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

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

Dec 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006epje...21..341f&link_type=abstract

The European Physical Journal E, Volume 21, Issue 4, December 2006, pp.341-347

Physics

1

Defects In Liquid Crystals, Continuum Models And Theories Of Liquid Crystal Structure, Colloids

Scientific paper

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.

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