Palffy-Muhoray Peter, Virga Epifanio G, Zheng Xiaoyu
Liquid Crystal Institute, Kent State University, OH, United States of America.
J Phys Condens Matter. 2017 Nov 29;29(47):475102. doi: 10.1088/1361-648X/aa942b.
Onsager's paper on phase transition and phase coexistence in anisotropic colloidal systems is a landmark in the theory of lyotropic liquid crystals. However, an uncompromising scrutiny of Onsager's original derivation reveals that it would be rigorously valid only for ludicrous values of the system's number density (of the order of the reciprocal of the number of particles). Based on Penrose's tree identity and an appropriate variant of the mean-field approach for purely repulsive, hard-core interactions, our theory shows that Onsager's theory is indeed valid for a reasonable range of densities.
昂萨格关于各向异性胶体系统中相变和相共存的论文是溶致液晶理论的一个里程碑。然而，对昂萨格原始推导进行严格审查后发现，它仅在系统数密度取荒谬值（粒子数倒数的量级）时才严格有效。基于彭罗斯的树恒等式以及针对纯排斥硬核相互作用的平均场方法的适当变体，我们的理论表明，昂萨格理论在合理的密度范围内确实是有效的。
