Design of Patchy Rhombi: From Close-Packed Tilings to OpenLattices

In the realm of functional materials, the production of two-dimensional structures with tunable porosity is ofparamount relevance for many practical applications: surfaces with regular arrays of pores can be used for selective adsorption orimmobilization of guest units that are complementary in shape and/or size to the pores, thus achieving, for instance, selectivefiltering or well-defined responses to external stimuli. The principles that govern the formation of such structures are valid atboth the molecular and the colloidal scale. Here we provide simple design directions to combine the anisotropic shape of thebuilding units-either molecules or colloids-and selective directional bonding. Using extensive computer simulations, weshow that regular rhombic platelets decorated with attractive and repulsive interaction sites form specific tilings, going smoothlyfrom close-packed arrangements to open lattices. The rationale behind the rich tiling scenario observed can be described interms of steric incompatibilities, unsatisfied bonding geometries, and interplays between local and long-range order.