Accessing Semi-Addressable Self Assembly with Efficient Structure Enumeration

TL;DR

This paper introduces an efficient enumeration algorithm that enables scalable inverse design of self-assembling structures in the semi-addressable regime, balancing reusability of building blocks with high yield.

Contribution

It develops a novel algorithm for enumerating possible structures from semi-addressable building blocks, facilitating robust inverse design in this scalable regime.

Findings

Semi-addressable designs can outperform fully-addressable ones in yield.

Reusing building blocks can increase the entropic gain and target yield.

The algorithm enables scalable and robust inverse design in self-assembly systems.

Abstract

Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of this inverse problem start with the so-called fully-addressable limit, where every particle in a target structure is different. This leads to clear design principles that often result in high assembly yield, but it is not a scaleable approach -- at some point, one must grapple with "reusing" building blocks, which lowers the degree of addressability and may cause a multitude of off-target structures to form, complicating the design process. Here, we solve a key obstacle preventing robust inverse design in the "semi-addressable regime" by developing a highly efficient algorithm that enumerates all structures that can be formed from a given set of building blocks. By combining this with established partition-function-based yield calculations, we show that it is almost always possible to find economical semi-addressable designs where the entropic gain from reusing building blocks outweighs the presence of off-target structures and even increases the yield of the target. Thus, not only does our enumeration algorithm enable robust and scalable inverse design in the semi-addressable regime, our results demonstrate that it is possible to operate in this regime while maintaining the level of control often associated with full addressability.