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In this work, a series of binary mixtures of patchy colloids with desired symmetries, including quadrangle, pentagon, hexagon, is studied by means of Metropolis Monte Carlo simulations. The patches on the colloid surface attract the droplets via the Pickering effect, while both the colloid-colloid and the droplet-droplet interactions are pure hard-core. We find a rich phase diagram by tuning the size ratio, particle packing fraction, angle parameter. The four-patch and six-patch colloids can easily assemble into the different crystal structures, while the five-patch colloids can form a local ordered state that is similar to a quasicrystal with a five-fold symmetry. In the self-assembled structures of six-patch colloids, both droplets and colloids form hexagonal orders, however, they arrange in themselves on different sublattices. Considering the four patches in a quadrilateral geometry, we show that the simulated systems undergoes a structural transition from a rectangle lattice to square lattice and then to rhombohedral lattice upon changing the characteristic angle. In addition, the absence of crystal structures in the trapezoidal patches suggests that the geometrical constraint in order to form the crystal states is that the patchy pattern needs to have the inversion center located at the diameter of the colloidal sphere.

Tunable crystal structures of binary mixtures of various patchy colloids and droplets