Director Field Configurations around a Spherical Particle in a Nematic Liquid Crystal

TL;DR

This study investigates the director field configurations around spherical particles in nematic liquid crystals, analyzing stability, transitions, and effects of parameters like particle size, magnetic field, and surface anchoring.

Contribution

It provides a numerical analysis of different director configurations and their stability, including transitions induced by size, magnetic field, and surface anchoring effects.

Findings

Dipole configuration is stable for micron-sized particles with strong surface anchoring.

Transitions between configurations are triggered by particle size reduction or magnetic field application.

Surface-ring configuration occurs with reduced surface anchoring strength and high saddle-splay constant.

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 occurence 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 K_24. A comparison with recent experiments by Poulin et al. gives a lower bound for W, i.e., W > 0.6 erg/cm^2 for the interface of water and pentylcyanobiphenyl (5CB) in the presence of the surfactant sodium dodecyl sulfate.