Block Copolymers beneath the Surface: Measuring and Modeling Complex Morphology at the Subdomain Scale

Block copolymer (BCP) melts are a paradigm for pluripotent molecular assembly, yielding a complex and expanding array of variable domain shapes and symmetries from a fairly simple and highly expandable class of molecular designs. This Perspective addresses recent advances in the ability to model and measure features of domain morphology that go beyond the now canonical metrics of D spacing, space group, and domain topology. Such subdomain features have long been the focus of theories seeking to explain and understand mechanisms of equilibrium structure formation in block copolymer melts, from inhomogeneous curvatures of an intermaterial dividing surface to variable domain thickness. Quantitative metrics of variable subdomain geometry, or packing frustration, are central to theoretical models of complex BCP phase formation, from bicontinuous networks to complex (e.g., Frank-Kasper) crystals, and new experimental methods bring the possibility of their quantitative tests into reach. Here we not only review generic approaches to quantify local domain morphologies that both connect directly to thermodynamic models of BCP assembly but also generalize to domains of arbitrary shape and topology. We then overview experimental methods for characterizing BCP morphology, focusing on recent advances that make accessible detailed and quantitative metrics of fine features of subdomain geometry. Beyond even the critical comparison between detailed predictive models and experimental measurements of complex BCP assembly, validation of these advances lays the foundation to “mold” morphology in BCP assemblies at ever finer subdomain scale, through controlled architectures and processing pathways.