Formation of complex spherical packing phases in diblock copolymer/homopolymer blends

The formation and relative stability of spherical packing phases in binary blends composed of AB-diblock copolymers and A-homopolymers are systematically studied using the self-consistent field theory applied to the freely-jointed chain model of polymers. Phase diagrams with different model parameters of the blends are constructed, revealing that the emergence of various complex spherical packing phases, including the Frank-Kasper σ phase and the Laves C14 and C15 phases, could be induced by the addition of the homopolymers. For BCC-forming diblock copolymers, a phase transition sequence of BCC → σ → C14 → C15 is predicted when the homopolymer concentration is increased. An analysis of the properties of A-domains reveals that their sizes are regulated by the differential localization of A-homopolymers. The resultant spherical domains of different sizes is a key factor to stabilize complex spherical packing phases, especially the Laves C14 and C15 phases. Furthermore, the phase behaviour is strongly affected by the chain length of the homopolymers. In particular, the addition of short homopolymers results in an expanded region of the cylindrical phase, whereas the addition of long homopolymers stabilizes the complex spherical packing phases. The theoretical results from current study are in good agreement with recent experiments and theory, and shed light to the formation of complex spherical packing phases in other self-assembling soft matter systems.