Colloidal crystal engineering of complex, low-symmetry architectures is challenging when isotropic building blocks are assembled. Here we describe an approach to generating such structures based upon programmable atom equivalents (nanoparticles functionalized with many DNA strands) and mobile electron equivalents (small particles functionalized with a low number of DNA strands complementary to the programmable atom equivalents). Under appropriate conditions, the spatial distribution of the electron equivalents breaks the symmetry of isotropic programmable atom equivalents, akin to the anisotropic distribution of valence electrons or coordination sites around a metal atom, leading to a set of well-defined coordination geometries and access to three new low-symmetry crystalline phases. All three phases represent the first examples of colloidal crystals, with two of them having elemental analogues (body-centred tetragonal and high-pressure gallium), while the third (triple double-gyroid structure) has no known natural equivalent. This approach enables the creation of complex, low-symmetry colloidal crystals that might find use in various technologies.
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The source code for HOOMD-blue is available at https://github.com/glotzerlab/hoomd-blue. The source code for the SAXS simulation is available at https://sites.google.com/site/byeongdu/software. The lattice segmentation and analysis codes for the electron microscopy images are available at https://github.com/JingshanDu/ImageLatticeAnalysis.
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We thank E. W. Roth (Northwestern University (NU)) for ultramicrotomy, S. Weigand (NU) for SAXS assistance and A. Das (NU) for helpful discussions. This work was supported primarily by 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 (award DE-SC0000989, for synthesis and molecular dynamics simulations, C.A.M. and S.C.G.) and also by the Air Force Office of Scientific Research (award FA9550-17-1-0348, for synthesis, spectroscopy and electron microscopy, C.A.M. and V.P.D.) and the Sherman Fairchild Foundation (for electron microscopy, C.A.M.). This work made use of the EPIC facility of Northwestern University’s NUANCE Center, which has received support from the SHyNE Resource (NSF ECCS-2025633), the IIN and Northwestern’s MRSEC programme (NSF DMR-1720139). This research also used the resources (Sector 5, the DuPont-Northwestern-Dow Collaborative Access Team ‘DND-CAT’, beamline 12-ID-B) of the Advanced Photon Source, which is a US Department of Energy Office of Science User Facility operated by Argonne National Laboratory (contract DE-AC02-06CH11357). Simulations were carried out using the resources at the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility (supported under contract DE-AC05-00OR22725). Computational resources and services were also provided by Advanced Research Computing at the University of Michigan.
The authors declare no competing interests.
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Supplementary Experimental Details, Computational Details, captions for Supplementary Videos 1–6, Tables 1–6 and Figs. 1–49.
Movement of a single EE (grey sphere) in the BCC metallic phase (transparent red spheres) with a periodic box condition (ϕPAE = 0.34) for 2 × 106 MD timesteps. All other simulation parameters are given in Supplementary Table 5.
Movement of a single EE (grey sphere) in the A15 tetrahedral phase (transparent purple spheres) with a periodic box condition (ϕPAE = 0.33) for 2 × 106 MD timesteps. All other simulation parameters are given in Supplementary Table 5.
Movement of a single EE (grey sphere) in the SC covalent phase (transparent orange spheres) with a periodic box condition (ϕPAE = 0.56) for 2 × 106 MD timesteps. All other simulation parameters are given in Supplementary Table 5.
Dynamics of EEs (light-grey and grey spheres) in the A15 tetrahedral phase (transparent purple spheres) with a periodic box condition (ϕPAE = 0.33) for 107 MD timesteps. All other simulation parameters are given in Supplementary Table 5. In the initial configuration, the EEs were coloured in both light-grey and grey based on their y-axis position. At the end of the simulation, the light-grey and grey EEs are well mixed, indicating the diffusive character of the EEs in the A15 phase.
Dynamics of EEs (light-grey and grey spheres) in the SC covalent phase (transparent orange spheres) with a periodic box condition (ϕPAE = 0.56) for 107 MD timesteps. All other simulation parameters are given in Supplementary Table 5. At the initial configuration, the EEs were coloured in both light-grey and grey based on their y-axis position. At the end of the simulation, the light-grey and grey EEs are not mixed, indicating the non-diffusive character of the EEs in the SC phase.
Phase transition from the initial BCC (red spheres) to the final FCC (blue spheres) in a periodic box condition (ϕPAE = 0.05 and ϕEE = 0.41) at a constant temperature \(T^ \ast /T_m^ \ast\) ≈ 0.67 for 5 × 107 MD timesteps. The solid cluster is fully surrounded by the gas-phase EEs (grey spheres). The crystal structures of the PAEs were identified by the bond order parameter (Q4; see Methods).
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Wang, S., Lee, S., Du, J.S. et al. The emergence of valency in colloidal crystals through electron equivalents. Nat. Mater. 21, 580–587 (2022). https://doi.org/10.1038/s41563-021-01170-5