Rolled Soft Actuators Based on P(VDF‐TrFE‐CTFE) Electrospun Nanofibers

Abstract

This study presents a novel rolled dielectric elastomer actuator, based on Poly(vinylidene fluoride‐trifluoroethylene‐chlorotrifluoroethylene), i.e., P(VDF‐TrFE‐CTFE), nanofibers that are fabricated by means of an electrospinning process. The soft actuator is realized by rolling a mat of two active layers, interleaved with two electrodes. The active layers are mats of P(VDF‐TrFE‐CTFE)‐based nanofibers, embedded in an elastomeric matrix of polydimethylsiloxane (PDMS). The electrodes are made of a mixture of carbon black and PDMS, bonded to the active layers by electrostatic adhesion force. The effects of the nanofibers in the soft actuators are investigated. Specimens of the soft actuator are realized that differ in the thickness of the nanofibrous mats used for the active layers, that is, 60 and 120 μm. An electromechanical characterization is performed to analyze and measure the axial force and axial displacements of the soft actuators when different electric fields are applied to the specimens in the transversal direction. The experimental results show that the presence of P(VDF‐TrFE‐CTFE)‐based nanofibers enhances the force‐to‐weight ratio of the soft actuators by up to 43.5%, and the energy density by up to 12.9%, compared to a control specimen with the active layer made of PDMS only.

Introduction

Dielectric elastomers (DE) are a class of soft material that is able to convert electrical energy into mechanical energy. Thanks to this property, DEs have been considered to be promising in a variety of fields, such as flexible energy harvesters,^[1] flexible sensors,^[2] and soft actuators.^[3]

Dielectric elastomer actuators (DEAs) are realized by interleaving DEs between two electrodes. To enhance the actuation forces, the rolled configuration has been introduced,^[4–6] in which the active layers and the electrodes are wounded to form a cylindrical structure. When an electric field is applied, the rolled actuator exhibits an elongation along its axial direction. This configuration also opens opportunities to connect the actuators in series or in parallel to scale up the overall stroke or force. It has been proved that the rolled configuration is suitable for building linear actuators in a compact manner,^[6–8] making it promising in the design of artificial muscles.^[3,9]

In our recent work, P(VDF-TrFE-CTFE)-based aligned nanofiber mats have been fabricated by the electrospinning technique and analyzed. In ref. [10], the variable stiffness properties under different voltages of the P(VDF-TrFE-CTFE)-based aligned nanofibers have been studied and applied to the broad field of variable stiffness joints.^[11] In ref. [12], the force-to-weight ratio and the specific stiffness have been evaluated to compare extruded films and electrospun aligned nanofibers of P(VDF-TrFE-CTFE). It has been shown that the electrospun nanofiber mat has a higher electrostrictive effect than the extruded film. In ref. [13], the specific work has been introduced and the effect of morphology and thickness has been further studied. In ref. [14], unimorph soft actuators have been designed by immersing P(VDF-TrFE-CTFE) nanofibers in a silicone matrix of polydimethylsiloxane (PDMS), and echo state networks have been used for modeling the nonlinear dynamic response of the actuators.^[15] All these previous studies focus on the unimorph configuration of the soft actuators. Although it has been proven that the electrospun aligned nanofibers of P(VDF-TrFE-CTFE) have high force-to-weight ratio, the achieved output force still remains low.

This study presents novel rolled DEAs, that have been realized by rolling two active layers, interleaved with two electrodes. The active layers are mats of electrospun P(VDF-TrFE-CTFE) nanofibers that have been immersed in an elastomeric matrix of PDMS, while the electrodes are made of a mixture of carbon black and PDMS. This study brings two novel contributions in the area of rolled soft actuators, that is, in the design of the active layer and in the fabrication procedures. Specifically, the active layer is a composite material that withstands high electric fields and, thanks to the presence of nanofibers, it is anisotropic, which is an important characteristic in soft actuators.^[14] Using an active layer of P(VDF-TrFE-CTFE)-based electrospun nanofibers immersed in a PDMS silicon matrix is not novel in DEAs, as it was presented in our previous work,^[14] it has only been used in soft actuators with a unimorph configuration and never in a rolled configuration. In general, in the current literature, there is no evidence of rolled soft actuators that use electrospun nanofibers in the active layer. Moreover, while using a composite of P(VDF-TrFE-CTFE)-based electrospun nanofibers and PDMS as the active layer of the rolled soft actuators, this study shows that the presence of nanofibers enhances the actuation capabilities in terms of energy density, when compared to a control rolled actuator without nanofibers. Regarding the fabrication process, a number of innovative procedures is introduced in this study. While the active layer and the electrodes are fabricated separately, the layers are joined together by electrostatic adhesive force. These fabrication procedures reduce the possibility of errors in the fabrication process, avoid the undesirable additional stiffness of the chemical adhesives used to attach the different layers, make the assembly/disassembly easier, and reduce the waste of material (the layers, which are wrongly produced or broken, can be easily substituted without wasting the other layers).

The remainder of this article is organized as follows. Section 2 describes the fabrication steps of the novel rolled soft actuators. In Section 3, the electromechanical characterization setup is introduced. Section 4 presents and discusses the results. Finally, concluding remarks are drawn in Section 5.

Experimental Section

This section describes the fabrication process of the novel rolled soft actuators proposed in this study and shown in Figure 1, which were realized by rolling a mat of two active layers, interleaved with two electrodes. To investigate the effects of the nanofibers in rolled soft actuators, different active layers were considered, that is, mats of P(VDF-TrFE-CTFE)-based nanofibers embedded in an elastomeric matrix of PDMS with two different thicknesses, that is, 60 and 120 μm, and one mat of PDMS only. The electrodes were made of a mixture of carbon black and PDMS, and they were bonded to the active layers by electrostatic adhesion force.

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P(VDF-TrFE-CTFE)

PVDF, a ferroelectric electroactive polymer, exhibits distinctive electromechanical properties and has attracted extensive research attention in the last decades.^[16–18] However, there are still very limited studies that focus on the rolled actuator made of PVDF-based polymer in spite of their high energy density. One possible reason is that these materials have a slower response than other dielectric material such as silicones, which limits their application when a fast actuation is required.^[6,19]

The ferroelectricity of PVDF was determined by its chain conformation and crystal structure.^[17] Because of the electronegativity of fluorine atoms, the monomer unit shows a large dipole moment, which leads to its electrostrictive response.^[20] This polymer can crystallize in five crystalline phases, which were identified as α, β, γ, δ, and ε.^[16,21] Among these phases, the most significant one with respect to the electromechanical properties was the β-phase.^[16,22] More β-phase can be obtained by incorporating comonomers which derived a wide variety of PVDF-based polymers.^[17]

Among these PVDF-based polymers, it was envisioned that the terpolymer P(VDF-TrFE-CTFE) may open the opportunities for emerging fields like artificial muscles on account of its outstanding relaxor ferroelectric properties and high dielectric constant.^[16,17,23] The TrFE comonomer unit can facilitate the formation of the all-trans conformation which means more β-phase.^[24,25] This comonomer unit can destabilize the conformation of α-phase and δ-phase and help to form more β-phase which enables stronger ferroelectric properties than pure PVDF.^[24] Thus, by introducing TrFE, the dielectric constant was considerably improved.^[17,26–28] The CTFE comonomer unit can split crystal regions and accelerate dipole flipping.^[24,29] As a comonomer unit considerably larger than VDF, CTFE can achieve physical pinning and increase the interchain spacing. Thus, the gauche conformation was formed.^[17] The pinning effect reduced the ferroelectric domain to nanometer size, which accelerated dipole flipping and reduced coupling to achieve low-hysteresis relaxor ferroelectric behavior.^[24] By introducing CTFE, the polymer showed relaxor ferroelectric properties.^[17]

Active Layers

P(VDF-TrFE-CTFE)-Based Aligned Nanofibers

The polymer used for the realization of the nanofibers was the P(VDF-TrFE-CTFE) (Solvene T, Solvay Specialty Polymers, Milano, Italy, www.solvay.com). Specifically, the used P(VDF-TrFE-CTFE) contained 63 mol% of VDF, 28 mol% of TrFE, and 9 mol% of CTFE. It had a Curie temperature of 16 °C and a relative permittivity of 45 at 1 kHz.

The P(VDF-TrFE-CTFE)-based aligned nanofibers were fabricated by electrospinning a polymeric solution of P(VDF-TrFE-CTFE) powder (30 wt%) and Acetone:DMF 55:45 (w/w).^[12] The electrospinning process was performed with an electrospinning machine (Spinbow, Bologna, Italy, www.spinbow.it), in which a needle (length of 55 mm and internal diameter of 0.84 mm) was connected to a 5 mL syringe (loading the polymeric solution) via polytetrafluoroethylene (PTFE, Teflon) tubing. A metallic drum was placed at a proper distance and covered with poly(ethylene)-coated paper. When a high positive voltage was applied to the needle, the polymeric solution was stretched by a high electrostatic field and collected at the drum,^[30] which was grounded. During the process, the drum rotated with a high speed to make sure the nanofibers were aligned in the same direction.^[31–33] The parameters used in the electrospinning machine for the fabrication of the aligned nanofibers are detailed in Table 1.

Table 1 Electrospinning parameters used for the production of the mats of the P(VDF-TrFE-CTFE)-based aligned nanofibers.

Parameters	Values
Flow rate [mL h−1]	0.55
Electric potential [kV]	16
Drum rotation speed [rpm]	4300
Distance needles-drum [cm]	16
Relative humidity [%]	23
Temperature [°C]	21

Two P(VDF-TrFE-CTFE)-based nanofiber mats were fabricated, with an average thickness of ≈60 and ≈120 μm and electrospinning duration time of ≈3 and ≈6 h, respectively. The thickness of the mats was measured three times at different positions with a metrology digital dial gauge (MEGAROD ALPA, Pontoglio, Italy, www.alpametrology.com). The mats were cut to obtain two specimens, hereafter called NF60 and NF120, whose dimensions and weight are reported in Table 2.

Table 2 Design parameters of the actuators and their different layers (length l, breadth b, thickness t, active length l_a, diameter d, and weight w).

	l [mm]	b [mm]	t [μm]	l a [mm]	d [mm]	w [g]
Nanofibrous Matsa)
NF60	60	30	≈60	–	–	≈0.063
NF120	60	30	≈120	–	–	≈0.118
	Active Layersb)
LNF0	60	30	≈165	–	–	≈0.280
LNF60	60	30	≈165	–	–	≈0.300
LNF120	60	30	≈165	–	–	≈0.320
	Electrode
Electrode	45	25	≈165	–	–	≈0.190
	Rolled Actuatorsc)
ANF0	–	–	–	≈16	≈6	≈0.94
ANF60	–	–	–	≈16	≈6	≈0.98
ANF120	–	–	–	≈16	≈6	≈1.02

The P(VDF-TrFE-CTFE)-based nanofiber mats were analyzed with a Supra 55 scanning electron microscopy (SEM) (Zeiss, Germany, www.zeiss.com) to examine the alignment of the nanofibers. To quantify the alignment, the SEM image was analyzed with the ImageJ software, with the Directionality plugin (www.imagej.net).^[34] As an example, Figure 2a depicts a SEM image of a portion of one mat, and the directionality histogram in Figure 1 reports the amount of fibers as a function of the fiber orientation, showing that the majority of the fibers were oriented in a preferential direction.

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PDMS-Based Matrix

The P(VDF-TrFE-CTFE)-based nanofiber mats were integrated in a PDMS-based matrix to fill the gaps between P(VDF-TrFE-CTFE) nanofibers.^[14] Specifically, the nanofibrous mats were integrated into a matrix of PDMS silicone elastomer (Sylgard 184, Silicone elastomer kit) with a ratio 10:1 of silicone and curing agent (Sylgard 184, Silicone elastomer kit).

Figure 3 summarizes the integration process, as previously introduced in ref. [14,35]. The solution was stirred and, afterward, placed in a vacuum chamber to remove air bubbles. The nanofibrous specimen was placed on a Teflon plate that was previously covered with a wide tape (width of 50 mm, length of 80 mm) with a smooth surface. Afterward, three layers of tape (each one with a thickness of 55 μm) were attached around the nanofibrous specimen and used as mold. The solution of PDMS and curing agent was, then, deposited on the specimen and leveled with a blade.^[35] To remove the air bubbles introduced in the depositing process, a precuring process in oven (10 min, 50 °C) and a second blading were adopted. The integration process was finalized by curing the composite (P(VDF-TrFE-CTFE)-based nanofiber and PDMS-based matrix) in oven (1 h, 90 °C).

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Active Layers

Overall, three active layers were realized in this study. Two active layers contained the specimens of the nanofibers (NF60 and NF120) integrated in the PDMS-based matrix: one active layer was made of PDMS-based matrix. The latter active layer was used to realize a rolled soft actuator that was used as control specimen. Table 2 reports the dimensions and weights of the three active layers, hereafter called LNF60, LNF120, and LNF0, respectively.

It should be noticed that, when picking up the active layer from the Teflon plate, both sides were smooth and a self-adhesive phenomenon occurred due to the electrostatic force. This inspired the idea to assemble the active layers and the flexible electrode (as described in the following section) with electrostatic force instead of other adhesives.

Flexible Electrodes

The flexible electrodes were made of a mixture of carbon black nanoparticles (super P, BET specific surface area of 62 ± 5.0 m²g⁻¹, average particles size of 40 nm) and PDMS (Sylgard 184, Silicone elastomer kit).^[36] To improve the electrostatic adhesion force, smooth processing was made on the previously proposed flexible electrodes.^[15]

Figure 4 summarizes the fabrication process of the flexible electrodes. A solution of 17.5 wt% of carbon nanoparticles were added to the PDMS. Then, the solution was prepared by adding 300 wt% of isopropanol and by magnetically stirring for 1 h at room temperature. Then, a curing agent (Sylgard 184, Silicone elastomer kit) was added to the mixture. After thorough stirring, the mixture was put in an oven (10 min, 40 °C) to evaporate the isopropanol. Two layers of tape (thickness of 110 μm) were attached around a rectangular area (length of 50 mm, breadth of 25 mm) on the Teflon plate and served as the mold. The mixture was deposited on a Teflon plate (covered with a wide smooth tape) with a blade and cured in the oven (1 h, 90 °C). After curing, it was noticed that the side that contacted the wide tape was smooth, and the other side was relatively rough. To smooth the rough side for the following electrostatic assembly process, another layer of PDMS (mixed with curing agent, weight ratio of 10:1) was deposited to finally form the flexible electrode. Table 2 reports the dimension and the weight of one electrode.

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Rolled Soft Actuator

Figure 5 shows the assembly process of the rolled soft actuators: the first active layer was placed on the workbench; then, the first flexible electrode and a lead wire were placed on the first active layer; afterwards, the second active layer was placed on the first electrode; finally, the second electrode and a second lead wire were placed on the second active layer. These steps should be conducted slowly, and the bubbles should be removed from the edges by applying some pressure on the layers. After having assembled the four layers, they were manually wound into a roll.

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Three categories of rolled soft actuators were realized with the active layers LNF0, LNF60, and LNF120 (see Table 2), hereafter called ANF0, ANF60, and ANF120, respectively. For each category, three specimens were realized (e.g., for the ANF0 category, the three specimens ANF0S1, ANF0S2, and ANF0S3 were realized). Table 2 reports the dimensions and weights of the three rolled soft actuators.

Observations on the Proposed Design

The fabrication process of the active layers and of the flexible electrodes in this study was inspired by our previous work.^[14] However, a key difference was that the different layers were fabricated separately, which brought to some benefits. 1) In the previous fabrication process, each layer can only be done after the previous layer was cured. If a fabrication defect occurs in the subsequent curing, the whole actuator is damaged and not usable anymore. This reduces the waste of materials during the fabrication process. 2) It is much easier to fabricate a single layer of good quality rather than directly fabricate a multilayer structure because possible fabrication defects (e.g., air bubbles) can accumulate layer by layer. The accumulated fabrication defects can make the subsequent fabrication steps difficult or even impossible. 3) Each layer can be checked before the assembly. 4) The fabrication of the active layers and the electrodes can be conducted in parallel, reducing the overall fabrication time, making it an overall more efficient process.

Another key difference in the fabrication process of this study is that the layers were attached by an electrostatic adhesive force, which brought to some additional benefits. 5) The layered structure does not have any undesirable additional stiffness caused by the chemical adhesives, which generates a negative impact on the flexibility of the active layer. 6) The assembly of the layered structure is more versatile, that is, if the position of the layer is not satisfactory, it can be easily redone. 7) When an electrical breakdown happens, the actuator can be disassembled, and the defect layer can be found and repaired, or replaced.

Electromechanical Characterization of the Rolled Soft Actuators

This section describes the experimental test setup and the electromechanical characterization of the P(VDF-TrFE-CTFE)-based rolled actuators. When an external electric field is applied via the two electrodes, a strain occurs in its axial direction on account of the synergistic effect of the Maxwell stress (i.e., the electrodes are attracted to each other and, as a consequence, the active layer is mechanically compressed) and of the electrostriction (i.e., the applied electric field induces a conformation change of the polymeric chains of the active layer).^[37]

Experimental Test Setup

The test setup consists of the test instrument ElectroPuls E1000 (Instron, Norwood (MA), USA, www.instron.us), which is equipped with the Instron dynamic load cell 2527-129 (capacity of 2 kN) and an optical encoder. A 10/10B-HS high-voltage amplifier (Trek Inc., Lockport, New York, USA, ) is connected through crocodile plugs to the lead wires of the rolled soft actuator and is operated through the DG1022 waveform generator (RIGOL Technologies, Beaverton, Oregon, USA, ). The Instron Wavematrix software records both the forces measured by the load cell and the applied voltages. The rolled actuators are placed inside the testing instrument with fixtures 3D printed in ABS material. The test setup is shown in Figure 6.

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Axial Force Test

The axial force is measured by performing a displacement control on the ElectroPuls E1000 test instrument. The instrument is controlled to maintain a fixed displacement, (i.e., the displacement of the actuator is constant), and the axial force, produced by the actuator upon stimulation with a voltage, is measured. A preload of 1 N is chosen to keep the rolled actuator in a stretched state during testing. This preload value is used for all the three specimens of the rolled actuators, in order to exclude the influence of the preload in this study. Different types of voltages waves have been applied. 1) Square voltages of 4 kV, applied five times at intervals of 10 s; 2) DC voltages ranged from 0 to 6 kV; and 3) sine wave voltages (amplitude of 4 kV, frequency of 100 mHz).

These voltages are high enough to demonstrate the elongation capabilities of the rolled actuators, while avoiding the risk of dielectric breakdown that has been observed to occur at 7 kV (42.4 MV m⁻¹) during the experiments.

Axial Displacement Test

The axial displacement is measured by performing a force control on the ElectroPuls E1000 test instrument. The instrument is controlled to maintain a fixed force (i.e., the preload of 1 N), and the axial displacement, produced by the actuator upon stimulation with a voltage, is measured. In this test, a square voltage of 4 kV is applied five times at intervals of 10 s.

Uniaxial Tensile Test

The uniaxial tensile test is designed that varies the displacement of the rolled actuator while its forces, resulting from the reaction to the tensile test itself and from the application of an electric field, are recorded. The actuator is placed in the ElectroPuls E1000 test instrument and preloaded at 1 N. After preloading, the displacement of the actuator is changed as follows. 1) The displacement between the fixtures is kept constant for 5 s and the desired voltage is applied. 2) The displacement between the fixtures is changed by applying an ascending ramp of 0.05 mm with a rate of 0.0025 mm s⁻¹. 3) The displacement between the fixtures is changed by applying a descending ramp of 0.05 mm with a rate of 0.0025 mm s⁻¹.

The actuator is stimulated by different voltages. It is important to note that the displacement range between the fixtures is chosen to maintain the actuator in the elastic phase of the materials. The test sequence is repeated three times on the same specimen. Moreover, before acquiring the data, a complete cycle without any applied voltage is performed to stabilize the mechanical behavior of the specimen.^[12] After this first cycle, the uniaxial tensile load test starts for different voltages from 0 to 6 kV.

Results and Discussion

This section shows the results of the electromechanical characterization of the rolled soft actuators. For the three categories of rolled soft actuators (i.e., ANF0, ANF60, and ANF120), three specimens have been realized (e.g., for the ANF0 category, the three specimens ANF0S1, ANF0S2, and ANF0S3 have been realized) for a total of nine rolled soft actuators.

Axial Force

Axial Force of Different Rolled Actuators Specimens

Table 3 reports the averages and standard deviations (s.d.) of the axial forces that have been obtained during the axial force tests on the different specimens.

Table 3 Mean and standard deviation (s.d.) of the axial forces, generated by different categories of actuators.

Actuator	Mean [mN]	s.d. [mN]
Rolled actuators (active layer of pure PDMS, without nanofibers)
ANF0S1 (specimen S1)	58.1	1.8
ANF0S2 (specimen S2)	59.8	1.9
ANF0S3 (specimen S3)	65.0	3.4
	Rolled actuators (active layer of a 60 μm nanofibrous mat in PDMS)
ANF60S1 (specimen S1)	86.2	1.4
ANF60S2 (specimen S2)	80.7	4.2
ANF60S3 (specimen S3)	76.9	4.0
	Rolled actuators (active layer of a 120 μm nanofibrous mat in PDMS)
ANF120S1 (specimen S1)	86.3	3.8
ANF120S2 (specimen S2)	86.6	6.4
ANF120S3 (specimen S3)	81.0	5.2

Figure 7a shows the means and standard deviations of the axial forces generated by different categories of actuators. From the figure, it is possible to note that the axial forces increase with the increase in the thickness of nanofibers. The actuator category ANF120 exhibits the highest value of mean axial force of 84.6 mN, when 4 kV voltage is applied. The mean axial force for the categories ANF0 and ANF60 is 61.0 and 81.3 mN, respectively. The mean axial force of ANF120 is 38.7% higher than that of ANF0. Moreover, the mean axial force of ANF120 is 4.1% higher than that of ANF60, which means that the effect of increasing the thickness of the nanofiber mat is not linear on the enhancement of the expansion capability.

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Axial Force at Different Voltages

ANF0S2, ANF60S3, and ANF120S2 are selected to represent category ANF0, ANF60, and ANF120, respectively. Figure 7b shows the axial forces (mean value of 5 trials) generated by the three different actuator categories when different voltages are applied. From the figure, it can be noted that, for all the specimens, the axial force increases when the voltage increases. Specifically, the axial forces under 6 kV are 136.8, 192.2, and 213.0 mN for ANF0, ANF60, and ANF120, respectively. The axial force of ANF120 is 55.7% and 10.8% higher than that of ANF0 and ANF60, respectively. The experimental data can be fitted by a quadratic interpolation, as expected from the quadratic relationship between the Maxwell stress and the applied electric field. The relationship between the axial force F (in mN) and the voltage V (in kV) is F = 3.75 V², F = 5.34 V², and F = 5.85 V² for ANF0, ANF60, and ANF120, respectively.

A major goal for soft actuator design is to achieve a high force-to-weight ratio, that is, a high ratio between the maximum axial force and the weight of the actuator.^[38] The force-to-weight ratios of ANF0, ANF60, and ANF120 are 145.5, 196.1, and 208.8 N kg⁻¹, respectively. The force-to-weight ratio of ANF120 is 43.5% higher than that of ANF0, indicating that the presence of the nanofibers enhances the actuator's output capability.

Axial Force with Sine Wave Voltage

When a force is applied to the polymer, the viscoelastic relaxation may be caused by slipping and sliding among polymer chains and rotation of joints among monomers. Moreover, subjected to an electric field, the polymer relaxes to a new state of polarization over a characteristic time and the process of reorientation of the molecular dipoles in a polar dielectric is called dielectric relaxation. Viscoelastic hysteresis has been shown to exert an adverse effect on actuators performances and cause positioning inaccuracy.^[39] In order to further investigate the viscous responses of the actuators, a sine wave voltage (amplitude of 4 kV, frequency of 100 mHz) is applied and the resulting axial force is plotted in Figure 8. ANF0S2, ANF60S3, and ANF120S2 are selected to represent category ANF0, ANF60, and ANF120, respectively. The test is repeated for 10 cycles (100 s in total). From the figure, it can be noted that the axial forces are always negative. This implies that the specimens expand, independently of the sign of the applied voltage. This behavior is due to the electrostrictive effect and, specifically, to the quadratic relationship between the expansion force and the electric polarization.^[37] The plots show good repeatability of the generated force when the same voltage is repeatedly applied over time. It can be noted that for all of the three categories, the peak-to-peak amplitude of the generated sinusoidal forces is close to the forces reported in Section 4.1.1 by the actuators, which indicates that the actuators reach almost a fully relaxation when the voltage decreases to zero and implies that the actuators have a fast dynamic response.

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Figure 9 shows the current under sine wave voltage (amplitude of 4 kV, frequency of 100 mHz). It can be noted that, although the voltage is in the order of kV, the current is of the order of μA, which ensures the safety of the soft actuators.

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The average power consumption can be evaluated by averaging the power over the test (100 s, 10 cycles). The maximum instantaneous power consumption can be calculated by multiplying the peak current by the corresponding voltage. The average power consumption and instantaneous power consumption can be calculated and are reported in Table 4. From the table, it can be seen that the actuators exhibit an overall low electrical power consumption (in the order of mW). Moreover, the power consumption increases with the increase in the thickness of nanofibers. The average power consumption of ANF120 is 17.4% higher than that of ANF0, and the instantaneous power consumption of ANF120 is 12.6% higher than that of ANF0. The increase in power consumption suggests an increase in the dielectric constant of the active layer due to the introduction of nanofibers into the PDMS matrix.^[14]

Table 4 The average power consumption (a.p.c.) and instantaneous power consumption (i.p.c.), generated by different categories of actuators.

Actuator	a.p.c. [mW]	i.p.c. [mW]
ANF0	1.15	4.59
ANF60	1.25	4.83
ANF120	1.35	5.17

Axial Displacement

Table 5 reports the averages and the standard deviations (s.d.) of the axial displacement that have been obtained during the axial displacement tests on the different specimens.

Table 5 Mean and standard deviation (s.d.) of the axial displacement, generated by different categories of actuators.

Actuators	Mean [μm]	s.d. [μm]
Rolled actuators (active layer of pure PDMS, without nanofibers)
ANF0S1 (specimen S1)	20.6	0.9
ANF0S2 (specimen S2)	23.2	1.3
ANF0S3 (specimen S3)	21.0	1.9
	Rolled actuators (active layer of a 60 μm nanofibrous mat in PDMS)
ANF60S1 (specimen S1)	17.8	1.3
ANF60S2 (specimen S2)	16.2	0.4
ANF60S3 (specimen S3)	18.6	1.5
	Rolled actuators (active layer of a 120 μm nanofibrous mat in PDMS)
ANF120S1 (specimen S1)	18.0	1.4
ANF120S2 (specimen S2)	15.2	1.1
ANF120S3 (specimen S3)	16.8	1.3

Figure 10a shows the means and standard deviations of the axial displacement generated by the different categories of actuators. From the figure, it is possible to note that the axial displacement decreases with the increase in the thickness of nanofibers. The actuator category ANF120 exhibits the lowest value of mean axial displacement of 16.7 μm, when a voltage of 4 kV is applied. The mean axial displacement for the categories ANF0 and ANF60 is 21.6 and 17.5 μm, respectively. The mean axial displacement of ANF120 is 22.7% lower than that of ANF0. This is due to the presence of nanofibers, which increases the stiffness of the actuator.^[8]

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It should be noted that there is a trade-off between the generated axial force and the axial displacement. Compared to ANF0, the ANF60 specimens lose 19.0% in displacement, but gain 33.3% in force. Compared to ANF0, the ANF120 specimens lose 22.7% in displacement, but gain 38.7% in force. From this, it is possible to conclude that the presence of nanofibers enhances the electrical response of the rolled actuator when compared to the case in which the active layer is realized by pure PDMS (without the nanofibers). Moreover, while thinner active layers and electrodes would allow for higher axial displacements, they would also lead to instability caused by film defects.^[4] As the primary goal of this study is to investigate the effects of the nanofibers rather than solely pursuing higher performances in terms of exerted axial forces or axial displacements, thicker electrodes and active layers are selected in this study to mitigate manufacturing-induced defects.

ANF0S2, ANF60S3, and ANF120S2 are selected to represent category ANF0, ANF60, and ANF120, respectively. Figure 10b shows the axial displacement (mean value of 5 trials) of three different categories of actuators when different voltages are applied. From the figure, it can be noted that, for all the specimens, the axial displacement increases when the voltage increases. Specifically, the axial displacement under 6 kV is 47.2, 39.6, and 37.6 μm for ANF0, ANF60, and ANF120, respectively. The axial displacement of ANF120 is 20.3% and 5.1% lower than that of ANF0 and ANF60, respectively. The experimental data can be fitted by a quadratic interpolation, as expected from the quadratic relationship between the Maxwell stress and the applied electric field. The relationship between the axial displacement D (in μm) and the voltage V (in kV) is D = 1.30 V², D = 1.1.0 V², and D = 1.02 V² for ANF0, ANF60, and ANF120, respectively.

Energy Density

The actuation performance is evaluated in terms of the energy density e of the actuator, which is given by^[6]1$e=\frac{1}{2}\frac{F_{\mathrm{A}}\delta }{m}$where F_A is the axial force, δ is the (free) displacement, and m is the mass of the actuator. For the actuators presented in this study, the energy density was 3.1 mJ kg⁻¹ for the AFN0 (no nanofibers), 3.4 mJ kg⁻¹ for the AFN60, and 3.5 mJ kg⁻¹ for the AFN120. The energy density of the ANF120 actuators is 12.9% and 2.9% higher than that of ANF0 and ANF60, respectively. Therefore, our study concludes that the presence of nanofibers enhances the actuation performances of the proposed rolled soft actuators.

Uniaxial Tensile Test

ANF0S2, ANF60S3, and ANF120S2 are selected to represent category ANF0, ANF60, and ANF120, respectively. Figure 11 shows the results of the uniaxial tensile test on the three different categories of actuators, when different voltages are applied.

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To obtain the stiffness of the specimens, a linear regression is performed on the data used to plot Figure 11, and their slope is the stiffness. The results show the mean and the standard deviation of three rounds of tests for each category. Figure 12 reports the stiffnesses of three different categories of actuators, when different voltages are applied. From the figure, it can be noted that the stiffness increases when the thickness of nanofibers increases. This indicates that the presence of nanofiber mat makes the actuator stiffer. In addition, for each actuator category, the stiffness decreases with the increase of voltages. This is because the actuator elongates when the voltage is applied, thus softening the actuator. Specifically, when a DC voltage of 6 kV is applied, the stiffnesses of ANF0, ANF60, and ANF120 are reduced by 6.2%, 3.1%, and 5.1% respectively compared to when no voltage is applied. It can be seen that the change in stiffness is not too significant, and the decrease of the stiffness is independent of the thickness of the nanofiber mat.

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Conclusion

This study proposed a rolled actuator based on which the active layers are realized with P(VDF-TrFE-CTFE)-based electrospun nanofiber intergrated in a PDMS matrix. In the rolled configuration, the active layers and the electrodes are fabricated separately and bonded by electrostatic adhesion force. This method improves the efficiency in the fabrication process and is prone to less fabrication defects. Different thicknesses (0, 60, 120 μm) of P(VDF-TrFE-CTFE) nanofiber mats are used to fabricate the soft actuators. The actuators are compact and with a low weight (about 1 g). The axial force of the actuators is evaluated when simulated by DC voltages, showing higher values in the case of the actuators with nanofiber mat. The rolled soft actuators exhibit a high force-to-weight ratio up to 208.8 N kg⁻¹. In addition, the axial forces when stimulated by AC electric field, are also evaluated, showing a fast viscoelastic relaxation. Moreover, the current flowing in the actuators, when stimulated by an AC electric field, is evaluated, demonstrating a low electrical power consumption of mW level.

This study concludes that the rolled actuator, in which the active layer includes P(VDF-TrFE-CTFE)-based electrospun nanofibers, has enhanced actuation capabilities in terms of energy density, when compared to a control rolled actuator without nanofibers. The rolled soft actuators based on P(VDF-TrFE-CTFE) electrospun nanofibers have a high potential in the field of soft actuators, due to their high force-to-weight ratio, fast viscoelastic relaxation, and low electrical power consumption.

Acknowledgements

This work was funded by the European Commission's Horizon 2020 Programme as part of the project MAGNIFY under grant no. 801378 and by the China Scholarship Council under grant no. 202006220018. The authors would like to thank Dr. Alessio Marrani (Solvay Specialty Polymers, Italy) for providing the P(VDF-TrFE- CTFE) material. The scanning electron microscopy images were taken at the Microscopy and Imaging Center (UMIC) of the University Medical Center Groningen (The Netherlands), sponsored by ZonMw grant 91111.006 (Zeiss Supra55 ATLAS).

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflict of Interest

The authors declare no conflict of interest.

Author Contributions

Jiahao Pan: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Project administration (equal); Software (lead); Validation (lead); Visualization (lead); Writing—original draft (lead); Writing—review & editing (equal). Riccardo D’Anniballe: Conceptualization (equal); Formal analysis (supporting); Methodology (supporting); Validation (supporting); Writing—review & editing (equal). Raffaella Carloni: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (lead); Supervision (lead); Writing—review & editing (equal).

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