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

Abstract

Using Density Functional Theory we theoretically study the orientational properties of uniform phases of hard kites -two isosceles triangles joined by their common base. Two approximations are used: Scaled Particle Theory, and a new approach which better approximates third virial coefficients of two-dimensional hard particles. By varying some of their geometrical parameters kites can be transformed into squares, rhombuses, triangles, and also very elongated particles, even reaching the hard-needle limit. Thus a fluid of hard kites, depending on the particle shape, can stabilize isotropic, nematic, tetratic and triatic phases. Different phase diagrams are calculated, including those of rhombuses, and kites with two of their equal interior angles fixed to 90 • , 60 • and 75 • . Kites with one of their unequal angles fixed to 72 • , which have been recently studied via Monte Carlo simulations, are also considered. We find that rhombuses and kites with two equal right angles and not too large anisometry stabilise the tetratic phase but the latter stabilize it to a much higher degree. By contrast, kites with two equal interior angles fixed to 60 • stabilize the triatic phase to some extent, although it is very sensitive to changes in particle geometry. Kites with the two equal interior angles fixed to 75 • have a phase diagram with both tetratic and triatic phases, but we show the nonexistence of a particle shape for which both phases are stable at different densities. Finally the success of the new theory in the description of orientational order in kites is shown by comparing with Monte Carlo simulations for the case where one of the unequal angles is fixed to 72 • . These particles also present a phase diagram with stable tetratic and triatic phases.

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

“…We choose n max = 5, which will be valid sufficiently close to the bifurcation point. Substituting (22) into Eqs. ( 12) and ( 13), we obtain…”

“…This in turn suggests similarities between dissipative and equilibrium systems in situations where entropic interactions play a dominant role, i.e., at high packing fractions. Recently, the T phase of kitelike particles was also found [21,22]. How regular polygons order in liquid-crystal and crystalline phases as density is varied depends strongly on the number of polygonal sides, an issue that was studied intensively via MC simulations [23].…”

Effect of clustering on the orientational properties of a fluid of hard right isosceles triangles

“…These phases possess symmetries that strongly depend on particle shape. Some of these phases were predicted theoretically and later confirmed by Monte Carlo (MC) simulations, and different theoretical models have been developed to explain the rich phase behavior of these 2D hard-core fluids and its particle shape dependence [5][6][7][8][9][10][11][12][13][14][15][16] .…”

Effect of combined roundness and polydispersity on the phase behavior of hard-rectangle fluids

“…The T phase can be stabilized by other geometrical shapes such as rhombuses [20] and kites [9,28] of particular shapes and ratios between their characteristic lengths. Indeed its stability region in the phase diagram seems to be very sensitive to these ratios and, what can be more important, to the roundness of the particle corners.…”