Stability of the Frank-Kasper σ-phase in BABC linear tetrablock terpolymers

The phase behavior of B1AB2C tetrablock terpolymer melts is systematically studied using the self-consistent field theory, focusing on the emergence and stability of the complex Frank-Kasper σ-phase. Our study starts with an investigation of the stability region of the σ phase for a generic model of B1AB2C terpolymers, in which the C-blocks form spherical domains immersed in the A/B matrix. Then, we examine the stability of the σ phase for a model system with a specific set of parameters mimicking poly(styrene-b-isoprene-b-styrene-b-ethylene oxide) (SISO) block copolymers which were examined in recent experiments. Our results reveal that the formation of the σ phase is mainly governed by two factors. The first factor is the conformational asymmetry between the A/B-blocks and the C-block, similar to that in conformationally asymmetric AB-type block copolymers. The second factor is the specific chain architecture of B1AB2C. The tetrablock architecture with a specific set of interaction parameters and compositions leads to the formation of large core-shell spherical domains, which amplifies the effect of interfacial energy and thereby stabilizes the σ phase.