Phase behavior of two-dimensional hard rod fluids

Abstract

Monte Carlo simulations are used to study two-dimensional hard rod fluids consisting of spherocylinders confined to lie in a plane. The phase behavior is mapped out as a function of the aspect ratio (L/D) of the particles, from the hard disc limit at one extreme (L/Dϭ0) to the thin hard needle limit at the other (L/Dϭϱ). For long rods, a 2D nematic phase is observed at high density in which the orientational correlation functions decay algebraically, indicating that the phase does not possess true long range orientational order. The simulation data indicate that the transition from this phase to the low density isotropic phase is continuous, via a Kosterlitz-Thouless disclination unbinding type mechanism, rather than first order. For short rods the nematic phase disappears so that, on expansion, the solid phase undergoes a first order transition directly to an isotropic phase. Although the latter phase is globally isotropic, we find evidence for strong local positional and orientational correlations between the particles. Where possible, the simulation results are compared and contrasted to experimental, simulation and theoretical data for other two-dimensional liquid crystalline systems.

Isotropic–nematic transition of long, thin, hard spherocylinders confined in a quasi-two-dimensional planar geometry

“…This value can also be compared with the 5.3 found in Ref. 3 for disco-rectangles with L/D ϭ15. The most interesting question, though, is how the transition density changes as a small lateral dimension is added.…”

Phase diagram of two-dimensional hard ellipses

“…An alternative way for determining an upper bound to the exact value of the isotropicnematic pressure is by means of analyzing the decay of the angular correlation function 9,19,20,22 , g 2 (r). The 2D nematic phase is characterized by a power-law decay of g 2 (r) ∼ r −η with η < η 2 = 1/4.…”

“…In the second place, in-between the solid and the liquid, Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY) 17,18 proposed the existence of a hexatic phase. This phase is characterized by quasi-long-range bond orientational correlations, similar to a two-dimensional nematic where orientation is also quasi-long-range ordered 9,[19][20][21][22] , but with a sixfold rather than twofold anisotropy. In their scenario, the solid melts into a hexatic phase, following a dislocation unbinding process, before turning into a liquid by means of disclination unbinding, for decreasing pressure.…”

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

“…Additionally, the free energies of the different phases should be computed so that the exact locations of the phase transitions could be identified. The final goal is to completely characterize the phase diagram of the hard rectangle system in the α − φ plane, as has been done, for example, for diskorectangles 22 and ellipses. 30 In addition to nematic and smectic phases, novel liquid crystal phases with tetratic order may be discovered.…”