Two-Step Self-Assembly Mechanisms and Crystal-Quasicrystal Transition Kinetics in DNA Dodecagonal Quasicrystals.

Quasicrystals are materials that exhibit long-range bond-orientational order without translational periodicity. Although various crystals and quasicrystals have been assembled from DNA nanomotifs, the self-assembly mechanisms of quasicrystals and the transition kinetics between crystals and quasicrystals remain poorly understood. Here, we introduce a coarse-grained patchy-particle-chain model for branched DNA nanomotifs to reveal the formation and transition kinetics of two-dimensional dodecagonal quasicrystals. The simulations capture the self-assembly of bridged 5- and 6-point-star DNA motifs into dodecagonal quasicrystals at appropriate stoichiometric ratios, consistent with experiments. The formation proceeds via a non-classical two-step self-assembly pathway, involving network-like intermediates, followed by nucleation and assimilation growth into ordered quasicrystals. By tuning DNA motif rigidity, the transition from hexagonal crystals to dodecagonal quasicrystals occurs through nucleation and growth at defect sites, whereas the reverse transition preferentially proceeds via destabilization of square-like arrangements, with both transitions driven by binding-energy differences. Rational design of 3- and 4-point-star DNA motifs further enables the assembly of decagonal quasicrystal approximants. These findings clarify the formation mechanisms of quasicrystals and crystal-quasicrystal transition kinetics, providing insights into symmetry breaking and structural reorganization in complex self-assembly systems.