Pivoting colloidal assemblies exhibit mechanical metamaterial behaviour

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Data availability The data that support the plots in this paper are available from Zenodo at https://doi.org/10.5281/zenodo.14886689 (ref. 45). Code availability The models supporting the findings of this study are described in the paper and its Supplementary Information. The code that supports the findings of this study is available from Zenodo at https://doi.org/10.5281/zenodo.14886689 (ref. 45). ReferencesHu, X. et al. Magnetic soft micromachines made of linked microactuator networks. Sci. Adv. 7, eabe8436 (2021).Article ADS CAS PubMed PubMed Central Google Scholar Smart, C. L. et al. Magnetically programmed diffractive robotics. Science 386, 1031–1037 (2024).Article ADS CAS PubMed Google Scholar Liu, Q. et al. Electronically configurable microscopic metasheet robots. Nat. Mater. 24, 109–115 (2024).Article ADS CAS PubMed Google Scholar McMullen, A., Muñoz Basagoiti, M., Zeravcic, Z. & Brujic, J. Self-assembly of emulsion droplets through programmable folding. 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Colloidal pivots enable Brownian mechanical metamaterials. Datasets. Zenodo https://doi.org/10.5281/zenodo.14886689 (2026).Download referencesAcknowledgementsWe gratefully acknowledge support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme through an ERC starting grant (D.J.K., no. 758383).Author informationAuthors and AffiliationsHuygens-Kamerlingh Onnes Laboratory, Leiden Institute of Physics, Leiden University, Leiden, The NetherlandsJulio Melio, Martin van Hecke & Daniela J. KraftAMOLF, Amsterdam, The NetherlandsMartin van HeckeLorentz Institute, Leiden Institute of Physics, Leiden University, Leiden, The NetherlandsSilke E. HenkesAuthorsJulio MelioMartin van HeckeSilke E. HenkesDaniela J. KraftContributionsJ.M., M.v.H. and D.J.K. designed the research and experiments. J.M. conducted the experiments. J.M. and S.E.H. performed simulations and theoretical modelling. All authors analysed the data, discussed the results and wrote the paper.Corresponding authorCorrespondence to Daniela J. Kraft.Ethics declarations Competing interests The authors declare no competing interests. Peer review Peer review information Nature thanks Yongxiang Gao, Christian Santangelo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available. Additional informationPublisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Extended data figures and tablesExtended Data Fig. 1 DNA functionalization scheme.a, Interaction matrix of particles functionalized with dsDNA strands A, A′, B and B′ as indicated. Particles have been functionalized with linkers AB (green), A′B (purple) and B′ (yellow) such that they can form bonds between their complementary strands, indicated by primes. b, This interaction matrix makes it possible to create mechanically stable triangular-shaped and diamond-shaped units in colloidal pivots using the depicted design.Extended Data Fig. 2 Design principles of rotating diamond structures.a, Schematics of rotating diamond lattices with particles of size rs and rb with angles θ1, θ2 and α indicated. b, Monodisperse particles (that is, for rs/rb = 1)