Department of Chemical and Biological Engineering, University of Wisconsin, Madison, Wisconsin 53706, USA.
Soft Matter. 2014 Feb 14;10(6):882-93. doi: 10.1039/c3sm51919h.
A first principles method is proposed to calculate the Frank elastic constants of nematic liquid crystals. These include the constants corresponding to standard splay, twist and bend deformations, and an often-ignored surface-like contribution known as saddle-splay. The proposed approach is implemented on the widely studied Gay-Berne (3, 5, 2, 1) model [J. G. Gay and B. J. Berne, J. Chem. Phys., 1981, 74, 3316], and the effects of temperature and system size on the elastic constants are examined in the nematic phase. The results of simulations for splay, twist, and bend elastic constants are consistent with those from previous literature reports. The method is subsequently applied to the saddle-splay elastic constant k24 which is found to exist at the limits of the Ericksen inequalities governing positive definite free energy. Finally, extensions of the method are discussed that present a new paradigm for in silico measurements of elastic constants.
提出了一种计算向列液晶的弗兰克弹性常数的第一性原理方法。这些常数包括对应于标准的展曲、扭曲和弯曲变形的常数，以及一种经常被忽视的称为鞍形展曲的表面样贡献。所提出的方法在广泛研究的 Gay-Berne（3,5,2,1）模型[J.G.Gay 和 B.J.Berne，J.Chem.Phys.，1981，74，3316]上实现，并在向列相中检查了温度和系统大小对弹性常数的影响。展曲、扭曲和弯曲弹性常数的模拟结果与先前文献报告中的结果一致。该方法随后应用于鞍形展曲弹性常数 k24，发现它存在于控制正定自由能的 Ericksen 不等式的极限内。最后，讨论了该方法的扩展，为弹性常数的计算机测量提出了一种新的范例。
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