Responsive materials1,2,3 have been used to generate structures with built-in complex geometries4,5,6, linear actuators7,8,9 and microswimmers10,11,12. These results suggest that complex, fully functional machines composed solely from shape-changing materials might be possible13. Nonetheless, to accomplish rotary motion in these materials still relies on the classical wheel and axle motifs. Here we explore geometric zero-energy modes to elicit rotary motion in elastic materials in the absence of a rigid wheel travelling around an axle. We show that prestrained polymer fibres closed into rings exhibit self-actuation and continuous motion when placed between two heat baths due to elastic deformations that arise from rotational-symmetry breaking around the rod's axis. Our findings illustrate a simple but robust model to create active motion in mechanically prestrained objects.
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de Gennes, P. G. Reflexions sur un type de polymères nematiques. C.R. Acad. Sci. Paris B 281, 101–103 (1975).
Küpfer, J. & Finkelmann, H. Nematic liquid single crystal elastomers. Macromol. Chem. Rapid Commun. 12, 717–726 (1991).
Tanaka, T., Nishio, I., Sun, S.-T. & Ueno-Nishio, S. Collapse of gels in electric field. Science 218, 467–469 (1982).
Klein, Y., Efrati, E. & Sharon, E. Shaping of elastic sheets by prescription of non-Euclidean metrics. Science 315, 1116–1120 (2007).
Kim, J., Hanna, J. A., Byun, M., Santangelo, C. D. & Hayward, R. C. Designing responsive buckled surfaces by halftone gel lithography. Science 335, 1201–1205 (2012).
Pezzulla, M., Shillig, S. A., Nardinocchi, P. & Holmes, D. P. Morphing of geometric composites via residual swelling. Soft Matter 11, 5812–5820 (2015).
Pelrine, R., Kornbluh, R., Pei, Q. & Joseph, J. High-speed electrically actuated elastomers with strain greater than 100%. Science 287, 836–839 (2000).
Haines, C. S. et al. Artificial muscles from fishing line and sewing thread. Science 343, 868–872 (2014).
Mirfakhrai, T., Madden, J. D. W. & Baughman, R. H. Polymer artificial muscles. Mater. Today 10, 30–38 (2007).
Dreyfus, R. et al. Microscopic artificial swimmers. Nature 437, 862–865 (2005).
Camacho-Lopez, M., Finkelmann, H., Palffy-Muhoray, P. & Shelley, M. Fast liquid–crystal elastomer swims into the dark. Nat. Mater. 3, 307–310 (2004).
Mourran, A., Zhang, H., Vinokur, R. & Möller, M. Soft microrobots employing nonequilibrium actuation via plasmonic heating. Adv. Mater. 29, 1604825 (2016).
Palagi et al. Structured light enables biomimetic swimming and versatile locomotion of photoresponsive soft microrobots. Nat. Mater. 15, 647–653 (2016).
Yamada, M. et al. Photomobile polymer materials: towards light-driven plastic motors. Angew. Chem. Int. Ed. 47, 4986–4988 (2008).
Ikegami, T., Kageyama, Y., Obara, K. & Takeda, S. Dissipative and autonomous square-wave self-oscillation of a macroscopic hybrid self-assembly under continuous light irradiation. Angew. Chem. Int. Ed. 55, 8239–8243(2016).
White, T. J. et al. A high frequency photodriven polymer oscillator. Soft Matter 4, 1796-8 (2008).
Zhang, X. et al. Photoactuators and motors based on carbon nanotubes with selective chirality distributions. Nat. Commun. 5, 2983 (2014).
Ionov, L. Hydrogel-based actuators: possibilities and limitations. Mater. Today 17, 494–503 (2014).
Ma, M., Guo, L., Anderson, D. G. & Langer, R. Bio-inspired polymer composite actuator and generator driven by water gradients. Science 339, 186–189 (2013).
Martin, P. C., Parodi, O. & Pershan, P. S. Unified hydrodynamic theory for crystals, liquid crystals, and normal fluids. Phys. Rev. A 6, 2401–2420 (1972).
Chaikin, P. & Lubensky, T. Principles of Condensed Matter Physics (Cambridge Univ. Press, Cambridge, 1995).
Kulić, I. M., Thaokar, R. & Schiessel, H. Twirling DNA rings, swimming nanomotors ready for a kickstart. Europhys. Lett. 72, 527–533 (2005).
Bhattacharya, K. & James, R. D. The material is the machine. Science 307, 53–54 (2005).
Audoly, B, . & Pomeau, Y. Elasticity and Geometry (Oxford Univ. Press, Oxford, 2010).
Müller, M. M., Ben Amar, M. & Guven, J. Conical defects in growing sheets. Phys. Rev. Lett. 101, 156104 (2008).
Starostin, E. L. & van der Heijden, G. H. M. The shape of a Möbius strip. Nat. Mater. 6, 563–567 (2007).
Marko, J. F. The internal ‘slithering’ dynamics of supercoiled DNA. Phys. A 244, 263–277 (1997).
Satir, P. Studies on Cilia. J. Cell Biol. 39, 77–94 (1968).
Bormashenko, E. et al. Self-propulsion of liquid marbles: Leidenfrost-like levitation driven by Marangoni flow. J. Phys. Chem. C 119, 9910–9915 (2015).
Linke, H. et al. Self-propelled Leidenfrost droplets. Phys. Rev. Lett. 96, 154502 (2006).
The authors acknowledge the Micro Nano Mechanics at ICS for providing the DMTA facility and thank A. Dutta for useful comments. This work was supported in part by the ANR grant Integrations.
The authors declare that they have no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Video Legends 1–7, Supplementary Methods, Supplementary Figures 1–13 and Supplementary References
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Baumann, A., Sánchez-Ferrer, A., Jacomine, L. et al. Motorizing fibres with geometric zero-energy modes. Nature Mater 17, 523–527 (2018). https://doi.org/10.1038/s41563-018-0062-0
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