Introduction

Soft robots, made of intrinsically soft and extensible materials, exhibit unprecedented adaptation, sensitivity, and agility due to their continuously deformable structure with muscle-like actuation. Thus, they possess huge potential applications in numerous fields, including minimally invasive medical treatments, lab-on-chips, and search-and-rescue missions1,2,3. As the core component of soft robots, actuators are required to generate an appropriate deformation to assume the desired postures and a sufficient output force to complete the desired action, such as grasping, supporting tools, and transporting objects4,5,6. However, it is an enormous challenge for a single material to simultaneously possess large deformations and high output force, arising from the inherent conflict between large strain and high stiffness from the mechanical perspective. Traditional materials involving ferroelectric ceramics or crystals can generate a sufficient output force due to their intrinsic high stiffness7,8. While the associated minute deformation and excessive rigidity seriously limit their applications in soft robots. Thus, a method for fabricating discontinuous ceramic sheets or fibers embedded in epoxy resin to form a macro-fiber composite (MFC) has been proposed to improve the deformability of such ceramics9. Unfortunately, the deformation of MFC actuators is still limited to micrometer levels, severely restricting their versatility in applications.

On the other hand, flexible polymers, such as electronic electroactive polymers, which include typical Poly(vinylidene fluoride) (PVDF)-based ferroelectric polymer10,11, and dielectric elastomers (DEs)12, have emerged as promising candidates for soft actuators. Since their advantages include lightweight, fast response, and deformability, they can be easily formed into any arbitrary shape. Nevertheless, large deformation in these polymers is only obtained near the breakdown electric field, where disastrous failure may occur. To ensure long-term reliability and safety, bulky monomer units such as chlorotrifluoroethylene (CTFE)13, chlorofluoroethylene14, and double bond15 have been introduced into the polymer chain. These relaxor ferroelectric polymers exhibit higher dielectric constant and actuation strain in comparison with typical ferroelectric polymers, such as Poly(vinylidene fluoride–trifluoroethylene) (P(VDF-TrFE)), as shown in Supplementary Table 1. And the modulus of the terpolymers is further decreased by 23%–93% relative to the copolymers16, which leads to the decreased output force. Also, the reported DEs17 with promising actuation performance (22.27% at 35 V/μm) exhibit a reduced modulus (from 2.78 to 1.14 MPa). However, low modulus reduces mechanical strength, which will trigger electromechanical instability and sudden “snap-through deformation”, increasing breakdown risk. Therefore, DEs are usually pre-stretched to prevent the mechanical instability18,19. Furthermore, the restricted output force for the DEs resulting from low modulus cannot be ignored. Overall, to expand their application, eEAP actuators with large actuation deformation have to overcome the limitation of their low output force.

To endow the current flexible eEAP actuators with a sufficient output force, nanocomposites modified by inorganic nanoparticles, such as ceramic or conductive nanofillers, were promoted20,21,22. Although polymer-based nanocomposites with high contents of nanofillers show an enhanced modulus, the large mismatch in the electric properties between the inorganic nanofillers and the organic matrix leads to the concentrated electric field in the polymer, increasing the probability of electric breakdown. Additionally, the generation of a high actuation stress is usually accompanied by a sacrificial strain. For example, the modulus of Poly-dimethylsiloxane using 40 wt% BaTiO3 fillers was enhanced from 0.673 to 1.44 MPa, while its breakdown strength decreased from 90.3 to 72.4 V/μm, and its thickness strain decreased from 30.8 to 16.7%22. Thus, the generation of high stiffness in nanocomposites is usually accompanied by a reduced strain. To date, few effective methods could achieve the concurrent optimization of the deformability and rigidity of eEAP actuators.

Here, the conflict between large deformability and high rigidity has been resolved through a novel strategy, which consists of modulating the orientations of the Al2O3@CNTs in P(VDF-TrFE-CTFE) (denoted as RT-TS) matrix via an electric field. Additionally, the nanocomposite polymer-based actuators were utilized to design soft robots inspired by inchworms and frogs, as shown in Fig. 1a. The nanocomposite with 1.1 wt% horizontally aligned Al2O3@CNTs exhibits 473% higher thickness strain than pure RT-TS at 30 V/μm. This enhancement arises from the concurrent contributions of Maxwell strain and amplified electrostrictive effects. Accordingly, the as-prepared nanocomposite actuator beam exhibits a bending angle of up to 215° at about 30 V/μm, while the actuator made by pure RT-TS membrane can only undergo an ignorable deformation. Simultaneously, the local stiffness of the nanocomposites is significantly enhanced by the horizontally aligned Al2O3@CNTs through the face-enhanced effect. As a result, the output force (4.7 mN at 30 V/μm) of the nanocomposite actuator is ~330% higher than that of pure RT-TS (1.1 mN at 78 V/μm). In turn, an ultra-high crawling speed of 24.0 mm/s (1.0 body length/s) for a frog-inspired soft robot under a low driving field of 25 V/μm is successfully realized utilizing the prepared nanocomposite actuator. Benefitting from the high output force, the soft robots made by the designed nanocomposite actuators demonstrate remarkable capabilities, including climbing slopes up to 52° or carrying loads equivalent to 8 times their body mass and 112 times the mass of the EAP actuator. This strategy of concurrently boosting the deformability and rigidity of the nanocomposite membrane offers a feasible and effective modulating method to optimize the performance of EAP actuators. It also promotes the development of soft actuators in the fields of biotechnology, medical technology, precision instruments, and so on.

Fig. 1: Preparation and characterization of the nanocomposites with aligned Al2O3@CNTs.
figure 1

a Schematic illustration of our soft robotic systems, which can perform climbing and load-carrying. b The schematic diagram of fabricating the nanocomposites with vertically and horizontally aligned Al2O3@CNTs to the surface via applying an electric field. The top inset in (b) is the SEM image of the cross-section for the R-RT-TS sample. The inset at the bottom in (b) is the TEM image of the Al2O3@CNTs. The thickness of Al2O3 is about 5 nm. c, d The SEM images of the cross-section for the nanocomposites with vertically (c) and horizontally (d) aligned Al2O3@CNTs. e, f Raman shifts of the G-band at 1588 cm−1 of V-RT-TS (e) and H-RT-TS (f) membrane for the azimuthal angle of 0° and 90°, respectively. g, h XRD patterns (g) and the calculated crystallinity based on the XRD patterns (h) of the nanocomposites with different concentrations and orientations of Al2O3@CNTs.

Full size image

Results

Preparation and characterization of the nanocomposites with aligned Al2O3@CNTs

Utilizing atomic layer deposition (ALD) technique, an ultrathin Al2O3 insulating layer with a thickness of 5 nm was deposited onto the surfaces of the CNTs to form core‑shell structured nanofillers, as described in our previous works23,24,25 and visually represented in the inset of Fig. 1b. The core-shell Al2O3@CNT was beneficial to achieve a high dielectric constant and stable breakdown strength in the nanocomposites, simultaneously. However, the output force of the soft actuator has not been investigated. In fact, it remains underexplored for the EAP actuator up to now, though it determines whether the actuator can realize the desired postures in soft robots. In this work, we employ the electric-field-assisted tape-casting method (Fig. 1b) to adjust the orientation of Al₂O₃@CNTs, aiming at simultaneously tailoring the dielectric and mechanical properties of the nanocomposites.

Here, the as-prepared membranes with different orientations of the Al2O3@CNTs (random, vertical, and horizontal to the surface of the nanocomposite membrane) are denoted as Rx-RT-TS, Vx-RT-TS, and Hx-RT-TS, respectively, where x represents the concentration of the Al2O3@CNTs. The randomly distributed Al2O3@CNTs can be observed in the cross-section image of the R-RT-TS sample, as shown in the inset of Fig. 1b. The cross-section morphologies of the nanocomposites with vertically and horizontally aligned Al2O3@CNTs are shown in Fig. 1c, d, respectively. The preferred orientation of the Al2O3@CNTs under an external electric field can be explained by the spontaneous movement of the Al2O3@CNTs from dipole-dipole interactions, caused by the transient polarization under alternating current (AC) and the charges concentrated between the nanofillers and the polymer matrix26,27,28.

To further verify the orientation of the Al2O3@CNTs in the polymer, polarized Raman spectroscopy of the nanocomposites at different azimuthal angles was conducted, where the angle corresponding to the aligned direction of the Al2O3@CNTs is defined as 0°. Generally, a stronger intensity of the Raman shift indicates a higher-ordered arrangement of Al2O3@CNTs along the direction of the beam’s polarization29. As shown in Fig. 1e, f, the intensity of Raman shift of the nanofillers’ G-band was measured at the azimuthal angle of 0° and 90° for V-RT-TS and H-RT-TS membranes, respectively. The intensity of the G-band at 1588 cm−1 for V-RT-TS and H-RT-TS at the azimuthal angle of 0° is ~62% and ~55% higher than that at the azimuthal angle of 90°, respectively, confirming the preferred orientation of the Al2O3@CNTs along the direction of the applied electric field30.

To study the effect of the nanofillers’ orientation and the applied electric field on the crystal structure of the nanocomposites, X-ray diffraction (XRD) patterns of the nanocomposites were measured and shown in Fig. 1g. The characteristic peak of the γ phase can be distinguished at about 18°, revealing the dominant relaxor ferroelectric phase of the RT-TS matrix. The peak areas for the different phases are obtained using the polynomial fitting method and shown in Supplementary Fig. 1. The calculated crystallinities of the different samples are shown in Fig. 1h. It can be observed that the overall crystallinity of the nanocomposites shows a slight increase with the increased Al2O3@CNTs concentration. Moreover, as shown in Supplementary Fig. 1, the diffraction peak shifts from 18.26° for pure RT-TS to 18.42° for V1.1-RT-TS, indicating a slight transition from the γ phase to the β phase.

Electromechanical properties

Considering safety and practicality, this work mainly focuses on the electromechanical behavior of the nanocomposites stimulated by electric fields below 100 V/μm. The thickness strain of the nanocomposite membrane was measured and shown in Supplementary Fig. 2. Under the same electric field, all of the samples modified by Al2O3@CNTs achieve a higher thickness strain than pure RT-TS, and the thickness strain of the nanocomposites increases with increasing nanofiller concentration. Among these nanocomposites, the V-RT-TS sample exhibits the highest thickness strain under low driving field. For example, under 30 V/μm, the thickness strain of the V1.1-RT-TS sample is 814% higher than that of pure RT-TS, as shown in Fig. 2a. The H-RT-TS and R-RT-TS samples show similar thickness strain performance. For instance, the thickness strain of the H1.1-RT-TS and R1.1-RT-TS samples is 473% and 478% higher than that of pure RT-TS at 30 V/μm, respectively. Except for the V1.1-RT-TS sample, the driving field of the other nanocomposites can reach up to 90 V/μm. It is related to the orientation of the Al2O3@CNTs in the nanocomposites. To understand the underlying mechanisms, the induced strain is expressed by the following equations13,24,31:

$${S}_{M}=\frac{(1+2\nu ){\varepsilon }_{0}{\varepsilon }_{r}}{2Y}{E}^{2}$$
(1)
$${S}_{E}=Q{P}^{2}$$
(2)

where SM is the Maxwell strain, SE is the electrostrictive strain, ν is Poisson’s ratio, Y is the elastic modulus, ε0 is the vacuum permittivity, εr is the dielectric constant of the nanocomposites, E is the applied electric field, Q is the electrostrictive coefficient, and P is the polarization under the electric field.

Fig. 2: The thickness strain, electric properties, and mechanical properties of the nanocomposites with different concentrations and orientations of Al2O3@CNTs.
figure 2

a The thickness strains under 30 V/μm and 90 V/μm of the nanocomposites with different concentrations and orientations of Al2O3@CNTs. b, c The dielectric properties (b) and the breakdown strength (c) of the nanocomposites with different concentrations and orientations of Al2O3@CNTs. The error bars in (c) represent the standard deviation obtained from at least nine measurements using different samples. d The simulated distribution of the electric field of the nanocomposites with vertically and horizontally aligned Al2O3@CNTs. e The ratios of εr to Y of the nanocomposites with different concentrations and orientations of Al2O3@CNTs. The error bars in (e) represent the standard deviation obtained from at least six measurements using different samples. f P-E loops of different nanocomposites. g The simulated polarization distribution of the nanocomposites with vertically and horizontally aligned Al2O3@CNTs. The color charts represent the variation of the electric field and polarization in the nanocomposites (for d and g). h Out-of-plane PFM amplitude and phase images of selected regions in V1.1-RT-TS sample. The DC modulation voltages of ± 45 V were applied for (h). i The amplitude and the phase hysteresis loops at various positions around the Al2O3@CNTs. The inset for i shows the morphology of the nanocomposite region with the marked measured points (3, 6, 9, 10, 11) and the height curves of the sample in different x-axis positions.

Full size image

Based on Eq. (1), the εr and Y are important factors affecting the Maxwell strain. Thus, the effects of the orientations of the Al2O3@CNTs on the dielectric properties of the nanocomposites were first systematically investigated. As shown in Fig. 2b, the εr of the samples modified by Al2O3@CNTs is larger than that of pure RT-TS and increases with increased Al2O3@CNTs concentration. It is attributed to the formation of micro-capacitors and the enhancement of interfacial polarization in the nanocomposite membranes32. Although the εr of the H-RT-TS sample is similar to that of the R-RT-TS sample, the dielectric loss of the H-RT-TS sample is successfully decreased. That is because the horizontally aligned Al2O3@CNTs can efficiently block the formation of conductive paths33. In contrast, the εr of the V-RT-TS sample is apparently higher than that of the R-RT-TS sample; however, the V-RT-TS sample also possesses the largest dielectric loss. Because the vertically aligned Al2O3@CNTs are more easily connected to form the conductive pathway, leading to higher conductive loss34,35. Thus, the average Eb values of V-RT-TS are the lowest among the other nanocomposites modified by Al2O3@CNTs, as shown in Fig. 2c. For example, the Eb are 135, 129, and 98 V/μm for H1.1-RT-TS, R1.1-RT-TS, and V1.1-RT-TS samples, respectively. It is further investigated by the simulated results in Fig. 2d and Supplementary Fig. 3a. The V-RT-TS sample exhibits the highest local electric field strength (953 V/μm), which increases the failure probability during the electrical treeing process, thereby reducing the Eb. In contrast, the enhanced Eb of the H-RT-TS sample is related to the lower local electric field strength (211 V/μm), resulting in an extended pathway of electrical trees33,36. In this work, we mainly investigate the nanocomposites with concentration within 1.1 wt%. Because the higher concentration of the nanofillers than 1.1 wt% results in continuously increased interfacial charges and further declined Eb. For example, the Eb of the R1.4-RT-TS rapidly decreases to 51 V/µm, as shown in Fig. 2c, which restricts the deformation and increases the probability of breakdown failure for the nanocomposites in practical applications.

Subsequently, the Y of the various nanocomposites was measured and is shown in Supplementary Fig. 4. The Y of the samples modified by Al2O3@CNTs is larger than that of pure RT-TS. And it increases with increasing Al2O3@CNTs concentration, due to the much higher elastic modulus of the inorganic fillers than that of the polymer matrix37,38. The orientation of the Al2O3@CNTs has a minor impact on the Y of the nanocomposites, attributed to the low content of the Al2O3@CNTs. The ratios of εr to Y of the various nanocomposites are calculated and presented in Fig. 2e. It can be observed that the enhancement in εr is more pronounced than the increase in Y. As a result, the εr/Y ratios of the R-RT-TS, V-RT-TS, and H-RT-TS samples are higher than that of the pure polymer, giving rise to a higher Maxwell strain. And, the V1.1-RT-TS membrane exhibits the highest value of εr/Y.

In addition to the Maxwell strain, the electrostrictive strain is another important contribution to the total thickness strain. According to Eq. (2), the polarization-electric field (P-E) hysteresis loops of the samples were measured and shown in Fig. 2f. It is found that the nanocomposites modified by Al2O3@CNTs exhibit significantly higher polarizations than pure RT-TS under an electric field of 50 V/μm and 1 Hz. The maximum polarization (Pmax) of the V-RT-TS sample is higher than that of the R-RT-TS and H-RT-TS samples. For example, the Pmax of V0.8-RT-TS, R0.8-RT-TS, and H0.8-RT-TS samples are 6.0, 5.3, and 5.1 μC/cm2, respectively, which are 216%, 179%, and 168% higher than that of pure RT-TS (1.9 μC/cm2), respectively. Additionally, the remanent polarization of the nanocomposites modified by Al2O3@CNTs is also higher than that of pure RT-TS, indicating that the dipoles are easily switched under low electric field. It is further confirmed by the simulation results presented in Fig. 2g and Supplementary Fig. 3b. The mismatch in conductivity between the Al2O3, CNTs, and the polymer matrix would boost the polarization in the interfacial region according to the Maxwell-Wagner–Sillars effect, thus forming microcapacitors and enhancing the overall polarization for nanocomposites. For V-RT-TS samples, the bipolar P-E loop gradually becomes a rounded shape, as indicated in Fig. 2f. It is mainly induced by the increased polarization loss and conduction loss in the V-RT-TS sample.

Role of the aligned Al2O3@CNTs on the polarization of the nanocomposites

For PVDF-based polymers, SE originates from the transition of chain conformation from twisted conformation into an extended conformation39,40, which is induced by the switched dipoles, as shown in Supplementary Fig. 5. The mechanism of the effect of the Al2O3@CNTs on the dipole orientations of the nanocomposites was investigated. It is clearly seen that there are few variations in amplitude and phase images in the pure RT-TS sample before and after applying modulation voltage neither under ± 40 V nor under ± 45 V, as shown in Supplementary Figs. 6a and 7. While, the considerable difference in both amplitude and phase images at the poled regions can be observed in the V1.1-RT-TS sample after poling under ± 40 V, as shown in Supplementary Fig. 6b. And the regions undergone completely inversed when the applied voltage is increased to ± 45 V, as shown in Fig. 2h. This suggests that the dipoles of the V1.1-RT-TS nanocomposite can be easily switched under low voltage. Furthermore, the local P-E hysteresis loops at various positions around the Al2O3@CNTs were measured. A 500-nm-thick V-RT-TS membrane was prepared on platinum-coated silicon wafers to analyze the ferroelectric response. As shown in the inset of Fig. 2i, the height of the membrane around the Al2O3@CNTs is approximately 40 nm higher than that of the surrounding regions. The same voltage of 10 V is applied to 20 points at different distances from the Al2O3@CNTs. And some representative points are numbered. It is clear that the amplitude of the P-E loops measured at the area surrounding the Al2O3@CNTs is higher than that of the polymer matrix far away from the Al2O3@CNTs, as shown in Fig. 2i. In particular, at the location closest to the Al2O3@CNTs, the butterfly curves can be preliminarily observed. Similarly, a phase switch of about 180° in the PFM phase loop concerned with the bias voltage is found at all of the investigated points. The coercive polarizing voltage is 3.4 V for point 3 (far away from the Al2O3@CNTs) and 1.4 V for point 11 (close to the Al2O3@CNTs). These results suggest that the dipoles of the polymer matrix near the Al2O3@CNTs are more easily switched under the same electric field.

Moreover, the conformation of the molecular chains surrounding the Al2O3@CNTs was investigated by Raman spectra. According to Fig. 3a, the characteristic D-band (1340 cm−1), G-band (1588 cm−1), and 2D-band (2693 cm−1) confirm the existence of the Al2O3@CNTs. And the peaks at 847 cm−1 and 812 cm−1 are associated with the β phase and γ phase of the polymer matrix41,42, respectively. The results of the Raman mapping measurements for pure RT-TS are shown in Supplementary Fig. 8a, b, suggesting the uniform distribution of the β phase and γ phase in the polymer. In Fig. 3b–d, there is no strong correlation between the distribution of the Al2O3@CNTs and the γ phase in the R-RT-TS, V-RT-TS, and H-RT-TS samples. Conversely, the β phase is slightly enhanced around the Al2O3@CNTs in the R-RT-TS sample. It is attributed to the hydrogen bonding and dipole interactions, which stretch the twisted molecular chains in the TTTG (T: trans, G: gauche) configuration to form a TTTT conformation43,44, as shown in the schematic of Fig. 3e. In the V-RT-TS and H-RT-TS samples, the β phase is significantly enhanced around the Al2O3@CNTs regions. It indicates that the interfacial charges accumulated under an external electric field may help to switch the dipoles to form the all-trans configuration, as shown in Fig. 3e.

Fig. 3: The effect of the Al2O3@CNTs on the conformational transition of the nanocomposites.
figure 3

a Raman spectra of the Al2O3@CNTs, pure RT-TS, and the nanocomposite with Al2O3@CNTs. b–d The distribution of the Raman intensity at 1588 cm−1, 847 cm−1, and 812 cm−1 of R-RT-TS (b), V-RT-TS (c), and H-RT-TS (d) samples. The area enclosed by the dashed line indicates the region with a higher concentration of Al2O3@CNTs than that in the other areas (for b–d). e The schematic diagram of the effect of the Al2O3@CNTs on the conformational transition under an electric field.

Full size image

Therefore, the enhancement of SE in the nanocomposites with aligned Al2O3@CNTs is attributed to two factors. The first one is the well-known interfacial charge. It gives rise to a built-in electric field, facilitating the switching of dipoles45. The second one is the increased presence of the all-trans conformations, which enables the dipoles to be more easily switched at low electric field39.

Performance of the EAP actuator based on the nanocomposite membrane

To visually investigate the electromechanical properties of the prepared nanocomposite membrane, a cantilever beam actuator based on the nanocomposite membrane was fabricated, as shown in Supplementary Fig. 9. The deformation of the H1.1-RT-TS actuator depending on the applied electric field is shown in Fig. 4a. And the deformation of the free end (yB) of the cantilever beam actuator can be expressed as follows46:

$${y}_{B}=-\frac{12{L}^{2}}{h}\frac{\nu \omega }{{\omega }^{2}+14\omega+1}{S}_{F}$$
(3)

where L and h are the length and thickness of the nanocomposite membrane, respectively. The ω represents Young’s modulus ratio of the tape substrate to the nanocomposite membrane. ν is the Poisson’s ratio of the nanocomposite film. SF represents the strain of the nanocomposite membrane in the thickness direction. According to Eq. (3), with the same inactive layer, the deformation of the cantilever beam actuator is mainly related to the thickness strain and the Young’s modulus of the nanocomposite membrane. Thus, benefitting from the increased thickness strain and Young’s modulus, the driving fields for the V-RT-TS and H-RT-TS actuators are substantially decreased in comparison with the pure RT-TS actuator, as shown in Fig. 4b and Supplementary Fig. 10. For example, at a bending angle of 100°, the driving fields for the nanocomposite actuator made by pure RT-TS, H1.1-RT-TS, and V1.1-RT-TS membranes are 51, 20, and 17 V/μm, respectively. What’s more, the H1.1-RT-TS actuator exhibits a maximum bending angle of 215° under about 30 V/μm, where the ignorable deformation is observed in the pure RT-TS actuator.

Fig. 4: The actuation performance of the EAP actuators.
figure 4

a The optical photos show the H1.1-RT-TS actuator’s deformation condition with the increasing driving electric field. b, c The bending angles (b) and the output force near the fixed end (c) of the actuators made by nanocomposites with various concentrations and orientations of Al2O3@CNTs under different electric fields. The inset in (c) shows a schematic diagram of the output force and bending angle of the actuator beam. d The average stiffness of the pure RT-TS and nanocomposites modified by Al2O3@CNTs. The inset in the upper left corner of (d) illustrates the measurement of the peak force model of atomic force microscopy (AFM). The insets in (d) show the distribution of stiffness in different nanocomposite membranes. The error bars in (d) represent the standard deviation obtained from the value of the sixteen points marked on the samples. e The simulated stress distribution of the pure RT-TS, V-RT-TS, and H-RT-TS membranes under the same compression force. f The schematic of the point-enhanced and face-enhanced effects on the stiffness of the nanocomposites with vertically and horizontally aligned Al2O3@CNTs, respectively. g Stability and repeatability for the output force of the H1.1-RT-TS actuator over 20000 cycles, when an AC electric field of 34 Vpp/μm is applied. h Comparison of output forces per unit volume measured at the free end of the actuator and the corresponding bending angles of the cantilever beam actuators in this work with other reported works48,49,50,51,52,53,54,55,56,57,58.

Full size image

As described above, the primary challenge is simultaneously attaining high output forces and high deformation of polymer actuators. Therefore, the output forces of the various actuators were accurately measured by placing a force sensor near the fixed end of each actuator, as shown in the inset of Fig. 4c. The output force of the actuator made by pure RT-TS membrane increases from 0.2 to 1.1 mN as the driving fields increase from 40 to 80 V/μm. Compared with the pure RT-TS actuator, all of the R-RT-TS, V-RT-TS, and H-RT-TS actuators generate higher output force. Especially, the H-RT-TS actuator generates the highest output force. Under 30 V/μm, the output force of the H1.1-RT-TS actuator reaches 4.7 mN, which is ~330% higher than that of the pure RT-TS actuator (1.1 mN) under 78 V/μm. Meanwhile, the output forces near the free end of each actuator were also measured, as shown in Supplementary Fig. 11. Under 30 V/μm, the output force near the free end of the H1.1-RT-TS actuator is 4.4 mN.

As for the cantilever beam, the output force at the end can be expressed as follows47:

$${F}_{{output}}=\frac{3K}{{L}^{3}}{y}_{B}$$
(4)

where L is the length of the nanocomposite membrane, K represents the bending stiffness of the cantilever beam, and yB is the deformation of the free end of the cantilever beam. According to this equation, except for deformation, stiffness is the other key factor to determine the output force. The output force of the H-RT-TS actuator is higher than that of the R-RT-TS actuator, though the deformations of the H-RT-TS and R-RT-TS actuators are nearly the same. It indicates that the proposed microstructure design can enhance the mechanical properties of the nanocomposite actuator without sacrificing its deformation. Thus, the peak force measurement mode of atomic force microscopy (AFM) was then used to investigate the stiffness of the nanocomposites, as shown in the inset in Fig. 4d. The stiffness distribution in the pure RT-TS and nanocomposite membranes with different orientations of Al2O3@CNTs is presented in the inset of Fig. 4d. The average stiffness obtained from the marked points in the images of stiffness distribution is displayed in Fig. 4d. It is evident that the incorporation of Al2O3@CNTs leads to an enhancement in the stiffness of the nanocomposite material from 0.46 mN/μm (pure RT-TS) to 0.60 mN/μm (R-RT-TS). Furthermore, by arranging the Al2O3@CNTs in vertical and horizontal orientations, the average stiffness of the nanocomposites is further improved to 0.66 mN/μm for V-RT-TS sample and 0.80 mN/μm for H-RT-TS sample, respectively. Notably, the enhancement of stiffness only occurs in certain regions of the V-RT-TS sample, while for the H-RT-TS sample, the stiffness of the entire polymer matrix is increased, resulting in the highest average stiffness value.

To explain this phenomenon, finite element simulations were performed to study the effect of the orientation of Al2O3@CNTs on the mechanical properties of the interfacial regions. Figure 4e describes the distribution of the stress in the pure RT-TS, V-RT-TS, and H-RT-TS samples under an applied pressure of 1.5 × 108 MPa. Clearly, the concentrated local stress at the interface regions between the Al2O3@CNTs and the polymer matrix is much higher than the average stress of the matrix. And, the region of increased stress surrounding the horizontally aligned Al2O3@CNTs is broader than that surrounding the vertically aligned Al2O3@CNTs. This phenomenon reveals the point-enhanced effect on the stiffness of the V-RT-TS sample and face-enhanced effect on the stiffness of the H-RT-TS sample, as depicted in the schematic of Fig. 4f. It can be easily understood through this example that a tent or a roof with a skeleton structure will be more stable than that of the corresponding one supported by a single fulcrum.

As shown in Fig. 4g and Supplementary Fig. 12, after 20000 cycles of deflection under an AC electrical field of 34 Vpp/μm (peak to peak voltage is denoted as Vpp), the output force near the fixed end and the free end of the H1.1-RT-TS actuator slightly decrease by 5% and 3%, respectively. These results indicate the good stability and reproducibility of the EAP actuator. Figure 4h shows the maximum output force per unit volume (measured near the free end of the actuator) and the corresponding bending angle of the as-prepared actuator in comparison with those of other reported cantilever beam actuators48,49,50,51,52,53,54,55,56,57,58. Although the MFC actuator and ceramic actuators exhibit a relatively high output force (about 1000 mN), their output force per unit volume remains low (ranging from 0.01 to 0.40 mN/mm³), and their bending angles are limited to less than 5°. The ion-exchange polymer metal composite, liquid-crystalline polymer, and PVDF-based polymer actuators possess a relatively high deformation. However, their output force per unit volume is also low due to inherently low stiffness. Moreover, the long response time or high driving voltage constitutes other significant drawbacks. In contrast, the nanocomposite actuator proposed in this work achieves not only high output force per unit volume (1.25 mN/mm3) but also a large bending angle up to 215°. Consequently, the designed EAP actuator simultaneously improves the deformation and output force under relatively low driving fields.

EAP-actuator-based bioinspired crawling soft robot

The H1.1-RT-TS actuator demonstrates large deformation, high output force, and long-term operational stability simultaneously, making it particularly suitable for soft robotic systems. In this work, it was employed as the driving component in a frog-inspired soft robot, whose structure and working principle are shown in Fig. 5a. The soft robot comprised a bow-shaped polyimide (PI) sheet as the body and an EAP actuator as the driving feet, as shown in Supplementary Fig. 13a. The motion of the soft robot was simulated using finite element analysis (FEA), as shown in Supplementary Movie 1. According to the simulated results, the schematic of the motion process of the soft robot during one motion cycle is shown in Fig. 5a. When an electric field is applied, the EAP actuator bends and generates an output force that exceeds the friction between the soft robot and the ground, thereby propelling the robot forward. As the electric field decreases, the stored potential energy from the previous stage is released, propelling the soft robot forward. Subsequently, the EAP actuator reverts to its initial shape, completing a full cycle of motion.

Fig. 5: The soft robots made by the EAP actuators and their performance.
figure 5

a Design and different gaits in the cross-sectional views of the frog-inspired soft robot. b Crawling process of the frog-inspired soft robot made by H1.1-RT-TS actuator on the zigzag surface. The inset in (b) shows the geometry dimension of the zigzag surface. c Crawling speed of the frog-inspired soft robot made by pure RT-TS and H1.1-RT-TS actuator under different driving fields and frequencies. The inserted photographs in c depict the crawling process of the frog-inspired soft robot on the sand. d Design and different gaits in the cross-sectional views of the “inchworm-like” soft robot. e Crawling process of the “inchworm-like” soft robot made by H1.1-RT-TS actuator on the zigzag surface. f Crawling speed of the “inchworm-like” soft robot made by pure RT-TS and H1.1-RT-TS actuators under diverse slopes. g Crawling process of the “inchworm-like” soft robot made by pure RT-TS actuator on a slope of 20°. h, i Crawling process of the “inchworm-like” soft robot made by H1.1-RT-TS actuator on a slope of 40° (h), and a slope of 52° (i), respectively. j Crawling process of the “inchworm-like” soft robot made by H1.1-RT-TS actuator on the smooth road with a slope of 30°. k The crawling process of the “inchworm-like” soft robots with a load of 0.14 g made by H1.1-RT-TS (left) and pure RT-TS (right) actuators, respectively. l Crawling process of the soft robot made by H1.1-RT-TS actuator with a load of 1.57 × g. All the scale bars in the figures are 1 cm.

Full size image

To facilitate the forward movement of the frog-inspired soft robot, it was placed on an anisotropic zigzag surface, where the foreside edge was vertical (Fig. 5b). This zigzag surface increases the forward friction during the motion processes of the EAP actuator. As shown in Fig. 5b and Supplementary Movie 2, the soft robot made by H1.1-RT-TS actuator can crawl 120 mm in 5 s under an alternating electric field of 25 V/μm and frequency of 5 Hz, which represents an average crawling speed of 24.0 mm/s (1.0 BL/s (body length/s)). Furthermore, the crawling speed increases with increasing frequency of the electric field, as shown in Fig. 5c. At a frequency of 5 Hz, the crawling speed of the soft robot made by the H1.1-RT-TS actuator under 25 V/μm is ~56% higher than that of the soft robot made by pure RT-TS actuator under 78 V/μm, attributed to the higher thickness strain and output force of the H1.1-RT-TS actuator. Then, the crawling performance of the frog-inspired robot was investigated on sand and shown in the inset of Fig. 5c and Supplementary Movie 2. The soft robot can crawl 78 mm in 8 s, corresponding to an average crawling speed of 0.4 BL/s.

According to the above results, frog-inspired soft robots effectively navigate rough terrains such as sandy ground. However, their locomotion stability may be compromised on steep slopes due to elevated centers of mass. Thus, an interesting “inchworm-like” soft robot was designed, as shown in Supplementary Fig. 13b. In this structure, the EAP actuator was fixed on the front section of the “inchworm”. The simulated and schematic motion processes of the soft robot are shown in the Supplementary Movie 1 and Fig. 5d. Under the applied field, the EAP actuator bends and generates a high output force. The reduced inclination angle of the EAP film (thereby lowering the center of mass) enhances the vertical force component, which subsequently increases the friction between the EAP film and the ground. Thus, the EAP actuator initially “grips” the ground and pulls the soft robot’s back part to move forward. As the electric field decreases, the deformation of the EAP actuator rebounds. At this stage, the sliding friction generated between the soft robot and the ground drives the soft robot to move forward.

From the above process, it can be observed that soft robots require both substantial actuation force to overcome frictional resistance and large deformation to achieve effective forward movement. The crawling properties of this soft robot on a zigzag surface were first investigated. As shown in Fig. 5e and Supplementary Movie 3, the soft robot made by H1.1-RT-TS actuator can crawl 87.6 mm in 4 s under an alternating electric field of 25 V/μm and frequency of 5 Hz, indicating an average crawling speed of 0.8 BL/s. It is 124% higher than that obtained for the soft robot made by pure RT-TS actuator at 78 V/μm, as shown in Fig. 5f. Additionally, the crawling applicability of the soft robot on sandpaper was studied and shown in Supplementary Fig. 14 and Supplementary Movie 3, with an average crawling speed of 0.2 BL/s.

The crawling capability of the soft robots was further confirmed on the zigzag surface with a slope of 20°. The soft robot made by the pure RT-TS actuator could hardly climb slopes at either 1 Hz or 5 Hz, as shown in Fig. 5g, Supplementary Fig. 15, and Supplementary Movie 4. Because the output force is too low to overcome the component of gravity in the direction of motion caused by the slope. While, benefiting from the obviously increased output force, the soft robot made by the H1.1-RT-TS actuator could successfully climb the slope. The average crawling speeds of this soft robot on a slope of 20° were measured at different frequencies and shown in Fig. 5f. These results are just slightly decreased compared to those obtained for the case of the smooth surface. When the slope increases to 40°, the soft robot is still capable of climbing the surface at an average crawling speed of 0.3 BL/s, as shown in Fig. 5h. As the slope increases further, the stability of the soft robot decreases because it shakes at high frequency. Notably, the soft robot could successfully crawl on a surface with a slope as high as 52° at a low frequency (0.5 Hz), as shown in Fig. 5i and Supplementary Movie 4. And the soft robot’s motion performance on the smooth road with a slope of 30° was also investigated. As shown in Fig. 5j and Supplementary Movie 5, the average crawling speed of the soft robot is 0.1 BL/s. This angle ranks relatively high among those ever-reported soft robots with simple structures59,60,61,62,63,64.

To further demonstrate the enhanced output force of the H-RT-TS actuator, the crawling capability of the soft robot was investigated under external load. Figure 5k and Supplementary Movie 6 show the crawling process of the soft robots with a load of 0.14 × g. The soft robot made by H1.1-RT-TS actuator moves at a speed of 0.2 BL/s on a zigzag surface under an alternating electric field of 25 V/μm and frequency of 3 Hz. Notably, the soft robot made by the pure RT-TS actuator can hardly move with the same load even after increasing the driving field to 78 V/μm. Consequently, the maximum load of the soft robot made by the H1.1-RT-TS actuator was quantified when it crawls on the smooth road. As shown in Fig. 5l and Supplementary Movie 7, the soft robot can successfully crawl with a load of 1.57 × g, which is equivalent to eightfold the total mass of the soft robot and 112-fold the mass of the EAP actuator. It indicates an ability for heavy-load transportation. The promising performance of the proposed EAP actuators opens a viable avenue for the development of various applications, such as soft robots, artificial muscle/skin, microfluidic pumps, and biomimetic devices.

To characterize the EAP actuator’s bandwidth and applicability, the dynamic response of the H1.1-RT-TS actuator was measured under different frequencies. Laser displacement sensors recorded the displacement of the cantilever beam’s free end in response to a sinusoidal-wave electric field of 16 Vpp/μm, revealing peak displacement at the resonance frequency. As shown in Supplementary Fig. 16a, at low frequencies (< 100 Hz), the displacement initially decreases and then maintains a stable value. When frequencies exceed 100 Hz, the displacement initially increases and then decreases with increasing frequency, as shown in Supplementary Fig. 16b. The maximal displacement occurs at 1.1 kHz. The time-resolved displacement response of the actuator under a square-wave electric field is presented in Supplementary Fig. 17. The displacement of the actuator reaches 90% of its maximum value within 0.19 s upon voltage application, and the deformed membrane returns to 90% of its original state within 0.07 s. It demonstrates a fast response feature.

Crawling speeds of both frog-inspired and “inchworm-like” soft robots on the smooth road were subsequently measured at different driving frequencies (Supplementary Fig. 18). The speed of the soft robots obviously increases at 20 Hz and maintains high crawling speeds (~1 BL/s) within the 50–200 Hz range, demonstrating broad-frequency stability. What’s more, as shown in Supplementary Fig. 19, the motion process of the EAP-driven soft robots can be easily regulated by changing the contact angle of the EAP film and ground and the ratio of width between the EAP film and PI film. It indicates the tunability of the soft robots to fulfill diverse application requirements.

Discussion

In this work, an effective strategy to modulate the orientation of Al2O3@CNTs in the relaxor polymer matrix-P(VDF-TrFE-CTFE) has been proposed to resolve the long-standing conflict in EAP between high rigidity and high deformability. The H1.1-RT-TS membrane realizes a 473% enhancement in thickness strain compared to pure RT-TS at a low electric field of 30 V/μm. This enhancement stems from the concurrent contributions of Maxwell strain and amplified electrostrictive effects, the former arising from the higher value of εr/Y and the latter from the more easily switched dipoles. The as-prepared H1.1-RT-TS actuator beam exhibits a bending angle up to 215° at about 30 V/μm. What’s more, the average stiffness of the nanocomposite is further improved by the horizontally aligned Al2O3@CNTs, enabling the H1.1-RT-TS actuator to achieve a ~ 330% improvement in output force (from 1.1 mN for pure RT-TS to 4.7 mN) at reduced operating fields (from 78 to 30 V/μm). Importantly, the output force per unit volume of this actuator is even higher than that of some ceramic and MFC actuators. Subsequently, the frog-inspired soft robot made by H1.1-RT-TS actuator achieves a high crawling speed of 24.0 mm/s (1.0 BL/s) under a low driving field of 25 V/μm. Owing to the ultrahigh output force, the “inchworm-like” soft robot made by H1.1-RT-TS actuator confirms its crawling ability on the zigzag surface with a slope of 52° and the smooth surface with a slope of 30°, which are relatively high values among the ever-reported robots with simple structures. Furthermore, the synergistically enhanced monolayer performance enables straightforward force amplification via simple stacking, providing a scalable method. These results demonstrate the promising applications of the nanocomposite actuator with enhanced rigidity and deformability in the fields of biotechnology, medical technology, precision instruments, biomimetic applications, and so on.

Methods

Materials preparation

CNTs with an average diameter ranging from 4 to 6 nm and a length of 0.5 to 2 μm were provided by Chengdu Organic Chemicals Co., Ltd. Core-shell structured Al2O3@CNTs were synthesized using the ALD technique. In detail, Trimethyl Aluminum and deionized water served as the aluminum and oxygen precursors, respectively. Each deposition cycle consisted of a precursor pulse for 0.2 s and a nitrogen purge for 8 s. After 50 cycles, an Al₂O₃ insulating layer with approximately 5 nm thickness was deposited. N,N-dimethylformamide (DMF) (99.5% purity) was procured from Sinopharm Chemical Reagent Co. Ltd. and utilized without additional purification. P(VDF-TrFE-CTFE) was acquired from Piezotech company, France.

Preparation of the nanocomposites with aligned Al2O3@CNTs

1 × g of P(VDF-TrFE-CTFE) was initially dissolved in 10 mL DMF and stirred overnight at room temperature. Different weight percentages of Al2O3@CNTs were then dispersed in the P(VDF-TrFE-CTFE) solution, and thorough mixing was achieved through tip sonication, resulting in a homogeneous suspension. The suspension was drop-cast onto the clean glass sheets. Glass slides with copper tape were connected to a combination of a high-voltage amplifier (610E, Trek, USA) and a signal generator (ROGOL, China). This setup is used to provide vertical and horizontal electric fields to the polymer solution, thereby aligning Al2O3@CNTs within the polymer along the direction of the electric field. The vertical and horizontal electric field intensities were both set to 200 Vpp/mm, with a frequency of 100 Hz. Following 20 min of orientation of Al2O3@CNTs in the electric field at 70 °C, the sample underwent heating at 120 °C for 1.5 h. Then, the sample underwent a further heating process at 142 °C for 10 min, and finally, rapid ice-quenching. The resulting membrane was then peeled off the substrate and dried at 40 °C for 24 h. The preparation process for the control sample was identical, except that no electric field was applied. The resulting nanocomposite membrane had a final thickness ranging from 20 ± 2 μm.

Structural and electrical characterization

The morphologies of core-shell structured Al2O3@CNTs were examined using Field Emission Transmission Electron Microscopy (TEM, JEOL Co., Japan). The cross-sections of the nanocomposite membranes were analyzed using Field Emission Scanning Electron Microscopy (SEM, FEI Quanta 250FEG). Polarized Raman spectroscopy, facilitated by a commercial micro-Raman system (Renishaw InVia Qontor), was employed to probe the orientations of Al2O3@CNTs and the conformational transition of the nanocomposites. Samples were excited with 785 nm radiation and systematically rotated to align with both horizontal and vertical polarization light directions, with signal intensity collected across various orientations. To assess the crystallinity of the nanocomposites, X-ray diffraction (XRD) patterns were obtained for all of the samples at room temperature using a PANalytical X-ray Diffraction Diffractometer of Empyrean, with Cu Kα1 radiation. The elastic modulus of the samples was measured by tensile tests using a precision tensile microstage (Linkam MFS 350, UK). At least 6 independent samples were measured for each type of nanocomposite to ensure data reliability. The polarization and its reorientation of the nanocomposites are measured using AFM (Cypher ES, Asylum Research) with piezoresponse force microscopy (PFM) mode. The local polarization inversion of the nanocomposite membrane was investigated using a high-voltage PFM module under a DC voltage of ± 40 V and ± 45 V over a scan area of 5 × 5 µm2. An atomic force microscopic system (AFM, BLU_402, NT-MDT, Europe) was used to investigate the morphologies and the stiffness of the nanocomposites.

Ag electrodes, 2.8 mm in diameter and 100 nm in thickness, were deposited onto the membranes (6.8 × 6.8 mm) by the magnetron plasma sputtering method. Dielectric properties were evaluated across a frequency range of 10−2–106 Hz utilizing an impedance analyzer (NOVOCONTROL Co, Germany). The P-E loops of nanocomposite membranes were measured at 1 Hz, employing a ferroelectric test system (Radiant RT-66). The thickness strain along the direction of the applied electric field was measured at 1 Hz using a photonic sensor (SP-S120, SIOS Meßtechnik GmbH, Germany). The electric breakdown strength of the nanocomposites was determined using a high-voltage power supply (RK2674A Withstanding Voltage Tester). At least 9 independent samples were measured for each type of nanocomposite to ensure data reliability.

Fabrication and performance characterization of cantilever beam actuator

100 nm thick Ag electrodes were deposited onto the 20 μm thick EAP membrane. Then, it was adhered to the 20 μm thick PI tape (inactive layer) and the geometry dimensions of the electrodes and EAP membrane are shown in Supplementary Fig. 9. The cantilever beam actuators were fixed with a conducting clamp and powered by a high-voltage source, which was generated by a signal generator (ROGOL, China) and an amplifier (610E, Trek, USA). The output force of the cantilever beam actuator was measured by a Nano Force Sensor (Nators Suzhou Technology Co., LTD). The displacement of the cantilever’s free end was measured by a laser displacement sensor (Shenzhen Shuoertai Sensor Co., Ltd.).

Finite element simulation

The two-phase structure of the nanocomposite systems was established by placing Al2O3@CNTs with different orientations inside the P(VDF-TrFE-CTFE) matrix. The electric field and polarization around the interface between Al2O3@CNTs and polymer matrix were simulated by the FEA method. In the simulated system, the diameter and length of CNTs were set as 5 nm and 2 μm, respectively, and the thickness of the Al2O3 shell layer on the surface of CNTs was set as 5 nm. In the two-dimensional model, the nanofillers were distributed in matrix (10 × 8 μm) in random, vertical, and horizontal directions. An electric field of 100 V/μm was applied. The electric parameters of the various materials in this system are listed in Supplementary Table 2.

The stress around the interface between nanofillers and polymer matrix was simulated by FEA method. The nanocomposite material is composed of Al2O3@CNTs unidirectionally embedded in the P(VDF-TrFE-CTFE) matrix. The cylindrical fibers are positioned at the center of the matrix. It is assumed that the Al2O3@CNTs exhibit transverse isotropy (modeled as orthotropic), while the P(VDF-TrFE-CTFE) matrix is isotropic. The material properties of the Al2O3@CNTs and P(VDF-TrFE-CTFE) matrix are provided in Supplementary Table 3.

Motion mechanisms of the soft robot were simulated using FEA method. The material parameters and dimensions are specified in Supplementary Table 4 and Supplementary Fig. 13. Here, the ground was simplified as a discrete rigid surface with a friction coefficient of 0.3 at the crawling robot-ground interface. A transverse strain of 0.1% was applied to the EAP actuators to initiate motion.

Fabrication of the EAP-actuator-based bioinspired crawling soft robot

The frog-inspired soft robot and “inchworm-like” soft robot were both fabricated by integrating components of a bow-shaped polyimide (PI) body and an EAP-actuated foot. The EAP-actuated feet were fabricated using the same method. First, 100 nm thick Ag electrodes were deposited onto the 20 μm thick EAP membrane, and two conductive Ag tapes were attached on each side of the electrodes, serving as connections between the soft robot and external power supply. Then, it was adhered to the 20 μm thick PI tape (inactive layer) to work as the actuator. The critical divergence of these two kinds of soft robots lies in the actuator position. The frog-inspired soft robot integrates EAP actuators in the hindfoot region with 70° ground contact angle, whereas the “inchworm-like” soft robot positions the EAP actuators in the forefoot region with 45° ground contact angle. The bow-shaped polyimide (PI) body and EAP-actuated feet were stuck together using a double‑sided adhesive (~50 µm, 3 M, USA). The geometry dimensions of different parts of the soft robots are shown in Supplementary Fig. 13a and Supplementary Fig. 13b. The EAP actuator was powered by an AC power supply, which was generated by a signal generator (ROGOL, China) and an amplifier (610E, Trek, USA).