Nascimento Eduardo S, Palffy-Muhoray Peter, Taylor Jamie M, Virga Epifanio G, Zheng Xiaoyu
Liquid Crystal Institute, Kent State University, Kent, Ohio 44240, USA.
Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.
Phys Rev E. 2017 Aug;96(2-1):022704. doi: 10.1103/PhysRevE.96.022704. Epub 2017 Aug 7.
The celebrated work of Onsager on hard particle systems, based on the truncated second order virial expansion, is valid at relatively low volume fractions for large aspect ratio particles. While it predicts the isotropic-nematic phase transition, it does not provide a realistic equation of state in that the pressure remains finite for arbitrarily high densities. In this work, we derive a mean field density functional form of the Helmholtz free energy for nematics with hard core repulsion. In addition to predicting the isotropic-nematic transition, the model provides a more realistic equation of state. The energy landscape is much richer, and the orientational probability distribution function in the nematic phase possesses a unique feature-it vanishes on a nonzero measure set in orientation space.
昂萨格关于硬粒子系统的著名工作基于截断的二阶维里展开，对于大纵横比粒子，在相对低的体积分数下是有效的。虽然它预测了各向同性 - 向列相转变，但它并没有提供一个现实的状态方程，因为对于任意高的密度，压力仍然是有限的。在这项工作中，我们推导了具有硬核排斥的向列相亥姆霍兹自由能的平均场密度泛函形式。除了预测各向同性 - 向列相转变外，该模型还提供了一个更现实的状态方程。能量景观要丰富得多，并且向列相中的取向概率分布函数具有一个独特的特征——它在取向空间的一个非零测度集上消失。
