Shared Services Canada, Montreal, Canada
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31
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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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32
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Khali SS, Chakraborty D, Chaudhuri D. Two-step melting of the Weeks-Chandler-Anderson system in two dimensions. SOFT MATTER 2021; 17:3473-3485. [PMID: 33656044 DOI: 10.1039/d0sm01484b] [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
We present a detailed numerical simulation study of a two-dimensional system of particles interacting via the Weeks-Chandler-Anderson potential, the repulsive part of the Lennard-Jones potential. With the reduction of density, the system shows a two-step melting: a continuous melting of solid to hexatic phase, followed by a first-order melting of hexatic to liquid. The solid-hexatic melting is consistent with the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young (BKTHNY) scenario and shows dislocation unbinding. The first-order melting of the hexatic to the liquid phase, on the other hand, displays defect-strings formed at the hexatic-liquid interfaces. We present a detailed phase diagram in the density-temperature plane.
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Affiliation(s)
- Shubhendu Shekhar Khali
- Department of Physical Science, Indian Institute Of Science Education and Research Mohali, Punjab 140306, India.
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33
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Darjani S, Koplik J, Pauchard V, Banerjee S. Glassy dynamics and equilibrium state on the honeycomb lattice: Role of surface diffusion and desorption on surface crowding. Phys Rev E 2021; 103:022801. [PMID: 33736017 DOI: 10.1103/physreve.103.022801] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Accepted: 01/21/2021] [Indexed: 11/07/2022]
Abstract
The phase behavior and adsorption kinetics of hard-core particles on a honeycomb lattice are studied by means of random sequential adsorption with surface diffusion. We concentrate on reversible adsorption by introducing a desorption process into our previous model and varying the equilibrium rate constant as a control parameter. We find that an exact prediction of the temporal evolution of fractional surface coverage and the surface pressure dynamics of reversible adsorption can be achieved by use of the blocking function of a system with irreversible adsorption of highly mobile particles. For systems out of equilibrium we observe several features of glassy dynamics, such as slow relaxation dynamics, the memory effect, and aging. In particular, the analysis of our system in the limit of small desorption probability shows simple aging behavior with a power-law decay. A detailed discussion of Gibbs adsorption isotherm for nonequilibrium adsorption is given, which exhibits a hysteresis between this system and its equilibrium counterpart.
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Affiliation(s)
- Shaghayegh Darjani
- Energy Institute and Department of Chemical Engineering, City College of New York, New York 10031, USA.,Benjamin Levich Institute and Department of Chemical Engineering, City College of New York, New York 10031, USA
| | - Joel Koplik
- Benjamin Levich Institute and Department of Physics, City College of New York, New York 10031, USA
| | - Vincent Pauchard
- Energy Institute and Department of Chemical Engineering, City College of New York, New York 10031, USA
| | - Sanjoy Banerjee
- Energy Institute and Department of Chemical Engineering, City College of New York, New York 10031, USA
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34
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Darjani S, Koplik J, Pauchard V, Banerjee S. Adsorption kinetics and thermodynamic properties of a binary mixture of hard-core particles on a square lattice. J Chem Phys 2021; 154:074705. [PMID: 33607911 DOI: 10.1063/5.0039706] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The adsorption kinetics and thermodynamic properties of a binary mixture on a square lattice are studied using the random sequential adsorption with surface diffusion (RSAD). We compare the adsorption of binary species with different equilibrium rate constants and effective rates of adsorption to a surface and find that the temporal evolution of surface coverages of both species can be obtained through the use of the blocking function of a system with irreversible adsorption of highly diffusive particles. Binary mixtures, when one of the components follows the random sequential adsorption (RSA) without surface diffusion and the other follows the RSAD model, display competitive adsorption in addition to cooperative phenomena. Specifically, (i) species replacement occurs over a long period of time, while the total coverage remains unchanged after a short time, (ii) the presence of the RSAD component shifts the jamming coverage to the higher values, and (iii) the maximum jamming coverage is obtained when the effective adsorption of the RSA type components is lower than the other adsorbing particles.
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Affiliation(s)
- Shaghayegh Darjani
- Energy Institute and Department of Chemical Engineering, City College of New York, New York, New York 10031, USA
| | - Joel Koplik
- Benjamin Levich Institute and Department of Physics, City College of New York, New York, New York 10031, USA
| | - Vincent Pauchard
- Energy Institute and Department of Chemical Engineering, City College of New York, New York, New York 10031, USA
| | - Sanjoy Banerjee
- Energy Institute and Department of Chemical Engineering, City College of New York, New York, New York 10031, USA
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35
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Fiedler M, Richthammer T. A lower bound on the displacement of particles in 2D Gibbsian particle systems. Stoch Process Their Appl 2021. [DOI: 10.1016/j.spa.2020.10.003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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36
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Mugita D, Isobe M. Non-equilibrium response and slow equilibration in hard disk systems. EPJ WEB OF CONFERENCES 2021. [DOI: 10.1051/epjconf/202124914004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The relaxation from a non-equilibrium state to the equilibrium depends on the methodologies and initial conditions. To investigate the microscopic mechanisms of equilibration systematically, we focus on the non-equilibrium response during the equilibration process induced by a disturbance of the homogeneous expansion of the simple hard disk systems. Large scale simulations by event-driven molecular dynamics revealed that an anomalous slow equilibration toward the liquid states emerges when starting from the co-existence phase. The origin of the slow decay mechanism is investigated using the probability distribution of local density and orientational order parameter.Their inhomogeneities seem to cause the anomalous slow equilibration.
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37
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Gurin P, Varga S, Odriozola G. Three-step melting of hard superdisks in two dimensions. Phys Rev E 2020; 102:062603. [PMID: 33465947 DOI: 10.1103/physreve.102.062603] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2020] [Accepted: 11/16/2020] [Indexed: 11/07/2022]
Abstract
We explore the link between the melting scenarios of two-dimensional systems of hard disks and squares through replica-exchange Monte Carlo simulations of hard superdisks. The well-known melting scenarios are observed in the disk and square limits, while we observe an unusual three-step scenario for dual shapes. We find that two mesophases mediate the melting: a hexatic phase and another fluid phase with a D_{2} local symmetry, we call it rhombatic, where both bond and particle orientational orders are quasi-long-range. Our results show that not only can the melting process of liquid-crystal forming molecules be complicated, where elongated shapes stabilize several mesophases, but also that of anisotropic quasispherical molecules.
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Affiliation(s)
- Péter Gurin
- Physics Department, Centre for Natural Sciences, University of Pannonia, P.O. Box 158, Veszprém H-8201, Hungary
| | - Szabolcs Varga
- Physics Department, Centre for Natural Sciences, 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, Avenida San Pablo 180, 02200 CD México, Mexico
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38
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Kraft A, Klapp SHL. Freezing and reentrant melting of hard disks in a one-dimensional potential: Predictions based on a pressure-balance equation. Phys Rev E 2020; 102:022606. [PMID: 32942413 DOI: 10.1103/physreve.102.022606] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2020] [Accepted: 07/29/2020] [Indexed: 11/07/2022]
Abstract
We investigate theoretically the freezing behavior of a two-dimensional system of hard disks on a one-dimensional external potential (typically called laser-induced freezing). As shown by earlier theoretical and numerical studies, one observes freezing of the modulated liquid upon increase of the substrate potential amplitude, and reentrant melting back into the modulated liquid when the substrate potential amplitude is increased even further. The purpose of our present work is to calculate the freezing and reentrant melting phase diagram based on information from the bulk system. To this end, we employ an integrated pressure-balance equation derived from density functional theory [Phys. Rev. E 101, 012609 (2020)2470-004510.1103/PhysRevE.101.012609]. Furthermore, we define a measure to quantify the influence of registration effects that qualitatively explain reentrant melting. Despite severe approximations, the calculated phase diagram shows good agreement with the known phase diagram obtained by Monte Carlo simulations.
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Affiliation(s)
- Alexander Kraft
- Technische Universität Berlin, Institut für Theoretische Physik, Straße des 17. Juni 135, 10623 Berlin, Germany
| | - Sabine H L Klapp
- Technische Universität Berlin, Institut für Theoretische Physik, Straße des 17. Juni 135, 10623 Berlin, Germany
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39
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Hoover WG, Hoover CG. From hard spheres and cubes to nonequilibrium maps with thirty-some years of thermostatted molecular dynamics. J Chem Phys 2020; 153:070901. [PMID: 32828089 DOI: 10.1063/5.0019038] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This is our current research perspective on models providing insight into statistical mechanics. It is necessarily personal, emphasizing our own interest in simulation as it developed from the National Laboratories' work to the worldwide explosion of computation of today. We contrast the past and present in atomistic simulations, emphasizing those simple models that best achieve reproducibility and promote understanding. Few-body models with pair forces have led to today's "realistic" simulations with billions of atoms and molecules. Rapid advances in computer technology have led to change. Theoretical formalisms have largely been replaced by simulations incorporating ingenious algorithm development. We choose to study particularly simple, yet relevant, models directed toward understanding general principles. Simplicity remains a worthy goal, as does relevance. We discuss hard-particle virial series, melting, thermostatted oscillators with and without heat conduction, chaotic dynamics, fractals, the connection of Lyapunov spectra to thermodynamics, and finally simple linear maps. Along the way, we mention directions in which additional modeling could provide more clarity and yet more interesting developments in the future.
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Affiliation(s)
- William Graham Hoover
- Ruby Valley Research Institute, Highway Contract 60, Box 601, Ruby Valley, Nevada 89833, USA
| | - Carol Griswold Hoover
- Ruby Valley Research Institute, Highway Contract 60, Box 601, Ruby Valley, Nevada 89833, USA
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40
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Loewe B, Chiang M, Marenduzzo D, Marchetti MC. Solid-Liquid Transition of Deformable and Overlapping Active Particles. PHYSICAL REVIEW LETTERS 2020; 125:038003. [PMID: 32745423 DOI: 10.1103/physrevlett.125.038003] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2019] [Revised: 04/24/2020] [Accepted: 06/16/2020] [Indexed: 06/11/2023]
Abstract
Experiments and theory have shown that cell monolayers and epithelial tissues exhibit solid-liquid and glass-liquid transitions. These transitions are biologically relevant to our understanding of embryonic development, wound healing, and cancer. Current models of confluent epithelia have focused on the role of cell shape, with less attention paid to cell extrusion, which is key for maintaining homeostasis in biological tissue. Here, we use a multiphase field model to study the solid-liquid transition in a confluent monolayer of deformable cells. Cell overlap is allowed and provides a way for modeling the precursor for extrusion. When cells overlap rather than deform, we find that the melting transition changes from continuous to first order like, and that there is an intermittent regime close to the transition, where solid and liquid states alternate over time. By studying the dynamics of five- and sevenfold disclinations in the hexagonal lattice formed by the cell centers, we observe that these correlate with spatial fluctuations in the cellular overlap, and that cell extrusion tends to initiate near fivefold disclinations.
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Affiliation(s)
- Benjamin Loewe
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - Michael Chiang
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - M Cristina Marchetti
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
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41
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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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42
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Padilla LA, Ramírez-Hernández A. Phase behavior of a two-dimensional core-softened system: new physical insights. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:275103. [PMID: 32155598 DOI: 10.1088/1361-648x/ab7e5c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
In this work, we report results of extensive computer simulations regarding the phase behavior of a core-softened system. By using structural and thermodynamic descriptors, as well as self-diffusion coefficients, we provide a comprehensive view of the rich phase behavior displayed by the particular instance of the model studied in here. Our calculations agree with previously published results focused on a smaller region in the temperature-density parameter space (Dudalov et al 2014 Soft Matter 10 4966). In this work, we explore a broader region in this parameter space, and uncover interesting fluid phases with low-symmetry local order, that were not reported by previous works. Solid phases were also found, and have been previously characterized in detail by (Kryuchkov et al 2018 Soft Matter 14 2152). Our results support previously reported findings, and provide new physical insights regarding the emergence of order as disordered phases transform into solids by providing radial distribution function maps and specific heat data. Our results are summarized in terms of a phase diagram.
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Affiliation(s)
- Luis A Padilla
- Department of Biomedical Engineering and Chemical Engineering, The University of Texas at San Antonio, San Antonio, TX 78249, United States of America
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43
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Siboni NH, Thorneywork AL, Damm A, Dullens RPA, Horbach J. Long-time self-diffusion in quasi-two-dimensional colloidal fluids of paramagnetic particles. Phys Rev E 2020; 101:042609. [PMID: 32422843 DOI: 10.1103/physreve.101.042609] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2019] [Accepted: 04/03/2020] [Indexed: 11/07/2022]
Abstract
The effect of hydrodynamic interactions (HI) on the long-time self-diffusion in quasi-two-dimensional fluids of paramagnetic colloidal particles is investigated using a combination of experiments and Brownian dynamics (BD) simulations. In the BD simulations, the direct interactions (DI) between the particles consist of a short-ranged repulsive part and a long-ranged part that is proportional to 1/r^{3}, with r the interparticle distance. By studying the equation of state, the simulations allow for the identification of the regime where the properties of the fluid are fully controlled by the long-ranged interactions, and the thermodynamic state solely depends on the dimensionless interaction strength Γ. In this regime, the radial distribution functions from the simulations are in quantitative agreement with those from the experiments for different fluid area fractions. This agreement confirms that the DI in the experiments and simulations are identical, which thus allows us to isolate the role of HI, as these are not taken into account in the BD simulations. Experiment and simulation fall onto a master curve with respect to the Γ dependence of D_{L}^{★}=D_{L}/(D_{0}Γ^{1/2}), with D_{0} the self-diffusion coefficient at infinite dilution and D_{L} the long-time self-diffusion coefficient. Our results thus show that, although HI affect the short-time self-diffusion, for a quasi-two-dimensional system with 1/r^{3} long-ranged DI, the reduced quantity D_{L}^{★} is effectively not affected by HI. Interestingly, this is in agreement with prior work on quasi-two-dimensional colloidal hard spheres.
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Affiliation(s)
- Nima H Siboni
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
| | - Alice L Thorneywork
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Park Road, Oxford OX1 3QZ, United Kingdom.,Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
| | - Alicia Damm
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Park Road, Oxford OX1 3QZ, United Kingdom
| | - Roel P A Dullens
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Park Road, Oxford OX1 3QZ, United Kingdom
| | - Jürgen Horbach
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
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44
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Tsiok EN, Gaiduk EA, Fomin YD, Ryzhov VN. Melting scenarios of two-dimensional Hertzian spheres with a single triangular lattice. SOFT MATTER 2020; 16:3962-3972. [PMID: 32249869 DOI: 10.1039/c9sm02262g] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We present a molecular dynamics simulation study of the phase diagram and melting scenarios of two-dimensional Hertzian spheres with exponent 7/2. We have found multiple re-entrant melting of a single crystal with a triangular lattice in a wide range of densities from 0.5 to 10.0. Depending on the position on the phase diagram, the triangular crystal has been shown to melt through both two-stage melting with a first-order hexatic-isotropic liquid transition and a continuous solid-hexatic transition as well as in accordance with the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young (BKTHNY) scenario (two continuous transitions with an intermediate hexatic phase). We studied the behavior of heat capacity and have shown that despite two-stage melting, the heat capacity has one peak which seems to correspond to a solid-hexatic transition.
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Affiliation(s)
- E N Tsiok
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Troitsk 108840, Moscow, Russia.
| | - E A Gaiduk
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Troitsk 108840, Moscow, Russia.
| | - Yu D Fomin
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Troitsk 108840, Moscow, Russia. and Moscow Institute of Physics and Technology, 9 Institutskiy Lane, Dolgoprudny City, Moscow Region, Russia
| | - V N Ryzhov
- Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, Troitsk 108840, Moscow, Russia.
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45
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Emergent tetratic order in crowded systems of rotationally asymmetric hard kite particles. Nat Commun 2020; 11:2064. [PMID: 32345964 PMCID: PMC7188800 DOI: 10.1038/s41467-020-15723-w] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2019] [Accepted: 03/24/2020] [Indexed: 11/16/2022] Open
Abstract
Considering multi-body systems of monodisperse hard Brownian particles, it remains challenging to predict the forms of order that can emerge in their dense assembled structures. Surprisingly, here, using Monte Carlo simulations, we show that tetratic-ordered phases emerge in a dense two-dimensional system of hard kites that are rotationally asymmetric and have opposite 72° and α ≈ 90° internal angles. We observe a new tetragonal rectangular crystal (TRX) phase possessing (quasi-)long-range fourfold molecular-orientational order. We propose a method based on local polymorphic configurations of neighboring particle pairs (LPC-NPPs) to understand this emergent tetratic order and show that LPC-NPPs can be useful for predicting orientational order in such systems. To examine the dependence of the tetratic order on α, we apply LPC-NPP analysis to other hard kites for 54° ≤ α ≤ 144°. Our work provides insight into the creation of novel ordered materials by rationally designing particle shape based on anticipated LPC-NPPs. For colloidal particles, it remains challenging to predict the forms of order that can emerge in their dense assembled structures. Here, the authors show, by Monte Carlo simulations, that tetratic-ordered phases emerge in a dense two-dimensional system of hard kites that are rotationally asymmetric.
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46
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Zhang J, Zhang Y, Bevan MA. Spatially varying colloidal phase behavior on multi-dimensional energy landscapes. J Chem Phys 2020; 152:054905. [DOI: 10.1063/1.5142609] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Affiliation(s)
- Jianli Zhang
- Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Yuanxing Zhang
- Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Michael A. Bevan
- Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
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47
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Martinsons M, Hielscher J, Kapfer SC, Schmiedeberg M. Event-chain Monte Carlo simulations of the liquid to solid transition of two-dimensional decagonal colloidal quasicrystals. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:475103. [PMID: 31342938 DOI: 10.1088/1361-648x/ab3519] [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
In event-chain Monte Carlo simulations, we model colloidal particles in two dimensions that interact according to an isotropic short-ranged pair potential which supports the two typical length scales present in decagonal quasicrystals. We investigate the assembled structures as we vary the density and temperature. Our special interest is related to the transition from quasicrystal to liquid. In contrast to the KTHNY melting theory for quasicrystals which predicts an intermediate pentahedratic phase, we find a one-step first-order melting transition. However, we discover that the slow relaxation of phasonic flips, i.e. rearrangements of the particles due to additional degrees of freedom in quasicrystals, changes the positional correlation functions, to the extent that structures with long-range orientational correlations, but exponentially decaying positional correlations, are observed.
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48
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Rana S, Samsuzzaman M, Saha A. Tuning the self-organization of confined active particles by the steepness of the trap. SOFT MATTER 2019; 15:8865-8878. [PMID: 31616877 DOI: 10.1039/c9sm01691k] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We consider the collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with small rotational fluctuations. They also interact with each other via soft, isotropic, repulsive potentials. The particles are confined in a circular trap. The steepness of the trap is tuneable. The average packing fraction of the particles is low. When the trap is steep, particles flock along its boundary. They form a polar cluster that spreads over the boundary. The cluster is not spatially ordered. We show that when the steepness is decreased beyond a threshold value, the cluster becomes round and compact and eventually spatial order (hexagonal) emerges in addition to the pre-established polar order. We investigate the kinetics of such ordering. We find that while rotating around the centre of the trap along its circular boundary, the cluster needs to roll around its centre of mass to be spatially ordered. We have studied the stability of the order when the trap is suddenly switched off. We find that for the particles with velocity alignment interaction, the decay of the spatial order is much slower than the particles without the alignment interaction.
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Affiliation(s)
- Shubhashis Rana
- S. N. Bose National Centre For Basic Sciences, Kolkata, 700098, India.
| | - Md Samsuzzaman
- Department of Physics, Savitribai Phule Pune University, Pune, 411007, India.
| | - Arnab Saha
- Department of Physics, Savitribai Phule Pune University, Pune, 411007, India.
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49
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Affiliation(s)
- Jianxiang Tian
- Department of Physics, Qufu Normal University (Confucius University), Qufu, People’s Republic of China
| | - Hua Jiang
- School of Physics and Electronic Engineering, Linyi University, Linyi, People’s Republic of China
| | - A. Mulero
- Department of Applied Physics, University of Extremadura, Badajoz, Spain
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50
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Oppenheimer N, Stein DB, Shelley MJ. Rotating Membrane Inclusions Crystallize Through Hydrodynamic and Steric Interactions. PHYSICAL REVIEW LETTERS 2019; 123:148101. [PMID: 31702169 DOI: 10.1103/physrevlett.123.148101] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2019] [Indexed: 06/10/2023]
Abstract
We show that rotating membrane inclusions can crystallize due to combined hydrodynamic and steric interactions. Alone, steric repulsion of unconfined particles, even with thermal fluctuations, does not lead to crystallization, nor do rotational hydrodynamic interactions which allow only a marginally stable lattice. Hydrodynamic interactions enable particles to explore states inaccessible to a nonrotational system, yet, unlike Brownian motion, Hamiltonian conservation confines the ensemble which, when combined with steric interactions, anneals into a stable crystal state.
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Affiliation(s)
- Naomi Oppenheimer
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
| | - David B Stein
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
| | - Michael J Shelley
- Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
- Courant Institute, New York University, New York, New York 10012, USA
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