Self-assembly of 21-arm star-like diblock copolymer in bulk and under cylindrical confinement

Phase behaviors of a 21-arm star-like diblock copolymer in bulk and under confinement were explored by using the pseudo-spectral method of a self-consistent mean field theory. An asymmetrical phase diagram in bulk was constructed by comparing the free energy of different structures. The gyroid phase was found to possess a large phase region when the inner block in the star-like diblock copolymer has a small volume fraction, suggesting the propensity to form the gyroid phase under this condition. Combined with the early experimental work, a scaling law correlating the period of lamellae D(multiarms) formed from multi-arm star-like block copolymers with the number of arms f was identified, that is, D(multiarms) = D/f(1/2), where D is the period of a linear diblock copolymer with the same degree of polymerization N as a star-like diblock copolymer. The scaling law was also substantiated by the scaling theory. The bridging fraction of the lamellae formed in a star-like diblock copolymer was nearly 100%, which is advantageous for improving its mechanical properties. Some interesting two-dimensional and three-dimensional morphologies were yielded under the cylindrical confinement, where a 3D double helix was found to be the most stable structure.