Abstract
We use Monte Carlo simulations and free-energy techniques to show that binary solutions of penta- and hexavalent two-dimensional patchy particles can form thermodynamically stable quasicrystals even at very narrow patch widths, provided their patch interactions are chosen in an appropriate way. Such patchy particles can be thought of as a coarse-grained representation of DNA multi-arm ‘star’ motifs, which can be chosen to bond with one another very specifically by tuning the DNA sequences of the protruding arms. We explore several possible design strategies and conclude that DNA star tiles that are designed to interact with one another in a specific but not overly constrained way could potentially be used to construct soft quasicrystals in experiment. We verify that such star tiles can form stable dodecagonal motifs using oxDNA, a realistic coarse-grained model of DNA.
Highlights
Since their discovery was reported in 1984 [1], quasicrystals have been extensively studied, and many have unusual electronic [2] and surface [3] properties
For precisely the same reason, this choice of patch width leaves us in a region of parameter space where, for pentavalent particles we considered previously [30, 31], the quasicrystal was not thermodynamically stable, as the patches are so narrow that it is not possible for six neighbours to bond competitively: instead, the σ phase was stable for pentavalent particles under these conditions [31]
We note that in the quasicrystals we studied previously [30, 31], the most common structural feature was a series of edge-sharing dodecagonal motifs; one of the most common such motifs is shown in figure 2(a)
Summary
Since their discovery was reported in 1984 [1], quasicrystals have been extensively studied, and many have unusual electronic [2] and surface [3] properties. We have recently observed an example of such a dodecagonal soft quasicrystal when studying the self-assembly behaviour of a two-dimensional patchy-particle system [30]. A competition is set up between such a non-uniform pentavalent co-ordination and the hexagonal co-ordination characteristic of crystals of spherically symmetric particles. These hexa- and pentavalent environments form square–triangle tilings, which are known to be capable of forming dodecagonal quasicrystals [40, 41].
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