Self-assembly of two-dimensional lattices driven by shape complementarity and attractive interactions

Abstract

Today, low-dimensional structures are finding an increasingly widespread use in various technological applications such as sensors, catalytic converters etc. Kagome lattice, along with other two-dimensional lattices generated from Archimedean tilings, are of particular interest because of their unique electronic, optical and magnetic properties. Here, based on two simple design principles: shape complementarity and minimization of frustration, we introduce a theoretical model that is able to self-assemble into all Archimedean lattices except one. Within this model each lattice site is represented by a single interacting particle with a specifically designed shape. The required shapes are triangles, squares, rhombi and other relatively simple geometrical figures. Each particle carries a single attractive patch designed to minimize the potential energy of the target structure. As the first step of the lattice assembly, the attractive interactions induce the formation of clusters that have space-filling shapes. At the second step, the clusters coalesce into a superlattice with the desired structure known as the cluster crystal. Monte Carlo simulations are carried out to prove that each target lattice is a) easy to assemble by the model and b) constitutes the minimum free energy conformation. Possible experimental realizations of the proposed model are discussed.