Toward the\nRelative Stability of Frank–Kasper\nPhases Formed by Neat Diblock Copolymer Melts and Binary Blends

Using\nthe well-developed polymer self-consistent field (SCF) calculations\nof the “standard” model, we found that the relative\nstability among seven Frank–Kasper phases (A15, σ, H,\nZ, pσ, C14, and C15) formed by both neat diblock copolymer (DBC)\nA-B melts and binary DBC blends is dominated by their internal-energy\ndensities (i.e., the repulsion between A and B blocks). This trend\nis also found in other SCF data (including those for the binary blends\nof DBC and a homopolymer) regardless of the detailed models used.\nWe further found that variations of the Helmholtz free-energy and\ninternal-energy curves of different FK phases are clearly correlated\nwith the average coordination number (CN) <i>z̅</i> of the Wigner–Seitz polyhedra (which is equivalent to the\naverage number of 6-fold rotation axes) in these FK phases, and defined\nthe internal-energy-weighted and the Helmholtz-free-energy-weighted\naverage CNs, which can be regarded as constant depending only on the\nFK phase similar to <i>z̅</i> but are more pertinent\nto its internal energy and Helmholtz free energy, respectively, than <i>z̅</i>. Finally, the change of the stable phase between\nσ and C14/C15 in binary DBC blends is mainly due to that in\nthe interchain repulsion.