Landau theories of Frank-Kasper spherical packing phases

The Frank-Kasper phases are a group of complex spherical packing phases, a subset of which have been discovered in a wide range of soft condensed matter systems. Motivated by this universality, we investigated the (meta-)stability of these phases across a family of phase field crystal models - Landau theories that describe the formation of crystalline phases. This work illuminates the interplay between short and long-range interactions that influence the formation of these phases in many different systems. In this talk I will discuss the general mechanisms that are found to promote the stability of these complex phases. I will also demonstrate how these mechanisms relate to the microscopic parameters of a diblock-copolymer system in which several Frank-Kasper phases appear.