  Self-assembled monolayers of microparticles encoding Archimedean and
non-regular tessellations promise unprecedented structure-property
relationships for a wide spectrum of applications in fields ranging from
optoelectronics to surface technology. Yet, despite numerous computational
studies predicting the emergence of exotic structures from simple interparticle
interactions, the experimental realization of non-hexagonal patterns remains
challenging. Not only kinetic limitations often hinder structural relaxation,
but also programming the inteparticle interactions during assembly, and hence
the target structure, remains an elusive task. Here, we demonstrate how a
single type of soft polymeric microparticle (microgels) can be assembled into a
wide array of complex structures as a result of simple pairwise interactions.
We first let microgels self-assemble at a water-oil interface into a
hexagonally packed monolayer, which we then compress to varying degrees and
deposit onto a solid substrate. By repeating this process twice, we find that
the resultant structure is not the mere stacking of two hexagonal patterns. The
first monolayer retains its hexagonal structure and acts as a template into
which the particles of the second monolayer rearrange to occupy interstitial
positions. The frustration between the two lattices generates new symmetries.
By simply varying the packing fraction of the two monolayers, we obtain not
only low-coordination structures such as rectangular and honeycomb lattices,
but also rhomboidal, hexagonal, and herringbone superlattices which display
non-regular tessellations. Molecular dynamics simulations show that these
structures are thermodynamically stable and develop from short-ranged repulsive
interactions, making them easy to predict, and thus opening new avenues to the
rational design of complex patterns.
