Interfaces of interfaces: modeling the structure of bicontinuous networks around grain boundaries

Self-assembled, bicontinuous structures formed by amphiphilic macromolecules, such as double gyroid or double diamond, are ideally triply periodic, intercatenated networks. In reality, they form domains that are separated by grain boundaries; notably, for double diamond grains assembled by diblock copolymers, these are twin boundaries. Current computational techniques are typically restricted to confined systems or periodic boundary conditions, making it challenging to model the structure around a grain boundary or assess their thermodynamic costs. Moreover, prior studies reveal that the lattice deformations of material surrounding these defects obey different rules than those describing atomic crystals, owing to the malleable morphology of these systems. Here, we introduce a coarse-grained geometric model that encapsulates the structural inhomogeneities induced by a bicontinuous grain boundary, suggesting that we can capture generic features governing self-assembly in terms of "liquid networks." We compare this model with results from strong segregation theory and experiments, and further compare with periodic grain boundary "sandwiches" modeled by self-consistent field theory. This work presents a method for testing and validating models of bicontinuous network defects.