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

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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 \(\xi\), 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 \(Q_{\alpha\beta}\) 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, \(\overline{F} = F/L_1 R_0\), with L 1 being the elastic constant, is almost independent of \(\xi\) 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.

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Authors and Affiliations

  1. Yokoyama Nano-structured Liquid Crystal Project, ERATO, Japan Science and Technology Agency, 5-9-9 Tokodai, 300-2635, Tsukuba, Japan

    Jun-ichi Fukuda, Makoto Yoneya & Hiroshi Yokoyama

  2. Nanotechnology Research Institute, AIST, 1-1-1 Umezono, 305-8568, Tsukuba, Japan

    Hiroshi Yokoyama

Authors
  1. Jun-ichi Fukuda
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  2. Makoto Yoneya
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  3. Hiroshi Yokoyama
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Correspondence to Jun-ichi Fukuda.

Additional information

Received: 10 December 2003, Published online: 2 March 2004

PACS:

61.30.Cz Molecular and microscopic models and theories of liquid crystal structure - 61.30.Jf Defects in liquid crystals - 82.20.Wt Computational modeling; simulation

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Fukuda, Ji., Yoneya, M. & Yokoyama, H. Nematic liquid crystal around a spherical particle: Investigation of the defect structure and its stability using adaptive mesh refinement. Eur. Phys. J. E 13, 87–98 (2004). https://doi.org/10.1140/epje/e2004-00043-2

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