Pattern Formation and Shape Changes in Self-Oscillating Polymer Gels

Selenium catalysis enables negative feedback organic oscillators

The construction of materials regulated by chemical reaction networks requires regulatory motifs that can be stacked together into systems with desired properties. Multiple autocatalytic reactions producing thiols are known. However, negative feedback loop motifs are unavailable for thiol chemistry. Here, we develop a negative feedback loop based on the selenocarbonates. In this system, thiols induce the release of aromatic selenols that catalyze the oxidation of thiols by organic peroxides. This negative feedback loop has two important features. First, catalytic oxidation of thiols follows Michaelis-Menten-like kinetics, thus increasing nonlinearity for the negative feedback. Second, the strength of the negative feedback can be tuned by varying substituents in selenocarbonates. When combined with the autocatalytic production of thiols in a flow reactor, this negative feedback loop induces sustained oscillations. The availability of this negative feedback motif enables the future construction of oscillatory, homeostatic, adaptive, and other regulatory circuits in life-inspired systems and materials.

Harmonic resonance and entrainment of propagating chemical waves by external mechanical stimulation in BZ self-oscillating hydrogels

Smart polymer materials that are nonliving yet exhibit complex "life-like" or biomimetic behaviors have been the focus of intensive research over the past decades, in the quest to broaden our understanding of how living systems function under nonequilibrium conditions. Identification of how chemical and mechanical coupling can generate resonance and entrainment with other cells or external environment is an important research question. We prepared Belousov-Zhabotinsky (BZ) self-oscillating hydrogels which convert chemical energy to mechanical oscillation. By cyclically applying external mechanical stimulation to the BZ hydrogels, we found that when the oscillation of a gel sample entered into harmonic resonance with the applied oscillation during stimulation, the system kept a "memory" of the resonant oscillation period and maintained it post stimulation, demonstrating an entrainment effect. More surprisingly, by systematically varying the cycle length of the external stimulation, we revealed the discrete nature of the stimulation-induced resonance and entrainment behaviors in chemical oscillations of BZ hydrogels, i.e., the hydrogels slow down their oscillation periods to the harmonics of the cycle length of the external mechanical stimulation. Our theoretical model calculations suggest the important roles of the delayed mechanical response caused by reactant diffusion and solvent migration in affecting the chemomechanical coupling in active hydrogels and consequently synchronizing their chemical oscillations with external mechanical oscillations.

Modeling of a light-fueled self-paddling boat with a liquid crystal elastomer-based motor

Active materials possess unique properties of being able to respond autonomously to external stimuli, yet realizing and regulating the motion behavior of active machines remains a major challenge. Conventional control approaches, including sensor control and external device control, are both complex and difficult to implement. In contrast, active materials-based self-oscillators offer distinct properties such as periodic motion and ease of regulation. Inspired by paddle boats, we have proposed a conceptual light-fueled self-paddling boat with a photothermally responsive liquid crystal elastomer (LCE)-based motor that operates under steady illumination and incorporates an LCE fiber. Based on the well-established dynamic LCE model and rotation dynamics, the dynamic equations for governing the self-paddling of the LCE-steered boat are derived, and the driving torque of the LCE-based motor and the paddling velocity of the LCE-steered boat are formulated successively. The numerical results show that two motion modes of the boat under steady illumination: the static mode and the self-paddling mode. The self-paddling regime arises from the competition between the light-fueled driving torque and the frictional torque. Moreover, the critical conditions required to trigger the self-paddling are quantitatively examined as well as the significant system parameters affecting the driving torque, angular velocity, and paddling velocity. The proposed conceptual light-fueled self-paddling LCE-steered boat exhibits benefits including customizable size and being untethered and ambient powered, which provides valuable insights into the design and application of micromachines, soft robotics, energy harvesters, and beyond.

A light-powered self-rotating liquid crystal elastomer drill

Self-oscillating systems can directly convert ambient energy to mechanical work, and new type self-oscillating systems are worth designing for applications in energy harvesters, engines, and actuators. Taking inspiration from the hand drill, we have developed a novel self-rotating drill system, which is consist of a turnplate and a liquid crystal elastomer (LCE) fiber under steady illumination. To investigate the self-rotating behaviors of the LCE drill, we have proposed a nonlinear theoretical model of the LCE drill under steady illumination based on the well-established dynamic LCE model. Numerical calculation reveals that the LCE drill can undergo a supercritical Hopf bifurcation between the static regime and the self-rotation regime. The self-rotation of drill originates from the contraction of winding portion of LCE fiber in illumination at winding state, and its continuous periodic motion is sustained by the interrelation between light energy and damping dissipation. The Hopf bifurcation conditions are also investigated in detail, as well as the vital system parameters affecting its frequency and amplitude. In contrast to the abundant existing self-oscillating systems, this self-rotating drill stands out due to its simple and lightweight structure, customizable dimensions, and high speed, and thus facilitates the design of compact and integrated systems, enhancing their applicability in microdevices and systems. This bears great significance in fields like micro-robotics, micro-sensors, and medical instruments, enabling the realization of smaller and higher-performance devices.

Modeling the light-powered self-rotation of a liquid crystal elastomer fiber-based engine

Self-oscillating systems possess the ability to convert ambient energy directly into mechanical work, and new types of self-oscillating systems are worth designing for practical applications in energy harvesters, engines and actuators. Taking inspiration from the four-stroke engine. A concept for a self-rotating engine is presented on the basis of photothermally responsive materials, consisting of a liquid crystal elastomer (LCE) fiber, a hinge and a turnplate, which can self-rotate under steady illumination. Based on the photo-thermal-mechanical model, a nonlinear theoretical model of the LCE-based engine under steady illumination is proposed to investigate its self-rotating behaviors. Numerical calculations reveal that the LCE-based engine experiences a supercritical Hopf bifurcation between the static regime and the self-rotation regime. The self-rotation of the LCE-based engine originates from the photothermally driven strain of the LCE fiber in illumination, and its continuous periodic motion is sustained by the correlation between photothermal energy and damping dissipation. The Hopf bifurcation conditions are also explored in detail, as well as the vital system parameters affecting self-rotation frequency. Compared to the abundant existing self-oscillating systems, this conceptual self-rotating LCE-based engine stands out due to its simple and lightweight structure, customizable dimensions and high speed, and it is expected to offer a broader range of design concepts applicable to soft robotics, energy harvesters, medical instruments, and so on.

Biomimetic growth in polymer gels

By modeling gels growing in confined environments, we uncover a biomimetic feedback mechanism between the evolving gel and confining walls that enables significant control over the properties of the grown gel. Our new model describes the monomer adsorption, polymerization and cross-linking involved in forming new networks and the resultant morphology and mechanical behavior of the grown gel. Confined between two hard walls, a thin, flat "parent" gel undergoes buckling; removal of the walls returns the gel to the flat structure. Polymerization and cross-linking in the confined parent generates the next stage of growth, forming a random copolymer network (RCN). When the walls are removed, the RCN remains in the buckled state, simultaneously "locking in" these patterns and increasing the Young's modulus by two orders of magnitude. Confinement of thicker gels between harder or softer 3D walls leads to controllable mechanical heterogeneities, where the Young's modulus between specific domains can differ by three orders of magnitude. These systems effectively replicate the feedback between mechanics and morphology in biological growth, where mechanical forces guide the structure formation throughout stages of growth. The findings provide new guidelines for shaping "growing materials" and introducing new approaches to matching form and function in synthetic systems.

Self-Rotation of Electrothermally Responsive Liquid Crystal Elastomer-Based Turntable in Steady-State Circuits

Self-excited motions, characterized by their ability to harness energy from a consistent environment and self-regulate, exhibit significant potential in micro-devices, autonomous robotics, sensor technology, and energy generation. This study introduces an innovative turntable system based on an electrothermally responsive liquid crystal elastomer (LCE). This system facilitates self-rotation within a steady-state circuit. Employing an electrothermal LCE model, we have modeled and numerically analyzed the nonlinear dynamics of an LCE-rope within steady-state circuits, utilizing the four-order Runge-Kutta method for calculations. The numerical results reveal the emergence of two distinct motion patterns in the turntable system under steady-state conditions: a self-rotation pattern and a static pattern. The self-rotation is initiated when the system's absorbed energy surpasses the energy lost due to damping effects. Furthermore, this paper delves into the critical conditions necessary for initiating self-rotation and examines the influence of various key dimensionless parameters on the system's rotation amplitude and frequency. These parameters include gravitational acceleration, the initial position of the mass ball, elastic stiffness of the LCE and spring, limiting temperature, heating zone angle, thermal shrinkage coefficient, and damping factor. Our computational findings establish that these parameters exert a modulatory impact on the rotation amplitude and period. This research enhances the understanding of self-excited motions and offers promising avenues for applications in energy harvesting, monitoring, soft robotics, medical devices, and micro- and nano-devices.

A Light-Powered Liquid Crystal Elastomer Roller

Achieving and controlling the desired movements of active machines is generally accomplished through precise control of artificial muscles in a distributed and serialized manner, which is a significant challenge. The emerging motion control strategy based on self-oscillation in active machines has unique advantages, including directly harvesting energy from constant ambient light, and it has no need for complex controllers. Inspired by the roller, we have innovatively developed a self-rolling roller that consists of a roller and a liquid crystal elastomer (LCE) fiber. By utilizing a well-established dynamic LCE model and subjecting it to constant illumination, we have investigated the dynamic behavior of the self-rolling roller. Based on numerical calculations, it has been discovered that the roller, when subjected to steady illumination, exhibits two distinct motion regimes: the static regime and the self-rolling regime. The self-rolling regime, characterized by continuous periodic rolling, is sustained by the interaction between light energy and damping dissipation. The continuous periodic rolling observed in the self-rolling regime is maintained through the interplay between the dissipation of damping and the absorption of light energy. In the static state, the rolling angle of the roller begins to decrease rapidly and then converges to zero. Detailed investigations have been conducted to determine the critical conditions required to initiate self-rolling, as well as the essential system parameters that influence its frequency and amplitude. The proposed self-rolling roller has superiorities in its simple structure, light weight, alternative to manual labor, and speediness. This advancement is expected to inspire greater design diversity in micromachines, soft robotics, energy harvesters, and similar areas.

A Programmable Actuator as Synthetic Earthworm

Natural earthworm with the ability to loosen soils that favors sustainable agriculture has inspired worldwide interest in the design of intelligent actuators. Given the inability to carry heavy loads and uncontrolled deformation, the vast majority of actuators can only perform simple tasks by bending, contraction, or elongation. Herein, a degradable actuator with the ability to deform in desired ways is presented, which successfully mimics the burrowing activities of earthworms to loosen soils with increased soil porosity by digging, grabbing, and lifting the soil when it receives rains. Such a scarifying actuator is made of degradable cellulose acetate and uncrosslinked polyacrylamide via the swelling-photopolymerizing method. The water absorption of polyacrylamide in moisture conditions causes rapid and remarkable bending. Such mechanical bending can be controlled in specific areas of the cellulose acetate film if polyacrylamide is polymerized in a patterned way, so as to generate complicated deformations of the whole cellulose acetate. Patterning polyacrylamide within cellulose acetate is achieved based on reversible surface protection by means of pen writing, rather than the traditional masking techniques. The water-induced deformation of programmable cellulose-based actuators is well preserved in soil, which is appropriate for promoting rain diffusion as well as root breath.

Self-Sustained Oscillation of Electrothermally Responsive Liquid Crystal Elastomer Film in Steady-State Circuits

Self-excited oscillations have the advantages of absorbing energy from a stable environment and Self-control; therefore, Self-excited motion patterns have broader applications in micro devices, autonomous robots, sensors and energy-generating devices. In this paper, a Self-sustained curling liquid crystal elastomer (LCE) film-mass system is proposed on the basis of electrothermally responsive materials, which can realize Self-oscillation under a steady-state current. Based on the contact model and dynamic LCE model, a nonlinear dynamics model of LCE film in steady-state circuits is developed and numerical calculations are carried out using the Runge-Kutta method. Through numerical calculations, it is demonstrated that LCE film-mass systems have two motion patterns in steady-state circuits: namely, a Self-oscillation pattern and a stationary pattern. Self-sustained curling of LCE film originates from the fact that the energy absorbed by the system exceeds the energy dissipated due to the damping effect. In addition, the critical conditions for triggering Self-oscillation and the effects of several key dimensionless system parameters on the amplitude and period of Self-oscillation are investigated in detail. Calculation results show that the height of electrolyte solution, gravitational acceleration, elastic modulus of LCE film, limit temperature, curvature coefficient, thermal shrinkage coefficient and damping factor all have a modulating effect on the amplitude and period of Self-oscillation. This research may deepen the understanding of Self-excited oscillation, with promising applications in energy harvesting, power generation, monitoring, soft robotics, medical devices, and micro and nano devices.

Macroscopic Pattern Formation of Alginate Gels in a Two-Dimensional System

Macroscopic spatial patterns were formed in calcium alginate gels when a drop of a calcium nitrate solution was placed on the center of a sodium alginate solution on a petri dish. These patterns have been classified into two groups. One is multi-concentric rings consisting of alternating cloudy and transparent areas observed around the center of petri dishes. The other is streaks extending to the edge of the petri dish, which are formed to surround the concentric bands between the concentric bands and the petri dish edge. We have attempted to understand the origins of the pattern formations using the properties of phase separation and gelation. The distance between two adjacent concentric rings was roughly proportional to the distance from where the calcium nitrate solution was dropped. The proportional factor p increased exponentially for the inverse of the absolute temperature of the preparation. The p also depended on the concentration of alginate. The pattern characteristics in the concentric pattern agreed with those in the Liesegang pattern. The paths of radial streaks were disturbed at high temperatures. The length of these streaks shortened with increasing alginate concentration. The characteristics of the streaks were similar to those of crack patterns resulting from inhomogeneous shrinkage during drying.

Capsule self-oscillating gels showing cell-like nonthermal membrane/shape fluctuations

A primary interest in cell membrane and shape fluctuations is establishing experimental models reflecting only nonthermal active contributions. Here we report a millimeter-scaled capsule self-oscillating gel model mirroring the active contribution effect on cell fluctuations. In the capsule self-oscillating gels, the propagating chemical signals during a Belousov-Zhabotinsky (BZ) reaction induce simultaneous local deformations in the various regions, showing cell-like shape fluctuations. The capsule self-oscillating gels do not fluctuate without the BZ reaction, implying that only the active chemical parameter induces the gel fluctuations. The period and amplitude depend on the gel layer thickness and the concentration of the chemical substrate for the BZ reaction. Our results allow for a solid experimental platform showing actively driven cell-like fluctuations, which can potentially contribute to investigating the active parameter effect on cell fluctuations.

Bobbing chemical garden tubes: oscillatory self-motion from buoyancy and catalytic gas production

Chemical reactions can induce self-propulsion by the production and ejection of gas bubbles from micro-rocket like cylindrical units. We describe related micro-submarines that change their depth in response to catalytic gas production. The structures consist of silica-supported CuO and are produced by utilizing the self-assembly rules of chemical gardens. In H₂O₂ solution, the tube cavity produces O₂(g) and the resulting buoyancy lifts the tube to the air-solution interface, where it releases oxygen and sinks back down to the bottom of the container. In 5 cm deep solutions, the resulting bobbing cycles have a period of 20-30 s and repeat for several hours. The ascent is characterized by a vertical orientation of the tube and a constant acceleration. During the descent, the tubes are oriented horizontally and sink at a nearly constant speed. These striking features are quantitatively captured by an analysis of the involved mechanical forces and chemical kinetics. The results show that ascending tubes increase their oxygen-production rate by the motion-induced injection of fresh solution into the tube cavity.

Self-sustained chaotic floating of a liquid crystal elastomer balloon under steady illumination

Self-sustained chaotic system has the capability to maintain its own motion through directly absorbing energy from the steady external environment, showing extensive application potential in energy harvesters, self-cleaning, biomimetic robots, encrypted communication and other fields. In this paper, a novel light-powered chaotic self-floating system is proposed by virtue of a nonlinear spring and a liquid crystal elastomer (LCE) balloon, which is capable of self-floating under steady illumination due to self-beating. The corresponding theoretical model is formulated by combining dynamic LCE model and Newtonian dynamics. Numerical calculations show that the periodic self-floating of LCE balloon can occur under steady illumination, which is attributed to the light-powered self-beating of LCE balloon with shading coating. Furthermore, the chaotic self-floating is presented to be developed from the periodic self-floating through period doubling bifurcation. In addition, the effects of system parameters on the self-floating behaviors of the system are also investigated. The detailed calculations demonstrate that the regime of self-floating LCE balloon depends on a combination of system parameters. The chaotic self-floating system of current study may inspire the design of other chaotic self-sustained motion based on stimuli-responsive materials, and have guiding significance for energy harvesters, self-cleaning, biomimetic robots, encrypted communication and other applications.

Self-Oscillating Curling of a Liquid Crystal Elastomer Beam under Steady Light

Self-oscillation absorbs energy from a steady environment to maintain its own continuous motion, eliminating the need to carry a power supply and controller, which will make the system more lightweight and promising for applications in energy harvesting, soft robotics, and microdevices. In this paper, we present a self-oscillating curling liquid crystal elastomer (LCE) beam-mass system, which is placed on a table and can self-oscillate under steady light. Unlike other self-sustaining systems, the contact surface of the LCE beam with the tabletop exhibits a continuous change in size during self-sustaining curling, resulting in a dynamic boundary problem. Based on the dynamic LCE model, we establish a nonlinear dynamic model of the self-oscillating curling LCE beam considering the dynamic boundary conditions, and numerically calculate its dynamic behavior using the Runge-Kutta method. The existence of two motion patterns in the LCE beam-mass system under steady light are proven by numerical calculation, namely self-curling pattern and stationary pattern. When the energy input to the system exceeds the energy dissipated by air damping, the LCE beam undergoes self-oscillating curling. Furthermore, we investigate the effects of different dimensionless parameters on the critical conditions, the amplitude and the period of the self-curling of LCE beam. Results demonstrate that the light source height, curvature coefficient, light intensity, elastic modulus, damping factor, and gravitational acceleration can modulate the self-curling amplitude and period. The self-curling LCE beam system proposed in this study can be applied to autonomous robots, energy harvesters, and micro-instruments.

Biomacromolecule-Fueled Transient Volume Phase Transition of a Hydrogel

A metabolic cycle-inspired hydrogel which exhibits the biomacromolecule-fueled transient volume phase transition is reported. This hydrogel has the affinity and digestive capacity for a fuel α-poly-L-lysine by incorporating acrylic acid and trypsin. The hydrogel captured fuel and transiently shrank owing to the construction of electrostatic cross-linkages. This process was inherently connected with the digestion of these cross-linkages and the release of oligo-lysine as waste, which induced the reswelling of the hydrogel at equilibrium. The transient volume change of the hydrogel realized the fuel-stimulated transient release of a payload. This study provides a strategy for engineering materials with biomacromolecule-fueled dynamic functions under the out-of-equilibrium condition.

Dynamical Behaviors of a Translating Liquid Crystal Elastomer Fiber in a Linear Temperature Field

Liquid crystal elastomer (LCE) fiber with a fixed end in an inhomogeneous temperature field is capable of self-oscillating because of coupling between heat transfer and deformation, and the dynamics of a translating LCE fiber in an inhomogeneous temperature field are worth investigating to widen its applications. In this paper, we propose a theoretic constitutive model and the asymptotic relationship of a LCE fiber translating in a linear temperature field and investigate the dynamical behaviors of a corresponding fiber-mass system. In the three cases of the frame at rest, uniform, and accelerating translation, the fiber-mass system can still self-oscillate, which is determined by the combination of the heat-transfer characteristic time, the temperature gradient, and the thermal expansion coefficient. The self-oscillation is maintained by the energy input from the ambient linear temperature field to compensate for damping dissipation. Meanwhile, the amplitude and frequency of the self-oscillation are not affected by the translating frame for the three cases. Compared with the cases of the frame at rest, the translating frame can change the equilibrium position of the self-oscillation. The results are expected to provide some useful recommendations for the design and motion control in the fields of micro-robots, energy harvesters, and clinical surgical scenarios.

Turing patterns by supramolecular self-assembly of a single salphen building block

In the 1950s, Alan Turing showed that concerted reactions and diffusion of activating and inhibiting chemical species can autonomously generate patterns without previous positional information, thus providing a chemical basis for morphogenesis in Nature. However, access to these patterns from only one molecular component that contained all the necessary information to execute agonistic and antagonistic signaling is so far an elusive goal, since two or more participants with different diffusivities are a must. Here, we report on a single-molecule system that generates Turing patterns arrested in the solid state, where supramolecular interactions are used instead of chemical reactions, whereas diffusional differences arise from heterogeneously populated self-assembled products. We employ a family of hydroxylated organic salphen building blocks based on a bis-Schiff-base scaffold with portions responsible for either activation or inhibition of assemblies at different hierarchies through purely supramolecular reactions, only depending upon the solvent dielectric constant and evaporation as fuel.

Research progress in self-oscillating polymer brushes

Polymer brushes possess unique changes in physical and chemical properties when they are exposed to external stimuli and have a wide range of applications. Self-oscillating polymers are anchored on surfaces of certain materials and are coupled with some self-oscillating reactions (with the Belousov–Zhabotinsky (BZ) reaction as an example) to form self-oscillating polymer brushes. As an independent field of stimulus response functional surface research, the development of new intelligent bionic materials has good potential. This article reviews the oscillation mechanisms of self-oscillating polymer brushes and their classifications. First, the oscillation mechanisms of self-oscillating polymer brushes are introduced. Second, the research progress in self-oscillating polymers is discussed in terms of the type of self-oscillation reactions. Finally, possible future developments of self-oscillating polymer brushes are prospected.

Polymer brushes possess unique changes in physical and chemical properties when they are exposed to external stimuli and have a wide range of applications.

Rotational Locomotion of an Active Gel Driven by Internal Chemical Signals

Chemical waves arising from coupled reaction and transport can serve as biomimetic "nerve signals" to study the underlying origin and regulation of active locomotion. During wave propagation in more than one spatial dimension, the propagation direction of spiral and pulse waves in a nanogel-based PAAm self-oscillating gel, i.e., the orientation of the driving force, may deviate from the normal direction to the wave fronts. Alternating forward and backward retrograde wave locomotion along the normal and tangential kinematic vectors with a phase difference leads to a curved path, i.e., rotational locomotion. This work indicates that appendages in an organism are not required for this type of locomotion. This locomotion mechanism reveals a general principle underlying the dynamical origin of biological helical locomotion and also suggests design approaches for complex locomotion of soft robots and smart materials.

Spatiotemporal dynamics of self-assembled structures in enzymatically induced agonistic and antagonistic conditions

Predicting and designing systems with dynamic self-assembly properties in a spatiotemporal fashion is an important research area across disciplines ranging from understanding the fundamental non-equilibrium features of life to the fabrication of next-generation materials with life-like properties. Herein, we demonstrate a spatiotemporal dynamics pattern in the self-assembly behavior of a surfactant from an unorganized assembly, induced by adenosine triphosphate (ATP) and enzymes responsible for the degradation or conversion of ATP. We report the different behavior of two enzymes, alkaline phosphatase (ALP) and hexokinase (HK), towards adenosine triphosphate (ATP)-driven surfactant assembly, which also results in contrasting spatiotemporal dynamic assembly behavior. Here, ALP acts antagonistically, resulting in transient self-assemblies, whereas HK shows agonistic action with the ability to sustain the assemblies. This dynamic assembly behavior was then used to program the time-dependent emergence of a self-assembled structure in a two-dimensional space by maintaining concentration gradients of the enzymes and surfactant at different locations, demonstrating a new route for obtaining 'spatial' organizational adaptability in a self-organized system of interacting components for the incorporation of programmed functionality.

Dynamic behavior of chemically tunable mechano-responsive hydrogels

Using theory and simulation, we model the mechanical behavior of gels that encompass loops and dangling chain ends. If the loops remain folded and dangling ends are chemically inert, then these topological features just serve as defects. If, however, the loops unfold to expose the hidden ("cryptic") binding sites and the ends of the dangling chains are reactive, these moieties can form bonds that improve the gel's mechanical properties. For gels with a lower critical solubility temperature (LCST), we systematically switch on the possible unfolding and binding events. To quantify the resulting effects, we derive equations for the gel's equilibrium and dynamic elastic moduli. We also use a finite element approach to simulate the gel's response to deformation and validate the analytic calculations. Herein, we show that the equilibrium moduli are highly sensitive to the presence of unfolding and binding transitions. The dynamical moduli are sensitive not only to these structural changes, but also to the frequency of deformation. For example, when reactive ends bind to exposed cryptic sites at T = 29 °C and relatively high frequency, the storage shear modulus is 119% greater than the corresponding equilibrium value, while the storage Young's modulus is 109% greater than at equilibrium. These findings provide guidelines for tuning the chemical reactivity of loops and dangling ends and the frequency of deformation to tailor the mechano-responsive behavior of polymer networks.

Moisture-induced autonomous surface potential oscillations for energy harvesting

A variety of autonomous oscillations in nature such as heartbeats and some biochemical reactions have been widely studied and utilized for applications in the fields of bioscience and engineering. Here, we report a unique phenomenon of moisture-induced electrical potential oscillations on polymers, poly([2-(methacryloyloxy)ethyl] dimethyl-(3-sulfopropyl) ammonium hydroxide-co-acrylic acid), during the diffusion of water molecules. Chemical reactions are modeled by kinetic simulations while system dynamic equations and the stability matrix are analyzed to show the chaotic nature of the system which oscillates with hidden attractors to induce the autonomous surface potential oscillation. Using moisture in the ambient environment as the activation source, this self-excited chemoelectrical reaction could have broad influences and usages in surface-reaction based devices and systems. As a proof-of-concept demonstration, an energy harvester is constructed and achieved the continuous energy production for more than 15,000 seconds with an energy density of 16.8 mJ/cm2. A 2-Volts output voltage has been produced to power a liquid crystal display toward practical applications with five energy harvesters connected in series.

Chemically controlled pattern formation in self-oscillating elastic shells

Patterns and morphology develop in living systems such as embryos in response to chemical signals. To understand and exploit the interplay of chemical reactions with mechanical transformations, chemomechanical polymer systems have been synthesized by attaching chemicals into hydrogels. In this work, we design autonomous responsive elastic shells that undergo morphological changes induced by chemical reactions. We couple the local mechanical response of the gel with the chemical processes on the shell. This causes swelling and deswelling of the gel, generating diverse morphological changes, including periodic oscillations. We further introduce a mechanical instability and observe buckling-unbuckling dynamics with a response time delay. Moreover, we investigate the mechanical feedback on the chemical reaction and demonstrate the dynamic patterns triggered by an initial deformation. We show the chemical characteristics that account for the shell morphology and discuss the future designs for autonomous responsive materials.

Controllable growth of interpenetrating or random copolymer networks

Interpenetrating and random copolymer networks are vital in a number of industrial applications, including the fabrication of automotive parts, damping materials, and tissue engineering scaffolds. We develop a theoretical model for a process that enables the controlled growth of interpenetrating network (IPNs), or a random copolymer network (RCN) of specified size and mechanical properties. In this process, a primary gel "seed" is immersed into a solution containing the secondary monomer and crosslinkers. After the latter species are absorbed into the primary network, the absorbed monomers are polymerized to form the secondary polymer chains, which then can undergo further crosslinking to form an IPN, or undergo inter-chain exchange with the existing network to form a RCN. The swelling and elastic properties of the IPN and RCN networks can be tailored by modifying the monomer and crosslinker concentrations in the surrounding solution, or by tuning the enthalpic interactions between the primary polymer, secondary monomer and solvent through a proper choice of chemistry. This process can be used repeatedly to fabricate gels with a range of mechanical properties from stiff, rigid materials to soft, flexible networks, allowing the method to meet the materials requirements of a variety of applications.

Autonomous Low-Reynolds-Number Soft Robots with Structurally Encoded Motion and Their Thermodynamic Efficiency

Soft low-Reynolds-number robotics hold the potential to significantly impact numerous fields including drug delivery, sensing, and diagnostics. Realizing this potential is predicated upon the ability to design soft robots tailored to their intended function. In this work, we identify the effect of different geometric and symmetry parameters on the motion of soft, autonomous robots that operate in the low-Reynolds-number regime and use organic fuel. The ability to power low-Reynolds-number soft robots using an organic fuel would provide a new avenue for their potential use in biomedical applications, as is the use of a polymeric biocompatible material as is done here. We introduce a simple and cost-effective 3D-printer-assisted method to fabricate robots of different shapes that is scalable and widely applicable for a variety of materials. The efficiency of chemical energy to mechanical energy conversion is measured in soft low-Reynolds-number robots for the first time, and their mechanism of motion is assessed. Motion is a result of a periodic and oscillatory change in the charge state of the gel. This work lays the groundwork for the structure-function design of soft, chemically operated, and autonomous low-Reynolds-number robots.

Microgel that swims to the beat of light

Complementary to the quickly advancing understanding of the swimming of microorganisms, we demonstrate rather simple design principles for systems that can mimic swimming by body shape deformation. For this purpose, we developed a microswimmer that could be actuated and controlled by fast temperature changes through pulsed infrared light irradiation. The construction of the microswimmer has the following features: (i) it is a bilayer ribbon with a length of 80 or 120 [Formula: see text]m, consisting of a thermo-responsive hydrogel of poly-N-isopropylamide coated with a 2-nm layer of gold and equipped with homogeneously dispersed gold nanorods; (ii) the width of the ribbon is linearly tapered with a wider end of 5 [Formula: see text]m and a tip of 0.5 [Formula: see text]m; (iii) a thickness of only 1 and 2 [Formula: see text]m that ensures a maximum variation of the cross section of the ribbon along its length from square to rectangular. These wedge-shaped ribbons form conical helices when the hydrogel is swollen in cold water and extend to a filament-like object when the temperature is raised above the volume phase transition of the hydrogel at [Formula: see text]. The two ends of these ribbons undergo different but coupled modes of motion upon fast temperature cycling through plasmonic heating of the gel-objects from inside. Proper choice of the IR-light pulse sequence caused the ribbons to move at a rate of 6 body length/s (500 [Formula: see text]m/s) with the wider end ahead. Within the confinement of rectangular container of 30 [Formula: see text]m height and 300 [Formula: see text]m width, the different modes can be actuated in a way that the movement is directed by the energy input between spinning on the spot and fast forward locomotion.

Mechanical Adaptability of Patterns in Constrained Hydrogel Membranes

Pattern formation and dynamic restructuring play a vital role in a plethora of natural processes. Understanding and controlling pattern formation in soft synthetic materials is important for imparting a range of biomimetic functionalities. Using a three-dimensional gel Lattice spring model, we focus on the dynamics of pattern formation and restructuring in thin thermoresponsive poly(N-isopropylacrylamide) membranes under mechanical forcing via stretching and compression. A mechanical instability due to the constrained swelling of a polymer network in response to the temperature quench results in out-of-plane buckling of these membranes. The depth of the temperature quench and applied mechanical forcing affect the onset of buckling and postbuckling dynamics. We characterize formation and restructuring of buckling patterns under the stretching and compression by calculating the wavelength and the amplitude of these patterns. We demonstrate dynamic restructuring of the patterns under mechanical forcing and characterize the hysteresis behavior. Our findings show that in the range of the strain rates probed, the wavelength prescribed during the compression remains constant and independent of the sample widths, while the amplitude is regulated dynamically. We demonstrate that significantly smaller wavelengths can be prescribed and sustained dynamically than those achieved in equilibrium in the same systems. We show that an effective membrane thickness may decrease upon compression due to the out-of-plane deformations and pattern restructuring. Our findings point out that mechanical forcing can be harnessed to control the onset of buckling, postbuckling dynamics, and hysteresis phenomena in gel-based systems, introducing novel means of tailoring the functionality of soft structured surfaces and interfaces.

Self-sustained eversion or inversion of a thermally responsive torus

When a cylindrical rod is placed on a flat and hot surface with a constant temperature, it can reach a steady state after certain time. In the steady state, though the temperature field inside the rod is inhomogeneous, it does not change with time. The inhomogeneous temperature change in the rod may induce inhomogeneous thermal expansion in it. Recent experiments have determined that if the rod is slightly curved, the inhomogeneous thermal expansion in the rod can drive its continuous and self-sustained rolling on a hot surface. It has been further shown that if the rod is bent to a closed torus and placed on a hot surface, the torus everts or inverts continuously due to the cross-coupling between the thermal field and the cyclic rotation. Such cyclic eversion or inversion of a torus can be regarded as a zero-elastic-energy mode because both the elastic energy and the shape of the torus remain unchanged during the rotation. In this article, we develop a coupled mechanics theory to model the continuous self-sustained eversion or inversion of a viscoelastic torus on a hot surface. We hope our modeling will inspire more novel designs of elastic motors being capable of zero-energy mode motion and help to quantitatively predict their performance.

Chemical pumps and flexible sheets spontaneously form self-regulating oscillators in solution

The synchronization of self-oscillating systems is vital to various biological functions, from the coordinated contraction of heart muscle to the self-organization of slime molds. Through modeling, we design bioinspired materials systems that spontaneously form shape-changing self-oscillators, which communicate to synchronize both their temporal and spatial behavior. Here, catalytic reactions at the bottom of a fluid-filled chamber and on mobile, flexible sheets generate the energy to "pump" the surrounding fluid, which also transports the immersed sheets. The sheets exert a force on the fluid that modifies the flow, which in turn affects the shape and movement of the flexible sheets. This feedback enables a single coated (active) and even an uncoated (passive) sheet to undergo self-oscillation, displaying different oscillatory modes with increases in the catalytic reaction rate. Two sheets (active or passive) introduce excluded volume, steric interactions. This distinctive combination of the hydrodynamic, fluid-structure, and steric interactions causes the sheets to form coupled oscillators, whose motion is synchronized in time and space. We develop a heuristic model that rationalizes this behavior. These coupled self-oscillators exhibit rich and tunable phase dynamics, which depends on the sheets' initial placement, coverage by catalyst and relative size. Moreover, through variations in the reactant concentration, the system can switch between the different oscillatory modes. This breadth of dynamic behavior expands the functionality of the coupled oscillators, enabling soft robots to display a variety of self-sustained, self-regulating moves.

Reversible Patterning Cross-Linked, Humidity-Responsive Polymer Films with Programmatically and Accurately Controlled Deformation

A series of novel humidity-responsive and photosensitive polymer films (PCA-PAA-PEG) are prepared. These films can be patterning cross-linked by the photodimerization of coumarin pendant groups. The humidity-induced deformation can be well controlled by the pattern because of the different modulus and hydrophilicity between cross-linked and un-cross-linked segments. In addition, the pattern can be erased and the deformation direction can be changed programmatically by the de-cross-linking-re-cross-linking approach due to the reversible photodimerization of coumarin groups. The cross-linking degree also affects the humidity responsiveness of the film. The deformation of the gradient patterning cross-linked film can be more accurately controlled. Moreover, the length and width ratio (L/W_s/W_h) of the un-cross-linked segment to the cross-linked segment affects the deformation of the films as well. When L/W_s/W_h is 5/2/1 or 5/3/1, the deformation is controllable, and when L/W_s/W_h is 5/1/1 or 5/4/1, the deformation is random at the initial stage, but the whole film will bend along the short axis in the end.

Self-Oscillating Membranes: Chemomechanical Sheets Show Autonomous Periodic Shape Transformation

While living organisms have mastered the dynamic control of residual stresses within sheets to induce shape transformation and locomotion, man-made implementations are rudimentary. We present the first autonomously shape-shifting sheets made of a gel that shrinks and swells in response to the phase of an oscillatory chemical (Belousov-Zhabotinsky) reaction. Propagating reaction-diffusion fronts induce localized deformation of the gel. We show that these localized deformations prescribe a spatiotemporal pattern of Gaussian curvature, leading to time-periodic global shape changes. We present the computational tools and experimental protocols needed to control this system, principally the relationship between the Gaussian curvature and the reaction phase, and optical imprinting of the wave pattern. Together, our results demonstrate a route for developing fully autonomous soft machines mimicking some of the locomotive capabilities of living organisms.

Autonomous oil flow generated by self-oscillating polymer gels

The previously reported gel and polymer actuators require external inputs, such as batteries, circuits, electronic circuits, etc., compared with autonomous motions produced by the living organisms. To realize the spontaneous motions, here, we propose to integrate a power supply, actuators, and control into a single-component self-oscillating hydrogel. We demonstrate self-actuating gel pumps driven by the oscillatory Belousov-Zhabotinsky (BZ) reaction without electronic components. We have developed the volume oscillation of gels synchronized with the BZ reaction (BZ gel). Since the self-actuating gel pumps are driven by chemo-mechanical energy from BZ gels, the self-actuating gel pumps don't require complex wiring designs, energy supply, and assembling. The mechanical work generated by BZ gels is extremely small. We formulated the thermodynamic cycle of BZ gels and maximized mechanical work. We found that pre-stretched BZ gel shows larger mechanical works. We physically separated the BZ gels and working fluid to create practical pumps. By using optimizing mechanical generated by BZ gels, we demonstrated the self-actuating gel pumps that transfer mechanical work through a stretchable elastomer membrane.

Harnessing biomimetic cryptic bonds to form self-reinforcing gels

Cryptic sites, which lay hidden in folded biomolecules, become exposed by applied force and form new bonds that reinforce the biomaterial. While these binding interactions effectively inhibit mechanical deformation, there are few synthetic materials that harness mechano-responsive cryptic sites to forestall damage. Here, we develop a computational model to design polymer gels encompassing cryptic sites and a lower critical solution temperature (LCST). LCST gels swell with a decrease in temperature, thereby generating internal stresses within the sample. The gels also encompass loops held together by the cryptic sites, as well as dangling chains with chemically reactive ends. A decrease in temperature or an applied force causes the loops to unfold and expose the cryptic sites, which then bind to the dangling chains. We show that these binding interactions act as "struts" that reinforce the network, as indicated by a significant decrease in the volume of the gel (from 44% to 80%) and shifts in the volume phase transition temperature. Once the temperature is increased or the deformation is removed, the latter "cryptic bonds" are broken, allowing the loops to refold and the gel to return to its original state. These findings provide guidelines for designing polymer networks with reversible, mechano-responsive bonds, which allow gels to undergo a self-stiffening behavior in response to a temperature-induced internal stress or external force. When applied as a coating, these gels can prevent the underlying materials from undergoing damage and thus, extend the lifetime of the system.

Chemomechanical origin of directed locomotion driven by internal chemical signals

Asymmetry in the interaction between an individual and its environment is generally considered essential for the directional properties of active matter, but can directional locomotions and their transitions be generated only from intrinsic chemical dynamics and its modulation? Here, we examine this question by simulating the locomotion of a bioinspired active gel in a homogeneous environment. We find that autonomous directional locomotion emerges in the absence of asymmetric interaction with the environment and that a transition between modes of gel locomotion can be induced by adjusting the spatially uniform intensity of illumination or certain kinetic and mechanical system parameters. The internal wave dynamics and its structural modulation act as the impetus for signal-driven active locomotion in a manner similar to the way in which an animal's locomotion is generated via driving by nerve pulses. Our results may have implications for the development of soft robots and biomimetic materials.

Programmed Locomotion of an Active Gel Driven by Spiral Waves

Active media that host spiral waves can display complex modes of locomotion driven by the dynamics of those waves. We use a model of a photosensitive stimulus-responsive gel that supports the propagation of spiral chemical waves to study locomotive transition and programmed locomotion. The mode transition between circular and toroidal locomotion results from the onset of spiral tip meandering that arises via a secondary Hopf bifurcation as the level of illumination is increased. This dynamic instability of the system introduces a second circular locomotion with a small diameter caused by tip meandering. The original circular locomotion with large diameter is driven by the push-pull asymmetry of the wavefront and waveback of the simple spiral waves initiated at one corner of gel. By harnessing this mode transition of the gel locomotion via coded illumination, we design programmable pathways of nature-inspired angular locomotion of the gel.

Programmable patterns in a DNA-based reaction-diffusion system

Biology offers compelling proof that macroscopic "living materials" can emerge from reactions between diffusing biomolecules. Here, we show that molecular self-organization could be a similarly powerful approach for engineering functional synthetic materials. We introduce a programmable DNA embedded hydrogel that produces tunable patterns at the centimeter length scale. We generate these patterns by implementing chemical reaction networks through synthetic DNA complexes, embedding the complexes in the hydrogel, and triggering with locally applied input DNA strands. We first demonstrate ring pattern formation around a circular input cavity and show that the ring width and intensity can be predictably tuned. Then, we create patterns of increasing complexity, including concentric rings and non-isotropic patterns. Finally, we show "destructive" and "constructive" interference patterns, by combining several ring-forming modules in the gel and triggering them from multiple sources. We further show that computer simulations based on the reaction-diffusion model can predict and inform the programming of target patterns.

Modeling the behavior of inclusions in circular plates undergoing shape changes from two to three dimensions

Growth of biological tissues and shape changes of thin synthetic sheets are commonly induced by stimulation of isolated regions (inclusions) in the system. These inclusions apply internal forces on their surroundings that, in turn, promote 2D layers to acquire complex 3D configurations. We focus on a fundamental building block of these systems, and consider a circular plate that contains an inclusion with dilative strains. Based on the Föppl-von Kármán (FvK) theory, we derive an analytical model that predicts the 2D-to-3D shape transitions in the system. Our findings are summarized in a phase diagram that reveals two distinct configurations in the post-buckling region. One is an extensive profile that holds close to the threshold of the instability, and the second is a localized profile, which preempts the extensive solution beyond the buckling threshold. While the former solution is derived as a perturbation around the flat configuration, assuming infinitesimal amplitudes, the latter solution is derived around a buckled state that is highly localized. We show that up to vanishingly small corrections that scale with the thickness, this localized configuration is equivalent to that expected for ultra-thin sheets, which completely relax compressive stresses. Our findings agree quantitatively with direct numerical minimization of the FvK energy. Furthermore, we extend the theory to describe shape transitions in polymeric gels, and compare the results with numerical simulations that account for the complete elastodynamic behavior of the gels. The agreement between the theory and these simulations indicates that our results are observable experimentally. Notably, our findings can provide guidelines to the analysis of more complicated systems that encompass interaction between several buckled inclusions.

Modeling the formation of double rolls from heterogeneously patterned gels

Both stimuli-responsive gels and growing biological tissue can undergo pronounced morphological transitions from two-dimensional (2D) layers into 3D geometries. We derive an analytical model that allows us to quantitatively predict the features of 2D-to-3D shape changes in polymer gels that encompasses different degrees of swelling within the sample. We analyze a particular configuration that emerges from a flat rectangular gel that is divided into two strips (bistrips), where each strip is swollen to a different extent in solution. The final configuration yields double rolls that display a narrow transition layer between two cylinders of constant radii. To characterize the rolls' shapes, we modify the theory of thin incompatible elastic sheets to account for the Flory-Huggins interaction between the gel and the solvent. This modification allows us to derive analytical expressions for the radii, the amplitudes, and the length of the transition layer within a given roll. Our predictions agree quantitatively with available experimental data. In addition, we carry out numerical simulations that account for the complete nonlinear behavior of the gel and show good agreement between the analytical predictions and the numerical results. Our solution sheds light on a stress focusing pattern that forms at the border between two dissimilar soft materials. Moreover, models that provide quantitative predictions on the final morphology in such heterogeneously swelling hydrogels are useful for understanding growth patterns in biology as well as accurately tailoring the structure of gels for various technological applications.

Towards feedback-controlled nanomedicines for smart, adaptive delivery

IMPACT STATEMENT

The timing and rate of release of pharmaceuticals from advanced drug delivery systems is an important property that has received considerable attention in the scientific literature. Broadly, these mostly fall into two classes: controlled release with a prolonged release rate or triggered release where the drug is rapidly released in response to an environmental stimulus. This review aims to highlight the potential for developing adaptive release systems that more subtlety modulate the drug release profile through continuous communication with its environment facilitated through feedback control. By reviewing the key elements of this approach in one place (fundamental principles of nanomedicine, enzymatic nanoreactors for medical therapies and feedback-controlled chemical systems) and providing additional motivating case studies in the context of chronobiology, we hope to inspire innovative development of novel "chrononanomedicines."

Under Diffusion Control: from Structuring Matter to Directional Motion

Self-organization in synthetic chemical systems is quickly developing into a powerful strategy for designing new functional materials. As self-organization requires the system to exist far from thermodynamic equilibrium, chemists have begun to go beyond the classical equilibrium self-assembly that is often applied in bottom-up supramolecular synthesis, and to learn about the surprising and unpredicted emergent properties of chemical systems that are characterized by a higher level of complexity and extended reactivity networks. The present review focuses on self-organization in reaction-diffusion systems. Selected examples show how the emergence of complex morphogenesis is feasible in synthetic systems leading to hierarchically and nanostructured matter. Starting from well-investigated oscillating reactions, recent developments extend diffusion-limited reactivity to supramolecular systems. The concept of dynamic instability is introduced and illustrated as an additional tool for the design of smart materials and actuators, with emphasis on the realization of motion even at the macroscopic scale. The formation of spatio-temporal patterns along diffusive chemical gradients is exploited as the main channel to realize symmetry breaking and therefore anisotropic and directional mechanical transformations. Finally, the interaction between external perturbations and chemical gradients is explored to give mechanistic insights in the design of materials responsive to external stimuli.

Designing the Slide-Ring Polymer Network with both Good Mechanical and Damping Properties via Molecular Dynamics Simulation

Through coarse-grained molecular dynamics simulation, we have successfully designed the chemically cross-linked (fixed junction) and the slide-ring (SR) systems. Firstly, we examine the dynamic properties such as the mean-square displacement, the bond, and the end-to-end autocorrelation functions as a function of the cross-linking density, consistently pointing out that the SR system exhibits much lower mobility compared with the fixed junction one at the same cross-linking density. This is further validated by a relatively higher glass transition temperature for the SR system compared with that of the fixed junction one. Then, we calculated the effect of the cross-linking density on the stretch-recovery behavior for the SR and fixed junction systems. Although the chain orientation of the SR system is higher than that of the fixed-junction system, the tensile stress is smaller than the latter. We infer that much greater chain sliding can occur during the stretch, because the movable ring structure homogeneously sustains the external force of the SR system, which, therefore, leads to much larger permanent set and higher hysteresis during the recovery process compared with the fixed-junction one. Based on the stretch-recovery behavior for various cross-linking densities, we obtain the change of the hysteresis loss, which is larger for the SR system than that of the fixed junction system. Lastly, we note that the relatively bigger compressive stress for the SR system results from the aggregation of the rigid rings compared with the fixed junction system. In general, compared with the traditionally cross-linked system, a deep molecular-level insight into the slide-ring polymer network is offered and thus is believed to provide some guidance to the design and preparation of the slide-ring polymer network with both good mechanical and damping properties.

Multiresponsive Kinematics and Robotics of Surface-Patterned Polymer Film

Soft robots, sensors, and energy harvesters require materials that are capable of converting external stimuli to visible deformations, especially when shape-programmable deformations are desired. Herein, we develop a polymer film that can reversibly respond to humidity, heating, and acetone vapors with the generation of shape-programmable large deformations. Poly(vinylidene fluoride) film, capable of providing acetone responsiveness, is designed with microchannel patterns created on its one side by using templates, and the microchannels-patterned side is then treated with hygroscopic 3-aminopropyltriethoxysilane (APTES) to give humidity/heating-responsive elements. The APTES-modified microchannels lead to anisotropic flexural modulus and hygroscopicity in the film, resulting in the shape-programmed kinematics depending on the orientations of surface microchannels. As the microchannels align at oblique/right angles with respect to the long axis of the film strips, the coiling/curling motions can be generated in response to the stimuli, and the better motion performances are found in humidity- and heating-driven systems. This material utilized in self-adaptive soft robots exhibits prominent toughness, powerful strength, and long endurance for converting humidity and heat to mechanical works including transportation of lightweight objects, automatic sensing cap, and mimicking crawling in nature. We thus believe that this material with shape-programmable multisensing capability might be suitable for soft machines and robotics.