Systems, articles, and methods related to dielectric elastomers

Abstract

Certain aspects of this disclosure relate to systems, articles, and methods involving dielectric elastomers. In some embodiments, a first layer comprising an elastomer (e.g., a dielectric elastomer) may be disposed on a second layer (e.g., an electrode layer). In some embodiments, the device is a dielectric elastomer actuator comprising a first layer comprising an elastomer, a second layer comprising a first plurality of particles and a second plurality of particles, and a third layer comprising the first plurality of particles and the second plurality of particles. In some embodiments, a first region of the second and / or third layer comprises the first plurality of particles. In some embodiments, a second region of the second and / or third layer comprises the second plurality of particles. In some embodiments, electrodes of the dielectric elastomer actuator may have suitable contact resistances to allow for advantageous response speeds and relatively high breakdown strengths.

Description

[0001] SYSTEMS, ARTICLES, AND METHODS RELATED TO DIELECTRIC ELASTOMERS

[0002] RELATED APPLICATIONS

[0003] This application claims priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application No. 63 / 582,864, filed September 15, 2023, and entitled “Electrode Design” and to U.S. Provisional Patent Application No. 63 / 582,791, filed September 14, 2023, and entitled “Device Reliability” which are incorporated herein by reference in their entirety for all purposes.

[0004] GOVERNMENT SPONSORSHIP

[0005] This invention was made with Government support under Contract No. 2011754 awarded by the National Science Foundation (NSF). The Government has certain rights in the invention.

[0006] TECHNICAL FIELD

[0007] Systems, articles, and methods related to dielectric elastomers are generally described.

[0008] SUMMARY

[0009] Systems, articles, and methods related to dielectric elastomers are generally described. The subject matter of the present disclosure involves, in some cases, interrelated products, alternative solutions to a particular problem, and / or a plurality of different uses of one or more systems and / or articles.

[0010] One aspect of the present disclosure generally involves articles related to dielectric elastomer actuators. In some embodiments, the article comprises a first layer comprising an elastomer; and a second layer disposed on the first layer, the second layer comprising a first region and a second region, wherein: the first region comprises a first plurality of particles, the second region comprises a second plurality of particles, and at least a portion of the first plurality of particles is proximate to at least a portion of the second plurality of particles. In some embodiments, the article comprises a first layer comprising an elastomer; a second layer disposed on a first side of the first layer; a third layer disposed on a second side of the first layer, wherein: the second and third layers each comprise a first region comprising a first plurality of particles, and a second region comprising a second plurality of particles, and at least a portion of the first plurality of particles are adjacent to at least a portion of the second plurality of particles. Another aspect of the present disclosure generally involves methods related to dielectric elastomer actuators. In some embodiments, the method comprises providing a first layer comprising an elastomer, the first layer positioned between a second layer and a third layer, wherein: the second and third layers comprise a first region and a second region, the first region comprises a first plurality of particles, the second region comprises a second plurality of particles, and at least a portion of first plurality of particles is adjacent to at least a portion of the second plurality of particles.

[0011] Other advantages and novel features of the present disclosure will become apparent from the following detailed description of various non-limiting embodiments of the disclosure when considered in conjunction with the accompanying figures. In cases where the present specification and a document incorporated by reference include conflicting and / or inconsistent disclosure, the present specification shall control.

[0012] BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Non-limiting embodiments of the present disclosure will be described by way of example with reference to the accompanying figures, which are schematic and are not intended to be drawn to scale unless otherwise indicated. In the figures, each identical or nearly identical component illustrated is typically represented by a single numeral. For purposes of clarity, not every component is labeled in every figure, nor is every component of each embodiment of the disclosure shown where illustration is not necessary to allow those of ordinary skill in the art to understand the disclosure. In the figures:

[0014] FIG. 1A is a schematic diagram showing a profile view of an article comprising a first layer and a second layer, according to some embodiments.

[0015] FIG. IB is a schematic diagram showing a cross-sectional view of an article comprising a first and second region of a second layer, according to some embodiments.

[0016] FIG. 1C is a schematic diagram showing a cross-sectional view of an article comprising a first region disposed on a second region, according to some embodiments.

[0017] FIG. ID is a schematic diagram showing a cross-sectional view of an article comprising a first layer, a second layer, and a third layer.

[0018] FIG. IE is a schematic diagram showing a cross-sectional view of an article comprising a plurality of elastomer layers and a plurality of electrode layers, according to some embodiments.

[0019] FIG. 2A is a schematic diagram showing a plan view of an article having a lead portion and an active portion, according to some embodiments.

[0020] FIG. 2B is a schematic diagram showing a plan view of an article wherein the second region is provided as channels in the first region, according to some embodiments. FIG. 2C is a schematic diagram showing a plan view of an article wherein the second region is dispersed in the first region, according to some embodiments.

[0021] FIGS. 3A-3I are diagrams depicting various stages of fabrication process associated with dielectric elastomer actuators, according to some embodiments.

[0022] FIGS. 4A-4I are diagrams and microscopy images depicting the hybrid electrode structure, according to some embodiments.

[0023] FIG. 5 is an scanning electron microscopy (SEM) image depict the contact region with a composite carbon black (CB) and carbon nanotube (CNT) structure., according to some embodiments.

[0024] FIG. 6A-6G shows circuits and data related to the resistive behavior of electrode layers, according to some embodiments.

[0025] FIG. 7A-7B describes the total resistance vs length of 5 mm wide test strips for CNT samples and CB+CNT composite samples, according to some embodiments.

[0026] FIG. 8 is a plot describing a comparison of R and C measurements made with an LCR meter on a DEA and its equivalent RC circuit, according to some embodiments.

[0027] FIGS. 9A-9G describe the breakdown strength of the pure and the coated material film, and the effect of the coating on the performance of the dielectric elastomer actuators, according to some embodiments.

[0028] FIG. 10 depict plots describing the stress as a function of strain over 100 cycles for all tested silicone-only and CNT+silicone samples, according to some embodiments.

[0029] FIG. 11 depicts the resistance over 100 cycles of 5-25% strain for all tested samples, according to some embodiments.

[0030] FIG. 12 depicts the resistance over 100 cycles of 5-105% strain for all tested samples, according to some embodiments.

[0031] FIG. 13 shows an SEM image of an unencapsulated electrode after a clearing event, according to some embodiments. A pinhole failure sits at the center of a non-conductive patch where CNTs have been ablated.

[0032] FIGS. 14A-14E describe the pre-clearing process for dielectric elastomer actuators, according to some embodiments.

[0033] FIG. 15 describes overview of the pre-clearing algorithm, according to some embodiments. Dashed lines indicate a change in preclearing strategy. A complete signal indicates that no over-current events have occurred during the episode associated with it. FIG. 16 shows a signal diagram of the hardware on which the pre-clearing algorithm is deployed. Communications between the host, target, and DAQ are digital, while signals sent between the DAQ, amplifier, and DEA are analog, according to some embodiments.

[0034] FIG. 17 is a schematic describing a single paddle electrode, according to some embodiments.

[0035] FIGS. 18A-18G generally describes the pre-clearing process that were evaluated on single-layer, paddle-shaped DEAs, according to some embodiments.

[0036] FIGS. 19A-19F generally describes data related to the resistive performance of hybrid electrodes, according to some embodiments.

[0037] FIGS. 20A-20D generally describes the relationship between breakdown strength and the device output, according to some embodiments.

[0038] FIGS. 21A-21B describes the total resistance vs length of 5 mm wide test strips of CB+CNT composite samples and CNT-only samples, according to some embodiments. The contact resistance is taken as the intercept of the linear fit, and 95% confidence interval bounds are plotted.

[0039] FIG. 22 is a diagram describing an overview of the DEAM fabrication process, according to some embodiments.

[0040] FIG. 23 is a diagram describing the mini-stack assembly process, according to some embodiments.

[0041] FIG. 24 is a diagram generally describing the electrode deposition process, according to some embodiments.

[0042] FIG. 25 is a diagram describing a cut that is made into the multilayer, exposing the nanoparticle cross-sections, according to some embodiments. The excess multilayer may be peeled away and discarded.

[0043] FIG. 26 is a diagram describing a colloidal graphite paint applied to the exposed crosssection and nearby copper leads, according to some embodiments. This also describes the creation of the electrical connection between DEAM electrodes and the external power supply, according to some embodiments.

[0044] FIG. 27 is a diagram of the paddle electrodes used to test the effect of CB+CNT vs CNT- only regions at the contacts on total device resistance, according to some embodiments

[0045] FIGS. 28A-28C are images describing the setup for measuring the blocked force of an artificial muscle, according to some embodiments.

[0046] FIGS. 29A-29B are plots describing the performance comparison of hybrid and CNT- only roll actuators, according to some embodiments. FIG. 30 is an SEM image showing the draping of CNT particles on larger CB agglomerates after spraying onto filter paper, according to some embodiments.

[0047] FIGS. 31-32 describes data associated with the cost of dielectric elastomer actuators, according to some embodiments.

[0048] DETAILED DESCRIPTION

[0049] Certain aspects of this disclosure relate to systems, articles, and methods involving dielectric elastomers. In some embodiments, a first layer comprising an elastomer (e.g., a dielectric elastomer) may be disposed on a second layer (e.g., an electrode layer) comprising one or more plurality of particles. The one or more plurality of particles may allow for devices comprising the first and second layer to have advantageous functionality. In some embodiments, the device is a dielectric elastomer actuator comprising a first layer comprising an elastomer, a second layer comprising a first plurality of particles and a second plurality of particles, and a third layer comprising the first plurality of particles and the second plurality of particles. In some embodiments, a first region of the second and / or third layer comprises the first plurality of particles. In some embodiments, a second region of the second and / or third layer comprises the second plurality of particles. In such embodiments, electrodes of the dielectric elastomer actuator may have suitable contact resistances to allow for relatively high response speeds and high breakdown strengths. In some embodiments, however, any of a variety of functionalities may also be introduced into devices comprising the first and second layers, as described in detail throughout this disclosure.

[0050] Dielectric elastomer actuators (DEAs) are a promising artificial muscle technology as they are generally strong enough to lift 50-times their own weight, fast enough to operate at tens of thousands of Hz, and soft enough to withstand shocks and impacts that would destroy other actuators. The direct electromechanical transduction mode of DEAs also may allow for integration with electronics - when a voltage is applied to electrodes sandwiching a thin elastomer membrane, a Maxwell stress compresses the membrane through its thickness and expands it in-plane.

[0051] While the energy density of a DEA membrane, in some embodiments, can match and even exceed that of natural muscle (0.4-40 J / kg), the total energy output of a single-layer device is generally limited. In order to produce an electric field high enough for actuation (~ 10- 100 V / pm) at the voltages that lab-scale amplifiers can supply (~l-10 kV), the membrane may be ~ 10-100 pm thick. This low thickness can generally limit the total device volume and thus its energy output. To scale up energy output - alternating layers of electrodes and elastomer membranes are often stacked to create a dielectric elastomer actuator multilayer (DEAM). The electrodes in a DEAM may meet various electromechanical specifications. The elastomers may have a low elastic modulus, typically tens to hundreds of kPa, to maximize actuator strain (typically 10-30%). To avoid limiting this strain, the electrode layer should add negligible mechanical impedance. The electrodes should also exhibit low electrical impedance to avoid limiting operating frequency (i.e., considering the low-pass behavior of the equivalent electrical circuit), and should remain conductive at the maximum operating strains. Finally, in order to increase the applied electrical field and thus mechanical work output, the electrodes should not excessively degrade the breakdown strength of the device by introducing localized defects.

[0052] These specifications are typically met using networks of conductive nanoparticles (NPs) such as carbon black (CB) or carbon nanotubes (CNTs). These NP networks provide lower stiffness and higher stretches than solid metal or polymer films, and present fewer practical implementation challenges than liquid metals, carbon grease, and ionogels; these networks can, in some embodiments, be patterned, as they can be mixed into inks and deposited wet or can be stuck onto elastomers in a dry stamping process, and the networks adhere to the elastomer surface rather than migrating along or into it. The particles can be deposited in nanometer-thick layers in which particles and their aggregates can slide past each other while maintaining contact, retaining conductivity even when stretched. Percolative NP networks also achieve low sheet resistances ( < 100 kQ / n) at low areal concentrations of particles, allowing for minimal stiffening (< 10% of elastomer stiffness), and allowing for a minimal impact on the transmittance of the elastomer film (< 97%).

[0053] While NP networks meet the stated electromechanical specifications, it may be difficult to design a NP ink that increases all performance variables simultaneously. One common challenge is the tradeoff between breakdown strength and conductivity, metrics which are needed for high- stress and high-frequency operation, respectively. Large particles and their aggregates concentrate electric fields and can be durable enough to withstand large currents (> 100 pA) experienced during dielectric breakdown events, wherein the applied field exceeds the local breakdown strength and the typically-insulating dielectric permits an arc of current. While this NP network durability preserves the electrode, it also allows enough energy to pass through the dielectric to permanently damage and short-circuit it. Smaller and more sparsely-distributed particles such as CNTs, in contrast, protect the device from catastrophic short-circuits. CNTs have a low cross- sectional area which produces high current densities that can destroy them even at relatively low currents (~20 / A). When a current spike exceeds this threshold, it destroys a patch of CNTs surrounding the failure site, rendering the area non-conductive and preventing further current flow. This protective “self-clearing” effect creates fault-tolerant electrodes with high effective breakdown strengths. Small and sparsely-distributed particles, however, yield much higher contact resistance than larger and more aggregated particles. Electrode layers comprises CNTs may be several nanometers thick, in some certain cases, and accordingly, it may be challenging to establish electrical communication with such a electrode. In order to connect the electrodes to a power supply, a cross-sectional cut is made through the DEAM and a conductive ink is applied, as shown in FIGS. 25-26. CNT networks provide little exposed surface to connect to at this cross section, yielding a high contact resistance that can dominate total device resistance. This limits the DEAM’s operating frequency and efficiency.

[0054] DEAM electrodes have been typically limited to a single nanoparticle ink patterned uniformly over the electrode, and could thus only achieve either high breakdown strength or low resistance. Composite inks combining larger and denser nanoparticles with smaller and less dense particles have been demonstrated to produce high breakdown strength in a single-layer DEA, but do not demonstrate low contact resistance or high breakdown strength in a multilayered device.

[0055] A batch-spray and stamp (BSS) electrode fabrication paradigm, however, facilitates selective patterning of multiple NP inks with only minimal tuning of manufacturing and material parameters. Unlike wet deposition processes such as jetting and gravure printing which may be tuned using oft-conflicting material properties to account for each ink’s interactions with the elastomer substrate (such as wetting behavior and surface chemistry), , BSS processes involve minimal tuning to deposit inks onto a separate carrier substrate. The disclosure described herein employs vacuum filtration to mechanically, rather than evaporatively, separate NPs from their solvents, which avoids inhomogeneities such as “coffee ring” effects without heavily tuning ink properties such as surface tension.

[0056] This decoupling of ink manufacturing properties from substrate properties allows for more rapid development of a library of NP inks with varying performance characteristics, and allows inks to be modularly deposited atop and in combination with one another. By applying a series of masks and spraying through them, these inks can be deposited only where are they advantageous. This spatial patterning capability may mitigate and / or resolve the breakdown-conductivity tradeoff.

[0057] Though CNTs patterned throughout the electrode body raise the DEAM’s breakdown strength, CNT often involve an extra “pre-clearing” step before operation. Manufacturing processes typically introduce defects such as air bubbles, thickness variations, and nanoparticle protrusions into the elastomer layer. These defects may lower the effective breakdown strength of the device by nucleating breakdown events. If this occurs during operation of the device, this may excessively damage the electrode, lowering device performance, or cause a permanent and / or catastrophic short circuit through the dielectric. To limit this, CNT-based devices are typically “pre-cleared” in advance of operation by applying a series of increasing voltages to the device until the desired operational voltage has been reached, clearing away each defect along the way. The device can then be safely operated up to that voltage.

[0058] Pre-clearing may increase the operating voltage of self-clearing electrodes, but the methods by which it is performed have been manual, uncontrolled, and unable to adapt their settings to clear the wide range of defects encountered. Most pre-clearing is performed by manually applying stepped DC signals and then waiting until pre-clearing events have ceased with little to no real-time feedback or control of the process. This may cause excessive degradation; attempting too large of a voltage increase at once may allow many clearing events to occur simultaneously, resulting in excessive degradation. Air bubbles, protrusions of nanoparticles into the elastomer, and thickness variations of the elastomer layer are among the wide range of defects that can nucleate breakdown events. Each defect can fail at a different voltage, with a different current, and with one of two failure modes: while most defects self-clear after a short spike in current, some form durable short circuits that cannot be cleared, which may lead to the device being discarded. Typical pre-clearing protocols involve minutes to hours of human operation and / or oversight, a labor requirement that precludes industrial- scale pre-clearing and thus commercial deployment of DEAs.

[0059] An adaptive pre-clearing algorithm was developed that is capable of evaluating and responding to the failure modes produced by various defects in each device. The algorithm generally limits current magnitude and duration (20 pA for less than 1 ms), applies only the minimum required clearing voltage for each defect, and uses high-frequency (100 Hz) bursts of current to clear durable shorts that have previously been difficult or impossible to clear. This algorithm also allows us to completely automate the process, eliminating the need for human supervision and opening a pathway to industrial-scale pre-clearing._CNTs patterned throughout the body of paddle-shaped electrodes seen in Fig. 17 enable breakdown strengths of 54.7 V / ,um, 61% higher than our previous batch-sprayed CB electrodes and 86.4% of the neat elastomer’s breakdown strength (63.4 V / ,um). CB patterned at the contacts of these electrodes, meanwhile, produces a 32x drop in contact resistance compared to CNTs, from 284.9 kQ (1425 kQmm) to 8.817 kQ (44.09 kQmm).

[0060] In some embodiments, the article comprises one or more layers. For example, as shown in FIG. 1A, article 100 comprises first layer 102 and second layer 104 disposed on first layer 102. As used herein, when a layer is referred to as being “on” or “disposed on” another layer, it can be directly disposed on the layer, or an intervening layer also may be present. A layer that is “directly on” or “directly disposed on” another layer is positioned with respect to the layer such that no intervening layer is present. In some embodiments, the first layer comprises an elastomer. Any of a variety of suitable elastomers can be used, as described elsewhere in this disclosure. In some embodiments, the second layer comprises a first region and a second region. For example, as shown in FIG. IB, second layer 104 comprises first region 104A and second region 104B. In some embodiments, the first region comprises a first plurality of particles and the second region comprises the second plurality of particles. Referring again to FIG. IB as an example, first region 104A comprises first plurality of particles 105A and second region 104B comprises second plurality of particles 105B. In some, but not all, embodiments, the first and second plurality of particles are conductive. More detail regarding the first and second plurality of particles can be found elsewhere in this disclosure.

[0061] In some embodiments, at least a portion of the first plurality of particles are adjacent to at least a portion of the second plurality of particles. For example, as shown in FIG. IB, first plurality of particles 105 A is adjacent to second plurality of particles 105B. The relative positions of the first plurality of particles and the second plurality of particles may allow for the first and second regions to interact with each other. In some embodiments, the first and second plurality of particles may electrically interact with each other such that the first region and the second region are in electrical communication with each other. It should be noted that the second layer may comprise additional regions having plurality of particles that not shown in FIG. IB.

[0062] In some embodiments, at least a portion of the first plurality of particles are disposed on at least a portion of the second plurality of particles. For example, as shown in FIG. 1C, first plurality of particles 105A of first region 104A is disposed on second plurality of particles 105B of second region 104B. In other words, first region 104A is disposed on second region 104B. In some embodiments, the second layer (e.g., an electrode layer) comprises the first plurality of particles disposed on the second plurality of particles such that the first and second plurality of particles may interact (e.g., electronically) with each other. Such interactions may allow for relatively low contact resistance between the second layer and external electronic devices (e.g., power supplies, characterization equipment such as voltmeters or ammeters). In some embodiments, disposing the first plurality of particles on the second plurality of particles may not only lead to advantageous interactions between the first and second plurality of particles, but also allow the article to fabricated via layer by layer deposition processing (e.g., vacuum filtration and / or deposition, sputtering, spin coating, stamping, blade coating, or scaleable roll to roll deposition methods). It should be noted that while the first and second plurality of particles are shown in FIG. 1C, additional particles, layers, and / or regions may be present. In some embodiments, the second layer comprises more than two distinguishable plurality of particles (e.g., at least 3, at least 4, at least 5, at least 6, or at least 10 and / or up to 20).

[0063] In some embodiments, the article is a dielectric elastomer actuator (DEA). In some embodiments, a dielectric elastomer actuator comprises an elastomer positioned between a first electrode layer and a second electrode layer. For example, as shown in FIG. ID, article 101 is a dielectric elastomer actuator comprising first layer 102 positioned between second layer 104 and third layer 106. Third layer 106 is disposed on first layer 102 on a side of first layer 102 opposite the second layer 104. In some embodiments, the third layer (e.g., a second electrode layer) may have any of the properties of the second layer (e.g., a first electrode layer) described herein. As one example of this, in some embodiments, the third layer comprises the first region comprising the first plurality of particles and the second region comprising the second plurality of particles. While the third layer can have any of the properties of the second layer, the third layer does not necessarily have identical properties as the second layer, but in some embodiments, the second layer and the third layer may be substantially identical. For example, as shown in FIG. ID, third layer 106 may have a substantially identical or identical structure to the structure of second layer 104 shown in FIGS. 1A-1C. In some embodiments, the second layer in any of the articles or dielectric elastomer actuators described herein may be substituted with the third layer., and vice versa.

[0064] In some embodiments, the second and third layers of the dielectric elastomer actuator are conductive. For example, turning back to FIG. IB, second layer 104 may be conductive if first plurality of particles 105 A, second plurality of particles 105B, and / or other particles (not shown) are conductive and at least partially form second 104 layer. Second layer 104 and third layer 104 may therefore serve as electrode layers of the dielectric elastomer. In some embodiments, an electrical potential can be applied between the second layer (e.g., the first electrode layer) and the third layer (e.g., the second electrode layer) to thereby generate a separation of charge in the first layer (e.g., the dielectric elastomer). An electrostatic interaction may occur between the second and third layers thereby imparting a force onto the first layer, expanding the first layer in geometric area and compressing the first layer in thickness. Accordingly, for the article to act as a dielectric elastomer, the second and third layer may, in some embodiments, need to be sufficiently conductive to serve as electrode layers. It should be noted that, in some embodiments, instead of an electrical potential, electromagnetic radiation may be applied to trigger the response described above.

[0065] In some embodiments, the dielectric elastomer actuator comprises a plurality of first layers (e.g., elastomer layers). For example, as shown in FIG. IE, dielectric elastomer actuator 101 comprises a plurality of first layers 104 positioned between second layer 104 and third layer 106. In some embodiments, dielectric elastomer actuators comprising a plurality of first layers (e.g., multilayer dielectric elastomer actuators), may, upon the application of a voltage between the second and third layers, have advantageously large force output, stroke, and / or displacement. In some embodiments, the articles described in FIGS. 1A-1C may represent units that can be stacked, arranged, and / or disposed on each other to form the structure of FIG. IE where third layer 106 is substantially identical to second layer 104.

[0066] In some embodiments, the first region serve as a lead portion and the second region serves as an active portion. For example, as shown in FIG. 2A, shows dielectric elastomer actuator 101 comprising second layer 104 and third layer 106 (not shown). First region 104A comprising first plurality of particles 105A is active portion 110 of dielectric elastomer actuator 101 while second region 104B comprising the second plurality of particles 105B is lead portion 108 of dielectric elastomer actuator 101. The lead portion, in some embodiments, may at least partially overlap the active portion such that electrical communication between the lead portion and the active portion is established. In some embodiments, the lead portion comprises the first plurality of particles (e.g., conductive particles) which may allow for electrical communication to be established between the lead portion and a voltage source external to the dielectric elastomer actuator. The active portion generally refers to the area of the dielectric elastomer that, upon applying a voltage between the second and third layers, expand in geometric area and / or reduce in thickness. It should be noted that while FIGS. 2A-2C depict the second layer as having a shape that comprises a portion of a circle and a portion of a polygon, other shapes may be possible as well. Auxiliary structure may also be included.

[0067] In some embodiments, the first region and / or the second region are patterned. For example, as shown in FIG. 2B, second region 104B is patterned such that second region 104B comprises a plurality of stripes and branches therefrom. In some embodiments, depending on any of a variety of properties of the second plurality of particles, patterning the second region may lead to enhanced functionality of the second region. In some embodiments, the second region may have a relatively high conductivity compared to the first region such that the second region act as power distribution channels throughout the second layer. While second region 104B, in FIG. 2B, describes depicts plurality of stripes and branches therefrom, it is not limited thereto. In some embodiments, the second region comprises a dendritic pattern comprising a plurality of channels and / or veins of varying widths. Accordingly, while some of the second regions 104B are parallel to each other, in some embodiments, second regions 104B may intersect and any of a variety of angles. In some embodiments, the second region may be dispersed throughout the first region. In some embodiments, the second region may be present as domains comprising the second plurality of particles. For example, as shown in FIG. 2C, second region 104B is dispersed throughout first region 104A in a plurality of domains. In some such embodiments, the second plurality of particles may have any of a variety of suitable electrical properties. In some embodiments, the second plurality of particles may have suitable adhesion properties to facilitate bonding and / or alter the adhesion between the second layer and additional layers (e.g., additional elastomer layers). It should be noted that the first and second regions may be disposed on the first layer in a single layer via a fluid (e.g., an ink) comprising the first and second plurality of particles.

[0068] Any of a variety of methods can be used to fabricate the devices described herein. Some of these methods are described in detail in Examples 1-3. In short, the second and / or third layer may involve depositing (e.g., via spraying) the first and / or second plurality of particles onto a carrier substrate. Solvent associated with the first and / or second plurality of particles may then be removed from the carrier substrate via vacuum filtration. The first and / or second plurality of particles may then be, optionally, further processed (e.g., laser welding, laser ablation, solvent etching, mechanically compacted, chemically doped using acids, etc.), before being disposed on the first layer via a stamping process.

[0069] Suitable second and third layers are described herein. In some embodiments, the second and / or third layers are electrode layers. The electrode layers may be sufficiently conductive such that, when an electrical potential is applied between the electrode layers (e.g., the second and third layers) an electrostatic interaction is induced between the electrodes layers. The electrostatic interaction may compress the first layer (e.g., the elastomer layer) to expand the first layer in area and compress the thickness of the first layer. In some embodiments, the second and third layers (e.g., the electrode layers) may also expand in area while the first layer expands. Accordingly, the second and third layers may remain conductive while expanded (e.g., under strain or deformation). In some embodiments, the second and third layers can remain electrically conductive under relatively high strains or under external sources such ultraviolet radiation. Particles (e.g., microparticles and / or nanoparticles) generally are capable of forming a network that, when conductive particles are used, form a conductive network (e.g., a percolation network) that can accommodate such strains. By using particles having different compositions, morphologies, properties, and / or sizes, additional functionalities can be introduced to electromechanical devices such as dielectric elastomer actuators. It should be noted that while, in some embodiments, the second and third layers may have substantially similar compositions and / or structures, in certain embodiments, the second and third layers may have entirely different compositions and / or structures. In some embodiments, the first and / or second plurality of particles include carbon fibers and / or epoxy to selectively stiffen regions of the dielectric elastomer actuator.

[0070] In some embodiments, the second and third layer each comprise the first region comprising the first plurality of particles and the second region comprising the second plurality of particles. In some embodiments, the first region is an active region of the dielectric elastomer actuator and the second region is a lead portion of the dielectric elastomer actuator. In some embodiments, the lead portion is in electrical communication with the active portion such that, when an electrical signal is applied to the lead portion, the electrical signal may be transmitted through the lead portion and into the active portion of the second and / or third layer which may function as electrode layers. It should be noted that, in some embodiments, the first and / or second regions are not related to the lead portion, and may represent regions of the second and / or third regions having distinct plurality of particles having different particle sizes, compositions, morphologies, and / or conductivities.

[0071] In some embodiments, the first and / or second plurality of particles comprises any of a variety of suitable particles. In some embodiments, the first plurality of particles comprises conductive particles. In some embodiments, conductive particles comprises a carbon-containing conductive material, a metal-containing conductive material, an organic conductor, a metal alloy, a conductive and semi conductive polymer, and / or any combination thereof. Examples of suitable carbon-containing conductive particles include, but are not limited to, carbon black (CB), graphite, graphene, and carbon nanotubes (CNTs, e.g., single-wall carbon nanotubes, multi-wall carbon nanotubes). Examples of suitable organic conductors include, but are not limited to, polyaniline (PANI) and poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS). Examples of suitable metal-containing conductive materials include, but are not limited to, ID conductive nanoparticles, such as copper nanowires, silver nanowires (AgNWs) and gold nanoparticles. In some embodiments, conductive particles may facilitate the formation of a conductive network (e.g., a percolation network) that allows at least a portion of the second and / or third layers to be conductive.

[0072] In some embodiments, the first and / or second plurality of particles comprises nanoparticles. Examples of suitable nanoparticles include, but are not limited to, metal nanostructures and metal particles, and nonconductive particle systems such as titanium dioxide (TiO2), barium titanate (BaTiO3), and silicon dioxide (SiO2). Examples of suitable semi- conductive nanoparticles include, but are not limited to, semi-conductive nanowires, zinc oxide (ZnO), zinc sulfide (ZnS), cadmium sulfide (CdS), cadmium selenide (CdSe), cadmium telluride (CdTe), and quantum dots.

[0073] In some embodiments, conductive, semiconductive, and / or nonconductive particles and dielectrics may be present in the first and / or second region. As a non-limiting example, particles such as ZnO may be used, which in some embodiments, may act as switchable conductors.

[0074] In some embodiments, electroluminescent particles and / or mechanochromic particles may be used. In some embodiments, particles configured to stiffen (e.g., locally stiffen) the dielectric elastomer actuator and / or impart anisotropy (e.g., anisotropy of mechanical properties) on the dielectric elastomer actuator.

[0075] In some embodiments, the non-limiting examples of suitable materials and particles for depositing can be mixed to enhance features including, but not limited to, durability. In some embodiments, inks (e.g., fluids, solutions, and / or suspensions) comprising the non-limiting examples of suitable materials and particles may be used.

[0076] In some embodiments, the first and / or second plurality of particle may be deposited onto a carrier substrate and / or the first layer (e.g., the elastomer layer) via any of a variety of methods, some of which are described herein. A few examples of such deposition methods include screen printing, spray deposition, and / or gravure coating. Other depositions methods, including those used to cast the elastomer layer (described elsewhere in the present disclosure) may also be used to deposit the second and / or third layers.

[0077] In some embodiments, the first and / or second plurality of particles comprise and / or may be mixed with adhesion promoters. An adhesion promoter may include urethanes such as polyurethane and / or room temperature vulcanizing (RTV) materials such as RTV silicone. The adhesion promoter may be included in low quantities, such as greater than 5 ppm, 10 ppm, or 100 ppm. In some embodiments, the adhesion promoter may be included in relatively high quantities to moderate the orientation of the DEA during actuation. The plurality of particles may be dispersed in a suitable solvent, including but not limited to, isopropanol (IPA), organic solvents such as toluene, dimethyl sulfoxide (DMSO), Hexane, and / or chloroform, or mixtures thereof. An adhesion promoter, without wishing to be bound by theory, may act as a binder. An adhesion promoter may modify the adhesion strength of a deposited material. The deposited material may be dried and / or exposed prior to a curing step. A curing step may involve exposure to time, UV, or elevated temperatures. The curing may be performed through a mask as can spraying. The curing can increase adhesion strength. UV exposure can be used to alter adhesion locally and / or globally. In some embodiments, using an adhesion promoter allow for relatively high adhesion between elastomer layers in multilayer configurations of dielectric elastomer actuators (e.g., see FIG. IE). Localized curing can allow for additional structuring of an electrode on a target substrate as only sections with overall low adhesion and interactions may transfer.

[0078] In some embodiments, the first and / or the second plurality of particles may aid in the manufacturing of the dielectric elastomer. In some embodiments, the first and / or second plurality of particles may reduce the adhesion between electrode layers and substrates used to stamp the electrode layers onto elastomer layers. Accordingly, in some but not all embodiments, the first and / or second plurality of particle provide enhanced functionality for the manufacturing of the dielectric elastomer actuators, rather than enhanced functionality for the dielectric elastomer actuator itself.

[0079] In some embodiments, the first and / or second plurality of particles may under any of a variety of processing after deposition. In some embodiments, the first and / or second plurality of particles may be laser- welded to increase the conductivity of the layer and / or the stiffness of the layer or at least a portion thereof.

[0080] In some embodiments, the first and / or second plurality of particle form a self-clearing network. In some embodiments, the self-clearing network generally involves a network of relatively high-aspect ratio nanoparticles. Such networks may allow for increased breakdown strength of dielectric elastomer actuators.

[0081] In some embodiments, the second and / or third layers are electrode layers. In some embodiments, the electrode layers may be at least partially transparent to electromagnetic radiation, such as electromagnetic radiation in the visible spectrum.

[0082] In some embodiments, the second and / or third layers may be chemically doped. In some embodiments, the second and / or third layer may be chemically doped using sulfuric acid. In some embodiments, the second and / or third layers are compacted (e.g., mechanically) using a press. Such compaction may allow for the plurality of particles in the second and / or third layers to increase in density and increase in conductivity compared to before the compaction was implemented.

[0083] In some embodiments, a stiffness of a composite comprising the first and second layer is within 10% (or within 15%, within 20%, within 30%, and / or within 40%) of a stiffness of the first layer.

[0084] In some embodiments, the first and / or second plurality of particles may have any of variety of suitable sizes. In some embodiments, the first and / or second plurality of particles have a maximum dimension greater than or equal to 10 nm, greater than or equal to 50 nm, greater than or equal to 100 nm, greater than or equal to 500 nm, greater than or equal to 1 micrometers, greater than or equal to 10 micrometers, greater than or equal to 50 micrometers, or greater than or equal to 100 micrometers. In some embodiments, the first and / or second plurality of particles have a maximum dimension less than or equal to 100 micrometers, less than or equal to 50 micrometers, less than or equal to 10 micrometers, less than or equal to 1 micrometer, less than or equal to 500 nm, less than or equal to 100 nm, less than or equal to 50 nm, or less than or equal to 10 nm. Combinations of these ranges are possible (e.g., greater than or equal to 10 nm and less than or equal to 100 micrometers). Other ranges are also possible.

[0085] In some embodiments, the first and / or second plurality of particles are deposited onto the first layer (e.g., the elastomer layer) as a single ink or as multiple inks. In either case, one or more layers comprising the first and / or second plurality of particles may deposited on the first layer to form the second and / or third layer.

[0086] In some embodiments, the first and / or second regions have any of a variety of sheet resistances. In some embodiments, the first and / or second regions has a sheet resistance greater than or equal to 1 kiloohm per sequare, greater than or equal to 10 kiloohm per square, greater than or equal to 25 kiloohm per square, greater than or equal to 50 kiloohm per square, greater than or equal to 100 kiloohm per square, greater than or equal to 250 kiloohm per square, greater than or equal to 500 kiloohm per square, and / or greater than or equal to 1 megaohm per square. In some embodiments, the first and / or second regions have a sheet resistance less than or equal to 1 megaohm per square, less than or equal to 500 kiloohm, less than or equal to 250 kiloohm per square, less than or equal to 100 kiloohm per square, less than or equal to 75 kiloohm per square, less than or equal to 50 kiloohm per square, less than or equal to 25 kiloohm per square, less than or equal to 10 kiloohm per square, and / or greater than or equal to 1 kiloohm per square. Combinations of these ranges are also possible (e.g., greater than or equal to 1 kiloohms per square and less than or equal to 1 megaohm per square). Other ranges are also possible. In some embodiments, the first and / or second region has sheet resistances sufficient to render at least a portion the second and / or third layers transparent or partially transparent (e.g., at least 87% transmittance at visible wavelengths).

[0087] In some embodiments, the second region is adjacent to the first region. For example, as shown in FIGS.1B-1C and 2A-2C, first region 104A and second region 104B are adjacent to each other. In some embodiments, the first region is disposed on the second region. It should be understood that while the above referenced figure show the first region and the second region adjacent to each other, in some embodiments, the first and second region may be proximate to each other and may not physically contact each other. That is, in some embodiments, the first plurality of particles and the second plurality of particles may not be in contact and / or in electrical communication with each other. In embodiments where the first and second plurality of particles are proximate to each other, the first and second plurality of particles may continue to influence actuation of the dielectric elastomer actuator. In one such example, the dielectric elastomer actuator may have a first plurality of particles comprising conductive particles and a second plurality of particles comprising stiff particles proximate to the first plurality of particles. However, in some cases, such as embodiments where the first and second plurality of particles are conductive, the first and second region may be in sufficient contact such the first and second regions are in electrical communication. In a similar manner, in some embodiments, the first plurality of particles is adjacent to the second plurality particles. In some but not all embodiments, at least a portion of the first plurality of particles is in contact with at least a portion of the second plurality of particles. Accordingly, at least a portion of the first plurality of particles may be in electrical communication with at least a portion of the second plurality of particles, when the first and the second plurality of particles are conductive. In embodiments where either the first and / or the second plurality of particles are not conductive, the first and second plurality of particles will not be in electrical communication with each other, regardless of whether the first and second plurality of particles are adjacent to each other.

[0088] In some embodiments, the dielectric elastomer actuator comprising the first and / or second plurality of particles may be capable of exhibiting functionality that would not otherwise exhibit in an otherwise identical dielectric elastomer actuator without either the first or second plurality particles. In some embodiments, the electrodes of the dielectric elastomer actuator has an advantageously low contact resistance. The contact resistance of the electrodes, in some embodiments, can be relatively low by depositing the first plurality of particles having a relatively small particle size and the second plurality of particles having a relatively large particle size. Without wishing to be bound by any particular theory, by having a variety of different particle sizes, aspect ratios, roughness, and / or orientations, the dielectric elastomer actuator may have a suitable resistance (e.g., in the first region) capable of inducing actuation when a voltage is applied between the electrodes while having electrodes with a sufficient contact resistance capable of allowing for high frequency operation of the dielectric elastomer actuator. The particles having a relatively large size may be positioned in the second region (e.g., the lead portion) while the particles having a relatively small size may be positioned in the first region (e.g., the active portion). In some embodiments, the lower contact resistance may directly and / or indirectly lead to advantageous performance of dielectric elastomer actuator including but not limited relatively high breakdown strengths and relatively high frequency response. In some embodiments, the functionality induced the first and / or second plurality of particles may be the result of at least some of the particles orientation within the second and / or third layer and / or the exposure of at least some particles to external doping. Such functionality may also be induced via surface structuring of the second and / or third layers.

[0089] In some embodiments, the first and / or second plurality of particles may create localized regions of stiffness in the second and / or third layers. In some embodiments, the first and / or second plurality of particles may be selectively deposited in the first and / or second regions such that each region has a different stiffness. Accordingly, in some embodiments, the stiffness of the first plurality of particles may be different than the stiffness of the second plurality of particles. Such regions of varying stiffness may allow for directional actuation of the dielectric elastomer actuator. In some embodiments, a stiffness of a composite comprising the second layer and the first layer is within at least 10% (or at least 15%, at least 20%, at least 25%, at least 30%, or at least 40%, and up to 60%, up to 70%, or up to 80%).

[0090] In some embodiments, the first and / or second plurality of particles may allow the dielectric elastomer actuator to exhibit sensing capabilities. In some embodiments, the first and / or second plurality of particles comprises an electroluminescent agent. Such agents may exhibit and / or emit light when exposed to electrical stimuli. In some embodiments, the electroluminescent agent may allow for visual feedback for the user and / or sensing systems proximate to the dielectric elastomer actuator. Similar to other particles described herein, the electroluminescent agent may be incorporated into a ink that may be directly and / or indirectly deposited on the elastomer layer.

[0091] In some embodiments, the first and / or second plurality of particles may allow the dielectric elastomer actuator to have power distribution channels. Such power distribution channels, in some embodiments, may have a relatively high conductivity compared to the rest of the electrode. In some embodiments, power distribution channels may increase the conductivity of the electrode layers of the dielectric elastomer actuator thereby allowing the dielectric elastomer actuator to have increased efficiency, increased electrical cutoff frequency, and / or easier modeling compared to an otherwise essentially identical dielectric elastomer actuator absent the powder distribution channels. In some embodiments, power distribution channels may increase the efficiency of the electrode layers of the dielectric elastomer actuator thereby allowing the dielectric elastomer actuator to have reduced power consumption compared to an otherwise essentially identical dielectric elastomer actuator absent the powder distribution channels. Relatively low power consumption may be advantageous in mobile and / or untethered applications. In some embodiments, power distribution channels may allow for the dielectric elastomer actuators to operate at relatively higher frequencies compared to an otherwise essentially identical dielectric elastomer actuator absent the powder distribution channels. Power distribution channels may also aid in computer modeling of dielectric elastomer actuators systems, leading to quicker development of advancements, as the effects of resistance of the electrodes are less impactful. In some embodiments, the power distribution channels may also have a direct and / or constrain the actuation itself.

[0092] In some embodiments, the dielectric elastomer actuator comprises any of a variety of suitable first layers. In some embodiments, the first layer is an elastomer. In some embodiments, the elastomer has a relatively low stiffness (e.g., a lower stiffness than the second and / or third layers) such that the elastomer may deform when a voltage is applied between the electrode layers of the dielectric elastomer actuator. In some embodiments, the elastomer along with the dielectric elastomer as a whole may deform in one or more directions when a sufficiently high electrical field is applied to the first layer.

[0093] The first elastomer layer may comprise any elastomer known in the art. In some embodiments, the elastomer comprises any electroactive polymer known in the art. Non-limiting examples of suitable elastomers include natural rubber, silicones (e.g., PDMS, EcoflexTM 00- 30, Sylgard 184 (S184), Wacker P7670), acrylics (e.g., 3MTM VHBTM 4910), polyurethane, and thermoplastics (e.g., SEBS - styrene-co-ethylene-co-butylene-co-styrene). In some embodiments, the elastomer is substantially non-tacky. In some embodiments, the elastomer is substantially tacky. In some embodiments, the elastomer may comprises an acrylic elastomer, a silicone elastomer, a polyurethane elastomer, a biomaterial elastomer, and / or combinations thereof. In some embodiments, the elastomer is a composite material comprising a cross-linked polymer network and any of a variety of polymeric and / or nonpolymeric additives (e.g., dielectric additives). It should be noted any suitable elastomers may be used as the first layer, and accordingly, other elastomers beyond the examples listed above and described herein may be used.

[0094] The dielectric elastomer actuators described herein may be fabricated using any of a variety of suitable methods. In some embodiments, the first layer (e.g., elastomer layers) of the dielectric elastomer actuator can be cast, sprayed, printed (e.g., via 3D printing or other additive manufacturing techniques ), and / or coated (e.g., via spin coating, blade coating, bar coating, or other roll-to-roll). In some embodiments, after the first layer is deposited, the first layer may undergo one or more curing processes to cross-link the first layer and form an elastomeric matrix. In some embodiments, the second and / or third layers of the dielectric elastomer actuator may be deposited onto the first layer via spray deposition, stamping, coating (e.g., via spin coating, blade coating, or bar coating), or other methods. In some embodiments, such methods involve the use of masks, screen printing, or pad printing to pattern the first region and / or the second region of the second and / or third layers. In some embodiments, a dielectric elastomer actuator comprises a first structure having a plurality of elastomer layers and a plurality of electrode layers, each electrode layer positioned between elastomer layer. In such embodiments, the dielectric elastomer actuator may be considered a multilayer dielectric elastomer actuator. In some embodiments, the dielectric elastomer actuator is a rolled dielectric elastomer actuator. More information regarding the fabrication of dielectric elastomer actuators and related fabrication processes can be found in International Application Publication No.

[0095] WO2024 / 058858, entitled “Dielectric Elastomer Actuators and Methods of Manufacturing thereof,” and filed on July 21, 2023, which is herein incorporated by reference in its entirety for all purposes.

[0096] The following examples are intended to illustrate certain embodiments of the present invention, but do not exemplify the full scope of the invention.

[0097] EXAMPLE 1

[0098] In this example, articles, systems, and methods related to dielectric elastomer actuators are described. Generally, the electrodes in a dielectric elastomer actuator multilayer (DEAM) may have certain electromechanical properties including but not limited to low stiffness, high conductivity, and high breakdown strength. Nanoparticle networks may meet these at least some of these requirements, but creating a single NP ink that can improve the aforementioned performance metrics is difficult. There is typically a tradeoff between conductivity and breakdown strength. Inks loaded with smaller particles such as CNTs may produce electrodes that can “self-clear,” yielding relatively high breakdown strengths, while inks loaded with larger particles such as CB provide ample surface for connecting to external electronics, lowering contact and overall resistance. Conventional DEAM electrodes have been limited to a single nanoparticle ink patterned uniformly over the electrode. This generally limits such electrodes to achieve either higher breakdown fields or lower resistance, and thus either high strength or high operating frequency. In this example, this tradeoff was generally mitigated with hybrid electrodes that pattern each nanoparticle where it is advantageous. CNTs patterned throughout the body of the electrode showed breakdown strengths of 54.7 V / pm, 61% higher than conventional batch- sprayed carbon black (CB) electrodes. CB patterned at the contacts produces a 194x drop in contact resistance compared to CNTs, from 2440 kQ to 12.6 kQ. The hybrid electrodes of this example embody a modular design process that allows for independent refinement of inks. The hybrid electrodes can be fabricated by a batch- spray and stamp paradigm that allow for the design and deposition of inks without consideration of the elastomer they will eventually be stamped onto.

[0099] Materials and Methods

[0100] Spray Ink Recipe

[0101] The following recipe is used to prepare CB and CNT inks before spraying. The following steps are used to make the CNT spray ink. By volume, 1 part stock CNT ink was mixed with 2 parts IPA (approximately 15 mL of this spray ink mixture is needed for each sheet of electrodes) in scintillation vial(s). The mixture was then bath sonicated for 30 minutes. The mixture was then loaded into a syringe, and placed syringe into a syringe pump. The IPA cosolvent in the CNT spray ink allows it to wet the hydrophobic filter paper. The following steps were carried out to make the carbon black (CB) ink. The stock CB ink was sonicated for 10 minutes at 75% power, 100% duty cycle. An ice bath was used to prevent overheating. Before particles settled out of solution (~30 min), the amount of stock ink to be used was extracted into a disposable cup and diluted by volume with IPA at 1:9 ratio. Approximately 50 mL of CB spray ink was needed for each electrode sheet. A stir bar was placed the mixture and the cup was placed onto a magnetic stir plate in spray gantry. The feed tube was then inserted.

[0102] CNT stock ink recipe

[0103] The following recipe was used to prepare the stock CNT ink used for spraying. 100 g of de-ionized (DI) water was added to 100 mg of CNT powder (P3 SWCNT, Carbon Solutions) in a glass vessel. The solution was tip-sonicated (QSonica Q500) for 30 minutes at 75% power with 30 sec on, 10 sec off duty cycle (40 minutes elapsed). An ice bath was used to prevent overheating. The mixture at 8100 RPM was then centrifuged for 60 min in 50 mL Falcon tubes. The supernatant was then extracted, leaving the bottom 5 mL. The relative concentration of the ink was then determined compared to a 17% transmittance sample. The ink was then diluted to 16x relative concentration. The determination of relative concentration accounts for variation in the sonication and centrifugation steps.

[0104] CB stock ink recipe

[0105] The following recipe was used to prepare the stock CB ink used for spraying. 80 g IPA was added to 800 mg CB (Printex XEB2, Orion Engineered Carbons). The resulting mixture was then tip-sonicated (QSonica Q500) for 30 minutes at 75% power, 100% duty cycle. An ice bath was used to prevent overheating.

[0106] Electrode deposition process The CB and CNT inks are first prepared according to the processes described above. Then, the inks were deposited onto the 220mm x 220mm filter paper (PTFE Membrane Stock, 45 ji / m pore size, Tisch). The CB ink was deposited first, and the CNT ink second. For each ink, the process as follows was used, differing where noted. The distance between the spray nozzle and the filter paper is 10cm. Filter paper was placed on a vacuum plate with four 1.5mm alignment pins, one in each comer, to fix the position. The mixture of equal parts IPA and water was sprayed onto the filter paper, ensuring the entire surface is completely wetted. The laser-cut mask (0.005” Dura-Lar Ultra-Clear Film, Grafix) was placed over the damp filter paper, using the same fouralignment pins. For deposition of CNT, an atomizer was used and (SONOZAP 130kHz Atomizer, Sonaer) set to 75% power. For CB, an air supply was turned on and set to 2 psi, while for CNT, the air supply was set to 2.5 psi, and the pro-wetting (IPA) air supply to 8 psi. The IPA pro-wetting is used to keep the filter paper wetted and enhances the uniformity of deposited CNTs. A syringe pump used to feed CNT was set to 2.5 mL / min and the IPA syringe pump was set to 3.5 mL / min. Then, a vacuum source was turned on and dispensing of the ink was initiated. The inks were deposited on the entire 220x220 mm mask area with a raster pattern sweeping over the surface of the filter paper at a feed rate of 2000 mm / min. The filter paper was then placed in the oven for 5 minutes at 50 degrees Celsius.

[0107] DEAMS Fabrication

[0108] DEAMs were fabricated by first batch- spraying nanoparticle inks onto 230x230 mm sheets of filter paper (RS40419, Tisch Scientific). The hybrid electrodes were deposited in a two- step process: first, a CB ink was sprayed onto filter paper through a mask to pattern the contact regions (FIG. 3a), and a vacuum plate underneath the filter separates the solvent from the NPs. This process was repeated with a CNT ink sprayed through another mask onto both the contacts and body of the electrode (FIG. 3b). The resulting electrodes on filter paper are shown in FIG. 3c. The use of vacuum filtration produces a more homogeneous network and generally involves less tuning of inks compared to the evaporation process used in because, without wishing to be bound by any particular theory, the mechanical separation method depends less strongly on ink and substrate properties such as surface energy. It is also faster - a single spray of a 230 x 230 mm sheet can be completed in 5 vs 30 minutes. The use of a low-cost disposable filter substrate also reduces cost by 96% compared to established stamp-transfer processes. The hybrid electrodes are then stamp-transferred onto an elastomer layer (FIG. 3d) and an elastomer layer is deposited via spin deposition or other processes (FIG. 3F). The elastomer was degassed and cured, and this electrode stamping and elastomer deposition sequence was repeated until a multilayer stack with the desired number of layers was achieved (FIG. 3f). A knife was used to slice into the contact region, exposing cross-sections of the electrode, and conductive paint (PELCO Colloidal Graphite, Ted Pella) was applied to the cross-section to connect the electrode to external electronics (FIG. 4c). Each of these stacks was then pre-cleared according to the process described in 3.8.13 to eliminate defects and ensure safe operation at high voltages (FIG. 3g). Each stack’s capacitance was measured, and those with capacitance below 80% of the theoretical value was discarded. These first-order “mini stacks,” usually on the order of ten layers, are then assembled into second-order “meta-stacks” to create stacks on the order of hundreds of layers. Mini stacks can be either laminated together to create taller stacks as in FIG. 3h, or a single long stack may be rolled up to create a many-layered cylinder (e.g., a rolled actuator). These processes are detailed elsewhere in this disclosure. This produces a final meta-stack on the order of hundreds of layers, as shown in FIG. 3i. The hybrid electrode deposition and transfer process was shown to be relatively fast, modular, scalable, and lowcost. As previously shown, this stamp transfer process is sufficiently fast enough to allow for high layer throughput and is compatible with a wide range of elastomers.

[0109] The fabrication process in this example generally involves the steps described as follows. A PET mask is placed atop the filter paper substrate, and an atomizing nozzle overhead sprays CB ink onto the filter paper while a vacuum is applied from below. The mask is then removed and discarded. The process is repeated with a CNT ink to pattern the electrode body (e.g., the active portion). The electrodes are then dried in an oven and stored in a dry box until ready for use. The electrodes are then stamp-transferred onto an elastomer substrate. The electrodes are then covered with another layer of elastomer using spin-coating or another elastomer deposition process. This process is repeated until the desired number of layers has been reached, in this case 10 DEA layers and an encapsulating layers on either end to protect the electrodes. A laser is then used to release-cut the “mini-stacks” and a knife is used to partition their PET substrate. Each mini-stack was individually pre-cleared to the working field and its capacitance was evaluated. Those with under 80% of the expected capacitance are discarded. The remainder are aligned on a jig and “meta-stacked” atop each other. A thin layer of elastomer is squeegeed and cured between each successive pair of mini-stacks. Once assembled into a full “meta-stack,” permanent contacts are made to connect to external electronics. This fabricated process in described in FIGS. 3A-3I and FIGS. 22-24. Artificial muscle DEAM fabrication

[0110] A batch-spraying and stamping process was used to create 10 10-layer DEAs which were then combined into a 100 layer DEAM. To make these 10-layer mini stacks, Elastosil P7670 was spin-coated onto a PET substrate loosely adhered to an acrylic base plate for rigidity during spin coating. The first and last layers were spin-coated at 1500 RPM, and the active layers were spun at 560 RPM for a thickness of 85 pm. Each stack had 11 electrodes for a total of 10 active layers. A protective sheet of PET was placed on top of the platter and then used a laser cutter (Universal Lasers VLS6.60) to release cut each mini stack, leaving a 0.5mm buffer around the edge of each mini stack to prevent exposing the electrodes to the air, which may cause premature breakdown. With the mini stacks cut out but still attached to the platter, excess silicone was removed. A knife was used to make a cut to expose the carbon black connections, then connected each stack to external electrical leads using conductive ink. After pre-clearing each mini stack to 45 V / pm using the preclearing processes described in the present disclosure, the capacitance was measured and those that dropped under 80% of the expected capacitance from Cexpect= were discarded, where n is the number of active layers, A is the active area of each layer, e is the permittivity of the dielectric material, and d is the distance between layers. With the remaining mini stacks, the handle layer of PET was removed from the base sheet of acrylic, the protective PET cover sheet was removed, the exposed surface was coated in a thin glue layer, each was then laid into a laser-cut mold to align subsequent mini stacks. These intermediate meta stacks were then placed in an oven at 60° for 15 minutes, at which point the PET substrate was removed and another mini stack was added, repeating the process until all 10 mini stacks were combined into one meta stack. The glue layer was made by depositing a small pool of Elastosil onto a sheet of PET, then squeegeeing the pool into a thin film. Each resulting glue layer was on the order of 5 pm thick. To avoid possible breakdown through air bubbles trapped in the glue layer, each mini stack was aligned so there was no field between subsequent stacks. With the completed stack, a cut was made through all layers of CB to expose a single face to connect to. The exposed CB face was then painted with conductive ink, the ink was connected to an external electrical lead, and then the dried ink was encapsulated with a layer of silicone to prevent flaking.

[0111] Artificial Muscle Characterization

[0112] To measure free displacement for the stack actuator, the device was suspended by the leads, and 3100V was applied sinusoidally at 1 and 5 Hz. Video was recorded at 30 fps, and then the free displacement was then measured through thickness strain using a custom MATLAB script. The expected strains are predicted with the voltage stretch relation given in: V = HA-2 / (o(A) / e) where V is the voltage between the electrodes, H is the active layer thickness, A is stretch, and o and e are stress and strain, respectively. The stress is given by o(A) = p(A2- A-4), where p is the shear modulus of the elastomer. To account for the added stiffness caused by the inactive area cut around the perimeter of the electrodes, a factor of 1.14 is multiplied into the measured shear modulus of Elastosil P7670, 70 x 103. This model predicts a maximum of 14% strain at 3070V for 85 m layers with an approximate breakdown field of 47V / pm, slightly under the measured value of 15% at 3100V. To perform a test to determine the frequency response of this stack, an amplifier capable of outputting a current of I = 2nfCV is needed, where f is the operating frequency in Hz, C is the capacitance of the stack (measured to be 4.6nF), and V is the operating voltage, 3100V in this case. Because the amplifier used herein is capable of outputting a current of 2mA, the maximum frequency at which it could drive this device is approximately 22 Hz. A full frequency sweep was not performed with this device. After measuring free displacement with minimal boundary constraints, the blocked force was measured with rigid connections on either end to minimize displacement. Tech Bond was used to attach the terminating faces of the actuator to 1 / 16” thick pieces of acrylic with embedded jewelry hooks to make these external connections. The caps were then attached via “S” hooks to a load cell on the top (Transducer Techniques MDB 2.5) and a micrometer stage on the bottom to control pre-tension. Because the Maxwell stress equation assumes an ideal electrode with complete coverage, and CNTs do not cover the entire area of the electrode, Cpt was introduced as a metric to account for capacitance loss through fractional coverage as well as from layer misalignment and pre-clearing after fabrication. It is defined as the ratio of the measured

[0113] Ae capacitance (4.6 nF) to the theoretical capacitance predicted by Ctheoreticai= n— = 5.3 nF, where n is the number of layers, the area A = 1.77 x 104m2, e = 2.5677 x 1011Fm and layer height H = 85pm, so Cpt= 4.6nF / 5.3nF = 0.86. With approximately 5% pre-strain in tension, a maximum actuation force of 4.5N was measured at a field of 43 V / pm before visible delamination occurred between mini stacks. This is only 63% of the expected value of 7.2 N given by Fexpected= Cpt* e * E2* A. Cure inhibition was suspected to prevent strong lamination between mini stacks, as the stacks were unable to be repaired in such a way as to prevent further delamination. Because the stack maintained the measured capacitance value after delamination occurred, testing was continued in compression so the actuation direction would match the pre-tension direction and there would be no risk of delamination. In the compression configuration, the stack was sandwiched between two acrylic plates connected to the load cell and micrometer stage. While this configuration does not represent a practical implementation for a stack actuator, the capability of the electrodes may be measure and should match the output once the delamination issue is resolved. With 1.5mm (14%) pre-strain in compression and a field of 45V / pm applied, a 6.9 N of force was achieved, 87% of the FeXpected of 8.0N at the corresponding field. During the manufacturing process, minor misalignments were observed between some stamped layers, likely due to stretched alignment pin holes on the filter paper. More careful observation and control of these alignment holes can help bring the force closer to the expected value, as well as increase Cpt.

[0114] Design of Roll Actuators

[0115] The design of a hybrid-electrode-DEA’s active region (electrode overlapped region) accommodates for additional height due to the addition of carbon black into the electrode. To avoid early breakdown of the DEAs, a 1 mm tall buffer zone between the active region and the carbon black electrode region was used on both ends of the DEA roll. In addition, during the cut release process, the carbon black region was cut to expose the hybrid electrode for wiring connections. These changes increase the height and mass of the roll actuators, leading to a shift in the resonant frequency, which is discussed elsewhere in this disclosure.

[0116] Roll actuator resonance analysis

[0117] When characterizing the actuator’s free displacement as a function of frequency, the resonance of the hybrid-electrode-rolled-actuators was observed to be lower than that of the previous DEAs. This result may be due to the geometry and mass change of the new hybrid electrode-DEAs, which was caused by the design. A hybrid-electrode DEA is 11.5 mm tall and weighs 155 mg, while a previous DEA is 9mm tall and weighs 110 mg. A roll actuator’s resonant frequency, w, is a function of its stiffness, k, and mass, The stiffness of the actuator was estimated based on the rolled actuators’ length, L, cross-sectional area, A, and the modulus of their constituent elastomer, E (k = EA L ). Therefore, the resonance of a rolled actuator can be determined by Equation 1 : Equation 1

[0118] The resonance, modulus, cross-sectional area, length, and effective mass of the hybrid-electrode - DEAs was defined to be coi, Ei, Ai, Li, and mi, respectively. Those of the conventional DEAs to be C02 E2, A2, L2, and m2, respectively. Based on the design parameters, the modulus and cross- sectional area of the two actuators are the same, but L2 = 1.28 Li. A simplified rolled DEA to be a spring-mass system and assumed the spring has a uniform linear density. The effective mass of a DEA can then be estimated to be one-third of its total mass. Together with the measurement mass of the rolled DEAs, it was determined that m2 = 1.4mi. Finally, the above calculations lead to 0)2 = 0.74 (JJI. The measured resonance of the previous DEAs was approximately 600 Hz.

[0119] Based on the model, the hybrid-electrode-DEAs were estimated to be 444 Hz, which is close to (10% higher than) the experimental result (400 Hz).

[0120] Roll actuator blocked force estimation

[0121] The electrical property of the pump is described with a RC circuit, consisting of a capacitor and a resistor in series. The driving signal of a DEA, Vc(t), is given by: Vc(t) = 1 1

[0122] - aVincos(cot + 4>) + - Vinand the current through the circuit as: ic(t) =

[0123] — - VinacoC • sin(cot + 0) where Vin is the amplitude of the signal, w is the angular frequency, and (|) is the phase shift. The amplitude coefficient a = ^==== , the phase shift 0 = tan-1(— RCco). When a voltage input is applied, the Maxwell stress generated across electrodes

[0124] 1 7 1 / v\ is: P = - epE = - eet - J2where P is the Maxwell stress, E is the electric field strength, V is the voltage between the electrodes, eeis the dielectric constant of the elastomer, and d is the dielectric elastomer thickness. The blocked force of a DEA is represented as: Fd(t) = S is the cross-sectional area of the actuator. Substituting in Vc(t) gives the driving force as: 15. J

[0125] Measurement of contact resistance

[0126] Contact resistance was measured by producing 5 mm test strip electrodes. These electrodes were stamped onto P7670 that had been spin-coated and cure onto laser-cut acrylic disks. The electrodes were then encapsulated with another spin-coated layer of elastomer. An X- Acto blade was then used to slice through opposite ends of the test strips to produce strips of lengths from 10 to 75 mm, in increments of 5 mm. The ends of these strips were gently peeled back from the acrylic substrate and copper tape was placed underneath them. The ends were replaced atop the copper tape and Pelco colloidal graphite paint was applied to the ends of the test strips to connect them electrically to the copper tape. After the conductive paint had dried, a digital multimeter (Fluke 179) was used to measure the resistance of each strip. Resistance was plotted as a function of length to produce FIGS. 7A-7B, and a linear fit was applied to the data. The contact resistance was taken to be the y-intercept of the trend line.

[0127] DEAM cost estimate

[0128] FIGS. 31-32 summarize the differences in material cost to produce an actuator with hybrid electrodes via the presented batch spray and stamp process ($2.48) compared to that to produce a CNT-only actuator with the mask-and-stamp process utilized ($59.68). The reference point used is a 1 x 1 x 1 cm actuator made up of 100 layers of 100 pm each. These parameters are similar to the “muscle” manufactured in this example. The main driver of cost for both actuators is the filter substrate. While the Advantec filters can theoretically be reused, the filteer’s performance quickly degrades with reuse, and thus in each filter was used to produce only a single electrode layer. For cost purposes they are thus treated as disposable, and account for 99% of the total. This calculation also assumes that 20 10 x 10 mm electrode layers can pack into an 0 mm diameter usable area of the filters, a relatively ideal assumption because of practical handling limitations. The Tisch filter paper, however, is orders of magnitude cheaper, costing $1.37 for the same area.

[0129] Device Architecture

[0130] A DEAM produced with the hybrid electrodes, shown in FIG. 4a, takes advantage of the differing network topographies produced by CNT and CB inks. Examining the volume of the DEAM in FIG. 4b, the small and sparsely-distributed CNTs shown in FIG. 4d can be easily cleared away during a breakdown event. FIG. 4b shows the volume of the DEAM spanning the network transition region and cut surface, before conductive paint is applied to the cut surface. CB particles and their aggregates, meanwhile, provide ample cross-sectional area to connect to, as illustrated in FIG. 4i when a conductive paint is applied as in FIG. 4c.

[0131] As shown in FIG. 5, the contact region is not composed of only CB particles. Rather, CNTs are deposited atop the CB particles, draping over and connecting CB aggregates. This orientation is flipped when the electrodes are stamped onto the elastomer substrate. FIG. 4f shows how this results in CNTs being mostly obscured by the CB aggregates that now rest above them, but some CNTs can be seen between cracks in the CB layer. This CB+CNT architecture was used instead of solely CB to simplify design of the electrodes and enhance conductivity of the contacts. Rather than attempt to determine the minimum overlap of CNT and CB regions to minimize any contact resistance at their transition, the entirety of the CB was covered. This layered composite also enhances conductivity. A sheet resistance test specimen demonstrated that regions with CB alone had sheet resistances of 39.87 ± 1.79 kQ / a and those with CNTs alone measured 49.52 ± 4.92 kQ / n. Assuming that these can be modeled as parallel resistances, the total sheet resistance was expected to be 22.09 kQ / n, but the measured resistance was 2.41 ± 0.29 kQ / n, 9.16x lower than expected. This discrepancy is likely due to the increased connectivity that the added CNTs grant to the CB aggregates. As seen in FIG. 4f, this CNT layer can bridge cracks and other breaks in the CB network. A similar effect has been noted in silver nanowire-CNT composites. The authors in also noted that the deposition of distinct strata was necessary to achieve this performance increase - a simple mixture of the inks was insufficient.

[0132] Reduced resistance increases operation frequency and efficiency

[0133] The resistance of an electrode R was modeled as the sum of its contact resistance Rcand the channel resistance Rch (FIG. 6a). Given the CNTs’ sheet resistance of 49.52 kQ / n, electrode designs with an aspect ratio on the order of unity have an Rch on the order of 100 kQ . As shown in FIG. 7A, however, this resistance is typically dominated by CNTs’ contact resistance. For a 5 mm-long contact, Rcis 2730 kQ , an order of magnitude greater than Rch. Adding CB (FIG. 7b) reduces this resistance Rcby 194 x to 12.6 kQ mm, making Rch the dominant resistance and dropping total resistance by an order of magnitude. FIG. 6b shows this effect for single- DEAlayer, paddle-shaped test devices with CNT only vs CB+CNT contacts. Each device was originally manufactured as a hybrid-electrode device and precleared to 250 V (7.84 V / m) to remove all initial shorts, and then capacitance and resistance measurements were taken on an LCR meter. In these typical devices made with CB+CNT contacts, the 12.6 kQ contact resistance accounts for only 16.4% of the measured device resistance of 76.8 kQ . In contrast, when the connection was remade by slicing through the CNT-only portion of the tab, the resistance increased to 2.00 M Q , indicating how strongly Rc,CNT-oniy dominates R. This lower contact resistance increases the electrical cutoff frequency of devices from 0.586 to 15.1 kHz (FIG. 6c), enabling high-frequency applications such as audio drivers, which may be able to produce tens of kHz. The cutoff frequency fcwas established as the frequency at which the voltage across the dielectric drops to -3 dB (“70%) of the applied voltage. This can be calculated using Equation 2: assuming that the circuit can be modeled as depicted in FIG. 6a: a resistance, R, in series with a capacitance, C. Other circuit models have incorporated a resistor in parallel with C to model the leakage current through the dielectric (typically on the order of nA), but such a large resistance is difficult to measure and as FIG. 8 demonstrates, this model behaves similarly to a real DEA without this inclusion. Plotted values Cn and Rn are normalized by their reference values R and C measured at 1000 Hz. For the real circuit, R = 270.5 kQ and C = 137.7 pF and for the DEA R = 270.2 kQ and C = 137.6 pF. The cutoff frequency fcis calculated as described elsewhere in this disclosure. The DEA behaves very similarly to its equivalent RC circuit below the cutoff frequency. The decreased resistance also improves, in this example, efficiency. FIG. 6b illustrates its effect on the dissipation factor D, which represents the ratio of real to reactive power in the DEA. At 1000 Hz, more power is lost to resistance than is oscillating reactively in a CNT-only device (DCNT =1.48), whereas less than a tenth is lost in a hybrid device (Dhybrid = 0.0672). This 22 x efficiency boost allows for smaller associated batteries and power electronics, enabling applications in compact consumer electronics and untethered micro-scale vehicles. The reduction in resistance is highly dependent on electrode geometry, however. While the paddle-shaped devices saw a 22 x reduction in contact resistance by adding CB to the contacts, a roll actuator saw only a 3% reduction from 39.2 to 38.2 kQ. This is likely due to differences in electrode contact length; the roll actuator electrodes were designed to reduce the influence of contact resistance by running the contacts along the entirety of the actuator’s 50 mm length. In contrast, the paddle-shaped electrodes are designed with a small 5 mm contact length whose resistance will be approximately 10 x greater and will dominate the overall resistance. Thus the total resistance of paddle-shaped electrodes is more sensitive to changes in contact resistance than is that of the roll actuators. This reduced resistance in designs with small contacts expands the viable design space. Previously, designers needed to consider the large impact of contact resistance on device resistance. While roll actuators reduce contact resistance by having a long contact that spans the length of the unrolled actuator, this generally adds an extra complication to fabrication; the ends of the actuator may be not only mechanically affixed but also electrically. Removing this consideration allows for independent, modular design of devices’ electrical and mechanical elements, allowing for integration into mechanical transmissions, power electronics, and other components of the system actuated by the DEAM. Enhanced breakdown strength increases actuator output

[0134] Breakdown is known as a sudden, steep, and irreversible increase in leakage current across the dielectric. This “hard breakdown” can thus be characterized as binary: failed or not failed, and the field at which the failure occurs is denoted as a specimen’s breakdown field. These fields are fit to a Weibull distribution, and the breakdown strength of the batch is taken to be the field at which there is a 1 — c1chance of failure. As discussed more thoroughly in elsewhere in this disclosure, however, CNT-based electrodes do not fail quickly and catastrophically. Rather, they fail gradually in a series of “self-clearing” that degrade their capacitances and thus actuation outputs, an example of which can be seen in FIGS. 9a-9G. To provide a comparison to other breakdown statistics, the failure of an individual device was defined as the electric field at which capacitance retention Cre, the ratio of current to original capacitance, drops to c1(FIG. 9b). The definition of device breakdown strength can thus be approximately understood as the point at which two-thirds of devices lose at least two-thirds of their output.

[0135] FIG. 9c shows how hybrid electrodes utilizing self-clearing CNTs in active regions achieve advantageous breakdown behavior to CB-only electrodes. The electrodes achieve not only 61% higher breakdown strength (54.7 vs 33.9 V / pm), but also 119% higher consistency = 20.21 vs 9.21). This breakdown strength approaches its upper limit, defined by that neat P7670 (63.4 V / pm), and exceeds the neat elastomer’s consistency = 9.39). This increased breakdown strength allows us to operate the devices at higher fields, increasing stress and strain outputs. As previously described, the batch spray process makes it easy to scale the number and size of DEA layers. This allows for the enhanced stresses and strains to be scaled to produce large forces and displacements. This was demonstrated with an “artificial muscle” 1.5 cm in diameter, 1 cm-thick, with 100 active layers (FIG. 9d). At its working field in free displacement, this device achieves 1.5 mm of displacement (14% strain) through its thickness, as shown in FIG. 4e. To test blocked force, the stack was pre-compressed by approximately 1.5 mm and measured the amount of force relaxed during actuation at 45 V / pm. The device produced 6.9 N of force (46 kPa), 260 x its own weight. This compares favorably with previous studies with similar elastomers that achieved 5% strain and 35 kPa stress, and is within 14% of the expected value of 8.0 N. Cpt = 0.86 is calculated as the ratio of the measured to theoretical capacitance values of the stack. The remaining discrepancy can be explained by such factors as incomplete coverage of CNTs, as seen in FIG. 4d, and misalignment during the stacking process. This accounting is enumerated elsewhere in the disclosure. A roll actuator made with hybrid electrodes achieves similar output to that from previous roll actuators made with a well- established process for stamping CNT electrodes. A hybrid electrode-roll- actuator. After preclearing up to 1750V, the equivalent R and C of the actuator was 25 kco and 1.50 nF, respectively. The expected performance (i.e., blocked force and free displacement) of the hybrid- electrode-actuator to be within 10% variation from the those having non-hybrid electrodes. The actuator’ s blocked force and free displacement was experimentally measured as a function of operation frequency, then compared the results with those of the rolls from the previous work. The blocked force was characterized with a force sensor (Nano- 17 Titanium, ATI Industrial Automation). The force sensor was fixed on a single-axis translation stage and placed the actuator under the sensor. To ensure blocking the actuator’ s motion during the test, the height of the sensor was lowered until it touched the actuator and applied a preload of 0.005N. The actuator was operated at 1000V during the test across various frequencies, and the result is shown in FIG. 9f. Since the actuator’s electrical time constant is much shorter than the operation period, the blocked force is independent of the frequency. Compared to other samples, the blocked force is about 9% less, close to the expected values. A laser vibrometer was applied to characterize the actuator free displacement (FIG. 9g). The resonance frequency of the hybrid- electrode-actuator was shifted down to 400Hz compared to the previous actuators due to an increase in the height and weight of the rolls. Experimental setups related to blocked force measurements are shown in FIGS. 28A-28C.

[0136] Stiffness of Dielectric Elastomer Actuators

[0137] To study the effects of cyclic strain on the electromechanical behavior of the electrodes, a single electrode layer was transferred onto a silicone film and then encapsulated, yielding a specimen 60pm thick, 80mm long, and 10mm wide. The specimen was mounted onto a polystyrene frame with silicone adhesive to aid in removal of the specimen from the acrylic platter used for spincoating. The specimen was then installed in a uniaxial tensile testing machine (Instron 68TM-10) to apply 100 cycles of strain from 5% to 25% while recording load and displacement. The resistance of the electrode was simultaneously measured using a digital multimeter (Key sight 34465 A). The mechanical and electrical data was then aligned manually during post-processing. The hybrid electrodes add negligible stiffness to the structure (Yeiectrode = (1.062+0.049) Yneatsiiicone (mean+standard deviation, n = 4)). The stress-strain curves and evolution of Young’s modulus for representative samples are shown in FIG. 6e. When subjected to cyclic extension from 5% to 25% strain (similar to strains expected during operation), the resistance of the electrodes was observed to have a close-to-linear response to applied strain and that the resistance of the electrode decreases relative to its initial resistance which, without wishing to be bound by any particular theory, may be due to alignment of the CNTs in the direction of stretching (FIG. 6d and FIG. 11). When subjected to cyclic strain over a range of 100%, the resistance increased relative to its initial value (FIG. 12).

[0138] Conclusion

[0139] The ability to modularly pattern properties across an electrode by patterning distinct nanoparticle inks in specified regions was demonstrated. This modularity may allow for designers to take advantage of nanoparticles’ unique advantages and avoid their disadvantages, reducing the difficulty of development while increasing performance. This capability was leveraged to resolve a previously tradeoff between strength and speed in DEAMs with nanoparticle electrodes. The principle that large particles such as CB can reduce contact resistance by 194x while small particles such as CNTs can increase breakdown strength by 61% was demonstrated. The high breakdown strength allows for devices such as an artificial muscles that can achieve muscle-like stresses of 46 kPa and muscle-like strains of 14%. A roll actuator achieved similar performance in both blocked force and free displacement. The low contact resistance makes DEAMs 26x faster, 22x more efficient, and better facilitates the design of DEAs. While the formulation presented here demonstrated a 26x reduction in resistance in the paddle form factor with small contacts, it did not produce noticeable reduction in devices with very long contacts such as roll actuators which already compensated for the high contact resistance of CNTs with a long contact length. The ink formulations and deposition parameters presented in this work, however, were not extensively tuned. Further work to increase vacuum filtration strength and increase CB areal density may yield improvements by decreasing CNT sheet resistance and further reducing contact resistance, respectively. While in this example CB and CNT-based inks were used, other inks and capabilities stemming from them can be implemented. The batch-spray and stamp process does not largely depend on ink and substrate material properties, allowing for quick development and deployment of novel inks. These inks could provide additional capabilities such as optical switching for on-thefly rewiring, high transparency or opacity for optical modification, low sheet resistance for power distribution, or electroluminescence for status monitoring and communication. The electrode fabrication method not only reduces development time and generally provides advantageous device performance; it also is also cheap and scalable. The materials costs are low - a 300x300 mm sheet of patterned electrodes costs only $2.50, mostly from the cost of the filter paper. Future work may investigate filter paper reuse and spray toolpaths to further reduce material costs. The batch-spray and stamp-transfer paradigm allows for virtually unlimited electrode area, and both electrode deposition and transfer operations could be implemented at high throughput in a roll-to-roll process. This scalability makes manufacturing of many-layered artificial muscles as well as large-area rolls possible, allowing high stresses and strains to be converted into large forces and displacement.

[0140] EXAMPLE 2

[0141] In this example, methods related to preclearing electrodes related to dielectric elastomer actuators are described. Defects in the dielectric and electrode of dielectric elastomer actuators can induce premature breakdown in DEAMs. Manufacturing processes can be tuned to reduce the number and severity of defects, but some defects are inevitable. Rather than rely upon the complete exclusion of defects for consistency, it is possible to use fault-tolerant networks of CNTs. When the electric field exceeds the limit for a given defect site, a breakdown event occurs and current flows through the CNT network around the site of failure. Each CNT can only support approximately 20 z A of current before being destroyed, so the current spike clears CNTs from a patch surrounding the failure site, as shown in FIG. 13. This “self-clearing” renders the patch non-conductive and prevents further current flow, isolating the short-circuit and protecting the local dielectric from further damage.

[0142] As the electric field is raised, other defects self-clear at their breakdown thresholds. Once all the defects for a given threshold field have been cleared, no more breakdown events occur and the device can be operated up to that field with minimal risk of breakdown. Thus “preclearing” a device to the desired working field Ewk before operation is advantageous; it allows reliable operation after deployment.

[0143] Pre-clearing is a balance, however: increasing electric field increases the Maxwell stress between electrodes, but as more defects clear with increasing field, the accumulated damage reduces the effective area of the electrodes. This degradation can be described with capacitance retention (Cre), the ratio of current device capacitance to initial. After each “target voltage” is applied, the capacitance can be measured with an LCR meter (Agilent E4980A). As FIGS. 11 A- 1 IE shows, C / Z. is generally stable until reaching a threshold at which it suddenly declines as clearing events become more numerous and severe. In order to maximize output stress, CreEwi? has been proposed as the objective function to maximize. To maximize output stress, but add additional terms to estimate the device’s output stress a as: a = CftCreeE2where c is the elastomer’s permittivity, E is the applied field, and t is the ratio of measured capacitance after fabrication to the theoretical capacitance accounts for the incomplete coverage of the electrode seen in FIG. 4d and other fabrication errors.

[0144] Pre-clearing algorithm

[0145] An automated pre-clearing algorithm was developed, detailed in FIG. 15, that clears away both minor and major defects without excessively degrading device performance. The preclearing algorithm first attempts a “ramp and hold” strategy. The ramp and hold strategy pictured in FIG. 14b applies a linear ramp of 1000 V / s to the DEA. Once the ramp reaches 85% of the last voltage that was reached, the ramp slows to 100 V / s, producing an elbow where the slope changes. The high initial slew rate makes the process time-effective, and the lower subsequent rate prevents excessive damage. Attempting too large of a voltage increase at once can cause excessive degradation by allowing many clearing events to occur simultaneously. It is known to apply clearing voltages in relatively large steps of tens to hundreds of volts. The 100 V / s ramp is much more conservative; given the 10 kHz sampling rate used, steps of 10 mV are theoretically possible. Practically, however, the 16-bit analog-digital conversion of the hardware described below yields a lower bound of 150 mV steps, and the total measured noise is typically ~1 V. Once the voltage reaches its target level, it is held for three seconds. If no current spike is detected, the process is considered complete and the device is successfully pre-cleared.

[0146] If a spike above 20 pA is detected during the process, however, then the current “episode” is immediately terminated. 20 p A was chosen as the threshold because it is the minimum approximate current needed to destroy a single CNT, and it is sufficiently higher than the Trek 610E amplifier’s current monitor noise floor of approximately 3 pA. Once the episode is terminated, the program examines the current- voltage (I-V) curve to determine what type of failure occurred. There are two types: a sudden spike in current, and a gradual increase in current as a function of voltage. The former indicates a “minor defect.” A single minor defect does not measurably affect the device’s capacitance or resistance. A major defect, however, causes a durable short-circuit through a dielectric layer. As seen in FIG. 14c, this short-circuit causes a quadratic increase in current with applied voltage, so the program detects these shorts by attempting a quadratic curve fit of the I-V curve. If the fit is good (R2 > 0.85) and the curve is concave-up, the program identifies the current increase as an indicator of a major defect, and a short detection flag is set.

[0147] Ramps cannot be used to effectively clear these major defects; 20 pA is not enough current to clear them, but using a higher current limit creates a positive feedback loop: more current further damages the dielectric, making it more conductive and involving more current to clear. These major defects may be spots of high CNT concentrations, as excessive CNT concentration has been shown to prevent effective clearing. To avoid this conductivity-current positive feedback loop, a high frequency (100 Hz) sinusoid is applied to the device for 10 seconds. Limiting the pulse width of a clearing signal can enhance breakdown strength. The “AC burst” signal similarly applies short bursts of high current to the device, limiting the amount of energy that can flow through the defect in a single cycle. FIG. 14d shows an AC burst used to clear a major defect. At the beginning of the episode, the peak current Imax is approximately 120 pA, and the current signal is positively offset, reflecting leakage through the defect. As defects are cleared, Imax stabilizes at 47 pA. This stable current can be estimated by the current required to charge an ideal capacitor: Imax= TifVmaxC where / and Vmax are the frequency and peak-to- peak voltage of the applied signal, and C is the capacitance of the device. For the 780 V, 100 Hz signal applied to the 134 pF device tested, imax=33 pA. The 30% discrepancy between Imax and Imax, possibly due to non-ideal behavior of the DEA, makes it difficult to use as a strong indicator of clearing success or failure, but it is useful for estimating how high of a current limit to set during the AC burst process. AC burst signals can still damage a device if not carefully limited, so the limit is set to approximately 200 pA more than the current needed to charge the capacitor, Imax-

[0148] The AC burst strategy is adaptive; if the episode completes without exceeding the current limit, Vmax is increased by ~ 15% for the next AC burst, and if it does not then Vmax is reduced by ~37%. This adaptability is necessary to automate the pre-clearing procedure; there is wide variation in the voltage required to clear a major defect, and this algorithm ensures that the minimum possible voltage is used to minimize potential damage. The approximate nature of the increases and reductions is due to a random prefactor. This prefactor, uniformly distributed from 0.975 to 1.025, ensures that the AC burst preclearing process does not become trapped in a deterministic sequence of applied voltages that cannot clear the defect, instead “exploring” the solution space for a suitable voltage. After the burst has completed, a three-second rest period allows thermal energy near the defect to dissipate.

[0149] Each AC burst is followed by a ramp and hold episode. This allows the program to assess whether the short was successfully cleared and take appropriate action. If an over-current event occurs and a short is still detected, an AC burst is again deployed. If a short is no longer detected, the short detection flag is unset, and Vmax is reset to its default value (500 V). This reset prevents the program from applying more than the minimum voltage to the next short. AC bursts are also deployed to hasten the pre-clearing process. Occasionally, the pre-clearing process becomes “stuck” around a certain voltage, with each ramp failing at the same voltage. If more than four ramps fail within 25 V of each other, the algorithm uses the adaptive AC burst strategy to quickly clear the associated defects.

[0150] The entire pre-clearing process typically takes 1-10 min for devices with a capacitance of 100-1000 pF. Generally, larger-capacitance devices take longer to clear, as the number of defects scales with total electrode area and device volume.

[0151] Hardware Implementation

[0152] The algorithm’s implementation is split across host and target computers as shown in FIG. 16. The data transfer rate between the two is limited, so their functions are structured such that the computers only need to communicate between episodes, approximately every few seconds. After an episode ends, the host receives a 30-second data buffer from the target computer. The target computer analyzes the data, checking for completion, type of defect, and other characteristics. It then uses these data to decide which signal to apply in the next episode, and sends signal parameters to the target. The target, which is running a Simulink model compiled into C-code, handles realtime tasks. It generates a desired voltage signal that is sent to the data acquisition (DAQ) system (National Instruments PCI 6259), and it monitors the current signal from the DAQ, setting the voltage to zero in the case of an over-current.

[0153] The compiled C-code runs at 10 kHz, enabling fast response to over-current events. FIG. 14e illustrates how, within 1 ms of a current spike, the capacitor is fully discharged. This minimizes the energy that can flow through a defect during a clearing event.

[0154] In this example, methods for assessing device quality were developed and compared. A breakdown metric based on Cre that allows for consistent comparison with literature was adopted. The breakdown strength may be uninformative for selecting an operating voltage for a device. Instead, Ewk, the field maximizing device Maxwell stress while minimizing clearing- induced performance degradation, may provide a more useful metric. Furthermore, a process for using this metric to select an optimal operating voltage was described.

[0155] Second, an algorithm for safely pre-clearing DEAMs was implemented it on a highspeed, automated system. An AC waveform applied to the DEA was shown to clear away major defects, while a DC ramp waveform was shown to be useful for clearing minor defects. Moreover, a simple method for detecting major defects based on a quadratic dependence of current on voltage was demonstrated. These techniques were demonstrated on a target computer which can run at 10 kHz, allowing for fast detection and response to current spikes. With this added safety, no human supervision is required and clearing can be completed quickly ( 1-10 minutes) and automatically.

[0156] Future work should investigate the sensitivity of omax and time to clear to various preclearing parameters, such as current limit during burst and ramp episodes and the rest period after bursts. This may lead to further gains in operating voltage and an increased understanding of the phenomena underlying pre-clearing. In the longer term, these phenomena should be explored in depth - a more causal understanding of how certain defects lead to failure may allow for better techniques to mitigate these defects in manufacturing and better clear them during preclearing.

[0157] EXAMPLE 3

[0158] In this example, fabrication and characterization of multilayer dielectric elastomer actuators with hybrid electrodes are generally described.

[0159] Materials and Methods

[0160] DEAMs were fabricated by first batch- spraying nanoparticle inks onto 220x220 mm sheets of filter paper (RS40419, Tisch Scientific) to produce hybrid electrodes. The inks are deposited in two steps: first, a CB ink is sprayed onto filter paper through a mask to pattern the contact regions, and a vacuum plate underneath the filter separates the solvent from the NPs. This process is repeated with a CNT ink sprayed through a second mask onto both the contacts and body of the electrode. The resulting electrodes on filter paper are pictured in FIG. 3F. Complete recipes and deposition processes are detailed elsewhere in this disclosure. As shown in FIG. 3F, hybrid electrode stamps were deposited onto filter paper. A central disk allows for inspection of each batch’s sheet resistance.

[0161] The use of vacuum filtration generally involves less tuning of inks compared to the evaporation processes because the mechanical separation method depends less strongly on ink and substrate properties such as surface energy. It is also generally faster - a single spray of a 220x220 mm sheet can be completed in 5 minutes with filtration vs 30 minutes with evaporation. The use of a low-cost disposable filter substrate also reduces cost by 92% compared to established stamp-transfer processes. The hybrid electrodes are then stamp-transferred onto an elastomer layer and an additional elastomer layer is deposited via spin deposition with a typical thickness of 30-80 pm. While this work exclusively uses spin-coated silicone for simplicity of analysis, BSS processes such as that presented here can accommodate a wide range of elastomers and elastomer deposition processes. The elastomer is degassed and cured, and this electrode stamping and elastomer deposition sequence is repeated until a multilayer stack with the desired number of layers has been achieved.

[0162] A craft knife is used to slice into the contact region, exposing cross-sections of the electrode, and conductive paint (PELCO Colloidal Graphite, Ted Pella) is applied to the crosssection to connect the electrode to external electronics (FIG. 25). Each of these stacks is then pre-cleared according to the process described in Example 2 to reduce defects and allow for safe operation at high voltages. Each stack’s capacitance is measured, and those with capacitance below 80% of the expected value were discarded.

[0163] The “mini stacks,” are typically on the order of ten layers thick. This is typically sufficient for thinner DEAMs, but to achieve more layers mini stacks are typically assembled into “meta stacks” on the order of hundreds of layers. Mini stacks can be laminated together to create taller stacks as shown FIG. 31, which depicts A DEAM of 100 active layers made from the stamps. Alternatively, a single long stack may be rolled up to create a many-layered cylinder as shown in FIGS. 29A-29B.

[0164] The hybrid electrodes utilize the differing network topographies produced by CNT and CB inks where they are most advantageous. FIG. 17 diagrams a single “paddle” electrode of the same design pictured in FIG. 17. CNTs are patterned over the active region of the electrode, i.e., the region which experiences the applied electric field. The sparse and fragile CNT networks that result, pictured in FIG. 4D showing scanning electron microscope (SEM) image of the active (CNT-only) region of an electrode, produce the desired self-clearing phenomenon that isolates short circuits. A small, 1 mm buffer region with only CNTs extends past the active region to prevent stray CB particles from precipitating breakdown in the active region. Unlike CNTs, CB forms larger and more durable agglomerates, as pictured in FIG. 4F which shows SEM image of the contact (CB+CNT) region. A crack in the center shows CNTs beneath. These aggregated CB networks are patterned at the contacts of the electrode, so that when a cut is made, ample cross- sectional area is exposed (FIG. 25) for the conductive paint to connect to. FIG. 26 shows representations of the cross sections of NP networks seen.

[0165] As seen in FIG. 30, the contact region comprises CNTs that are deposited atop the CB particles, draping over and connecting CB aggregates. This orientation is flipped when the electrodes are stamped onto the elastomer substrate. FIG. 4F shows how this results in CNTs being mostly obscured by the CB aggregates that now rest above them, but some CNTs can be seen between cracks in the CB layer. This CB+CNT architecture was used instead of CB alone to simplify the design of the electrodes and enhance conductivity of the contacts. Rather than attempt to determine the minimum overlap of CNT and CB regions to minimize any contact resistance at the transition pictured in FIG. 4E, the entirety of the CB was covered with CNTs. This layered composite also improved conductivity in this example. A sheet resistance test specimen demonstrated that regions with CB alone had sheet resistances of 39.87 ± 1.79 kQ / n and those with CNTs alone measured 49.52 ± 4.92 kQ / n. Assuming that these can be modeled as parallel resistances, the total sheet resistance was expected to be 22.09 kQ / n, but the measured resistance was 2.41 ± 0.29 kQ / n, 9.16x lower than expected (N=3). This discrepancy, without wishing to be bound by any particular theory, is likely due to the increased connectivity that the added CNTs grant to the CB aggregates. As seen in the center of FIG. 4F, this CNT layer can bridge cracks and other breaks in the CB network. A similar effect may be seen in silver nanowire-CNT composites. Deposition of distinct strata may be involved to observe this performance increase - a simple mixture of the inks was insufficient.

[0166] To demonstrate that the above fabrication process produces actuators with similar performance to that of typical rolled actuators, the actuators replicated blocked forces within 13.6% of the other rolled actuators.

[0167] Preclearing protocol

[0168] After each mini-stack is fabricated, it is pre-cleared to its working voltage. This may allow it to operate with little risk of a breakdown event occurring. A pre-clearing algorithm may be able to both respond quickly to current spikes and perform high-level logic functions to analyze and adapt to heterogeneous failure events. This was done by splitting the algorithm across two timescales and two computers, as detailed in FIG. 16. A target computer handles high-frequency (10 kHz) tasks with a Simulink model that has been compiled into C code. Before each episode, the host computer defines parameters of the desired pre-clearing voltage signal. During the episode, the target generates this signal and sends it to the data acquisition (DAQ) system (National Instruments PCI 6259). The target also monitors current draw via the DAQ- if current exceeds a set threshold, the voltage is immediately set to zero and the episode is terminated. This shutoff procedure allows us to limit the amount of energy that flows through a breakdown site. FIGS. 18A-18G illustrates how, within 1 ms of a current spike, the capacitor is fully discharged, and FIG. 18B shows how this limits damage to a small (< 100 pm) distance from the breakdown site. As shown in FIG. 18A current spike above 20 pA that triggers termination of a pre-clearing episode. The time between the spike and a full discharge is ~1 ms. Once an episode terminates, either as a result of signal completion or earlier termination because of a current spike, the target sends all data from the episode to the host computer. The host computer performs the high-level logic that allows it to adapt to heterogeneous failures resulting from the range of defects within and across devices. Upon the termination of an episode, the host evaluates whether and how the device failed during the episode, and based on this it specifies a signal for the next episode. This logic is diagrammed in FIG. 15, and can be expressed with only five binary decisions.

[0169] For the first episode, the pre-clearing algorithm attempts a “ramp and hold” strategy. The ramp and hold strategy pictured in FIG. 18C applies a linear ramp of 1000 V / s to the DEA. The first is terminated by a current spike at a voltage of Viast. The second ramp rises to 0.85 V at 1000 V / s and then slows to 100 V / s. The ramp-and hold (and thus the pre-clearing process) completes successfully after holding the target voltage of 1400 V for three seconds. Once the ramp reaches 85% of the last voltage that was reached, the ramp slows to 100 V / s. The high initial slew rate makes the process time-effective, and the lower subsequent rate prevents excessive damage as the voltage approaches the previous breakdown threshold. The 100 V / s ramp is conservative; given the 10 kHz sampling rate of the DAQ, steps of 10 mV are theoretically possible. Practically, however, the total measured noise is typically ~1 V, still one to two orders of magnitude smaller than previous efforts. Once the voltage reaches its target level, it is held for three seconds. If no current spike is detected, the process is considered complete and the device is successfully pre-cleared.

[0170] If a current spike above 20 pA is detected during the process, however, the current episode is immediately terminated by the target computer and the voltage is set to zero. 20 p A was chosen as the threshold because it is the minimum approximate current needed to destroy a single CNT, and it is sufficiently higher than the Trek 610E amplifier’s current monitor noise floor of approximately 3 pA. Once the episode is terminated, the program examines the currentvoltage (I-V) curve to determine what type of failure occurred. As pictured in FIG. 18D, there are two types: a sudden spike in current, and a gradual increase in current as a function of voltage. The former indicates a minor defect. A single minor defect does not measurably affect the device’s capacitance or resistance. A major defect, however, causes a durable short-circuit through a dielectric layer. The major failure produces a quadratic dependence of current on voltage. The minor failure, in contrast, produces a sudden spike in current, seen at ~450V. This short-circuit causes a quadratic increase in current with applied voltage, so the program detects these shorts by attempting a quadratic curve fit of the I-V curve. If the fit is good (R2> 0.85) and the curve is concave-up, the program identifies the current increase as an indicator of a major defect, and a short detection flag is set. The superlinear increase in current with voltage suggests that the voltage is changing the resistance of the short-circuit; this may be the result of increasing voltage allowing for current to cross an increasing number and size of nanoscale gaps proximal to the breakdown site, increasing conductivity. Ramps cannot be used to effectively clear these major defects; 20 pA is not usually sufficient current to clear them, but using a higher current limit creates a positive feedback loop: more current further damages the dielectric, making it more conductive and requiring more current to clear. These defects may be spots of high CNT concentrations, as excessive CNT concentration may limit effective clearing. To break this conductivity-current positive feedback loop, a high-frequency (100 Hz) sinusoid is applied to the device for 10 seconds. Limiting the pulse width of a clearing signal may enhance breakdown strength. Accordingly, the “AC burst” signal similarly applies short bursts of high current to the device, limiting the amount of energy that can flow through the defect in a single cycle. FIG. 18E shows an AC burst used to clear a major defect in a single-active-layer device with the geometry shown in FIG. 17. An initial clearing period evidenced by current spikes and offsets is followed by a stable period. At the beginning of the episode, the peak current Imax is approximately 120 pA, and the current signal is positively offset, reflecting current through the defect(s). As defects are cleared, Imaxstabilizes at 47 pA. This stable current can be estimated by the current required to charge an ideal capacitor: Imax = TrfVmaxC where / and Vmax are the frequency and peak-to-peak voltage of the applied signal, respectively, and C is the capacitance of the device. For the 780 V, 100 Hz signal applied to the 134 pF device tested, 1^=33 pA. The 30% discrepancy between Imax and Imax, possibly due to non-ideal behavior of the DEA, makes it an unreliable indicator of clearing success or failure, but it is useful for estimating how high of a current limit to set during the AC burst process. AC burst signals can still damage a device if not carefully limited, so the limit is set to approximately 200 pA more than the current needed to charge the capacitor, Imax.

[0171] The AC burst strategy is adaptive; if the episode completes without exceeding the current limit, Vmax is increased by ~ 15% for the next AC burst, and if it does not then Vmax is reduced by ~37%. This adaptability is necessary to automate the pre-clearing procedure; there is wide variation in the voltage involved to clear a major defect, and this algorithm ensures that the minimum possible voltage is used, minimizing damage. The approximate nature of the increases and reductions is due to a random prefactor. This prefactor, uniformly distributed from 0.975 to 1.025, ensures that the AC burst pre-clearing process does not become trapped in a deterministic sequence of applied voltages that cannot clear the defect, instead exploring the solution space for a suitable voltage. After the burst has completed, a three-second rest period allows thermal energy near the defect to dissipate.

[0172] Each AC burst is followed by a ramp and hold episode, as shown in FIG. 18F. After initial ramp-and-hold episodes, a major failure is detected. The program adapts to clear the failure by progressively increasing the burst voltage from 500 to 780 V. A ramp-and-hold is employed after each burst to assess whether the short has been cleared. Once it is clear, the program reverts to ramp-and-hold episodes. This allows the program to assess whether the short was successfully cleared and take appropriate action. If an over-current event occurs and a short is still detected, an AC burst is again deployed. If a short is no longer detected, the short detection flag is unset, and V^is reset to its default value (500 V). This reset prevents the program from applying more than the minimum voltage to the next short. AC bursts are also deployed to hasten the pre-clearing process. Occasionally, the pre-clearing process becomes “stuck” around a certain voltage, with each ramp failing at the same voltage. If more than four ramps fail within 25 V of each other, the algorithm uses the adaptive AC burst strategy to quickly clear the associated defects.

[0173] The entire pre-clearing process typically takes 1-10 min for devices with a capacitance of 100-1000 pF. Generally, larger-capacitance devices take longer to clear, as the number of defects scales with total electrode area and device volume.

[0174] Pre-clearing is a balance between increasing device output and limiting degradation. Increasing the target clearing voltage allows for a higher working field Ewk during operation, but as more defects clear with increasing clearing field, the accumulated damage reduces the effective area of the electrodes. This degradation can be described with capacitance retention (Cre), the ratio of current to initial device capacitance. After each target voltage is applied, the capacitance can be measured with an LCR meter (Agilent E4980A). As FIG. 18G illustrates, Creis generally stable until reaching a threshold at which it suddenly declines as clearing events become more numerous and severe. The maximum predicted stress <7 = 51 kPa occurs at 47.0 V / zm, before the breakdown strength 54.7 V / zm is reached. The high variation in Cre at 0 V is an artifact of initial conductive paths through the dielectric layer before preclearing, possibly from stray NPs. In order to maximize output stress, CreE2a& been proposed as the objective function to maximize. To maximize output stress, but add additional terms to estimate the device’s output stress G as G = CfeCreeE2where e is the elastomer’s permittivity, E is the applied field, and Cfeis the ratio of measured capacitance after fabrication to the expected capacitance — , where A is the area of each electrode and H is the thickness of the dielectric between them. Cfeaccounts for fabrication errors such as the incomplete coverage of the electrode seen in FIG. 4D.

[0175] The pre-clearing algorithm is split across host and target computers, and the command and feedback signals are routed through a DAQ and high voltage amplifier, as noted in FIG. 16. The host computer’s logic, executed after each episode, is fully enumerated in FIG. 15. Communications between the host, target, and DAQ are digital, while signals sent between the DAQ, amplifier, and DEA are analog.

[0176] Reduced Contact Resistance

[0177] The resistance of an electrode R was modeled as the sum of its contact resistance Rcand the resistance from the body of the electrode Re(FIG. 19A). The total resistance R is the sum of contact resistance 7?cand the resistance through the body of the electrode Re. Given the CNTs’ sheet resistance of 49.52 kQ / n, electrode designs with an aspect ratio on the order of unity have an Reon the order of 100 kQ. This resistance, however, is typically dominated by CNTs’ contact resistance. As shown in FIG. 21 A, Rcis 284.9 ± 151.3 kQ (mean ± 95% CI) for a 5 mm-long contact. Adding CB (FIG. 21B) reduces this resistance Rcby 32x to 8.817 ± 3.649 kQ, making Rethe dominant resistance and lowering R to approximately the value of Re.

[0178] FIG. 19B shows this effect for N=12 single-DEA-layer, paddle-shaped test devices with CNT only vs CB+CNT contacts. Each device was originally manufactured as a hybrid-electrode device and pre-cleared to 250 V (7.84 V / zm), and then capacitance and resistance measurements were taken on an ECR meter. This yielded a mean resistance of 76.8 kQ at 1000 Hz. After taking measurements with CB+CNT contacts, the contacts were remade by slicing through the CNT- only portion of the tab and discarding the CB+CNT composite contacts, as diagrammed in FIG. 27. When the connections were remade in the CNT-only region, the mean resistance increased to 1930 kQ. This indicates that Rcstrongly dominates R for CNT-only electrodes. CNT-only contacts are not only more resistive, but also far more variable. This is possibly due to the sparse topography of CNT networks relative to CB networks shown in FIGS. 4D-F leading to large variations in local cross-sections (FIGS. 4G- J) and sensitivity to cut conditions. The range of resistances within 1 SDiogof the mean increases from [64.2, 92.0] kQ for CB+CNT contacts to [981, 3800] kQ for CNT-only contacts. This variability, also exhibited in contact resistance measurements in FIG. 21A, makes electrical analysis of CNT-only electrodes challenging. Estimating the difference between contact resistances as the difference in total resistances between CNT- and composite-contact devices yields RC= 1853 kQ, while the difference between contact resistances measured with dedicated tests was ARC= 276. 1 kQ. This difficulty is compounded by the potential impact of other factors such as elastomer compliance, the effect of pre-clearing, and environmental variability.

[0179] This lower contact resistance increases the electrical cutoff frequency of devices from 0.586 to 15.1 kHz (FIG. 19C), enabling high-frequency applications such as audio drivers, which may be able to produce tens of kHz. The cutoff frequency fcwas defined as the frequency at which the voltage across the dielectric drops to -3 dB (~70%) of the applied voltage. This can be calculated as fc= assuming that the circuit can be modeled as depicted in FIG. 19A: a resistance, R, in series with a capacitance, C. FIG. 8 demonstrates how this simple model sufficiently captures the circuit’s behavior.

[0180] The decreased resistance also enhances efficiency. FIG. 19D illustrates its effect on the dissipation factor D, which represents the ratio of real to reactive power in the DEA. Lines in B- D represent the mean, and shaded error bounds represent ±1 SD / o#. At 1000 Hz, more power is lost to resistance than is oscillating reactively in a CNT-only device (DCNT= 1.49), whereas less than a tenth is lost in a hybrid device (Phyb d= 0.067). This 22x efficiency boost allows for smaller associated batteries and power electronics, enabling applications in compact consumer electronics and untethered micro-scale vehicles.

[0181] The reduction in resistance is somewhat dependent on electrode geometry, however. While the paddle-shaped devices saw a 22x reduction in contact resistance by adding CB to the contacts, a roll actuator of the design presented in saw only a 3% reduction from 39.2 to 38.2 kQ. While these results are complicated by changes in manufacturing and preclearing process, this small difference is likely due in part to differences in electrode contact length; the roll actuator electrodes were designed to minimize the influence of contact resistance by running the contacts along the entirety of the actuator’s 50 mm length. In contrast, the paddle-shaped electrodes are designed with a small 5 mm contact length. This contact width should be kept relatively small: for a stacked actuator, the contact regions are along the direction of actuation rather than at fixed attachment points at the end of a roll, thus low contact widths limit additional mechanical impedance. Therefore, the total resistance of paddle-shaped electrodes is far more sensitive to changes in contact resistance than is that of the roll actuators. Hybrid electrodes with composite CB+CNT contacts thus provide the greatest benefit to devices that benefit from smaller contacts in order to either reduce mechanical impedance or simplify device assembly.

[0182] To study the effects of cyclic strain on the electromechanical behavior of the electrodes, a single electrode layer was transferred onto a silicone film and then encapsulated, yielding a specimen 60 urn thick, 50 mm long, and 10 mm wide. The specimen was mounted onto a polystyrene frame with silicone adhesive to aid in removal of the specimen from the acrylic platter used for spin-coating. The specimen was then installed in a uniaxial tensile testing machine (Instron 68TM-10) which applied 100 cycles of strain from 5% to 25% while recording load and displacement. The resistance of the electrode was simultaneously measured using a digital multimeter (Keysight 34465A). The mechanical and electrical data was then aligned manually during post-processing.

[0183] The batch-sprayed and stamped CB electrodes contribute negligible stiffness, and the CNT networks similarly had negligible stiffness added to the active region of the hybrid electrodes (Ye / ecfrode = (1.062 ± 0.049)xY neatsiiicone, mean ± standard deviation, n = 4). The stressstrain curves and evolution of Young’s modulus for representative samples are shown in Fig. 19E.

[0184] Contact resistance was measured by producing 5 mm wide test strip electrodes at various lengths. Hybrid and CNT-only electrodes were sprayed using the same process described previously, with the location of different test strip lengths distributed randomly throughout the spray area. These electrodes were stamped onto ~ 100 urn thick P7670 that had been spin-coated and cured onto aluminized Mylar tacked onto laser-cut acrylic disks. The aluminized Mylar was etched with a CO2 laser cutter, leaving conductive regions at the ends of the test electrodes to serve as probe pads. After stamping, the electrodes were encapsulated with another spin-coated layer of elastomer. An X-Acto blade was then used to slice through opposite ends of the test strips to produce strips of lengths from 10 to 75 mm. After the excess silicone was removed, Pelco colloidal graphite was used to create the electrical connection between the exposed electrode and the probe pad. After the conductive paint had dried, a digital multimeter (Fluke 179) was used to measure the resistance of each strip. The resistance taken for a single test strip was the average of ten samples, as reported by the multimeter. Resistance was plotted as a function of length as shown in FIGS. 21A-21B, and a linear fit was applied to the data. The contact resistance was taken to be the y-intercept of the trend line, and its confidence bound is taken to be that of the intercept. The fit of composite samples shown in FIG. 21 A had an R2= .774, and the 95% CI of the intercept ( / ?<) is [5.168, 12.47]. The fit of CNT-only samples is much worse (R2= .0708), indicating little correlation of resistance with length. This is likely due to wide variability in CNT contact resistance. The 95% CI of the intercept (Rc) is [133.5, 436.2].

[0185] FIG. 10 shows additional representative datasets characterizing the stress-strain behavior over 100 cycles for specimens of silicone-only and silicone-encapsulated electrodes. Each of the two layers of silicone in both samples were spin-coated for 60s at 1500rpm on an acrylic platter then allowed to cure, before stamping (if necessary) and the next layer of silicone deposition. The presence of CNTs results in a 6% stiffer specimen compared to the silicone-only samples.

[0186] FIG. 11 and 12 show additional representative datasets characterizing the resistancestrain behavior over 100 cycles of strain to 20% and 100% for silicone-encapsulated electrodes. The samples were fabricated as discussed previously. All specimens subjected to strain cycles from 5% to 25% showed a decrease in resistance with more cycles applied (FIG. 11). For larger strains, from 5% to 105%, the behavior was less consistent, with specimens exhibiting increasing, decreasing, and no change in their resistance to strain curve (FIG. 12). With these two sets of results, the resistance evolves beneficially (higher cutoff frequency, less resistive losses) when a device is subjected to strains up to 20%. When subjected to larger strains, the electrodes can increase in resistance deleteriously, but, importantly, the electrodes retain their nominal resistance values within an order of magnitude. When subjected to cyclic extension from 5% to 25% strain (similar to strains expected during operation), it was observed that the resistance of the electrodes has a close-to-linear response to applied strain and that the resistance of the electrode decreases relative to its initial resistance which may be due to alignment of the CNTs in the direction of stretching (FIG. 19F and FIG. 11). When subjected to cyclic strain over a range of 100%, the resistance increased relative to its initial value (FIG. 12).

[0187] For results displayed in log- space (FIGS. 19B-D), the data were fit to log-normal distributions. While most resistance values clustered around the median, a few were much higher, likely due to manufacturing defects and inhomogeneities. Since dissipation factor and cutoff frequency are products of resistance, they display a similar distribution. Log-normal distributions better fit these assymmetric data than normal distributions do. Error bounds for the data were thus calculated by fitting to log-normal distributions in log- space, calculating the mean and standard deviation (SDlog), and then transforming these values back into linear space. CNT-only active regions maintain breakdown strength and actuator output

[0188] The electrodes of a DEA can strongly affect its breakdown strength and behavior. The electrodes introduce defects into the device that lower its strength compared to that of the neat material. CB electrodes, for example, have been shown to lower breakdown strength by 16-36% compared to neat silicone.

[0189] Breakdown has typically been defined as a sudden, steep, and irreversible increase in leakage current across the dielectric. This “hard breakdown” can thus be characterized as binary: failed or not failed, and the field at which the failure occurs is denoted as a specimen’s breakdown field. These fields are fit to a Weibull distribution, and the breakdown strength of the batch is taken to be the field at which there is a 1 - e-1chance of failure. As discussed earlier, however, CNT-based electrodes do not fail quickly and catastrophically. Rather, they fail in a series of self-clearing events that incrementally degrade their capacitances and thus actuation outputs. To provide a comparison to other breakdown statistics, the failure of an individual device was defined as the electric field at which capacitance retention Cre, the ratio of current to original capacitance, drops to e1(FIG. 20A). The definition of device breakdown strength can > 2 thus be approximately understood as the applied field at which 3 of devices lose at least 3 of their output.

[0190] FIG. 20B shows how hybrid electrodes utilizing self-clearing CNTs in active regions achieve advantageous breakdown strength to CB-only electrodes. The dielectric in each device is a 32 pm thick layer of Elastosil P7670. ft is the slope of the curve in Weibull-space, and indicates consistency. This is 86.4% of their upper limit, the breakdown strength of neat P7670 (63.4 V / pm). In addition, they achieve relative high consistency (Phybrid = 20.21) than the neat elastomer (Pneat = 9.39). This high strength and consistency, along with the non-catastrophic self-clearing mechanisms of CNT networks, allows for the scaling of high performance to larger DEAMs.

[0191] The batch spray process makes it possible to scale the number and size of DEA layers. This allows for the enhanced stresses and strains to be scaled to produce large forces and displacements. This was demonstrated with an artificial muscle 1.5 cm in diameter, 1 cm thick, with 100 active layers (FIG. 20C). In free displacement and with an applied field of 45 V / pm, this device achieves 1.5 mm of displacement (14% strain) through its thickness, as shown in FIG. 20D. To evaluate blocked force output, the stack was pre-compressed by approximately 1.5 mm and measured the amount of force relaxed during actuation at 45 V / pm. The device produced 6.9 N of force (39 kPa), 260* its own weight. This compares with other devices with similar elastomers that achieved 5% strain and 35 kPa stress at a similar applied field (48 V / pm). It is also within 14% of the expected value of 8.0 N as calculated using the equations above for this device. The ratio of the measured capacitance as-fabricated to expected capacitance values of the stack was Cfe = 0.86, which may be due to such factors as incomplete coverage of CNTs and misalignment during the stacking process.

[0192] Cost Estimates

[0193] Tables 1 and 2 summarize the differences in material cost to produce an actuator with hybrid electrodes via the presented batch spray and stamp process ($22.22) vs that to produce a CNT-only actuator with a comparative mask-and-stamp process ($273.87). The reference point used is an artificial muscle of the same design as presented in the examples of the present disclosure (100 15-mm-diameter active layers, each 85 pm thick).

[0194] The main driver of cost for both actuators is the filter substrate. While the Advantec filters can theoretically be reused, their performance quickly degrades with reuse, and each filter was used to produce only a single electrode layer in the comparative process. For cost purposes they are thus treated as disposable, and account for 86% ($236.54) of the total cost. This calculation also assumes that 20 10 x 10 mm electrode layers can pack into an 80 mm diameter usable area of the filters, a reasonable assumption because of practical handling limitations. The Tisch filter paper, however, is an order of magnitude cheaper, costing $12.56 for the same area. Additionally, the CNT ink based on P3 CNTs (Carbon Solutions) is far more cost effective than the Invisicon 1210 ink from Nano-C, lowering the CNT cost from $30.00 to $3.36.

[0195] Costs could be further reduced by increasing the areal density of stamp electrodes in a given sheet. Currently, only 48 paddle electrodes are patterned onto each sheet for ease of handling, but a simple rectangular pattern of the paddle electrodes with 20 mm spacing would allow for 121 electrodes on a single sheet. Such an increase would proportionally decrease the major drivers of cost: PET for masks, filter paper for electrode stamps, and CNTs for the ink.

[0196] Table 1: Accounting of the costs of the comparative mask-and-stamp process.

[0197] Table 2: Accounting of the costs for the batch spray and stamping of hybrid electrodes presented in this work.

[0198] Results and Discussion

[0199] This example demonstrates that spatially-patterned hybrid electrodes can exhibit advantageous performance in DEAMs. Hybrid electrodes can achieve low contact resistances without sacrificing high breakdown strength, and vice versa. Practical methods of fabricating and pre-clearing these hybrid electrodes that allow for their development and deployment at scale.

[0200] The ability to modularly pattern distinct properties across an electrode by patterning distinct nanoparticle inks. This modularity allows designers to take advantage of nanoparticles’ unique advantages and avoid their disadvantages, reducing the difficulty of development while increasing performance.

[0201] The capability to resolve a previously fundamental tradeoff between strength and speed in DEAMs made with nanoparticle electrodes was evaluated. It was demonstrated that CB placed at the contacts can reduce contact resistance by 32x while self-clearing CNTs patterned in active regions of the electrode can maintain high breakdown strengths (54.7 V / zm) that approach the strength of neat elastomer (63.4 V / ,um). The high breakdown strength results in muscle-like stresses of 39 kPa and muscle-like strains of 14%. Its consistency (fi = 20.21) also allows us maintain this in a centimeter-scale artificial muscle with 100 DEA layers. The low contact resistance makes DEAMs 26x faster and 22x more efficient than those with CNT-only electrodes, making higher-frequency and untethered use cases of more viable for DEAMs. The lower contact resistance also reduces the need for long contacts such as those used in roll actuators, expanding the range of actuator designs and possible applications.

[0202] CNT concentration may have a strong affect on breakdown strength, so further optimization of inks may yield breakdown strengths closer to the limit set by the neat material. Similarly, optimization of spray deposition parameters such as vacuum strength and spray pattern may yield advantageous homogeneity and thus higher conductivity and / or breakdown strength in CNT regions. Tuning fabrication parameters such as mask thickness and alignment methods may also allow for smaller features and reduced buffer zones, allowing for millimeter- and micron-scale devices.

[0203] CB and CNT-based inks was used in this work, but other inks and the capabilities that stem from them would be may be possible to implement. The batch-spray and stamp process depends only minimally on ink and substrate material properties, allowing for relatively quick development and deployment of inks. These inks could provide additional functionalities such as optical switching for on-the-fly rewiring, high transparency or opacity for optical modification, low sheet resistance for power distribution (e.g., via power distribution channels), or electroluminescence for status monitoring and communication.

[0204] The electrode fabrication method not only reduces development time and improves device performance; it is also relatively cheap and easily scalable. The materials costs are low - a 220x220 mm sheet of patterned electrodes requires only $6.87, mostly from the cost of the filter paper. Future work may investigate filter paper reuse and spray toolpath tuning to further reduce material costs. The batch-spray and stamp-transfer paradigm allows for virtually unlimited electrode area, and both electrode deposition and transfer operations could be implemented at high throughput in a roll-to-roll process. This scalability makes manufacturing of many-layered artificial muscles and large-area rolls possible, allowing high stresses and strains to be converted into large forces and displacements. Larger actuators could be used to drive mechanisms for higher load tasks such as electroadhesion, electrostatic clutching, mechanical counterpressure, and stiffness variation.

[0205] An algorithm for safely pre-clearing CNT- and hybrid-electrode DEAMs was developed and implemented it on a high-speed, automated system. An AC waveform applied to the DEA can clear away major defects, while a DC ramp waveform is useful for clearing minor defects. Moreover, a simple discriminant was developed for detecting major defects based on a quadratic dependence of current on voltage. These techniques were implemented on a target computer which can run at 10 kHz, allowing for fast detection and response to current spikes. With this added safety, no human supervision is required and clearing can be completed quickly ( 1-10 minutes) and automatically, potentially enabling industrial-scale production of DEAMs and the acceleration of DEAM research.

[0206] While several embodiments of the present invention have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and / or structures for performing the functions and / or obtaining the results and / or one or more of the advantages described herein, and each of such variations and / or modifications is deemed to be within the scope of the present invention. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and / or configurations will depend upon the specific application or applications for which the teachings of the present invention is / are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments of the invention described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, the invention may be practiced otherwise than as specifically described and claimed. The present invention is directed to each individual feature, system, article, material, and / or method described herein. In addition, any combination of two or more such features, systems, articles, materials, and / or methods, if such features, systems, articles, materials, and / or methods are not mutually inconsistent, is included within the scope of the present invention.

[0207] The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.”

[0208] The phrase “and / or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Other elements may optionally be present other than the elements specifically identified by the “and / or” clause, whether related or unrelated to those elements specifically identified unless clearly indicated to the contrary. Thus, as a non-limiting example, a reference to “A and / or B,” when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A without B (optionally including elements other than B); in another embodiment, to B without A (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc.

[0209] As used herein in the specification and in the claims, “or” should be understood to have the same meaning as “and / or” as defined above. For example, when separating items in a list, “or” or “and / or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as “only one of’ or “exactly one of,” or, when used in the claims, “consisting of,” will refer to the inclusion of exactly one element of a number or list of elements. In general, the term “or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e. “one or the other but not both”) when preceded by terms of exclusivity, such as “either,” “one of,” “only one of,” or “exactly one of.” “Consisting essentially of,” when used in the claims, shall have its ordinary meaning as used in the field of patent law.

[0210] As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and / or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.

[0211] As used herein, “wt%” is an abbreviation of weight percentage. As used herein, “at%” is an abbreviation of atomic percentage.

[0212] Some embodiments may be embodied as a method, of which various examples have been described. The acts performed as part of the methods may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include different (e.g., more or less) acts than those that are described, and / or that may involve performing some acts simultaneously, even though the acts are shown as being performed sequentially in the embodiments specifically described above.

[0213] Use of ordinal terms such as “first,” “second,” “third,” etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements.

[0214] In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of’ and “consisting essentially of’ shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.

Claims

CLAIMSWhat is claimed is:

1. An article, comprising: a first layer comprising an elastomer; and a second layer disposed on the first layer, the second layer comprising a first region and a second region, wherein: the first region comprises a first plurality of particles, the second region comprises a second plurality of particles, and at least a portion of the first plurality of particles is proximate to at least a portion of the second plurality of particles.

2. An article, comprising: a first layer comprising an elastomer; a second layer disposed on a first side of the first layer; a third layer disposed on a second side of the first layer, wherein: the second and third layers each comprise a first region comprising a first plurality of particles, and a second region comprising a second plurality of particles, and at least a portion of the first plurality of particles is adjacent to at least a portion of the second plurality of particles.

3. A method, comprising: providing a first layer comprising an elastomer, the first layer positioned between a second layer and a third layer, wherein: the second and third layers comprise a first region and a second region, the first region comprises a first plurality of particles, the second region comprises a second plurality of particles, and at least a portion of first plurality of particles is adjacent to at least a portion of the second plurality of particles.

4. The article or method of anyone of the preceding claims, wherein the article is a dielectric elastomer actuator having a breakdown strength at least 10% greater than anotherwise essentially identical article without the second plurality of conductive particles.

5. The article or method of anyone of the preceding claims, wherein the first region is an active portion of the second layer and the second region is a lead portion of the second layer.

6. The article or method of anyone of the preceding claims, wherein a line resistance of the lead portion is less than or equal to 50 kQ*mm.

7. The article or method of anyone of the preceding claims, wherein a gross contact resistance of the lead portion is less than or equal to 100 k .

8. The article or method of anyone of the preceding claims, wherein a stiffness of a composite comprising the first and second layer is within 10% of a stiffness of the first layer.

9. The article or method of anyone of the preceding claims, wherein the elastomer comprises an acrylic elastomer, a polyurethane elastomer, a biomaterial, a silicone elastomer, and / or combinations thereof.

10. The article or method of anyone of the preceding claims, wherein the first plurality of particles comprises a plurality of nanoparticles11. The article or method of anyone of the preceding claims, wherein the plurality of nanoparticles comprise silver nano wires and / or carbon nanotubes.

12. The article or method of anyone of the preceding claims, wherein the plurality of nanoparticles form a conductive network.

13. The article or method of anyone of the preceding claims, wherein the first and / or second plurality of particles comprise semiconducting particles.

14. The article or method of anyone of the preceding claims, wherein the first and / or second plurality of particles comprise nonconducting particles.

15. The article or method of anyone of the preceding claims, wherein the second plurality of conductive particles comprise carbon black.

16. The article or method of anyone of the preceding claims, wherein the first region has a sheet resistance greater than or equal to 1 kQ / sq and the second region has a sheet resistance less than or equal to 1 kQ / sq.

17. The article or method of anyone of the preceding claims, providing a third layer disposed on the first layer such that the first layer is positioned between the second layer and the third layer.

18. The article or method of anyone of the preceding claims, further comprising providing an electrical potential difference between the second layer and the third layer such that the first layer deforms in one or more directions.

19. The article or method of anyone of the preceding claims, wherein the first and / or the second plurality of particles are conductive.

20. The article or method of anyone of the preceding claims, wherein the second and / or third layer is disposed on the first layer via a stamping process.

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