Living cilia stir, sweep and steer via swirling strokes of complex bending and twisting, paired with distinct reverse arcs1,2. Efforts to mimic such dynamics synthetically rely on multimaterial designs but face limits to programming arbitrary motions or diverse behaviours in one structure3,4,5,6,7,8. Here we show how diverse, complex, non-reciprocal, stroke-like trajectories emerge in a single-material system through self-regulation. When a micropost composed of photoresponsive liquid crystal elastomer with mesogens aligned oblique to the structure axis is exposed to a static light source, dynamic dances evolve as light initiates a travelling order-to-disorder transition front, transiently turning the structure into a complex evolving bimorph that twists and bends via multilevel opto-chemo-mechanical feedback. As captured by our theoretical model, the travelling front continuously reorients the molecular, geometric and illumination axes relative to each other, yielding pathways composed from series of twisting, bending, photophobic and phototropic motions. Guided by the model, here we choreograph a wide range of trajectories by tailoring parameters, including illumination angle, light intensity, molecular anisotropy, microstructure geometry, temperature and irradiation intervals and duration. We further show how this opto-chemo-mechanical self-regulation serves as a foundation for creating self-organizing deformation patterns in closely spaced microstructure arrays via light-mediated interpost communication, as well as complex motions of jointed microstructures, with broad implications for autonomous multimodal actuators in areas such as soft robotics7,9,10, biomedical devices11,12 and energy transduction materials13, and for fundamental understanding of self-regulated systems14,15.
Your institute does not have access to this article
Subscribe to Nature+
Get immediate online access to the entire Nature family of 50+ journals
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
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 request.
All codes needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Information. Additional data related to this paper are available from the corresponding author upon request.
Sleigh, M. A. The Biology of Cilia and Flagella (Pergamon Press, 1962).
Gilpin, W., Bull, M. S. & Prakash, M. The multiscale physics of cilia and flagella. Nat. Rev. Phys. 2, 74–88 (2020).
Hu, W., Lum, G. Z., Mastrangeli, M. & Sitti, M. Small-scale soft-bodied robot with multimodal locomotion. Nature 554, 81–85 (2018).
Van Oosten, C. L., Bastiaansen, C. W. M. & Broer, D. J. Printed artificial cilia from liquid-crystal network actuators modularly driven by light. Nat. Mater. 8, 677–682 (2009).
Gu, H. et al. Magnetic cilia carpets with programmable metachronal waves. Nat. Commun. 11, 2637 (2020).
Rus, D. & Tolley, M. T. Design, fabrication and control of soft robots. Nature 521, 467–475 (2015).
Huang, H. W., Sakar, M. S., Petruska, A. J., Pané, S. & Nelson, B. J. Soft micromachines with programmable motility and morphology. Nat. Commun. 7, 12263 (2016).
Wu, Z. L. et al. Three-dimensional shape transformations of hydrogel sheets induced by small-scale modulation of internal stresses. Nat. Commun. 4, 1586 (2013).
Tottori, S. et al. Magnetic helical micromachines: fabrication, controlled swimming, and cargo transport. Adv. Mater. 24, 811–816 (2012).
Wehner, M. et al. An integrated design and fabrication strategy for entirely soft, autonomous robots. Nature 536, 451–455 (2016).
Yan, X. et al. Multifunctional biohybrid magnetite microrobots for imaging-guided therapy. Sci. Robot. 2, eaaq1155 (2017).
Nelson, B. J., Kaliakatsos, I. K. & Abbott, J. J. Microrobots for minimally invasive medicine. Annu. Rev. Biomed. Eng. 12, 55–85 (2010).
Osada, Y. & Rossi, D. D. Polymer Sensors and Actuators (Springer, 2013).
Noorduin, W. L., Grinthal, A., Mahadevan, L. & Aizenberg, J. Rationally designed complex, hierarchical microarchitectures. Science 340, 832–837 (2013).
Lerch, M. M., Grinthal, A. & Aizenberg, J. Viewpoint: homeostasis as inspiration—toward interactive materials. Adv. Mater. 32, 1905554 (2020).
Hippler, M. et al. Controlling the shape of 3D microstructures by temperature and light. Nat. Commun. 10, 232 (2019).
Lahikainen, M., Zeng, H. & Priimagi, A. Design principles for non-reciprocal photomechanical actuation. Soft Matter 16, 5951–5958 (2020).
Kim, Y., Yuk, H., Zhao, R., Chester, S. A. & Zhao, X. Printing ferromagnetic domains for untethered fast-transforming soft materials. Nature 558, 274–279 (2018).
Kotikian, A., Truby, R. L., Boley, J. W., White, T. J. & Lewis, J. A. 3D printing of liquid crystal elastomeric actuators with spatially programed nematic order. Adv. Mater. 30, 1706164 (2018).
Lahikainen, M., Zeng, H. & Priimagi, A. Reconfigurable photoactuator through synergistic use of photochemical and photothermal effects. Nat. Commun. 9, 4148 (2018).
Palagi, S. et al. Structured light enables biomimetic swimming and versatile locomotion of photoresponsive soft microrobots. Nat. Mater. 15, 647–653 (2016).
Yan, Z. et al. Mechanical assembly of complex, 3D mesostructures from releasable multilayers of advanced materials. Sci. Adv. 2, e1601014 (2016).
Zhang, H., Koens, L., Lauga, E., Mourran, A. & Möller, M. A light-driven microgel rotor. Small 15, 1903379 (2019).
Zhang, Y. et al. Seamless multimaterial 3D liquid-crystalline elastomer actuators for next-generation entirely soft robots. Sci. Adv. 6, eaay8606 (2020).
Qian, X. et al. Artificial phototropism for omnidirectional tracking and harvesting of light. Nat. Nanotechnol. 14, 1048–1055 (2019).
Aizenberg, M., Okeyoshi, K. & Aizenberg, J. Inverting the swelling trends in modular self-oscillating gels crosslinked by redox-active metal bipyridine complexes. Adv. Funct. Mater. 28, 1704205 (2018).
He, X. et al. Synthetic homeostatic materials with chemo-mechano-chemical self-regulation. Nature 487, 214–218 (2012).
Gelebart, A. H. et al. Making waves in a photoactive polymer film. Nature 546, 632–636 (2017).
Serak, S. et al. Liquid crystalline polymer cantilever oscillators fueled by light. Soft Matter 6, 779–783 (2010).
Corbett, D. & Warner, M. Linear and nonlinear photoinduced deformations of cantilevers. Phys. Rev. Lett. 99, 174302 (2007).
Corbett, D., Van Oosten, C. L. & Warner, M. Nonlinear dynamics of optical absorption of intense beams. Phys. Rev. A 78, 013823 (2008).
White, T. J. & Broer, D. J. Programmable and adaptive mechanics with liquid crystal polymer networks and elastomers. Nat. Mater. 14, 1087–1098 (2015).
Bisoyi, H. K. & Li, Q. Light-driven liquid crystalline materials: from photo-induced phase transitions and property modulations to applications. Chem. Rev. 116, 15089–15166 (2016).
Buguin, A., Li, M. H., Silberzan, P., Ladoux, B. & Keller, P. Micro-actuators: when artificial muscles made of nematic liquid crystal elastomers meet soft lithography. J. Am. Chem. Soc. 128, 1088–1089 (2006).
Yao, Y. et al. Multiresponsive polymeric microstructures with encoded predetermined and self-regulated deformability. Proc. Natl Acad. Sci. USA 115, 12950–12955 (2018).
Küpfer, J. & Finkelmann, H. Nematic liquid single crystal elastomers. Makromol. Chem. Rapid Commun. 12, 717–726 (1991).
Liu, L. et al. Light tracking and light guiding fiber arrays by adjusting the location of photoresponsive azobenzene in liquid crystal networks. Adv. Opt. Mater. 8, 2000732 (2020).
Lin, X., Saed, M. O. & Terentjev, E. M. Continuous spinning aligned liquid crystal elastomer fibers with a 3D printer setup. Soft Matter 17, 5436–5443 (2021).
Ware, T. H., McConney, M. E., Wie, J. J., Tondiglia, V. P. & White, T. J. Voxelated liquid crystal elastomers. Science 347, 982–984 (2015).
Pilz Da Cunha, M., Van Thoor, E. A. J., Debije, M. G., Broer, D. J. & Schenning, A. P. H. J. Unravelling the photothermal and photomechanical contributions to actuation of azobenzene-doped liquid crystal polymers in air and water. J. Mater. Chem. C 7, 13502–13509 (2019).
Barrett, C. J., Mamiya, J. I., Yager, K. G. & Ikeda, T. Photo-mechanical effects in azobenzene-containing soft materials. Soft Matter 3, 1249–1261 (2007).
Waters, J. T. et al. Twist again: dynamically and reversibly controllable chirality in liquid crystalline elastomer microposts. Sci. Adv. 6, eaay5349 (2020).
Serra, F. & Terentjev, E. M. Effects of solvent viscosity and polarity on the isomerization of azobenzene. Macromolecules 41, 981–986 (2008).
Erb, R. M., Sander, J. S., Grisch, R. & Studart, A. R. Self-shaping composites with programmable bioinspired microstructures. Nat. Commun. 4, 1712 (2013).
Sydney Gladman, A., Matsumoto, E. A., Nuzzo, R. G., Mahadevan, L. & Lewis, J. A. Biomimetic 4D printing. Nat. Mater. 15, 413–418 (2016).
Karothu, D. P. et al. The rise of the dynamic crystals. J. Am. Chem. Soc. 31, 13256–13272 (2020).
Kaspar, C., Ravoo, B. J., van der Wiel, W. G., Wegner, S. V. & Pernice, W. H. P. The rise of intelligent matter. Nature 594, 345–355 (2021).
Turiv, T. et al. Topology control of human fibroblast cells monolayer by liquid crystal elastomer. Sci. Adv. 6, p.eaaz6485 (2020).
Hauser, A. W., Sundaram, S. & Hayward, R. C. Photothermocapillary oscillators. Phys. Rev. Lett. 121, 158001 (2018).
Babu, D. et al. Acceleration of lipid reproduction by emergence of microscopic motion. Nat. Commun. 12, 2959 (2021).
This work was primarily supported by the US Army Research Office, under grant number W911NF-17-1-0351. K.B. and B.D. were supported by the National Science Foundation (NSF) through the Harvard University Materials Research Science and Engineering Center (MRSEC) under award DMR-2011754. M.M.L. was supported by the Netherlands Organization for Scientific Research (NWO, Rubicon Fellowship 019.182EN.027). 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), supported by the NSF ECCS award no. 1541959. We thank M. Aizenberg, M. Pilz Da Cunha, M. Liu, A. Chen and Y. Zhao for discussions.
The authors declare no competing interests.
Peer review information
Nature thanks Peter Hesketh and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary materials and methods, theoretical models 1–3, results and Figs. 1–35 and captions for videos 1–10.
Single deformation mode versus multimodal deformations under mild UV intensity (15 mW cm−2).
Light intensity-dependent self-regulated non-linear actuation.
Photoactuation of an LCE square micropost with oblique mesogen alignment illuminated from opposite directions at high light intensity (115 mW cm−2) results in mirrored stroke-like deformation trajectories.
Effect of geometry and temperature on the light-responsive deformation of microposts with oblique mesogen alignment.
Effect of irradiation duration and intervals.
Self-sorted patterns appearing in microstructure arrays on illumination through interpost communication.
Spacing-dependent interpost communication in 2D pillar arrays.
Amplification of ‘defects’ in arrays of microposts with oblique mesogen.
Photoresponse of jointed microstructures.
Simulation results of the photoresponsive behaviour of L-, V-, T- and palm-tree-shaped LCE microactuators (Supplementary Fig. 31) with horizontal, vertical or oblique global director alignment exhibiting a range of non-trivial motions interesting for soft robotic applications.
About this article
Cite this article
Li, S., Lerch, M.M., Waters, J.T. et al. Self-regulated non-reciprocal motions in single-material microstructures. Nature 605, 76–83 (2022). https://doi.org/10.1038/s41586-022-04561-z