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Self-assembly of uniform polyhedral silver nanocrystals into densest packings and exotic superlattices


Understanding how polyhedra pack into extended arrangements is integral to the design and discovery of crystalline materials at all length scales1,2,3. Much progress has been made in enumerating and characterizing the packing of polyhedral shapes4,5,6, and the self-assembly of polyhedral nanocrystals into ordered superstructures7,8,9. However, directing the self-assembly of polyhedral nanocrystals into densest packings requires precise control of particle shape10, polydispersity11, interactions and driving forces 12. Here we show with experiment and computer simulation that a range of nanoscale Ag polyhedra can self-assemble into their conjectured densest packings6. When passivated with adsorbing polymer, the polyhedra behave as quasi-hard particles and assemble into millimetre-sized three-dimensional supercrystals by sedimentation. We also show, by inducing depletion attraction through excess polymer in solution, that octahedra form an exotic superstructure with complex helical motifs rather than the densest Minkowski lattice13. Such large-scale Ag supercrystals may facilitate the design of scalable three-dimensional plasmonic metamaterials for sensing14,15, nanophotonics16 and photocatalysis17.

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Figure 1: Self-assembly of dense polyhedron lattices.
Figure 2: Long-range order of assembled lattices.
Figure 3: Gravitational driving force and packings near surfaces.
Figure 4: Polymer-mediated nanocrystal interactions.
Figure 5: Ag octahedra assemble into a previously unknown lattice in the presence of excess PVP.


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This work was partially supported by the Defense Advanced Research Projects Agency. The shape-selective synthesis part of the work is supported by the Director, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, of the US Department of Energy under contract no DE-AC02-05CH11231. M.G. was supported by the Austrian Science Fund (FWF) under grant no J 3106-N16. M.G. and P.L.G. were supported by the National Science Foundation under grant no CHE-0910981. A.W-C. was supported by the US Department of Energy under contract no DE-AC02-05CH11231. Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract no DE-AC02-05CH11231. P.Y. thanks the National Science Foundation for the Waterman Award.

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J.H. and M.G. both contributed extensively to this work. J.H. initiated the study, conceived and conducted the experiments, analysed results and cowrote the paper. M.G. identified all crystal structures, conceived and implemented the simulations and theoretical models, analysed results and cowrote the paper. A.W-C. suggested simulations and experiments, analysed results, helped prepare figures and cowrote the paper. P.L.G. suggested simulations and experiments, analysed results and cowrote the paper. P.Y. initiated the study, suggested experiments, analysed results and cowrote the paper.

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Correspondence to Michael Grünwald or Peidong Yang.

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The authors declare no competing financial interests.

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Henzie, J., Grünwald, M., Widmer-Cooper, A. et al. Self-assembly of uniform polyhedral silver nanocrystals into densest packings and exotic superlattices. Nature Mater 11, 131–137 (2012).

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