论文标题
嵌入在列液液晶体中的立方微片：一项兰道de-de-de-gennes研究
Cubic microlattices embedded in nematic liquid crystals: a Landau de-Gennes study
论文作者
论文摘要
我们考虑了一个稀释型宿主中连接的立方晶格支架的Landau-de Gennes模型。我们分析了两种情况的均质极限，其中嵌入颗粒的晶格或不提出立方对称性，然后计算复合材料的自由有效能量。在立方对称情况下，我们强加了不同类型的表面锚定能密度，例如四分之一，Rapini-Papoular或更通用的版本，在这种情况下，我们表明我们可以从相应的体积电位（尤其是相过渡温度）中调整任何系数。在损失立方对称性的情况下，我们证明了有效的自由能函数现在具有附加项的相似结果，该术语描述了域内液晶颗粒的首选比对变化。此外，我们计算了表面能融合到同质均质的速度的收敛速率，以及自由能的最小值趋向于趋于降低均质自由能的最小值。
We consider a Landau-de Gennes model for a connected cubic lattice scaffold in a nematic host, in a dilute regime. We analyse the homogenised limit for both cases in which the lattice of embedded particles presents or not cubic symmetry and then we compute the free effective energy of the composite material. In the cubic symmetry case, we impose different types of surface anchoring energy densities, such as quartic, Rapini-Papoular or more general versions, and, in this case, we show that we can tune any coefficient from the corresponding bulk potential, especially the phase transition temperature. In the case with loss of cubic symmetry, we prove similar results in which the effective free energy functional has now an additional term, which describes a change in the preferred alignment of the liquid crystal particles inside the domain. Moreover, we compute the rate of convergence for how fast the surface energies converge to the homogenised one and also for how fast the minimisers of the free energies tend to the minimiser of the homogenised free energy.
