Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory
Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory
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DOI：
10.1017/s0956792509990210
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发表时间：
2008-08
影响因子：
1.9
通讯作者：
A. Majumdar
中科院分区：
文献类型：
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作者：
A. Majumdar
我们在连续介质 Landau-de Gennes 理论中研究三维几何结构中的平衡液晶构型。我们根据温度和材料相关常数获得了平衡标量阶参数的显式界限。我们明确量化了 Landau-de Gennes 预测匹配的温度范围以及 Landau-de Gennes 预测与 Q 张量阶参数的概率二阶矩定义不匹配的温度范围。一致性体系可以解释为朗道-德热内斯理论的有效性体系，因为朗道-德热内斯理论预测了低温体系中平衡标量序参数的大值——大于1。我们讨论了修改后的朗道-德热讷能量泛函，它产生所有温度状态下平衡标量阶参数的物理实际值。
We study equilibrium liquid crystal configurations in three-dimensional geometries, within the continuum Landau-de Gennes theory. We obtain explicit bounds for the equilibrium scalar order parameters in terms of the temperature and material-dependent constants. We explicitly quantify the temperature regimes where the Landau-de Gennes predictions match and the temperature regimes where the Landau-de Gennes predictions do not match the probabilistic second-moment definition of the Q-tensor order parameter. The regime of agreement may be interpreted as the regime of validity of the Landau-de Gennes theory since the Landau-de Gennes theory predicts large values of the equilibrium scalar order parameters – larger than unity, in the low-temperature regime. We discuss a modified Landau-de Gennes energy functional which yields physically realistic values of the equilibrium scalar order parameters in all temperature regimes.