Toward the Relative Stability of Frank-Kasper Phases Formed by Neat Diblock Copolymer Melts and Binary Blends

Using the well-developed polymer self-consistent field (SCF) calculations of the "standard" model, we found that the relative stability among seven Frank-Kasper phases (A15, sigma, H, Z, p sigma, C14, and C15) formed by both neat diblock copolymer (DBC) A-B melts and binary DBC blends is dominated by their internal-energy densities (i.e., the repulsion between A and B blocks). This trend is also found in other SCF data (including those for the binary blends of DBC and a homopolymer) regardless of the detailed models used. We further found that variations of the Helmholtz free-energy and internal-energy curves of different FK phases are clearly correlated with the average coordination number (CN) z of the Wigner-Seitz polyhedra (which is equivalent to the average number of 6-fold rotation axes) in these FK phases, and defined the internal-energy-weighted and the Helmholtz-free-energy-weighted average CNs, which can be regarded as constant depending only on the FK phase similar to z but are more pertinent to its internal energy and Helmholtz free energy, respectively, than z. Finally, the change of the stable phase between sigma and C14/C15 in binary DBC blends is mainly due to that in the interchain repulsion.