Rational Design of Anisotropic Colloids to Self-assemble Open Lattices with Omnidirectional Band Gaps

Patchy colloids possessing anisotropic interactions are versatile building blocks for the self-assembly of complex functional materials. The main challenge in assembling these materials is the rational and efficient discovery of colloidal architectures and chemistries that make the desired aggregate both thermodynamically stable and kinetically accessible. We have previously devised an inverse design strategy termed “landscape engineering” wherein we combine molecular simulations, nonlinear dimensionality reduction, and genetic algorithms to recover and sculpt the low-dimensional free energy landscape governing assembly by rational modulation of building block design. We apply this data-driven design strategy to perform de novo design of patchy colloids that spontaneously assemble into an open pyrochlore lattice with an omnidirectional photonic bandgap. Our particle design assembles the crystal in a two-stage hierarchy where tetrahedral clusters representing the fundamental motif of the crystal are formed at high temperature with >90% yield, and then a gentle ramp to low temperature induces the aggregation of the tetrahedra into the pyrochlore lattice. Our design approach can be extended to other finite-sized and periodic assemblies including Platonic solids and diamond lattices.