Morphogenesis and topological evolution of a frustrated nematic liquid crystal under confinement.

Liquid crystals (LC) represent topological soft matter that spontaneously form assemblies of constituents and mesoscale textures to minimize free energy. Depending on boundary conditions, they exhibit transformable topological defects, whose study provides fundamental insights applicable to a wide array of disciplines. However, their three-dimensional (3D) structures and dynamics remain largely unexplored due to the subdiffraction limit length scales and submillisecond time scales characteristic of conventional molecular LCs. Here, we report a morphogenesis from conventional nematic tactoids to a unique flower-shaped morphology using a colloidal LC composed of Eu3+-doped LaPO4 nanorods. We demonstrate 3D orientational tomography based on polarized photoluminescence spectroscopy of the Eu3+ dopants, revealing dramatic topological and topographical modulations. We find that this morphogenesis is driven by a theoretically unexpected vertical anchoring of the nanorods on the substrate, which exerts conflicting boundary conditions and leads to a competition between elastic energy and relatively weak surface tension. Our results provide valuable insights into how energy balance in topological matter can be modulated by tuning physicochemical properties of its building blocks.