Gyroid versus double-diamond in ABC triblock copolymer melts

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Abstract
Monodisperse melts of ABC linear triblock copolymer are examined using self-consistent field theory (SCFT). Our study is restricted to symmetric triblocks, where the A and C blocks are equal in size and the A/B and B/C interactions are identical. Furthermore, we focus on the regime where B forms the majority domain. This system has been studied earlier using density functional theory (DFT), strong-segregation theory (SST), and Monte Carlo (MC), and it corresponds closely to a series of isoprene–styrene–vinylpyridine triblocks examined by Mogi and co-workers. In agreement with these previous studies, we find stable lamellar, complex, cylindrical, and spherical phases. In the spherical phase, the minority A and C domains alternate on a body-centered cubic lattice. In order to produce alternating A and C domains in the cylinder phase, the melt chooses a tetragonal packing rather than the usual hexagonal one. This amplifies the packing frustration in the cylinder phase, which results in a large complex phase region. Contrary to the previous evidence that the complex phase is double-diamond, we predict the gyroid morphology. The earlier theoretical results are easily rationalized and the experimental data are, in fact, more consistent with gyroid.