Abstract
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.
Highlights
Quasicrystals are characterized by long-range order in the absence of translational periodicity, and often exhibit symmetries not feasible in periodic crystals
The initial examples were found in metallic alloy systems with the most common symmetries being icosahedral[1] and decagonal,[2] but with metastable octagonal[3] and dodecagonal[4] quasicrystals being observed
Full details of each patchy particle model that we study are tabulated in the Supporting Information
Summary
Quasicrystals are characterized by long-range order (exemplified by sharp Bragg peaks in their diffraction patterns) in the absence of translational periodicity, and often exhibit symmetries not feasible in periodic crystals. The 5- and 6-coordinate environments in the dodecagon are both feasible when the particles’ patches are sufficiently wide To realize such a quasicrystal, for particles with instead a fixed maximum number of interaction partners, requires a mixture of 5- and 6-patch particles,[26] this being achieved experimentally in systems of multiarm DNA tiles on a surface.[32]. We extend this approach to obtain 3D dodecagonal quasicrystals, exploring the additional complexities that the added dimension brings. It is noteworthy that many of the dodecagonal quasicrystals previously observed in simulations have been for 2D12–14,25,26 or quasi2D17,33 systems In this pair potential, the interaction is described by a Lennard-Jones repulsive core and an attractive tail modulated by angular and torsional dependent functions: II.
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