Local structure analysis of the hard-disk fluid near melting

Mituś, Antoni C.; Weber, H.; Marx, Dominik

doi:10.1103/physreve.55.6855

Cited by 52 publications

(51 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For φ > 0.5, there is an increase of temperature with increasing filling fraction as interaction between neighbors becomes increasingly more common up to φ ∼ 0.7 at which the curve for the flat bottom plate coincides with the curve for the rough bottom plate. It is interesting to note that the value at which this matching occurs is close to the point of crystallization of disks in 2D, φ c = 0.716 [5,41,42]. At this point, the large number of collisions between neighboring particles thermalizes the particles, independently of the details of the heating, i.e.…”

Section: Driven Monolayers: Granular Temperaturementioning

confidence: 99%

Forcing independent velocity distributions in an experimental granular fluid

2007

View full text Add to dashboard Cite

We present experimental results on the velocity statistics of a uniformly heated granular fluid, in a quasi-2D configuration. We find the base state, as measured by the single particle velocity distribution P (c), to be universal over a wide range of filling fractions and only weakly dependent on all other system parameters. There is a consistent overpopulation in the distribution's tails, which scale as P ∝ exp(−A × c −3/2 ). More generally, P (c) deviates from a Maxwell-Boltzmann by a second order Sonine polynomial with a single adjustable parameter, in agreement with recent theoretical analysis of inelastic hard spheres driven by a stochastic thermostat. To our knowledge, this is the first time that Sonine deviations have been measured in an experimental system.

show abstract

Section: Driven Monolayers: Granular Temperaturementioning

confidence: 99%

Forcing independent velocity distributions in an experimental granular fluid

2007

View full text Add to dashboard Cite

show abstract

“…¶ The estimated values of the freezing density for N ϭ 32, 42, 50, and 72 are nc ϭ 0.891, 0.904, 0.917, and 0.929, respectively, for square-well hard sphere clusters and nc ϭ 0.815, 0.840, 0.891, and 0.891, respectively, for minimal second moment clusters. We can compare these critical densities to the freezing densities of hard disks on a spherical surface (nc ϭ 0.87) (15) and a flat surface (nc ϭ 0.89) (30,31) and square-well hard disks and hard spheres with ϭ 0.20 (nc ϭ 0.808) in two dimensions (32), all of which are fairly close. We thus take 0.87 ϳ 0.89 as a rough estimate of the freezing density for our system of square-well hard spheres, keeping in mind that this quantity is calculated in the limit of a large spherical surface or a flat surface.…”

Section: Self-assembly Of Cones and Spherical Particles (Moderate To mentioning

confidence: 99%

A precise packing sequence for self-assembled convex structures

Chen¹,

Zhang²,

Glotzer

2007

Proc. Natl. Acad. Sci. U.S.A.

115

111

View full text Add to dashboard Cite

Molecular simulations of the self-assembly of cone-shaped particles with specific, attractive interactions are performed. Upon cooling from random initial conditions, we find that the cones self-assemble into clusters and that clusters comprised of particular numbers of cones (e.g., 4 -17, 20, 27, 32, and 42) have a unique and precisely packed structure that is robust over a range of cone angles. These precise clusters form a sequence of structures at specific cluster sizes (a ''precise packing sequence'') that for small sizes is identical to that observed in evaporation-driven assembly of colloidal spheres. We further show that this sequence is reproduced and extended in simulations of two simple models of spheres self-assembling from random initial conditions subject to convexity constraints, including an initial spherical convexity constraint for moderate-and large-sized clusters. This sequence contains six of the most common virus capsid structures obtained in vivo, including large chiral clusters and a cluster that may correspond to several nonicosahedral, spherical virus capsids obtained in vivo. Our findings suggest that this precise packing sequence results from free energy minimization subject to convexity constraints and is applicable to a broad range of assembly processes.colloids ͉ self-assembly ͉ simulation ͉ virus assembly T he recent fabrication by means of evaporation-driven selfassembly of colloidal clusters containing micrometer-sized plastic spheres arranged in perfect polyhedra (1) has generated much excitement in the materials community. Precise structures such as these are rare in materials self-assembly problems (2, 3), with some notable, recent exceptions (e.g., refs. 4-6). In biology, however, precise structures are commonplace. A classic example is that of viruses, in which protein subunits, or small groups of protein subunits called capsomers, self-organize into precisely structured shells with icosahedral and other symmetries (7). Although obtained via wholly different processes, the precise packing of colloidal clusters [often referred to as colloidal ''molecules'' (8)] and virus capsids motivates us to investigate, in this article, the minimum set of organizing principles required for the self-assembly of precise structures such as these.One interesting building block shape that self-organizes into precise structures is the cone. Certain amphiphilic nanoparticles (9), molecules (4, 10, 11), and some virus capsomers (12, 13) that self-assemble into precise structures can, to first approximation, be modeled as cone-shaped particles associating via weak attractive interactions. What are the rules that govern the selfassembly of finite numbers of cones into precise clusters? Tsonchev et al. (14) presented a geometric packing analysis to explain the spherical shape resulting from the self-assembly of N cone-shaped amphiphilic nanoparticles in the limit of very large N, in which local hexagonal packing of hard cones is assumed. For clusters of smaller numbers of particles, however, the f...

show abstract

“…But the results of such small systems are affected by large finite-size effects. Simulations performed in the last years used Monte Carlo (MC) techniques either with constant volume (NV T ensemble) [11,12,13,14,15,16,17,18,19,20,21] or constant pressure (NpT ensemble) [22,23,24]. Zollweg, Chester and Leung [11] made detailed investigations of large systems up to 16384 particles, but draw no conclusives about the order of the phase transition.…”

mentioning

confidence: 99%

“…Their conclusions were based on the examination of the bond-orientational order parameter of different systems up to 15876 particles and hard-crystalline wall boundary conditions. Mitus, Weber and Marx [15] studied the local structure of a system with 4096 hard disks. From the linear behaviour of a local order parameter they derived bounds for a possible coexistence region.…”

mentioning

confidence: 99%

The hexatic phase of the two-dimensional hard disk system

Jaster¹

2004

Physics Letters A

View full text Add to dashboard Cite

We report Monte Carlo results for the two-dimensional hard disk system in the transition region. Simulations were performed in the N V T ensemble with up to 1024 2 disks. The scaling behaviour of the positional and bond-orientational order parameter as well as the positional correlation length prove the existence of a hexatic phase as predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young theory.The analysis of the pressure shows that this phase is outside a possible first-order transition.Key words: Hard disk model, Two-dimensional melting, KTHNY theory PACS: 64.70.Dv, 64.60.CnThe nature of the two-dimensional melting transition has been an unsolved problem for many years [1,2]. The Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory [3,4,5,6] predicts two continuous transitions. The first transition occurs when the solid (quasi-long-range positional order, long-range orientational order) undergoes a dislocation unbinding transition to the hexatic phase (short-range positional order, quasi-long-range orientational order). The second transition is the disclination unbinding transition which transforms this hexatic phase into an isotropic phase (short-range positional and orientational order). An alternative scenario has been proposed by Chui [7,8]. He presented a theory via spontaneous generation of grain boundaries, i.e. collective excitations of dislocations. He found that grain boundaries may be generated before the dislocations unbind if the core energy of dislocations is sufficiently small, and predicted a first-order transition. This is characterized by a coexistence region of the solid and isotropic phase, while no hexatic phase exists. Another proposal was given by Glaser and Clark [2]. They considered a detailed theory where the transition is handled as a condensation of localized, thermally generated geometrical defects and found also a first-order transition. Calculations based on the density-functional approach were done by Ryzhov and

show abstract

Local structure analysis of the hard-disk fluid near melting

Cited by 52 publications

References 36 publications

Forcing independent velocity distributions in an experimental granular fluid

Forcing independent velocity distributions in an experimental granular fluid

A precise packing sequence for self-assembled convex structures

The hexatic phase of the two-dimensional hard disk system

Contact Info

Product

Resources

About