SAT-assembly: A new approach for designing self-assembling systems

TL;DR

This paper introduces SAT-assembly, a novel framework that designs interaction rules for patchy particles to self-assemble into specific structures while avoiding competing metastable states, demonstrated with a cubic diamond structure.

Contribution

It presents a new inverse design method using SAT solving to create interaction rules for self-assembling systems with multiple components and controlled assembly pathways.

Findings

Successfully designed interactions for cubic diamond structure

Avoided formation of competing polymorphs like hexagonal structure

Validated the approach through numerical simulations

Abstract

We propose a general framework for solving inverse self-assembly problems, i.e. designing interactions between elementary units such that they assemble spontaneously into a predetermined structure. Our approach uses patchy particles as building blocks, where the different units bind at specific interaction sites (the patches), and we exploit the possibility of having mixtures with several components. The interaction rules between the patches is determined by transforming the combinatorial problem into a Boolean satisfiability problem (SAT) which searches for solutions where all bonds are formed in the target structure. Additional conditions, such as the non-satisfiability of competing structures (e.g. metastable states) can be imposed, allowing to effectively design the assembly path in order to avoid kinetic traps. We demonstrate this approach by designing and numerically simulating a cubic diamond structure from four particle species that assembles without competition from other polymorphs, including the hexagonal structure.