Directionally Interacting Spheres and Rods Form Ordered Phases

The structures formed by mixtures of dissimilarly shaped nanoscale objects can significantly enhance our ability to produce nanoscale architectures. However, understanding their formation is a complex problem due to the interplay of geometric effects (entropy) and energetic interactions at the nanoscale. Spheres and rods are perhaps the most basic geometrical shapes and serve as convenient models of such dissimilar objects. The ordered phases formed by each of these individual shapes have already been explored, however, when mixed, spheres and rods have demonstrated only limited structural organization to date. Here, we show using experiments and theory that the introduction of directional attractions between rod ends and isotropically interacting spherical nanoparticles (NPs) through DNA base pairing leads to the formation of ordered three-dimensional lattices. The spheres and rods arrange themselves in a complex alternating manner, where the spheres can form either a face-centered cubic (FCC) or hexagonal close-packed (HCP) lattice, or a disordered phase, as observed by in situ X-ray scattering. Increasing NP diameter at fixed rod length yields an initial transition from a disordered phase to the HCP crystal, energetically stabilized by rod-rod attraction across alternating crystal layers, as revealed by theory. In the limit of large NPs, the FCC structure is instead stabilized over the HCP by rod entropy. We, therefore, propose that directionally specific attractions in mixtures of anisotropic and isotropic objects offer insight into unexplored self-assembly behavior of noncomplementary shaped particles.