Soft robotics informs how an early echinoderm moved.

The transition from sessile suspension to active mobile detritus feeding in early echinoderms (c.a. 500 Mya) required sophisticated locomotion strategies. However, understanding locomotion adopted by extinct animals in the absence of trace fossils and modern analogues is extremely challenging. Here, we develop a biomimetic soft robot testbed with accompanying computational simulation to understand fundamental principles of locomotion in one of the most enigmatic mobile groups of early stalked echinoderms-pleurocystitids. We show that these Paleozoic echinoderms were likely able to move over the sea bottom by means of a muscular stem that pushed the animal forward (anteriorly). We also demonstrate that wide, sweeping gaits could have been the most effective for these echinoderms and that increasing stem length might have significantly increased velocity with minimal additional energy cost. The overall approach followed here, which we call "Paleobionics," is a nascent but rapidly developing research agenda in which robots are designed based on extinct organisms to generate insights in engineering and evolution.

Material assembly from collective action of shape-changing polymers.

Some animals form transient, responsive and solid-like ensembles through dynamic structural interactions. These ensembles demonstrate emergent responses such as spontaneous self-assembly, which are difficult to achieve in synthetic soft matter. Here we use shape-morphing units comprising responsive polymers to create solids that self-assemble, modulate their volume and disassemble on demand. The ensemble is composed of a responsive hydrogel, liquid crystal elastomer or semicrystalline polymer ribbons that reversibly bend or twist. The dispersions of these ribbons mechanically interlock, inducing reversible aggregation. The aggregated liquid crystal elastomer ribbons have a 12-fold increase in the yield stress compared with cooled dispersion and contract by 34% on heating. Ribbon type, concentration and shape dictate the aggregation and govern the global mechanical properties of the solid that forms. Coating liquid crystal elastomer ribbons with a liquid metal begets photoresponsive and electrically conductive aggregates, whereas seeding cells on hydrogel ribbons enables self-assembling three-dimensional scaffolds, providing a versatile platform for the design of dynamic materials.

A multifunctional shape-morphing elastomer with liquid metal inclusions.

Natural soft tissue achieves a rich variety of functionality through a hierarchy of molecular, microscale, and mesoscale structures and ordering. Inspired by such architectures, we introduce a soft, multifunctional composite capable of a unique combination of sensing, mechanically robust electronic connectivity, and active shape morphing. The material is composed of a compliant and deformable liquid crystal elastomer (LCE) matrix that can achieve macroscopic shape change through a liquid crystal phase transition. The matrix is dispersed with liquid metal (LM) microparticles that are used to tailor the thermal and electrical conductivity of the LCE without detrimentally altering its mechanical or shape-morphing properties. Demonstrations of this composite for sensing, actuation, circuitry, and soft robot locomotion suggest the potential for versatile, tissue-like multifunctionality.

Soft actuators by electrochemical oxidation of liquid metal surfaces.

The surface energy of liquid metals can be electrochemically controlled over a wide range of values - from near zero to 500 mJ m-2- using a low voltage potential (∼1 V). This enables the ability to create soft-matter actuators that exhibit a high work density on small scales. We demonstrate that a liquid metal (LM) meniscus wetted between two copper pads can function as an electrochemical soft actuator whose force and shape are controllable by tuning the LM surface energy. Energy minimization models are presented in order to predict the actuator performance as a function of LM droplet and Cu pad dimensions. The results suggest that the electrochemical LM actuator has a unique combination of high work density, biologically-relevant activation frequency, and low operational voltage that stands out from other classes of soft-matter actuators.

A Soft Resistive Sensor with a Semicircular Cross-Sectional Channel for Soft Cardiac Catheter Ablation.

The field of soft robotics has attracted the interest of the medical community due to the ability of soft elastic materials to traverse the abnormal environment of the human body. However, sensing in soft robotics has been challenging due to the sensitivity of soft sensors to various loading conditions and the nonlinear signal responses that can arise under extreme loads. Ideally, soft sensors should provide a linear response under a specific loading condition and provide a different response for other loading directions. With these specifications in mind, our team created a soft elastomeric sensor designed to provide force feedback during cardiac catheter ablation surgery. Analytical and computational methods were explored to define a relationship between resistance and applied force for a semicircular, liquid metal filled channel in the soft elastomeric sensor. Pouillet's Law is utilized to calculate the resistance based on the change in cross-sectional area resulting from various applied pressures. FEA simulations were created to simulate the deformation of the sensor under various loads. To confirm the validity of these simulations, the elastomer was modeled as a neo-Hookean material and the liquid metal was modeled as an incompressible fluid with negligible shear modulus under uniaxial compression. Results show a linearly proportional relationship between the resistance of the sensor and the application of a uniaxial force. Altering the direction of applied force results in a quadratic relationship between total resistance and the magnitude of force.

Network topologies dictate electromechanical coupling in liquid metal-elastomer composites.

Elastomers embedded with micro- and nanoscale droplets of liquid metal (LM) alloys like eutectic gallium-indium (EGaIn) can exhibit unique combinations of elastic, thermal, and electrical properties that are difficult to achieve using rigid filler. For composites with sufficient concentrations of liquid metal, the LM droplets can form percolating networks that conduct electricity and deform with the surrounding elastomer as the composite is stretched. Surprisingly, experimental measurements performed on LM-embedded elastomers (LMEEs) show that the total electrical resistance of the composite increases only slightly even as the elastomer is stretched to several times its natural length. In contrast, Pouillet's law would predict an exponential increase in resistance (Ω) with stretch (λ) due to the incompressibility of liquid metal and elastomer. In this manuscript, we perform a computational analysis to examine the unique electromechanical properties of conductive LMEE composites. Our analysis suggests that the gauge factor that quantifies electromechanical coupling (i.e. G = {ΔΩ/Ω0}/λ) decreases with increasing tortuosity of the conductive pathways formed by the connected LM droplets. A dimensionless parameter for path tortuosity can be used to estimate G for statistically homogeneous LMEE composites. These results rationalize experimental observations and provide insight into the influence of liquid metal droplet assembly on the functionality of the composite.

Size of liquid metal particles influences actuation properties of a liquid crystal elastomer composite.

Composites of liquid crystal elastomer (LCE) that are electrically conductive have the potential to function as soft "artificial muscle" actuators that can be reversibly stimulated with electrical Joule-heating. Conductivity can be achieved by embedding the LCE with droplets of an alloy of gallium and indium that is liquid at room temperature. These soft artificial muscles are capable of >50% reversible actuation with an applied load. The key to actuation at high loadings of liquid metal (LM) is that the droplets deform with the surrounding matrix. By controlling the size of LM droplets through simple processing techniques, we show that the actuator properties of the LM-LCE muscle can be tuned. For example, composites with smaller liquid metal particles (ca. 10 µm or less) are stiffer than those with larger liquid metal particles (ca. >100 µm) and are capable of greater force output. However, smaller particles reduce actuation strain and composites with large particles exhibit significantly greater stroke length. Such tunability in actuation properties permits the fabrication of specialized soft artificial muscles, where processing of the composite controls actuation strain and actuation force.

Controllable load sharing for soft adhesive interfaces on three-dimensional surfaces.

For adhering to three-dimensional (3D) surfaces or objects, current adhesion systems are limited by a fundamental trade-off between 3D surface conformability and high adhesion strength. This limitation arises from the need for a soft, mechanically compliant interface, which enables conformability to nonflat and irregularly shaped surfaces but significantly reduces the interfacial fracture strength. In this work, we overcome this trade-off with an adhesion-based soft-gripping system that exhibits enhanced fracture strength without sacrificing conformability to nonplanar 3D surfaces. Composed of a gecko-inspired elastomeric microfibrillar adhesive membrane supported by a pressure-controlled deformable gripper body, the proposed soft-gripping system controls the bonding strength by changing its internal pressure and exploiting the mechanics of interfacial equal load sharing. The soft adhesion system can use up to ∼26% of the maximum adhesion of the fibrillar membrane, which is 14× higher than the adhering membrane without load sharing. Our proposed load-sharing method suggests a paradigm for soft adhesion-based gripping and transfer-printing systems that achieves area scaling similar to that of a natural gecko footpad.

High thermal conductivity in soft elastomers with elongated liquid metal inclusions.

Soft dielectric materials typically exhibit poor heat transfer properties due to the dynamics of phonon transport, which constrain thermal conductivity (k) to decrease monotonically with decreasing elastic modulus (E). This thermal-mechanical trade-off is limiting for wearable computing, soft robotics, and other emerging applications that require materials with both high thermal conductivity and low mechanical stiffness. Here, we overcome this constraint with an electrically insulating composite that exhibits an unprecedented combination of metal-like thermal conductivity, an elastic compliance similar to soft biological tissue (Young's modulus < 100 kPa), and the capability to undergo extreme deformations (>600% strain). By incorporating liquid metal (LM) microdroplets into a soft elastomer, we achieve a ∼25× increase in thermal conductivity (4.7 ± 0.2 W⋅m-1⋅K-1) over the base polymer (0.20 ± 0.01 W⋅m-1·K-1) under stress-free conditions and a ∼50× increase (9.8 ± 0.8 W⋅m-1·K-1) when strained. This exceptional combination of thermal and mechanical properties is enabled by a unique thermal-mechanical coupling that exploits the deformability of the LM inclusions to create thermally conductive pathways in situ. Moreover, these materials offer possibilities for passive heat exchange in stretchable electronics and bioinspired robotics, which we demonstrate through the rapid heat dissipation of an elastomer-mounted extreme high-power LED lamp and a swimming soft robot.

An autonomously electrically self-healing liquid metal-elastomer composite for robust soft-matter robotics and electronics.

Large-area stretchable electronics are critical for progress in wearable computing, soft robotics and inflatable structures. Recent efforts have focused on engineering electronics from soft materials-elastomers, polyelectrolyte gels and liquid metal. While these materials enable elastic compliance and deformability, they are vulnerable to tearing, puncture and other mechanical damage modes that cause electrical failure. Here, we introduce a material architecture for soft and highly deformable circuit interconnects that are electromechanically stable under typical loading conditions, while exhibiting uncompromising resilience to mechanical damage. The material is composed of liquid metal droplets suspended in a soft elastomer; when damaged, the droplets rupture to form new connections with neighbours and re-route electrical signals without interruption. Since self-healing occurs spontaneously, these materials do not require manual repair or external heat. We demonstrate this unprecedented electronic robustness in a self-repairing digital counter and self-healing soft robotic quadruped that continue to function after significant damage.

Analysis of the Efficiency of Surfactant-Mediated Stabilization Reactions of EGaIn Nanodroplets.

A methodology based on light scattering and spectrophotometry was developed to evaluate the effect of organic surfactants on the size and yield of eutectic gallium/indium (EGaIn) nanodroplets formed in organic solvents by ultrasonication. The process was subsequently applied to systematically evaluate the role of headgroup chemistry as well as polar/apolar interactions of aliphatic surfactant systems on the efficiency of nanodroplet formation. Ethanol was found to be the most effective solvent medium in promoting the formation and stabilization of EGaIn nanodroplets. For the case of thiol-based surfactants in ethanol, the yield of nanodroplet formation increased with the number of carbon atoms in the aliphatic part. In the case of the most effective surfactant system-octadecanethiol-the nanodroplet yield increased by about 370% as compared to pristine ethanol. The rather low overall efficiency of the reaction process along with the incompatibility of surfactant-stabilized EGaIn nanodroplets in nonpolar organic solvents suggests that the stabilization mechanism differs from the established self-assembled monolayer formation process that has been widely observed in nanoparticle formation.

Gelation and mechanical response of patchy rods.

We perform Brownian dynamics simulations to study the gelation of suspensions of attractive, rod-like particles. We show that in detail the rod-rod surface interactions can dramatically affect the dynamics of gelation and the structure and mechanics of the networks that form. If the attraction between the rods is perfectly smooth along their length, they will collapse into compact bundles. If the attraction is sufficiently corrugated or patchy, over time, a rigid space-spanning network will form. We study the structure and mechanical properties of the networks that form as a function of the fraction of the surface, f, that is allowed to bind. Surprisingly, the structural and mechanical properties are non-monotonic in f. At low f, there are not a sufficient number of cross-linking sites to form networks. At high f, rods bundle and form disconnected clusters. At intermediate f, robust networks form. The elastic modulus and yield stress are both non-monotonic in the surface coverage. The stiffest and strongest networks show an essentially homogeneous deformation under strain with rods re-orienting along the extensional axis. Weaker, more clumpy networks at high f re-orient relatively little with strong non-affine deformation. These results suggest design strategies for tailoring surface interactions between rods to yield rigid networks with optimal mechanical properties.

Liquid Metal Actuators: A Comparative Analysis of Surface Tension Controlled Actuation.

Liquid metals, with their unique combination of electrical and mechanical properties, offer great opportunities for actuation based on surface tension modulation. Thanks to the scaling laws of surface tension, which can be electrochemically controlled at low voltages, liquid metal actuators stand out from other soft actuators for their remarkable characteristics such as high contractile strain rates and higher work densities at smaller length scales. This review summarizes the principles of liquid metal actuators and discusses their performance as well as theoretical pathways toward higher performances. The objective is to provide a comparative analysis of the ongoing development of liquid metal actuators. The design principles of the liquid metal actuators are analyzed, including low-level elemental principles (kinematics and electrochemistry), mid-level structural principles (reversibility, integrity, and scalability), and high-level functionalities. A wide range of practical use cases of liquid metal actuators from robotic locomotion and object manipulation to logic and computation is reviewed. From an energy perspective, strategies are compared for coupling the liquid metal actuators with an energy source toward fully untethered robots. The review concludes by offering a roadmap of future research directions of liquid metal actuators.

Safe Supervisory Control of Soft Robot Actuators.

Although soft robots show safer interactions with their environment than traditional robots, soft mechanisms and actuators still have significant potential for damage or degradation particularly during unmodeled contact. This article introduces a feedback strategy for safe soft actuator operation during control of a soft robot. To do so, a supervisory controller monitors actuator state and dynamically saturates control inputs to avoid conditions that could lead to physical damage. We prove that, under certain conditions, the supervisory controller is stable and verifiably safe. We then demonstrate completely onboard operation of the supervisory controller using a soft thermally actuated robot limb with embedded shape memory alloy actuators and sensing. Tests performed with the supervisor verify its theoretical properties and show stabilization of the robot limb's pose in free space. Finally, experiments show that our approach prevents overheating during contact, including environmental constraints and human touch, or when infeasible motions are commanded. This supervisory controller, and its ability to be executed with completely onboard sensing, has the potential to make soft robot actuators reliable enough for practical use.

Statistical field theory of polarizable polymer chains with nonlocal dipolar interactions.

The electromechanical response of polymeric soft matter to applied electric fields is of fundamental scientific interest as well as relevant to technologies for sensing and actuation. Several existing theoretical and numerical approaches for polarizable polymers subject to a combined applied electric field and stretch are based on discrete monomer models. In these models, accounting for the interactions between the induced dipoles on monomers is challenging due to the nonlocality of these interactions. On the other hand, the framework of statistical field theory provides a continuous description of polymer chains that potentially enables a tractable way to account for these interactions. However, prior formulations using this framework have been restricted to the case of weak anisotropy of the monomer polarizability. This paper formulates a general approach based in the framework of statistical field theory to account for the nonlocal nature of the dipolar interactions without any restrictions on the anisotropy or nonlinearity of the polarizability of the monomer. The approach is based on three key elements: (1) the statistical field theory framework, in which the discrete monomers are regularized to a continuous dipole distribution, (2) a replacement of the nonlocal dipole-dipole interactions by the local electrostatics partial differential equation with the continuous dipole distribution as the forcing, and (3) the use of a completely general relation between the polarization and the local electric field. Rather than treat the dipole-dipole interactions directly, the continuous description in the field theory enables the computationally tractable nonlocal-to-local transformation. Further, it enables the use of a realistic statistical-mechanical ensemble wherein the average far-field applied electric field is prescribed, rather than prescribing the applied field at every point in the polymer domain. The model is applied, using the finite element method, to study the electromechanical response of a polymer chain in the ensemble with fixed far-field applied electric field and fixed chain stretch. The nonlocal dipolar interactions are found to increase, over the case where dipole-dipole interactions are neglected, the magnitudes of the polarization and electric field by orders of magnitude as well as significantly change their spatial distributions. Next, the effect of the relative orientation between the applied field and the chain on the local electric field and polarization is studied. The model predicts that the elastic response of the polymer chain is linear, consistent with the Gaussian approximation, and largely unchanged by the orientation of the applied electric field, though the polarization and local electric field distributions are significantly impacted.

Intrinsically Multistable Soft Actuator Driven by Mixed-Mode Snap-Through Instabilities.

Actuators utilizing snap-through instabilities are widely investigated for high-performance fast actuators and shape reconfigurable structures owing to their rapid response and limited reliance on continuous energy input. However, prevailing approaches typically involve a combination of multiple bistable actuator units and achieving multistability within a single actuator unit still remains an open challenge. Here, a soft actuator is presented that uses shape memory alloy (SMA) and mixed-mode elastic instabilities to achieve intrinsically multistable shape reconfiguration. The multistable actuator unit consists of six stable states, including two pure bending states and four bend-twist states. The actuator is composed of a pre-stretched elastic membrane placed between two elastomeric frames embedded with SMA coils. By controlling the sequence and duration of SMA activation, the actuator is capable of rapid transition between all six stable states within hundreds of milliseconds. Principles of energy minimization are used to identify actuation sequences for various types of stable state transitions. Bending and twisting angles corresponding to various prestretch ratios are recorded based on parameterizations of the actuator's geometry. To demonstrate its application in practical conditions, the multistable actuator is used to perform visual inspection in a confined space, light source tracking during photovoltaic energy harvesting, and agile crawling.

Selective and Controlled Grafting from PVDF-Based Materials by Oxygen-Tolerant Green-Light-Mediated ATRP.

Poly(vinylidene fluoride) (PVDF) shows excellent chemical and thermal resistance and displays high dielectric strength and unique piezoelectricity, which are enabling for applications in membranes, electric insulators, sensors, or power generators. However, its low polarity and lack of functional groups limit wider applications. While inert, PVDF has been modified by grafting polymer chains by atom transfer radical polymerization (ATRP), albeit via an unclear mechanism, given the strong C-F bonds. Herein, we applied eosin Y and green-light-mediated ATRP to modify PVDF-based materials. The method gave nearly quantitative (meth)acrylate monomer conversions within 2 h without deoxygenation and without the formation of unattached homopolymers, as confirmed by control experiments and DOSY NMR measurements. The gamma distribution model that accounts for broadly dispersed polymers in DOSY experiments was essential and serves as a powerful tool for the analysis of PVDF. The NMR analysis of poly(methyl acrylate) graft chain-ends on PVDF-CTFE (statistical copolymer with chlorotrifluoroethylene) was carried out successfully for the first time and showed up to 23 grafts per PVDF-CTFE chain. The grafting density was tunable depending on the solvent composition and light intensity during the grafting. The initiation proceeded either from the C-Cl sites of PVDF-CTFE or via unsaturations in the PVDF backbones. The dehydrofluorinated PVDF was 20 times more active than saturated PVDF during the grafting. The method was successfully applied to modify PVDF, PVDF-HFP, and Viton A401C. The obtained PVDF-CTFE-g-PnBMA materials were investigated in more detail. They featured slightly lower crystallinity than PVDF-CTFE (12-18 vs 24.3%) and had greatly improved mechanical performance: Young's moduli of up to 488 MPa, ductility of 316%, and toughness of 46 × 106 J/m3.

A Gradient Stiffness-Programmed Circuit Board by Spatially Controlled Phase-Transition of Supercooled Hydrogel for Stretchable Electronics Integration.

Due to emerging demands in soft electronics, there is an increasing need for material architectures that support robust interfacing between soft substrates, stretchable electrical interconnects, and embedded rigid microelectronics chips. Though researchers have adopted rigid-island structures to solve the issue, this approach merely shifts stress concentrations from chip-conductor interfaces to rigid-island-soft region interfaces in the substrate. Here, a gradient stiffness-programmed circuit board (GS-PCB) that possesses high stretchability and stability with surface mounted chips is introduced. The board comprises a stiffness-programmed hydrogel substrate and a laser-patterned liquid metal conductor. The hydrogel simultaneously obtains a large stiffness disparity and robust interfaces between rigid-islands and soft regions. These seemingly contradictory conditions are accomplished by adopting a gradient stiffness structure at the interfaces, enabled by combining polymers with different interaction energies and a supercooled sodium acetate solution. By integrating the gel with laser-patterned liquid metal with exceptional properties, GS-PCB exhibits higher electromechanical stability than other rigid-island research. To highlight the practicality of this approach, a finger-sensor device that successfully distinguishes objects by direct physical contact is fabricated, demonstrating its stability under various mechanical disturbances.

Liquid-phase gallium-indium alloy electronics with microcontact printing.

Liquid-phase electronic circuits are patterned on an elastomer substrate with a microcontact printer. The printer head dips into a pool of a liquid-phase gallium-indium alloy, e.g., eutectic gallium-indium (EGaIn) or gallium-indium-tin (Galinstan), and deposits a single drop on a silicone elastomer substrate. After patterned deposition, the liquid-phase circuit is sealed with an additional layer of silicone elastomer. We also demonstrate patterned deposition of the liquid-phase GaIn alloy with a molded polydimethylsiloxane stamp that is manually inked and pressed into an elastomer substrate. As with other liquid-phase electronics produced through needle injection or masked deposition, the circuit is elastically deformable and can be stretched to several times its natural length without losing electronic functionality. In contrast to existing fabrication techniques, microcontact printing and stamp lithography can be used to produce circuits with any planar geometric feature, including electrodes with large planar area, intersecting and closed-loop wires, and combs with multiple terminal electrodes. In air, the surface of the coalesced droplets oxidize to form a thin oxide skin that preserves the shape of the circuit during sealing. This first demonstration of soft-lithography fabrication with liquid-phase GaIn alloy expands the space of allowable circuit geometries and eliminates the need for mold or mask fabrication.

Dielectric Elastomers with Liquid Metal and Polydopamine-Coated Graphene Oxide Inclusions.

Suspending microscale droplets of liquid metals like eutectic gallium-indium (EGaIn) in polydimethylsiloxane (PDMS) has been shown to dramatically enhance electrical permittivity without sacrificing the elasticity of the host PDMS matrix. However, increasing the dielectric constant of EGaIn-PDMS composites beyond previously reported values requires high EGaIn loading fractions (>50% by volume) that can result in substantial increases in density and loss of material integrity. In this work, we enhance permittivity without further increasing EGaIn loading by incorporating polydopamine (PDA)-coated graphene oxide (GO) and partially reduced GO. In particular, we show that the combination of EGaIn and PDA-GO within a PDMS matrix results in an elastomer composite with a high dielectric constant (∼10-57), a low dissipation factor (∼0.01), and rubber-like compliance and elasticity.