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.

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.

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.

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.

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.

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.

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.

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.

Soft magnetic thin film deformation with a bistable electropermanent magnet.

Physically soft magnetic materials (PSMMs) represent an emerging class of materials that can change shape or rheology in response to an external magnetic field. However, until now, no studies have investigated using an electropermanent magnet (EPM) and magnetic repulsion to magnetically deform PSMMs. Such capabilities would enable the ability to deform PSMMs without the need for continuous electrical input and produce PSMM film deformation without an air gap, as would be required with magnetic attraction. To address this, we introduce a PSMM-EPM architecture in which the shape of a soft deformable thin film is controlled by switching between bistable on/off states of the EPM circuit. We characterized the deflection of a PSMM thin film when placed at controlled distances normal to the surface of the EPM and compared its response for cases when the EPM is in the 'on' and 'off' states. This work is the first to demonstrate a magnetically repelled soft deformable thin film that achieves two electronically-controlled modes of deformation through the on and off states of an EPM. This work has the potential to advance the development of new magneto-responsive soft materials and systems.

A multimodal sensing ring for quantification of scratch intensity.

BACKGROUND: An objective measurement of chronic itch is necessary for improvements in patient care for numerous medical conditions. While wearables have shown promise for scratch detection, they are currently unable to estimate scratch intensity, preventing a comprehensive understanding of the effect of itch on an individual. METHODS: In this work, we present a framework for the estimation of scratch intensity in addition to the detection of scratch. This is accomplished with a multimodal ring device, consisting of an accelerometer and a contact microphone, a pressure-sensitive tablet for capturing ground truth intensity values, and machine learning algorithms for regression of scratch intensity on a 0-600 milliwatts (mW) power scale that can be mapped to a 0-10 continuous scale. RESULTS: We evaluate the performance of our algorithms on 20 individuals using leave one subject out cross-validation and using data from 14 additional participants, we show that our algorithms achieve clinically-relevant discrimination of scratching intensity levels. By doing so, our device enables the quantification of the substantial variations in the interpretation of the 0-10 scale frequently utilized in patient self-reported clinical assessments. CONCLUSIONS: This work demonstrates that a finger-worn device can provide multidimensional, objective, real-time measures for the action of scratching.

Chronic itch can be caused by many medical conditions including eczema and psoriasis. Itch leads to scratching behaviors that can affect a person's sleep, productivity, mood, and overall well-being. We developed a ring device that can be placed on a person's finger to measure the intensity of scratching. Different types and intensities of scratching behavior could be distinguished in human volunteers. Further development of this device should enable more consistent and comprehensive measurement of scratching behaviors and help doctors and patients to better understand, and treat, chronic itch.

Gecko adhesion based sea star crawler robot.

Over the years, efforts in bioinspired soft robotics have led to mobile systems that emulate features of natural animal locomotion. This includes combining mechanisms from multiple organisms to further improve movement. In this work, we seek to improve locomotion in soft, amphibious robots by combining two independent mechanisms: sea star locomotion gait and gecko adhesion. Specifically, we present a sea star-inspired robot with a gecko-inspired adhesive surface that is able to crawl on a variety of surfaces. It is composed of soft and stretchable elastomer and has five limbs that are powered with pneumatic actuation. The gecko-inspired adhesion provides additional grip on wet and dry surfaces, thus enabling the robot to climb on 25° slopes and hold on statically to 51° slopes.

Coaxially printed magnetic mechanical electrical hybrid structures with actuation and sensing functionalities.

Soft electromagnetic devices have great potential in soft robotics and biomedical applications. However, existing soft-magneto-electrical devices would have limited hybrid functions and suffer from damaging stress concentrations, delamination or material leakage. Here, we report a hybrid magnetic-mechanical-electrical (MME) core-sheath fiber to overcome these challenges. Assisted by the coaxial printing method, the MME fiber can be printed into complex 2D/3D MME structures with integrated magnetoactive and conductive properties, further enabling hybrid functions including programmable magnetization, somatosensory, and magnetic actuation along with simultaneous wireless energy transfer. To demonstrate the great potential of MME devices, precise and minimally invasive electro-ablation was performed with a flexible MME catheter with magnetic control, hybrid actuation-sensing was performed by a durable somatosensory MME gripper, and hybrid wireless energy transmission and magnetic actuation were demonstrated by an untethered soft MME robot. Our work thus provides a material design strategy for soft electromagnetic devices with unexplored hybrid functions.

Recyclable Thin-Film Soft Electronics for Smart Packaging and E-Skins.

Despite advances in soft, sticker-like electronics, few efforts have dealt with the challenge of electronic waste. Here, this is addressed by introducing an eco-friendly conductive ink for thin-film circuitry composed of silver flakes and a water-based polyurethane dispersion. This ink uniquely combines high electrical conductivity (1.6 × 105 S m-1 ), high resolution digital printability, robust adhesion for microchip integration, mechanical resilience, and recyclability.  Recycling is achieved with an ecologically-friendly processing method to decompose the circuits into constituent elements and recover the conductive ink with a decrease of only 2.4% in conductivity. Moreover, adding liquid metal enables stretchability of up to 200% strain, although this introduces the need for more complex recycling steps. Finally, on-skin electrophysiological monitoring biostickers along with a recyclable smart package with integrated sensors for monitoring safe storage of perishable foods are demonstrated.

Statistical field theory for nonlinear elasticity of polymer networks with excluded volume interactions.

Polymer networks formed by cross linking flexible polymer chains are ubiquitous in many natural and synthetic soft-matter systems. Current micromechanics models generally do not account for excluded volume interactions except, for instance, through imposing a phenomenological incompressibility constraint at the continuum scale. This work aims to examine the role of excluded volume interactions on the mechanical response. The approach is based on the framework of the self-consistent statistical field theory of polymers, which provides an efficient mesoscale approach that enables the accounting of excluded volume effects without the expense of large-scale molecular modeling. A mesoscale representative volume element is populated with multiple interacting chains, and the macroscale nonlinear elastic deformation is imposed by mapping the end-to-end vectors of the chains by this deformation. In the absence of excluded volume interactions, it recovers the closed-form results of the classical theory of rubber elasticity. With excluded volume interactions, the model is solved numerically in three dimensions using a finite element method to obtain the energy, stresses, and linearized moduli under imposed macroscale deformation. Highlights of the numerical study include: (i) the linearized Poisson's ratio is very close to the incompressible limit without a phenomenological imposition of incompressibility; (ii) despite the harmonic Gaussian chain as a starting point, there is an emergent strain-softening and strain-stiffening response that is characteristic of real polymer networks, driven by the interplay between the entropy and the excluded volume interactions; and (iii) the emergence of a deformation-sensitive localization instability at large excluded volumes.

Multimaterial Printing of Liquid Crystal Elastomers with Integrated Stretchable Electronics.

Liquid crystal elastomers (LCEs) have grown in popularity in recent years as a stimuli-responsive material for soft actuators and shape reconfigurable structures. To make these material systems electrically responsive, they must be integrated with soft conductive materials that match the compliance and deformability of the LCE. This study introduces a design and manufacturing methodology for combining direct ink write (DIW) 3D printing of soft, stretchable conductive inks with DIW-based "4D printing" of LCE to create fully integrated, electrically responsive, shape programmable matter. The conductive ink is composed of a soft thermoplastic elastomer, a liquid metal alloy (eutectic gallium indium, EGaIn), and silver flakes, exhibiting both high stretchability and conductivity (order of 105 S m-1). Empirical tuning of the LCE printing parameters gives rise to a smooth surface (<10 µm) for patterning the conductive ink with controlled trace dimensions. This multimaterial printing method is used to create shape reconfigurable LCE devices with on-demand circuit patterning that could otherwise not be easily fabricated through traditional means, such as an LCE bending actuator able to blink a Morse code signal and an LCE crawler with an on/off photoresistor controller. In contrast to existing fabrication methodologies, the inclusion of the conductive ink allows for stable power delivery to surface mount devices and Joule heating traces in a highly dynamic LCE system. This digital fabrication approach can be leveraged to push LCE actuators closer to becoming functional devices, such as shape programmable antennas and actuators with integrated sensing.

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.

Controlling C2C12 Cytotoxicity on Liquid Metal Embedded Elastomer (LMEE).

Liquid metal embedded elastomers (LMEEs) are highly stretchable composites comprising microscopic droplets of eutectic gallium-indium (EGaIn) liquid metal embedded in a soft rubber matrix. They have a unique combination of mechanical, electrical, and thermal properties that make them attractive for potential applications in flexible electronics, thermal management, wearable computing, and soft robotics. However, the use of LMEEs in direct contact with human tissue or organs requires an understanding of their biocompatibility and cell cytotoxicity. In this study, the cytotoxicity of C2C12 cells in contact with LMEE composites composed of EGaIn droplets embedded with a polydimethylsiloxane (PDMS) matrix is investigated. In particular, the influence of EGaIn volume ratio and shear mixing time during synthesis on cell proliferation and viability is examined. The special case of electrically-conductive LMEE composites in which a percolating network of EGaIn droplets is created through "mechanical sintering" is also examined. This study in C2C12 cytotoxicity represents a first step in determining whether LMEE is safe for use in implantable biomedical devices and biohybrid systems.

A Method for 3D Printing and Rapid Prototyping of Fieldable Untethered Soft Robots.

Because they are made of elastically deformable and compliant materials, soft robots can passively change shape and conform to their environment, providing potential advantages over traditional robotics approaches. However, existing manufacturing workflows are often labor intensive and limited in their ability to create highly integrated three-dimensional (3D) heterogeneous material systems. In this study, we address this with a streamlined workflow to produce field-deployable soft robots based on 3D printing with digital light processing (DLP) of silicone-like soft materials. DLP-based 3D printing is used to create soft actuators (2.2 g) capable of exerting up to 0.5 Newtons of force that are integrated into a bioinspired untethered soft robot. The robot walks underwater at speeds comparable with its biological analog, the brittle star. Using a model-free planning algorithm and feedback, the robot follows remote commands to move to desired positions. Moreover, we show that the robot is able to perform untethered locomotion outside of a laboratory and in a natural aquatic environment. Our results represent progress in soft robot manufacturing autonomy for a 3D printed untethered soft robot.

Reconfigurable Electrical Networks within a Conductive Hydrogel Composite.

Soft materials that exhibit compliance, programmability, and reconfigurability can have a transformative impact as electronic skin for applications in wearable electronics/soft robotics. There has been significant progress in soft conductive materials; however, achieving electrically controlled and reversible changes in conductivity and circuit connectivity remains challenging. To overcome this limitation, a soft material architecture with reconfigurable conductive networks of silver flakes embedded within a hydrogel matrix is presented. The conductive networks can be reversibly created/disconnected through various stimuli, including current, humidity, or temperature. Such stimuli affect electrical connectivity of the hydrogel by controlling its water content, which can be modulated by evaporation under ambient conditions (passive dehydration), evaporation through electrical Joule heating (active dehydration), or absorption of additional water (rehydration). The resulting change in electrical conductivity is reversible and repeatable, endowing the composite with on-demand reconfigurable conductivity. To highlight this material's unique properties, it is shown that conductive traces can be reconfigured after severe damage and revert to lower conductivity after rehydration. Additionally, a quadruped robot is demonstrated that can respond to stimuli by changing direction following exposure to excess water, thereby achieving reprogrammable locomotion behaviors.

Exploiting ferrofluidic wetting for miniature soft machines.

Miniature magnetic soft machines could significantly impact minimally invasive robotics and biomedical applications. However, most soft machines are limited to solid magnetic materials, whereas further progress also relies on fluidic constructs obtained by reconfiguring liquid magnetic materials, such as ferrofluid. Here we show how harnessing the wettability of ferrofluids allows for controlled reconfigurability and the ability to create versatile soft machines. The ferrofluid droplet exhibits multimodal motions, and a single droplet can be controlled to split into multiple sub-droplets and then re-fuse back on demand. The soft droplet machine can negotiate changing terrains in unstructured environments. In addition, the ferrofluid droplets can be configured as a liquid capsule, enabling cargo delivery; a wireless omnidirectional liquid cilia matrix capable of pumping biofluids; and a wireless liquid skin, allowing multiple types of miniature soft machine construction. This work improves small magnetic soft machines' achievable complexity and boosts their future biomedical applications capabilities.