Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory
Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory
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DOI：
10.1080/15421401003795555
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发表时间：
2010-01-01
影响因子：
0.7
通讯作者：
Majumdar, Apala
中科院分区：
文献类型：
--
作者：
Ball, John M.;Majumdar, Apala
我们定义了一个能有效地介于平均场Maier-Saupe能量和连续统Landau-de Gennes能量泛函之间的能量泛函，它既能描述空间均匀系统，也能描述非均匀系统。在平均场方法中，主要宏观变量Q张量序参数是根据概率分布函数的二阶矩来定义的。这个定义对Q张量序参数的本征值施加了一定的约束，这可以解释为物理约束。我们定义了一个热致体势，当Q张量序参数的本征值接近物理上不现实的值时，该体势就会爆炸。因此，这种连续能泛函的极小化子在所有温度范围内都具有物理上真实的序参数。我们研究了体势的渐近性，结果表明，在考虑物理约束的情况下，该模型还预测了一阶向列相-各向同性相变。相反，在Landau-de Gennes框架中，Q张量序参数的定义通常与概率分布函数无关，并且该理论对低温区域的平衡序参数做出了物理上不切实际的预测。
We define a continuum energy functional that effectively interpolates between the mean-field Maier-Saupe energy and the continuum Landau-de Gennes energy functional and can describe both spatially homogeneous and inhomogeneous systems. In the mean-field approach the main macroscopic variable, the Q-tensor order parameter, is defined in terms of the second moment of a probability distribution function. This definition imposes certain constraints on the eigenvalues of the Q-tensor order parameter, which may be interpreted as physical constraints. We define a thermotropic bulk potential which blows up whenever the eigenvalues of the Q-tensor order parameter approach physically unrealistic values. As a consequence, the minimizers of this continuum energy functional have physically realistic order parameters in all temperature regimes. We study the asymptotics of this bulk potential and show that this model also predicts a first-order nematic-isotropic phase transition, whilst respecting the physical constraints. In contrast, in the Landau-de Gennes framework the Q-tensor order parameter is often defined independently of the probability distribution function, and the theory makes physically unrealistic predictions about the equilibrium order parameters in the low-temperature regime.