Effect of confining walls on the interaction between particles in a nematic liquid crystal

We investigate theoretically how the confining walls of a nematic cell affect the interaction of particles mediated by the elastic deformation of a nematic liquid crystal. We consider the case where strong homeotropic or planar anchoring is imposed on the flat parallel walls so that the director on the wall surfaces is fixed and uniform alignment is achieved in the bulk. This set-up is more realistic experimentally than any other previous theoretical studies concerning the elastic-deformation-mediated interactions that assume an infinite medium. When the anchoring on the particle surfaces is weak, an exact expression of the interaction between two particles can be obtained. The two-body interaction can be regarded as the interaction between one particle and an infinite array of 'mirror images' of the other particle. We also obtain the 'self-energy' of one particle, the interaction of a particle with confining walls, which is interpreted along the same way as the interaction of one particle with its mirror images. We show that the walls play a different role in homeotropic and planar cells, which is attributed to the difference in the symmetry of the cells. We also present the landscapes of the interaction energy when one particle is fixed and demonstrate that the interaction is sensitively dependent on the fixed particle as well as the interparticle distance.