Entropic size control of self-assembled filaments

Controlling the size and shape of assembled structures is a fundamental challenge in self-assembly and is highly relevant in material design and biology. Here, we show that specific but promiscuous short-range binding interactions make it possible to economically assemble linear filaments of user-defined length. Our approach leads to independent control over the mean and width of the filament size distribution and allows us to smoothly explore design trade-offs between assembly quality (spread in size) and cost (number of particle species). We employ a simple hierarchical assembly protocol to minimize assembly times and show that multiple stages of hierarchy make it possible to extend our approach to the assembly of higher-dimensional structures. Our work provides a conceptually simple solution to size control that is applicable to a broad range of systems, from DNA nanoparticles to supramolecular polymers and beyond.