标准密度泛函理论不能描述硬直角等腰三角形流体的相行为
Failure of standard density functional theory to describe the phase behavior of a fluid of hard right isosceles triangles
摘要：
利用扩展的Scaled-Particle密度泛函理论研究了硬直角等腰三角形流体的第三维里系数。我们表明，唯一的取向有序的稳定的液晶相的理论预测是单轴向液晶相，与二阶维里理论。相比之下，蒙特卡罗模拟预测奇异的液晶相表现出四次和八次相关性，取向分布函数分别有四个和八个等效峰。这证明了基于二体和三体相关性的标准密度泛函理论在描述二维硬直角三角形流体中的高对称取向相时的失败，并指出有必要重新制定理论以考虑高阶体相关性和最终的粒子自组装和聚集效应。这条途径可能是一个巨大的挑战，为未来的研究，我们讨论了一些基本的想法，构建一个修改后的版本的密度泛函理论，以考虑这些集群效应。
英文摘要：
A fluid of hard right isosceles triangles was studied using an extension of Scaled-Particle Density-Functional Theory which includes the exact third virial coefficient. We show that the only orientationally ordered stable liquid-crystal phase predicted by the theory is the uniaxial nematic phase, in agreement with the second-order virial theory. By contrast, Monte Carlo simulations predict exotic liquid-crystal phases exhibiting tetratic and octatic correlations, with orientational distribution functions having four and eight equivalent peaks, respectively. This demonstrates the failure of the standard Density Functional Theory based on two and three-body correlations to describe high-symmetry orientational phases in two-dimensional hard right-triangle fluids, and points to the necessity to reformulate the theory to take into account high-order body correlations and ultimately particle self-assembling and clustering effects. This avenue may represent a great challenge for future research, and we discuss some fundamental ideas to construct a modified version of Density-Functional Theory to account for these clustering effects.
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