Theory of Complex Spherical Packing Phases in Surfactant Systems

The emergence and stability of complex spherical phases from a vast number of soft matter systems have been attracting tremendous attention recently. In particular, recent experiments have demonstrated the formation of Frank-Kasper and Laves phases (A15, σ, C14 and C15) in surfactant systems. Specifically, it has been shown that micelles self-assembled from amphiphilic molecules in water could pack and form these complex spherical packing phases in the presence of hydrocarbon molecules. Theoretically, we model the surfactant molecules by short diblock copolymers composed of a hydrophilic head and a hydrophobic tail. The phase behaviour of the model system is examined by using self-consistent field theory applied to a model system of short diblock copolymers and homopolymers. Our results indicate that the complex spherical packing phases could become stable for a set of model parameters corresponding to surfactant systems. Phase diagrams containing a large number of complex phases are constructed. The theoretical results demonstrate that the emergence and stability of complex spherical packing phases could be regulated by surfactant composition and concentration, thus shedding light to the understanding of the formation mechanisms of complex phases in soft matter systems.