Packing Frustration in Block Copolymer Double Gyroids: Is it really all about the tubular domains?

Understanding the molecular-scale mechanisms that lead to self-assembly of complex 3D morphologies remains an active area of research in soft matter systems. Block copolymers (BCPs) provide an exciting avenue to probe these mechanisms due to advancements in theory, synthesis and characterization tools. In this talk, we will revisit the thermodynamic connection between stability of triply-periodic network (TPN) phases, such as the Double Gyroid (DG), and packing frustration, or the variation in chain extension required by space filling constraint. We propose Medial Thickness (MT) analysis which provides a generic and practical measure of domain thickness of BCP morphologies of any arbitrary topology. Based on MT analysis of both theoretical models and experimental measurements of inter-block dividing surfaces of DG, we argue that previous measures of domain thickness severely overestimate both magnitude and dispersity of chain extension required to fill the tubular domains of TPN, belying the heuristic picture that their dominant thermodynamic costs arise from the stretching to reach the center of tubular interconnects. These insights also lead us to revisit longstanding question about absence of DG in the equilibrium phase diagram of strongly-segregated BCPs.