Programmable Self-Assembly of Nanoplates into Bicontinuous Nanostructures

Self-assembly isthe process by which individual componentsarrangethemselves into an ordered structure by changing the shapes, components,and interactions. It has enabled us to construct an extensive rangeof geometric forms on many length scales. Nevertheless, the potentialof two-dimensional polygonal nanoplates to self-assemble into extendedthree-dimensional structures with compartments and corridors has remainedunexplored. In this paper, we show coarse-grained Monte Carlo simulationsdemonstrating self-assembly of hexagonal/triangular nanoplates viacomplementary interactions into faceted, sponge-like "bicontinuouspolyhedra" (or infinite polyhedra) whose flat walls partitionspace into a pair of mutually interpenetrating labyrinths. Two bicontinuouspolyhedra can be self-assembled: the regular (or Platonic) Petrie-Coxeterinfinite polyhedron (denoted {6,4|4}) and the semi-regular Hart "gyrangle".The latter structure is chiral, with both left- and right-handed versions.We show that the Petrie-Coxeter assembly is constructed fromtwo complementary populations of hexagonal nanoplates. Furthermore,we find that the 3D chiral Hart gyrangle can be assembled from identicalachiral triangular nanoplates decorated with regioselective complementaryinteraction sites. The assembled Petrie-Coxeter and Hart polyhedraare faceted versions of two of the simplest triply periodic minimalsurfaces, namely, Schwarz's primitive and Schoen's gyroidsurfaces, respectively, offering alternative routes to those bicontinuousnanostructures, which are widespread in synthetic and biological materials.