Orientable and non‐orientable director fields for liquid crystals
Orientable and non‐orientable director fields for liquid crystals
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DOI：
10.1002/pamm.200700489
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发表时间：
2007-12
期刊：
影响因子：
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通讯作者：
J. Ball;A. Zarnescu
中科院分区：
文献类型：
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作者：
J. Ball;A. Zarnescu
单轴双折射液晶通常使用Oseen-Frank理论来建模，其中棒状分子的平均取向通过单位矢量场n来描述。这个理论有一个明显的缺点，就是它不尊重n应该等价于−n的首尾对称性;也就是说，n不是在单位球面<$2中取值，而是在球面中取值，并确定了相对的点，即在真实的射影平面<$P2中。朗道-德热纳理论通过使用张量Q = s（n <$n − pseudonId）来尊重这种对称性。在非零常数标量序参量s的情况下，当指向矢场是可定向的时，朗道-德让尼斯理论等价于奥森-弗兰克理论。
Uniaxial nematic liquid crystals are often modelled using the Oseen‐Frank theory, in which the mean orientation of the rodlike molecules is described through a unit vector field n. This theory has the apparent drawback that it does not respect the head‐to‐tail symmetry in which n should be equivalent to −n; that is, instead of n taking values in the unit sphere 𝕊2, it should take values in the sphere with opposite points identified, i.e. in the real projective plane ℝP2. The Landau‐de Gennes theory respects this symmetry by working with the tensor Q = s (n ⊗ n − ⅓Id). In the case of a non‐zero constant scalar order parameter s the Landau‐de Gennes theory is equivalent to that of Oseen‐Frank when the director field is orientable.