Landau Theory of Complex Spherical Packing Phases

A large number of complex spherical phases, such as the Frank-Kasper phases (e.g., the σ, A15, C14 and C15 phases), have been observed in various soft matter systems. Understanding the formation of these novel ordered structures presents an interesting challenge to the soft matter community. We are developing Landau theories that are capable of describing the occurrence and stability of these phases. Our research indicates that the A15 and σ phases may emerge as stable or metastable phases in systems described by a Landau theory derived from the statistical mechanics of block copolymers. We will discuss our results and their significance to the mechanisms for the formation of complex spherical phases in soft matter systems.