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Colloidal quasicrystals engineered with DNA


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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Fig. 1: Structure models of dodecagonal quasicrystals (DDQCs) and triclinic crystals of decahedral NPs.
Fig. 2: Experimental and simulated structures assembled from decahedral NPs.
Fig. 3: Global order analysis of DDQCs.
Fig. 4: Local order analysis of DDQCs.

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


  1. Mirkin, C. A., Letsinger, R. L., Mucic, R. C. & Storhoff, J. J. A DNA-based method for rationally assembling nanoparticles into macroscopic materials. Nature 382, 607–609 (1996).

    Article  CAS  Google Scholar 

  2. Jones, M. R., Seeman, N. C. & Mirkin, C. A. Programmable materials and the nature of the DNA bond. Science 347, 1260901 (2015).

    Article  Google Scholar 

  3. Winfree, E., Liu, F., Wenzler, L. A. & Seeman, N. C. Design and self-assembly of two-dimensional DNA crystals. Nature 394, 539–544 (1998).

    Article  CAS  Google Scholar 

  4. Laramy, C. R., O’Brien, M. N. & Mirkin, C. A. Crystal engineering with DNA. Nat. Rev. Mater. 4, 201–224 (2019).

    Article  CAS  Google Scholar 

  5. Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951 (1984).

    Article  CAS  Google Scholar 

  6. Glotzer, S. Quasicrystals: the thrill of the chase. Nature 565, 156–159 (2019).

    Article  CAS  Google Scholar 

  7. Steinhardt, P. The Second Kind of Impossible: The Extraordinary Quest for a New Form of Matter (Simon & Schuster, 2019).

  8. Wang, N., Chen, H. & Kuo, K. Two-dimensional quasicrystal with eightfold rotational symmetry. Phys. Rev. Lett. 59, 1010 (1987).

    Article  CAS  Google Scholar 

  9. Chen, H., Li, D. & Kuo, K. New type of two-dimensional quasicrystal with twelvefold rotational symmetry. Phys. Rev. Lett. 60, 1645 (1988).

    Article  CAS  Google Scholar 

  10. Li, X. & Kuo, K. Decagonal quasicrystals with different periodicities along the tenfold axis in rapidly solidified Al–Ni alloys. Philos. Mag. Lett. 58, 167–171 (1988).

    Article  CAS  Google Scholar 

  11. Talapin, D. V. et al. Quasicrystalline order in self-assembled binary nanoparticle superlattices. Nature 461, 964–967 (2009).

    Article  CAS  Google Scholar 

  12. Nagaoka, Y., Zhu, H., Eggert, D. & Chen, O. Single-component quasicrystalline nanocrystal superlattices through flexible polygon tiling rule. Science 362, 1396–1400 (2018).

    Article  CAS  Google Scholar 

  13. Haji-Akbari, A. et al. Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra. Nature 462, 773–777 (2009).

    Article  CAS  Google Scholar 

  14. Haji-Akbari, A., Engel, M. & Glotzer, S. C. Degenerate quasicrystal of hard triangular bipyramids. Phys. Rev. Lett. 107, 215702 (2011).

    Article  Google Scholar 

  15. Je, K., Lee, S., Teich, E. G., Engel, M. & Glotzer, S. C. Entropic formation of a thermodynamically stable colloidal quasicrystal with negligible phason strain. Proc. Natl Acad. Sci. USA 118, e2011799118 (2021).

    Article  CAS  Google Scholar 

  16. Damasceno, P. F., Engel, M. & Glotzer, S. C. Predictive self-assembly of polyhedra into complex structures. Science 337, 453–457 (2012).

    Article  CAS  Google Scholar 

  17. Cersonsky, R. K., van Anders, G., Dodd, P. M. & Glotzer, S. C. Relevance of packing to colloidal self-assembly. Proc. Natl Acad. Sci. USA 115, 1439–1444 (2018).

    Article  CAS  Google Scholar 

  18. Sánchez-Iglesias, A. et al. High-yield seeded growth of monodisperse pentatwinned gold nanoparticles through thermally induced seed twinning. J. Am. Chem. Soc. 139, 107–110 (2017).

    Article  Google Scholar 

  19. Auyeung, E. et al. DNA-mediated nanoparticle crystallization into Wulff polyhedra. Nature 505, 73–77 (2014).

    Article  Google Scholar 

  20. Auyeung, E., Macfarlane, R. J., Choi, C. H. J., Cutler, J. I. & Mirkin, C. A. Transitioning DNA‐engineered nanoparticle superlattices from solution to the solid state. Adv. Mater. 24, 5181–5186 (2012).

    Article  CAS  Google Scholar 

  21. Lin, H. et al. Clathrate colloidal crystals. Science 355, 931–935 (2017).

    Article  CAS  Google Scholar 

  22. Oxborrow, M. & Henley, C. L. Random square–triangle tilings: a model for twelvefold-symmetric quasicrystals. Phys. Rev. B 48, 6966 (1993).

    Article  CAS  Google Scholar 

  23. Nugent, P. J. et al. Step-terrace morphology and reactivity to C60 of the five-fold icosahedral Ag–In–Yb quasicrystal. Philos. Mag. 91, 2862–2869 (2011).

    Article  CAS  Google Scholar 

  24. Heilbronner, R. P. The autocorrelation function: an image processing tool for fabric analysis. Tectonophysics 212, 351–370 (1992).

    Article  Google Scholar 

  25. Gähler, F. in Quasicrystalline Materials: Proceedings of the ILL/CODEST Workshop (eds Janot, C. & Dubois, J.) 272–284 (World Scientific, 1988).

  26. Ishimasa, T., Nissen, H.-U. & Fukano, Y. New ordered state between crystalline and amorphous in Ni–Cr particles. Phys. Rev. Lett. 55, 511 (1985).

    Article  CAS  Google Scholar 

  27. Ishimasa, T., Iwami, S., Sakaguchi, N., Oota, R. & Mihalkovič, M. Phason space analysis and structure modelling of 100 Å-scale dodecagonal quasicrystal in Mn-based alloy. Philos. Mag. 95, 3745–3767 (2015).

    Article  CAS  Google Scholar 

  28. Stampfli, P. A dodecagonal quasi-periodic lattice in 2 dimensions. Helv. Chim. Acta 59, 1260–1263 (1986).

    Google Scholar 

  29. Ritsch, S., Nissen, H.-U. & Beeli, C. Phason related stacking disorder in decagonal Al–Co–Ni. Phys. Rev. Lett. 76, 2507 (1996).

    Article  CAS  Google Scholar 

  30. Shin, M. & Strandburg, K. J. Random tiling approach to the structure of decagonal quasicrystals. J. Non Cryst. Solids 153, 253–257 (1993).

    Article  Google Scholar 

  31. Jeong, H.-C. & Steinhardt, P. J. Finite-temperature elasticity phase transition in decagonal quasicrystals. Phys. Rev. B 48, 9394 (1993).

    Article  CAS  Google Scholar 

  32. Edagawa, K., Suzuki, K. & Takeuchi, S. HRTEM observation of phason flips in Al–Cu–Co decagonal quasicrystal. J. Alloy. Compd. 342, 271–277 (2002).

    Article  CAS  Google Scholar 

  33. Jones, M. R. et al. DNA–nanoparticle superlattices formed from anisotropic building blocks. Nat. Mater. 9, 913–917 (2010).

    Article  CAS  Google Scholar 

  34. Anderson, J. A., Irrgang, M. E. & Glotzer, S. C. Scalable Metropolis Monte Carlo for simulation of hard shapes. Comput. Phys. Commun. 204, 21–30 (2016).

    Article  CAS  Google Scholar 

  35. Anderson, J. A., Glaser, J. & Glotzer, S. C. HOOMD-blue: a Python package for high-performance molecular dynamics and hard particle Monte Carlo simulations. Comput. Mater. Sci. 173, 109363 (2020).

    Article  CAS  Google Scholar 

  36. Glaser, J. et al. Strong scaling of general-purpose molecular dynamics simulations on GPUs. Comput. Phys. Commun. 192, 97–107 (2015).

    Article  CAS  Google Scholar 

  37. Towns, J. et al. XSEDE: accelerating scientific discovery. Comput. Sci. Eng. 16, 62–74 (2014).

    Article  Google Scholar 

  38. Haji-Akbari, A., Engel, M. & Glotzer, S. C. Phase diagram of hard tetrahedra. J. Chem. Phy. 135, 194101 (2011).

    Article  Google Scholar 

  39. Frenkel, D. & Ladd, A. J. New Monte Carlo method to compute the free energy of arbitrary solids. Application to the fcc and hcp phases of hard spheres. J. Chem. Phy. 81, 3188–3193 (1984).

    Article  CAS  Google Scholar 

  40. Chandler, D., Weeks, J. D. & Andersen, H. C. Van der Waals picture of liquids, solids, and phase transformations. Science 220, 787–794 (1983).

    Article  CAS  Google Scholar 

  41. Spellings, M., Marson, R. L., Anderson, J. A. & Glotzer, S. C. GPU accelerated discrete element method (DEM) molecular dynamics for conservative, faceted particle simulations. J. Comput. Phys. 334, 460–467 (2017).

    Article  Google Scholar 

  42. van Damme, R., Coli, G. M., van Roij, R. & Dijkstra, M. Classifying crystals of rounded tetrahedra and determining their order parameters using dimensionality reduction. ACS Nano 14, 15144–15153 (2020).

    Article  Google Scholar 

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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.

Author information

Authors and Affiliations



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.

Corresponding authors

Correspondence to Luis M. Liz-Marzán, Sharon C. Glotzer or Chad A. Mirkin.

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The authors declare no competing interests.

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Peer review information

Nature Materials thanks Chengde Mao, Walter Steurer and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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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.

Supplementary information

Supplementary Information

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. (2023).

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