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

The phase behavior of B(1)AB(2)C tetrablock terpolymer melts is systematically studied using the self-consistent field theory, focusing on the emergence and stability of the complex Frank-Kasper sigma-phase. Our study starts with an investigation of the stability region of the sigma phase for a generic model of B(1)AB(2)C terpolymers, in which the C-blocks form spherical domains immersed in the A/B matrix. Then, we examine the stability of the s 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 sigma 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 B(1)AB(2)C. 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 sigma phase.