论文标题
轴向对称的3D天空中的弹性相互作用的理论在密闭的手性列液晶和天空袋中
Theory of elastic interaction between axially symmetric 3D skyrmions in confined chiral nematic liquid crystals and in skyrmion bags
论文作者
论文摘要
我们研究了充满胆固醇液体晶体的薄细胞中轴向对称的3D高敏颗粒（Torons，Hopfions）。在这种情况下，手性项在远距离上的贡献变小，3D Skyrmion可以将其描述为具有不同手性的多极矩的列中非常具体的粒子。我们表明，渐近的小天空可以作为具有六个多极力矩的粒子呈现。因此，我们找到了围绕3D Skyrmion周围的远场导演配置的精确分析解决方案，以及在具有厚度$ l $的同型细胞中3D Skyrmions之间的弹性相互作用电位的精确分析表达。与实验的比较使我们能够恢复一个小3D天空的大约多极系数。我们还根据其中的抗kyrmions的数量$ n $ n $ n $ n $ n介绍了天际袋的扩展，并与实验达成协议。 一路上，我们确定了无限列液晶和密封的同型电池中的手性轴向对称胶体粒子围绕轴向对称的胶体粒子，并考虑了带有订单$ l = 1÷6 $的高阶弹性项。我们还发现了此类颗粒之间的弹性相互作用势。
We study axially symmetrical 3D skyrmionic particles (torons, hopfions) in a thin homeotropic cell filled with a cholesteric liquid crystal. In this case, the contribution of the chirality term on far distances becomes small and a 3D skyrmion can be described as a very specific particle in nematic with multipole moments of different chiralities. We show that small skyrmions asymptotically can be presented as a particle with six multipole moments. Thus, we find the exact analytical solution for the far field director configuration around the 3D skyrmion and the exact analytical expression for the elastic interaction potential between 3D skyrmions in a homeotropic cell with thickness $L$. The comparison with the experiment allows us to recover approximately multipole coefficients of one small 3D skyrmion. We also describe the expansion of the skyrmion bag analytically depending on the number $N$ of anti-skyrmions in it and obtain an agreement with the experiment. Along the way, we determined the director field around a chiral axially symmetric colloidal particle in the unlimited nematic liquid crystal and in the confined homeotropic cell, taking into account higher order elastic terms with orders $l=1÷6$. We also have found the elastic interaction potential between such particles.
