Fukuda J, Yokoyama H
Nanotechnology Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, 305-8568, Tsukuba, Japan.
Eur Phys J E Soft Matter. 2006 Dec;21(4):341-7. doi: 10.1140/epje/i2006-10072-6. Epub 2007 Feb 9.
We study numerically the effect of an external magnetic or electric field on the director profiles of a nematic liquid crystal around a spherical particle. We pay particular attention to the stability of a hyperbolic hedgehog defect accompanying the particle, which transforms into a Saturn-ring defect encircling the particle under a sufficiently strong external field. We focus on the particle size dependence of the two important threshold field strengths: the "thermodynamic-transition" field strength H1 at which the hedgehog and the Saturn-ring configurations have the equal free energy, and the critical field strength H2 at which the hedgehog loses its (meta)stability. Our numerical results demonstrate that while H1 is non-monotonically dependent on the particle radius R0, H2 monotonically increases with R0 and the dependence of H2 is weak for large R0. The non-monotonic dependence of H1 on R0 can be explained by comparing the energies of the two configurations and assuming the dependence of those energies on a rescaled field. A crude argument of the energetics of a hyperbolic hedgehog defect under an external field shows that for an asymptotically large R0 the critical field strength is independent of R0, which agrees with our numerical finding.
我们通过数值方法研究了外部磁场或电场对球形颗粒周围向列型液晶指向矢分布的影响。我们特别关注伴随颗粒的双曲刺猬缺陷的稳定性，在足够强的外部场作用下，该缺陷会转变为环绕颗粒的土星环缺陷。我们着重研究了两个重要阈值场强与颗粒尺寸的关系：刺猬构型和土星环构型具有相等自由能时的“热力学转变”场强H1，以及刺猬失去（亚）稳定性时的临界场强H2。我们的数值结果表明，虽然H1对颗粒半径R0呈非单调依赖关系，但H2随R0单调增加，且对于大R0，H2的依赖关系较弱。通过比较两种构型的能量并假设这些能量对重标场的依赖关系，可以解释H1对R0的非单调依赖关系。对外部场作用下双曲刺猬缺陷能量的粗略论证表明，对于渐近大的R0，临界场强与R0无关，这与我们的数值结果相符。
