Elastic interaction between colloidal particles in confined nematic liquid crystals.

The theory of elastic interaction of micrometer-sized axially symmetric colloidal particles immersed into confined nematic liquid crystal has been proposed. General formulas are obtained for the self-energy of one colloidal particle and interaction energy between two particles in arbitrary confined nematic liquid crystals with strong anchoring condition on the bounding surfaces. Particular cases of dipole-dipole interaction in the homeotropic and planar nematic cell with thickness L are considered and found to be exponentially screened on far distances with decay length lambdadd=L/pi. It is predicted that bounding surfaces in the planar cell crucially change the attraction and repulsion zones of usual dipole-dipole interaction. As well it is predicted that the decay length in quadrupolar interaction is two times smaller than for the dipolar case in the homeotropic cell.