Frank-Kasper Phases Self-Assembled from a Linear A₁B₁A₂B₂ Tetrablock Copolymer

The Frank-Kasper (FK) phases self-assembled from block copolymer systems have attracted abiding interest. In this work, the formation mechanism of the complex FK phases from the self-assembly of simple A₁B₁A₂B₂ tetrablock copolymers is investigated using self-consistent field theory (SCFT). For a typical set of parameter spaces, we utilize SCFT to construct a number of phase diagrams. In these phase diagrams, the FK phases exhibit a notable stability region. The stable region of the FK phases reveals that the distribution of A₁ and A₂ blocks can be precisely regulated by tuning the ratio of the A₁/A₂ block, wherein the long A₁ blocks can aggregate within the "core" while the short A₂ blocks can form the "shell" of a spherical domain in the FK phases, respectively, to accommodate the sizes and shapes of the spherical domains in the complex spherical packing phases. Besides, we also demonstrate that the existence of the B₂ block plays a crucial factor to stabilize the FK phases.