Stabilizing the Frank-Kasper Phases via Binary Blends of Diblock Copolymers.

The emergence of the complex Frank-Kasper phases from binary mixtures of diblock copolymers is studied using the self-consistent field theory. The relative stability of different ordered phases, including the Frank-Kasper σ and 15 phases containing nonspherical minority domains with different sizes, is examined by a comparison of their free energy. The resulting phase diagrams reveal that the σ phase occupies a large region in the phase space of the system. The formation mechanism of the σ phase is elucidated by the distribution of the two diblock copolymers with different lengths and compositions. In particular, the segregation of the two types of copolymers, occurring among different domains and within each domain, provides a mechanism to regulate the size and shape of the minority domains, thus enhancing the stability of the Frank-Kasper phases. These findings provide insight into understanding the formation of the Frank-Kasper phases in soft matter systems and a simple route to obtain complex ordered phases using block copolymer blends.