Eur. Phys. J. E (2006) 21: 341-347
https://doi.org/10.1140/epje/i2006-10072-6

Regular Article

Stability of the director profile of a nematic liquid crystal around a spherical particle under an external field

¹ Nanotechnology Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, 305-8568, Tsukuba, Japan
² Liquid Crystal Nano-System Project, ERATO/SORST, Japan Science and Technology Agency, 5-9-9 Tokodai, 300-2635, Tsukuba, Japan

^* e-mail: fukuda.jun-ichi@aist.go.jp

Received: 8 November 2006
Accepted: 4 January 2007
Published online: 9 February 2007

Abstract

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.