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Liquid-induced topological transformations of cellular microstructures


The fundamental topology of cellular structures—the location, number and connectivity of nodes and compartments—can profoundly affect their acoustic1,2,3,4, electrical5, chemical6,7, mechanical8,9,10 and optical11 properties, as well as heat1,12, fluid13,14 and particle transport15. Approaches that harness swelling16,17,18, electromagnetic actuation19,20 and mechanical instabilities21,22,23 in cellular materials have enabled a variety of interesting wall deformations and compartment shape alterations, but the resulting structures generally preserve the defining connectivity features of the initial topology. Achieving topological transformation presents a distinct challenge for existing strategies: it requires complex reorganization, repacking, and coordinated bending, stretching and folding, particularly around each node, where elastic resistance is highest owing to connectivity. Here we introduce a two-tiered dynamic strategy that achieves systematic reversible transformations of the fundamental topology of cellular microstructures, which can be applied to a wide range of materials and geometries. Our approach requires only exposing the structure to a selected liquid that is able to first infiltrate and plasticize the material at the molecular scale, and then, upon evaporation, form a network of localized capillary forces at the architectural scale that ‘zip’ the edges of the softened lattice into a new topological structure, which subsequently restiffens and remains kinetically trapped. Reversibility is induced by applying a mixture of liquids that act separately at the molecular and architectural scales (thus offering modular temporal control over the softening–evaporation–stiffening sequence) to restore the original topology or provide access to intermediate modes. Guided by a generalized theoretical model that connects cellular geometries, material stiffness and capillary forces, we demonstrate programmed reversible topological transformations of various lattice geometries and responsive materials that undergo fast global or localized deformations. We then harness dynamic topologies to develop active surfaces with information encryption, selective particle trapping and bubble release, as well as tunable mechanical, chemical and acoustic properties.

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Fig. 1: Strategy for topological transformation of cellular structures.
Fig. 2: Experimental characterization of the assembly and disassembly of a triangular lattice.
Fig. 3: Generalization of topological transformation principle.
Fig. 4: Exemplary applications of lattice structures undergoing topological transformations.

Data availability

The data supporting the findings of this study are included within the paper and its Supplementary Information files and are available from the corresponding author upon reasonable request.


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This work was supported by the National Science Foundation (NSF) through the Designing Materials to Revolutionize and Engineer our Future (DMREF) programme under award number DMR-1922321 and the Harvard University Materials Research Science and Engineering Center (MRSEC) under award number DMR-2011754 (theory and computational studies), and by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under award number DE-SC0005247 (experiment and characterization). Microfabrication and scanning electron microscopy were performed at the Center for Nanoscale Systems (CNS) at Harvard, a member of the National Nanotechnology Coordinated Infrastructure Network (NNCI), which is supported by the NSF under NSF ECCS award number 1541959. We thank D. Y. Kim for fruitful discussions.

Author information

Authors and Affiliations



S.L., B.D., K.B. and J.A. conceived and initiated the project. S.L., A.S.-Y., J.K., R.S.M. and C.T.Z. performed the experiments. B.D. performed the theoretical modelling and image analysis. J.L. and S.Y. performed the finite-element modelling and pattern designs. S.L., B.D. and A.G. analysed the experimental data. K.B. and J.A. supervised the project. All co-authors provided useful feedback and contributed to the manuscript.

Corresponding author

Correspondence to Joanna Aizenberg.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Robin Ras, Arnaud Saint-Jalmes, Scott Waitukaitis and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

This file contains Supplementary Materials and Methods, Theoretical Model, Supplemental Results including Supplementary Figures 1 to 17, and legends for Supplementary Videos 1 to 7.

Peer Review File

Supplementary Video 1

Inducible relaxation of an isolated LCP microplate and a hexagonal lattice after trapping in the deformed state.

Supplementary Video 2

Elasto-capillary assembly of a triangular lattice into a hexagonal lattice.

Supplementary Video 3

Robustness of the transformed topology.

Supplementary Video 4

Disassembly of the hexagonal lattice back to the initial triangular topology.

Supplementary Video 5

Hierarchical transformation of a diamond lattice by first transforming to a hexagonal topology via acetone and then inducing a phase transition of an oriented LCP.

Supplementary Video 6

Elasto-capillary assembly over a larger area without and with phase design.

Supplementary Video 7

Demonstration of properties and applications made possible by topological transformation of the cellular structures.

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Li, S., Deng, B., Grinthal, A. et al. Liquid-induced topological transformations of cellular microstructures. Nature 592, 386–391 (2021).

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