Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Self-regulated non-reciprocal motions in single-material microstructures

Nature volume 605, pages 76–83 (2022)Cite this article

Subjects

Abstract

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Three non-collinear symmetry axes and their dynamic opto-chemo-mechanical feedback enable an infinite set of self-regulated motions in a compositionally uniform microstructure.
Fig. 2: In a micropost with oblique director alignment, distinct elementary deformation modes are evoked by irradiation from different directions.
Fig. 3: High-resolution programming of diverse stroke-like motions.
Fig. 4: Collective self-regulated deformation dynamics in arrays of microposts.
Fig. 5: Higher order self-regulated dynamics in jointed compositionally uniform microactuators.

Similar content being viewed by others

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 request.

Code availability

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.

References

  1. Sleigh, M. A. The Biology of Cilia and Flagella (Pergamon Press, 1962).

  2. Gilpin, W., Bull, M. S. & Prakash, M. The multiscale physics of cilia and flagella. Nat. Rev. Phys. 2, 74–88 (2020).

    Article  Google Scholar 

  3. Hu, W., Lum, G. Z., Mastrangeli, M. & Sitti, M. Small-scale soft-bodied robot with multimodal locomotion. Nature 554, 81–85 (2018).

    Article  CAS  PubMed  ADS  Google Scholar 

  4. 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).

    Article  PubMed  ADS  CAS  Google Scholar 

  5. Gu, H. et al. Magnetic cilia carpets with programmable metachronal waves. Nat. Commun. 11, 2637 (2020).

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  6. Rus, D. & Tolley, M. T. Design, fabrication and control of soft robots. Nature 521, 467–475 (2015).

    Article  CAS  PubMed  ADS  Google Scholar 

  7. 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).

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  8. 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).

    Article  PubMed  ADS  CAS  Google Scholar 

  9. Tottori, S. et al. Magnetic helical micromachines: fabrication, controlled swimming, and cargo transport. Adv. Mater. 24, 811–816 (2012).

    Article  CAS  PubMed  Google Scholar 

  10. Wehner, M. et al. An integrated design and fabrication strategy for entirely soft, autonomous robots. Nature 536, 451–455 (2016).

    Article  CAS  PubMed  ADS  Google Scholar 

  11. Yan, X. et al. Multifunctional biohybrid magnetite microrobots for imaging-guided therapy. Sci. Robot. 2, eaaq1155 (2017).

    Article  PubMed  Google Scholar 

  12. Nelson, B. J., Kaliakatsos, I. K. & Abbott, J. J. Microrobots for minimally invasive medicine. Annu. Rev. Biomed. Eng. 12, 55–85 (2010).

    Article  CAS  PubMed  Google Scholar 

  13. Osada, Y. & Rossi, D. D. Polymer Sensors and Actuators (Springer, 2013).

  14. Noorduin, W. L., Grinthal, A., Mahadevan, L. & Aizenberg, J. Rationally designed complex, hierarchical microarchitectures. Science 340, 832–837 (2013).

    Article  CAS  PubMed  ADS  Google Scholar 

  15. Lerch, M. M., Grinthal, A. & Aizenberg, J. Viewpoint: homeostasis as inspiration—toward interactive materials. Adv. Mater. 32, 1905554 (2020).

    Article  CAS  Google Scholar 

  16. Hippler, M. et al. Controlling the shape of 3D microstructures by temperature and light. Nat. Commun. 10, 232 (2019).

    Article  PubMed  PubMed Central  ADS  CAS  Google Scholar 

  17. Lahikainen, M., Zeng, H. & Priimagi, A. Design principles for non-reciprocal photomechanical actuation. Soft Matter 16, 5951–5958 (2020).

    Article  CAS  PubMed  ADS  Google Scholar 

  18. 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).

    Article  CAS  PubMed  ADS  Google Scholar 

  19. 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).

    Article  CAS  Google Scholar 

  20. Lahikainen, M., Zeng, H. & Priimagi, A. Reconfigurable photoactuator through synergistic use of photochemical and photothermal effects. Nat. Commun. 9, 4148 (2018).

    Article  PubMed  PubMed Central  ADS  CAS  Google Scholar 

  21. Palagi, S. et al. Structured light enables biomimetic swimming and versatile locomotion of photoresponsive soft microrobots. Nat. Mater. 15, 647–653 (2016).

    Article  CAS  PubMed  ADS  Google Scholar 

  22. Yan, Z. et al. Mechanical assembly of complex, 3D mesostructures from releasable multilayers of advanced materials. Sci. Adv. 2, e1601014 (2016).

    Article  PubMed  PubMed Central  ADS  CAS  Google Scholar 

  23. Zhang, H., Koens, L., Lauga, E., Mourran, A. & Möller, M. A light-driven microgel rotor. Small 15, 1903379 (2019).

    Article  CAS  Google Scholar 

  24. Zhang, Y. et al. Seamless multimaterial 3D liquid-crystalline elastomer actuators for next-generation entirely soft robots. Sci. Adv. 6, eaay8606 (2020).

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  25. Qian, X. et al. Artificial phototropism for omnidirectional tracking and harvesting of light. Nat. Nanotechnol. 14, 1048–1055 (2019).

    Article  CAS  PubMed  ADS  Google Scholar 

  26. 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).

    Article  CAS  Google Scholar 

  27. He, X. et al. Synthetic homeostatic materials with chemo-mechano-chemical self-regulation. Nature 487, 214–218 (2012).

    Article  CAS  PubMed  ADS  Google Scholar 

  28. Gelebart, A. H. et al. Making waves in a photoactive polymer film. Nature 546, 632–636 (2017).

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  29. Serak, S. et al. Liquid crystalline polymer cantilever oscillators fueled by light. Soft Matter 6, 779–783 (2010).

    Article  CAS  ADS  Google Scholar 

  30. Corbett, D. & Warner, M. Linear and nonlinear photoinduced deformations of cantilevers. Phys. Rev. Lett. 99, 174302 (2007).

    Article  CAS  PubMed  ADS  Google Scholar 

  31. Corbett, D., Van Oosten, C. L. & Warner, M. Nonlinear dynamics of optical absorption of intense beams. Phys. Rev. A 78, 013823 (2008).

    Article  ADS  CAS  Google Scholar 

  32. White, T. J. & Broer, D. J. Programmable and adaptive mechanics with liquid crystal polymer networks and elastomers. Nat. Mater. 14, 1087–1098 (2015).

    Article  CAS  PubMed  ADS  Google Scholar 

  33. 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).

    Article  CAS  PubMed  Google Scholar 

  34. 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).

    Article  CAS  PubMed  Google Scholar 

  35. Yao, Y. et al. Multiresponsive polymeric microstructures with encoded predetermined and self-regulated deformability. Proc. Natl Acad. Sci. USA 115, 12950–12955 (2018).

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  36. Küpfer, J. & Finkelmann, H. Nematic liquid single crystal elastomers. Makromol. Chem. Rapid Commun. 12, 717–726 (1991).

    Article  Google Scholar 

  37. 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).

    Article  CAS  Google Scholar 

  38. 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).

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  39. Ware, T. H., McConney, M. E., Wie, J. J., Tondiglia, V. P. & White, T. J. Voxelated liquid crystal elastomers. Science 347, 982–984 (2015).

    Article  CAS  PubMed  ADS  Google Scholar 

  40. 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).

    Article  CAS  Google Scholar 

  41. 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).

    Article  CAS  PubMed  ADS  Google Scholar 

  42. Waters, J. T. et al. Twist again: dynamically and reversibly controllable chirality in liquid crystalline elastomer microposts. Sci. Adv. 6, eaay5349 (2020).

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  43. Serra, F. & Terentjev, E. M. Effects of solvent viscosity and polarity on the isomerization of azobenzene. Macromolecules 41, 981–986 (2008).

    Article  CAS  ADS  Google Scholar 

  44. Erb, R. M., Sander, J. S., Grisch, R. & Studart, A. R. Self-shaping composites with programmable bioinspired microstructures. Nat. Commun. 4, 1712 (2013).

    Article  PubMed  ADS  CAS  Google Scholar 

  45. Sydney Gladman, A., Matsumoto, E. A., Nuzzo, R. G., Mahadevan, L. & Lewis, J. A. Biomimetic 4D printing. Nat. Mater. 15, 413–418 (2016).

    Article  CAS  PubMed  ADS  Google Scholar 

  46. Karothu, D. P. et al. The rise of the dynamic crystals. J. Am. Chem. Soc. 31, 13256–13272 (2020).

    Google Scholar 

  47. 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).

    Article  CAS  PubMed  ADS  Google Scholar 

  48. Turiv, T. et al. Topology control of human fibroblast cells monolayer by liquid crystal elastomer. Sci. Adv. 6, p.eaaz6485 (2020).

    Article  ADS  CAS  Google Scholar 

  49. Hauser, A. W., Sundaram, S. & Hayward, R. C. Photothermocapillary oscillators. Phys. Rev. Lett. 121, 158001 (2018).

    Article  CAS  PubMed  ADS  Google Scholar 

  50. Babu, D. et al. Acceleration of lipid reproduction by emergence of microscopic motion. Nat. Commun. 12, 2959 (2021).

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

Download references

Acknowledgements

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.

Author information

Author notes

  1. These authors contributed equally: Shucong Li, Michael M. Lerch

Authors and Affiliations

  1. Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA

    Shucong Li, Yuxing Yao & Joanna Aizenberg

  2. John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    Michael M. Lerch, Bolei Deng, Reese S. Martens, Do Yoon Kim, Katia Bertoldi, Alison Grinthal & Joanna Aizenberg

  3. Stratingh Institute for Chemistry, University of Groningen, Groningen, the Netherlands

    Michael M. Lerch

  4. Chemical Engineering Department, University of Pittsburgh, Pittsburgh, PA, USA

    James T. Waters & Anna C. Balazs

Authors
  1. Shucong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael M. Lerch
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. James T. Waters
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Bolei Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Reese S. Martens
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yuxing Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Do Yoon Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Katia Bertoldi
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Alison Grinthal
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Anna C. Balazs
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Joanna Aizenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.L., M.M.L. and J.A. conceived the project. S.L. and Y.Y. synthesized the side-on LCE monomer used for fabrication. S.L., M.M.L., R.S.M. and D.Y.K. performed the experiments. B.D. and K.B. performed theoretical modelling and image tracking. A.C.B. and J.T.W. performed finite element modelling. S.L., M.M.L., A.G., R.S.M. and B.D. analysed the experimental data. J.A. supervised the project. All co-authors provided useful feedback and contributed to the manuscript.

Corresponding author

Correspondence to Joanna Aizenberg.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks Peter Hesketh and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

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

Supplementary information

Supplementary Information

Supplementary materials and methods, theoretical models 1–3, results and Figs. 1–35 and captions for videos 1–10.

Peer Review File

Supplementary Video 1

Single deformation mode versus multimodal deformations under mild UV intensity (15 mW cm−2).

Supplementary Video 2

Light intensity-dependent self-regulated non-linear actuation.

Supplementary Video 3

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.

Supplementary Video 4

Effect of geometry and temperature on the light-responsive deformation of microposts with oblique mesogen alignment.

Supplementary Video 5

Effect of irradiation duration and intervals.

Supplementary Video 6

Self-sorted patterns appearing in microstructure arrays on illumination through interpost communication.

Supplementary Video 7

Spacing-dependent interpost communication in 2D pillar arrays.

Supplementary Video 8

Amplification of ‘defects’ in arrays of microposts with oblique mesogen.

Supplementary Video 9

Photoresponse of jointed microstructures.

Supplementary Video 10

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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-022-04561-z

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing