Eur. Phys. J. B 10, 311-321 (1999)
https://doi.org/10.1007/s100510050860

Director field configurations around a spherical particle in a nematic liquid crystal

Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany

Corresponding author: ^a holger@itap.physik.uni-stuttgart.de

Received: 2 November 1998
Published online: 15 July 1999

Abstract

We study the director field around a spherical particle immersed in a uniformly aligned nematic liquid crystal and assume that the molecules prefer a homeotropic orientation at the surface of the particle. Three structures are possible: a dipole, a Saturn-ring, and a surface-ring configuration, which we investigate by numerically minimizing the Frank free energy supplemented by a magnetic-field and a surface term. In the dipole configuration, which is the absolutely stable structure for micron-size particles and sufficiently strong surface anchoring, a twist transition is found and analyzed. We show that a transition from the dipole to the Saturn ring configuration is induced by either decreasing the particle size or by applying a magnetic field. The effect of metastability and the occurrence of hysteresis in connection with a magnetic field are discussed. The surface-ring configuration appears when the surface-anchoring strength W is reduced. It is also favored by a large saddle-splay constant K₂₄. A comparison with recent experiments [CITE] gives a lower bound for W, i.e., for the interface of water and pentylcyanobiphenyl (5CB) in the presence of the surfactant sodium dodecyl sulfate.