Theory of Complex Spherical Packing Phases in Diblock Copolymer/Homopolymer Blends

The formation of complex spherical packing phases in binary and ternary diblock copolymer/homopolymer blends is studied using self-consistent field theory (SCFT). The polymeric blends are composed of A-sphere-forming AB diblock copolymers mixed with B-selective (C) homopolymers and A-selective (D) homopolymers, resembling surfactant/water and surfactant/water/oil systems. It is observed that the addition of C homopolymers stabilizes the Frank-Kasper (FK) sigma and A15 phases, and further addition of D homopolymers enables the appearance of the Laves C14 and C15 phases. Compared with neat AB diblock copolymers, the FK sigma phase is predicted to become an equilibrium phase in the AB/C blends at lower conformational asymmetry. In the AB/C/D blends, the C and D homopolymers are localized in the B-rich matrix and A-rich cores, respectively, synergistically stabilizing the complex spherical packing phases. The theoretically predicted phase behaviors of the AB/C and AB/C/D blends are consistent with experiments on polymeric blends and surfactant systems. These results provide insights into the emergence of complex spherical packings in soft matter systems composed of amphiphiles and selective additives.