Two features at the two-dimensional freezing transitions

Abstract

We studied the two-dimensional freezing transitions in monolayers of microgel colloidal spheres with shortranged repulsions in video-microscopy experiments, and monolayers of hard disks, and Yukawa particles in simulations. These systems share two common features at the freezing points: (1) the bimodal distribution profile of the local orientational order parameter; (2) the two-body excess entropy, s 2 , reaches −4.5 ± 0.5 k B . Both features are robust and sensitive to the freezing points, so that they can potentially serve as empirical freezing criteria in two dimensions. Compared with the conventional freezing criteria, the first feature has no finite-size ambiguities and can be resolved adequately with much less statistics; and the second feature can be directly measured in macroscopic experiments without the need for microscopic information. We studied the two-dimensional freezing transitions in monolayers of microgel colloidal spheres with short-ranged repulsions in video-microscopy experiments, and monolayers of hard disks, and Yukawa particles in simulations. These systems share two common features at the freezing points: Two features at the two-dimensional freezing transitions(1) the bimodal distribution profile of the local orientational order parameter; (2) the two-body excess entropy, s 2 , reaches −4.5 ± 0.5 k B . Both features are robust and sensitive to the freezing points, so that they can potentially serve as empirical freezing criteria in two dimensions. Compared with the conventional freezing criteria, the first feature has no finite-size ambiguities and can be resolved adequately with much less statistics; and the second feature can be directly measured in macroscopic experiments without the need for microscopic information.

Bond-orientational order and Frank’s constant in two-dimensional colloidal hard spheres

“…Around φ = 0.65-0.69, however, there is a marked change in slope, which coincides with the start of the liquid-hexatic coexistence region. In [42] it was reported that at the melting transition −S 2 /k B takes the value of 4.5, which is indicated by the dashed horizontal line in figure 4(b). Our data reach this value at an area fraction of just over φ = 0.69, i.e.…”

Roles of Energy Dissipation in a Liquid-Solid Transition of Out-of-Equilibrium Systems

“…However, the first-order nature of the liquid-hexatic transition is very weak, and the transition roughly obeys the KTHNY scenario. This basic behavior is common to other systems including particles interacting with soft repulsive potentials [13][14][15][16] and those with attractive potentials such as the Lennard-Jones potential [17], although it has recently be shown that the nature of the transitions depends on the softness of the potential in a delicate manner [16]. Monolayer granular matter has provided a model experimental system to study this fundamental problem.…”

Towards frustration of freezing transition in a binary hard-disk mixture

“…The fluid becomes unstable when the average centre-to-centre distance between alternating nearest neighbors becomes shorter than two disk diameters and the resulting gap between them is shorter than hard-core diameter and does not allow for the central disk to wander. Such a caging concept allows for both the quantitative and qualitative description of the thermodynamics of freezing transition in monodisperse hard-disk fluid and has been already utilized to discuss percolation [8].…”