Accessing the Frank-Kasper sigma Phase of Block Copolymer with Small Conformational Asymmetry via Selective Solvent Solubilization in the Micellar Corona

Large conformational asymmetry has been considered as an essential ingredient for accessing the Frank-Kasper (FK) phase in a neat block copolymer (bcp) melt. This criterion can be relaxed by blending the bcp with the corresponding homopolymer, where the homopolymer is incorporated into the micellar core in the dry-brush regime. While the solubilization of the homopolymer in the micellar corona in the wet-brush regime has also been demonstrated to yield the FK sigma phase in a bcp system bearing a large conformational asymmetry parameter (epsilon > 1.5), we demonstrate here that this is also true for the system with small conformational asymmetry. A cylinder-forming poly(ethylene oxide)-block-poly(1,2-butadiene) (PEO-b-PB) with a epsilon of 1.2 was blended with a small amount of selective solvent, which was either a PB homopolymer (h-PB) or dodecylbenzene (DB) to yield the mixtures forming the spherical micelles composed of the PEO core and the corona containing the wet-brush mixture of PB blocks and the selective solvents. Both types of mixtures were found to form the FK sigma phase in a narrow region near the cylindersphere phase boundary. We argue that, under a given volume fraction (f(PEO)) and size of the PEO core, the shorter PB coronal blocks in the bcp/solvent mixtures are more strained than the longer PB blocks in the corresponding neat diblock; therefore, the spherical phase is accessed at a higher PEO core fraction to alleviate the excess entropic penalty. The formation of a larger core (at a higher f(PEO)) and the stronger propensity to alleviate the packing frustration of the more strained PB coronal blocks in the bcp/selective solvent mixture creates an effect equivalent to increasing the conformational asymmetry and hence promotes the core to adopt the polyhedral geometry templated by the Voronoi cells of the lattice. The micelles approaching the polyhedral interface limit then favor the packing in the FK sigma phase to minimize the total free energy.