Complete Photonic Band Gaps with Nonfrustrated ABC Bottlebrush Block Polymers

Bottlebrush block polymers are a promising platform for self-assembled photonic materials, yet most work has been limited to one-dimensional photonic crystals based on the lamellar phase. Here we demonstrate with simulation that nonfrustrated ABC bottlebrush block polymers can be used to self-assemble three-dimensional photonic crystals with complete photonic band gaps. To show this, we have developed a computational approach that couples self-consistent field theory (SCFT) simulations to Maxwell's equations, thereby permitting a direct link between molecular design, self-assembly, and photonic band structures. Using this approach, we calculate the phase diagram of nonfrustrated ABC bottlebrush block polymers and identify regions where the alternating gyroid and alternating diamond phases are stable. By computing the photonic band structures of these phases, we demonstrate that complete band gaps can be found in regions of thermodynamic stability, thereby suggesting a route to realize these photonic materials experimentally. Furthermore, we demonstrate that gap size depends on volume fraction, segregation strength, and polymer architecture, and we identify a design strategy based on symmetry breaking that can achieve band gaps for lower values of refractive index contrast. Taken together, the approach presented here provides a powerful and flexible tool for predicting both the self-assembly and photonic band structures of polymeric materials.