Free-Energy Functional Method for Inverse Problem of Self Assembly

TL;DR

This paper introduces a variational free-energy functional method to solve the inverse self-assembly problem, successfully predicting interparticle interactions that lead to desired 2D crystal structures.

Contribution

It presents a novel theoretical approach based on a free energy functional to reconstruct interparticle potentials from target structures.

Findings

Successfully predicted potentials for square, honeycomb, and kagome lattices.

Monte Carlo simulations confirmed formation of target lattices from predicted interactions.

The method effectively solves the inverse self-assembly problem for 2D crystals.

Abstract

A new theoretical approach is described for the inverse self-assembly problem, i.e., the reconstruction of the interparticle interaction from a given structure. This theory is based on the variational principle for the functional that is constructed from a free energy functional in combination with Percus's approach [J. Percus, Phys. Rev. Lett. vol.8, 462 (1962)]. In this theory, the interparticle interaction potential for the given structure is obtained as the function that maximizes the functional. As test cases, the interparticle potentials for two-dimensional crystals, such as square, honeycomb, and kagome lattices, are predicted by this theory. The formation of each target lattice from an initial random particle configuration in Monte Carlo simulations with the predicted interparticle interaction indicates that the theory is successfully applied to the test cases.