Ultra-sensitive and resilient compliant strain gauges for soft machines.

Soft machines are a promising design paradigm for human-centric devices1,2 and systems required to interact gently with their environment3,4. To enable soft machines to respond intelligently to their surroundings, compliant sensory feedback mechanisms are needed. Specifically, soft alternatives to strain gauges-with high resolution at low strain (less than 5 per cent)-could unlock promising new capabilities in soft systems. However, currently available sensing mechanisms typically possess either high strain sensitivity or high mechanical resilience, but not both. The scarcity of resilient and compliant ultra-sensitive sensing mechanisms has confined their operation to laboratory settings, inhibiting their widespread deployment. Here we present a versatile and compliant transduction mechanism for high-sensitivity strain detection with high mechanical resilience, based on strain-mediated contact in anisotropically resistive structures (SCARS). The mechanism relies upon changes in Ohmic contact between stiff, micro-structured, anisotropically conductive meanders encapsulated by stretchable films. The mechanism achieves high sensitivity, with gauge factors greater than 85,000, while being adaptable for use with high-strength conductors, thus producing sensors resilient to adverse loading conditions. The sensing mechanism also exhibits high linearity, as well as insensitivity to bending and twisting deformations-features that are important for soft device applications. To demonstrate the potential impact of our technology, we construct a sensor-integrated, lightweight, textile-based arm sleeve that can recognize gestures without encumbering the hand. We demonstrate predictive tracking and classification of discrete gestures and continuous hand motions via detection of small muscle movements in the arm. The sleeve demonstration shows the potential of the SCARS technology for the development of unobtrusive, wearable biomechanical feedback systems and human-computer interfaces.

Dissipation and energy propagation across scales in an active cytoskeletal material.

Living systems are intrinsically nonequilibrium: They use metabolically derived chemical energy to power their emergent dynamics and self-organization. A crucial driver of these dynamics is the cellular cytoskeleton, a defining example of an active material where the energy injected by molecular motors cascades across length scales, allowing the material to break the constraints of thermodynamic equilibrium and display emergent nonequilibrium dynamics only possible due to the constant influx of energy. Notwithstanding recent experimental advances in the use of local probes to quantify entropy production and the breaking of detailed balance, little is known about the energetics of active materials or how energy propagates from the molecular to emergent length scales. Here, we use a recently developed picowatt calorimeter to experimentally measure the energetics of an active microtubule gel that displays emergent large-scale flows. We find that only approximately one-billionth of the system's total energy consumption contributes to these emergent flows. We develop a chemical kinetics model that quantitatively captures how the system's total thermal dissipation varies with ATP and microtubule concentrations but that breaks down at high motor concentration, signaling an interference between motors. Finally, we estimate how energy losses accumulate across scales. Taken together, these results highlight energetic efficiency as a key consideration for the engineering of active materials and are a powerful step toward developing a nonequilibrium thermodynamics of living systems.

Barocaloric Effects in Dialkylammonium Halide Salts.

Barocaloric effects─solid-state thermal changes induced by the application and removal of hydrostatic pressure─offer the potential for energy-efficient heating and cooling without relying on volatile refrigerants. Here, we report that dialkylammonium halides─organic salts featuring bilayers of alkyl chains templated through hydrogen bonds to halide anions─display large, reversible, and tunable barocaloric effects near ambient temperature. The conformational flexibility and soft nature of the weakly confined hydrocarbons give rise to order-disorder phase transitions in the solid state that are associated with substantial entropy changes (>200 J kg-1 K-1) and high sensitivity to pressure (>24 K kbar-1), the combination of which drives strong barocaloric effects at relatively low pressures. Through high-pressure calorimetry, X-ray diffraction, and Raman spectroscopy, we investigate the structural factors that influence pressure-induced phase transitions of select dialkylammonium halides and evaluate the magnitude and reversibility of their barocaloric effects. Furthermore, we characterize the cyclability of thin-film samples under aggressive conditions (heating rate of 3500 K s-1 and over 11,000 cycles) using nanocalorimetry. Taken together, these results establish dialkylammonium halides as a promising class of pressure-responsive thermal materials.

Instrumented cardiac microphysiological devices via multimaterial three-dimensional printing.

Biomedical research has relied on animal studies and conventional cell cultures for decades. Recently, microphysiological systems (MPS), also known as organs-on-chips, that recapitulate the structure and function of native tissues in vitro, have emerged as a promising alternative. However, current MPS typically lack integrated sensors and their fabrication requires multi-step lithographic processes. Here, we introduce a facile route for fabricating a new class of instrumented cardiac microphysiological devices via multimaterial three-dimensional (3D) printing. Specifically, we designed six functional inks, based on piezo-resistive, high-conductance, and biocompatible soft materials that enable integration of soft strain gauge sensors within micro-architectures that guide the self-assembly of physio-mimetic laminar cardiac tissues. We validated that these embedded sensors provide non-invasive, electronic readouts of tissue contractile stresses inside cell incubator environments. We further applied these devices to study drug responses, as well as the contractile development of human stem cell-derived laminar cardiac tissues over four weeks.

Highly stretchable and tough hydrogels.

Hydrogels are used as scaffolds for tissue engineering, vehicles for drug delivery, actuators for optics and fluidics, and model extracellular matrices for biological studies. The scope of hydrogel applications, however, is often severely limited by their mechanical behaviour. Most hydrogels do not exhibit high stretchability; for example, an alginate hydrogel ruptures when stretched to about 1.2 times its original length. Some synthetic elastic hydrogels have achieved stretches in the range 10-20, but these values are markedly reduced in samples containing notches. Most hydrogels are brittle, with fracture energies of about 10 J m(-2) (ref. 8), as compared with ∼1,000 J m(-2) for cartilage and ∼10,000 J m(-2) for natural rubbers. Intense efforts are devoted to synthesizing hydrogels with improved mechanical properties; certain synthetic gels have reached fracture energies of 100-1,000 J m(-2) (refs 11, 14, 17). Here we report the synthesis of hydrogels from polymers forming ionically and covalently crosslinked networks. Although such gels contain ∼90% water, they can be stretched beyond 20 times their initial length, and have fracture energies of ∼9,000 J m(-2). Even for samples containing notches, a stretch of 17 is demonstrated. We attribute the gels' toughness to the synergy of two mechanisms: crack bridging by the network of covalent crosslinks, and hysteresis by unzipping the network of ionic crosslinks. Furthermore, the network of covalent crosslinks preserves the memory of the initial state, so that much of the large deformation is removed on unloading. The unzipped ionic crosslinks cause internal damage, which heals by re-zipping. These gels may serve as model systems to explore mechanisms of deformation and energy dissipation, and expand the scope of hydrogel applications.

Adhesion between highly stretchable materials.

Recently developed high-speed ionic devices require adherent laminates of stretchable and dissimilar materials, such as gels and elastomers. Adhesion between stretchable and dissimilar materials also plays important roles in medicine, stretchable electronics, and soft robots. Here we develop a method to characterize adhesion between materials capable of large, elastic deformation. We apply the method to measure the debond energy of elastomer-hydrogel bilayers. The debond energy between an acrylic elastomer and a polyacrylamide hydrogel is found to be about 0.5 J m(-2), independent of the thickness and the crosslink density of the hydrogel. This low debond energy, however, allows the bilayer to be adherent and highly stretchable, provided that the hydrogel is thin and compliant. Furthermore, we demonstrate that nanoparticles applied at the interface can improve adhesion between the elastomer and the hydrogel.

Kinetic Role of Carbon in Solid-State Synthesis of Zirconium Diboride using Nanolaminates: Nanocalorimetry Experiments and First-Principles Calculations.

Reactive nanolaminates afford a promising route for the low-temperature synthesis of zirconium diboride, an ultrahigh-temperature ceramic with metallic properties. Although the addition of carbon is known to facilitate sintering of ZrB2, its effect on the kinetics of the formation reaction has not been elucidated. We have employed a combined approach of nanocalorimetry and first-principles theoretical studies to investigate the kinetic role of carbon in the synthesis of ZrB2 using B4C/Zr reactive nanolaminates. Structural characterization of the laminates by XRD and TEM reveal that the reaction proceeds via interdiffusion of the B4C and Zr layers, which produces an amorphous Zr3B4C alloy. This amorphous alloy then crystallizes to form a supersaturated ZrB2(C) compound. A kinetic analysis shows that carbon lowers the energy barriers for both interdiffusion and crystallization by more than 20%. Energetic calculations based on first-principles modeling suggest that the reduction of the diffusion barrier may be attributed to the stronger bonding between Zr and C as compared to the bonding between Zr and B.

First-Principles Theoretical Studies and Nanocalorimetry Experiments on Solid-State Alloying of Zr-B.

The thermodynamics and kinetics of the solid-state alloying of Zr-B, underlying a variety of synthesis processes of the ultrahigh-temperature ceramic ZrB2, are widely unknown. We investigate the energetics, diffusion kinetics, and structural evolution of this system using first-principles computational methods. We identify the diffusion pathways in the interpenetrating network of interstitial sites for a single B atom and demonstrate a dominant rate-controlling step from the octahedral to the crowdion site that is distinct from the conventional mechanism of octahedral-tetrahedral transition in hexagonal close-packed structures. In the intermediate compounds ZrBx, 0 < x ≤ 2, the diffusivity of B is highly dependent on the composition while reaching a minimum for ZrB. The activation barrier of diffusion in ZrB2 is in good agreement with nanocalorimetry measurements performed on Zr/B reactive nanolaminates.

A model of ideal elastomeric gels for polyelectrolyte gels.

The concept of the ideal elastomeric gel is extended to polyelectrolyte gels and verified using a polyacrylamide-co-acrylic acid hydrogel as a model material system. A comparison between mixing and ion osmosis shows that the mixing osmosis is larger than the ion osmosis for small swelling ratios, while the ion osmosis dominates for large swelling ratios. We show further that the non-Gaussian chain effect becomes important in the elasticity of the polymer network at the very large swelling ratios that may occur under certain conditions of pH and salinity. We demonstrate that the Gent model captures the non-Gaussian chain effect well and that it provides a good description of the free energy associated with the stretching of the network. The model of ideal elastomeric gels fits the experimental data very well.

Mechanical behavior of poly(methyl methacrylate)-based ionogels.

Ionogels are formed when a cross-linked polymer network absorbs an ionic liquid. Ionogels are ionic conductors and, as such, are being considered for use in stretchable electronics and artificial muscles or nerves. The use of ionogels in these applications is limited in part by their mechanical behavior. Here we present an ionogel prepared by swelling covalently cross-linked poly(methyl methacrylate) in 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide. The resulting ionogel is compliant, stretchable, and relatively tough. We demonstrate that the swelling ratio, elastic modulus, stretchability, and fracture energy of the ionogel depend sensitively on the cross-link density of the polymer network. The behavior of the ionogel is well captured by the model of the ideal elastomeric gel combined with the Flory-Huggins model for the energy of mixing.

Measurements of the fracture energy of lithiated silicon electrodes of Li-ion batteries.

We have measured the fracture energy of lithiated silicon thin-film electrodes as a function of lithium concentration. To this end, we have constructed an electrochemical cell capable of testing multiple thin-film electrodes in parallel. The stress in the electrodes is measured during electrochemical cycling by the substrate curvature technique. The electrodes are disconnected one by one after delithiating to various states of charge, that is, to various concentrations of lithium. The electrodes are then examined by optical microscopy to determine when cracks first form. All of the observed cracks appear brittle in nature. By determining the condition for crack initiation, the fracture energy is calculated using an analysis from fracture mechanics. In the same set of experiments, the fracture energy at a second state of charge (at small concentrations of lithium) is measured by determining the maximum value of the stress during delithiation. The fracture energy was determined to be Γ = 8.5 ± 4.3 J/m(2) at small concentrations of lithium (~Li0.7Si) and have bounds of Γ = 5.4 ± 2.2 J/m(2) to Γ = 6.9 ± 1.9 J/m(2) at larger concentrations of lithium (~Li2.8Si). These values indicate that the fracture energy of lithiated silicon is similar to that of pure silicon and is essentially independent of the concentration of lithium. Thus, lithiated silicon demonstrates a unique ability to flow plastically and fracture in a brittle manner.

Morphological evolution of Si nanowires upon lithiation: a first-principles multiscale model.

Silicon is a promising anode material for high-capacity Li-ion batteries. Recent experiments show that lithiation of crystalline silicon nanowires leads to highly anisotropic morphologies. This has been interpreted as due to anisotropy in equilibrium interface energies, but this interpretation does not capture the dynamic, nonequilibrium nature of the lithiation process. Here, we provide a comprehensive explanation of experimentally observed morphological changes, based on first-principles multiscale simulations. We identify reaction paths and associated structural transformations for Li insertion into the Si {110} and {111} surfaces and calculate the relevant energy barriers from density functional theory methods. We then perform kinetic Monte Carlo simulations for nanowires with surfaces of different orientations, which reproduce to a remarkable degree the experimentally observed profiles and the relative reaction front rates.

Kinetics of initial lithiation of crystalline silicon electrodes of lithium-ion batteries.

Electrochemical experiments were conducted on {100}, {110}, and {111} silicon wafers to characterize the kinetics of the initial lithiation of crystalline Si electrodes. Under constant current conditions, we observed constant cell potentials for all orientations, indicating the existence of a phase boundary that separates crystalline silicon from the amorphous lithiated phase. For a given potential, the velocity of this boundary was found to be faster for {110} silicon than for the other two orientations. We show that our measurements of varying phase boundary velocities can accurately account for anisotropic morphologies and fracture developed in crystalline silicon nanopillars. We also present a kinetic model by considering the redox reaction at the electrolyte/lithiated silicon interface, diffusion of lithium through the lithiated phase, and the chemical reaction at the lithiated silicon/crystalline silicon interface. From this model, we quantify the rates of the reactions at the interfaces and estimate a lower bound on the diffusivity through the lithiated silicon phase.

Reactive flow in silicon electrodes assisted by the insertion of lithium.

In the search for high-energy density materials for Li-ion batteries, silicon has emerged as a promising candidate for anodes due to its ability to absorb a large number of Li atoms. Lithiation of Si leads to large deformation and concurrent changes in its mechanical properties, from a brittle material in its pure form to a material that can sustain large inelastic deformation in the lithiated form. These remarkable changes in behavior pose a challenge to theoretical treatment of the material properties. Here, we provide a detailed picture of the origin of changes in the mechanical properties, based on first-principles calculations of the atomic-scale structural and electronic properties in a model amorphous silicon (a-Si) structure. We regard the reactive flow of lithiated silicon as a nonequilibrium process consisting of concurrent Li insertion driven by unbalanced chemical potential and flow driven by deviatoric stress. The reaction enables the material to flow at a lower level of stress. Our theoretical model is in excellent quantitative agreement with experimental measurements of lithiation-induced stress on a Si thin film.

Lithium-assisted plastic deformation of silicon electrodes in lithium-ion batteries: a first-principles theoretical study.

Silicon can host a large amount of lithium, making it a promising electrode for high-capacity lithium-ion batteries. Recent experiments indicate that silicon experiences large plastic deformation upon Li absorption, which can significantly decrease the stresses induced by lithiation and thus mitigate fracture failure of electrodes. These issues become especially relevant in nanostructured electrodes with confined geometries. On the basis of first-principles calculations, we present a study of the microscopic deformation mechanism of lithiated silicon at relatively low Li concentration, which captures the onset of plasticity induced by lithiation. We find that lithium insertion leads to breaking of Si-Si bonds and formation of weaker bonds between neighboring Si and Li atoms, which results in a decrease in Young's modulus, a reduction in strength, and a brittle-to-ductile transition with increasing Li concentration. The microscopic mechanism of large plastic deformation is attributed to continuous lithium-assisted breaking and re-forming of Si-Si bonds and the creation of nanopores.

A Micromachined Picocalorimeter Sensor for Liquid Samples with Application to Chemical Reactions and Biochemistry.

Calorimetry has long been used to probe the physical state of a system by measuring the heat exchanged with the environment as a result of chemical reactions or phase transitions. Application of calorimetry to microscale biological samples, however, is hampered by insufficient sensitivity and the difficulty of handling liquid samples at this scale. Here, a micromachined calorimeter sensor that is capable of resolving picowatt levels of power is described. The sensor consists of low-noise thermopiles on a thin silicon nitride membrane that allow direct differential temperature measurements between a sample and four coplanar references, which significantly reduces thermal drift. The partial pressure of water in the ambient around the sample is maintained at saturation level using a small hydrogel-lined enclosure. The materials used in the sensor and its geometry are optimized to minimize the noise equivalent power generated by the sensor in response to the temperature field that develops around a typical sample. The experimental response of the sensor is characterized as a function of thermopile dimensions and sample volume, and its capability is demonstrated by measuring the heat dissipated during an enzymatically catalyzed biochemical reaction in a microliter-sized liquid droplet. The sensor offers particular promise for quantitative measurements on biological systems.

Chemically Coupled Interfacial Adhesion in Multimaterial Printing of Hydrogels and Elastomers.

Functional devices that use hydrogels as ionic conductors and elastomers as dielectrics have the advantage of being soft, stretchable, transparent, and biocompatible, making them ideal for biomedical applications. These devices are typically fabricated by manual assembly. Techniques for the manufacturing of soft materials have generally not looked at integrating multiple dissimilar materials. Silane coupling agents have recently shown promise for creating strong bonds between hydrogels and elastomers but have yet to be used in the extrusion printing of complex devices that integrate both hydrogels and elastomers. Here, we demonstrate the viability of silane coupling agents in a system with the rheology and functional composition necessary for three-dimensional (3D) extrusion printing of hydrogel-elastomer materials, specifically polyacrylamide (PAAm) hydrogel and poly(dimethylsiloxane) (PDMS) hydrophobic elastomer. By introducing a charge-neutral surfactant in the PDMS and adjusting silane concentrations in the PAAm, cast material samples demonstrate strong adhesion. We were also able to achieve an interfacial toughness of up to Γ = 193 ± 6.3 J/m2 for a fully extrusion printed PAAm hydrogel-on-PDMS bilayer. This result demonstrates that an integration strategy based on silane coupling agents makes it possible for extrusion printing of a wide variety of hydrogel and silicone elastomers.

Lightweight Highly Tunable Jamming-Based Composites.

Tunable-impedance mechanisms can improve the adaptivity, robustness, and efficiency of a vast array of engineering systems and soft robots. In this study, we introduce a tunable-stiffness mechanism called a "sandwich jamming structure," which fuses the exceptional stiffness range of state-of-the-art laminar jamming structures (also known as layer jamming structures) with the high stiffness-to-mass ratios of classical sandwich composites. We experimentally develop sandwich jamming structures with performance-to-mass ratios that are far greater than laminar jamming structures (e.g., a 550-fold increase in stiffness-to-mass ratio), while simultaneously achieving tunable behavior that standard sandwich composites inherently cannot achieve (e.g., a rapid and reversible 1800-fold increase in stiffness). Through theoretical and computational models, we then show that these ratios can be augmented by several orders of magnitude further, and we provide an optimization routine that allows designers to build the best possible sandwich jamming structures given arbitrary mass, volume, and material constraints. Finally, we demonstrate the utility of sandwich jamming structures by integrating them into a wearable soft robot (i.e., a tunable-stiffness wrist orthosis) that has negligible impact on the user in the off state, but can reduce muscle activation by an average of 41% in the on state. Through these theoretical and experimental investigations, we show that sandwich jamming structures are a lightweight highly tunable mechanism that can markedly extend the performance limits of existing structures and devices.

Design Molecular Topology for Wet-Dry Adhesion.

Recent innovations highlight the integration of diverse materials with synthetic and biological hydrogels. Examples include brain-machine interfaces, tissue regeneration, and soft ionic devices. Existing methods of strong adhesion mostly focus on the chemistry of bonds and the mechanics of dissipation but largely overlook the molecular topology of connection. Here, we highlight the significance of molecular topology by designing a specific bond-stitch topology. The bond-stitch topology achieves strong adhesion between preformed hydrogels and various materials, where the hydrogels have no functional groups for chemical coupling, and the adhered materials have functional groups on the surface. The adhesion principle requires a species of polymer chains to form a bond with a material through complementary functional groups and form a network in situ that stitches with the polymer network of a hydrogel. We study the physics and chemistry of this topology and describe its potential applications in medicine and engineering.

High-throughput analysis of thin-film stresses using arrays of micromachined cantilever beams.

We report on a technique for making high-throughput residual stress measurements on thin films by means of micromachined cantilever beams and an array of parallel laser beams. In this technique, the film of interest is deposited onto a silicon substrate with micromachined cantilever beams. The residual stress in the film causes the beams to bend. The curvature of the beams, which is proportional to the residual stress in the film, is measured by scanning an array of parallel laser beams generated with a diffraction grating along the length of the beams. The reflections of the laser beams are captured using a digital camera. A heating stage enables measurement of the residual stress as a function of temperature. As the curvature of each beam is determined by the local stress in the film, the film stress can be mapped across the substrate. This feature makes the technique a useful tool for the combinatorial analysis of phase transformations in thin films, especially when combined with the use of films with lateral composition gradients. As an illustration, we apply the technique to evaluate the thermomechanical behavior of Fe-Pd binary alloys as a function of composition.