Tetratic order in the phase behavior of a hard-rectangle system

Aleksandar Donev, Joshua Burton, Frank H. Stillinger, Salvatore Torquato

Research output: Contribution to journalArticle

Abstract

Previous Monte Carlo investigations by Wojciechowski have found two unusual phases in two-dimensional systems of anisotropic hard particles: a tetratic phase of fourfold symmetry for hard squares [Comput. Methods Sci. Tech. 10, 235 (2004)], and a nonperiodic degenerate solid phase for hard-disk dimers [Phys. Rev. Lett. 66, 3168 (1991)]. In this work, we study a system of hard rectangles of aspect ratio two, i.e., hard-square dimers (or dominos), and demonstrate that it exhibits phases with both of these unusual properties. The liquid shows quasi-long-range tetratic order, with no nematic order. The solid phase we observe is a nonperiodic tetratic phase having the structure of a random tiling of the square lattice with dominos with the well-known degeneracy entropy 1.79 kB per particle. Our simulations do not conclusively establish the thermodynamic stability of this orientationally disordered solid; however, there are strong indications that this phase is glassy. Our observations are consistent with a two-stage phase transition scenario developed by Kosterlitz and co-workers with two continuous phase transitions, the first from isotropic to tetratic liquid, and the second from tetratic liquid to solid. We obtain similar results with both a classical Monte Carlo method using true rectangles and a novel molecular dynamics algorithm employing rectangles with rounded corners.

Original languageEnglish (US)
Article number054109
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume73
Issue number5
DOIs
StatePublished - 2006

Fingerprint

rectangles
Phase behavior
solid phases
liquids
dimers
Dimers
Liquids
Phase transitions
Monte Carlo method
aspect ratio
Hard disk storage
indication
entropy
molecular dynamics
Molecular dynamics
Aspect ratio
thermodynamics
Thermodynamic stability
Monte Carlo methods
Entropy

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Tetratic order in the phase behavior of a hard-rectangle system. / Donev, Aleksandar; Burton, Joshua; Stillinger, Frank H.; Torquato, Salvatore.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 73, No. 5, 054109, 2006.

Research output: Contribution to journalArticle

Donev, Aleksandar ; Burton, Joshua ; Stillinger, Frank H. ; Torquato, Salvatore. / Tetratic order in the phase behavior of a hard-rectangle system. In: Physical Review B - Condensed Matter and Materials Physics. 2006 ; Vol. 73, No. 5.
@article{8072b84e3ad046e4880a1ccf9b90b14a,
title = "Tetratic order in the phase behavior of a hard-rectangle system",
abstract = "Previous Monte Carlo investigations by Wojciechowski have found two unusual phases in two-dimensional systems of anisotropic hard particles: a tetratic phase of fourfold symmetry for hard squares [Comput. Methods Sci. Tech. 10, 235 (2004)], and a nonperiodic degenerate solid phase for hard-disk dimers [Phys. Rev. Lett. 66, 3168 (1991)]. In this work, we study a system of hard rectangles of aspect ratio two, i.e., hard-square dimers (or dominos), and demonstrate that it exhibits phases with both of these unusual properties. The liquid shows quasi-long-range tetratic order, with no nematic order. The solid phase we observe is a nonperiodic tetratic phase having the structure of a random tiling of the square lattice with dominos with the well-known degeneracy entropy 1.79 kB per particle. Our simulations do not conclusively establish the thermodynamic stability of this orientationally disordered solid; however, there are strong indications that this phase is glassy. Our observations are consistent with a two-stage phase transition scenario developed by Kosterlitz and co-workers with two continuous phase transitions, the first from isotropic to tetratic liquid, and the second from tetratic liquid to solid. We obtain similar results with both a classical Monte Carlo method using true rectangles and a novel molecular dynamics algorithm employing rectangles with rounded corners.",
author = "Aleksandar Donev and Joshua Burton and Stillinger, {Frank H.} and Salvatore Torquato",
year = "2006",
doi = "10.1103/PhysRevB.73.054109",
language = "English (US)",
volume = "73",
journal = "Physical Review B-Condensed Matter",
issn = "1098-0121",
publisher = "American Physical Society",
number = "5",

}

TY - JOUR

T1 - Tetratic order in the phase behavior of a hard-rectangle system

AU - Donev, Aleksandar

AU - Burton, Joshua

AU - Stillinger, Frank H.

AU - Torquato, Salvatore

PY - 2006

Y1 - 2006

N2 - Previous Monte Carlo investigations by Wojciechowski have found two unusual phases in two-dimensional systems of anisotropic hard particles: a tetratic phase of fourfold symmetry for hard squares [Comput. Methods Sci. Tech. 10, 235 (2004)], and a nonperiodic degenerate solid phase for hard-disk dimers [Phys. Rev. Lett. 66, 3168 (1991)]. In this work, we study a system of hard rectangles of aspect ratio two, i.e., hard-square dimers (or dominos), and demonstrate that it exhibits phases with both of these unusual properties. The liquid shows quasi-long-range tetratic order, with no nematic order. The solid phase we observe is a nonperiodic tetratic phase having the structure of a random tiling of the square lattice with dominos with the well-known degeneracy entropy 1.79 kB per particle. Our simulations do not conclusively establish the thermodynamic stability of this orientationally disordered solid; however, there are strong indications that this phase is glassy. Our observations are consistent with a two-stage phase transition scenario developed by Kosterlitz and co-workers with two continuous phase transitions, the first from isotropic to tetratic liquid, and the second from tetratic liquid to solid. We obtain similar results with both a classical Monte Carlo method using true rectangles and a novel molecular dynamics algorithm employing rectangles with rounded corners.

AB - Previous Monte Carlo investigations by Wojciechowski have found two unusual phases in two-dimensional systems of anisotropic hard particles: a tetratic phase of fourfold symmetry for hard squares [Comput. Methods Sci. Tech. 10, 235 (2004)], and a nonperiodic degenerate solid phase for hard-disk dimers [Phys. Rev. Lett. 66, 3168 (1991)]. In this work, we study a system of hard rectangles of aspect ratio two, i.e., hard-square dimers (or dominos), and demonstrate that it exhibits phases with both of these unusual properties. The liquid shows quasi-long-range tetratic order, with no nematic order. The solid phase we observe is a nonperiodic tetratic phase having the structure of a random tiling of the square lattice with dominos with the well-known degeneracy entropy 1.79 kB per particle. Our simulations do not conclusively establish the thermodynamic stability of this orientationally disordered solid; however, there are strong indications that this phase is glassy. Our observations are consistent with a two-stage phase transition scenario developed by Kosterlitz and co-workers with two continuous phase transitions, the first from isotropic to tetratic liquid, and the second from tetratic liquid to solid. We obtain similar results with both a classical Monte Carlo method using true rectangles and a novel molecular dynamics algorithm employing rectangles with rounded corners.

UR - http://www.scopus.com/inward/record.url?scp=33644531570&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33644531570&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.73.054109

DO - 10.1103/PhysRevB.73.054109

M3 - Article

VL - 73

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 5

M1 - 054109

ER -