The key-lock mechanism in nematic colloidal dispersions

We consider the interaction of two-dimensional colloids, in nematic liquid crystals, with walls or geometrical boundaries. The interactions between colloidal disks and flat walls, with homeotropic boundary conditions, are always repulsive. The repulsions may be turned into strong attractions at structured or sculpted walls with cavities, matching closely the shape and size of the colloids. This key-lock type of interaction is analyzed in detail for spherocylindrical cavities of various length to breath ratios, by minimizing the Landau-de Gennes free energy functional of the orientational order parameter. We find that the attractions occur only for walls with cavities within a small range of the colloidal size and for a narrow range of orientations around the wall's symmetry axis.