Programming patchy particles to form three-dimensional dodecagonal quasicrystals.

Model patchy particles have been shown to be able to form a wide variety of structures, including symmetric clusters, complex crystals, and even two-dimensional quasicrystals. Here, we investigate whether we can design patchy particles that form three-dimensional quasicrystals, in particular targeting a quasicrystal with dodecagonal symmetry that is made up of stacks of two-dimensional quasicrystalline layers. We obtain two designs that are able to form such a dodecagonal quasicrystal in annealing simulations. The first is a one-component system of seven-patch particles but with wide patches that allow them to adopt both seven- and eight-coordinated environments. The second is a ternary system that contains a mixture of seven- and eight-patch particles and is likely to be more realizable in experiments, for example, using DNA origami. One interesting feature of the first system is that the resulting quasicrystals very often contain a screw dislocation.

Programming patchy particles to form complex periodic structures.

We introduce a scheme to design patchy particles so that a given target crystal is the global free-energy minimum at sufficiently low temperature. A key feature is a torsional component to the potential that only allows binding when particles have the correct relative orientations. In all examples studied, the target crystal structures readily assembled on annealing from a low-density fluid phase, albeit with the simpler target structures assembling more rapidly. The most complex example was a clathrate with 46 particles in its primitive unit cell. We also explored whether the structural information encoded in the particle interactions could be further reduced. For example, removing the torsional restrictions led to the assembly of an alternative crystal structure for the BC8-forming design, but the more complex clathrate design was still able to assemble because of the greater remaining specificity.