Encoding Lattice Symmetry of Nanoparticle Self-Assembly through Programmable Valences

In atomic and molecular systems, directional interactions, as defined by a valence, guide formation of complexly organized lattice structures. Translating the idea of valence-driven interactions to nanoparticle systems would open great opportunity of controlling material fabrications through self-assembly. However, understanding the relationships between directional interactions and the resultant phases and packing structures remains a nontrivial fundamental problem. Here, we present a study of binary self-assembly system built from nano-objects with directional interactions, valence-programmable DNA mesh balls, and with isotropic interactions, inorganic nanoparticles. Our study reveals that controllable phase behaviors can be achieved by tailoring interactions through valence modes and size ratios between DNA mesh balls and nanoparticles. By prescribing 8 different valence modes for mesh balls, we have observed assembly of 2D and 3D crystalline phases with distinct crystallographic symmetries, as uncovered by <i>in situ</i> small-angle X-ray scattering. We have established a theoretical framework based on thermodynamics and geometric constrains that explains the discovered self-assembly behavior for the presented binary system with directional and isotropic interactions. Our combined experimental and theoretical work provides a roadmap for rational design of complex self-assembled structures through bonds engineering.