Landau theory of complex spherical packing phases

The complex spherical packing phases, including the Frank-Kasper σ and A15 phases, appear in a diverse array of soft-condensed matter systems. The universality of these novel ordered structures points to some common underlying physics that can be probed by a suitable Landau theory. The stability of several complex phases was investigated in two theories that are often used to study pattern formation: The Landau-Brazovskii and Ohta-Kawasaki models. Unexpectedly, these phases were found to be stable in the former theory and not the latter. Appropriately scaled, these two free-energy functionals favour periodic modulation of the order parameter at a particular wave number, and differ only in the shape of the free-energy about this value. Motivated by this result, we studied how the shape of the free-energy about its optimal wave number can influence the relative stability of the complex phases over the BCC and FCC spherical phases. This talk is concerned with how these results can inform us of the general mechanisms guiding the formation of the complex spherical phases.