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

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.

A simple solution to the problem of self-assembling cubic diamond crystals

“…Since it is desirable to keep the number of distinct particle types as low as possible for ease of manufacturing and experimental preparation, we seek to find the minimum set of particle species that can assemble into a CD lattice without any defects or alternative assemblies. We formulate the design problem as a SAT problem [31,32], which is a collection of Boolean clauses (see Methods and Supp. Table S1) that encode the topology as given by the 16-particle unit cell for CD lattice (Supp.…”

“…The procedure has been described in detail in Refs. [31,32]. Briefly, we formulate the inverse design problem as a Boolean Satisfiability Problem.…”

“…Recently we have introduced a novel framework, named SAT-assembly [31,32], to design patchy particle systems that can assemble into any desired structure. Through a mapping to a Boolean satisfiability problem (SAT), the structure is encoded into the interaction map describing the bonds that can be formed between the different particles.…”

Encoding Hierarchical 3D Architecture through Inverse Design of Programmable Bonds

“…The power of colored assembly has been demonstrated for DNA structures, where arbitrarily designed 3D structures of ~100 nm were assembled from a large number of unique DNA bricks 26 , patterns of sub-micron 2D structures from DNA tiles 27 and patterned pegboards 28 , and quasi-crystals 29,30 . It has been recognized through computational efforts that colored interactions provide enormous capabilities for the design of complex organizations 10,13,31,32 . However, for creating material systems from functional nanocomponents, the main unresolved question is how to self-assemble a designed, hierarchically organized 3D architecture that can integrate multiple nanocomponent types as prescribed?…”

“…Much knowledge has been gained about the contribution of shapes, interactions, and entropic effects to self-assembly processes [5][6][7][8][9][10] . However, beyond understanding the effects of system parameters for achieving desired material functions, there is an increasing need to generate nanomaterials on demand, with specifically prescribed structure and composition using inverse design approaches 5,6,[11][12][13] . Addressing this challenge of nanoscale manufacturing can have a tremendous technological impact due the lack of scalable and broadly applicable methods for the fabrication of designed, three-dimensional (3D) nanomaterials.…”