论文标题
硬风筝流体中的定向顺序：密度功能理论研究
Orientational ordering in a fluid of hard kites: A density-functional-theory study
论文作者
论文摘要
使用密度函数理论，我们从理论上研究了硬风筝均匀阶段的定向特性 - 两个同步的三角形由它们的共同基础连接在一起。使用了两个近似值：缩放粒子理论和一种新方法，该方法更好地近似于二维硬粒子的第三个病毒系数。通过改变其一些几何参数，风筝可以转变为正方形，菱形，三角形以及非常细长的颗粒，甚至达到了硬针极限。因此，根据粒子的形状，硬风筝的液体可以稳定各向同性，列表，跨三边形和三边形相。计算了不同的相图，包括菱形的相图，以及固定为$ 90^{\ circ} $，$ 60^{\ circ} $和$ 75^{\ circ} $的两个相等内部角度的风筝。还考虑了最近通过Monte Carlo Simulations研究的，其固定在$ 72^{\ Circ} $中的风筝之一。我们发现，具有两个相等角的菱形和风筝，而不是太大的轴测表使四个相位稳定，但是后者将其稳定在更高的程度上。相比之下，固定在$ 60^{\ circ} $的两个相等内部角度的风筝在某种程度上稳定了三级相，尽管它对粒子几何形状的变化非常敏感。具有固定在$ 75^{\ Circ} $的两个相等内部角度的风筝具有带有四边形和三边形相的相图，但我们显示了粒子形状的不存在，在不同的密度下，这两个阶段都稳定。最后，通过与蒙特卡洛仿真相比，在一个不等角度固定为$ 72^{\ circ} $的情况下，显示了新理论在风筝的描述中的成功。这些颗粒还具有稳定的跨四个相和三边形相的相图。
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 $90^{\circ}$, $60^{\circ}$ 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 stabilise the tetratic phase but the latter stabilize it to a much higher degree. By contrast, kites with two equal interior angles fixed to $60^{\circ}$ 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 phase diagrams with stable tetratic and triatic phases.
