Active Materials for Functional Origami

In recent decades, origami has been explored to aid in the design of engineering structures. These structures span multiple scales and have been demonstrated to be used toward various areas such as aerospace, metamaterial, biomedical, robotics, and architectural applications. Conventionally, origami or deployable structures have been actuated by hands, motors, or pneumatic actuators, which can result in heavy or bulky structures. On the other hand, active materials, which reconfigure in response to external stimulus, eliminate the need for external mechanical loads and bulky actuation systems. Thus, in recent years, active materials incorporated with deployable structures have shown promise for remote actuation of light weight, programmable origami. In this review, active materials such as shape memory polymers (SMPs) and alloys (SMAs), hydrogels, liquid crystal elastomers (LCEs), magnetic soft materials (MSMs), and covalent adaptable network (CAN) polymers, their actuation mechanisms, as well as how they have been utilized for active origami and where these structures are applicable is discussed. Additionally, the state-of-the-art fabrication methods to construct active origami are highlighted. The existing structural modeling strategies for origami, the constitutive models used to describe active materials, and the largest challenges and future directions for active origami research are summarized.

Shape-Tunable 4D Printing of LCEs via Cooling Rate Modulation: Stimulus-Free Locking of Actuated State at Room Temperature

Liquid crystal elastomers (LCEs) have garnered considerable attention in the field of four-dimensional (4D) printing due to their large, reversible, and anisotropic shape-morphing capabilities. By utilizing direct ink writing, intricate LCE structures with programmable shape morphing can be achieved. However, the maintenance of the actuated state for LCEs requires continuous and substantial external stimuli, presenting challenges for practical applications, particularly under ambient conditions. This study reports a straightforward and effective physical approach to lock the actuated state of LCEs through rapid cooling while preserving their reversible performance. Rapid cooling significantly reduces the mobility of the lightly cross-linked network in LCEs, resulting in a notably slow recovery of mesogen alignment. As a result, the locked LCE structures retain their actuated state even at room temperature. Moreover, we demonstrate the ability to achieve tunable shapes between the original and actuated states by modulating the cooling rate, i.e., varying the temperature and type of cooling medium. The proposed method opens up new possibilities to achieve stable and tunable shape locking of soft devices for engineering applications.

Recent Advances in 4D Printing of Liquid Crystal Elastomers

Liquid crystal elastomers (LCEs) are renowned for their large, reversible, and anisotropic shape change in response to various external stimuli due to their lightly cross-linked polymer networks with an oriented mesogen direction, thus showing great potential for applications in robotics, bio-medics, electronics, optics, and energy. To fully take advantage of the anisotropic stimuli-responsive behaviors of LCEs, it is preferable to achieve a locally controlled mesogen alignment into monodomain orientations. In recent years, the application of 4D printing to LCEs opens new doors for simultaneously programming the mesogen alignment and the 3D geometry, offering more opportunities and higher feasibility for the fabrication of 4D-printed LCE objects with desirable stimuli-responsive properties. Here, the state-of-the-art advances in 4D printing of LCEs are reviewed, with emphasis on both the mechanisms and potential applications. First, the fundamental properties of LCEs and the working principles of the representative 4D printing techniques are briefly introduced. Then, the fabrication of LCEs by 4D printing techniques and the advantages over conventional manufacturing methods are demonstrated. Finally, perspectives on the current challenges and potential development trends toward the 4D printing of LCEs are discussed, which may shed light on future research directions in this new field.

Flow-network-controlled shape transformation of a thin membrane through differential fluid storage and surface expansion

The mechanical properties of a thin, planar material, perfused by an embedded flow network, have been suggested to be potentially changeable locally and globally by fluid transport and storage, which can result in both small- and large-scale deformations such as out-of-plane buckling. In these processes, fluid absorption and storage eventually cause the material to locally swell. Different parts can hydrate and swell unevenly, prompting a differential expansion of the surface. In order to computationally study the hydraulically induced differential swelling and buckling of such a membrane, we develop a network model that describes both the membrane shape and fluid movement, coupling mechanics with hydrodynamics. We simulate the time-dependent fluid distribution in the flow network based on a spatially explicit resistor network model with local fluid-storage capacitance. The shape of the surface is modeled by a spring network produced by a tethered mesh discretization, in which local bond rest lengths are adjusted instantaneously according to associated local fluid content in the capacitors in a quasistatic way. We investigate the effects of various designs of the flow network, including overall hydraulic traits (resistance and capacitance) and hierarchical architecture (arrangement of major and minor veins), on the specific dynamics of membrane shape transformation. To quantify these effects, we explore the correlation between local Gaussian curvature and relative stored fluid content in each hierarchy by using linear regression, which reveals that stronger correlations could be induced by less densely connected major veins. This flow-controlled mechanism of shape transformation was inspired by the blooming of flowers through the unfolding of petals. It can potentially offer insights for other reversible motions observed in plants induced by differential turgor and water transport through the xylem vessels, as well as engineering applications.

Regimes in the Response of Photomechanical Materials

Photomechanical materials perform mechanical work in response to illumination. Photoisomerization-based photomechanical materials may operate in different regimes depending on the intensity of the illuminating light. We examine the photoresponse of liquid crystalline azo-acrylate networks and show that a material property, the characteristic intensity of the material, defines the boundaries between different regimes. Asymptotic analysis indicates that whereas at low relative light levels, photostress is proportional to intensity, at high levels, it is proportional to fluence. Model predictions are in good agreement with the experimental results.

Is there only one equilibrium configuration for spontaneous bending of liquid crystal elastomer circular plates with free edges?

In this paper, the spontaneous bending of a liquid crystal elastomer (LCE) circular plate under light illumination is investigated. The large bending deformation configurations for the LCE circular plate with free edges are obtained by minimizing the potential energy. It is found that for an LCE circular plate with random distribution of liquid crystal molecules, if the light intensity is small, there is only one equilibrium configuration for bending of the LCE circular plate. However, when the light intensity reaches a critical value, the circular plate will buckle and there will be three possible equilibrium configurations. On the other hand, for an LCE circular plate with uniform orientation of liquid crystal molecules, the strain induced by light is anisotropic, and there is only one equilibrium configuration. In addition, bending shapes of the LCE circular plate depend on its thickness. These results may be useful for designing light-driven LCE devices.

Nematic liquid crystalline elastomers are aeolotropic materials

Continuum models describing ideal nematic solids are widely used in theoretical studies of liquid crystal elastomers. However, experiments on nematic elastomers show a type of anisotropic response that is not predicted by the ideal models. Therefore, their description requires an additional term coupling elastic and nematic responses, to account for aeolotropic effects. In order to better understand the observed elastic response of liquid crystal elastomers, we analyse theoretically and computationally different stretch and shear deformations. We then compare the elastic moduli in the infinitesimal elastic strain limit obtained from the molecular dynamics simulations with the ones derived theoretically, and show that they are better explained by including nematic order effects within the continuum framework.

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

Boundary effect on the spontaneous deformation of a liquid crystal elastomer plate with arbitrary director orientation

Except for director orientation, the deformation modes of constrained liquid crystal elastomer thin plate display specimen geometry size dependence due to the boundary effect. In this paper, the effect of plate geometry size on the spontaneous deformation of a simply supported liquid crystal elastomer plate is studied. The relation between the deformation modes with director orientation and plate geometry size are investigated. Results show that the deformation modes are decided by the director orientation for a certain liquid crystal elastomer, but the geometry size affects the mode transformation with respect to the director. These results are supposed to be used in the design and application of liquid crystal elastomer-based smart actuators or sensors.

Direct Ink Writing Based 4D Printing of Materials and Their Applications

4D printing has attracted academic interest in the recent years because it endows static printed structures with dynamic properties with the change of time. The shapes, functionalities, or properties of the 4D printed objects could alter under various stimuli such as heat, light, electric, and magnetic field. Briefly, 4D printing is the development of 3D printing with the fourth dimension of time. Among the fabrication techniques that have been employed for 4D printing, the direct ink writing technique shows superiority due to its open source for various types of materials. Herein, the state-of-the-art achievements about the topic of 4D printing through direct ink writing are summarized. The types of materials, printing strategies, actuated methods, and their potential applications are discussed in detail. To date, most efforts have been devoted to shape-shifting materials, including shape memory polymers, hydrogels, and liquid crystal elastomers, showing great prospects in areas ranging from the biomedical field to robotics. Finally, the current challenges and outlook toward 4D printing based on direct ink writing are also pointed out to leave open a significant space for future innovation.

Light-induced spontaneous bending of a simply supported liquid crystal elastomer rectangular plate

Designing the director alignment of a liquid crystal elastomer (LCE) is a key tuning approach for LCE based smart devices. In this paper, the spontaneous strain of the LCE with arbitrary three-dimensional director orientation is derived, and the governing equation for a simply supported LCE rectangular plate is established. By using the finite difference method, the bending configurations are obtained. Different from the freestanding case, three bending modes, that is, unimodal, bimodal, and trimodal modes, are observed for the simply supported rectangular LCE plate. The relation between the bending modes and the director orientation is established. This paper enhances the understanding and facilitates the design of LCE based intelligent light driven devices.

Travelling waves on photo-switchable patterned liquid crystal polymer films directed by rotating polarized light

Nature employs travelling waves to generate propulsion of fluids, cells and organisms. This has inspired the development of responsive material systems based on different external triggers. Especially light-actuation is suitable because of its remote control and scalability, but often complex, moving light sources are required. Here, we developed a method that only requires flood exposure by rotating the linear polarization of light to generate propagating surface waves on azobenzene-modified liquid crystalline polymer films. We built a photomechanical computational model that accounts for the attenuation of polarized light and trans-to-cis isomerization of azobenzene. A non-uniform in-plane distribution of the liquid crystal molecules allows for the generation of travelling surface waves whose amplitude, speed and direction can be controlled through the intensity, rotation direction and rotation speed of the linear polarization of a light source. Our method opens new avenues for motion control based on light-responsive topographical transformations for application in microfluidic lab-on-chip systems and soft robotics.

Tunable wrinkling of thin nematic liquid crystal elastomer sheets

Instabilities in thin elastic sheets, such as wrinkles, are of broad interest both from a fundamental viewpoint and also because of their potential for engineering applications. Nematic liquid crystal elastomers offer a new form of control of these instabilities through direct coupling between microscopic degrees of freedom, resulting from orientational ordering of rodlike molecules, and macroscopic strain. By a standard method of dimensional reduction, we construct a plate theory for thin sheets of nematic elastomer. We then apply this theory to the study of the formation of wrinkles due to compression of a thin sheet of nematic liquid crystal elastomer atop an elastic or fluid substrate. We find the scaling of the wrinkle wavelength in terms of material parameters and the applied compression. The wavelength of the wrinkles is found to be nonmonotonic in the compressive strain due to the presence of the nematic. Finally, due to soft modes, the critical stress for the appearance of wrinkles can be much higher than in an isotropic elastomer and depends nontrivially on the manner in which the elastomer was prepared.

Patterning nonisometric origami in nematic elastomer sheets

Nematic elastomers dramatically change their shape in response to diverse stimuli including light and heat. In this paper, we provide a systematic framework for the design of complex three dimensional shapes through the actuation of heterogeneously patterned nematic elastomer sheets. These sheets are composed of nonisometric origami building blocks which, when appropriately linked together, can actuate into a diverse array of three dimensional faceted shapes. We demonstrate both theoretically and experimentally that the nonisometric origami building blocks actuate in the predicted manner, and that the integration of multiple building blocks leads to complex, yet predictable and robust, shapes. We then show that this experimentally realized functionality enables a rich design landscape for actuation using nematic elastomers. We highlight this landscape through examples, which utilize large arrays of these building blocks to realize a desired three dimensional origami shape. In combination, these results amount to an engineering design principle, which provides a template for the programming of arbitrarily complex three dimensional shapes on demand.

Topographical changes in photo-responsive liquid crystal films: a computational analysis

Switchable materials in response to external stimuli serve as building blocks to construct microscale functionalized actuators and sensors. Azobenzene-modified liquid crystal (LC) polymeric networks, that combine liquid crystalline orientational order and elasticity, reversibly undergo conformational changes powered by light. We present a computational framework to describe photo-induced topographical transformations of azobenzene-modified LC glassy polymer coatings. A nonlinear light penetration model is combined with an opto-mechanical constitutive relation to simulate various ordered and corrugated topographical textures resulting from aligned or randomly distributed LC molecule orientations. Our results shed light on the fundamental physical mechanisms of light-triggered surface undulations and can be used as guidelines to optimize surface modulation and roughness in emerging fields that involve haptics interfacing, friction control and wetting manipulation.

Liquid crystal elastomer coatings with programmed response of surface profile

Stimuli-responsive liquid crystal elastomers with molecular orientation coupled to rubber-like elasticity show a great potential as elements in soft robotics, sensing, and transport systems. The orientational order defines their mechanical response to external stimuli, such as thermally activated muscle-like contraction. Here we demonstrate a dynamic thermal control of the surface topography of an elastomer prepared as a coating with a pattern of in-plane molecular orientation. The inscribed pattern determines whether the coating develops elevations, depressions, or in-plane deformations when the temperature changes. The deterministic dependence of the out-of-plane dynamic profile on the in-plane orientation is explained by activation forces. These forces are caused by stretching-contraction of the polymer networks and by spatially varying molecular orientation. The activation force concept brings the responsive liquid crystal elastomers into the domain of active matter. The demonstrated relationship can be used to design coatings with functionalities that mimic biological tissues such as skin.

Four-dimensional Printing of Liquid Crystal Elastomers

Three-dimensional structures capable of reversible changes in shape, i.e., four-dimensional-printed structures, may enable new generations of soft robotics, implantable medical devices, and consumer products. Here, thermally responsive liquid crystal elastomers (LCEs) are direct-write printed into 3D structures with a controlled molecular order. Molecular order is locally programmed by controlling the print path used to build the 3D object, and this order controls the stimulus response. Each aligned LCE filament undergoes 40% reversible contraction along the print direction on heating. By printing objects with controlled geometry and stimulus response, magnified shape transformations, for example, volumetric contractions or rapid, repetitive snap-through transitions, are realized.

Guided Folding of Nematic Liquid Crystal Elastomer Sheets into 3D via Patterned 1D Microchannels

Two-dimensional liquid-crystal elastomer (LCE) sheets with preprogrammed topological defects are prepared by aligning liquid-crystal monomers within micropatterned epoxy channels, followed by photopolymerization. Upon heating, the LCE films form various three-dimensional structures in agreement with theoretical design. The miniaturized LCE actuators offer large-area work capacities (≈1.05 J m^-2 ) to lift over 700 times their own weight.

Programming complex shapes in thin nematic elastomer and glass sheets

Nematic elastomers and glasses are solids that display spontaneous distortion under external stimuli. Recent advances in the synthesis of sheets with controlled heterogeneities have enabled their actuation into nontrivial shapes with unprecedented energy density. Thus, these have emerged as powerful candidates for soft actuators. To further this potential, we introduce the key metric constraint which governs shape-changing actuation in these sheets. We then highlight the richness of shapes amenable to this constraint through two broad classes of examples which we term nonisometric origami and lifted surfaces. Finally, we comment on the derivation of the metric constraint, which arises from energy minimization in the interplay of stretching, bending, and heterogeneity in these sheets.

Nonlinear photomechanics of nematic networks: upscaling microscopic behaviour to macroscopic deformation

A liquid crystal network whose chromophores are functionalized by photochromic dye exhibits light-induced mechanical behaviour. As a result, the micro-scaled thermotropic traits of the network and the macroscopic phase behaviour are both influenced as light alternates the shape of the dyes. In this paper, we present an analysis of this photomechanical behaviour based on the proposed multiscale framework, which incorporates the molecular details of microstate evolution into a continuum-based understanding. The effects of trans-to-cis photoisomerization driven by actinic light irradiation are first examined using molecular dynamics simulations, and are compared against the predictions of the classical dilution model; this reveals certain characteristics of mesogenic interaction upon isomerization, followed by changes in the polymeric structure. We then upscale the thermotropic phase-related information with the aid of a nonlinear finite element analysis; macroscopic deflection with respect to the wide ranges of temperature and actinic light intensity are thereby examined, which reveals that the classical model underestimates the true deformation. This work therefore provides measures for analysing photomechanics in general by bridging the gap between the micro- and macro-scales.

Geometry of thin nematic elastomer sheets

A thin sheet of nematic elastomer attains 3D configurations depending on the nematic director field upon heating. In this Letter, we describe the intrinsic geometry of such a sheet and derive an expression for the metric induced by general nematic director fields. Furthermore, we investigate the reverse problem of constructing a director field that induces a specified 2D geometry. We provide an explicit recipe for how to construct any surface of revolution using this method. Finally, we show that by inscribing a director field gradient across the sheet's thickness, one can obtain a nontrivial hyperbolic reference curvature tensor, which together with the prescription of a reference metric allows dictation of actual configurations for a thin sheet of nematic elastomer.

Liquid crystal polymer networks: preparation, properties, and applications of films with patterned molecular alignment

Monolithically ordered liquid crystal polymer networks are formed by the photoinitiated polymerization of multifunctional liquid crystal monomers. This paper describes the relevant principles and methods, the basic structure-property relationships in terms of mesogenic properties of the monomers, and the mechanical and optical properties of the polymers. Strategies are discussed to control the molecular orientation by various means and in all three dimensions. The versatility of the process is demonstrated by two examples of films with a patterned molecular order. It is shown that patterned retarders can be made by a two-step polymerization process which is successfully employed in a transflective display principle. A transflective display is a liquid crystal display that operates in both a reflective mode using ambient light and a transmissive mode with light coming from a backlight system. Furthermore, a method is discussed to create a patterned film in a single polymerization process. This film has alternating planar chiral nematic areas next to perpendicularly oriented (so-called homeotropic) areas. When applied as a coating to a substrate, the film changes its surface texture. During exposure to UV light, it switches from a flat to a corrugated state.

Light controlled friction at a liquid crystal polymer coating with switchable patterning

We describe a new methodology that enables dynamical control of motion through modulating the friction at coating surfaces by exposing to UV light. The principle is based on reversible switching of the surface topographies of the coating by light. The coating surface transfers from flat in the dark to corrugated in the presence of UV by forming regular ridge-like line gratings. Both the static and the kinetic friction coefficient are investigated in a dynamic manner by switching between the off (flat surface) and the activated (with ridges) state. By dynamically changing the friction, we are able to bring the sample from a static state into motion via UV exposure. When in motion, the friction coefficient can be altered further by modulating the light conditions. For example, a smooth sliding can transfer into an interlocking state, or vice versa. Moreover, we can dynamically reduce the contact area in the interface and thus lowering friction forces.

Response of constrained glassy splay-bend and twist nematic sheets to light and heat

A general approach is proposed to analyze the complex photo- or thermo-response of glassy splay-bend and twist nematic sheets with boundary constraints. The governing equations are two-dimensional, as in the classical plate theory. However, the solution can generate exact three-dimensional displacement and stress distributions within the interior of the sheets, except the boundary layer whose width is of the same order of the sheet thickness.

Mechanical frustration and spontaneous polygonal folding in active nematic sheets

We analyze the bending response to light or heat of a solid nematic disk with a director twisted from being radial on the upper surface to be azimuthal on the lower. We find a number of curl lobes determined purely by the geometry of the mechanical frustration that arises during the response.

Blueprinting nematic glass: systematically constructing and combining active points of curvature for emergent morphology

Much recent progress has been made in the study of nematic solids, both glassy and elastomeric, particularly in the realm of stress-free, defect-driven deformation in thin sheets of material. In this paper we consider a subset of texture domains in nematic glasses that are simple to synthesize, and explore the ways that these simple domains may be compatibly combined to yield analogs of the traditional smooth disclination defect textures seen in standard liquid crystals. We calculate the deformation properties of these constructed textures, and show that, subject to the compatibility constraints of the construction, these textures may be further combined to achieve shape blueprinting of three-dimensional structures from flat sheets.

Gaussian curvature from flat elastica sheets

We discuss methods of reversibly inducing non-developable surfaces from flat sheets of material at the micro-scale all the way to macroscopic objects. We analyse the elastic ground states of a nematic glass in the membrane approximation as a function of temperature for disclination defects of topological charge +1. An aim is to show that by writing an appropriate director field into such a solid, one could create a surface with Gaussian curvature, dynamically switchable from flat sheets while avoiding stretch energy. In addition to the prospect of programmable structures, such surfaces offer actuation via stretch in thin systems since when illumination is subsequently removed, unavoidable stretches return.

Anisotropic response of glassy splay-bend and twist nematic cantilevers to light and heat

A gradient of director through the thickness of a nematic glass cantilever gives a gradient in the large distortions such materials suffer in response to temperature or illumination changes. We first sketch, within isotropic elasticity, how such gradients cause these cantilevers to respond by bending. We then derive the response within the anisotropic elasticity expected for uniaxial solids. Because, in general, spontaneously bending cantilevers have regions of elongation and contraction (with respect to their neutral state), internal stresses are generated, the magnitude of which depends on the anisotropic, fourth rank modulus tensor and in particular on its local alignment arising from the director's spatial distribution. We show that despite elastic complexity, bend is simply linear in the anisotropy of thermo-optical response, with a slope depending on the structure of the modulus tensor, justifying the previous literature on spontaneously bending cantilevers. We also explicitly consider two important director distributions--splay-bend and twist. Splay-bend cantilevers have no anticlastic (double-bend, saddle) response in the isotropic case or for some values of the anisotropic modulus tensor. Twist cantilevers have maximal anticlasticity in the isotropic case which we show to be weakly modified by anisotropy of elastic moduli.