Frank-Kasper Phases in Block Polymers

The discovery of the Frank-Kasper Sigma phase in diblock copolymer and tetrablock terpolymer melts catalyzed a renewed interest over the past decade in understanding particle-forming phases in block polymer systems. This Perspective provides a concise overview of the Frank-Kasper phases seen to date in block polymers (A15, Sigma, and the C14 and C15 Laves phases) and mechanisms known to produce them: conformational asymmetry in neat diblock copolymer melts, interfacial segregation effects in diblock copolymer blends, particle swelling in diblock copolymer/homopolymer blends, and matrix segregation effects in neat tetrablock terpolymer melts. While a qualitative understanding of the emergence of Frank-Kasper phases in block polymer systems has been achieved, a number of outstanding questions remain, in particular those arising from the low degree of polymerization used in experiments, nonequilibrium effects during thermal processing, and the large design space available in blends and multiblock systems. This Perspective discusses potential avenues for future research related to these areas as well as overarching issues underlying the connections between Frank-Kasper phase formation in block polymers to other soft matter and metals.