Ilg Patrick
ETH Zürich, Department of Materials, Polymer Physics, HCI H541, CH-8093 Zürich, Switzerland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 1):061709. doi: 10.1103/PhysRevE.85.061709. Epub 2012 Jun 22.
The macroscopic theory of nematics is conveniently described in terms of the phenomenological Landau-de Gennes free energy. Here we show how such an effective free energy can be obtained explicitly from a microscopic model via the help of a systematic coarse-graining procedure. We test our approach for the two- and three-dimensional Lebwohl-Lasher model of nematics. The effective free energy that we obtain is consistent with the phenomenological Landau-de Gennes form for weak orientational ordering and the Maier-Saupe theory of the isotropic-nematic transition. For strong orientational ordering, however, the effective free energy increases rapidly and diverges logarithmically near the fully oriented state. The explicit form for the regularized Landau-de Gennes potential proposed here restricts the order parameter to physical admissible values and reproduces our numerical data accurately.
向列相的宏观理论可以方便地用唯象的朗道 - 德热纳自由能来描述。在这里，我们展示了如何通过系统的粗粒化过程，从微观模型中明确地获得这样一个有效的自由能。我们对二维和三维向列相的勒布霍尔 - 拉舍模型测试了我们的方法。我们得到的有效自由能在弱取向有序时与唯象的朗道 - 德热纳形式以及各向同性 - 向列相转变的迈尔 - 绍佩理论一致。然而，对于强取向有序，有效自由能迅速增加，并在完全取向状态附近对数发散。这里提出的正则化朗道 - 德热纳势的显式形式将序参量限制在物理上可允许的值，并准确地再现了我们的数值数据。
