Abstract
In principle, designing and synthesizing almost any class of colloidal crystal is possible. Nonetheless, the deliberate and rational formation of colloidal quasicrystals has been difficult to achieve. Here we describe the assembly of colloidal quasicrystals by exploiting the geometry of nanoscale decahedra and the programmable bonding characteristics of DNA immobilized on their facets. This process is enthalpy-driven, works over a range of particle sizes and DNA lengths, and is made possible by the energetic preference of the system to maximize DNA duplex formation and favour facet alignment, generating local five- and six-coordinated motifs. This class of axial structures is defined by a square–triangle tiling with rhombus defects and successive on-average quasiperiodic layers exhibiting stacking disorder which provides the entropy necessary for thermodynamic stability. Taken together, these results establish an engineering milestone in the deliberate design of programmable matter.
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Data availability
All the data supporting the findings of this study are included in the Article and its Supplementary Information files, and are available from the corresponding author on reasonable request.
Code availability
Source code for HOOMD-blue is available at https://github.com/glotzerlab/hoomd-blue.
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Acknowledgements
This material is based upon work supported by the Air Force Office of Scientific Research under awards FA9550-17-1-0348 and FA9550-22-1-0300 (nanoparticle synthesis and assembly); the Center for Bio-Inspired Energy Science, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences under award DE-SC0000989 (oligonucleotide synthesis); and the Sherman Fairchild Foundation, Inc. (EM characterization). Z.H. acknowledges support by the NU Graduate School Cluster in Biotechnology, Systems, and Synthetic Biology, which is affiliated with the Biotechnology Training Program funded by NIGMS grant T32 GM008449. This work made use of the EPIC facility of the NUANCE Center at NU, which has received support from the Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF DMR-1720139 and NNCI-1542205); the International Institute for Nanotechnology (IIN); the Keck Foundation; and the State of Illinois, through the IIN. The simulation work is supported as part of the Center for Bio-Inspired Energy Science, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences under award number DE-SC0000989. This work uses the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562; XSEDE award DMR 140129. This research was supported in part through computational resources and services supported by Advanced Research Computing at the University of Michigan, Ann Arbor. L.M.L.-M. acknowledges funding from the Spanish Ministry of Science and Innovation (grant number PID2020-117779R) and the Maria de Maeztu Units of Excellence Program from the Spanish State Research Agency (grant number MDM-2017-0720). This research used resources of the Advanced Photon Source, a US Department of Energy (DOE) Office of Science user facility at Argonne National Laboratory and is based on research supported by the US DOE Office of Science-Basic Energy Sciences, under contract number DE-AC02-06CH11357.
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W.Z., Y. Li, A.S.-I. and M.G. synthesized the nanoparticles. W.Z., H.L. and Y. Li performed the colloidal crystallization and material characterization. Y. Lim and S.L. designed and performed the simulations. B.L. contributed SAXS data interpretation and simulation. S.C.G., L.M.L.-M. and C.A.M. supervised the project. All authors analysed the data, interpreted the data and contributed to the writing of the manuscript.
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Extended data
Extended Data Fig. 1 Stacking behaviour of S1 and S2 tiles of DDQC.
(a) Top and side views of a column of S1 tiles. Connecting the centres of only red particles gives triangle tiles and connecting the centres of only green particles gives square tiles of the smallest length scale (S1). (b) Top and side views of a column of inflated (S2) square tiles. Connecting the centres of blue particles give S2 square tiles. Connecting the centres of both blue and yellow particles give S1 square and triangle tiles decomposing the S2 square tiles. The S2 square tile is uniform along the column. The decomposition is not unique and can be alternating along the column as shown in the image. (c) Top and side views of a column of inflated (S2) triangle tiles. The S1 tiles decomposing the S2 triangle tiles show different configurations along the column.
Extended Data Fig. 2 FFT analysis of a simulated DNA-functionalized decahedron DDQC.
FFT results calculated from (a) a slab and (b) a whole sample. (c, d) Side view of the whole DDQC sample from different orientations. This sample is the same sample with Fig. 2g, and each sphere represents the centre of a decahedron. The FFT pattern in (a) was calculated from a slab in the purple-dashed box in (c). The FFT pattern in (b) was calculated from a whole sample, and it shows line-like features (red arrows) together with dominant peaks. It is attributed to the existence of a subdomain in the black-dashed box whose 12-fold symmetry is slightly rotated from the overall 12-fold symmetry.
Extended Data Fig. 3 Densest packing of hard rounded decahedra.
(a, b) SEM images of a triclinic crystalline structure formed by slow-drying decahedral NPs on a surface. (c) Comparison of the highest packing fraction (\(N\times {v}_{0}/{V}_{{\rm{Box}}}\), where v0 is the volume of a particle) for four simulated structures: Quasicrystal Approximant (QA) (Supplementary Fig. 14), Triclinic (Tri), Rhombohedral (Rh), and Hexagonal (Hex), with increasing rounding radius (lrr) of the hard decahedra. Solid markers are the packing fraction of the densest crystals obtained from the packing simulations of systems with N = 2 or 4. Open markers are the maximum packing fractions of each phase obtained by compressing the constructed crystal structures (Methods). (d–g) Structural illustration of rounded decahedra (\({l}_{{rr}}/{l}_{{edge}} \sim 0.18\)) packed into the four crystalline lattices.
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Supplementary Figs 1–26 and Tables 1–3.
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Zhou, W., Lim, Y., Lin, H. et al. Colloidal quasicrystals engineered with DNA. Nat. Mater. 23, 424–428 (2024). https://doi.org/10.1038/s41563-023-01706-x
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DOI: https://doi.org/10.1038/s41563-023-01706-x
