Orientation of a solid particle embedded in a monodomain nematic liquid crystal

Abstract

A problem of the equilibrium orientation of an elongated solid particle put inside a uniformly aligned nematic liquid crystal is studied. The particle is assumed to be sufficiently large so that the orientational distortions it causes may be treated in the framework of the continuum theory. Three kinds of anchoring of nematic material on the particle surface are considered: two of the planar, and one of the homeotropic type. We prove that, depending on the anchoring strength, the stable orientation of the particle major axis may be either perpendicular (weak anchoring) or parallel (strong anchoring) to the unperturbed director of the liquid-crystalline domain. The dimensionless parameter controlling the situation is the ratio \ensuremath{\omega} of the transverse size of the particle to the extrapolation length of the nematic material. The transition from the perpendicular to the parallel orientation of the particle takes place at \ensuremath{\omega}\ensuremath{\sim}1.