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 that 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 ${90}^{\circ }, {60}^{\circ }$, and ${75}^{\circ }$. Kites with one of their unequal angles fixed to ${72}^{\circ }$, 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 stabilize the tetratic phase but the latter stabilize it to a much higher degree. By contrast, kites with two equal interior angles fixed to ${60}^{\circ }$ 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 ${75}^{\circ }$ 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 ${72}^{\circ }$. These particles also present a phase diagram with stable tetratic and triatic phases.

中文翻译：

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硬风筝流体中的定向排序：密度泛函理论研究

使用密度泛函理论，我们从理论上研究了硬风筝的均匀相的定向特性-两个等腰三角形由它们的共同底面相连。使用了两种近似方法：缩放粒子理论和一种新方法，该方法可以更好地近似二维硬粒子的第三维里系数。通过改变一些几何参数，风筝可以被转换成正方形，菱形，三角形以及非常细长的粒子，甚至达到硬针极限。因此，硬风筝的流体，根据颗粒形状，可以稳定各向同性，向列相，四相和三相。计算出不同的相图，包括菱形的相图和固定有两个相等内角的风筝${90}^{\circ }， {60}^{\circ }$和 ${75}^{\circ }$。固定不等角度之一的风筝${72}^{\circ }$也考虑了最近通过蒙特卡洛模拟进行研究的。我们发现菱形和风筝具有两个相等的直角并且没有太大的等轴测线，可以稳定四相相，但是后者可以将其稳定到更高的程度。相比之下，固定有两个相等内角的风筝${60}^{\circ }$尽管它对粒子几何形状的变化非常敏感，但它在一定程度上稳定了三相相。固定两个相等内角的风筝${75}^{\circ }$虽然具有具有四相和三相的相图，但是我们显示了不存在两种形状在不同密度下都稳定的颗粒形状。最后，与不等角之一固定为的情况下的蒙特卡罗模拟比较，表明了新理论在风筝定向顺序描述中的成功。${72}^{\circ }$。这些颗粒还呈现出具有稳定的四相和三相的相图。