From Microscopic Theory to Macroscopic Theory: a Systematic Study on Modeling for Liquid Crystals
From Microscopic Theory to Macroscopic Theory: a Systematic Study on Modeling for Liquid Crystals
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DOI：
10.1007/s00205-014-0792-3
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发表时间：
2014-09
影响因子：
2.5
通讯作者：
Jiequn Han;Yi Luo;Wei Wang;Pingwen Zhang;Zhifei Zhang
中科院分区：
文献类型：
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作者：
Jiequn Han;Yi Luo;Wei Wang;Pingwen Zhang;Zhifei Zhang
在本文中，我们提出了一个系统的液晶建模方法，建立微观理论和宏观理论之间的联系。在第一部分中，我们提出了一个新的基于Onsager分子理论的液晶Q张量模型。通过单轴假设，可以从导出的Q张量理论中恢复出Oseen-Frank理论，并可以检验Oseen-Frank模型中的系数。此外，近晶-A相的特征可以由导出的宏观模型。在第二部分中，我们从Doi的动力学理论出发，利用Bingham闭包导出了一个新的动力学Q张量模型，它服从能量耗散律。此外，Ericksen-Leslie系统也可以从新的Q-张量系统通过在局部平衡点附近进行展开而导出。
In this paper, we propose a systematic way of liquid crystal modeling to build connections between microscopic theory and macroscopic theory. In the first part, we propose a newQ-tensor model based on Onsager’s molecular theory for liquid crystals. The Oseen–Frank theory can be recovered from the derivedQ-tensor theory by making a uniaxial assumption, and the coefficients in the Oseen–Frank model can be examined. In addition, the smectic-A phase can be characterized by the derived macroscopic model. In the second part, we derive a new dynamicQ-tensor model from Doi’s kinetic theory by the Bingham closure, which obeys the energy dissipation law. Moreover, the Ericksen–Leslie system can also be derived from newQ-tensor system by making an expansion near the local equilibrium.