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

Abstract

We formulate the scaled particle theory for a general mixture of hard isosceles triangles and calculate different phase diagrams for the one-component fluid and for certain binary mixtures. The fluid of hard triangles exhibits a complex phase behavior: (i) the presence of a triatic phase with sixfold symmetry, (ii) the isotropic-uniaxial nematic transition is of first order for certain ranges of aspect ratios, and (iii) the one-component system exhibits nematic-nematic transitions ending in critical points. We found the triatic phase to be stable not only for equilateral triangles but also for triangles of similar aspect ratios. We focus the study of binary mixtures on the case of symmetric mixtures: equal particle areas with aspect ratios (κ_{i}) symmetric with respect to the equilateral one, κ_{1}κ_{2}=3. For these mixtures we found, aside from first-order isotropic-nematic and nematic-nematic transitions (the latter ending in a critical point): (i) a region of triatic phase stability even for mixtures made of particles that do not form this phase at the one-component limit, and (ii) the presence of a Landau point at which two triatic-nematic first-order transitions and a nematic-nematic demixing transition coalesce. This phase behavior is analogous to that of a symmetric three-dimensional mixture of rods and plates.

Failure of standard density functional theory to describe the phase behavior of a fluid of hard right isosceles triangles

“…Experiments with particles of square sections did not find the T phase [3], but this was due to the roundness of the corners, as proved by Monte Carlo (MC) simulations [4]. The stability of T [5][6][7][8][9][10] and T R [11][12][13] phases as a function of particle shape was also confirmed by theoretical and simulation works on two-dimensional hard-particle fluids. Experiments on monolayers of vibrated granular cylinders [14][15][16][17] and squares [18] also showed the presence of stationary nonequilibrium T -like textures in the arrangement of particles.…”

Iridescence in nematics: Photonic liquid crystals of nanoplates in absence of long-range periodicity

“…By contrast, forming visible color by nematic structure is notoriously difficult due to the lack of long-range periodicity in most nematic phases. Most theories of lyotropic nematic phase have focused on its orientationally ordered features (21,22), while the possibility of structural coloration has yet to elicit much attention. To date, the only colorful nematic materials were found to be chiral nematic (N*) phase with the prerequisite of a chiral structure (23), which limits the choices of nanoscale building blocks.…”

Orientational ordering in a fluid of hard kites: A density-functional-theory study

“…However, as we showed in Ref. 29 , a fluid of hard triangles (also a non-symmetric particle) has equilibrium N and TR phases with orientational distribution functions having the symmetry h(φ) = h(π − φ), a property directly related to the nonnegativity of the odd-index Fourier amplitudes of the function A spt (φ) 29 :…”

“…Theoretical studies using MC simulations 23,24 and DFT [25][26][27] predicted the stability of the T phase long before the experiments were conducted. By contrast, theoretical studies of the TR phase 28,29 appeared after the phase was discovered in experiments 22 .…”