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Monolithic shape-programmable dielectric liquid crystal elastomer actuators

Monolithic shape-programmable dielectric liquid crystal elastomer actuators SCIENCE ADVANCES RESEARCH ARTICLE MATERIALS SCIENCE Copyright © 2019 The Authors, some rights reserved; Monolithic shape-programmable dielectric liquid exclusive licensee American Association crystal elastomer actuators for the Advancement of Science. No claim to 1 1 1 1 1 Zoey S. Davidson *, Hamed Shahsavan , Amirreza Aghakhani , Yubing Guo , Lindsey Hines , original U.S. Government 2 2 1,3 Yu Xia , Shu Yang , Metin Sitti Works. Distributed under a Creative Soft robotics may enable many new technologies in which humans and robots physically interact, yet the nec- Commons Attribution essary high-performance soft actuators still do not exist. The optimal soft actuators need to be fast and forceful NonCommercial and have programmable shape changes. Furthermore, they should be energy efficient for untethered applica- License 4.0 (CC BY-NC). tions and easy to fabricate. Here, we combine desirable characteristics from two distinct active material systems: fast and highly efficient actuation from dielectric elastomers and directed shape programmability from liquid crystal elastomers. Via a top-down photoalignment method, we program molecular alignment and local- ized giant elastic anisotropy into the liquid crystal elastomers. The linearly actuated liquid crystal elastomer monoliths achieve strain rates over 120% per second with an energy conversion efficiency of 20% while moving loads over 700 times the elastomer weight. The electric actuation mechanism offers unprecedented opportu- nities toward miniaturization with shape programmability, efficiency, and more degrees of freedom for applica- tions in soft robotics and beyond. INTRODUCTION A high voltage applied to the compliant electrodes induces an The underlying rigid actuation mechanisms of traditional robotics, electrostatic pressure, so-called Maxwell stress, and, hence, deforms electric motors, or hydraulic and pneumatic actuators hinder robot the DE. The electrical actuation mechanism can result in a much higher miniaturization and, more importantly, robot use in human collab- operating efficiency (ratio of mechanical work to input electrical energy) orative environments. Compliant actuators are the missing key to and a higher actuation speed than those of LCEs (7, 8). Besides enabling robots to interface with humans (1). The ideal compliant functioning as soft linear actuators, DE actuators could be applied to soft actuators will have high efficiency, strength-to-weight ratio, work grippers, haptic devices, or optical devices, which, however, require capacity, and shape programmability to perform complex functions. complex shape change (6). Despitesomeimpressivedemonstrations, Like an artificial muscle, soft actuators with these properties would DE actuators have not yet gained widespread use in soft robotics partly substantially advance technologies for potential applications in aero- because of the need for prestrain or the challenge of fabricating devices space, robotics, medical devices, energy harvesting devices, and wear- with complex deformation profiles (14). Overcoming these challenges ables (2–4). Among many soft actuators that have been explored, and expanding the applications of DE actuators require material dielectric elastomers (DEs) appear promising and even outperform innovation for the next generation of high-performance DEs with skeletal muscle in some aspects (5–8). Separately, liquid crystal elasto- shape programmability (20, 21). mers (LCEs) have demonstrated reversible large mechanical deforma- LCEs are rubbery polymers with anisotropic bulk properties im- tion by light actuation and thermal actuation near the phase transition parted by their constituent molecular anisotropy. Most prior works temperature (9, 10). Recent advances in photoalignment and micro- on LCE actuation have focused on thermal or light-driven mechanisms. fabrication techniques have enabled preprogramming of liquid crys- Heat or light temporarily disrupts the anisotropic molecular order, tal alignment in microscopic regions for complex shape morphing known as the director field (n), thereby creating internal stresses and (11, 12). However, both actuator types have their drawbacks: DE anisotropic bulk deformation (10, 11, 18). The local LCE director field films need to be prestrained macroscopically (13) or require multi- can be preprogrammed to create complex shape changes when actu- step fabrication methods, which make it difficult to program minia- ated. However, light actuation is inefficient, and thermal actuation is turized actuators with local shape changing (14). Meanwhile, direct both slow and inefficient; thus, they are poorly suited for applications conversion of electrical energy to mechanical work using LCEs has, that require high energy efficiency and fast actuation such as robotics. until now, remained limited because of the small strains generated Direct electrical actuation of LCEs is a highly sought-after technology (15–19). However, we demonstrate that the ability to pattern LCE (17). A few previous studies have demonstrated electrical actuation of molecules in a locally varying alignment, thus tailoring spatial var- LCEs by coupling an electric field to the molecular dielectric anisotro- iations of the mechanical compliance, enables more efficient DE ac- py or sometimes to the intrinsic polarization of the LCE or LCE tuators with preprogrammable degree and direction of actuation. composite; thus, an electric field drives molecular reorientation to cre- Typically, DE actuators function by the electrostatic attraction ate bulk strains. However, these methods require elevated tempera- between two compliant electrodes coated on opposing sides of tures or use of carbon nanotubes to enhance the electric response; an isotropic DE to form a variable resistor-capacitor (Fig. 1A) (13). otherwise, only small actuation strains are produced at room tempera- ture (15, 16, 22–24). In this work, we directly exploit the large mechanical anisotropy of LCEs without relying on molecular rotation Physical Intelligence Department, Max Planck Institute for Intelligent Systems, during electric actuation. We further use recent advances in the Stuttgart, Germany. Department of Materials Science and Engineering, University patterning of LCE films to tailor the local anisotropic elasticity and of Pennsylvania, Philadelphia, PA, USA. School of Medicine and School of Engi- Poisson’s ratios for highly efficient and shape-programmable DEs, neering, Koç University, Istanbul, Turkey. *Corresponding author. Email: davidson@is.mpg.de which we refer to as a dielectric LCE actuator (DLCEA; Fig. 1B). By Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 1of9 | SCIENCE ADVANCES RESEARCH ARTICLE Fig. 1. Device schematic, mechanical, and electrical characterization. (A) Schematic of a traditional isotropic DE actuator in off and on states. (B) Schematic of a uniaxial aligned dielectric LCE actuator (DLCEA) in off and on states. Liquid crystal molecular alignment; the director, n, is indicated by a double-headed arrow and defines the stiffer direction of the LCE. When actuated by a voltage, V, the material thins and stretches perpendicular to the alignment greater than parallel to the director. (C) The DLCEA mechanical stress and normalized capacitance (C) response to strain over the DLCEA linear regime are characterized at a strain rate of 0.1% per second. aligning LCE molecules in local domains, we achieve electric-driven field (fig. S5A). Using a simplified finite element model, we find, for actuation and shape morphing at room temperature and demonstrate large elastic anisotropy, that a given Maxwell stress produces nearly large, fast, and forceful strains. two times the linear expansion strain observed in an isotropic material with a modulus equal to the soft direction (fig. S5B). Other works with similar LCE chemistry have observed one-dimensional (1D) trans- RESULTS lational crystallinity, which may explain the particularly large elastic Uniaxially aligned DLCEA characterization anisotropy observed in this work (27, 29). The LCE films are fabricated in a two-step process recently developed We then characterized uniaxial DLCEAs in isometric (constant by some of the authors (25, 26). Briefly, an oligomer is synthesized strain; Fig. 2A) and isotonic (constant force; Fig. 2B) configurations. In before LCE film fabrication by a thiol-acrylate click reaction; a com- isometric tests, we applied initial strains to DLCEA devices and mon diacrylate reactive liquid crystal monomer is chain-extended by allowed a relaxation period before the application of high voltages Michael addition with a dithiol linker molecule. The exact component (fig. S6A). From the active stress reduction, we observe two relation- ratios, choice of monomer, and dithiol linker can all be tuned to adjust ships between the strain, the voltage applied, and active stresses, which 2 2 the specific mechanical properties of the final LCE film (26, 27). We fit with the model of Maxwell stress, p º V /d ,where V is the ap- es produced large areas of a well-ordered uniaxial LCE (figs. S1 and S2) plied voltage and d is the LCE film thickness. First, actuation at larger with giant elastic anisotropy (Fig. 1C). In all experiments, we actuated initial strains produces higher active nominal stress reductions; the DLCEAs at room temperature and only in the linear regime of strains isometric prestrain results in thinning of the LCE and, thus, higher (fig. S3). We can also locally program the LCE director field by photo- Maxwell stress for a given voltage (Fig. 2A). With an LCE, it appears alignment to create a spatially programmed command surface and to that additional strain thins the material at a rate fast enough to offset locally orient the LCE director (28). Last, we applied compliant grease the increasing restoring force such that a given actuation voltage electrodes to both sides of the LCE film to create the DLCEA devices results in larger active stresses. We also observe that, for each fixed (fig. S4). Further details can be found in Materials and Methods. strain, the active nominal stress reduction during isometric tests in- To characterize the fundamental properties of DLCEAs, we first creases quadratically with increasing voltage (fig. S6B). At the highest made monodomain, uniaxially aligned LCE films. The electrodes voltages tested, we measured peak active nominal stress reduction in coated on uniaxial DLCEAs enable simultaneous measurement of excess of 50 kPa. However, for the device with the director, n||u,the capacitance and stress versus strain applied to the LCE film (Fig. 1C). active stresses are relatively much smaller because of the much higher When strains (u) are applied parallel to the director, n||u, the LCE is modulus. When held with an isometric strain, the DLCEA behaves more than an order of magnitude stiffer than when strains are ap- like a variable stiffness spring, and in the case of n⊥u, 5% initial strain, plied perpendicular to the director, n⊥u, which indicates a high de- and 2 kV actuation voltage, the Maxwell stress–induced expansion of gree of elastic anisotropy. Similarly, the difference in slope of the the LCE nearly compensates for the entirety of the isometric strain– normalized capacitance between the DLCEA devices with different induced stress. We also performed isopotential tests in which the director orientation indicates anisotropy in Poisson’sratio.TheDLCEA DLCEA is strained under a constant voltage. These tests indicate capacitance is proportional to the area of the film coated by the electrode the expected actuation stroke of a loaded DLCEA when a voltage is and inversely proportional to the film thickness. Thus, Poisson’sratio applied (fig. S7). anisotropy causes the film’s thickness and area to change at different Next, we take the same DLCEA and perform isotonic tests by sus- rates depending on the direction of strain relative to the LCE director pending varying weights from the free end of the DLCEA to generate Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 2of9 | SCIENCE ADVANCES RESEARCH ARTICLE Fig. 2. Characterization of uniaxial DLCEA demonstrates the capabilities of a DLCEA actuator device. (A) Isometric (constant strain) tests. Measured active nominal stress reduction with various initial isometric strains (u) for devices assembled with the LCE director n⊥u and n‖u and a photograph of an assembled DLCEA device with n⊥u.(B) Isotonic (constant force) tests. Contractile discharge strain trajectories under various loads measured by a high-speed camera with actuation voltages of 3 kV. Inset: The corresponding measurements of electrical discharge. (C) Fundamental actuator characteristics are computed from the contraction trajectory and measurement of ^ ^ the discharge current found in (B), including strain (u), peak strain rate (u ), peak specific power P ), specific energy (E), and efficiency. Photo credits: Zoey S. Davidson. peak peak constant load forces and initial nominal strains, u (Fig. 2B and fig. the DLCEA contraction trajectory, we compute fundamental perform- S8). DLCEAs in the n||u configuration do not show an appreciable ance metrics both for the pure elastic response and for the extended active strain at any initial loading for even the highest voltages tested creeping contraction (Fig. 2C and fig. S8C). because of their significantly higher elastic modulus (movie S1). However, DLCEAs with the n⊥u configuration exhibit fast active Complex programmable shape actuation strains up to 5% with the application of 3 kV for the heaviest loading To achieve complex shape actuation, LCEs typically function by tested, 0.27 N, approximately 790 times the weight of the bare LCE programming spatially varying in-plane contractilestrainwhenheated film (35 mg). We perform isotonic contractile tests by abruptly above a phase transition. However, the DE actuation mechanism is not discharging weighted DLCEA devices and capture the subsequent based on a heat induced phase transition, but generates in-plane ex- motion with high-speed video (fig. S8B and movie S2). With in- pansion strains. Thus, boundary conditions play a significant role in creasing load and initial strain, the DLCEA capacitance increases, determining the realized DLCEA shape change. To better understand which can be seen in the shifted discharge curves in the inset of the role of boundary conditions on DLCEAs, we performed a funda- Fig. 2B. In all cases, the electrical discharge time, approximately mental characterization of the bucklingeffect causedbythe elastomer’s 1 ms, is much faster than that needed for the contraction of DLCEA, expansion between fixed boundaries (Fig. 3, A and B, and movie S3). within 60 ms, which indicates that the system is currently limited by The buckling amplitude increases with increasing voltage and, at 2.5 kV, the viscoelastic properties of the LCE. We also observed significant creates out-of-plane peak-to-peak strokes greater than 1800% of the viscous losses in the contractions that are apparent from the continued LCE film thickness of approximately 80 mm corresponding to a linear creeping contraction after the initial elastic response (fig. S8B). From strain of approximately 5% (Fig. 3C and fig. S9A). Actuation speed is Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 3of9 | SCIENCE ADVANCES RESEARCH ARTICLE another important characteristic for potential DLCEA applications. We tuated DLCEA in Fig. 4F shows that the defects could buckle both up applied a sinusoidally varying 1-kV potential to measure the change in and down. actuation amplitude as a function of the applied frequency (Fig. 3D and fig. S9B). The actuation amplitude decays exponentially with the fre- quency but is still a perceivable 50 mmat30Hzand 1kV. DISCUSSION We designed spatially varying LCE director configurations, aiming When using the DLCEA as a linear actuator, we expect larger anisot- to demonstrate the ability to preprogram complex patterns in 2D, ropy in Poisson’s ratio to produce higher efficiency and require lower followed by electrical actuation of the films into 3D forms (11, 25). electric fields for actuation compared to a similar isotropic material Depending on the programmed director field, the LCE film buckles (32). Compared to other LCE actuators, the actuation efficiency of out of plane with locally positive (Fig. 4A) or negative Gaussian cur- approximately 20% reported here is remarkable; to our knowledge, vature (Fig. 4B). These shapes are often called cones and anti-cones, actuation efficiency in LCEs has not been reported before owing to and the theory describing this form of deformation in elastic media their low energy conversion efficiency, which we estimate, for exam- was previously described by Modes et al. (30). We understand these ple, to be less than 0.001% in a thermally actuated LCE according to shape changes by considering a simplified model of an anisotropic DE (18). Note that this estimate is based on the initial stroke only; a con- made from stiff concentric rings embedded in a soft elastomer (31). stant current is needed to maintain LCE in the contracted state. Fur- These rings prevent expansion along the rings but allow expansion thermore, our DLCEA efficiency compares favorably to a recent in the radial direction leading to a frustration and out-of-plane buckling. example of an isotropic DE actuator with highly optimized electrodes, A similar argument holds for radial stiff elements. The double-headed reporting 1.5% efficiency (7). We expect that reducing viscous loss and red arrows in Fig. 4 (A and B) indicate the soft expansion directions. creep, indicated here by the hysteresis loop in Fig. 1C and extended con- We created a pixelated array of topological defects by spatially pro- traction in Fig. 2B, will further improve the situation for fast and effi- gramming light polarization with a pattern of linear film polarizers cient DLCEAs. (Fig. 4C) to locally orient the LCE director as in Fig. 4D. The director We believe that the demonstrated high efficiency reported in our forms a lattice of radial and azimuthal defect types that, when elec- system is due to the anisotropy of the elastic modulus and Poisson’s trically actuated, buckle out of plane because of incompatible in- ratio. Generally speaking, elastomers are volume conserving; thus, planestrains (Fig.4Eand movieS4).Wemeasuredthe height of extension in one direction causes a contraction in the other directions. the DLCEA surface in the discharged (0 V) and actuated (2.5 kV; However, the contraction in LCE films is greater perpendicular to the Fig. 4F) states. To do so, we stably held the device in its actuated shape director. In other words, when an LCE film is strained perpendicular at 2.5 kV for more than 3 hours while drawing less than 1 mA, con- to the director, it contracts in thickness, which is also perpendicular to firming its high stability and low power consumption. The locally the director, and thus faster than the contraction in width that is programmed height change and the accompanying formation of parallel to the director. When strained parallel to the director, the Gaussian curvatures are clearly visible from the circular traces enclos- LCE contracts equally in both thickness and width (assuming that ing the central radial defect type (Fig. 4G). The out-of-plane buckling the cross section is isotropic). It is worth mentioning that this last creates peak-to-peak height differences of over 1600 mm, a 2000% point is not certain: As mentioned previously, 1D translation crystal- growth from the initial film thickness of approximately 80 mm linity is common in this class of LCE (27, 29). In particular, the 1D corresponding to a 22% areal strain. The lower right corner of the ac- crystal planes may be at some angle to the LCE director, thus breaking Fig. 3. Uniaxial out-of-plane buckling DLCEA. (A) Off and (B) on states of a uniaxial DLCEA device with fixed boundary condition. Expansion along the soft direction creates out-of-plane buckling, which displaces a fine thread held taut across the surface. (C) Experimental measurement of buckling as a function of the applied voltage. (D) Frequency response of buckling uniaxial DLCEA at 1 kV. The 0.1-Hz actuation amplitude is approximately 130 mm. Photo credits: Zoey S. Davidson. Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 4of9 | SCIENCE ADVANCES RESEARCH ARTICLE Fig. 4. Pixelated DLCEA. Programmed shape actuation, such as a dimple pattern deformation, is possible by patterning the director configuration into an azimuthal- radial defect lattice. (A) Azimuthal defect types deform into a cone with locally positive Gaussian curvature, and (B) radial defect types deform into an anti-cone with locally negative (saddle-like) Gaussian curvature. In (A) and (B), the double-headed red arrows indicate the soft direction. (C) The defects are patterned using a pixelated array of polarizing films with the designed local orientations. (D) Viewed through crossed polarizers, the fabricated LCE film has pixelated uniaxial alignment, indicated by dashed white lines, forming a defect lattice. (E) When charged to 2.5 kV, there is a large visible deformation of the surface. (F) The profilometry measured height map of the grease-covered LCE is nearly flat with no charge and varies over 1.6 mm when charged to 2.5 kV. The dash-dot and dash circles in (F) are traces of height depicted in (G). The change from approximately constant height to a sinusoidally varying height indicates a change in sign of the local Gaussian curvature. Scale bars, 4 mm. Photo credits: Zoey S. Davidson. the symmetry informing the assumption of equal contraction in width the DLCEA is multistable, we only ever observe a single actuated state and thickness when straining parallel to the director. Tuning this 1D for each sample (11). We hypothesize that the symmetry that would crystallinity may play an important role in further improving the enable multistability is likely broken by gravity during the tests or by linear actuation capabilities of DLCEAs. uneven photocrosslinking of LCE films during device fabrication. To further illuminate the advantages of elastic anisotropy, we Nevertheless, our demonstration of local changes in the Gaussian cur- consider a simplified DE model with a nearly volume-conserving vature indicates that our method can be potentially generalized to rea- elastomer material having large Poisson’s ratio anisotropy and under lize a large variety of programmable shape changes (30). In addition to no load (see fig. S5). In this model, nearly all compression strain due programming in-plane director orientations, it is also possible to to the Maxwell stress creates an extension strain in the soft direction program the LCE director orientation along the film thickness. As of the elastomer. In other words, the Maxwell strain through the seen in fig. S10, we have assembled DLCEAs with a twisted LCE con- thickness of the material, u = P /E , results in strain u and nearly figuration where the director rotates by nearly 90° from the top to the z es z y no strain u . In an isotropic elastomer, the same Maxwell strain bottom surface. When an electric field is applied, the twisted DLCEA would result in only half as much strain because the volume-conserving produces twisting motions where the magnitude depends on the LCE strain would be split evenly into u and u . For linear actuators, this is geometry in addition to the material’s intrinsic properties (33). x y thefirst advantageofaDLCEA; theactuation voltageneededto achieve a given strain is reduced. The second advantage of anisotro- py to linear actuators comes from energetic considerations of the CONCLUSION same system. The elastic energy density of deformation is quadratic Here, by combining the desirable characteristics of DEs and LCEs in a in strain; thus, in the simplified model presented here, there will be single material platform, we demonstrate superior actuation per- no energy component from strains in the x direction. Furthermore, formance from electrically actuated DLCEAs, including high energy for a given desired linear extensional strain, the input electric field conversion efficiency (20%), high actuation speed (120% per second), 2 2 energy (º V /d ) will also be less because the required Maxwell and programmable shape change from 2D to 3D with more than strain is smaller than in an isotropic DE. Thus, an anisotropic DE 1800% out-of-plane stroke. To achieve larger actuation forces, multi- actuator can achieve an equivalent strain as an isotropic DE linear layer DLCEA stacks could be an option, as demonstrated in LCE and actuator, but with higher efficiency. Both the no-load and perfect DE multilayer stacks (7, 34), although it would require the develop- uniaxial elastomer assumptions may be relaxed, and viscoelastic ment of an alternative soft electrode. Furthermore, even more general effects may be added to build a more complete model. shape changes, i.e., nonlocal Gaussian curvature, may be realized by The material Poisson’s ratio anisotropy is also an important fea- spatially programming both the LCE alignment and local cross-linking ture for enabling programmed shape change actuation. The actuated density. (compressed) LCE transversely expands anisotropically to create the Insights into the integration of active materials with top-down observed shape changes. Although, in principle, the buckled shape of microfabrication techniques and electroactuation mechanism presented Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 5of9 | SCIENCE ADVANCES RESEARCH ARTICLE here could offer exciting opportunities when coupling DLCEAs with LCE fabrication and characterization 3D printing, origami and kirigami actuation strategies, and distributed The previously prepared oligomer was melted together with additional control systems toward creating multifunctional soft robots in a scal- RM82 and a small amount of photoinitiator to cross-link the oligomer able fashion at a low material and build cost. The electroactuation chains into an elastomer network. Inmoredetail, theLCE oligomerand mechanism can also be applied to other technologies, including energy an additional RM82 LCE monomer were melted together in 1:1 molar harvesting and storage, medical devices, wearable technology, and ratio, assuming that the oligomer consists purely of chains of single- aerospace. Furthermore, fast and dynamic modulation could be useful unit length RM82 capped by 1,5-PDT on both ends (26). Thus, the in displays and optical applications. mixture consisted of excess thiol groups, which were likely responsible for a significant portion of the final LCE viscous losses (see the section Uniaxially aligned DLCEA characterization), but this sparse cross- MATERIALS AND METHODS linking also promoted softness necessary to achieve larger actuation Materials strains. The melt was mixed for only 2 to 3 min at 120°C and then de- 1,5-Pentanedithiol (1,5-PDT; >99%), 1,8-diazabicycloundec-7-ene gassed forapproximately 3 minina vacuum oven at 90°C. One weight (DBU), butylatedhydroxytoluene (BHT), and magnesium sulfate percent DMPA was added and carefully stirred in so as not to reintro- (MgSO ; anhydrous powder) were purchased from Sigma-Aldrich duce air bubbles. and used as received. Hydrochloric acid (HCl), dimethylformamide The isotropic LCE melt was then poured onto the BY-coated glass (DMF), and dichloromethane (DCM) were purchased from Fischer at 80°C and then carefully sandwiched with a second hot BY-coated Scientific. The photoinitiator 2,2-dimethoxy-2-phenylacetophenone glass substrate. The BY-LCE-BY sandwich was cooled into the aligned (DMPA) was purchased from Toronto Research Chemicals. Brilliant (nematic) phase, approximately 73°C, and then gradually cooled to Yellow (BY) was purchased from Tokyo Chemical Industry. The liquid room temperature during which time it aligned with the spatial crystal monomer, 1,4-bis-[4-(6-acryloyloxy-hexyloxy)benzoyloxy]-2- programming imparted by the BY coating, and the defects arising methylbenzene (RM82; >95%), was purchased from Wilshire Technol- from the phase transition were annealed. Once the LCE cools to room ogies Inc. and used without further purification. Conductive carbon temperature, it was cured in ultraviolet light with an OmniCure S2000 grease, NyoGel 756G, was purchased from Newgate Simms. arc source. After exposure to ultraviolet light polymerized the LCE in its programmed state, we immersed the BY-LCE-BY sandwich in wa- LCE oligomer synthesis ter to release the LCE from the BY-coated glass substrates. We fabricated LCE films in a two-step process recently developed by The final LCE film thickness was confirmed by confocal laser some of the authors (25, 26). An oligomer was synthesized before profilometry from regions cut to make actuators (described below). LCE film fabrication by a thiol-acrylate click reaction; the reactive Good alignment and few defects in the LCE are essential character- liquid crystal monomer RM82 was chain-extended by Michael addi- istics of the film to impart the largest possible elastic anisotropy and tion with 1,5-PDT. In a typical synthesis, 12.5 g of RM82 was mixed achieve optimal materials properties. The high contrast between the with 5.06 g of 1,5-PDT in 120 ml of DCM with three drops of DBU orientations of the LCE between crossed polarizers is visible in fig. S1. catalyst. After 16 hours of stirring at room temperature, the solution After sheets of LCE were separated from the glass substrates, they was rinsed in a separation funnel with 1 M HCl, 0.1 M HCl, and deio- were rinsed in water to remove residual BY and dried with nitrogen. nized water successively. The DCM-product mixture was then dried The LCE sheets were placed back on glass substrates and carefully in- with 25 g of MgSO for 30 min, which was then filtered. BHT (50 mg) spected to identify the defect and bubble-free regions for the fabrica- was added to the clear DCM and product mixture before rotary evap- tion of DLCEA devices. For uniaxial DLCEA devices, the cleanest oration and direct vacuum until a thick white oligomer remained. The identified regions were cut into rectangular pieces typically 14 mm oligomer was stored at −30°C for up to 2 months. by 34 mm with a typical weight of 35 mg. This size film was chosen for ease of handling and for the electrical actuation constraints de- Substrate preparation scribed below. Smaller neighboring regions, 20 mm by 5 mm, were Glass slides, typically 5 cm by 5 cm and 8 cm by 10 cm, were cleaned used to initially characterize the stress-strain behavior of the LCE in an ultrasound bath with deionized water, isopropanol, and ace- and the large strain behavior. tone. Next, the slides were dried with nitrogen and then treated by The edges of the laser-cut regions on the larger film were then oxygen plasma. A mixture of 1 weight % BY dissolved in DMF was spin- inspected by laser confocal interferometry (KEYENCE VK-X210) to coated onto the slides and then dried on a hot plate at 120°C. Spacers cut confirm the as-fabricated height of the LCE films. We found that from polyimide or Mylar plastic, with thicknesses of 65 or 75 mm, were nominally 65-mm Kapton produces approximately 70-mm LCE films placed along the edges on one of the BY coat sides of the glass slides; and that nominally 75-mm Mylar produces approximately 83-mmLCE then, two slides were placed with the BY-coated faces toward each other. films. The thicknesses may vary by as much as ±10% across the as- Large paper clips held the slides together with a polarizer film placed on produced LCE sheet (fig. S2). one side. A custom 447-nm light-emitting diode (LED) light source was used to illuminate the BY-coated glass through the polarizer film, there- DLCEA fabrication by photo-programming the BY molecule orientations. To program lo- In the next step of DLCEA fabrication (fig. S4), we attached compliant cally varying Gaussian curvature, the polarizer film was cut into pixels and electrodes to both sides of the LCE film using an electrically conductive then reassembled by hand on a glass slide with the desired orientations carbon grease, NyoGel 756G, frequently used in other DE systems (35). (see Fig. 4C). The thin layer of BY molecules rearranged perpen- To apply the carbon grease, the LCE was first clamped in 3D-printed dicular to the incident light polarization to create a spatially photo- plastic clips with copper tape leads designed to facilitate attaching the programmed command surface that then locally oriented the LCE device to the equipment used for tests described below and in the director (28). section Uniaxially aligned DLCEA characterization. Some degree of Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 6of9 | SCIENCE ADVANCES RESEARCH ARTICLE misalignment in the clamping process was unavoidable. The clipped From the system symmetry and inserting into this equation the re- LCE was held in a laser-cut Plexiglas assembly jig and masked with a lationship between the mechanical anisotropy, E /n = E /n , and the y yx x xy low-adhesive removable tape placed around the edges of the LCE film. assumption that v =0.5,we obtained values for n ≈ 0.04 and n ≈ xy yx yz The masking adhesive tape created a border region at the LCE edges 0.84. Taken with the measured values of the elastic moduli (Fig. 1C), with no electrode grease, which served to prevent shorting of the de- E and E , the stiffness tensor was fully defined. These values indicated x y vice during actuation at high voltages. A 2-mm gap around the edges that the LCE was unexpectedly compressible. However, this was un- was found to be sufficient to prevent shorting at the voltages tested (see likely and due to at least three factors: The capacitance Q factor de- Fig. 2A). The grease was applied by painting with a swab applicator, creased from 32 to 22 at 20% strain, and slight prestrains were and excess was removed with a straight paper edge. The entire Plexiglas unavoidable in measuring the moduli, E and E , of the LCE. These x y jig with LCE film was weighed before and after application of grease are in addition to the possibility of partially crystalline ordering (smec- electrodes to find the grease weight, whichwas typically30mgintotal tic C phase) as mentioned in the text. Together, these factors lead to an for both electrodes of the DLCEA. Other high-conductivity electrode error that may account for the apparent compressibility. materials can achieve better performance while adding much less Isometric tests were performed by quasistatically increasing ap- weight and cross-sectional area (7); alternative electrode materials will plied voltages to prestrained samples. Following capacitance measure- be studied in future studies of these actuators. ments, the DLCEA still clamped in the rheometer was strained to a fixed amount (5, 10, 15, and 20%) and then allowed to relax for a pe- Poisson’s ratio anisotropy and DLCEA isometric and riod until the creep in measured stress was much smaller than the in- isopotential tests duced stress (fig. S6A). The actuation voltage (Heinzinger LNC-10 kV) Throughout this work, we tested and actuated DLCEAs at room tem- was increased 100 V every 15 s starting from 500 V. The middle 5 s of perature and only in the linear regime where strains do not induce each period was sampled to measure the active change in stress due to reorientation of the LCE director. We typically found the onset of soft the applied voltage. The log-active nominal stress reduction versus log- mode deformation (director reorientation) at a critical strain of 45 to voltage relationship for all isometric strains had a slope of 2.0 (fig. S6B), 50% for n⊥u as in fig. S3. following the relationship given by the Maxwell stress equation. We characterized laser-cut uniaxial DLCEAs mechanically and Isopotential tests were performed by straining the DLCEA first with no electrically (Fig. 1C and fig. S2). Tensile tests were performed in a applied voltage, and then 2 kV was applied (fig. S7). The difference in in- TA Instruments DHR3, and simultaneous capacitance measurements duced stress between the 0- and 2-kV curves indicated the expected stroke were made with a Hameg 8118 LCR meter. Typically, the uniaxial when the DLCEA was operated as an actuator under a constant load. DLCEAs fabricated with 65-mm spacers and electrodes coated on both sides with an area of 1 cm by 3 cm have a zero strain capacitance of DLCEA isotonic tests approximately 300 pF. We observed a dependence between the rate of To characterize the fundamental properties of the LCE as a muscle- capacitance growth and the direction of the tensile strain of the LCE like actuator, we performed tests on DLCEAs strained by a constant film relative to the director. The capacitance of DLCEAs strained per- gravitational load, F . Weights hung from the DLCEA induced an pendicular to the director grew faster than those strained parallel to initial strain that thins the material, thus aiding in larger actuation the director. We can model how strains affect the DLCEA capacitance. for higher initial loadings. When a voltage was applied to the DLCEA The capacitance of a parallel-plate capacitor (or a DLCEA) is with n ⊥ F , the system adopted a new length due to the changed elastic response of the LCE. The LCE was strain stiffening, so the weight D D A stopped when the forces balanced; however, after an initial elastic re- 0 ⊥ C ¼ sponse, the DLCEA continued to creep because of the viscoelastic properties of the LCE. Gradually, the strain increased until it eventually where D is the permittivity of free space and D is the relative per- reached a steady state. After some time, an electrical short path was 0 ⊥ mittivity perpendicular to the liquid crystal director (note that the provided to the electrodes of the DLCEA by a custom switching mech- reactive mesogen used in this work, RM82, is known to have a neg- anism. The DLCEA was thus discharged and abruptly contracted elas- ative dielectric anisotropy, i.e., D > D ). The rectangular area covered tically and then continued to further contract slowly again owing to the ⊥ ‖ by the electrode is A = S × S , and the film thickness is d (see fig. S5 viscoelasticity (Fig. 2 and fig. S8). In the case of n‖F ,there is no appre- x y g for the schematic and coordinate system). When the DLCEA is ciable actuation along the loading direction because of the substantially strained by u (perpendicular to the director), the thickness decreases higher stiffness (movie S1); therefore, no further tests were conducted u = − u n and the width along x decreases u = −u n .The thick- on this configuration of DLCEA. z y yz x y yx ness and area become (1 + u )d =(1 − u n )d and (1 + u )S (1 + u )S = Simultaneously with the actuation, a high-speed camera (Vision z y yz y y x x (1 + u )(1 − u n )A, respectively. Thus, the capacitance becomes Research v641) was hand-triggered. For the contraction data presented y y yx in Fig. 2B, the camera captured at 1400 frames per second. The video frame during which the high voltage was switched was identified by a D D ð1 þ u Þð1  u n ÞA 0 ⊥ y y yx C ¼ pair of LEDs triggered by the same solid-state relay as the high-voltage ð1  u n Þd y yz switches. The discharge current was measured across a resistor di- vider pair in series with the DLCEA using an oscilloscope (Tektronix We next normalize by the capacitance at zero strain and then Taylor MDO4024C). A schematic of the high-voltage switching mechanism expand for small strains, i.e., to only the linear term used to measure discharge current by reading the voltage, V , across a known resistor, R , is shown in fig. S8A. The actuation also depended on the applied voltages, and for each load, voltages of 2, 2.5, and 3 kV C ¼ð1 þð1 þ n  n Þu Þ yz yx y were tested on the same DLCEA (fig. S8C). Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 7of9 | SCIENCE ADVANCES RESEARCH ARTICLE Video data from the contractile tests were tracked with Tracker modulus G ¼ E (with the assumption that Young’smodulus 13 11 Video Analysis (36) and then analyzed using custom Python scripts. and Bulk modulus are equal). The geometric boundary condition In these tests, the high voltage was switched on for approximately was defined as one-side clamped. The normal pressure load (100 kPa, 20 s before discharge so that the DLCEA would reach its actuated as a representative of Maxwell stress) was applied to the top side of the stable rest length. Initial distances were marked by hand in Tracker LCE sheet by considering the margin of the electrodes as 2 mm, and a Analysis and then compared to known component sizes to compute roller boundary condition was set to the bottom side of the LCE. A distances and, subsequently, energy, power, and efficiency measure- constant force was applied to the free edge of the LCE beam, opposite ments. Oscilloscope data were also analyzed using custom Python to the clamped edge, to induce deflection and simulated a gravita- code. A baseline capacitive charge was subtracted from the measured tional load. discharge by measuring the discharge with no DLCEA attached to the switch; each meter of high-voltage cable has a capacitance of approx- Efficiency comparison to thermal LCE actuation imately 100 pF. In the work by Petsch et al. (18), a thin wire heater was embedded The mechanical work done by the actuator while discharging was inside an aligned LCE. When heated, the device contracted along computed from the mass of the attached load, m ,and the its aligned direction. The reported 90% contraction response time displacement found by high-speed video, i.e., W = m gDh,where in that work was between 20 and 30 s. In the example reported in mech L g is the gravitational acceleration, 9.8 m/s ,and Dh is the displacement the text, they achieved a 1.85-mm stroke with a 2.25-g test load and of the mass. The electrical energy input to the system, W ¼ QV, 430 mW of input power. The stroke efficiency then is el was found by integrating the discharge current measured as a volt- age, V , over the known resistor, R , and multiplying by the applied 2 D D 2:25 g 9:8m=s 1:85 mm _ _ 6 voltage (e.g., 3 kV). Last, the efficiency was computed from the ratio ≈5  10 20 s 430 mW of these energies, W /W . _ mech el Finite element simulations of the effect of Poisson’s or about 0.0005% for the stroke only. To maintain that stroke, a con- ratio anisotropy stant current must be applied. The finite element simulations were carried out using the Structural Mechanics Module of COMSOL Multiphysics 5.3a (COMSOL, 2008). Uniaxially buckling DLCEA and frequency Several mesh refinement steps were performed to guarantee conver- response characterization gence of the results. For the no-load simulations of DLCEA (fig. S5B), A uniaxial LCE film was constrained at its edges by a laser-cut Plexiglas the LCE film was modeled as a thin anisotropic sheet (width, 14 mm; frame. The film was carefully placed on top of the frame so as not to length, 30 mm) with an initial thickness of 80 mm. The compliance and induce prestrain or leave any slack. A central square carbon grease stiffness matrices describing the anisotropic material with Voigt nota- electrode was painted onto the film on both sides through a low- tion were computed using five independent elastic constants adhesive removable tape mask. The in-plane length of the film grew along the soft direction, but because of the fixed boundary conditions, 2 3 1 n n it created a buckled wrinkling pattern. The height of the wrinkle pat- 12 13 00 0 tern was measured by laser confocal profilometry in the off state and 6 E E E 7 11 11 11 6 7 n 1 n every 250 V starting from 500 V to 2.5 kV. In the 2.5-kV activated 21 23 6 7 00 0 6 7 state, the out-of-plane peak-to-peak stroke was 1.47 mm or 1800% 6 E E E 7 22 22 22 6 7 n n 1 31 32 of the LCE film thickness, which was approximately 80 mm. 6 7 00 0 6 7 To determine the frequency response of the uniaxial buckling E E E 33 33 33 6 7 S ¼ 6 1 7 DLCEA, we applied a sinusoidally varying 1 kV supplied by a Physik 6 7 000 00 6 7 2G Instrumente E-107 piezo high-voltage amplifier. The input signal 6 7 6 1 7 was generated by a function generator (Tektronix). The motion of 6 000 0 0 7 6 7 the DLCEA membrane was observed by a Thorlabs Telesto optical 2G 4 5 coherence tomography microscope. The DLCEA film maximum height 000 0 0 2G was first found manually in the dc on state and subsequently observed in the same location for various frequencies (Fig. 3D and fig. S9B). C ¼ S Programmed buckling of DLCEA where the following relations are valid assuming that “1” is x, i.e., along The defect array was achieved by programming light polarization the nematic director from laser-cut squares of a linear polarizer film that was stitched back into the desired grid on a glass slide using NOA65 ultraviolet curing glue. The stitched pieces of polarizing squares were not perfectly be- n ¼ n ; n ¼ n ; n ¼ n ; n ¼ n ; 12 13 21 12 31 21 32 23 side each other because of imperfections in the laser-cutting step and difficulty in manual stitching. However, the unaligned boundaries be- G ¼ ; E ¼ E ; G ¼ G 23 22 33 13 12 2ð1 þ n Þ tween aligned regions in the LCE film were small and did not appar- ently affect the actuation response. To demonstrate the effect of anisotropy on the performance of Similar to the uniaxial buckling, after fabrication of the LCE and the actuator, we swept the value of E from 1 to 20 MPa while as- removing it from the BY-coated glass slides, we fixed the LCE film suming Poisson’sratios v =0.5 and n =0.9 − n and shear to a laser-cut Plexiglas frame and covered the programmed region 12 23 21 Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 8of9 | SCIENCE ADVANCES RESEARCH ARTICLE 18. S. Petsch, R. Rix, B. Khatri, S. Schuhladen, P. Müller, R. Zentel, H. Zappe, Smart artificial with electrically conductive carbon grease. The programmed region muscle actuators: Liquid crystal elastomers with integrated temperature feedback. was easily distinguished under ambient lighting from the surrounding Sens. Actuators A Phys. 231,44–51 (2015). areas because of the mismatch in the index of refraction between iso- 19. C. M. Spillmann, J. Naciri, B. R. Ratna, R. L. B. Selinger, J. V. 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Nature 410, 447–450 Published 22 November 2019 (2001). 10.1126/sciadv.aay0855 16. T. Guin, B. A. Kowalski, R. Rao, A. D. Auguste, C. A. Grabowski, P. F. Lloyd, V. P. Tondiglia, B. Maruyama, R. A. Vaia, T. J. White, Electrical control of shape in voxelated liquid Citation: Z. S. Davidson, H. Shahsavan, A. Aghakhani, Y. Guo, L. Hines, Y. Xia, S. Yang, M. Sitti, crystalline polymer nanocomposites. ACS Appl. Mater. Interfaces 10, 1187–1194 (2018). Monolithic shape-programmable dielectric liquid crystal elastomer actuators. Sci. Adv. 5, 17. R. Verduzco, Shape-shifting liquid crystals. Science 347, 949–950 (2015). eaay0855 (2019). Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 9of9 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Science Advances Pubmed Central

Monolithic shape-programmable dielectric liquid crystal elastomer actuators

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SCIENCE ADVANCES RESEARCH ARTICLE MATERIALS SCIENCE Copyright © 2019 The Authors, some rights reserved; Monolithic shape-programmable dielectric liquid exclusive licensee American Association crystal elastomer actuators for the Advancement of Science. No claim to 1 1 1 1 1 Zoey S. Davidson *, Hamed Shahsavan , Amirreza Aghakhani , Yubing Guo , Lindsey Hines , original U.S. Government 2 2 1,3 Yu Xia , Shu Yang , Metin Sitti Works. Distributed under a Creative Soft robotics may enable many new technologies in which humans and robots physically interact, yet the nec- Commons Attribution essary high-performance soft actuators still do not exist. The optimal soft actuators need to be fast and forceful NonCommercial and have programmable shape changes. Furthermore, they should be energy efficient for untethered applica- License 4.0 (CC BY-NC). tions and easy to fabricate. Here, we combine desirable characteristics from two distinct active material systems: fast and highly efficient actuation from dielectric elastomers and directed shape programmability from liquid crystal elastomers. Via a top-down photoalignment method, we program molecular alignment and local- ized giant elastic anisotropy into the liquid crystal elastomers. The linearly actuated liquid crystal elastomer monoliths achieve strain rates over 120% per second with an energy conversion efficiency of 20% while moving loads over 700 times the elastomer weight. The electric actuation mechanism offers unprecedented opportu- nities toward miniaturization with shape programmability, efficiency, and more degrees of freedom for applica- tions in soft robotics and beyond. INTRODUCTION A high voltage applied to the compliant electrodes induces an The underlying rigid actuation mechanisms of traditional robotics, electrostatic pressure, so-called Maxwell stress, and, hence, deforms electric motors, or hydraulic and pneumatic actuators hinder robot the DE. The electrical actuation mechanism can result in a much higher miniaturization and, more importantly, robot use in human collab- operating efficiency (ratio of mechanical work to input electrical energy) orative environments. Compliant actuators are the missing key to and a higher actuation speed than those of LCEs (7, 8). Besides enabling robots to interface with humans (1). The ideal compliant functioning as soft linear actuators, DE actuators could be applied to soft actuators will have high efficiency, strength-to-weight ratio, work grippers, haptic devices, or optical devices, which, however, require capacity, and shape programmability to perform complex functions. complex shape change (6). Despitesomeimpressivedemonstrations, Like an artificial muscle, soft actuators with these properties would DE actuators have not yet gained widespread use in soft robotics partly substantially advance technologies for potential applications in aero- because of the need for prestrain or the challenge of fabricating devices space, robotics, medical devices, energy harvesting devices, and wear- with complex deformation profiles (14). Overcoming these challenges ables (2–4). Among many soft actuators that have been explored, and expanding the applications of DE actuators require material dielectric elastomers (DEs) appear promising and even outperform innovation for the next generation of high-performance DEs with skeletal muscle in some aspects (5–8). Separately, liquid crystal elasto- shape programmability (20, 21). mers (LCEs) have demonstrated reversible large mechanical deforma- LCEs are rubbery polymers with anisotropic bulk properties im- tion by light actuation and thermal actuation near the phase transition parted by their constituent molecular anisotropy. Most prior works temperature (9, 10). Recent advances in photoalignment and micro- on LCE actuation have focused on thermal or light-driven mechanisms. fabrication techniques have enabled preprogramming of liquid crys- Heat or light temporarily disrupts the anisotropic molecular order, tal alignment in microscopic regions for complex shape morphing known as the director field (n), thereby creating internal stresses and (11, 12). However, both actuator types have their drawbacks: DE anisotropic bulk deformation (10, 11, 18). The local LCE director field films need to be prestrained macroscopically (13) or require multi- can be preprogrammed to create complex shape changes when actu- step fabrication methods, which make it difficult to program minia- ated. However, light actuation is inefficient, and thermal actuation is turized actuators with local shape changing (14). Meanwhile, direct both slow and inefficient; thus, they are poorly suited for applications conversion of electrical energy to mechanical work using LCEs has, that require high energy efficiency and fast actuation such as robotics. until now, remained limited because of the small strains generated Direct electrical actuation of LCEs is a highly sought-after technology (15–19). However, we demonstrate that the ability to pattern LCE (17). A few previous studies have demonstrated electrical actuation of molecules in a locally varying alignment, thus tailoring spatial var- LCEs by coupling an electric field to the molecular dielectric anisotro- iations of the mechanical compliance, enables more efficient DE ac- py or sometimes to the intrinsic polarization of the LCE or LCE tuators with preprogrammable degree and direction of actuation. composite; thus, an electric field drives molecular reorientation to cre- Typically, DE actuators function by the electrostatic attraction ate bulk strains. However, these methods require elevated tempera- between two compliant electrodes coated on opposing sides of tures or use of carbon nanotubes to enhance the electric response; an isotropic DE to form a variable resistor-capacitor (Fig. 1A) (13). otherwise, only small actuation strains are produced at room tempera- ture (15, 16, 22–24). In this work, we directly exploit the large mechanical anisotropy of LCEs without relying on molecular rotation Physical Intelligence Department, Max Planck Institute for Intelligent Systems, during electric actuation. We further use recent advances in the Stuttgart, Germany. Department of Materials Science and Engineering, University patterning of LCE films to tailor the local anisotropic elasticity and of Pennsylvania, Philadelphia, PA, USA. School of Medicine and School of Engi- Poisson’s ratios for highly efficient and shape-programmable DEs, neering, Koç University, Istanbul, Turkey. *Corresponding author. Email: davidson@is.mpg.de which we refer to as a dielectric LCE actuator (DLCEA; Fig. 1B). By Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 1of9 | SCIENCE ADVANCES RESEARCH ARTICLE Fig. 1. Device schematic, mechanical, and electrical characterization. (A) Schematic of a traditional isotropic DE actuator in off and on states. (B) Schematic of a uniaxial aligned dielectric LCE actuator (DLCEA) in off and on states. Liquid crystal molecular alignment; the director, n, is indicated by a double-headed arrow and defines the stiffer direction of the LCE. When actuated by a voltage, V, the material thins and stretches perpendicular to the alignment greater than parallel to the director. (C) The DLCEA mechanical stress and normalized capacitance (C) response to strain over the DLCEA linear regime are characterized at a strain rate of 0.1% per second. aligning LCE molecules in local domains, we achieve electric-driven field (fig. S5A). Using a simplified finite element model, we find, for actuation and shape morphing at room temperature and demonstrate large elastic anisotropy, that a given Maxwell stress produces nearly large, fast, and forceful strains. two times the linear expansion strain observed in an isotropic material with a modulus equal to the soft direction (fig. S5B). Other works with similar LCE chemistry have observed one-dimensional (1D) trans- RESULTS lational crystallinity, which may explain the particularly large elastic Uniaxially aligned DLCEA characterization anisotropy observed in this work (27, 29). The LCE films are fabricated in a two-step process recently developed We then characterized uniaxial DLCEAs in isometric (constant by some of the authors (25, 26). Briefly, an oligomer is synthesized strain; Fig. 2A) and isotonic (constant force; Fig. 2B) configurations. In before LCE film fabrication by a thiol-acrylate click reaction; a com- isometric tests, we applied initial strains to DLCEA devices and mon diacrylate reactive liquid crystal monomer is chain-extended by allowed a relaxation period before the application of high voltages Michael addition with a dithiol linker molecule. The exact component (fig. S6A). From the active stress reduction, we observe two relation- ratios, choice of monomer, and dithiol linker can all be tuned to adjust ships between the strain, the voltage applied, and active stresses, which 2 2 the specific mechanical properties of the final LCE film (26, 27). We fit with the model of Maxwell stress, p º V /d ,where V is the ap- es produced large areas of a well-ordered uniaxial LCE (figs. S1 and S2) plied voltage and d is the LCE film thickness. First, actuation at larger with giant elastic anisotropy (Fig. 1C). In all experiments, we actuated initial strains produces higher active nominal stress reductions; the DLCEAs at room temperature and only in the linear regime of strains isometric prestrain results in thinning of the LCE and, thus, higher (fig. S3). We can also locally program the LCE director field by photo- Maxwell stress for a given voltage (Fig. 2A). With an LCE, it appears alignment to create a spatially programmed command surface and to that additional strain thins the material at a rate fast enough to offset locally orient the LCE director (28). Last, we applied compliant grease the increasing restoring force such that a given actuation voltage electrodes to both sides of the LCE film to create the DLCEA devices results in larger active stresses. We also observe that, for each fixed (fig. S4). Further details can be found in Materials and Methods. strain, the active nominal stress reduction during isometric tests in- To characterize the fundamental properties of DLCEAs, we first creases quadratically with increasing voltage (fig. S6B). At the highest made monodomain, uniaxially aligned LCE films. The electrodes voltages tested, we measured peak active nominal stress reduction in coated on uniaxial DLCEAs enable simultaneous measurement of excess of 50 kPa. However, for the device with the director, n||u,the capacitance and stress versus strain applied to the LCE film (Fig. 1C). active stresses are relatively much smaller because of the much higher When strains (u) are applied parallel to the director, n||u, the LCE is modulus. When held with an isometric strain, the DLCEA behaves more than an order of magnitude stiffer than when strains are ap- like a variable stiffness spring, and in the case of n⊥u, 5% initial strain, plied perpendicular to the director, n⊥u, which indicates a high de- and 2 kV actuation voltage, the Maxwell stress–induced expansion of gree of elastic anisotropy. Similarly, the difference in slope of the the LCE nearly compensates for the entirety of the isometric strain– normalized capacitance between the DLCEA devices with different induced stress. We also performed isopotential tests in which the director orientation indicates anisotropy in Poisson’sratio.TheDLCEA DLCEA is strained under a constant voltage. These tests indicate capacitance is proportional to the area of the film coated by the electrode the expected actuation stroke of a loaded DLCEA when a voltage is and inversely proportional to the film thickness. Thus, Poisson’sratio applied (fig. S7). anisotropy causes the film’s thickness and area to change at different Next, we take the same DLCEA and perform isotonic tests by sus- rates depending on the direction of strain relative to the LCE director pending varying weights from the free end of the DLCEA to generate Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 2of9 | SCIENCE ADVANCES RESEARCH ARTICLE Fig. 2. Characterization of uniaxial DLCEA demonstrates the capabilities of a DLCEA actuator device. (A) Isometric (constant strain) tests. Measured active nominal stress reduction with various initial isometric strains (u) for devices assembled with the LCE director n⊥u and n‖u and a photograph of an assembled DLCEA device with n⊥u.(B) Isotonic (constant force) tests. Contractile discharge strain trajectories under various loads measured by a high-speed camera with actuation voltages of 3 kV. Inset: The corresponding measurements of electrical discharge. (C) Fundamental actuator characteristics are computed from the contraction trajectory and measurement of ^ ^ the discharge current found in (B), including strain (u), peak strain rate (u ), peak specific power P ), specific energy (E), and efficiency. Photo credits: Zoey S. Davidson. peak peak constant load forces and initial nominal strains, u (Fig. 2B and fig. the DLCEA contraction trajectory, we compute fundamental perform- S8). DLCEAs in the n||u configuration do not show an appreciable ance metrics both for the pure elastic response and for the extended active strain at any initial loading for even the highest voltages tested creeping contraction (Fig. 2C and fig. S8C). because of their significantly higher elastic modulus (movie S1). However, DLCEAs with the n⊥u configuration exhibit fast active Complex programmable shape actuation strains up to 5% with the application of 3 kV for the heaviest loading To achieve complex shape actuation, LCEs typically function by tested, 0.27 N, approximately 790 times the weight of the bare LCE programming spatially varying in-plane contractilestrainwhenheated film (35 mg). We perform isotonic contractile tests by abruptly above a phase transition. However, the DE actuation mechanism is not discharging weighted DLCEA devices and capture the subsequent based on a heat induced phase transition, but generates in-plane ex- motion with high-speed video (fig. S8B and movie S2). With in- pansion strains. Thus, boundary conditions play a significant role in creasing load and initial strain, the DLCEA capacitance increases, determining the realized DLCEA shape change. To better understand which can be seen in the shifted discharge curves in the inset of the role of boundary conditions on DLCEAs, we performed a funda- Fig. 2B. In all cases, the electrical discharge time, approximately mental characterization of the bucklingeffect causedbythe elastomer’s 1 ms, is much faster than that needed for the contraction of DLCEA, expansion between fixed boundaries (Fig. 3, A and B, and movie S3). within 60 ms, which indicates that the system is currently limited by The buckling amplitude increases with increasing voltage and, at 2.5 kV, the viscoelastic properties of the LCE. We also observed significant creates out-of-plane peak-to-peak strokes greater than 1800% of the viscous losses in the contractions that are apparent from the continued LCE film thickness of approximately 80 mm corresponding to a linear creeping contraction after the initial elastic response (fig. S8B). From strain of approximately 5% (Fig. 3C and fig. S9A). Actuation speed is Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 3of9 | SCIENCE ADVANCES RESEARCH ARTICLE another important characteristic for potential DLCEA applications. We tuated DLCEA in Fig. 4F shows that the defects could buckle both up applied a sinusoidally varying 1-kV potential to measure the change in and down. actuation amplitude as a function of the applied frequency (Fig. 3D and fig. S9B). The actuation amplitude decays exponentially with the fre- quency but is still a perceivable 50 mmat30Hzand 1kV. DISCUSSION We designed spatially varying LCE director configurations, aiming When using the DLCEA as a linear actuator, we expect larger anisot- to demonstrate the ability to preprogram complex patterns in 2D, ropy in Poisson’s ratio to produce higher efficiency and require lower followed by electrical actuation of the films into 3D forms (11, 25). electric fields for actuation compared to a similar isotropic material Depending on the programmed director field, the LCE film buckles (32). Compared to other LCE actuators, the actuation efficiency of out of plane with locally positive (Fig. 4A) or negative Gaussian cur- approximately 20% reported here is remarkable; to our knowledge, vature (Fig. 4B). These shapes are often called cones and anti-cones, actuation efficiency in LCEs has not been reported before owing to and the theory describing this form of deformation in elastic media their low energy conversion efficiency, which we estimate, for exam- was previously described by Modes et al. (30). We understand these ple, to be less than 0.001% in a thermally actuated LCE according to shape changes by considering a simplified model of an anisotropic DE (18). Note that this estimate is based on the initial stroke only; a con- made from stiff concentric rings embedded in a soft elastomer (31). stant current is needed to maintain LCE in the contracted state. Fur- These rings prevent expansion along the rings but allow expansion thermore, our DLCEA efficiency compares favorably to a recent in the radial direction leading to a frustration and out-of-plane buckling. example of an isotropic DE actuator with highly optimized electrodes, A similar argument holds for radial stiff elements. The double-headed reporting 1.5% efficiency (7). We expect that reducing viscous loss and red arrows in Fig. 4 (A and B) indicate the soft expansion directions. creep, indicated here by the hysteresis loop in Fig. 1C and extended con- We created a pixelated array of topological defects by spatially pro- traction in Fig. 2B, will further improve the situation for fast and effi- gramming light polarization with a pattern of linear film polarizers cient DLCEAs. (Fig. 4C) to locally orient the LCE director as in Fig. 4D. The director We believe that the demonstrated high efficiency reported in our forms a lattice of radial and azimuthal defect types that, when elec- system is due to the anisotropy of the elastic modulus and Poisson’s trically actuated, buckle out of plane because of incompatible in- ratio. Generally speaking, elastomers are volume conserving; thus, planestrains (Fig.4Eand movieS4).Wemeasuredthe height of extension in one direction causes a contraction in the other directions. the DLCEA surface in the discharged (0 V) and actuated (2.5 kV; However, the contraction in LCE films is greater perpendicular to the Fig. 4F) states. To do so, we stably held the device in its actuated shape director. In other words, when an LCE film is strained perpendicular at 2.5 kV for more than 3 hours while drawing less than 1 mA, con- to the director, it contracts in thickness, which is also perpendicular to firming its high stability and low power consumption. The locally the director, and thus faster than the contraction in width that is programmed height change and the accompanying formation of parallel to the director. When strained parallel to the director, the Gaussian curvatures are clearly visible from the circular traces enclos- LCE contracts equally in both thickness and width (assuming that ing the central radial defect type (Fig. 4G). The out-of-plane buckling the cross section is isotropic). It is worth mentioning that this last creates peak-to-peak height differences of over 1600 mm, a 2000% point is not certain: As mentioned previously, 1D translation crystal- growth from the initial film thickness of approximately 80 mm linity is common in this class of LCE (27, 29). In particular, the 1D corresponding to a 22% areal strain. The lower right corner of the ac- crystal planes may be at some angle to the LCE director, thus breaking Fig. 3. Uniaxial out-of-plane buckling DLCEA. (A) Off and (B) on states of a uniaxial DLCEA device with fixed boundary condition. Expansion along the soft direction creates out-of-plane buckling, which displaces a fine thread held taut across the surface. (C) Experimental measurement of buckling as a function of the applied voltage. (D) Frequency response of buckling uniaxial DLCEA at 1 kV. The 0.1-Hz actuation amplitude is approximately 130 mm. Photo credits: Zoey S. Davidson. Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 4of9 | SCIENCE ADVANCES RESEARCH ARTICLE Fig. 4. Pixelated DLCEA. Programmed shape actuation, such as a dimple pattern deformation, is possible by patterning the director configuration into an azimuthal- radial defect lattice. (A) Azimuthal defect types deform into a cone with locally positive Gaussian curvature, and (B) radial defect types deform into an anti-cone with locally negative (saddle-like) Gaussian curvature. In (A) and (B), the double-headed red arrows indicate the soft direction. (C) The defects are patterned using a pixelated array of polarizing films with the designed local orientations. (D) Viewed through crossed polarizers, the fabricated LCE film has pixelated uniaxial alignment, indicated by dashed white lines, forming a defect lattice. (E) When charged to 2.5 kV, there is a large visible deformation of the surface. (F) The profilometry measured height map of the grease-covered LCE is nearly flat with no charge and varies over 1.6 mm when charged to 2.5 kV. The dash-dot and dash circles in (F) are traces of height depicted in (G). The change from approximately constant height to a sinusoidally varying height indicates a change in sign of the local Gaussian curvature. Scale bars, 4 mm. Photo credits: Zoey S. Davidson. the symmetry informing the assumption of equal contraction in width the DLCEA is multistable, we only ever observe a single actuated state and thickness when straining parallel to the director. Tuning this 1D for each sample (11). We hypothesize that the symmetry that would crystallinity may play an important role in further improving the enable multistability is likely broken by gravity during the tests or by linear actuation capabilities of DLCEAs. uneven photocrosslinking of LCE films during device fabrication. To further illuminate the advantages of elastic anisotropy, we Nevertheless, our demonstration of local changes in the Gaussian cur- consider a simplified DE model with a nearly volume-conserving vature indicates that our method can be potentially generalized to rea- elastomer material having large Poisson’s ratio anisotropy and under lize a large variety of programmable shape changes (30). In addition to no load (see fig. S5). In this model, nearly all compression strain due programming in-plane director orientations, it is also possible to to the Maxwell stress creates an extension strain in the soft direction program the LCE director orientation along the film thickness. As of the elastomer. In other words, the Maxwell strain through the seen in fig. S10, we have assembled DLCEAs with a twisted LCE con- thickness of the material, u = P /E , results in strain u and nearly figuration where the director rotates by nearly 90° from the top to the z es z y no strain u . In an isotropic elastomer, the same Maxwell strain bottom surface. When an electric field is applied, the twisted DLCEA would result in only half as much strain because the volume-conserving produces twisting motions where the magnitude depends on the LCE strain would be split evenly into u and u . For linear actuators, this is geometry in addition to the material’s intrinsic properties (33). x y thefirst advantageofaDLCEA; theactuation voltageneededto achieve a given strain is reduced. The second advantage of anisotro- py to linear actuators comes from energetic considerations of the CONCLUSION same system. The elastic energy density of deformation is quadratic Here, by combining the desirable characteristics of DEs and LCEs in a in strain; thus, in the simplified model presented here, there will be single material platform, we demonstrate superior actuation per- no energy component from strains in the x direction. Furthermore, formance from electrically actuated DLCEAs, including high energy for a given desired linear extensional strain, the input electric field conversion efficiency (20%), high actuation speed (120% per second), 2 2 energy (º V /d ) will also be less because the required Maxwell and programmable shape change from 2D to 3D with more than strain is smaller than in an isotropic DE. Thus, an anisotropic DE 1800% out-of-plane stroke. To achieve larger actuation forces, multi- actuator can achieve an equivalent strain as an isotropic DE linear layer DLCEA stacks could be an option, as demonstrated in LCE and actuator, but with higher efficiency. Both the no-load and perfect DE multilayer stacks (7, 34), although it would require the develop- uniaxial elastomer assumptions may be relaxed, and viscoelastic ment of an alternative soft electrode. Furthermore, even more general effects may be added to build a more complete model. shape changes, i.e., nonlocal Gaussian curvature, may be realized by The material Poisson’s ratio anisotropy is also an important fea- spatially programming both the LCE alignment and local cross-linking ture for enabling programmed shape change actuation. The actuated density. (compressed) LCE transversely expands anisotropically to create the Insights into the integration of active materials with top-down observed shape changes. Although, in principle, the buckled shape of microfabrication techniques and electroactuation mechanism presented Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 5of9 | SCIENCE ADVANCES RESEARCH ARTICLE here could offer exciting opportunities when coupling DLCEAs with LCE fabrication and characterization 3D printing, origami and kirigami actuation strategies, and distributed The previously prepared oligomer was melted together with additional control systems toward creating multifunctional soft robots in a scal- RM82 and a small amount of photoinitiator to cross-link the oligomer able fashion at a low material and build cost. The electroactuation chains into an elastomer network. Inmoredetail, theLCE oligomerand mechanism can also be applied to other technologies, including energy an additional RM82 LCE monomer were melted together in 1:1 molar harvesting and storage, medical devices, wearable technology, and ratio, assuming that the oligomer consists purely of chains of single- aerospace. Furthermore, fast and dynamic modulation could be useful unit length RM82 capped by 1,5-PDT on both ends (26). Thus, the in displays and optical applications. mixture consisted of excess thiol groups, which were likely responsible for a significant portion of the final LCE viscous losses (see the section Uniaxially aligned DLCEA characterization), but this sparse cross- MATERIALS AND METHODS linking also promoted softness necessary to achieve larger actuation Materials strains. The melt was mixed for only 2 to 3 min at 120°C and then de- 1,5-Pentanedithiol (1,5-PDT; >99%), 1,8-diazabicycloundec-7-ene gassed forapproximately 3 minina vacuum oven at 90°C. One weight (DBU), butylatedhydroxytoluene (BHT), and magnesium sulfate percent DMPA was added and carefully stirred in so as not to reintro- (MgSO ; anhydrous powder) were purchased from Sigma-Aldrich duce air bubbles. and used as received. Hydrochloric acid (HCl), dimethylformamide The isotropic LCE melt was then poured onto the BY-coated glass (DMF), and dichloromethane (DCM) were purchased from Fischer at 80°C and then carefully sandwiched with a second hot BY-coated Scientific. The photoinitiator 2,2-dimethoxy-2-phenylacetophenone glass substrate. The BY-LCE-BY sandwich was cooled into the aligned (DMPA) was purchased from Toronto Research Chemicals. Brilliant (nematic) phase, approximately 73°C, and then gradually cooled to Yellow (BY) was purchased from Tokyo Chemical Industry. The liquid room temperature during which time it aligned with the spatial crystal monomer, 1,4-bis-[4-(6-acryloyloxy-hexyloxy)benzoyloxy]-2- programming imparted by the BY coating, and the defects arising methylbenzene (RM82; >95%), was purchased from Wilshire Technol- from the phase transition were annealed. Once the LCE cools to room ogies Inc. and used without further purification. Conductive carbon temperature, it was cured in ultraviolet light with an OmniCure S2000 grease, NyoGel 756G, was purchased from Newgate Simms. arc source. After exposure to ultraviolet light polymerized the LCE in its programmed state, we immersed the BY-LCE-BY sandwich in wa- LCE oligomer synthesis ter to release the LCE from the BY-coated glass substrates. We fabricated LCE films in a two-step process recently developed by The final LCE film thickness was confirmed by confocal laser some of the authors (25, 26). An oligomer was synthesized before profilometry from regions cut to make actuators (described below). LCE film fabrication by a thiol-acrylate click reaction; the reactive Good alignment and few defects in the LCE are essential character- liquid crystal monomer RM82 was chain-extended by Michael addi- istics of the film to impart the largest possible elastic anisotropy and tion with 1,5-PDT. In a typical synthesis, 12.5 g of RM82 was mixed achieve optimal materials properties. The high contrast between the with 5.06 g of 1,5-PDT in 120 ml of DCM with three drops of DBU orientations of the LCE between crossed polarizers is visible in fig. S1. catalyst. After 16 hours of stirring at room temperature, the solution After sheets of LCE were separated from the glass substrates, they was rinsed in a separation funnel with 1 M HCl, 0.1 M HCl, and deio- were rinsed in water to remove residual BY and dried with nitrogen. nized water successively. The DCM-product mixture was then dried The LCE sheets were placed back on glass substrates and carefully in- with 25 g of MgSO for 30 min, which was then filtered. BHT (50 mg) spected to identify the defect and bubble-free regions for the fabrica- was added to the clear DCM and product mixture before rotary evap- tion of DLCEA devices. For uniaxial DLCEA devices, the cleanest oration and direct vacuum until a thick white oligomer remained. The identified regions were cut into rectangular pieces typically 14 mm oligomer was stored at −30°C for up to 2 months. by 34 mm with a typical weight of 35 mg. This size film was chosen for ease of handling and for the electrical actuation constraints de- Substrate preparation scribed below. Smaller neighboring regions, 20 mm by 5 mm, were Glass slides, typically 5 cm by 5 cm and 8 cm by 10 cm, were cleaned used to initially characterize the stress-strain behavior of the LCE in an ultrasound bath with deionized water, isopropanol, and ace- and the large strain behavior. tone. Next, the slides were dried with nitrogen and then treated by The edges of the laser-cut regions on the larger film were then oxygen plasma. A mixture of 1 weight % BY dissolved in DMF was spin- inspected by laser confocal interferometry (KEYENCE VK-X210) to coated onto the slides and then dried on a hot plate at 120°C. Spacers cut confirm the as-fabricated height of the LCE films. We found that from polyimide or Mylar plastic, with thicknesses of 65 or 75 mm, were nominally 65-mm Kapton produces approximately 70-mm LCE films placed along the edges on one of the BY coat sides of the glass slides; and that nominally 75-mm Mylar produces approximately 83-mmLCE then, two slides were placed with the BY-coated faces toward each other. films. The thicknesses may vary by as much as ±10% across the as- Large paper clips held the slides together with a polarizer film placed on produced LCE sheet (fig. S2). one side. A custom 447-nm light-emitting diode (LED) light source was used to illuminate the BY-coated glass through the polarizer film, there- DLCEA fabrication by photo-programming the BY molecule orientations. To program lo- In the next step of DLCEA fabrication (fig. S4), we attached compliant cally varying Gaussian curvature, the polarizer film was cut into pixels and electrodes to both sides of the LCE film using an electrically conductive then reassembled by hand on a glass slide with the desired orientations carbon grease, NyoGel 756G, frequently used in other DE systems (35). (see Fig. 4C). The thin layer of BY molecules rearranged perpen- To apply the carbon grease, the LCE was first clamped in 3D-printed dicular to the incident light polarization to create a spatially photo- plastic clips with copper tape leads designed to facilitate attaching the programmed command surface that then locally oriented the LCE device to the equipment used for tests described below and in the director (28). section Uniaxially aligned DLCEA characterization. Some degree of Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 6of9 | SCIENCE ADVANCES RESEARCH ARTICLE misalignment in the clamping process was unavoidable. The clipped From the system symmetry and inserting into this equation the re- LCE was held in a laser-cut Plexiglas assembly jig and masked with a lationship between the mechanical anisotropy, E /n = E /n , and the y yx x xy low-adhesive removable tape placed around the edges of the LCE film. assumption that v =0.5,we obtained values for n ≈ 0.04 and n ≈ xy yx yz The masking adhesive tape created a border region at the LCE edges 0.84. Taken with the measured values of the elastic moduli (Fig. 1C), with no electrode grease, which served to prevent shorting of the de- E and E , the stiffness tensor was fully defined. These values indicated x y vice during actuation at high voltages. A 2-mm gap around the edges that the LCE was unexpectedly compressible. However, this was un- was found to be sufficient to prevent shorting at the voltages tested (see likely and due to at least three factors: The capacitance Q factor de- Fig. 2A). The grease was applied by painting with a swab applicator, creased from 32 to 22 at 20% strain, and slight prestrains were and excess was removed with a straight paper edge. The entire Plexiglas unavoidable in measuring the moduli, E and E , of the LCE. These x y jig with LCE film was weighed before and after application of grease are in addition to the possibility of partially crystalline ordering (smec- electrodes to find the grease weight, whichwas typically30mgintotal tic C phase) as mentioned in the text. Together, these factors lead to an for both electrodes of the DLCEA. Other high-conductivity electrode error that may account for the apparent compressibility. materials can achieve better performance while adding much less Isometric tests were performed by quasistatically increasing ap- weight and cross-sectional area (7); alternative electrode materials will plied voltages to prestrained samples. Following capacitance measure- be studied in future studies of these actuators. ments, the DLCEA still clamped in the rheometer was strained to a fixed amount (5, 10, 15, and 20%) and then allowed to relax for a pe- Poisson’s ratio anisotropy and DLCEA isometric and riod until the creep in measured stress was much smaller than the in- isopotential tests duced stress (fig. S6A). The actuation voltage (Heinzinger LNC-10 kV) Throughout this work, we tested and actuated DLCEAs at room tem- was increased 100 V every 15 s starting from 500 V. The middle 5 s of perature and only in the linear regime where strains do not induce each period was sampled to measure the active change in stress due to reorientation of the LCE director. We typically found the onset of soft the applied voltage. The log-active nominal stress reduction versus log- mode deformation (director reorientation) at a critical strain of 45 to voltage relationship for all isometric strains had a slope of 2.0 (fig. S6B), 50% for n⊥u as in fig. S3. following the relationship given by the Maxwell stress equation. We characterized laser-cut uniaxial DLCEAs mechanically and Isopotential tests were performed by straining the DLCEA first with no electrically (Fig. 1C and fig. S2). Tensile tests were performed in a applied voltage, and then 2 kV was applied (fig. S7). The difference in in- TA Instruments DHR3, and simultaneous capacitance measurements duced stress between the 0- and 2-kV curves indicated the expected stroke were made with a Hameg 8118 LCR meter. Typically, the uniaxial when the DLCEA was operated as an actuator under a constant load. DLCEAs fabricated with 65-mm spacers and electrodes coated on both sides with an area of 1 cm by 3 cm have a zero strain capacitance of DLCEA isotonic tests approximately 300 pF. We observed a dependence between the rate of To characterize the fundamental properties of the LCE as a muscle- capacitance growth and the direction of the tensile strain of the LCE like actuator, we performed tests on DLCEAs strained by a constant film relative to the director. The capacitance of DLCEAs strained per- gravitational load, F . Weights hung from the DLCEA induced an pendicular to the director grew faster than those strained parallel to initial strain that thins the material, thus aiding in larger actuation the director. We can model how strains affect the DLCEA capacitance. for higher initial loadings. When a voltage was applied to the DLCEA The capacitance of a parallel-plate capacitor (or a DLCEA) is with n ⊥ F , the system adopted a new length due to the changed elastic response of the LCE. The LCE was strain stiffening, so the weight D D A stopped when the forces balanced; however, after an initial elastic re- 0 ⊥ C ¼ sponse, the DLCEA continued to creep because of the viscoelastic properties of the LCE. Gradually, the strain increased until it eventually where D is the permittivity of free space and D is the relative per- reached a steady state. After some time, an electrical short path was 0 ⊥ mittivity perpendicular to the liquid crystal director (note that the provided to the electrodes of the DLCEA by a custom switching mech- reactive mesogen used in this work, RM82, is known to have a neg- anism. The DLCEA was thus discharged and abruptly contracted elas- ative dielectric anisotropy, i.e., D > D ). The rectangular area covered tically and then continued to further contract slowly again owing to the ⊥ ‖ by the electrode is A = S × S , and the film thickness is d (see fig. S5 viscoelasticity (Fig. 2 and fig. S8). In the case of n‖F ,there is no appre- x y g for the schematic and coordinate system). When the DLCEA is ciable actuation along the loading direction because of the substantially strained by u (perpendicular to the director), the thickness decreases higher stiffness (movie S1); therefore, no further tests were conducted u = − u n and the width along x decreases u = −u n .The thick- on this configuration of DLCEA. z y yz x y yx ness and area become (1 + u )d =(1 − u n )d and (1 + u )S (1 + u )S = Simultaneously with the actuation, a high-speed camera (Vision z y yz y y x x (1 + u )(1 − u n )A, respectively. Thus, the capacitance becomes Research v641) was hand-triggered. For the contraction data presented y y yx in Fig. 2B, the camera captured at 1400 frames per second. The video frame during which the high voltage was switched was identified by a D D ð1 þ u Þð1  u n ÞA 0 ⊥ y y yx C ¼ pair of LEDs triggered by the same solid-state relay as the high-voltage ð1  u n Þd y yz switches. The discharge current was measured across a resistor di- vider pair in series with the DLCEA using an oscilloscope (Tektronix We next normalize by the capacitance at zero strain and then Taylor MDO4024C). A schematic of the high-voltage switching mechanism expand for small strains, i.e., to only the linear term used to measure discharge current by reading the voltage, V , across a known resistor, R , is shown in fig. S8A. The actuation also depended on the applied voltages, and for each load, voltages of 2, 2.5, and 3 kV C ¼ð1 þð1 þ n  n Þu Þ yz yx y were tested on the same DLCEA (fig. S8C). Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 7of9 | SCIENCE ADVANCES RESEARCH ARTICLE Video data from the contractile tests were tracked with Tracker modulus G ¼ E (with the assumption that Young’smodulus 13 11 Video Analysis (36) and then analyzed using custom Python scripts. and Bulk modulus are equal). The geometric boundary condition In these tests, the high voltage was switched on for approximately was defined as one-side clamped. The normal pressure load (100 kPa, 20 s before discharge so that the DLCEA would reach its actuated as a representative of Maxwell stress) was applied to the top side of the stable rest length. Initial distances were marked by hand in Tracker LCE sheet by considering the margin of the electrodes as 2 mm, and a Analysis and then compared to known component sizes to compute roller boundary condition was set to the bottom side of the LCE. A distances and, subsequently, energy, power, and efficiency measure- constant force was applied to the free edge of the LCE beam, opposite ments. Oscilloscope data were also analyzed using custom Python to the clamped edge, to induce deflection and simulated a gravita- code. A baseline capacitive charge was subtracted from the measured tional load. discharge by measuring the discharge with no DLCEA attached to the switch; each meter of high-voltage cable has a capacitance of approx- Efficiency comparison to thermal LCE actuation imately 100 pF. In the work by Petsch et al. (18), a thin wire heater was embedded The mechanical work done by the actuator while discharging was inside an aligned LCE. When heated, the device contracted along computed from the mass of the attached load, m ,and the its aligned direction. The reported 90% contraction response time displacement found by high-speed video, i.e., W = m gDh,where in that work was between 20 and 30 s. In the example reported in mech L g is the gravitational acceleration, 9.8 m/s ,and Dh is the displacement the text, they achieved a 1.85-mm stroke with a 2.25-g test load and of the mass. The electrical energy input to the system, W ¼ QV, 430 mW of input power. The stroke efficiency then is el was found by integrating the discharge current measured as a volt- age, V , over the known resistor, R , and multiplying by the applied 2 D D 2:25 g 9:8m=s 1:85 mm _ _ 6 voltage (e.g., 3 kV). Last, the efficiency was computed from the ratio ≈5  10 20 s 430 mW of these energies, W /W . _ mech el Finite element simulations of the effect of Poisson’s or about 0.0005% for the stroke only. To maintain that stroke, a con- ratio anisotropy stant current must be applied. The finite element simulations were carried out using the Structural Mechanics Module of COMSOL Multiphysics 5.3a (COMSOL, 2008). Uniaxially buckling DLCEA and frequency Several mesh refinement steps were performed to guarantee conver- response characterization gence of the results. For the no-load simulations of DLCEA (fig. S5B), A uniaxial LCE film was constrained at its edges by a laser-cut Plexiglas the LCE film was modeled as a thin anisotropic sheet (width, 14 mm; frame. The film was carefully placed on top of the frame so as not to length, 30 mm) with an initial thickness of 80 mm. The compliance and induce prestrain or leave any slack. A central square carbon grease stiffness matrices describing the anisotropic material with Voigt nota- electrode was painted onto the film on both sides through a low- tion were computed using five independent elastic constants adhesive removable tape mask. The in-plane length of the film grew along the soft direction, but because of the fixed boundary conditions, 2 3 1 n n it created a buckled wrinkling pattern. The height of the wrinkle pat- 12 13 00 0 tern was measured by laser confocal profilometry in the off state and 6 E E E 7 11 11 11 6 7 n 1 n every 250 V starting from 500 V to 2.5 kV. In the 2.5-kV activated 21 23 6 7 00 0 6 7 state, the out-of-plane peak-to-peak stroke was 1.47 mm or 1800% 6 E E E 7 22 22 22 6 7 n n 1 31 32 of the LCE film thickness, which was approximately 80 mm. 6 7 00 0 6 7 To determine the frequency response of the uniaxial buckling E E E 33 33 33 6 7 S ¼ 6 1 7 DLCEA, we applied a sinusoidally varying 1 kV supplied by a Physik 6 7 000 00 6 7 2G Instrumente E-107 piezo high-voltage amplifier. The input signal 6 7 6 1 7 was generated by a function generator (Tektronix). The motion of 6 000 0 0 7 6 7 the DLCEA membrane was observed by a Thorlabs Telesto optical 2G 4 5 coherence tomography microscope. The DLCEA film maximum height 000 0 0 2G was first found manually in the dc on state and subsequently observed in the same location for various frequencies (Fig. 3D and fig. S9B). C ¼ S Programmed buckling of DLCEA where the following relations are valid assuming that “1” is x, i.e., along The defect array was achieved by programming light polarization the nematic director from laser-cut squares of a linear polarizer film that was stitched back into the desired grid on a glass slide using NOA65 ultraviolet curing glue. The stitched pieces of polarizing squares were not perfectly be- n ¼ n ; n ¼ n ; n ¼ n ; n ¼ n ; 12 13 21 12 31 21 32 23 side each other because of imperfections in the laser-cutting step and difficulty in manual stitching. However, the unaligned boundaries be- G ¼ ; E ¼ E ; G ¼ G 23 22 33 13 12 2ð1 þ n Þ tween aligned regions in the LCE film were small and did not appar- ently affect the actuation response. To demonstrate the effect of anisotropy on the performance of Similar to the uniaxial buckling, after fabrication of the LCE and the actuator, we swept the value of E from 1 to 20 MPa while as- removing it from the BY-coated glass slides, we fixed the LCE film suming Poisson’sratios v =0.5 and n =0.9 − n and shear to a laser-cut Plexiglas frame and covered the programmed region 12 23 21 Davidson et al., Sci. Adv. 2019;5 : eaay0855 22 November 2019 8of9 | SCIENCE ADVANCES RESEARCH ARTICLE 18. S. Petsch, R. Rix, B. Khatri, S. Schuhladen, P. Müller, R. Zentel, H. Zappe, Smart artificial with electrically conductive carbon grease. The programmed region muscle actuators: Liquid crystal elastomers with integrated temperature feedback. was easily distinguished under ambient lighting from the surrounding Sens. Actuators A Phys. 231,44–51 (2015). areas because of the mismatch in the index of refraction between iso- 19. C. M. Spillmann, J. Naciri, B. R. Ratna, R. L. B. Selinger, J. V. 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