Structure and energetics of grain boundaries in self-assembled double-gyroid block copolymer networks

Abstract

Grain boundaries (GBs) are ubiquitous defects in crystalline materials. However, they remain less explored in block copolymer ordered phases. Here, we develop a self-consistent field theory framework to investigate GB structure and energetics in double-gyroid (DG) diblock copolymer networks. The GB energy landscape is obtained as a function of GB orientation, which reveals multiple local minima representing distinct network-switching GBs. Remarkably, the global minimum is a previously unidentified asymmetric-tilt network-switching GB (ATNS), exhibiting a lower energy than the experimentally observed $(422)$ twin boundary (TB). Comparative analyses of representative low- (ATNS, $(422)$ TB) and high-energy twist ($(0\bar{1}\bar{1})$, $(100)$ TNSs) GBs reveal that, unlike enthalpy-dominated hard matter, GB stability in DG networks is predominantly entropy-driven. Twist-type GBs generate new nodes and disrupt nodal coplanarity, causing chain packing frustration and large entropy penalties. Conversely, the ATNS preserves favorable network connectivity and minimizes conformational constraints on polymer chains, making it the energetically preferred GB.