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

摘要

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 H-1 at which the hedgehog and the Saturn-ring configurations have the equal free energy, and the critical field strength H-2 at which the hedgehog loses its (meta)stability. Our numerical results demonstrate that while H-1 is non-monotonically dependent on the particle radius R-0, H-2 monotonically increases with R-0 and the dependence of H-2 is weak for large R-0. The non-monotonic dependence of H-1 on R-0 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 R-0 the critical field strength is independent of R-0, which agrees with our numerical finding.