Emergence of Frank–Kasper Phases from Chemically Simple Block Copolymer: Poly(ethylene oxide)- block -polyisoprene and Its Dry-Brush Blends

The Frank-Kasper (FK) phases, also known as tetrahedrally close-packed structures, represent a unique class of ordered morphologies characterized by large unit cells with multiple nonequivalent lattice sites. To date, only a limited number of linear AB-type block copolymers (BCPs) have been shown to form FK phases. Here, we systematically investigate a sphere-forming poly-(ethylene oxide)-block-poly-(1,4-isoprene) (PEO-b-PI) with a conformational asymmetry parameter ε ≈ 1.26 and identify it as a new linear diblock system capable of forming the FK σ phase. In the neat PEO-b-PI, an abrupt enlargement of micelle size was observed across the BCC-to-σ lattice transition, despite a reduction in diblock molecular weight, indicating the pronounced influence of lattice symmetry on micelle dimensions at the onset of FK phase formation. To further expand the accessible FK phase regime, we employed a dry-brush blending strategy by incorporating homopolymer PEO (h-PEO) into a BCC-forming PEO-b-PI. With increasing h-PEO content, the blends exhibited a lyotropic BCC → σ → C14 → C15 phase transition sequence consistent with the theoretical predictions. Detailed structural analysis revealed systematic variations in micelle characteristics with h-PEO composition, arising from the interplay among different free energy components. Notably, the FK phases in this system were stabilized over an unusually broad composition window, allowing the Laves C15 phase to persist up to nearly symmetric compositions, significantly beyond the stability limits reported for conventional BCP/homopolymer blends.