Designing colloidal ground state patterns using short-range isotropic interactions

TL;DR

This paper develops a lattice model for designing colloidal particles with specific ground state patterns using short-range isotropic interactions, providing a method to reliably achieve unique crystal structures.

Contribution

It introduces a theoretical framework and a design recipe for creating unique ground state patterns in colloids with pairwise specific interactions.

Findings

Lower bounds for interaction range depend on pattern complexity.

A design recipe guarantees unique ground states for many crystal structures.

Monte Carlo simulations confirm the theoretical predictions.

Abstract

DNA-coated colloids are a popular model system for self-assembly through tunable interactions. The DNA-encoded linkages between particles theoretically allow for very high specificity, but generally no directionality or long-range interactions. We introduce a two-dimensional lattice model for particles of many different types with short-range isotropic interactions that are pairwise specific. For this class of models, we address the fundamental question whether it is possible to reliably design the interactions so that the ground state is unique and corresponds to a given crystal structure. First, we determine lower limits for the interaction range between particles, depending on the complexity of the desired pattern and the underlying lattice. Then, we introduce a `recipe' for determining the pairwise interactions that exactly satisfies this minimum criterion, and we show that it is sufficient to uniquely determine the ground state for a large class of crystal structures. Finally, we verify these results using Monte Carlo simulations.