Programmable Self-Assembly of Nanoplates into Bicontinuous Nanostructures

Self-assembly is the process by which individual components arrange themselves into an ordered structure by changing shapes, components, and interactions. It has enabled us to construct a remarkable range of geometric forms at many length scales. However, the potential of two-dimensional polygonal nanoplates to self-assemble into extended three-dimensional structures with compartments and corridors has not been explored. In this presentation, we demonstrate coarse-grained Monte Carlo simulations showing self-assembly of hexagonal/triangular nanoplates via complementary interactions into facetted, sponge-like "bicontinuous polyhedra" whose flat walls partition space into a pair of mutually interpenetrating labyrinths. Two bicontinuous polyhedra can be self-assembled: the regular Petrie-Coxeter infinite polyhedron (denoted {6,4|4}) and the semi-regular Hart "gyrangle". The latter structure is chiral and has both left- and right-handed version. We show that the Petrie-Coxeter assembly is constructed from two complementary populations of hexagonal nanoplates. Remarkably, we find that the 3D chiral Hart gyrangle can be assembled from identical achiral triangular nanoplates decorated with regioselective complementary interaction sites. The assembled Petrie-Coxeter and Hart polyhedra are facetted versions of two of the simplest triply-periodic minimal surfaces, namely Schwarz' Primitive and Schoen's Gyroid surfaces respectively. These findings offer new ways to create those bicontinuous nanostructures, which are prevalent in synthetic and biological materials.