Design of patchy rhombi: from close-packed tilings to open lattices

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