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

Abstract

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.

Control the Self‐assembly of Block Copolymers by Tailoring the Packing Frustration

“…However, the packing frustration of minority blocks also makes a nonnegligible contribution to the self‐assembly of block copolymers. [ 19 ] The packing frustration of blocks within the interface curvature is strongly related with the nonuniformity of chain stretching inside the cone‐shaped space within the curvature (Figure 1). Therefore, to achieve a gradual radial distribution of minority blocks can relieve the packing frustration.…”

“…[ 12‐16 ] Among these techniques, self‐ consistent field theory (SCFT) has been proven to be one of the most successful methods for the study of the phase separation of block copolymers. [ 17‐19 ] On one hand, SCFT can accurately calculate the free energy of different ordered phases and thus identify their relative stability in the self‐assembly of block copolymer melts. On the other hand, it can separate the interfacial energy from the entropic contribution to the free energy and calculate the density distribution of each segment, which is critical to revealing the effect of molecular architecture on the self‐assembly behaviors of block copolymers.…”

Double Gyroid Morphologies in Precise Ion-Containing Multiblock Copolymers Synthesized via Step-Growth Polymerization

“…Specifically, polymer chains should minimize the interfacial area and uniformly fill the domains defined for each block species. 29 , 30 Linear diblock copolymers that satisfy both conditions are often limited to only a few volume fraction range according to the self-consistent field theory (SCFT) calculation ( Figure 2 a). 31 Experimentally, PS- b -PI diblock copolymers self-assemble into the DG structures at f PI = 0.36–0.39 and 0.65–0.68 ( Figure 2 b).…”

Stability of cubic single network phases in diblock copolymer melts

“…For example, the threefold connected DG is less frustrated than the fourfold connected DD, because more struts are connected to a single node in the DD, which makes its node bulkier. While packing frustration has received considerable attention as the origin of NET phase formation in diblock polymers, the extent to which the average mean curvature of the NET microstructure matches the spontaneous curvature of the interface produced by the block polymer also plays an important role in the morphology selection 19,21 . Moreover, the interfacial area per chain, which governs the amount of A/B contact, also contributes to phase selection.…”