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.

中文翻译：

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通过胶体均质设计向列液晶的有效体势

我们考虑了一个向列宿主中悬浮小胶体包裹体的 Landau-de Gennes 模型。我们在夹杂物的边界处施加了合适的锚定条件，并且我们在稀释状态下工作——即夹杂物的尺寸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。通过研究均质化极限，并证明局部最小化器的严格收敛结果，我们计算了掺杂材料的有效自由能。特别地，我们认为不仅可以通过适当地选择表面锚固能量密度来调谐相位过渡温度，而且可以通过阶段转变温度，而是可以调整四个地LANDAU-DE Gennes批量电位的任何系数。