Light-driven continuous rotating Möbius strip actuators

The Möbius strip, a fascinating topological structure with unique properties stemming from its torsional strain distribution, has inspired numerous studies across various disciplines. Its single-sided nature and tendency to redistribute torsional strain away from the twist region suggest the possibility of creating actuators exhibiting continuous deformations rather than discrete state changes. Existing research on continuous rotary motion in elastic materials, such as that observed in pre-strained elastic torus polymer rods, highlights the importance of factors like topological prestrain and rotational symmetry breaking to achieve such motion. However, previous attempts to create Möbius strip actuators have resulted in simple shrinkage rather than continuous rotation, largely due to the lack of symmetry breaking in the actuator design. This study aims to address these limitations by designing and fabricating Möbius strip actuators from photothermally responsive liquid crystal elastomers (LCEs). LCEs are chosen for their reversible, large-amplitude shape deformations triggered by external stimuli, making them suitable candidates for the development of advanced actuators and shape-morphing materials.

The authors review existing literature on Möbius strips, highlighting their unique topological properties and potential for actuation. They discuss previous work on continuous rotary motion in elastic materials, emphasizing the role of topological prestrain and rotational symmetry breaking. Prior attempts to create Möbius strip actuators that only resulted in simple shrinkage are also reviewed, setting the stage for the current study's approach to address these limitations by introducing a contraction gradient in the design of the actuators.

The researchers utilized a liquid crystal elastomer (LCE) as the base material for the actuators. This LCE material incorporates a near-infrared (NIR) absorbing dye (YHD796) to enable remote light control via photothermal conversion. The LCE synthesis involved combining poly(methylhydrosiloxane) (PMHS) as the macromolecular backbone, 4-methoxyphe-nyl-4-(1-buteneoxy)benzoate (MBB) as the mesogenic monomer, and crosslinkers 4-bis-undec-10-enyloxy-benzene (11UB) and 4-[4-(vinyloxy)butoxy]phenyl 4-[4-(vinyloxy)-butoxy]benzoate (VBPB) to tune the phase transition temperature. Two types of LCE ribbons were prepared: LCE796 (dye-embedded, uniaxially stretched) and LCE0 (polydomain, unstretched). Initially, single-layered Möbius strips (S-Möbius[+1] and S-Möbius[+2]) were fabricated, but these only exhibited shrinkage under NIR irradiation. This led to the development of bilayered Möbius strip actuators (B-Möbius[+1], B-Möbius[+2], and B-Möbius[-2]), created by combining LCE796 and LCE0 layers. The bilayered strips demonstrated rotation under NIR stimulation but this rotation stopped once the inside and outside layers were no longer successive. To achieve continuous rotation, a circular cylinder was introduced inside the B-Möbius[+2] strip, preventing the formation of helically writhed loops that previously terminated the rotation. Finally, continuous rotating C-Möbius[+1] strip actuators were developed using a gradient bilayered LCE ribbon with a continuous, defect-free, homeotropic, and homogeneous photothermal-contraction-gradient structure created by a two-step process involving a tilted PTFE mold and uniaxial stretching. The characterization of the LCE films involved measuring photothermal shrinkage ratios and 2D wide-angle X-ray scattering (2D-WAXS) to assess the mesogen alignment gradient. The rotation speed of the actuators was analyzed as a function of NIR light intensity, scanning rate, and ribbon elasticity.

The study demonstrates that the design of the Möbius strip actuator is critical for achieving continuous rotation. Single-layered actuators only exhibited shrinkage under NIR irradiation. Bilayered actuators showed rotation, but this was limited by the formation of helically writhed loops. The introduction of a circular cylinder inside the bilayered actuator enabled continuous rotation. The creation of a continuous, defect-free, homeotropic, and homogeneous photothermal-contraction-gradient structure in the C-Möbius[+1] actuator was crucial for achieving continuous in situ rotation. The rotation speed of the C-Möbius[+1] actuator was found to depend on NIR light intensity, scanning rate, and ribbon elasticity. Specifically, a moderate light intensity of 0.7 W cm⁻² and a scanning rate resulting in a temperature around 83 °C were optimal. An elasticity modulus above 0.45 MPa was necessary for continuous rotation. Detailed statistical analysis of the actuator's motion dynamics revealed that the locus of twist point follows a circular trajectory, while other points on the strip execute a flip motion correlated with the twist rotation. This correlation could be described by a Boltzmann function. Miniaturization of the C-Möbius[+1] actuator further improved the rotation speed and energy efficiency. Moreover, light-fuelled rolling robots were created based on the B-Möbius[+2] design, demonstrating both clockwise/anticlockwise rotation and curvilinear trajectory motion. The C-Möbius[-1] actuator was also successfully tested, showing continuous clockwise rotation.

The successful fabrication of continuous rotating Möbius strip actuators addresses the limitations of previous attempts to create such devices. The key to achieving continuous rotation lies in the strategic creation of a contraction gradient within the actuator's structure and the elimination of defect points that interrupt the continuous motion. The results demonstrate the importance of material selection (LCEs), precise control of the fabrication process, and an understanding of the interplay between photothermal effects, stress gradients, and the topological geometry of the Möbius strip. The findings have implications for the development of advanced actuators and shape-morphing materials with applications in various fields, including robotics, microfluidics, and biomedical engineering.

This research successfully demonstrates the fabrication and characterization of light-driven, continuous rotating Möbius strip actuators. The key innovation lies in the design of a continuous, defect-free, gradient structure within the actuator, eliminating the limitations observed in previous attempts. The study showcases the potential of these actuators for applications requiring continuous, controlled motion. Future research could focus on exploring different LCE materials, optimizing the design for improved efficiency and speed, and investigating applications in micro-robotics and other areas.

While this study successfully demonstrates the concept of continuous rotating Möbius strip actuators, several limitations should be noted. The fabrication process is relatively complex and requires precise control of parameters such as stretching rate and light intensity. The current design relies on NIR light as the stimulus, limiting its applicability in certain environments. Further research is needed to explore alternative actuation methods. The long-term durability and stability of the actuators under continuous operation also require further investigation.