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


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.

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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.

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.


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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

Authors and Affiliations



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.

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

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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.

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Li, S., Lerch, M.M., Waters, J.T. et al. Self-regulated non-reciprocal motions in single-material microstructures. Nature 605, 76–83 (2022).

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