Demixing and orientational ordering in mixtures of rectangular particles

Abstract

Using scaled-particle theory for binary mixtures of two-dimensional hard particles with orientational degrees of freedom, we analyse the stability of phases with orientational order and the demixing phase behaviour of a variety of mixtures. Our study is focused on cases where at least one of the components consists of hard rectangles, or a particular case of these, hard squares. A pure fluid of hard rectangles has recently been shown to exhibit, aside from the usual uniaxial nematic phase, an additional oriented phase, called tetratic phase, possessing two directors, which is the analog of the biaxial or cubatic phases in three-dimensional fluids. There is evidence, based on computer simulation studies, that the tetratic phase might be stable with respect to phases with lower translational symmetry for rectangles with low aspect ratios. As hard rectangles are mixed, in increasing concentration, with other particles not possessing stable tetratic order by themselves, the tetratic phase is destabilised, via a first-or second-order phase transition, to uniaxial nematic or isotropic phases; for hard rectangles of low aspect ratio (hard squares in particular), tetratic order persists in a relatively large range of volume fractions. The order of these transitions depends on the particle geometry and dimensions, and also on the thermodynamic conditions of the mixture.The second component of the mixture has been chosen to be hard discs or disco-rectangles, the geometry of which is different from that of rectangles, leading to packing frustration and demixing behaviour, or simply rectangles of different aspect ratio but with the same particle area, or different particle area but with the same aspect ratio. These mixtures may be good candidates for observing thermodynamically stable tetratic phases in monolayers of hard particles. Finally, demixing between fluid (isotropic-tetratic or tetratic-tetratic) phases is seen to occur in mixtures of hard squares of different sizes when the size ratio is sufficiently large.

Domain walls in two-dimensional nematics confined in a small circular cavity

“…For such large length-to-width ratios a fluid of HR undergoes a phase transition from an I phase to a nematic (N) at rather low densities [30][31][32][33][34][35]. The bulk transition is continuous and probably of the Kosterlitz-Thouless type; this detail is irrelevant here since, due to the completely confined geometry, there can be no true phase transition in the circular cavity and one expects a possibly abrupt but in any case gradual change from the I phase to the N phase.…”

Density Functional Theories of Hard Particle Systems

“…In Fig. 7.16 (b), we show the demixing scenario of a mixture of freely rotating hard squares with asymmetry ratio r = 10 [173]. We can observe the presence of a lower and upper critical points, apart from a tricritical point below which the isotropic-tetratic nematic transition is of second order.…”

“…Somoza and Tarazona selected for the weight the Mayer function f (r,Ω,Ω ) and imposed the requirement the functional recovered the Onsager limit at low densities. Thus, if we define the number of HR which interact with a given particle placed at r and oriented alongΩ as N (r,Ω) = dr dΩ ρ(r ,Ω )f (r − r ,Ω,Ω ) (7.171) and the number of interacting rods in the parallel particle approximation (considering that all of them have the symmetry of an ellipsoid of revolution with the same volume) 172) with ρ(r) = dΩρ(r,Ω), the proposed functional is defined by 173) where the CS-WDA for a fluid of PHEs was selected to calculate the free energy per particle. Thus, the angular correlations are taken through the scaling factor N (r,Ω)/N PHE (r).…”

Uniform phases in fluids of hard isosceles triangles: One-component fluid and binary mixtures

“…The symmetry of the confining external potential can (i) change the relative stability between different LC phases with respect to the bulk and (ii) induce the presence of topological defects in the N director field. On the other hand, mixtures of anisotropic particles in 2D can exhibit, in analogy with their 3D counterparts, different demixing scenarios [27][28][29]. However, I-I demixing was not found in mixtures of two-dimensional hard bodies [30].…”