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

Abstract

The Pmtrue3‾ 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 Pmtrue3‾ 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.