Fast Generation of Potentials for Self-Assembly of Particles

TL;DR

This paper introduces a fast, heuristic geometric and trend optimization approach to design isotropic and anisotropic particle interaction potentials that reliably self-assemble into specific lattices like honeycomb and kagome.

Contribution

It presents a novel, computation-free geometric method and a robust trend optimization technique for designing potentials that produce desired self-assembled structures.

Findings

Successful formation of honeycomb lattices using the proposed methods.

Robust creation of kagome lattices with anisotropic potentials.

Trend optimization effectively handles noisy, expensive objective functions.

Abstract

We address the inverse problem of designing isotropic pairwise particle interaction potentials that lead to the formation of a desired lattice when a system of particles is cooled. The design problem is motivated by the desire to produce materials with pre-specified structure and properties. We present a heuristic computation-free geometric method, as well as a fast and robust trend optimization method that lead to the formation of high quality honeycomb lattices. The trend optimization method is particularly successful since it is well-suited to efficient optimization of the noisy and expensive objective functions encountered in the self-assembly design problem. We also present anisotropic potentials that robustly lead to the formation of the kagome lattice, a lattice that has not previously been obtained with isotropic potentials.