Tetrahedral Liquid-Crystalline Networks: An A15-Like Frank–Kasper Phase Based on Rod-Packing

Abstract

The Pm (Formula presented.) n cubic and other low-symmetry Frank–Kasper phases are known to be formed by soft spheres, ranging from metals to block copolymer micelles and colloidal nanoparticles. Here, we report a series of X-shaped polyphiles composed of sticky rods and two non-symmetric branched side-chains, which self-assemble into the first example of a cubic liquid-crystalline phase representing a tetrahedral network of rods with a Pm (Formula presented.) n lattice. It is the topological dual to the Weaire–Phelan foam, being the Voronoi tessellation of the A15 sphere packing, from which this network is obtained by Delaunay triangulation.