Nematic LC shells are promising candidates for building blocks of colloidal crystals, since the inevitably formed topological surface defects are in principle capable of connecting multiple shells into a three-dimensional network. With a precise control over the defect arrangement in shells, this process represents the colloidal analogy to the guided orbital bonding on the molecular level. By performing numerical simulations to find the equilibrium configuration of various shell geometries, we try to understand the setscrews of defect formation and gain control over the precise defect arrangements.

Our numerical simulation approach allows us to study geometries that are highly challenging to investigate in experiment:
By replacing the inner droplet of the shell with a polyhedron, we were able to show that the introduced vertices and edges offer a versatile guidance mechanisms for the arrangement of topological defects. By varying the size of tetrahedra or cuboids we demonstrate precise control over the relative position of two surface defects at the outer shell interface. This observation is rather surprising, since sphere, cube and tetrahedron share the same homotopy class , i.e. they can continously be transformed into each other, as shown in the video on the left. Consequently, the topological constraints imposed by the inner interface should be identical in all three cases.

Graphic_Summary_of_Simulation_results

The shape of the inner interface dramatically changes the defect location. In this summary the cross-section show the location of topological surfae defects (blue semicirlces) and the bulk director field configuration (dashed lines) within the red planes cutting through the different 3D shell models on top. The images on the bottom are representative virtual textures, obtained by numerical simulations and calculated for light transmission along the z-axis.