Self-templating assembly of soft microparticles into complex tessellations

Encoding Archimedean and non-regular tessellations in self-assembled colloidal crystals promises unprecedented structure-dependent properties for applications ranging from low-friction coatings to optoelectronic metamaterials^1-7. Yet, despite numerous computational studies predicting exotic structures even from simple interparticle interactions^8-12, the realization of complex non-hexagonal crystals remains experimentally challenging^13-18. Here we show that two hexagonally packed monolayers of identical spherical soft microparticles adsorbed at a liquid-liquid interface can assemble into a vast array of two-dimensional micropatterns, provided that they are immobilized onto a solid substrate one after the other. The first monolayer retains its lowest-energy hexagonal structure and acts as a template onto which the particles of the second monolayer are forced to rearrange. The frustration between the two lattices elicits symmetries that would not otherwise emerge if all the particles were assembled in a single step. Simply by varying the packing fraction of the two monolayers, we obtain not only low-coordinated structures such as rectangular and honeycomb lattices, but also rhomboidal, hexagonal and herringbone superlattices encoding non-regular tessellations. This is achieved without directional bonding, and the structures formed are equilibrium structures: molecular dynamics simulations show that these structures are thermodynamically stable and develop from short-range repulsive interactions, making them easy to predict, and thus suggesting avenues towards the rational design of complex micropatterns.