Abstract
We consider energy minimizing configurations of a nematic liquid crystal around a spherical colloid particle, in the context of the Landau–de Gennes model. The nematic is assumed to occupy the exterior of a ball B r0, and satisfy homeotropic weak anchoring at the surface of the colloid and approach a uniform uniaxial state as \({|x|\to\infty}\). We study the minimizers in two different limiting regimes: for balls which are small \({r_0\ll L^{\frac12}}\) compared to the characteristic length scale \({L^{\frac 12}}\), and for large balls, \({r_0\gg L^{\frac12}}\). The relationship between the radius and the anchoring strength W is also relevant. For small balls we obtain a limiting quadrupolar configuration, with a “Saturn ring” defect for relatively strong anchoring, corresponding to an exchange of eigenvalues of the Q-tensor. In the limit of very large balls we obtain an axisymmetric minimizer of the Oseen–Frank energy, and a dipole configuration with exactly one point defect is obtained.
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Alama, S., Bronsard, L. & Lamy, X. Minimizers of the Landau–de Gennes Energy Around a Spherical Colloid Particle. Arch Rational Mech Anal 222, 427–450 (2016). https://doi.org/10.1007/s00205-016-1005-z
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DOI: https://doi.org/10.1007/s00205-016-1005-z