Predicting Stable and Metastable Frank-Kasper Phases in Block Polymers Using Self-Consistent Field Theory

Frank-Kasper (FK) phases are topologically closed-packed structures containing particles with disparate shapes and sizes. Hence, these phases are typically found in multicomponent systems such as intermetallic alloys and surfactant solutions. Recently, one member of the FK-phases family, the FK σ phase, was observed in sphere-forming diblock copolymers, which are single-component materials. Inspired by this experimental discovery, self-consistent field theory (SCFT) calculations were performed to understand the origins of such complex structures in block polymers. We developed a physically informed and robust approach to perform successful SCFT calculations of complex structures. Using this approach, we found that many such structures exist on the free energy surface of diblock copolymers. Importantly, the calculations show that various FK phases have nearly degenerate free energies, suggesting that different structures can be observed experimentally by altering the nucleation pathway on multidimensional free energy surface. We will demonstrate the significance of these calculations in the context of our recent discovery of two new FK phases in poly(isoprene-b-lactide) diblock copolymers.