Interfacial geometry in particle-forming phases of diblock copolymers

Abstract

Frank-Kasper phases are complex particle packings known to form in a wide variety of hard and soft materials, including single-component AB diblock copolymer melts. An important open question in the context of this system is why these lower-symmetry packings are selected over the classical, higher-symmetry, body-centered cubic phase. To address this question, we simulated a library of diblock copolymer melts under intermediate-segregation conditions using self-consistent field theory and performed a combination of geometric and thermodynamic analyses. Our findings show that imprinting of the enclosing Voronoi polyhedra onto the micelle core is generally weak, but nonetheless coincides with sharpening of the interface between A and B monomers compared to more spherical cores. The corresponding reduction in enthalpy, which is the dominant contribution to the free energy, drives the bcc-$\ensuremath{\sigma}$ transition, overcoming increases in stretching penalties and giving way to more polyhedral micelle cores. These results offer insight into the stability and formation of Frank-Kasper phases under experimentally realistic conditions.