Optimized Interactions for Targeted Self-Assembly: Application to Honeycomb Lattice

TL;DR

This paper introduces an inverse statistical-mechanical method to design interaction potentials that enable spontaneous self-assembly of complex structures, including crystalline, amorphous, and quasicrystalline configurations, exemplified by the honeycomb lattice.

Contribution

It presents a novel computational approach to optimize isotropic pair potentials for targeted self-assembly of specific structures like the honeycomb lattice.

Findings

Successfully designed an isotropic potential for honeycomb lattice formation.

Demonstrated the method's ability to target amorphous and crystalline structures.

Potential applications in photonic materials with desired bandgap properties.

Abstract

We devise an inverse statistical-mechanical methodology to find optimized interaction potentials that lead spontaneously to a target many-particle configuration. Target structures can possess varying degrees of disorder, thus extending the traditional idea of self-assembly to incorporate both amorphous and crystalline structures as well as quasicrystals. For illustration purposes, our computational technique is applied to yield an optimized isotropic (non-directional) pair potential that spontaneously yields the three-coordinated honeycomb lattice as the ground state structure in two dimensions. This target choice is motivated by its three-dimensional analog, the diamond lattice, which is known to possess desirable photonic bandgap properties.