Eur. Phys. J. E (2004) 13: 87-98
https://doi.org/10.1140/epje/e2004-00043-2

Nematic liquid crystal around a spherical particle: Investigation of the defect structure and its stability using adaptive mesh refinement

¹ Yokoyama Nano-structured Liquid Crystal Project, ERATO, Japan Science and Technology Agency, 5-9-9 Tokodai, 300-2635, Tsukuba, Japan
² Nanotechnology Research Institute, AIST, 1-1-1 Umezono, 305-8568, Tsukuba, Japan

^* e-mail: fukuda@nanolc.jst.go.jp

Abstract

We investigate the orientation profile and the structure of topological defects of a nematic liquid crystal around a spherical particle using an adaptive mesh refinement scheme developed by us previously. The previous work [J. Fukuda et al., Phys. Rev. E 65, 041709 (2002)] was devoted to the investigation of the fine structure of a hyperbolic hedgehog defect that the particle accompanies and in this paper we present the equilibrium profile of the Saturn ring configuration. The radius of the Saturn ring r _d in units of the particle radius R ₀ increases weakly with the increase of , the ratio of the nematic coherence length to R ₀. Next we discuss the energetic stability of a hedgehog and a Saturn ring. The use of adaptive mesh refinement scheme together with a tensor orientational order parameter allows us to calculate the elastic energy of a nematic liquid crystal without any assumption of the structure and the energy of the defect core as in the previous similar studies. The reduced free energy of a nematic liquid crystal, , with L ₁ being the elastic constant, is almost independent of in the hedgehog configuration, while it shows a logarithmic dependence in the Saturn ring configuration. This result clearly indicates that the energetic stability of a hedgehog to a Saturn ring for a large particle is definitely attributed to the large defect energy of the Saturn ring with a large radius.