(471a) Generalizing Strong-Segregation Theory to Arbitrarily Complex Block Copolymer Geometries

Block copolymers can self-assemble into a rich variety of space-filling equilibrium phases, from triply-periodic network phases, to a variety of sphere phases, including Frank-Kasper phases. However, the flexibility of polymer molecules to fill space in many different ways makes it difficult to develop intuition for why one complex phase is more stable than another, let alone any heuristic for targeting self-assembly into complex structures. To address this, we consider the limit of strongly segregated block copolymers, in which strong repulsion between blocks leads to sharp interfaces and polymer conformations are strongly stretched, resembling molten brushes. These simplifications make strong segregation theory (SST) the ideal tool for studying the interplay between molecular packing and the geometry of self-assembled structures. The applicability of SST is limited by two major problems: (i) strong assumptions on how polymer chains tessellate space and (ii) failure of the parabolic brush theory to describe regions of positive mean curvature. We demonstrate an improved computational approach to SST that relaxes previous assumptions about how chains tessellate space and incorporates a brush theory that is valid for positive mean curvature. With these improvements, we can start to use SST to study complex phases.