Shape-tuning the colloidal assemblies in nematic liquid crystals

Colloidal platelets are natural building blocks for the shape-controlled assembly of two-dimensional periodic lattices and can form versatile optical elements. Using three-dimensional (3D) numerical modelling, we demonstrate the self-assembly of triangular, square and pentagonal sub-micrometer sized platelets in a thin layer of nematic liquid crystal. Torques acting on individual platelets are calculated, showing that platelets with quadrupolar symmetry (squares, hexagons, etc) are, orientationally, more strongly bound than platelets with dipolar symmetry (triangles, pentagons) which is important for switching applications. Inter-platelet potentials are shown to depend in a complex way on the orientations of the platelets, exhibiting easy and hard reorientation axes and multiple minima. Linear chains of elastic dipoles form into two-dimensional periodic lattices via interesting rotational and translational shifts, to minimize the distortions in the surrounding nematic medium.