arXiv 1608.069252016-08-24cond-mat.soft

用代数方法反演nematic liquid crystals的鞍形张开弹性常数$K_{24}$

Retrieving the saddle-splay elastic constant $K_{24}$ of nematic liquid crystals from an algebraic approach

Sébastien Fumeron, Fernando Moraes, Erms Pereira

备注：: Accepted to be published in The European Physical Journal E
发表信息：: Eur. Phys. J. E (2016) 39: 83
DOI：: 10.1140/epje/i2016-16083-8

摘要：

光干涉实验的物理学对于向列相液晶来说是成熟的。使用众所周知的技术，它是可能的，以获得重要的数量，如微分散射截面和鞍展弹性常数$K_{24}$。然而，通常的方法来检索后者涉及到调整的计算参数，通过视觉之间的比较实验光干涉图案或$^{2}H-NMR$的光谱图案产生的逃逸径向向错，和他们的计算模拟对应。为了避免这样的比较，我们发展了一种代数方法获得鞍展弹性常数$K_{24}$。考虑到逃逸径向向错内的毛细管半径$R_{0}$的几十微米，我们使用度量的方法来研究光的传播（在标量波近似），靠近管的表面，并确定由于缺陷的光干涉图案。后者负责与唯一角度$ϕ_{0}$相关的明确定义的干涉峰的存在。由于这个角度取决于因素，如折射率，曲率弹性常数，锚定制度，表面锚定强度和半径$R_{0}$，测量$ϕ_{0}$从干涉实验涉及两个不同的半径允许我们代数检索$K_{24}$。我们的方法使我们能够给第一个报告的估计$K_{24}$的溶致变色液晶日落黄FCF：$K_{24}=2.1\ pN$。

英文摘要：

The physics of light interference experiments is well established for nematic liquid crystals. Using well-known techniques, it is possible to obtain important quantities, such as the differential scattering cross section and the saddl-splay elastic constant $K_{24}$. However, the usual methods to retrieve the latter involves an adjusting of computational parameters through the visual comparisons between the experimental light interference pattern or a $^{2}H-NMR$ spectral pattern produced by an escaped-radial disclination, and their computational simulation counterparts. To avoid such comparisons, we develop an algebraic method for obtaining of saddle-splay elastic constant $K_{24}$. Considering an escaped-radial disclination inside a capillary tube with radius $R_{0}$ of tens of micrometers, we use a metric approach to study the propagation of the light (in the scalar wave approximation), near to the surface of the tube and to determine the light interference pattern due to the defect. The latter is responsible for the existence of a well-defined interference peak associated to a unique angle $ϕ_{0}$. Since this angle depends on factors such as refractive indexes, curvature elastic constants, anchoring regime, surface anchoring strength and radius $R_{0}$, the measurement of $ϕ_{0}$ from the interference experiments involving two different radii allows us to algebraically retrieve $K_{24}$. Our method allowed us to give the first reported estimation of $K_{24}$ for the lyotropic chromonic liquid crystal Sunset Yellow FCF: $K_{24}=2.1\ pN$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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