含铁磁性夹杂物的双相液晶复合材料的有效模型
Effective models for nematic liquid crystals composites with ferromagnetic inclusions
摘要：
双折射液晶的分子对外加磁场的反应是沿着磁场的方向重新定向。由于液晶的介电各向异性很小，因此需要相对较大的场来引起显著的液晶响应。如Brochard和de Gennes在1970年提出的，这种相互作用可以在铁磁颗粒在液晶基质中的胶体悬浮液中得到增强。这些粒子与磁场对齐的能力，同时引起磁性分子的重新取向，大大增加了混合物的磁响应。基本上，颗粒提供了通过表面锚定与液晶相互作用的易磁化轴。我们推导出铁磁在稀极限下的有效能量的表达式，即当粒子数趋于无穷大而它们的总体积分数趋于零时。混合物的总能量被假定为体弹性液晶贡献、液晶在颗粒表面上的锚定能量以及颗粒与所施加的磁场之间的相互作用的磁能的总和。均匀化的极限铁磁能量得到严格使用变分方法。它概括了以前在物理文献中报道的正式表达式。
英文摘要：
Molecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix---ferronematics--- as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and, simultaneously, cause reorientation of the nematic molecules, greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in a physical literature.
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