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Nanoscale phonon dynamics in self-assembled nanoparticle lattices

Nature Materials volume 24, pages 1616–1625 (2025)Cite this article

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Abstract

Geometry and topology endow mechanical frames with unusual properties from shape morphing to phonon wave manipulation, enabling emerging technologies. Despite important advances in macroscopic frames, the realization and phonon imaging of nanoscale mechanical metamaterials has remained challenging. Here we extend the principle of topologically engineered mechanical frames to self-assembled nanoparticle lattices, resolving phonon dynamics using liquid-phase transmission electron microscopy. The vibrations of nanoparticles in Maxwell lattices are used to measure properties that have been difficult to obtain, such as phonon band structures, nanoscale spring constants and nonlinear lattice deformation paths. Studies of five different lattices reveal that these properties are modulated by nanoscale colloidal interactions. Our discrete mechanical model and simulations capture these interactions and the critical role of effects beyond nearest neighbours, bridging mechanical metamaterials with nanoparticle self-assembly. Our study provides opportunities for understanding and manufacturing self-assembled nanostructures for phonon manipulation, offering solution processability, transformability and emergent functions at underexplored scales of length, frequency and energy density.

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Fig. 1: Self-assembled Maxwell lattice from gold nanocubes with structural degeneracy.
Fig. 2: Direct imaging of phonon dynamics and integrated theoretical framework to extract phonon band structures using PMN.
Fig. 3: Effect of inter-NP interactions and lattice types on phonon band structures and spring constants.
Fig. 4: PMN analysis of differently sized sublattices to show the fast convergence of phonon band structure and spring constant measurement at small systems.
Fig. 5: Collective deformation paths of Maxwell lattices upon thermal agitation.

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Data availability

The data that support the findings of this study are available via GitHub at https://github.com/chenlabUIUC/Phonon-mapping-nanoscopy.

Code availability

The codes for the PMN analysis and BD simulations developed in this study are available via GitHub at https://github.com/chenlabUIUC/Phonon-mapping-nanoscopy.

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Acknowledgements

Experiments and theoretical modelling for the equilibrium NP self-assemblies in this work were supported by the Office of Naval Research under award number MURI N00014-20-1-2479 (C.Q., E.S., J.L., X.M. and Q.C.). Validation analysis of non-equilibrium self-assemblies were supported by US National Science Foundation under Cooperative Agreement No. 2243104, “Center for Complex Particle Systems (COMPASS)” Science and Technology Center (P.P. and Q.C.). The BD simulation effort of this work integrated with experiment was supported by the Defense Established Program to Stimulate Competitive Research (DEPSCoR) grant no. FA9550-20-1-0072 (Z.M. and W.P.) and Army Research Office grant no. W911NF2310256 (Z.M., Q.C. and W.P.). We thank Nicholas A. Kotov and Roberto Merlin for helpful discussions.

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Author notes

  1. These authors contributed equally: Chang Qian, Ethan Stanifer.

Authors and Affiliations

  1. Department of Materials Science and Engineering, Grainger College of Engineering, University of Illinois, Urbana, IL, USA

    Chang Qian, Lehan Yao, Binbin Luo, Chang Liu, Jiahui Li, Puquan Pan & Qian Chen

  2. Department of Physics, University of Michigan, Ann Arbor, MI, USA

    Ethan Stanifer & Xiaoming Mao

  3. Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI, USA

    Zhan Ma & Wenxiao Pan

  4. Department of Chemistry, University of Illinois, Urbana, IL, USA

    Qian Chen

  5. Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, IL, USA

    Qian Chen

  6. Materials Research Laboratory, University of Illinois, Urbana, IL, USA

    Qian Chen

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Contributions

C.Q. and Q.C. designed the experiments. C.Q. and B.L. performed the experiments. C.Q., L.Y., C.L. and Q.C. carried out the CG modelling and single-particle tracking analysis. E.S. and X.M. developed the discrete mechanical model and theory. C.Q., J.L., P.P. and E.S. performed the PMN analysis. Z.M. and W.P. performed the BD simulations with ML-based inter-NP interaction modelling. C.Q. and Q.C. wrote the first draft of the paper. All authors contributed to the writing of the paper. Q.C., X.M. and W.P. supervised the work.

Corresponding authors

Correspondence to Wenxiao Pan, Xiaoming Mao or Qian Chen.

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Supplementary information

Supplementary Information

Supplementary Text, Notes 1–14, Tables 1–15, Figs. 1–31, captions for Supplementary Videos 1–5 and References.

Supplementary Video 1

Synchronized liquid-phase TEM video showing the self-assembly of a rhombic Maxwell lattice from colloidal gold nanocubes. Left, the liquid-phase TEM video with tracked centroid positions of individual cubes (yellow) overlaid. Right, the bond network constructed from the centroid positions. Rhombuses are coloured according to θtilt. The video was captured at I = 22 mM; playback is at 10 f.p.s., real time. Dose rate: 10.9 e− Å−2 s−1. Scale bars, 300 nm.

Supplementary Video 2

BD simulation of square-to-rhombic lattice relaxation. The simulation starts from an initial configuration of 81 cubes organized on a two-dimensional square lattice at I = 22 mM. Left: the mean θtilt (± s.d.) of the BD system (as shown on the right) plotted on the inter-NP interaction energy curve derived from CG interaction modelling to trace the relaxation dynamics from a metastable square lattice to the stable rhombic lattice. Right: BD simulation of the cube assembly. Cubes are represented by black squares. Rhombuses are coloured according to θtilt. After ~1,500 simulation steps, the system relaxes into a rhombic lattice of θ = 80°.

Supplementary Video 3

Workflow of PMN analysis. The liquid-phase TEM video was captured at I = 22 mM; playback is at 10 f.p.s., real time. Dose rate: 10.9 e− Å−2 s−1. Scale bars, 200 nm.

Supplementary Video 4

Liquid-phase TEM videos of the Maxwell lattice regions for the PMN analysis. Two selected liquid-phase TEM video regions of different ionic strengths used for the PMN analysis, overlaid with tracked centroid positions and trajectories of single NPs after drift correction (coloured according to the elapsed time). Dose rates: 10.9 e− Å−2 s−1 for I = 27 mM; 14.4 e− Å−2 s−1 for I = 110 mM. Scale bars, 100 nm.

Supplementary Video 5

Liquid-phase TEM video showing deformation paths of TB migration. Liquid-phase TEM video (left) overlaid with tracked centroid positions of particles (yellow), synchronized with the bond network and rhombuses coloured according to θtilt (right, same colour scale as in Fig. 5a). TBs are noted by the green lines to highlight the migration. The video is captured using a K2 direct electron detector camera in IS mode at 400 f.p.s.; playback is at 10 f.p.s., which is 0.05 × real time. Dose rate: 10.2 e− Å−2 s−1. I = 22 mM. Scale bars, 200 nm.

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Qian, C., Stanifer, E., Ma, Z. et al. Nanoscale phonon dynamics in self-assembled nanoparticle lattices. Nat. Mater. 24, 1616–1625 (2025). https://doi.org/10.1038/s41563-025-02253-3

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