The absence of the C36 Laves phase in diblock polymer melts and blends

Under specific conditions, spherical diblock polymer micelles self-assemble into complex spatially periodic packings called Frank-Kasper phases that mimic the packing of atoms in certain metal alloys. Two recently observed examples include the C14 and C15 Laves phases, which are stable phases in AB diblock polymer/core-homopolymer blends. In metals, the C36 Laves phase is also commonly observed in systems similar to those that form C14 and C15. However, C36 has not been observed in any form of soft matter. To provide an explanation for this phenomenon, we used self-consistent field theory to examine the morphology and free energy of Laves phases in both neat diblock polymer melts, where Laves phases are predicted to be metastable, and diblock polymer/core-homopolymer blends. We find that the free energy of the C36 morphology bisects the free energies of C14 and C15 as a result of the structures of these phases, in which C36 is composed of half C14-type layers and half C15-type layers. The presence of this apparent "interfacial energy" penalty between layers, combined with the fact that transitions between Laves phases are expected to be facile in block polymers, suggests that C36 is unlikely to form as a stable self-assembled morphology in diblock polymer systems.