Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation
Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation
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DOI：
10.1142/s0218202520500086
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发表时间：
2020-02-01
影响因子：
3.5
通讯作者：
Zarnescu, Arghir
中科院分区：
文献类型：
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作者：
Canevari, Giacomo;Zarnescu, Arghir
我们考虑了向列型宿主中小胶体包裹体悬浮的Landau-de Gennes模型。我们在夹杂物的边界施加适当的锚定条件，并在稀释区工作，即夹杂物的尺寸远远小于它们之间的典型分离距离，因此夹杂物占据的总体积很小。通过研究均匀极限，证明了局部极小点的严格收敛结果，我们计算了掺杂材料的有效自由能。特别指出，通过适当选择表面锚定能密度，不仅可以调谐四次Landau-de Gennes体势的相变温度，而且可以调谐体势的任何系数。
We consider a Landau-de Gennes model for a suspension of small colloidal inclusions in a nematic host. We impose suitable anchoring conditions at the boundary of the inclusions, and we work in the dilute regime - i.e. the size of the inclusions is much smaller than the typical separation distance between them, so that the total volume occupied by the inclusions is small. By studying the homogenised limit, and proving rigorous convergence results for local minimisers, we compute the effective free energy for the doped material. In particular, we show that not only the phase transition temperature, but also any coefficient of the quartic Landau-de Gennes bulk potential can be tuned, by suitably choosing the surface anchoring energy density.