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The emergence of valency in colloidal crystals through electron equivalents


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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Fig. 1: Assemblies of PAE–EE colloidal crystals and simulation models.
Fig. 2: Formation of nine distinct PAE–EE assemblies controlled by DNA-based interactions.
Fig. 3: MD simulations of the structural configurations and dynamics in equilibrium phases.
Fig. 4: Local structural analysis based on STEM and MD simulations.
Fig. 5: Colloidal gyroid crystal structure.
Fig. 6: Enantiotropic crystal–crystal phase transitions induced by the redistribution of EEs.

Data availability

All other data generated or analysed during this study are included in the Supplementary Information. Further data are available from the corresponding authors upon request. Source data are provided with this paper

Code availability

The source code for HOOMD-blue is available at The source code for the SAXS simulation is available at The lattice segmentation and analysis codes for the electron microscopy images are available at


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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.

Author information

Authors and Affiliations



C.A.M. and S.C.G. directed the research. S.W. performed the synthesis and X-ray scattering experiments. S.L. performed the MD simulations. J.S.D. and S.W. performed the electron microscopy studies. S.W. and B.L. performed the SAXS simulations. All authors contributed to the data analysis and manuscript preparation.

Corresponding authors

Correspondence to Byeongdu Lee, Sharon C. Glotzer or Chad A. Mirkin.

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Competing interests

The authors declare no competing interests.

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Nature Materials thanks Hao Yan and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Experimental Details, Computational Details, captions for Supplementary Videos 1–6, Tables 1–6 and Figs. 1–49.

Reporting Summary

Supplementary Video 1

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.

Supplementary Video 2

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.

Supplementary Video 3

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.

Supplementary Video 4

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.

Supplementary Video 5

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.

Supplementary Video 6

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).

Source data

Source Data Fig. 2

Experimental and simulated SAXS results, correlation with the structural parameters from the experiments.

Source Data Fig. 3

Structural and kinetic parameters from the molecular dynamics and experiments.

Source Data Fig. 6

Temperature-dependent SAXS results.

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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).

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