团簇效应对硬直角等腰三角形流体取向性质的影响
Effect of clustering on the orientational properties of a fluid of hard right isosceles triangles
摘要：
最近的研究表明，硬直角三角形流体具有四重和准八重（八度）取向对称性。然而，二维各向异性流体的标准密度泛函理论，基于两体相关性，并扩展到包含三体相关性，未能描述这些对称性。为了解释八度对称性的起源，我们假设强的粒子聚集是一个关键因素。我们使用缩放粒子理论来分析硬直角三角形和正方形的四种二元混合物，其中三种是单组分流体的极端模型，其中直角三角形可以作为单体实体与三角形二聚体，正方形二聚体或正方形四聚体一起存在。相图表现出丰富的现象学，与分层和三相共存。更重要的是，在某些情况下，三角形的取向分布函数在相对粒子角0、$π/2,$和$π$处具有同样高的峰，表示四重四阶，但也有位于$π/4$和$3π/4$处的次峰，这是八重八阶的特征。此外，我们扩展的二元混合物模型的四元混合物组成的四种类型的集群：单体，三角形和正方形的二聚体，和正方形的四聚体。该混合物使用比例粒子理论在固定簇分数的限制下进行分析。除了明显的四阶相促进四聚体，我们发现，对于某些集群组合物，单体的总取向分布函数可以表现出准八倍（八度）对称性。该研究提供了证据的重要性的集群来解释特殊的取向性质的液晶相在一些二维流体。
英文摘要：
Recent studies have shown the fluid of hard right triangles to possess fourfold and quasi-eightfold (octatic) orientational symmetries. However, the standard density-functional theory for two-dimensional anisotropic fluids, based on two-body correlations, and an extension to incorporate three-body correlations, fail to describe these symmetries. To explain the origin of octatic symmetry we postulate strong particle clustering as a crucial ingredient. We use Scaled Particle Theory to analyze four binary mixtures of hard right triangles and squares, three of them being extreme models for a one-component fluid, where right triangles can exist as monomeric entities together with triangular dimers, square dimers or square tetramers. Phase diagrams exhibit a rich phenomenology, with demixing and three-phase coexistences. More important, under some circumstances the orientational distribution function of triangles has equally high peaks at relative particle angles 0, $π/2,$ and $π$, signalling fourfold, tetratic order, but also secondary peaks located at $π/4$ and $3π/4$, a feature of eightfold, octatic order. Also, we extend the binary mixture model to a quaternary mixture consisting of four types of clusters: monomers, triangular and square dimers, and square tetramers. This mixture is analyzed using Scaled Particle Theory under the restriction of fixed cluster fractions. Apart from the obvious tetratic phase promoted by tetramers, we found that, for certain cluster compositions, the total orientational distribution function of monomers can exhibit quasi-eightfold (octatic) symmetry. The study gives evidence on the importance of clustering to explain the peculiar orientational properties of liquid-crystal phases in some two dimensional fluids.
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