This paper presents an analytic theory for the self-assembly of polyhedral nanoparticles (NPs) based on their crystal structures in non-Euclidean space. It demonstrates that geometrical frustration of particle shapes, combined with competing interparticle interactions, leads to controllable self-assembly of complex structures. Applying the theory to tetrahedral NPs, the researchers find high-yield and enantiopure self-assembly of helicoidal ribbons, agreeing with experimental observations. The theory offers a framework for assembling simple polyhedral building blocks into complex morphologies with tunable optical activity, relevant to emerging technologies.

Francesco Serafin, Jun Lu, Nicholas Kotov, Kai Sun, Xiaoming Mao