Interaction of spherical particles dispersed in a liquid crystal above the nematic-isotropic phase transition

The effective interaction of micron-size particles immersed in a nematic liquid crystal at temperatures above the nematic-isotropic phase transition is examined. Using the Landau-de Gennes theory we describe the surface-induced ordering of the liquid crystal. Modeling a spherical particle by a sequence of conical surfaces enables us to draw an analogy with the partial ordering in a thin nematic film and to obtain an analytical expression for the two-particle interaction. Special attention is paid to the dependence of the effective interaction on temperature and on the interfacial coupling parameters, which are chosen in agreement with recent experiments. We show that the interaction as a function of the interparticle distance exhibits a potential barrier of the order of kT. The height of the barrier decreases exponentially with increasing temperature while it grows linearly with the interfacial coupling parameters.