Size limits of self-assembled colloidal structures made using specific interactions

Significance Nature uses hierarchical assembly to make complex structures such as biomolecules, virus shells, and microtubules with high fidelity. Today a key challenge is to translate this process to artificial systems, which hinges on understanding the fundamental questions of efficiency and scalability of self-assembly. Although self-assembly has been studied for decades, the principles behind it and its fundamental and practical limits are still largely unknown. In this paper we establish size limitations for assembling structures of controlled size and shape out of colloidal particles with specific interactions. Inspired by simulations of structures with highly variable shapes and sizes, we develop an understanding of yield through a general theory of excited states that compete with the desired structure in assembly. We establish size limitations for assembling structures of controlled size and shape out of colloidal particles with short-ranged interactions. Through simulations we show that structures with highly variable shapes made out of dozens of particles can form with high yield, as long as each particle in the structure binds only to the particles in their local environment. To understand this, we identify the excited states that compete with the ground-state structure and demonstrate that these excited states have a completely topological characterization, valid when the interparticle interactions are short-ranged. This allows complete enumeration of the energy landscape and gives bounds on how large a colloidal structure can assemble with high yield. For large structures the yield can be significant, even with hundreds of particles.