Ultralight soft electrostatic actuators based on solid-liquid-gas architectures

Domain: chemistry
Published: 2026-02-19
Editorial outcome: major_revision

Abstract
Soft actuators enable versatile and adaptable robots capable of operating in unstructured environments and close to humans. Soft electrostatic actuators utilizing electrohydraulic principles are particularly promising, combining all-around actuation performance with portable driving electronics. These electrohydraulic actuators harness liquid dielectrics enclosed in solid dielectric shells to sustain high electric fields; the liquid dielectric however constitutes most of the actuator mass, limiting power-to-weight ratio. Here, we present ultralight soft electrostatic actuators based on solid-liquid-gas architectures: the introduction of gaseous dielectrics as a third phase substantially improves power-to-weight ratio by reducing actuator mass and increasing actuation speed. Through theoretical and experimental analyses, we pinpoint the fundamental performance limit as the electrical breakdown in the gas, governed by Paschen’s law, thereby providing a guideline for selection of gaseous dielectrics. Using the Peano-HASEL (hydraulically amplified self-healing electrostatic) actuator as a model system, we identify a gas mixture of C4F7N and CO2 that enables outstanding specific energy of 51.4 J kg-1 (a nine-fold improvement over conventional Peano-HASELs); using ambient air as gaseous dielectric we still achieve 33.5 J kg-1 and a power-to-weight ratio of 1600 W kg-1 (a five- and eleven-fold improvement). We illustrate these enhanced performance metrics in a jumping robot, showing a 60% increase in jump height, highlighting the wide potential of ultralight soft electrostatic actuators for adaptable and agile robotic systems.

Introduction
Robotic systems greatly impact our society by performing tasks with superhuman precision, strength, and repeatability, particularly in controlled environments such as factory floors1. However, conventional robots that are based on rigid materials often struggle in situations that require versatility and adaptability, and they can be unsafe near people2–4. In contrast, soft robots are based on deformable materials, inspired by structures found in nature such as muscles and skin5, and they show promise for operation in unstructured environments and near the human body3,4,6–9. To drive soft robotic systems, a variety of actuation technologies have been explored10,11, including fluidic12–14, (electro-)chemical15,16, and thermal17–20 actuation. Among these technologies, soft electrostatic actuators driven by high electric fields combine excellent speed and efficiency, with self-sensing capabilities, a high level of controllability, portability, and facile integration with electronic control systems21–23.

Dielectric elastomer actuators (DEAs) are based on solid dielectrics in the form of elastomeric membranes sandwiched between compliant electrodes24, and they are the first technology that highlighted the outstanding attributes of soft electrostatic actuators25–28. However, DEAs typically require stacked designs to achieve large linear contraction upon activation, necessitating specialized fabrication procedures using stretchable materials, and often suffer from limited reliability11,29.

To address these limitations, soft electrostatic actuators based on solid-liquid architectures were introduced; the use of a second, liquid phase of dielectric, offers a higher level of design flexibility, it enables the use of flexible but inextensible polymer films, and it introduces the ability to self-heal from dielectric breakdown events30. Especially, soft electrohydraulic actuators further utilize the liquid dielectric for coupling electrostatic and hydraulic forces; this concept of electrohydraulic amplification has been demonstrated in hydraulically amplified self-healing electrostatic (HASEL) actuators, which offer versatile actuation modes30–33 while featuring all-around actuation performance rivaling biological muscles11,30. HASELs have been demonstrated in various applications, spanning from biomimetic underwater robots and musculoskeletal jumping robots to wearable haptic devices34–39. Other examples of electrohydraulic actuators include electrostatic bellow muscle (EBM) actuators, which demonstrated additional energy harvesting capabilities22, and hydraulically amplified taxels (HAXELs), which enabled dense arrays of small actuators for wearable haptic devices40–42. Unlike electrohydraulic actuators, Rossiter et al. showed that limited use of liquid dielectric in the zipping region without utilizing hydraulic amplification can initiate and drive electrostatic actuation upon voltage application, resulting in very lightweight actuators with open structures43–45. However, this design cannot tap into the benefits of electrohydraulic amplification, and the open structures make it challenging to retain the liquid dielectric, potentially reducing the robustness of actuation. Electrohydraulic actuators, conversely, face challenges from the substantial mass of the liquid dielectric affecting crucial mass-based performance metrics, such as specific energy and specific power. One proposed approach to reduce mass while maintaining performance involves miniaturizing electrohydraulic actuators37,46; however, downscaling comes with its own challenges, including mechanical constraints from film stiffness, fringe-field effects, and fabrication complexities at smaller scales, ultimately limiting overall performance46.

Here, we present ultralight soft electrostatic actuators based on solid-liquid-gas architectures, where we introduce a third phase into the solid-liquid structures of electrohydraulic actuators in the form of a gaseous dielectric that replaces a large portion of the liquid dielectric. Through a combination of theoretical analysis and experimental validation, we show that Paschen’s law47,48 can be used to determine the fundamental limits of actuator performance using this strategy, predicting a maximum ratio of gaseous dielectric for a given set of actuation conditions and materials properties of the dielectrics. We used the Peano-HASEL actuator32, a type of soft electrohydraulic actuator that linearly contracts upon actuation, as a model system to study the fundamental mechanisms46,49,50 and to demonstrate the benefits of using the solid-liquid-gas architecture. The resulting three-phase soft electrostatic actuators achieved outstanding performance metrics when ambient air was used as the gaseous dielectric—a specific energy of 33.5 J kg−1 and a power-to-weight ratio of 1600 W kg−1, which translates to a 532% and 1130% improvement, respectively, compared to the conventional Peano-HASEL actuators. Additionally, the three-phase actuators achieved an 83% higher strain rate (2840% s−1) and a 70% wider bandwidth (c.a. 100 Hz), indicating a substantial improvement of actuation speed. We showcased the outstanding performance of these actuators in a jumping robot, which exhibited a 60% increase in jump height and a 32% reduction in take-off time when compared to its solid-liquid counterpart. We also identified a gas mixture of C4F7N and CO2 with particularly high dielectric strength, that enabled outstanding specific energy of 51.4 J kg−1 (a nine-fold improvement over conventional Peano-HASELs), underlining a key advantage of implementing the proposed solid-liquid-gas architectures in closed structures that can enclose gaseous dielectrics with tailored properties.

Results
Modelsystembasedonsolid-liquid-gasarchitecture
WeusedthePeano-HASELactuatorasamodelsystemtoexploretheconcept of solid-liquid-gas architecture. The conventional Peano-HASEL actuator, based on a solid-liquid architecture, consists of thin, flexible, but inextensible solid dielectric shells forming a pouch. This pouch is partially coated with flexible electrodes and filled with liquid dielectric. When a voltage Φ is applied across the electrodes, the attractive electrostatic force progressively closes the electrodes. This “zipping” motion displaces the liquid dielectric, which in turn generates a contractile strain capable of lifting loads32. Throughout this process, the liquid dielectric serves a dual purpose: sustaining high electric fields and hydraulically transmitting the electrostatic force (Pascal’s principle), making it essential for this actuation mechanism. However, in the solid-liquid architecture, the liquid dielectric constitutes a large portion of the actuator mass m_act, with only thin and lightweight solid dielectric shells surrounding it; nearly 90% of the m_act is liquid for the most widely used length scale, with pouch width and length in the cm-range. Exploring solid-liquid-gas architectures, by replacing an equivalent volume of liquid dielectric with a gaseous dielectric, offers a substantial reduction of the m_act. However, for a gaseous dielectric to take over the dual role of liquid dielectrics in sustaining high electric fields and transmitting the electrostatic force, its lower breakdown strength43,51 and compressibility may alter the actuation mechanism, potentially influencing the performance of gas-containing actuators.

To evaluate how different combinations of dielectric phases influence actuator response, we examined various configurations of liquid and gaseous dielectrics. We used a conventional solid-liquid Peano-HASEL actuator as a reference, then fabricated solid-liquid-gas and solid-gas variants for comparison. Air served as the gaseous dielectric due to its accessibility, non-flammability, and non-toxicity. Under a representative actuation condition (7 kV actuation voltage and 1 N applied load), the solid-liquid-gas actuator demonstrated a comparable actuation stroke to the reference solid-liquid actuator while featuring an 84% mass reduction (m_1 = 1.9 g, m_2 = 0.3 g), thereby highlighting an important benefit of using the solid-liquid-gas architecture. In contrast, the solid-gas actuator failed to actuate (χ_3 = 0), despite its drastic decrease in actuator mass (m_3 = 0.2 g).

As shown in Fig. 1c, we attribute this lack of actuation in the solid-gas actuator to premature dielectric breakdown in the gas, due to the lower dielectric strength of gaseous dielectrics compared to liquid dielectrics. This figure qualitatively illustrates the strength of the electric field and the proximity to dielectric breakdown in both liquid and gaseous dielectrics. In all configurations, the electric field peaks near the “zipping front”, where the zipping region propagates, and rapidly decays away from it. The liquid dielectric in the solid-liquid configuration provides sufficient insulation against dielectric breakdown, sustaining the high electric fields required for actuation. On the other hand, the gaseous dielectric in the solid-gas configuration is prone to breakdown at the same voltage, preventing actuation. However, having a small amount of liquid dielectric near the zipping front, where the electric field is concentrated, effectively shields the actuator from breakdown, allowing stable actuation in the solid-liquid-gas configuration.

In the following sections, we further examine the effects of gas inclusion, focusing on its lower dielectric strength and compressibility, to analyze the fundamental mechanisms that determine the maximum gas ratio allowed for preserving actuation performance under a given set of actuation conditions.

Quasi-staticperformance
To determine the maximum gas ratio allowed, we examined quasi-static force-strain characteristics of actuators with varying volume fractions of air, ranging from 0% to 100%. As qualitatively illustrated in Fig. 2a, sufficient liquid dielectric near the zipping front is expected to shield against dielectric breakdown, leaving compressibility of the gaseous dielectric as the other main factor potentially decreasing performance. In contrast, insufficient liquid dielectric should result in dielectric breakdown in air, preventing effective actuation.

To achieve quasi-static actuation, we applied a slow voltage ramp of 1 kV s−1, gradually reaching to a maximum voltage of 8 kV across the actuators at various constant forces. We then measured the resulting strains at the maximum voltage. In the resulting force-strain plots, we observed no notable deviation in the curves spanning from 0% to 90% air-fill. However, as the percentage of air-fill increased beyond 90%, actuation strain rapidly decreased, with actuators eventually completely failing to actuate at 100% air-fill. This result shows that, up to 90% air-fill, the inclusion of air has a negligible influence on force-strain characteristics (and consequently work output), despite the lower breakdown strength and compressibility of air. To further investigate this experimental observation, we derived an analytical model of three-phase Peano-HASELs based on the solid-liquid-gas architecture, which accounts for the compressibility of gas, confirming that gas compressibility has negligible influence on the performance of the actuators investigated here. The model predicts negligible deviation between isentropic and isothermal extremes under typical actuation conditions; therefore, we assume isothermal conditions throughout this study without compromising the validity of the results. Combining these modeling results with our experimental observation, we hypothesize that the loss of actuation strain beyond 90% air-fill results from an insufficient amount of liquid dielectric near the zipping front.

To further investigate this hypothesis, we rotated the actuator by 180 degrees from an orientation where electrodes are located at the bottom (“best orientation”) to another orientation where the electrodes are located at the top (“worst orientation”). In this worst orientation, gravity pulls the liquid dielectric away from the zipping front, leaving only a small amount held in place by surface tension, for protection against dielectric breakdown. Still, the liquid dielectric consistently remains at the zipping front throughout actuation, regardless of the actuator orientation. The force-strain curves indicate that deviation from the fully liquid-filled reference curves starts to become noticeable above air-fill of 70% (lower than the 90% limit observed in the best orientation), supporting our hypothesis that insufficient liquid dielectric at the zipping front is the primary cause for performance loss at very high air-fill levels.

We tested the influence of air fill on force relaxation related to charge accumulation. During prolonged actuation under constant voltage and force, the introduction of air had a negligible effect on charge accumulation behavior.

To quantify performance in intermediate orientations, we tested actuators positioned horizontally. The force-strain responses closely matched those of the best orientation up to 90% air-fill. This result indicates that up to an air-fill of 90% the performance of actuators will be consistent for all orientations between the best and the horizontal orientation.

As a key parameter to assess the performance, we calculated specific energies (J kg−1) of our actuators, defined as the area under force-strain curves (i.e., the maximum mechanical work in one actuation cycle) divided by the actuator mass. As shown in Fig. 2e, the specific energy increased with higher air-fill ratios, peaking at a certain point. Notably, in the best actuator orientation, specific energy reached a maximum of 33.5 J kg−1 at 97% air-fill, representing a 532% enhancement over a reference actuator with 0% air-fill. In the worst actuator orientation, the specific energy reached a maximum of 23.3 J kg−1 at 95% air-fill, representing a 291% enhancement over a reference actuator with 0% air-fill in the same orientation. However, further increases in air-fill ratio beyond this point caused the specific energy to drop sharply to zero. The next section is devoted to understanding the fundamental mechanisms behind this performance drop, focusing on dielectric breakdown in gas as a key performance limitation.

Identificationoffundamentalperformancelimits
To quantitatively examine the correlation between actuation performance and dielectric breakdown in air, we first established a theoretical threshold, based on Paschen’s law, for predicting dielectric breakdown of air in our actuator. Paschen’s law describes the breakdown voltage of gases between parallel metal electrodes, where an electron avalanche initiates dielectric breakdown in the gas. Although factors such as electrode shape and dielectric layers shielding the electrodes may alter the breakdown characteristics of gas, we adopted Paschen’s law as the foundation for our prediction, speculating that this mechanism still governs air breakdown in our actuator. Indeed, our experiments confirmed that actuator failure is correlated with dielectric breakdown of air as predicted by Paschen’s laws.

To establish the theoretical threshold for predicting breakdown of air in our actuator, we integrated Paschen’s law with the analytical model derived in the previous section. This combined model is represented on a plane spanned by the x-axis of pressure times distance and the y-axis of voltage (hereafter we refer to this plane as the “Paschen’s plane”), which provides an effective framework for analyzing the dielectric breakdown characteristics of gases. Paschen’s curve for air, Φ_air = f(p, d), divides this plane into a “safe” region (no dielectric breakdown) and an “unsafe” region (dielectric breakdown in air may occur). Our model then maps the actuator status onto this plane, indicating whether the actuator is protected from dielectric breakdown or not. The representative model-derived line shows the continuous change of the actuator status under a typical actuation scenario. This scenario involves increasing the voltage Φ for an actuator with a given liquid volume V_liq under a constant load F. Specifically, when given the set of values (F, Φ, V_liq) describing actuation conditions, our model identifies the resulting actuator status (p, d, Φ_air) and maps it onto the Paschen’s plane. Here, p is the air pressure inside the actuator, d is the distance between solid dielectric shells along the liquid-gas interface (where breakdown is most probable), and Φ_air is the potential difference across the air gap at the liquid-gas interface. As the voltage Φ across the specific reference actuator is increased, the actuator encounters three distinct states: At point (a), the actuator does not exhibit zipping due to low voltage, so p and d remain at their initial values. Point (b) represents the state after the onset of zipping, where the actuator status lies in the safe region below Paschen’s curve, allowing actuation. At point (c), Φ_air exceeds the critical threshold, causing dielectric breakdown of air and thus actuation failure. This critical threshold Φ_B, which predicts impending breakdown of air, can be identified by locating the intersection between Paschen’s curve, Φ_air = f(p, d), and the model-derived line (p∙d, Φ_air), as determined by the following equations:

p_ext + w(L_p - l_e(F, Φ, V_liq)) cos α / A(F, Φ) = p(F, Φ, V_liq)

d(F, Φ, V_liq) = (L_p - l_e(F, Φ, V_liq)) (cos[θ(α(F, Φ), l_e(F, Φ, V_liq), V_liq)] - cos[α(F, Φ)])

Φ_air(F, Φ, V_liq) = d(F, Φ, V_liq) ε_s Φ / (2t ε_air + d(F, Φ, V_liq) ε_s)

For the above formulas we assume 1) a flat meniscus and 2) a uniform electric field, treating the solid dielectric shells as parallel plates at a distance d, with the effective potential across air Φ_air at the liquid-gas interface. Here, w and L_p are the width and length of a single actuator pouch, l_e is the zipped length of electrodes, α is half of the central angle of the arcs in the simplified cross section of the actuator, θ describes the location of the liquid-gas interface, ε_s and ε_air are the dielectric constants of the solid dielectric and air, respectively, and t is the thickness of the solid dielectric shell.

Now we map the predicted breakdown points, where Paschen’s curve intersects with the model-derived line for various conditions of F and V_liq, onto the F-Φ plane, which describes actuation conditions. For a given V_liq, these breakdown points form a line on the F-Φ plane, represented as an orange line (Paschen’s limit). This line now divides the F-Φ plane into a safe region (no dielectric breakdown) and an unsafe region (dielectric breakdown in air). The gray region indicates model predicted zero-strain, for conditions where the actuator has reached its blocking force. We validated our model with experiments using quasi-statically actuated actuators with air-fill ratios of 90%, 95%, and 99%. At constant forces, we slowly ramped the voltage and measured strains, recording failures when the measured strain fell below expected values, relative to reference actuators without air-fill. In Fig. 3c we mark data points where no actuation was observed due to blocking force by gray circles, data points with successful actuation by green-filled gray circles, and data points with failed actuation by yellow-filled gray circles. As dielectric breakdown is subject to statistical variations, we visualize the transition from successful actuation to failed actuation using a color gradient spanning from green to yellow. Overall, our experimental results generally align well with the theoretical predictions: the experimentally observed region of high probability of successful actuation (predominantly green-filled circles) is separated by the theoretically predicted boundary, from a region of low probability of successful actuation (predominantly yellow-filled circles). The good agreement between experimental results and our modeling approach, combining Paschen’s law with our analytical actuator model, confirms our hypothesis that the onset of electrical breakdown in the gas phase governs the upper limit for air-fill ratio. This hypothesis was further confirmed with a simplified experimental setup with measured p and d in an open system.

Dynamicperformance
In the previous sections, we examined the effects of air inclusion on quasi-static actuation. In this section, we present experimental results to investigate the effects of air inclusion on high-speed and high-frequency actuation. Specifically, we examined the step response and frequency response of three-phase Peano-HASEL actuators with air-fill ratios varying from 0% to 90%. All tests were conducted in the best orientation (electrodes located at the bottom of the actuator).

For the step response analysis, we applied a step voltage input with Φ_peak = 8 kV to actuators loaded with dead weights ranging from 0.1 N (10 g) to 4.9 N (500 g). Displacement data was recorded using a high-speed camera. The step response featured an accelerating phase, marking the initial period of actuator contraction, until the point where acceleration reaches zero (χ̈=0); this accelerating phase can be used to evaluate actuator performance. Fig. 4b illustrates the resulting displacement data during the accelerating phase, at a representative actuation condition of Φ_peak = 8 kV and dead weight of Mg = 0.1 N. Particularly, the speed rose abruptly from actuators with 60% to 80% air-fill. Accordingly, we categorized actuators with 0, 20, 40 and 60% air-fill as the “liquid-dominant group”, and those with 80% and 90% air-fill as the “gas-dominant group”. In supplementary information, we show that this speed increase stems from reduced inertia of liquid rather than changes in the effective viscosity of liquid-gas mixtures, as all the tested actuators operate in the inertial rather than the viscous regime.

For a quantitative assessment of the response speed, we characterized the peak strain rates by taking the derivative of the measured displacement data. The liquid-dominant and gas-dominant groups showed a noticeable difference in peak strain rates, especially for lower dead weights, with the difference diminishing for heavier loads. Overall, this diminishment in difference indicates that there are two regions: one where inertia of actuator mass dominates (towards lower dead weights) and another one where inertia of external load dominates (towards higher dead weights); from a practical perspective, it implies that the speed-increase for air-filled actuators is particularly pronounced when lifting low external loads. Peak power values for the liquid-dominant group rose gradually with increasing dead weight up to the maximum weight evaluated here; peak powers in the gas-dominant group exceeded values of the liquid-dominant group, especially in the region with low external loads. Importantly, the reduced actuator mass resulted in substantially higher peak specific powers in the gas-dominant group across the entire range of dead weights.

To investigate frequency response, we applied sinusoidal voltage inputs with Φ_peak = 6.0 kV. Actuators were connected to two springs (k=0.004 N/m), designed to exert an approximately constant force of 1 N at any displacement during testing. Fig. 4g shows the normalized amplitude over the tested frequency range. Actuators with up to 40% air-fill showed an increase in bandwidth (amplitudes above the -3 dB threshold), approximately from 60 Hz to 100 Hz, which we attribute to reduced inertia. However, at air-fill ratios above 40% the bandwidth started to decrease again; we speculate that dynamic splashing of liquid dielectric caused a decrease of the volume of liquid dielectric near the zipping front at high actuation frequencies, leading to dielectric breakdown of air and decreased actuator performance. The amplitude of the 0% air-filled reference actuator increases with frequency, peaking around 40 Hz. We found that this behavior is related to the internal motion of the liquid within the pouch—an intrinsic dynamic characteristic of electrohydraulic actuators; for frequencies around 30 Hz the motion of the liquid dielectric inside the pouch becomes synchronized with the driving frequency of the actuator, amplifying displacement.

Notably, three-phase Peano-HASELs demonstrated substantially higher response speed and specific power, particularly in gas-dominant actuators at relatively low loads where actuator inertia dominates. Specifically, at an air-fill ratio of 90%, the peak strain rate reached 3760% s−1 with a dead weight of 10 g (0.1 N), 40% higher than that of the reference actuator with 0% air-fill; the peak strain rate reached 2840% s−1 with a dead weight of 20 g (0.2 N), 80% higher than that of the reference actuator. Additionally, the peak specific power reached 1600 W kg−1 with a dead weight of 20 g (0.2 N), 11.3 times higher than that of the reference actuator with 0% air-fill.

All analyses above were conducted in the best orientation; similar evaluations in the worst orientation are provided in supplementary information.

We assessed the long-term durability of the actuators through 100,000-cycle tests. All tested actuators survived 100,000 cycles without failure; we only observed a decay of actuator strains starting at cycle numbers beyond 1,000, which we attribute to charge retention effects stemming from the use of single polarity signals in these tests. Importantly, the actuator without any gas filling exhibited a very similar decay of actuation strain over cycles, indicating that the use of gas filling does not substantially change the durability of actuators up to 100,000 cycles.

Demonstrationofagilityofajumpingrobot
To highlight the capabilities of three-phase soft electrostatic actuators, we demonstrated their performance in a jumping robot. As shown in Fig. 5, this robot consisted of multiple layers of quadrant donut-shaped HASEL actuators, arranged in three units, stacked vertically. As shown in the cross-sectional view, in contrast to Peano-HASELs, which contract in length, donut HASELs expand in height, with both geometries relying on the same electrostatic zipping mechanism. Here, the rapid height expansion of donut HASELs enabled jumping when a step voltage was applied.

Two robots were constructed with identical geometries, differing only in their dielectric architectures: one based on a solid-liquid design and the other one on a solid-liquid-gas design. To enhance stability and balance during jumping, we slightly increased the amount of liquid dielectric in the bottom unit (Unit 1) in the solid-liquid-gas design. The resulting total masses of the robots were 24.2 g and 5.0 g, respectively. The experimental procedures involved a step input of 6 kV, with the voltage ON state sustained for 50 ms. The robot with the solid-liquid-gas architecture achieved a 60% higher jump height with a 32% shorter take-off time compared to the solid-liquid counterpart, highlighting the increased agility of the robot based on the three-phase design.

High-dielectric-strengthgasforenhancedperformanceinsolid-liquid-gasarchitectures
As demonstrated above, a limitation of the performance of electrostatic actuators with solid-liquid-gas architectures is the dielectric breakdown of the gaseous phase. Closed electrostatic actuators, such as HASELs, HAXELs, and EBMs, offer the possibility of utilizing a high-dielectric-strength gas (HDSG) to improve performance considerably; HDSGs can prevent dielectric breakdown under conditions where air would typically fail. To demonstrate this idea, we used a HDSG in the form of a mixture of C4F7N and CO2, which offers dielectric strength comparable to SF6 but with substantially lower global warming potential. To fill the actuators with HDSG, we used a glove box setup to prevent contamination with ambient air. With the method used for evaluating quasi-static performance, we showed that HDSG-filled actuators achieved stable operation up to 98% gas-fill in the best orientation and up to 80% in the worst orientation—considerable improvements over the 90% and 70% thresholds observed with air, respectively. As a result, the maximum specific energy increased to 51.4 J kg−1 at 98% HDSG-fill in the best orientation, and 30.0 J kg−1 at 95% HDSG-fill in the worst orientation.

We further evaluated the dynamic performance of HDSG-filled actuators using the same method used as in Fig. 4. As shown in Fig. 7, these actuators achieved broader bandwidths under cyclic voltage inputs in both the best and worst orientations compared with actuators having identical air-fill ratios. This improvement confirms that the use of HDSG successfully diminished the issue raised in the Dynamic performance section: at high actuation frequencies, dynamic splashing of the liquid dielectric reduces its local volume near the zipping front, leading to dielectric breakdown through air and lower performance. In contrast, actuator response to a step voltage input showed negligible improvement over the air-filled version.

Methods
Detailsofactuatorfabrication
Throughout the study, Peano-HASEL actuators were fabricated using the same solid-liquid-gas material system with identical geometric parameters. The process involved bonding solid dielectric—biaxially oriented polyester films (Mylar 850-15, Petroplast GmbH) using a CNC heat sealer to create rectangular shells with a width w = 6 cm and a length L_p = 2 cm. Carbon ink, applied as flexible electrodes (Cl-2051, Nagase ChemteX America LLC), was screen printed on both sides of the shells. The shells were then filled with liquid dielectric (Silicone oil M5, Carl Roth) and gaseous dielectric (ambient air or HDSG), with a total volume of fluids (V_tot = w L_p^2/4π) chosen to theoretically form a cylinder when the electrodes are fully zipped. Acrylic frames were attached to the top and bottom of the shells for load application. These acrylic frames were not accounted for when measuring the actuator mass. For visualization purposes (in the section Model system based on solid-liquid-gas architecture; Fig. 1b and Supplementary Movie 1), a pigment (Beta-Carotene, SIGMA-ALDRICH Chemie GmbH) was added to the transparent silicone oil, and a transparent Pedot:PSS ink (Orgacon EL-P5015, Agfa-Gevaert N.V.) was used instead of the carbon ink.

We filled the actuators with the high-dielectric-strength gas (C4F7N gas mixture: 20.00% - C4-FN; 2,3,3,3-tetrafluoro-2-(trifluoromethyl) propanonitrile and 80.00% - CO2; carbon dioxide; DILO Armaturen und Anlagen GmbH) in a glove box setup (GB0004; MSE Supplies®) to prevent contamination with ambient air.

Experimentalsetup
In the experiments, the actuators were vertically suspended from the upper frame and the loads were attached to the lower frame. For visualization purposes, in the section Model system based on solid-liquid-gas architecture, the actuators were horizontally suspended and connected to a 100g dead weight via a pulley system. A dual-mode lever system (310LR-C dual-mode lever arm system, Aurora Scientific Inc.) capable of simultaneously generating constant forces and measuring strains was used to apply loads for quasi-static analyses, dead weights for step response analysis and springs for frequency response analysis. Actuation strains were measured using the dual-mode lever system for the quasi-static analyses, a high-speed camera (Phantom v2640, Vision Research Inc.) tracking a marker (tracking software: Tracker) for the step response analysis, and a laser displacement sensor (LK-H157, Keyence) for the frequency response analysis. The input voltage signals were amplified by a high voltage amplifier (Trek® 610E, Advanced Energy Industries, Inc.). Another amplifier with a higher output current range (Trek® 50/12, Advanced Energy Industries, Inc.) was used for the dynamic analyses and the jumping robot demonstration.

Fabricationandexperimentaldetailsofthedielectricbreakdowntestinasimplifiedsetup
Rigid acrylic plates were fixed at an angle of 27.6° relative to each other. Biaxially oriented polyester films (Mylar 850-15, Petroplast GmbH), each bearing 2 cm × 6 cm carbon electrodes (Cl-2051, Nagase ChemteX America LLC) printed on their outer surfaces, were securely bonded to the angled acrylic plates. The sides of the assembly were sealed using thin transparent acrylic plates. A varying amount of liquid dielectric (Silicone oil M5, Carl Roth) was added to fill the electrode gap. A voltage ramp was applied at a rate of 1 kV s−1, with a 2-second hold at each 1 kV increment from 5 to 10 kV. This pattern was repeated for 100 cycles, alternating polarity each cycle. Using the measured current profiles, the breakdown voltages were recorded as the voltages at which the first current spikes occurred in each cycle.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This study is the result of a series of ongoing studies of HASEL actuators by the authors group. I salute the authors for their\nongoing research attitude.\nIn this study, the authors presented ultralight HASEL based on solid-liquid-gas architectures. As a results, the authors\nimproved power-to-weight ratio by reducing actuator mass and increasing actuation speed. The key point is that the weight\nis reduced by replacing most of the dielectric liquid with air in HASEL. From the point of view of the mechanical\nperformanice of the HASEL, the actuation performace was improved. However, the design of the HASEL is quite similar to\nprevious Rossiter's works[43, 44, 45] as cited in the paper. Thus, there is little novelty in the design for new actuators. A few\ncomments are noted below.\n1. The purpose of this study is to improve the power-to-weight ratio by reducing actuator mass. Why didn't the authors\ninvestigate gases lighter than air?\n2. The electrical breakdown is critical for electrostatic actuation. Why didn't the authors investigate gases with higher\nelectrical breakdown voltages?\n3. Have the authors verified experimentally that the simplified mathematical model is valid? What about static models in\nparticular? What are the effects of gravity and how much deviation is there between the experiment and the ideal model in\nSupplementary Figure 2 ?", "reviewer_2": "This work presents a novel soft electrostatic actuator based on a solid-liquid-gas structure, which demonstrates significant\nenhancement on the actuation performance of specific energy and power-to-weight ratio. It is interesting and brings some\nnew perspectives to the electrostatic actuators. Some issues need to be addressed before publication.\n1.It is assumed in the manuscript that liquid dielectric always exists at the zipping front due to surface tension. Can the\nauthors use microscope photos or other pictures to prove this?\n2.Will the maximum ratio of gaseous dielectric be influenced by the actuator orientation? If so, the limits should be discussed\nunder the condition of worst orientation.\n3.The effect of actuator orientations on actuation force and strain needs to be further discussed.\n4.Does the composition or dielectric properties of the air have any impact on actuation behavior?\n5.Long-term stability and reliability are critical for flexible actuators. Have the authors carried out cycle tests?\n6.Since the liquid can move and oscillate in the air, the three-phase actuators are seem to be more unstable compared to the\nconventional Peano-HASELs. How to ensure the stability of the actuator output, especially in periodic high-frequency\nresponse?", "reviewer_3": "The manuscript presents an interesting approach to modifying the well‐known Peano‐HASEL actuator by partially replacing\nthe liquid dielectric with a gas, forming a solid–liquid–gas architecture. The authors provide high quality and extensive\nexperimental validation, including quasi-static tests, dynamic response analyses, and a jumping robot demonstration. The\nproposed idea reduces mass and provide important improvements in performance metrics (specific energy, strain rate,\npower-to-weight ratio) of the Peano actuator; however, the conceptual novelty, solely connected to the partial filling\napproach, appears limited since the fundamental actuator design is already established in previous work\n(adequately cited in the manuscript).\nAn accompanying theoretical framework based on Paschen’s law is introduced (which could potentially represent a\nvaluable contribution) to explain the onset of dielectric breakdown, but there are some critical points regarding this.\nMajor Points:\n1. Theoretical Model:\nThe current theoretical framework is quite simplistic; it uses Paschen’s law with simplified assumptions (e.g., fixed geometry,\nflat meniscus, uniform field) to predict breakdown. However, the actual actuator features a complex interplay between liquid\nand gas, with dynamic variations such as variable gas gaps and trapped gas bubbles.\nIt is not clear how the static model maps onto the real dynamic fluid conditions observed (e.g., as seen in the supplementary\nvideos). In this regard, the provided validation study, developed by testing the actuator as a whole, may not be effective. For\na convincing validation, I suggest performing experiments on a dedicated, simplified, controlled setup aimed at isolating and\nvalidating the model parameters. This would help to limit the number of uncontrolled variables.\n2. Thermal and Pressure Effects:\nAlthough introducing air reduces mass, the inherent compressibility of gas could lead to unwanted effects when the actuator\nis subjected to temperature and pressure variations. The authors should address whether changes in these conditions might\nalter performance (e.g., stroke). A simple dedicated theoretical/experimental study examining the influence of\nthermal/pressure expansion on actuation behavior should be added. A discussion should also be introduced, highlighting\npossible connected limitations (e.g., underwater robotics?).\n3. Long-term Durability:\nThe cyclical operational stability of the actuator should be shown, as differences may appear between the first and\nsubsequent cycles due to changes induced in the interfaces between the fluid and gas. Thus, it would be valuable to see\ncyclical data and (possibily) preliminary discussion on degradation mechanisms that might occur over many cycles.\nMinor Points:\n• Assumption of Isothermal Conditions:\nThe model presented in the supplementary material applies Boyle’s law (pV = constant) under the assumption of isothermal\nconditions. While this assumption may hold in quasi-static regimes, it should be clarified how dynamic conditions—where\nheat exchange may occur at a slower rate—could affect the model's validity.\n• Force Relaxation Phenomena due to Charging:\nIt would be beneficial to know if any force relaxation related to charge accumulation behavior was observed during testing\nand whether the introduction of gas has any influence on such phenomena."}, "author_response": "Highlights of major revisions\nWe would like to take this opportunity to thank all reviewers, who have given very insightful and\nconstructive feedback, which we have addressed with a variety of new experimental results and major\nrevisions; overall, we are excited to report that these revisions have substantially improved both the\nnovelty and the quality of our manuscript.\nKey updates include:\n• Identification of C F N/CO gas mixtures for use as high-dielectric-strength gas (HDSG);\n4 7 2\ndevelopment of a fabrication procedure for HDSG-filled actuators that achieve substantially\nimproved actuator performance (33.5 J kg-1 for air-filled actuators → 51.4 J kg-1 for HDSG-filled\nactuators).\n• Development of a new experimental setup with a simplified geometry to confirm Paschen’s law\nof dielectric breakdown as the fundamental limit for gas-filling.\n• Evaluation of actuator performance in an additional (horizontal) orientation.\n• Evaluation of long-term stability and reliability; experimental demonstration of 100,000 actuation\ncycles without failure.\n• Extension of the analytical model to include both isothermal and isentropic conditions, as well as\nevaluation of the effects of external pressure and temperature.\nWe have revised the manuscript to address all reviewer comments in detail. Below, please find a point-\nby-point response to all comments. We also enclose the revised manuscript, in which all changes are\nhighlighted in yellow.\nReviewer 1\nReviewer 1, general comment:\n“This study is the result of a series of ongoing studies of HASEL actuators by the authors group. I salute\nthe authors for their ongoing research attitude.\nIn this study, the authors presented ultralight HASEL based on solid-liquid-gas architectures. As a result,\nthe authors improved power-to-weight ratio by reducing actuator mass and increasing actuation speed.\nThe key point is that the weight is reduced by replacing most of the dielectric liquid with air in HASEL.\nFrom the point of view of the mechanical performance of the HASEL, the actuation performance was\nimproved. However, the design of the HASEL is quite similar to previous Rossiter's works[43, 44, 45] as\ncited in the paper. Thus, there is little novelty in the design for new actuators.”\nResponse:\nAs the reviewer points out, the performance improvement enabled by the solid-liquid-gas architecture is\none important outcome of this paper. Additionally, the paper features two novel aspects, which we feel\nare important advances over existing literature; we have revised the manuscript to more clearly articulate\nthese advances:\n1) HASEL actuators and the actuators developed by Rossiter and colleagues share liquid-enhanced\nelectrostatic zipping as an actuation mechanism. However, Rossiter’s actuators are open\nstructures, which directly interact with the surrounding air, whereas HASELs based on the solid-\nliquid-gas architecture are closed structures, where air can be replaced with other gases that\nfeature high dielectric strength. Stimulated by insightful comments of reviewers 1 and 2, in the\nprocess of this major revision, we have identified a C F N/CO gas mixture for use as high-\n4 7 2\ndielectric-strength gas (HDSG); we have further developed a fabrication procedure for HDSG-\nfilled actuators that achieve substantially improved actuator performance (33.5 J kg-1 for air-filled\nactuators → 51.4 J kg-1 for HDSG-filled actuators; see detailed discussion in Reviewer 1,\ncomment 2).\n2) Building upon Paschen’s law, we derived a model to predict dielectric breakdown through gas in\nHASELs based on the solid-liquid-gas architecture; through theoretical and experimental\nanalyses, we pinpoint the fundamental performance limit as the electrical breakdown in the gas,\nthereby providing a guideline for selection of gaseous dielectrics. The model introduced in the\nmanuscript should, in principle, also be applicable for determining the minimum amount of liquid\nin Rossiter’s actuators. To confirm that the model also works for open structures, we performed\ndielectric breakdown tests of liquid-gas interfaces in a simplified setup (see detailed discussion in\nReviewer 3, comment 1)\nReviewer 1, comment 1:\n“The purpose of this study is to improve the power-to-weight ratio by reducing actuator mass. Why didn't\nthe authors investigate gases lighter than air?”\nResponse:\nThe use of gases lighter than air indeed reduces the weight of the actuator. However, our calculations\nindicate that the mass of the gas is negligible compared to the liquid and solid dielectrics, when\nconsidering the centimeter-scale we are currently operating at (even at an air-fill ratio of 100%, the mass\nof the gas accounts for less than 2% of the total weight). Still, for larger-scale actuators with substantial\ngas volumes, buoyancy effects could become more relevant. Using gases lighter than air, thus could be an\ninteresting approach for applications where extremely lightweight actuators are critical.\nTo reflect this point, we have revised the Discussion section as follows:\nMain text, page 15, line 351 (Discussion): “Additionally, for applications where extremely lightweight\nactuators are critical, using larger-scale actuators that are filled with gases lighter than air to exploit\nbuoyancy effects are an interesting direction of research—on the centimeter-scale and below, however,\nthe mass of the gas is negligible compared to the mass of the solid dielectric.”\nReviewer 1, comment 2:\n“The electrical breakdown is critical for electrostatic actuation. Why didn't the authors investigate gases\nwith higher electrical breakdown voltages?”\nResponse:\nWe appreciate this very insightful suggestion. As described above in our response to Reviewer 1 general\ncomment, a key advantage of HASELs based on the proposed solid-liquid-gas architecture—enabled by\nits closed structure—is the possibility of using gaseous dielectrics with tailored properties to enhance\nelectrostatic actuation.\nOur model suggests that using high-dielectric-strength gas (HDSG) can lead to considerable performance\ngains, and thus motivated us to invest substantial experimental efforts to develop a fabrication procedure\nfor HDSG-filled actuators that promise to achieve substantially improved actuator performance. We are\nexcited to report that these efforts have resulted in a substantial improvement of actuator performance:\nfrom 33.5 J kg-1 for air-filled actuators to 51.4 J kg-1 for HDSG-filled ones, even surpassing the\nperformance of mammalian muscle (c.a. 40 J kg-1) [R1]. For these experiments, we used a C F N/CO gas\n4 7 2\nmixture as the HDSG, which offers dielectric strength comparable to SF but with substantially lower\n6\nglobal warming potential [R2, R3]. During quasi-static actuation, the HDSG-filled actuators enabled\nreliable actuation up to 98% fill in the best orientation and up to 80% fill in the worst orientation—\nconsiderable improvements over the 90% and 70% thresholds observed with air, respectively.\nWe added these results as a new Figure 6, which shows a direct performance comparison between air-\nfilled and HDSG-filled actuators, to the manuscript. We also added a new section High-dielectric-\nstrength gas for enhanced performance in solid-liquid-gas architectures and revised Abstract,\nIntroduction, Discussion, and Methods to implement the new points and findings as shown below.\n[R1] J. D. Madden et al., Artificial muscle technology: physical principles and naval prospects, IEEE J.\nOcean. Eng. 29, 706-728, 2004\n[R2] M. Rabie et al., Assessment of eco-friendly gases for electrical insulation to replace the most potent\nindustrial greenhouse gas SF6, Environmental Science & Technology, 2018.\n[R3] J. Owens et al. Recent development of two alternative gases to SF6 for high voltage electrical power\napplications, Energies, 2021.\nMain text, page 13, line 310:\n“High-dielectric-strength gas for enhanced performance in solid-liquid-gas architectures\nAs demonstrated above, a limitation of the performance of electrostatic actuators with solid-liquid-gas\narchitectures, is the dielectric breakdown of the gaseous phase. Closed electrostatic actuators, such as\nHASELs, HAXELs, and EBMs, offer the possibility of utilizing a high-dielectric-strength gas (HDSG) to\nimprove performance considerably; HDSGs can prevent dielectric breakdown under conditions where air\nwould typically fail (Fig. 6a). To demonstrate this idea, we used a HDSG in the form of a mixture of\nC F N and CO (see Methods for details), which offers dielectric strength comparable to SF but with\n4 7 2 6\nsubstantially lower global warming potential55,56. With the method used for evaluating quasi-static\nperformance as in Fig. 2 (see Methods for details), we showed that HDSG-filled actuators achieved stable\noperation up to 98% gas-fill in the best orientation and up to 80% in the worst orientation (Fig. 6b)—\nconsiderable improvements over the 90% and 70% thresholds observed with air, respectively. Fig. 6c\nprovides a direct comparison of the force-strain curves of air-filled and HDSG-filled actuators. As a\nresult, the maximum specific energy increased to 51.4 J kg-1 at 98% HDSG-fill in the best orientation, and\n30.0 J kg-1 at 95% HDSG-fill in the worst orientation (Fig. 6d). To fill the actuators with HDSG, we used\na glove box setup illustrated in Supplementary Fig. 15, to prevent contamination with ambient air (see\nMethods for details).”\nMain text, new Figure 6:\n“\nFigure 6. Use of high-dielectric-strength gas (HDSG) enables actuators with improved\nperformance.\na Schematic of actuators with the same amount of liquid dielectric filled with air (left) and high-\ndielectric-strength gas (HDSG; right); a C F N/CO gas mixture was used in this study. Dielectric\n4 7 2\nstrength of air is insufficient to prevent dielectric breakdown near the zipping front, while the HDSG\nprovides sufficient insulation with the same amount of liquid dielectric. b Force-strain curves of actuators\nfilled with HDSG in the best and worst orientation. The actuation was stable up to 98% HDSG-fill in the\nbest orientation, improved from the 90% threshold with air. In the worst orientation, the actuation was\nstable up to 80% HDSG-fill, improved from the 70% threshold with air. c Comparison between air-filled\nand HDSG-filled actuators, in the best and worst orientations. d Corresponding specific energy of\nactuators in both best and worst orientations when filled with air or HDSG. In the best orientation, the\nmaximum specific energy reached 51.4 J kg-1 at 98% HDSG-fill, substantially higher than the specific\nenergy of 33.5 J kg-1 when using air.”\nMain text, page 1, line 18 (Abstract): “Through theoretical and experimental analyses, we pinpoint the\nfundamental performance limit as the electrical breakdown in the gas, governed by Paschen's law, thereby\nproviding a guideline for selection of gaseous dielectrics. Using the Peano-HASEL (hydraulically\namplified self-healing electrostatic) actuator as a model system, we identify a gas mixture of C F N and\n4 7\nCO that enables outstanding specific energy of 51.4 J kg-1 (a nine-fold improvement over conventional\nweight ratio of 1600 W kg-1 (a five- and eleven-fold improvement).”\nMain text, page 3, line 67 (Introduction): “Through a combination of theoretical analysis and\nexperimental validation, we show that Paschen’s law can be used to determine the fundamental limits of\nactuator performance using this strategy, predicting a maximum ratio of gaseous dielectric for a given set\nof actuation conditions and materials properties of the dielectrics. We used the Peano-HASEL actuator, a\ntype of soft electrohydraulic actuator that linearly contracts upon actuation, as a model system to study\nthe fundamental mechanisms and to demonstrate the benefits of using the solid-liquid-gas architecture.\nThe resulting three-phase soft electrostatic actuators achieved outstanding performance metrics when\nambient air was used as the gaseous dielectric—a specific energy of 33.5 J kg-1 and a power-to-weight\nratio of 1600 W kg-1, which translate to a 532% and 1130% improvement, respectively, compared to the\nconventional Peano-HASEL actuators. Additionally, the three-phase actuators achieved an 83% higher\nstrain rate (2840 % s-1) and a 70% wider bandwidth (c.a. 100 Hz) indicating a substantial improvement of\nactuation speed. We showcased the outstanding performance of these actuators in a jumping robot, which\nexhibited a 60% increase in jump height and a 32% reduction in take-off time when compared to its solid-\nliquid counterpart. We also identified a gas mixture of C F N and CO with particularly high dielectric\n4 7 2\nstrength, that enabled outstanding specific energy of 51.4 J kg-1 (a nine-fold improvement over\nconventional Peano-HASELs), underlining a key advantage of implementing the proposed solid-liquid-\ngas architectures in closed structures that can enclose gaseous dielectrics with tailored properties.”\nMain text, page 13, line 326 (Discussion): “We introduced ultralight soft electrostatic actuators based on\na solid-liquid-gas architecture, demonstrating substantial performance improvements using Peano-\nHASELs as a model system. When filled with ambient air as the gaseous dielectric, the three-phase\nPeano-HASELs achieved a specific energy of 33.5 J kg-1, narrowing the gap to the 40 J kg-1 of biological\nmuscles, and a specific power of 1600 W kg-1, which far exceeds the 200 W kg-1 typical of muscles57,58.\nThis performance can be further enhanced by employing gases with tailored dielectric properties.\nSpecifically, by using a gas mixture of C F N and CO , which has a higher dielectric strength than air, the\n4 7 2\nactuators reached a specific energy of 51.4 J kg-1—surpassing that of biological muscle.”\nMain text, page 14, line 349 (Discussion): “In closed actuators, the gaseous dielectrics can be actively\nengineered. Here, we have demonstrated that high-dielectric-strength gases can substantially improve\nactuator stability and performance.”\nNew Supplementary Figure 15:\n“\nSupplementary Figure 15. Glove box setup for fabrication of HDSG-filled actuators.\nSchematic of the glove box setup used to fill actuators with HDSG, a gas mixture of C F N and CO . The\n4 7 2\nglove box is maintained at 1 bar CO . A dedicated gas line delivers HDSG into syringes equipped with\n2 2\nin the glove box helps prevent contamination with ambient air.”\nMain text, page 16, line 393 (Methods): “We filled the actuators with the high-dielectric-strength gas\n(C -FN gas mixture: 20.00%-C -FN; 2,3,3,3-tetrafluoro-2-(trifluoromethyl)propanonitrile and 80.00 %-\n4 4\nCO ; carbon dioxide; DILO Amaturen und Anlagen GmbH) in a glove box setup (GB0004; MSE\nReviewer 1, comment 3:\n“Have the authors verified experimentally that the simplified mathematical model is valid? What about\nstatic models in particular?”\nResponse:\nWe validated our static model through two independent approaches:\n(a) Theoretical convergence: Our model reduces to a well-established electrostatic actuation model\nfor Peano-HASEL actuators [R1] when the amount of gas-fill approaches 0%, confirming its\nconsistency with existing frameworks.\n(b) Experimental validation: We experimentally verified our static model, particularly the prediction\nof our model that the relative difference in performance is negligible across varying gas-fill\nratios.\n[R1] N. Kellaris et al., An analytical model for the design of Peano-HASEL actuators with drastically\nimproved performance, Extreme Mech. Lett. 29, 100449, 2019\nWe added these findings in a new Supplementary Figure 4 as shown below.\nNew Supplementary Figure 4:\n“\nSupplementary Figure 4. Model verification.\na Force-strain curves predicted by the new model incorporating compressibility of gaseous dielectric. The\nnew model converges to the established model for Peano-HASEL actuators1 (red line) when the amount\nof gas-fill approaches 0% (black line). b Force-strain curves obtained from experiments. As predicted by\nthe model, negligible deviation is observed across gas-fill ratios.”\nReviewer 1, comment 4:\n“What are the effects of gravity and how much deviation is there between the experiment and the ideal\nmodel in Supplementary Figure 2?”\nResponse:\nThe deviation between the experiment and the ideal model is now shown in the new SI figure 4b, as\ndescribed above in the response to Reviewer 1 comment 3.\nGravity influences the distribution of liquid inside the pouch. It causes the liquid dielectric to pool at the\nbottom of the actuators. As a result, the air-fill ratio up to which actuation was stable depended on the\norientation (up to 90% in the best orientation and 70% in the worst). Below these limits, the effect of\ngravity on actuator performance during quasi-static actuation was negligible, as the experimentally\ndetermined force-strain curves were independent of the orientation. To further examine potential\ngravitational effects, we performed experiments with actuators in the horizontal orientation. The force-\nstrain curves remained consistent up to 90% air-fill (new panel Fig. 2d), and their specific energy was\nnearly identical to actuators in vertical orientations (Fig. 2e). Based on these findings, we expect actuators\nup to 90% air-fill to exhibit consistent performance in any orientation between the best and horizontal\norientations. We included these findings in the Quasi-static performance section and Figure 2d, e in the\nmain text, as shown below. Additionally, we added a discussion of possible strategies to mitigate the\norientation dependence on the performance of the actuators in the Discussion section.\nMain text, page 7, line 164: “To quantify performance in intermediate orientations, we tested actuators\npositioned horizontally (Fig. 2d). The force-strain responses closely matched those of the best orientation\nup to 90% air-fill. This result indicates that up to an air-fill of 90% the performance of actuators will be\nconsistent for all orientations between the best and the horizontal orientation.”\nMain text, page 16, line 368 (Discussion): “Actuator orientation and dynamic effects were found to\ninfluence actuator performance by redistributing liquid dielectric within the pouch. This effect may\ncompromise the practicality of these actuators in certain applications where stable liquid retention\nbetween the electrodes cannot be guaranteed. Several strategies could mitigate this effect. Selecting solid-\nliquid-gas combinations with higher surface tension (e.g., surface treatments or oleophilic metamaterials)\ncan improve liquid retention near the pouch edges, counteracting gravitational or inertial forces. In\naddition, incorporating porous internal structures such as sponges or gels may help retain liquid in the\ndesired places and prevent local depletion.”\nFigure 2 with new panels with corresponding changes to the figure captions:\n“\nFigure 2. Evaluation of quasi-static performance of Peano-HASEL actuators based on solid-liquid-\ngas architectures.\na Schematic of actuators with different amounts of liquid dielectric; sufficient liquid near the zipping\nfront prevents dielectric breakdown, while insufficient liquid increases the probability of breakdown of\nthe gaseous dielectric. b Force-strain curves of actuators with varying percentages of air-fill in the \"best\"\norientation (electrodes at the bottom). Performance was stable up to 90% air-fill, then it declined abruptly,\ncompletely failing at 100% air-fill. c Force-strain curves of actuators with varying percentages of air-fill\nin the \"worst\" orientation (electrodes at the top). Performance was stable up to 70% air-fill (lower than the\n90% limit observed in the best orientation), then declined abruptly, completely failing at 100% air-fill. d\nForce-strain curves of actuators with varying percentages of air-fill in the horizontal orientation.\nPerformance was stable up to 90% air-fill, then it declined abruptly, completely failing at 100% air-fill. e\nSpecific energy as a function of percentage of air-fill for the three orientations, with a peak of 33.5 J kg-1\nat 97% air-fill in the best orientation.”\nReviewer 2\nReviewer 2, comment 1:\n“This work presents a novel soft electrostatic actuator based on a solid-liquid-gas structure, which\ndemonstrates significant enhancement on the actuation performance of specific energy and power-to-\nweight ratio. It is interesting and brings some new perspectives to the electrostatic actuators. Some issues\nneed to be addressed before publication.”\n“It is assumed in the manuscript that liquid dielectric always exists at the zipping front due to surface\ntension. Can the authors use microscope photos or other pictures to prove this?”\nResponse:\nWe appreciate this positive evaluation of our work. To verify if liquid dielectric remains present at the\nzipping front during actuation, we recorded videos of actuators equipped with transparent electrodes and a\ndyed liquid dielectric. For the transparent electrodes, we used conductive polyacrylamide hydrogel in the\nbest and worst orientations, and transparent Pedot:PSS ink for the horizontal orientation. In all cases, the\ntransparent silicone oil was dyed using beta-carotene as a pigment. The footages confirmed that liquid\nconsistently remains at the zipping front throughout actuation, regardless of orientation. We included\nthese results in the Quasi-static performance section, new Supplementary Figure 5, and in the\nSupplementary Movie 1 (00:41-00:49).\nMain text, page 7, line 153: “In this worst orientation, gravity pulls the liquid dielectric away from the\nzipping front, leaving only a small amount held in place by surface tension, for protection against\ndielectric breakdown. Still, the liquid dielectric consistently remains at the zipping front throughout\nactuation, regardless of the actuator orientation, as shown in Supplementary Fig. 5.”\nRevised Supplementary Movie 1 (00:41-00:49) with additional comment “Liquid consistently remains at\nthe zipping front”:\nNew Supplementary Figure 5:\n“\nSupplementary Figure 5. Retention of liquid dielectric at zipping front.\nVideo snapshots demonstrating the presence of liquid at the zipping front throughout actuation, in the\nbest, worst, and horizontal orientations. Best and worst orientation experiments were performed at an\nearlier stage of research, using hydrogel electrodes; horizontal orientation experiments were performed\nlater using pedot:PSS electrodes—these different experimental conditions should, however, not influence\nthe presence of liquid at the zipping front.”\nReviewer 2, comment 2:\n“Will the maximum ratio of gaseous dielectric be influenced by the actuator orientation? If so, the limits\nshould be discussed under the condition of worst orientation.”\nResponse:\nThe reviewer is correct that the maximum amount of air-fill depends on the orientation of the actuators as\nthe amount of liquid in the zipping front also depends on the orientation of the actuator. To more clearly\ndifferentiate the limits of different orientations, we modified the section Quasi-static performance as\nshown below. We also added an in-depth discussion of the influence of orientation on the actuation\nperformance in the following response to Reviewer 2 comment 3.\nMain text, page 7, line 171: “Notably, in the best actuator orientation, specific energy reached a maximum\nof 33.5 J kg-1 at 97% air-fill, representing a 532% enhancement over a reference actuator with 0% air-fill.\nIn the worst actuator orientation, the specific energy reached a maximum of 23.3 J kg-1 at 95% air-fill,\nrepresenting a 291% enhancement over a reference actuator with 0% air-fill in the same orientation.”\nReviewer 2, comment 3:\n“The effect of actuator orientations on actuation force and strain needs to be further discussed.”\nResponse:\nTo further investigate the effect of actuator orientations on actuation force and strain, we performed\nadditional experiments with actuators in the horizontal orientation.\n[Please refer to our detailed response below, reproduced from our response to Reviewer 1, comment 4.]\nThe force-strain curves remained consistent up to 90% air-fill (new panel Fig. 2d), and their specific\nenergy was nearly identical to actuators in vertical orientations (Fig. 2e). Based on these findings, we\nexpect actuators up to 90% air-fill to exhibit consistent performance in any orientation between the best\nand horizontal orientations. We included these findings in the Quasi-static performance section and\nFigure 2d, e in the main text, as shown below. Additionally, we added a discussion of possible strategies\nto mitigate the orientation dependence on the performance of the actuators in the Discussion section.\nMain text, page 7, line 164: “To quantify performance in intermediate orientations, we tested actuators\npositioned horizontally (Fig. 2d). The force-strain responses closely matched those of the best orientation\nup to 90% air-fill. This result indicates that up to an air-fill of 90% the performance of actuators will be\nconsistent for all orientations between the best and the horizontal orientation.”\nMain text, page 16, line 368 (Discussion): “Actuator orientation and dynamic effects were found to\ninfluence actuator performance by redistributing liquid dielectric within the pouch. This effect may\ncompromise the practicality of these actuators in certain applications where stable liquid retention\nbetween the electrodes cannot be guaranteed. Several strategies could mitigate this effect. Selecting solid-\nliquid-gas combinations with higher surface tension (e.g., surface treatments or oleophilic metamaterials)\ncan improve liquid retention near the pouch edges, counteracting gravitational or inertial forces. In\naddition, incorporating porous internal structures such as sponges or gels may help retain liquid in the\ndesired places and prevent local depletion.”\nFigure 2 with new panels with corresponding changes to the figure captions:\n“\nFigure 2. Evaluation of quasi-static performance of Peano-HASEL actuators based on solid-liquid-\ngas architectures.\na Schematic of actuators with different amounts of liquid dielectric; sufficient liquid near the zipping\nfront prevents dielectric breakdown, while insufficient liquid increases the probability of breakdown of\nthe gaseous dielectric. b Force-strain curves of actuators with varying percentages of air-fill in the \"best\"\norientation (electrodes at the bottom). Performance was stable up to 90% air-fill, then it declined abruptly,\ncompletely failing at 100% air-fill. c Force-strain curves of actuators with varying percentages of air-fill\nin the \"worst\" orientation (electrodes at the top). Performance was stable up to 70% air-fill (lower than the\n90% limit observed in the best orientation), then declined abruptly, completely failing at 100% air-fill. d\nForce-strain curves of actuators with varying percentages of air-fill in the horizontal orientation.\nPerformance was stable up to 90% air-fill, then it declined abruptly, completely failing at 100% air-fill. e\nSpecific energy as a function of percentage of air-fill for the three orientations, with a peak of 33.5 J kg-1\nat 97% air-fill in the best orientation.”\nReviewer 2, comment 4:\n“Does the composition or dielectric properties of the air have any impact on actuation behavior?”\nResponse:\nThank you for your insightful suggestion. Building upon your suggestion, we explored gases with\ndielectric properties distinct from air, and demonstrated that the use of high-dielectric-strength gas\n(HDSG) can substantially improve actuator performance.\n[Please refer to our detailed response below, reproduced from our response to Reviewer 1, comment 2]\nOur model suggests that using high-dielectric-strength gas (HDSG) can lead to considerable performance\ngains, and thus motivated us to invest substantial experimental efforts to develop a fabrication procedure\nfor HDSG-filled actuators that promise to achieve substantially improved actuator performance. We are\nexcited to report that these efforts have resulted in a substantial improvement of actuator performance:\nfrom 33.5 J kg-1 for air-filled actuators to 51.4 J kg-1 for HDSG-filled ones, even surpassing the\nperformance of mammalian muscle (c.a. 40 J kg-1) [R1]. For these experiments, we used a C F N/CO gas\n4 7 2\nmixture as the HDSG, which offers dielectric strength comparable to SF but with substantially lower\n6\nglobal warming potential [R2, R3]. During quasi-static actuation, the HDSG-filled actuators enabled\nreliable actuation up to 98% fill in the best orientation and up to 80% fill in the worst orientation—\nconsiderable improvements over the 90% and 70% thresholds observed with air, respectively.\nWe added these results as a new Figure 6, which shows a direct performance comparison between air-\nfilled and HDSG-filled actuators, to the manuscript. We also added a new section High-dielectric-\nstrength gas for enhanced performance in solid-liquid-gas architectures and revised Abstract,\nIntroduction, Discussion, and Methods to implement the new points and findings as shown below.\n[R1] J. D. Madden et al., Artificial muscle technology: physical principles and naval prospects, IEEE J.\nOcean. Eng. 29, 706-728, 2004\n[R2] M. Rabie et al., Assessment of eco-friendly gases for electrical insulation to replace the most potent\nindustrial greenhouse gas SF6, Environmental Science & Technology, 2018.\n[R3] J. Owens et al. Recent development of two alternative gases to SF6 for high voltage electrical power\napplications, Energies, 2021.\nMain text, page 13, line 310:\n“High-dielectric-strength gas for enhanced performance in solid-liquid-gas architectures\nAs demonstrated above, a limitation of the performance of electrostatic actuators with solid-liquid-gas\narchitectures, is the dielectric breakdown of the gaseous phase. Closed electrostatic actuators, such as\nHASELs, HAXELs, and EBMs, offer the possibility of utilizing a high-dielectric-strength gas (HDSG) to\nimprove performance considerably; HDSGs can prevent dielectric breakdown under conditions where air\nwould typically fail (Fig. 6a). To demonstrate this idea, we used a HDSG in the form of a mixture of\nC F N and CO (see Methods for details), which offers dielectric strength comparable to SF but with\n4 7 2 6\nsubstantially lower global warming potential55,56. With the method used for evaluating quasi-static\nperformance as in Fig. 2 (see Methods for details), we showed that HDSG-filled actuators achieved stable\noperation up to 98% gas-fill in the best orientation and up to 80% in the worst orientation (Fig. 6b)—\nconsiderable improvements over the 90% and 70% thresholds observed with air, respectively. Fig. 6c\nprovides a direct comparison of the force-strain curves of air-filled and HDSG-filled actuators. As a\nresult, the maximum specific energy increased to 51.4 J kg-1 at 98% HDSG-fill in the best orientation, and\n30.0 J kg-1 at 95% HDSG-fill in the worst orientation (Fig. 6d). To fill the actuators with HDSG, we used\na glove box setup illustrated in Supplementary Fig. 15, to prevent contamination with ambient air (see\nMethods for details).”\nMain text, new Figure 6:\n“\nFigure 6. Use of high-dielectric-strength gas (HDSG) enables actuators with improved\nperformance.\na Schematic of actuators with the same amount of liquid dielectric filled with air (left) and high-\ndielectric-strength gas (HDSG; right); a C F N/CO gas mixture was used in this study. Dielectric\n4 7 2\nstrength of air is insufficient to prevent dielectric breakdown near the zipping front, while the HDSG\nprovides sufficient insulation with the same amount of liquid dielectric. b Force-strain curves of actuators\nfilled with HDSG in the best and worst orientation. The actuation was stable up to 98% HDSG-fill in the\nbest orientation, improved from the 90% threshold with air. In the worst orientation, the actuation was\nstable up to 80% HDSG-fill, improved from the 70% threshold with air. c Comparison between air-filled\nand HDSG-filled actuators, in the best and worst orientations. d Corresponding specific energy of\nactuators in both best and worst orientations when filled with air or HDSG. In the best orientation, the\nmaximum specific energy reached 51.4 J kg-1 at 98% HDSG-fill, substantially higher than the specific\nenergy of 33.5 J kg-1 when using air.”\nMain text, page 1, line 18 (Abstract): “Through theoretical and experimental analyses, we pinpoint the\nfundamental performance limit as the electrical breakdown in the gas, governed by Paschen's law, thereby\nproviding a guideline for selection of gaseous dielectrics. Using the Peano-HASEL (hydraulically\namplified self-healing electrostatic) actuator as a model system, we identify a gas mixture of C F N and\n4 7\nCO that enables outstanding specific energy of 51.4 J kg-1 (a nine-fold improvement over conventional\nweight ratio of 1600 W kg-1 (a five- and eleven-fold improvement).”\nMain text, page 3, line 67 (Introduction): “Through a combination of theoretical analysis and\nexperimental validation, we show that Paschen’s law can be used to determine the fundamental limits of\nactuator performance using this strategy, predicting a maximum ratio of gaseous dielectric for a given set\nof actuation conditions and materials properties of the dielectrics. We used the Peano-HASEL actuator, a\ntype of soft electrohydraulic actuator that linearly contracts upon actuation, as a model system to study\nthe fundamental mechanisms and to demonstrate the benefits of using the solid-liquid-gas architecture.\nThe resulting three-phase soft electrostatic actuators achieved outstanding performance metrics when\nambient air was used as the gaseous dielectric—a specific energy of 33.5 J kg-1 and a power-to-weight\nratio of 1600 W kg-1, which translate to a 532% and 1130% improvement, respectively, compared to the\nconventional Peano-HASEL actuators. Additionally, the three-phase actuators achieved an 83% higher\nstrain rate (2840 % s-1) and a 70% wider bandwidth (c.a. 100 Hz) indicating a substantial improvement of\nactuation speed. We showcased the outstanding performance of these actuators in a jumping robot, which\nexhibited a 60% increase in jump height and a 32% reduction in take-off time when compared to its solid-\nliquid counterpart. We also identified a gas mixture of C F N and CO with particularly high dielectric\n4 7 2\nstrength, that enabled outstanding specific energy of 51.4 J kg-1 (a nine-fold improvement over\nconventional Peano-HASELs), underlining a key advantage of implementing the proposed solid-liquid-\ngas architectures in closed structures that can enclose gaseous dielectrics with tailored properties.”\nMain text, page 13, line 326 (Discussion): “We introduced ultralight soft electrostatic actuators based on\na solid-liquid-gas architecture, demonstrating substantial performance improvements using Peano-\nHASELs as a model system. When filled with ambient air as the gaseous dielectric, the three-phase\nPeano-HASELs achieved a specific energy of 33.5 J kg-1, narrowing the gap to the 40 J kg-1 of biological\nmuscles, and a specific power of 1600 W kg-1, which far exceeds the 200 W kg-1 typical of muscles57,58.\nThis performance can be further enhanced by employing gases with tailored dielectric properties.\nSpecifically, by using a gas mixture of C F N and CO , which has a higher dielectric strength than air, the\n4 7 2\nactuators reached a specific energy of 51.4 J kg-1—surpassing that of biological muscle.”\nMain text, page 14, line 349 (Discussion): “In closed actuators, the gaseous dielectrics can be actively\nengineered. Here, we have demonstrated that high-dielectric-strength gases can substantially improve\nactuator stability and performance.”\nNew Supplementary Figure 15:\n“\nSupplementary Figure 15. Glove box setup for fabrication of HDSG-filled actuators.\nSchematic of the glove box setup used to fill actuators with HDSG, a gas mixture of C F N and CO . The\n4 7 2\nglove box is maintained at 1 bar CO . A dedicated gas line delivers HDSG into syringes equipped with\n2 2\nin the glove box helps prevent contamination with ambient air.”\nMain text, page 16, line 393 (Methods): “We filled the actuators with the high-dielectric-strength gas\n(C -FN gas mixture: 20.00%-C -FN; 2,3,3,3-tetrafluoro-2-(trifluoromethyl)propanonitrile and 80.00 %-\n4 4\nCO ; carbon dioxide; DILO Amaturen und Anlagen GmbH) in a glove box setup (GB0004; MSE\nReviewer 2, comment 5:\n“Long-term stability and reliability are critical for flexible actuators. Have the authors carried out cycle\ntests?”\nResponse:\nWe performed a 100,000-cycle-long durability test on actuators with 0% air (reference) and 70% air in\nboth the best and worst orientations. The actuators were fabricated identically to those used in the\nfrequency response experiments (see Method). We applied a sinusoidal excitation voltage (6 kV peak,\nsingle polarity) at 5 Hz and approximately 1 N of preload with springs, analogous to the frequency\nresponse tests (Supplementary Figure 12, new Supplementary Figure 6b).\nFor each condition, we tested seven samples. No sample failed within the tested 100,000 cycles. Stroke\nmeasurements from one representative sample per condition were recorded using a laser displacement\nsensor. The stroke amplitudes, normalized by their respective initial values, remained stable up to 10,000\ncycles, after which a gradual decline was observed, likely due to charge retention effects [R1].\nImportantly, the level of degradation was similar for all conditions, including the 0% air reference,\nindicating that the presence of air has negligible impact on long-term durability under these actuation\nconditions.\n[R1] I.-D. Sirbu, et al., Electrostatic actuators with constant force at low power loss using matched\ndielectrics, Nature Electronics, 2023.\nThese results are added in the section Dynamic performance, in a new Supplementary Figure 6b, and\nSupplementary Note as follows:\nMain text, page 12, line 290: “We assessed the long-term durability of the actuators through 100,000-\ncycle tests. All samples remained functional after 100,000 cycles, with a slight, gradual decline in stroke\nobserved after 10,000 cycles, regardless of air fill or actuator orientation, indicating a negligible impact of\nair on long-term durability (see Supplementary Fig. 6b and Supplementary Note).”\nSupplementary Information page 15, line 238:\n“Prolonged actuation in cyclic actuation\nTo assess long-term durability of the actuators, we performed 100,000-cycle-long durability tests with\nactuators with 0% air (reference) and 70% air in the best and worst orientations (7 samples for each fill\nand orientation). The fabrication procedure was identical to those described for the frequency response\nexperiments specified in Methods section in the main text. A sinusoidal voltage signal (6kV peak, single\npolarity) at 5 Hz was used for actuation (Supplementary Fig. 6b). A nearly constant force of 1 N was\napplied using the springs specified in Supplementary Fig. 12. The spring resonance frequency was well\nseparated from the 5 Hz actuation frequency.\nUnder this operating condition, all seven tested samples for each condition—0% air, 70% air in best and\nworst orientations—remained functional after 100,000 cycles. For each condition, stroke measurements\nwere obtained from one representative sample, using the laser displacement sensor described in the\nMethods section. The stroke amplitudes, normalized by their respective initial values, remained stable up\nto 10,000 cycles, after which a gradual decline was observed, likely due to charge retention effects6. The\nlevel of degradation was similar for all cases, including the reference actuator with 0% air, indicating that\nthe presence of air has negligible impact on long-term durability under these actuation conditions.”\nNew Supplementary Figure 6b and corresponding figure caption:\n“\nSupplementary Figure 6. Prolonged actuation at constant voltage and in cyclic actuation.\nb Normalized amplitude over 100,000 cycles under a sinusoidal voltage signal, for actuators with 0% air-\nfill (reference) and with 70% air-fill. At this specific actuation condition, all seven samples for each case\nremained functional after 100,000 cycles. Actuator stroke was normalized with the initial stroke of each\nactuator, to show the actuator behavior over many cycles. For all three cases, the normalized amplitude\nremained stable up to 10,000 cycles, after which a gradual decline was observed, likely due to charge\nretention effects6. The level of degradation was similar for all cases, including the reference actuator with\n0% air, suggesting that the presence of air has negligible impact on long-term durability.”\nReviewer 2, comment 6:\n“Since the liquid can move and oscillate in the air, the three-phase actuators are seem to be more\nunstable compared to the conventional Peano-HASELs. How to ensure the stability of the actuator\noutput, especially in periodic high-frequency response?”\nResponse:\nThis effect was only noticeable at frequencies above 10 Hz in our experiments (Figure 4g). At higher\nactuation frequencies, the data indeed suggest that redistribution of the liquid dielectric within the pouch\ncan affect performance. To address this instability of the actuation in high frequencies, we now propose\nstrategies to mitigate redistribution of liquid in the Discussion section, including the use of solid-liquid-\ngas combinations with higher surface tension and surface treatments of solid dielectric, to enhance liquid\nretention:\n[Please refer to our detailed response below, reproduced from our response to Reviewer 2, comment 3.]\nMain text, page 16, line 368 (Discussion): “Actuator orientation and dynamic effects were found to\ninfluence actuator performance by redistributing liquid dielectric within the pouch. This effect may\ncompromise the practicality of these actuators in certain applications where stable liquid retention\nbetween the electrodes cannot be guaranteed. Several strategies could mitigate this effect. Selecting solid-\nliquid-gas combinations with higher surface tension (e.g., surface treatments or oleophilic metamaterials)\ncan improve liquid retention near the pouch edges, counteracting gravitational or inertial forces. In\naddition, incorporating porous internal structures such as sponges or gels may help retain liquid in the\ndesired places and prevent local depletion.”\nReviewer 3\nReviewer 3, general comment:\n“The manuscript presents an interesting approach to modifying the well‐known Peano‐HASEL actuator\nby partially replacing the liquid dielectric with a gas, forming a solid–liquid–gas architecture. The\nauthors provide high quality and extensive experimental validation, including quasi-static tests, dynamic\nresponse analyses, and a jumping robot demonstration. The proposed idea reduces mass and provide\nimportant improvements in performance metrics (specific energy, strain rate, power-to-weight ratio) of\nthe Peano actuator; however, the conceptual novelty, solely connected to the partial filling approach,\nappears limited since the fundamental actuator design is already established in previous work\n(adequately cited in the manuscript).”\nResponse:\nWe appreciate the positive evaluation of the quality of our work; regarding conceptual novelty, we would\nlike to refer to our response to reviewer 1, general comment:\n[Please refer to our detailed response below, reproduced from our response to Reviewer 1, general\ncomment.]\nAs the reviewer points out, the performance improvement enabled by the solid-liquid-gas architecture is\none important outcome of this paper. Additionally, the paper features two novel aspects, which we feel\nare important advances over existing literature; we have revised the manuscript to more clearly articulate\nthese advances:\n1) HASEL actuators and the actuators developed by Rossiter and colleagues share liquid-enhanced\nelectrostatic zipping as an actuation mechanism. However, Rossiter’s actuators are open\nstructures, which directly interact with the surrounding air, whereas HASELs based on the solid-\nliquid-gas architecture are closed structures, where air can be replaced with other gases that\nfeature high dielectric strength. Stimulated by insightful comments of reviewers 1 and 2, in the\nprocess of this major revision, we have identified a C F N/CO gas mixture for use as high-\n4 7 2\ndielectric-strength gas (HDSG); we have further developed a fabrication procedure for HDSG-\nfilled actuators that achieve substantially improved actuator performance (33.5 J kg-1 for air-filled\nactuators → 51.4 J kg-1 for HDSG-filled actuators; see detailed discussion in Reviewer 1,\ncomment 2).\n2) Building upon Paschen’s law, we derived a model to predict dielectric breakdown through gas in\nHASELs based on the solid-liquid-gas architecture; through theoretical and experimental\nanalyses, we pinpoint the fundamental performance limit as the electrical breakdown in the gas,\nthereby providing a guideline for selection of gaseous dielectrics. The model introduced in the\nmanuscript should, in principle, also be applicable for determining the minimum amount of liquid\nin Rossiter’s actuators. To confirm that the model also works for open structures, we performed\ndielectric breakdown tests of liquid-gas interfaces in a simplified setup (see detailed discussion in\nReviewer 3, comment 1)\nReviewer 3, comment 1:\n“An accompanying theoretical framework based on Paschen’s law is introduced (which could potentially\nrepresent a valuable contribution) to explain the onset of dielectric breakdown, but there are some\ncritical points regarding this. For a convincing validation, I suggest performing experiments on a\ndedicated, simplified, controlled setup aimed at isolating and validating the model parameters. This\nwould help to limit the number of uncontrolled variables.”\nResponse:\nWe thank the reviewer for this constructive and important suggestion. As suggested, we conducted\ndielectric breakdown tests of liquid-gas interfaces in a simplified setup, which demonstrated a good\nalignment with our theoretical framework based on Paschen’s law.\nAs the reviewer noted, in the main manuscript, the air pressure inside actuator P and electrode gap d were\ninferred from analytical models rather than directly measured. To validate our theoretical framework\nunder more controlled conditions, we designed a simplified experimental setup using rigid acrylic plates\nthat were angled with respect to each other to replicate the zipping front of the actuators, as shown in a\nnew Supplementary Figure 9a and b.\nIn this setup, carbon electrodes were printed on the outer side of solid dielectric films which were\nsecurely bonded to the acrylic plates to prevent movement during voltage application. The electrode gap\nwas filled with varying amounts of liquid dielectric—sufficient, insufficient, and none (Supplementary\nFig. 9c). In this setup open to the ambient air, the air pressure P was constant at atmospheric pressure, and\nthe electrode gap d remained constant.\nWe applied the activation voltage pattern used in the tests described in the Identification of fundamental\nperformance limits section in the main text: a ramp of 1 kV s-1 with a 2-second hold at each 1 kV step\nfrom 5 to 10 kV, repeated for 100 cycles with alternating polarity. With the application of the voltage, as\nshown in the new Supplementary Figure 9d, the setup with sufficient liquid dielectric (left, electrodes\nfully covered) exhibited only a few and minor current spikes, indicating effective insulation. In contrast,\nthe setup with insufficient liquid dielectric (middle; electrodes partially covered) exhibited frequent\ncurrent spikes, particularly at higher voltages. The setup with no liquid dielectric (right) exhibited\nnumerous current spikes, even at low voltages. The new Supplementary Figure 9e provides an overview\nof the distribution of voltages at which the first current spikes occurred in each cycle.\nTo quantitatively test the theoretical prediction by Paschen’s law, we analyzed the case of insufficient-\nliquid. The atmospheric pressure was measured to be 973.3 hPa (730.0 Torr) using a barometer, and the\nelectrode gap at the liquid-air interface was estimated to be 1.70 mm based on image analysis. These\nvalues were then plotted on the Paschen’s curve for air (new Supplementary Fig. 9f). The intersection\npoint of the orange (Paschen’s curve for air) and black (measured value) lines indicates the predicted\nimpending dielectric breakdown of air within the setup. The zoomed-in view shows that most breakdown\nevents align well with the value predicted from Paschen’s law.\nWe have added these findings as a new Supplementary Figure 9, and updated the main text in the\nIdentification of fundamental performance limits section as follows:\nMain text, page 10, line 236: “This hypothesis was further confirmed with a simplified experimental setup\nwith measured p and d in an open system (Supplementary Fig. 9; see Methods for details).”\nMain text, page 17, line 410 (Methods):\n“Fabrication and experimental details of the dielectric breakdown test in a simplified setup\nRigid acrylic plates were fixed at an angle of 27.6 ° relative to each other. Biaxially oriented polyester\nfilms (Mylar 850-15, Petroplast GmbH), each bearing 2 cm x 6 cm carbon electrodes (Cl-2051, Nagase\nChemteX America LLC) printed on their outer surfaces, were securely bonded to the angled acrylic\nplates. The sides of the assembly were sealed using thin transparent acrylic plates. A varying amount of\nliquid dielectric (Silicone oil M5, Carl Roth) was added to fill the electrode gap. A voltage ramp was\napplied at a rate of 1 kV s-1, with a 2-second hold at each 1 kV increment from 5 to 10 kV. This pattern\nwas repeated for 100 cycles, alternating polarity each cycle. Using the measured current profiles, the\nbreakdown voltages were recorded as the voltages at which the first current spikes occurred in each\ncycle.”\nNew Supplementary Figure 9:\n“\nSupplementary Figure 9. Dielectric breakdown test of liquid-gas interfaces in a simplified setup.\nA simplified experimental setup using rigid acrylic plates (a, b) to replicate the zipping front of actuators\nunder three conditions (c): sufficient (left), insufficient (middle), and no (right) liquid dielectric. Carbon\nelectrodes were printed on the outer surfaces of solid dielectric films which were securely bonded to the\nacrylic plates. d Measured current profiles for each condition, when actuators were exposed to the typical\nactivation voltage pattern used for actuator evaluation. Therefore, an identical voltage signal ramping at 1\nkV s-1 and pausing for 2 seconds at every 1 kV step from 5 to 10 kV was applied for 100 cycles (10\nvoltage cycles are shown in the figure; however, current data for all 100 cycles is shown, so that all\ncurrent spikes are visible), with polarity reversed each cycle. The setup with sufficient liquid dielectric\n(left; electrodes fully covered) exhibited only a few and minor current spikes, indicating effective\ninsulation. In contrast, the setup with insufficient liquid dielectric (middle; electrodes partially covered)\nexhibited frequent current spikes, particularly at higher voltages. The setup with no liquid dielectric\n(right) exhibited numerous current spikes, even at low voltages. e Voltages at which the first current\nspikes occurred in each cycle. The white line denotes the median value, and the thick black bars denote\nthe standard deviation; the thin black bar shows the data range from lowest to highest value, avoiding\noutliers. The width of the colored areas indicates the number of recoded breakdown events for a given\nvoltage. f Paschen’s curve for air (orange) intersecting with a black line denoting the measured value of\natmospheric pressure p, which was measured to be 973.3 hPa (730.0 Torr), and the electrode gap along\nthe liquid-air interface d, which was 1.70 mm. The intersection point of the orange and black lines\nindicates the predicted impending dielectric breakdown of air within the setup. The zoomed-in view\nshows that most breakdown events align well with the value predicted from Paschen’s law.”\nReviewer 3, comment 2:\n“Although introducing air reduces mass, the inherent compressibility of gas could lead to unwanted\neffects when the actuator is subjected to temperature and pressure variations. The authors should address\nwhether changes in these conditions might alter performance (e.g., stroke). A simple dedicated\ntheoretical/experimental study examining the influence of thermal/pressure expansion on actuation\nbehavior should be added. A discussion should also be introduced, highlighting possible connected\nlimitations (e.g., underwater robotics?)”\nResponse:\nWe expanded our analytical model to incorporate the effects of external pressure and temperature.\nThis updated model allows us to predict performance of actuator (in terms of force-strain behavior)\nunder various environmental conditions.\nAssuming fabrication under standard room conditions (p = 1.0 bar, T = 20 °C) and isothermal actuation\n0 0\nunder different external pressure and temperature conditions, we examined deviations under design\nconditions enveloping representative outdoor conditions. We varied external pressure (p = 0.8 to 1.1\next\nbar) at the same external temperature (T = 20 °C), and the external temperature (T = -30 to 70 °C) at\next ext\nthe same external pressure (p = 1.0 bar), and compared the resulting force-strain curves. Here, we\next\npresent only the 100% gas-filled actuator case as it is the most extreme case regarding environmental\neffects. Even though the actuator does not work in experiments with 100% gas-fill (due to dielectric\nbreakdown through the gas gap), in our model it allows a conservative estimation of the influence of the\ncompressibility of the gas on the actuation performance, when the external pressure and temperature\nchange.\nThe new Supplementary Figure 16a and b show that changes in external pressure and temperature change\nboth the maximum generated actuation forces and the maximum actuation strain, as the contained gas\nchanges volume. These variations remain small for typical variations of the environmental conditions.\nAs the reviewer noted, in extreme environments, compressibility effects become more pronounced.\nHowever, it is possible to counteract changes in actuation behavior through fabrication and design\nchanges, as we show with an example that could occur, in extreme environments such as underwater.\nAs shown in the new Supplementary Figure 16c, increasing the external pressure to 3.0 bar at an external\ntemperature of 20 °C considerably changes the force-strain curve of an actuator that was filled with gas p\n0\n= 1.0 bar and T = 20 °C. The resulting decrease of the gas volume increases the blocking force, but\n0\ndrastically reduces the maximum actuation stroke, because the electrodes are fully zipped before the angle\nα reaches 90 °. By increasing the electrode length, the full range of actuation strains can be achieved\n(dashed line in Supplementary Fig. 16c). Additionally, when a high external pressure is anticipated, the\nactuator can be pre-filled at a higher pressure to match the external pressure (p = 3.0 bar to match the\nfill\np = 3.0 bar); compressibility effects then become negligible, and the original performance is recovered.\next\nOf course, when the external pressure conditions undergo dynamic changes (such as when an underwater\nrobot dives up and down), the force-strain characteristics of actuators would also undergo dynamic\nchanges; in these cases, the control algorithms for the actuators would have to be adapted to account for\nthese changes in actuation behavior.\nWe added these results in the Supplementary Information, revised Supplementary Figure 2, new\nSupplementary Figure 16, and Discussion.\nSupplementary Information page 6, line 81:\nA. Isothermal actuation\nDuring isothermal actuation, the actuator deforms sufficiently slowly to always be thermally\nequilibrated to the surroundings (at constant external pressure 𝑝 and temperature 𝑇 ).\next ext\nAssuming ideal gas behavior, the equation of the state of the contained gas can be described as\n𝑝𝑉 𝑝 𝑉\ngas\n=\ngas.0 gas.0\n(20)\n𝑇 𝑇\n𝐹 α 𝑉 𝑇\n𝑝 = 𝑝 + ( )= 𝑝\ngas.0 ext\next 𝑤(𝐿 −𝑙 ) cos α 0 2 𝑇\np e 𝑤(𝐿 p −𝑙 e ) α−sin α cos α 0 (21)\n( )−𝑉\n2 α2 liq\nB. Isentropic actuation\nDuring isentropic actuation, the actuator deforms sufficiently fast to prevent any heat exchange\nwith the surroundings. Assuming ideal gas behavior, the equation of the state of the contained gas\ncan be described as\n𝑐\nγ γ p\n𝑝𝑉 = 𝑝 𝑉 (where γ= ) (22)\ngas 0 gas.0 𝑐\nv\nCombining equations (13), (18), and (22) leads to\nγ\n𝐹 α 𝑉\ngas.0\n𝑝 = 𝑝 + ( )= 𝑝 (23)\next 𝑤(𝐿 −𝑙 ) cosα 0 2\np e 𝑤(𝐿 p −𝑙 e ) α−sinαcosα\n( )−𝑉\n( 2 α2 liq )\nWith the calculated α(𝐹,Φ) from equation (19), equations (21) or (23) can be used to calculate 𝑙 as a\ne\nfunction of given external load F, voltage Φ, volume of liquid 𝑉 , external pressure 𝑝 , and in case of\nliq ext\nisothermal actuation, temperature 𝑇 .\next\n𝑙 = 𝑔(𝐹,Φ,𝑉 ,𝑝 ,(𝑇 ))\ne liq ext ext (24)\nEventually, equations (19) and (24) uniquely define the two independent geometric variables α and 𝑙 at\ne\nthe given actuation conditions; (α(𝐹,Φ), 𝑙 (𝐹,Φ,𝑉 ,𝑝 ,(𝑇 ))).\ne liq ext ext\nRevised Supplementary Figure 2 and corresponding figure caption:\n“\nSupplementary Figure 2. Analytical model of three-phase Peano-HASEL actuators.\na Schematic of the actuator at fabricated state, with a given geometry (length L , width w, electrode length\np\nL ) and selection of dielectrics (liquid volume V , initial gas volume V ) under the atmospheric\ne liq gas.0\npressure (p = p ) and room temperature (T = T ). The angle α parameterizes the shape of the\n0 atm 0 room\nactuator. b Schematic of the actuator at initial state, under different pressure and temperature conditions\n(p and T ). The angle α parameterizes the shape of the actuator. The volume of the gas inside the\next ext\nactuator will be affected by the external pressure and temperature conditions, thus changing the initial\ncentral angle α and initial length of actuator 𝑙 . c Actuator during actuation (applied load F, voltage Φ),\n0 0\nwith electrodes zipped to a length l . The actuation process changes the gas pressure p, and thus the\ne\nvolume of gas V . Stored electrical energy is determined by the shell material (thickness t; dielectric\ngas\nconstant ε).”\ns\nNew Supplementary Figure 16:\n“\nSupplementary Figure 16. Effects of external pressure and temperature during isothermal\nactuation\na Calculated force-strain curves of a 100% gas-filled actuator under different external pressures (0.8 and\n1.1 bar) at 20 ℃, when the actuator is filled at a pressure p = 1.0 bar and temperature T = 20 ℃.\n0 0\nb\nCalculated force-strain curves under different external temperatures (-30 and 70 ℃) at 1.0 bar, when the\nactuator is filled at a pressure p = 1.0 bar and temperature T = 20 ℃.\n0 0\nc Calculated force-strain curves\nunder 3.0 bar external pressure at 20 ℃, representing an underwater condition. When the actuator is\ninitially filled at 1.0 bar, it exhibits reduced strain at low forces and enhanced strain at high forces due to\nthe compressed internal gas volume. Under such high pressure, the gas volume considerably decreases,\nrequiring extended electrodes to reach the cylindrical shape at fully zipped state, especially at low forces.\nWhen the actuator is filled at 3.0 bar to match the external pressure, compressibility becomes negligible\nand the original force-strain behavior is recovered.”\nSupplementary Information page 8, line 108: “In Supplementary Fig. 16, the changes in force-strain\ncharacteristic under different external temperature and pressure conditions is predicted using 100% gas-\nfilled actuator as the most extreme case regarding environmental effects. Even though the actuator does\nnot work in experiments with 100% gas fill (due to dielectric breakdown through the gas gap), in our\nmodel it allows a conservative estimation of the influence of the compressibility of the gas on the\nactuation performance, when the external pressure and temperature change. Again, materials system and\ngeometry of the actuators are identical to the ones described in Methods section in the main text.\nAssuming fabrication under standard room conditions (p = 1.0 bar, T = 20 ℃) and isothermal actuation\n0 0\nunder different external pressure and temperature conditions, we examined deviations under design\nconditions enveloping representative outdoor conditions. We varied the external pressure (p = 0.8 to 1.1\next\nbar) at the same external temperature (T = 20 ℃), and the external temperature (T = -30 to 70 ℃) at\next ext\nthe same external pressure (p = 1.0 bar), and compared the resulting force-strain curves.\next\nSupplementary Fig. 16 a and b show that changes in external pressure and temperature change both the\nmaximum generated actuation forces and the maximum actuation strain, as the contained gas changes\nvolume. These variations remain small for typical variations of the environmental conditions. It is\npossible to counteract changes in actuation behavior through fabrication and design changes, as we show\nwith an example that could occur, in extreme environments such as underwater. As shown in the\nSupplementary Fig. 16c, increasing the external pressure to 3.0 bar at an external temperature of 20 °C\nconsiderably changes the force-strain curve of an actuator that was filled with gas p = 1.0 bar and T = 20\n0 0\n°C. The resulting decrease of the gas volume increases the blocking force, but drastically reduces the\nmaximum actuation stroke, because the electrodes are fully zipped before the angle α reaches 90 °. By\nincreasing the electrode length, the full range of actuation strains can be achieved (dashed line in\nSupplementary Fig. 16c). Additionally, when a high external pressure is anticipated, the actuator can be\npre-filled at a higher pressure to match the external pressure (p = 3.0 bar to match the p = 3.0 bar);\nfill ext\ncompressibility effects then become negligible, and the original force-strain behavior is recovered.”\nMain text, page 15, line 355 (Discussion): “Our analytical model, which incorporates compressibility of\ngas, also provides insights into how actuator performance may vary under different environmental\npressures and temperatures. Although the compressibility of the gas had negligible effects under standard\nconditions, performance may differ when the environmental conditions change (Supplementary Fig. 16a\nand b). Whereas the changes in actuation behavior are small for typical environmental variations,\ncompressibility effects become more pronounced in extreme pressure and temperature environments. For\nexample, high external pressure environments during underwater operation can noticeably compress the\ncontained gas, severely altering the actuation behavior (Supplementary Fig. 16c). In such cases, however,\nthe gas fill and the actuator design can be adjusted—pre-filling actuators at a higher pressure to match the\nexternal pressure, and increasing electrode length—to the targeted environmental operating conditions\n(Supplementary Fig. 16c). When the external pressure conditions undergo dynamic changes (such as\nwhen an underwater robot dives up and down), the force-strain characteristics of actuators would also\nundergo dynamic changes; in these cases, the control algorithms for the actuators would have to be\nadapted to account for these changes in actuation behavior.”\nReviewer 3, comment 3:\n“The cyclical operational stability of the actuator should be shown, as differences may appear between\nthe first and subsequent cycles due to changes induced in the interfaces between the fluid and gas. Thus,\nit would be valuable to see cyclical data and (possibily) preliminary discussion on degradation\nmechanisms that might occur over many cycles.”\nResponse:\n[Please refer to our detailed response below, reproduced from our response to Reviewer 2, comment 5.]\nWe performed a 100,000-cycle-long durability test on actuators with 0% air (reference) and 70% air in\nboth the best and worst orientations. The actuators were fabricated identically to those used in the\nfrequency response experiments (see Method). We applied a sinusoidal excitation voltage (6 kV peak,\nsingle polarity) at 5 Hz and approximately 1 N of preload with springs, analogous to the frequency\nresponse tests (Supplementary Figure 12, new Supplementary Figure 6b).\nFor each condition, we tested seven samples. No sample failed within the tested 100,000 cycles. Stroke\nmeasurements from one representative sample per condition were recorded using a laser displacement\nsensor. The stroke amplitudes, normalized by their respective initial values, remained stable up to 10,000\ncycles, after which a gradual decline was observed, likely due to charge retention effects [R1].\nImportantly, the level of degradation was similar for all conditions, including the 0% air reference,\nindicating that the presence of air has negligible impact on long-term durability under these actuation\nconditions.\n[R1] I.-D. Sirbu, et al., Electrostatic actuators with constant force at low power loss using matched\ndielectrics, Nature Electronics, 2023.\nThese results are added in the section Dynamic performance, in a new Supplementary Figure 6b, and\nSupplementary Note as follows:\nMain text, page 12, line 290: “We assessed the long-term durability of the actuators through 100,000-\ncycle tests. All samples remained functional after 100,000 cycles, with a slight, gradual decline in stroke\nobserved after 10,000 cycles, regardless of air fill or actuator orientation, indicating a negligible impact of\nair on long-term durability (see Supplementary Fig. 6b and Supplementary Note).”\nSupplementary Information page 15, line 238:\n“Prolonged actuation in cyclic actuation\nTo assess long-term durability of the actuators, we performed 100,000-cycle-long durability tests with\nactuators with 0% air (reference) and 70% air in the best and worst orientations (7 samples for each fill\nand orientation). The fabrication procedure was identical to those described for the frequency response\nexperiments specified in Methods section in the main text. A sinusoidal voltage signal (6kV peak, single\npolarity) at 5 Hz was used for actuation (Supplementary Fig. 6b). A nearly constant force of 1 N was\napplied using the springs specified in Supplementary Fig. 12. The spring resonance frequency was well\nseparated from the 5 Hz actuation frequency.\nUnder this operating condition, all seven tested samples for each condition—0% air, 70% air in best and\nworst orientations—remained functional after 100,000 cycles. For each condition, stroke measurements\nwere obtained from one representative sample, using the laser displacement sensor described in the\nMethods section. The stroke amplitudes, normalized by their respective initial values, remained stable up\nto 10,000 cycles, after which a gradual decline was observed, likely due to charge retention effects6. The\nlevel of degradation was similar for all cases, including the reference actuator with 0% air, indicating that\nthe presence of air has negligible impact on long-term durability under these actuation conditions.”\nNew Supplementary Figure 6b and corresponding figure caption:\n“\nSupplementary Figure 6. Prolonged actuation at constant voltage and in cyclic actuation.\nb Normalized amplitude over 100,000 cycles under a sinusoidal voltage signal, for actuators with 0% air-\nfill (reference) and with 70% air-fill. At this specific actuation condition, all seven samples for each case\nremained functional after 100,000 cycles. Actuator stroke was normalized with the initial stroke of each\nactuator, to show the actuator behavior over many cycles. For all three cases, the normalized amplitude\nremained stable up to 10,000 cycles, after which a gradual decline was observed, likely due to charge\nretention effects6. The level of degradation was similar for all cases, including the reference actuator with\n0% air, suggesting that the presence of air has negligible impact on long-term durability.”\nReviewer 3, comment 4:\n“The model presented in the supplementary material applies Boyle’s law (pV = constant) under the\nassumption of isothermal conditions. While this assumption may hold in quasi-static regimes, it should be\nclarified how dynamic conditions—where heat exchange may occur at a slower rate—could affect the\nmodel's validity.”\nResponse:\nThe reviewer is correct that the temperature of the gas may change during non-quasi-static deformation.\nWhile isothermal deformation represents perfect thermal equilibrium with the surroundings, isentropic\ndeformation represents the opposite extreme—no heat exchange at all. The actual behavior of actuators\nwill lie between the isothermal and isentropic extremes. We added a model modified for isentropic\ndeformation to the Supplementary Information. This model leads to nearly the same force-strain curve as\nisothermal deformation and the reference actuator (0% air), as shown in the new panel Supplementary\nFig. 3e. As a result, we conclude that dynamic conditions will lead to the almost same actuation behavior\nas for isothermal conditions.\nWe made the following changes to the main text and Supplementary Information:\nMain text, page 7, line 146: “The model predicts negligible deviation between isentropic and isothermal\nextremes under typical actuation conditions (see Supplementary Fig. 3e); therefore, we assume isothermal\nconditions throughout this study without compromising the validity of the results.”\n[Please refer to our derivation below, reproduced from our response to Reviewer 3, comment 2. The\nresulting Supplementary Figure 3 and Supplementary Note are newly presented here in response to this\ncomment.]\nSupplementary Information page 6, line 86:\n“\nB. Isentropic actuation\nDuring isentropic actuation, the actuator deforms sufficiently fast to prevent any heat exchange\nwith the surroundings. Assuming ideal gas behavior, the equation of the state of the contained gas\ncan be described as\n𝑐\nγ γ p\n𝑝𝑉 = 𝑝 𝑉 (where γ= ) (22)\ngas 0 gas.0 𝑐\nv\nCombining equations (13), (18), and (22) leads to\nγ\n𝐹 α 𝑉\ngas.0\n𝑝 = 𝑝 + ( )= 𝑝 (23)\next 𝑤(𝐿 −𝑙 ) cosα 0 2\np e 𝑤(𝐿 p −𝑙 e ) α−sinαcosα\n( )−𝑉\n( 2 α2 liq )\nWith the calculated α(𝐹,Φ) from equation (19), equations (21) or (23) can be used to calculate 𝑙 as a\ne\nfunction of given external load F, voltage Φ, volume of liquid 𝑉 , external pressure 𝑝 , and in case of\nliq ext\nisothermal actuation, temperature 𝑇 .\next\n𝑙 = 𝑔(𝐹,Φ,𝑉 ,𝑝 ,(𝑇 ))\ne liq ext ext (24)\nEventually, equations (19) and (24) uniquely define the two independent geometric variables α and 𝑙 at\ne\nthe given actuation conditions; (α(𝐹,Φ), 𝑙 (𝐹,Φ,𝑉 ,𝑝 ,(𝑇 ))).\ne liq ext ext\n[The results shown below are newly presented]\nSupplementary Figure 3 with new panels with corresponding changes to the figure captions:\n“\nSupplementary Figure 3. Results of the analytical model of three-phase Peano-HASEL actuators.\na Schematic illustration and parameterization of the model. b Theoretically calculated volume of pouch\nand zipped length of the actuators, at 0% (fully liquid-filled) and 100% (fully gas-filled) gas-fill ratios,\nunder 8 kV voltage. The compressibility of the gas leads to pressure and volume changes of the gas\nduring actuation. c Pouch shape of actuators at 0% and 100% gas-fill at 8 kV voltage and 20 N force,\ndrawn based on calculations. Despite an increased gas pressure and a resulting reduction in gas volume,\nthe larger zipped length (l > l ) compensates for the compressed gas volume, yielding nearly\ne.gas e.liq\nidentical actuator lengths (l ≈ l ). d Force-strain curves of actuators with varying gas-fills, based on the\ngas liq\nanalytical model, assuming isothermal deformation. e Force-strain curves of 100% gas-filled actuators are\ncompared under both isothermal and isentropic processes.”\nSupplementary Information page 7, line 105: “Notably, isentropic deformation and isothermal\ndeformation lead to very similar force-strain curves compared to a reference actuator with 0% air-fill. In a\nreal application, the conditions will lie between the isothermal and isentropic extremes, which shows that\ncompressibility is negligible under the analyzed conditions.”\nReviewer 3, comment 5:\n“It would be beneficial to know if any force relaxation related to charge accumulation behavior was\nobserved during testing and whether the introduction of gas has any influence on such phenomena.”\nResponse:\nTo address this question, we performed actuation tests, during which we measured the actuation strain as\na function of time under constant voltage and constant force. We tested three actuators: a reference\nactuator with 0% air-fill and actuators with 70% air-fill in the best and worst orientations. All actuators\nmaintained a nearly constant amplitude over 600s; the air-filled actuators did not exhibit worse relaxation\ncompared to the reference actuator.\nThese results are added in the section Quasi-static performance, in a new Supplementary Figure 6a, and\nSupplementary Note as follows:\nMain text, page 7, line 161: “We tested the influence of air fill on force relaxation related to charge\naccumulation52. During prolonged actuation under constant voltage and force, the introduction of air had a\nnegligible effect on charge accumulation behavior (Supplementary Note, Supplementary Fig. 6a).”\nNew Supplementary Figure 6a and corresponding figure caption:\n“\nSupplementary Figure 6. Prolonged actuation at constant voltage and in cyclic actuation.\na Actuation strokes normalized by their initial strokes as a function of time, under constant voltage and\nforce. For all three cases, the normalized amplitude remained almost constant, indicating no negative\ninfluence from the presence of air.”\nSupplementary Information page 15, line 227:\n“Prolonged actuation at constant voltage\nTo test force relaxation related to charge accumulation6, we measured the actuation stroke of actuators\nunder constant voltage and force for 600 seconds. We compared an actuator with 0% air-fill (reference)\nwith actuators with 70% air-fill in the best and worst orientations. At t = 0, a constant voltage of 8 kV and\na constant force of 1 N were applied, using the high voltage amplifier and the dual-mode lever system\ndescribed in the Methods section in the main text (also see Supplementary Fig. 1). For all three cases, the\nnormalized amplitude—normalized with the initial stroke of each actuator—remained nearly constant\nover the duration of 600 seconds. After 600 seconds, the amplitudes of the 0% air-filled actuator\n(reference) and the 70% air-filled actuator in the best orientation dropped by 3.3% and 0.0004% from\ntheir initial amplitudes, respectively, while the 70% air-filled actuator in the worst orientation showed an\nincrease of 1.6%. These findings suggest that the introduction of air has a negligible influence on the\ncharge accumulation behavior.”\nReviewer 1\n“The paper maintains its novelty by adding the gas with high dielectric strength in response to the\nprevious comment. However, Figures 3, 4, and 5 remain unchanged. Considering the overall scenario,\nexperiments and considerations regarding gases with high dielectric strength should be added to ensure\nconsistency.”\nResponse:\nFollowing this constructive reviewer suggestion, we have performed additional experiments to elucidate\nthe influence of the high-dielectric-strength gas (HDSG; C F N/CO mixture) in the other experiments\n4 7 2\npresented in this study. Figures 3, 4, and 5 include: (i) actuation failures modeled by Paschen’s law\n(Figure 3), (ii) evaluation of dynamic performance (Figure 4), and (iii) demonstration of enhanced\nactuator performance in a jumping robot (Figure 5).\nSpecifically, we performed additional experiments, focusing on dynamic actuator performance. Under\nsinusoidal voltage input (± 6 kV), HDSG-filled actuators exhibited a broader bandwidth, maintaining their\namplitude at higher frequencies where the air-filled actuators exhibited reduced amplitude (i.e., below -3\ndB relative to their amplitude at 1 Hz). Under step voltage input (8 kV), however, the actuation threshold\nremained unchanged: both air-filled and HDSG-filled actuators operated stably up to 90% fill and failed\nbeyond 95% fill, resulting in similar peak specific power profiles. These results indicate that while the\nhigher dielectric strength of HDSG effectively mitigates breakdown during high-frequency cyclic\nactuation—where gas pressure and electrode gap distance vary with the voltage—it does not fully\nsuppress breakdown under rapid voltage changes where these internal parameters remain constant.\nGiven that the step-response performance of HDSG-filled actuators showed negligible improvement over\nair-filled ones, the performance of the jumping robot shown in Figure 5 does not substantially change\nwhen replacing air with HDSG.\nFigure 3, which focuses on identifying the fundamental performance limits, cannot be replicated using\nHDSG because no Paschen’s curve data (breakdown voltage across different pressure-distance values) are\navailable in the literature for this gas mixture, and generating such data lies beyond the scope of this\npaper. Nevertheless, the experiments conducted with air in the previous version sufficiently validated our\nkey hypothesis that actuator failure originates from dielectric breakdown in the gaseous phase.\nWe have incorporated the new experimental findings into the revised manuscript as Figure 7 within the\nsection High-dielectric-strength gas for enhanced performance in solid-liquid-gas architectures, and as\nSupplementary Figure 17, as shown below:\nMain text, new Figure 7:\n“\nFigure 7. Use of high-dielectric-strength gas (HDSG) enables actuators with improved bandwidth.\nNormalized amplitude of the actuators filled with air (dashed lines) and high-dielectric-strength gas\n(HDSG; solid lines). Actuators filled with the HDSG (C F N/CO gas mixture) exhibited increased\n4 7 2\nbandwidth compared to the actuators filled with the same amount of air. a In the best orientation,\nactuators filled with 60% HDSG achieved a bandwidth above 100 Hz, improved from 80 Hz of the 60%\nair-filled actuator. Similarly, 80% and 90% HDSG-filled actuators achieved improved bandwidths of 90\nHz and 70 Hz, compared to 40 Hz and 10 Hz for the corresponding air-filled actuators, respectively. b In\nthe worst orientation, actuators filled with 80% and 90% HDSG achieved bandwidths of 80 Hz and 20\nHz, improved from 10 Hz and 2 Hz for the corresponding air-filled actuators, respectively.\n”\nNew Supplementary Figure 17:\n“\nSupplementary Figure 17. Evaluation of actuator performance under step voltage input with high-\ndielectric-strength gas (HDSG). Peak strain rate, peak power, and peak specific power of actuators filled\nwith air (marked with crosses) and high-dielectric-strength gas (HDSG; marked with circles), when\nactuators are driven by a step voltage input. a In the best orientation, air-filled actuators exhibited stable\nperformance up to 90% air-fill, following the blue trend line obtained from the gas-dominant group (filled\nwith air) in the main text; actuation failed beyond 90% fill. The use of HDSG did not extend this\nthreshold. b In the worst orientation, HDSG-filled actuator showed stable actuation up to 40% fill, which\nwas not improved compared to the 60% of air-filled actuators. Error bars represent standard deviations for\nn ≥ 5 trials.\n”\nMain text, page 14, line 323: “To fill the actuators with HDSG, we used a glove box setup illustrated in\nSupplementary Fig. 16, to prevent contamination with ambient air (see Methods for details). With the\nmethod used for evaluating quasi-static performance as in Fig. 2 (see Methods for details), we showed\nthat HDSG-filled actuators achieved stable operation up to 98% gas-fill in the best orientation and up to\n80% in the worst orientation (Fig. 6b)—considerable improvements over the 90% and 70% thresholds\nobserved with air, respectively. Fig. 6c provides a direct comparison of the force-strain curves of air-filled\nand HDSG-filled actuators. As a result, the maximum specific energy increased to 51.4 J kg-1 at 98%\nHDSG-fill in the best orientation, and 30.0 J kg-1 at 95% HDSG-fill in the worst orientation (Fig. 6d).\nWe further evaluated the dynamic performance of HDSG-filled actuators using the same method used as\nin Fig. 4 (see Methods for details). As shown in Fig. 7, these actuators achieved broader bandwidths\nunder cyclic voltage inputs in both the best and worst orientations compared with actuators having\nidentical air-fill ratios. This improvement confirms that the use of HDSG successfully diminished the\nissue raised in the Dynamic performance section: at high actuation frequencies, dynamic splashing of the\nliquid dielectric reduces its local volume near the zipping front, leading to dielectric breakdown through\nair and lower performance. In contrast, actuator response to a step voltage input showed negligible\nimprovement over the air-filled version (Supplementary Fig. 17).”\nReviewer 2\n“The authors have addressed my previous concerns. The paper is recommended for publication.”\nResponse:\nWe appreciate the positive feedback on our revised manuscript.\nReviewer 3\nReviewer 3, general comment:\n“The authors have responded to most of the questions and provided a substantial amount of additional\nwork and experiments. In particular, the in-depth analysis of breakdown phenomena is a very valuable\naddition to the manuscript, enhancing both its novelty and impact. Moreover, the theoretical elaborations\nadequately address my previous comments. There are, however, a few aspects that could be considered in\na further minor revision”\nReviewer 3, comment 1:\n“Durability tests – Long-term durability tests have been conducted, achieving 100k cycles before\ndegradation. The authors should provide a critical discussion of this result, as it appears to represent a\nworsening compared to the durability previously obtained with other multilayer liquid/solid actuators\nproposed by their group and by other research teams.”\nResponse:\nWe thank the reviewer for raising this important point, as we might not have been clear enough in\ndescribing our experimental results regarding durability of gas filled actuators. All the actuators we tested\nsurvived 100k cycles without failure; we only observed a decay of actuator strains starting at cycle\nnumbers beyond 1k, which we attribute to charge retention effects [R1] stemming from the use of single\npolarity signals in these tests. Importantly, the actuator without any gas filling exhibited a very similar\ndecay of actuation strain with frequency, indicating that the use of gas filling does not substantially\nchange durability of actuators up to 100k cycles. Systematic testing of actuator lifetime, including proper\nstatistics, is a very time-consuming undertaking, and beyond the scope of this paper.\nTo clarify the above points, we edited a paragraph in the section Dynamic performance in the main text.\n[R1] I.-D. Sîrbu et al., Electrostatic actuators with constant force at low power loss using matched\ndielectrics, Nat. Electron., 6, 888-899, 2023\nMain text, page 13, line 294: “We assessed the long-term durability of the actuators through 100,000-\ncycle tests. All tested actuators survived 100,000 cycles without failure; we only observed a decay of\nactuator strains starting at cycle numbers beyond 1,000, which we attribute to charge retention effects52\nstemming from the use of single polarity signals in these tests. Importantly, the actuator without any gas\nfilling exhibited a very similar decay of actuation strain over cycles, indicating that the use of gas filling\ndoes not substantially change durability of actuators up to 100,000 cycles (see Supplementary Fig. 6b and\nSupplementary Note).”\nReviewer 3, comment 2:\n“Bandwidth testing – I am moderately skeptical about the bandwidth tests. It is difficult to explain why an\nincrease in amplitude is observed in most cases. For example, actuators with 0% air show an\namplification of almost 6 dB at 40 Hz. Could this not be attributable to a structural resonance due to the\nmass of the attached frame? Wouldn’t this compromise the evaluation of the actual bandwidth of the\nactuation system?”\nResponse:\nWe thank the reviewer for this thoughtful observation regarding the amplitude increase, peaking around\nof the liquid within the pouch—an intrinsic dynamic characteristic of electrohydraulic actuators—rather\nthan from structural resonance of the test setup. We first carefully analyzed all possible resonance modes\nof the test setup, and concluded that all resonance modes would occur at frequencies far away from the\nfrequency for which we observed amplitude increase (peaking at 40 Hz). We then further experimentally\ncharacterized the dynamics of the actuator, following the approach of Rothemund et al. [R1]. We\nmeasured the rise time (t = 0.016 s; the time to reach the overshoot displacement) and fall time (t\nr.overshoot f\n= 0.017 s) under 6 kV step voltage input and 100 g of external loading. These times are comparable to\nhalf the period of 30 Hz (T/2 = 0.0167 s), suggesting that the transient movement of the liquid becomes\nsynchronized with the driving frequency of the actuator for frequencies around 30 Hz, amplifying\ndisplacement amplitude. This explanation is consistent with the observation that this amplification effect\nis reduced when air is introduced—more turbulent liquid motion disrupts the in-phase motion.\nThese new findings are added in the section Dynamic performance in the main text, and as\nSupplementary Figure 14.\n[R1] P. Rothemund et al., Dynamics of electrohydraulic soft actuators, Proc. Natl. Acad. Scid. USA, 117,\n16207-16213, 2020\nNew Supplementary Figure 14:\n“\nSupplementary Figure 14. Evaluation of rising and falling responses of the actuators when driven\nwith square wave voltage signals. a Step voltage input (6 kV) lasting for 1 s and the corresponding\nactuator displacement, with the rising and falling responses shown in b and c, respectively. b Rising\nresponse of the actuator. The time to reach the overshoot displacement is t = 0.016 s. c Falling\nr.overshoot\nresponse of the actuator when the voltage is turned off. The time to return to the initial position is t =\nfalling\n0.017 s. These rising and falling times correspond to half the period of 30 Hz (T/2 = 0.0167 s).\n”\nMain text, page 12, line 280:\n“The amplitude of the 0% air-filled reference actuator increases with frequency, peaking around 40 Hz.\nWe found that this behavior is related to the internal motion of the liquid within the pouch—an intrinsic\ndynamic characteristic of electrohydraulic actuators; for frequencies around 30 Hz the motion of the\nliquid dielectric inside the pouch becomes synchronized with the driving frequency of the actuator,\namplifying displacement; for details see Supplementary Fig. 14.”\nReviewer 3, comment 3:\n“Use of C₄F₇N gas – The additional tests employing C₄F₇N gas are quite interesting. I would encourage\nthe authors to comment on the possible toxicity of this gas, and whether they see any limitations in its use\nfor their actuators, or conversely, if they consider it to be perfectly safe under all conditions without\nspecial precautions.”\nResponse:\nWe thank the reviewer for this useful suggestion. The safety of C F N (commercially known as NovecTM\n4 7\n4710, 3MTM) has been well studied [R1], and detailed safety information is available in the\nmanufacturer’s Safety Data Sheet [R2]. According to these sources, C F N is not classified as a CMR\n4 7\nsubstance (carcinogenicity, mutagenicity, reproductive toxicity) and exhibits low acute inhalation toxicity\n(4-h LC > 10,000 ppm, GHS classification of Category 4 or higher).\nin a controlled environment—such as a well-ventilated area or fume hood—the risks after being sealed\nare minimal. However, caution is required if actuator breakdown occurs, as localized arcing may produce\ntoxic decomposition byproducts (e.g., CO, CO , HF). Appropriate precautions should therefore be taken\n2\nduring disposal or in the event of electrical failure.\nA brief discussion summarizing these considerations has been added to the Discussion section as below.\n[R1] J. Owens et al., Recent development of two alternative gases to SF6 for high voltage electrical\npower applications, Energies, 14(16), 5051, 2021\n[R2] Safety Data Sheet, 3M™ Novec™ 4710 Insulating Gas; 3M Company: St. Paul, MN, USA, 2019\nMain text, page 17, line 389:\n“C F N (also known as NovecTM 4710, 3MTM) exhibits low acute inhalation toxicity (4-h LC > 10,000\n4 7 50\nppm) and is not classified as carcinogenic, mutagenic, or reprotoxic56,61. Since the gas remains sealed\nwithin the actuator pouch, normal operation poses minimal risk when fabrication is performed in a well-\nventilated area or fume hood. However, electrical breakdown can generate toxic decomposition\nbyproducts (e.g., CO, CO , HF), so appropriate precautions are required during disposal or in the event of\n2\nactuator failure.”"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The paper maintains its novelty by adding the gas with high dielectric strength in response to the previous comment. However, Figures 3, 4, and 5 remain unchanged. Considering the overall scenario, experiments and considerations regarding gases with high dielectric strength should be added to ensure consistency.", "reviewer_2": "The authors have addressed my previous concerns. The paper is recommended for publication.", "reviewer_3": "The authors have responded to most of the questions and provided a substantial amount of additional work and experiments. In particular, the in-depth analysis of breakdown phenomena is a very valuable addition to the manuscript, enhancing both its novelty and impact. Moreover, the theoretical elaborations adequately address my previous comments. There are, however, a few aspects that could be considered in a further minor revision:\n1) Durability tests – Long-term durability tests have been conducted, achieving 100k cycles before degradation. The authors should provide a critical discussion of this result, as it appears to represent a worsening compared to the durability previously obtained with other multilayer liquid/solid actuators proposed by their group and by other research teams.\n2) Bandwidth testing – I am moderately skeptical about the bandwidth tests. It is difficult to explain why an increase in amplitude is observed in most cases. For example, actuators with 0% air show an amplification of almost 6 dB at 40 Hz. Could this not be attributable to a structural resonance due to the mass of the attached frame? Wouldn’t this compromise the evaluation of the actual bandwidth of the actuation system?\n3) Use of C₄F₇N gas – The additional tests employing C₄F₇N gas are quite interesting. I would encourage the authors to comment on the possible toxicity of this gas, and whether they see any limitations in its use for their actuators, or conversely, if they consider it to be perfectly safe under all conditions without special precautions."}, "author_response": "Reviewer 1\n“The paper maintains its novelty by adding the gas with high dielectric strength in response to the\nprevious comment. However, Figures 3, 4, and 5 remain unchanged. Considering the overall scenario,\nexperiments and considerations regarding gases with high dielectric strength should be added to ensure\nconsistency.”\nResponse:\nFollowing this constructive reviewer suggestion, we have performed additional experiments to elucidate\nthe influence of the high-dielectric-strength gas (HDSG; C F N/CO mixture) in the other experiments\n4 7 2\npresented in this study. Figures 3, 4, and 5 include: (i) actuation failures modeled by Paschen’s law\n(Figure 3), (ii) evaluation of dynamic performance (Figure 4), and (iii) demonstration of enhanced\nactuator performance in a jumping robot (Figure 5).\nSpecifically, we performed additional experiments, focusing on dynamic actuator performance. Under\nsinusoidal voltage input (± 6 kV), HDSG-filled actuators exhibited a broader bandwidth, maintaining their\namplitude at higher frequencies where the air-filled actuators exhibited reduced amplitude (i.e., below -3\ndB relative to their amplitude at 1 Hz). Under step voltage input (8 kV), however, the actuation threshold\nremained unchanged: both air-filled and HDSG-filled actuators operated stably up to 90% fill and failed\nbeyond 95% fill, resulting in similar peak specific power profiles. These results indicate that while the\nhigher dielectric strength of HDSG effectively mitigates breakdown during high-frequency cyclic\nactuation—where gas pressure and electrode gap distance vary with the voltage—it does not fully\nsuppress breakdown under rapid voltage changes where these internal parameters remain constant.\nGiven that the step-response performance of HDSG-filled actuators showed negligible improvement over\nair-filled ones, the performance of the jumping robot shown in Figure 5 does not substantially change\nwhen replacing air with HDSG.\nFigure 3, which focuses on identifying the fundamental performance limits, cannot be replicated using\nHDSG because no Paschen’s curve data (breakdown voltage across different pressure-distance values) are\navailable in the literature for this gas mixture, and generating such data lies beyond the scope of this\npaper. Nevertheless, the experiments conducted with air in the previous version sufficiently validated our\nkey hypothesis that actuator failure originates from dielectric breakdown in the gaseous phase.\nWe have incorporated the new experimental findings into the revised manuscript as Figure 7 within the\nsection High-dielectric-strength gas for enhanced performance in solid-liquid-gas architectures, and as\nSupplementary Figure 17, as shown below:\nMain text, new Figure 7:\n“\nFigure 7. Use of high-dielectric-strength gas (HDSG) enables actuators with improved bandwidth.\nNormalized amplitude of the actuators filled with air (dashed lines) and high-dielectric-strength gas\n(HDSG; solid lines). Actuators filled with the HDSG (C F N/CO gas mixture) exhibited increased\n4 7 2\nbandwidth compared to the actuators filled with the same amount of air. a In the best orientation,\nactuators filled with 60% HDSG achieved a bandwidth above 100 Hz, improved from 80 Hz of the 60%\nair-filled actuator. Similarly, 80% and 90% HDSG-filled actuators achieved improved bandwidths of 90\nHz and 70 Hz, compared to 40 Hz and 10 Hz for the corresponding air-filled actuators, respectively. b In\nthe worst orientation, actuators filled with 80% and 90% HDSG achieved bandwidths of 80 Hz and 20\nHz, improved from 10 Hz and 2 Hz for the corresponding air-filled actuators, respectively.\n”\nNew Supplementary Figure 17:\n“\nSupplementary Figure 17. Evaluation of actuator performance under step voltage input with high-\ndielectric-strength gas (HDSG). Peak strain rate, peak power, and peak specific power of actuators filled\nwith air (marked with crosses) and high-dielectric-strength gas (HDSG; marked with circles), when\nactuators are driven by a step voltage input. a In the best orientation, air-filled actuators exhibited stable\nperformance up to 90% air-fill, following the blue trend line obtained from the gas-dominant group (filled\nwith air) in the main text; actuation failed beyond 90% fill. The use of HDSG did not extend this\nthreshold. b In the worst orientation, HDSG-filled actuator showed stable actuation up to 40% fill, which\nwas not improved compared to the 60% of air-filled actuators. Error bars represent standard deviations for\nn ≥ 5 trials.\n”\nMain text, page 14, line 323: “To fill the actuators with HDSG, we used a glove box setup illustrated in\nSupplementary Fig. 16, to prevent contamination with ambient air (see Methods for details). With the\nmethod used for evaluating quasi-static performance as in Fig. 2 (see Methods for details), we showed\nthat HDSG-filled actuators achieved stable operation up to 98% gas-fill in the best orientation and up to\n80% in the worst orientation (Fig. 6b)—considerable improvements over the 90% and 70% thresholds\nobserved with air, respectively. Fig. 6c provides a direct comparison of the force-strain curves of air-filled\nand HDSG-filled actuators. As a result, the maximum specific energy increased to 51.4 J kg-1 at 98%\nHDSG-fill in the best orientation, and 30.0 J kg-1 at 95% HDSG-fill in the worst orientation (Fig. 6d).\nWe further evaluated the dynamic performance of HDSG-filled actuators using the same method used as\nin Fig. 4 (see Methods for details). As shown in Fig. 7, these actuators achieved broader bandwidths\nunder cyclic voltage inputs in both the best and worst orientations compared with actuators having\nidentical air-fill ratios. This improvement confirms that the use of HDSG successfully diminished the\nissue raised in the Dynamic performance section: at high actuation frequencies, dynamic splashing of the\nliquid dielectric reduces its local volume near the zipping front, leading to dielectric breakdown through\nair and lower performance. In contrast, actuator response to a step voltage input showed negligible\nimprovement over the air-filled version (Supplementary Fig. 17).”\nReviewer 2\n“The authors have addressed my previous concerns. The paper is recommended for publication.”\nResponse:\nWe appreciate the positive feedback on our revised manuscript.\nReviewer 3\nReviewer 3, general comment:\n“The authors have responded to most of the questions and provided a substantial amount of additional\nwork and experiments. In particular, the in-depth analysis of breakdown phenomena is a very valuable\naddition to the manuscript, enhancing both its novelty and impact. Moreover, the theoretical elaborations\nadequately address my previous comments. There are, however, a few aspects that could be considered in\na further minor revision”\nReviewer 3, comment 1:\n“Durability tests – Long-term durability tests have been conducted, achieving 100k cycles before\ndegradation. The authors should provide a critical discussion of this result, as it appears to represent a\nworsening compared to the durability previously obtained with other multilayer liquid/solid actuators\nproposed by their group and by other research teams.”\nResponse:\nWe thank the reviewer for raising this important point, as we might not have been clear enough in\ndescribing our experimental results regarding durability of gas filled actuators. All the actuators we tested\nsurvived 100k cycles without failure; we only observed a decay of actuator strains starting at cycle\nnumbers beyond 1k, which we attribute to charge retention effects [R1] stemming from the use of single\npolarity signals in these tests. Importantly, the actuator without any gas filling exhibited a very similar\ndecay of actuation strain with frequency, indicating that the use of gas filling does not substantially\nchange durability of actuators up to 100k cycles. Systematic testing of actuator lifetime, including proper\nstatistics, is a very time-consuming undertaking, and beyond the scope of this paper.\nTo clarify the above points, we edited a paragraph in the section Dynamic performance in the main text.\n[R1] I.-D. Sîrbu et al., Electrostatic actuators with constant force at low power loss using matched\ndielectrics, Nat. Electron., 6, 888-899, 2023\nMain text, page 13, line 294: “We assessed the long-term durability of the actuators through 100,000-\ncycle tests. All tested actuators survived 100,000 cycles without failure; we only observed a decay of\nactuator strains starting at cycle numbers beyond 1,000, which we attribute to charge retention effects52\nstemming from the use of single polarity signals in these tests. Importantly, the actuator without any gas\nfilling exhibited a very similar decay of actuation strain over cycles, indicating that the use of gas filling\ndoes not substantially change durability of actuators up to 100,000 cycles (see Supplementary Fig. 6b and\nSupplementary Note).”\nReviewer 3, comment 2:\n“Bandwidth testing – I am moderately skeptical about the bandwidth tests. It is difficult to explain why an\nincrease in amplitude is observed in most cases. For example, actuators with 0% air show an\namplification of almost 6 dB at 40 Hz. Could this not be attributable to a structural resonance due to the\nmass of the attached frame? Wouldn’t this compromise the evaluation of the actual bandwidth of the\nactuation system?”\nResponse:\nWe thank the reviewer for this thoughtful observation regarding the amplitude increase, peaking around\nof the liquid within the pouch—an intrinsic dynamic characteristic of electrohydraulic actuators—rather\nthan from structural resonance of the test setup. We first carefully analyzed all possible resonance modes\nof the test setup, and concluded that all resonance modes would occur at frequencies far away from the\nfrequency for which we observed amplitude increase (peaking at 40 Hz). We then further experimentally\ncharacterized the dynamics of the actuator, following the approach of Rothemund et al. [R1]. We\nmeasured the rise time (t = 0.016 s; the time to reach the overshoot displacement) and fall time (t\nr.overshoot f\n= 0.017 s) under 6 kV step voltage input and 100 g of external loading. These times are comparable to\nhalf the period of 30 Hz (T/2 = 0.0167 s), suggesting that the transient movement of the liquid becomes\nsynchronized with the driving frequency of the actuator for frequencies around 30 Hz, amplifying\ndisplacement amplitude. This explanation is consistent with the observation that this amplification effect\nis reduced when air is introduced—more turbulent liquid motion disrupts the in-phase motion.\nThese new findings are added in the section Dynamic performance in the main text, and as\nSupplementary Figure 14.\n[R1] P. Rothemund et al., Dynamics of electrohydraulic soft actuators, Proc. Natl. Acad. Scid. USA, 117,\n16207-16213, 2020\nNew Supplementary Figure 14:\n“\nSupplementary Figure 14. Evaluation of rising and falling responses of the actuators when driven\nwith square wave voltage signals. a Step voltage input (6 kV) lasting for 1 s and the corresponding\nactuator displacement, with the rising and falling responses shown in b and c, respectively. b Rising\nresponse of the actuator. The time to reach the overshoot displacement is t = 0.016 s. c Falling\nr.overshoot\nresponse of the actuator when the voltage is turned off. The time to return to the initial position is t =\nfalling\n0.017 s. These rising and falling times correspond to half the period of 30 Hz (T/2 = 0.0167 s).\n”\nMain text, page 12, line 280:\n“The amplitude of the 0% air-filled reference actuator increases with frequency, peaking around 40 Hz.\nWe found that this behavior is related to the internal motion of the liquid within the pouch—an intrinsic\ndynamic characteristic of electrohydraulic actuators; for frequencies around 30 Hz the motion of the\nliquid dielectric inside the pouch becomes synchronized with the driving frequency of the actuator,\namplifying displacement; for details see Supplementary Fig. 14.”\nReviewer 3, comment 3:\n“Use of C₄F₇N gas – The additional tests employing C₄F₇N gas are quite interesting. I would encourage\nthe authors to comment on the possible toxicity of this gas, and whether they see any limitations in its use\nfor their actuators, or conversely, if they consider it to be perfectly safe under all conditions without\nspecial precautions.”\nResponse:\nWe thank the reviewer for this useful suggestion. The safety of C F N (commercially known as NovecTM\n4 7\n4710, 3MTM) has been well studied [R1], and detailed safety information is available in the\nmanufacturer’s Safety Data Sheet [R2]. According to these sources, C F N is not classified as a CMR\n4 7\nsubstance (carcinogenicity, mutagenicity, reproductive toxicity) and exhibits low acute inhalation toxicity\n(4-h LC > 10,000 ppm, GHS classification of Category 4 or higher).\nin a controlled environment—such as a well-ventilated area or fume hood—the risks after being sealed\nare minimal. However, caution is required if actuator breakdown occurs, as localized arcing may produce\ntoxic decomposition byproducts (e.g., CO, CO , HF). Appropriate precautions should therefore be taken\n2\nduring disposal or in the event of electrical failure.\nA brief discussion summarizing these considerations has been added to the Discussion section as below.\n[R1] J. Owens et al., Recent development of two alternative gases to SF6 for high voltage electrical\npower applications, Energies, 14(16), 5051, 2021\n[R2] Safety Data Sheet, 3M™ Novec™ 4710 Insulating Gas; 3M Company: St. Paul, MN, USA, 2019\nMain text, page 17, line 389:\n“C F N (also known as NovecTM 4710, 3MTM) exhibits low acute inhalation toxicity (4-h LC > 10,000\n4 7 50\nppm) and is not classified as carcinogenic, mutagenic, or reprotoxic56,61. Since the gas remains sealed\nwithin the actuator pouch, normal operation poses minimal risk when fabrication is performed in a well-\nventilated area or fume hood. However, electrical breakdown can generate toxic decomposition\nbyproducts (e.g., CO, CO , HF), so appropriate precautions are required during disposal or in the event of\n2\nactuator failure.”"}, {"round": 3, "reviewer_comments": {"reviewer_1": "The paper is well revised and should be published.", "reviewer_3": "I confirm the authors have addressed my initial concerns and the manuscript is eligible for publication."}, "author_response": ""}]

Decision letter