Tovkach O. Interactions and structures formation in confined liquid crystal colloids

A general method of the theoretical description of the elastic interactions between colloidal particles of arbitrary shape and size in a confined nematic liquid crystal is proposed. Influence of an external electric or magnetic field on the interactions is also examined. A role of high order elastic multipoles in one-, two- and three-dimensional colloidal structures is analyzed. The existence of colloidal structures governed by surface patterns on the substrates of a nematic cell is theoretically predicted as well. It is shown that the lower as compared to nematics symmetry of cholesteric and smectic liquid crystal phases results in the interaction potentials which differ significantly from their nematic counterparts.