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

Abstract

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, σ, H, Z, pσ, 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) z̅ 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 z̅ but are more pertinent to its internal energy and Helmholtz free energy, respectively, than z̅. Finally, the change of the stable phase between σ and C14/C15 in binary DBC blends is mainly due to that in the interchain repulsion.