Formation of dodecagonal quasicrystals in two-dimensional systems of patchy particles

The behaviour of two-dimensional patchy particles with five and seven regularly arranged patches is investigated by computer simulation. For higher pressures and wider patch widths, hexagonal crystals have the lowest enthalpy, whereas at lower pressures and for narrower patches, lower density crystals with five nearest neighbours that are based on the (3(2),4,3,4) tiling of squares and triangles become lower in enthalpy. Interestingly, in regions of parameter space near to that where the hexagonal crystals become stable, quasicrystalline structures with dodecagonal symmetry form on cooling from high temperature. These quasicrystals can be considered as tilings of squares and triangles and are probably stabilized by the large configurational entropy associated with all the different possible such tilings. The potential for experimentally realizing such structures using DNA multi-arm motifs is also discussed.