High-Frequency, low-voltage oscillations of dielectric elastomer actuators

Integrating active motion control in stretchable objects requires highly compliant actuators. Many researchers in the soft robotics field have investigated actuators that are soft and capable of actively changing their shape. Examples include soft pneumatic actuators, ^1,2) stretchable pumps, ^3,4) shape-memory polymers, ⁵⁾ gel actuators, ^6–8) and dielectric elastomer actuators (DEAs). ^9–13)

DEAs have a simple structure that can be used to create a bioinspired robot (e.g., a DEA insect ¹⁴⁾). DEAs are a promising soft actuator technology due to their high energy density, ^15,16) and fast response_. ^17,18) DEAs consists of a dielectric elastomer (DE) membrane sandwiched between two stretchable electrodes (Fig. 1). Applying a voltage to stretchable electrodes generates an attractive electrostatic force between the electrodes. Typically, a kV range is required to drive DEAs with a thickness of hundreds of micrometers. The electrostatic force generated between the electrodes produces a pressure that squeezes the DE membrane in the thickness direction (z-direction) and expands the in-plane direction (xy-plane) due to the incompressibility effect of the elastomer. The amount of pressure (P) generated can be expressed using the Maxwell pressure ¹⁹⁾ as.

$$\begin{eqnarray}&&P={\varepsilon }_{0}{\varepsilon }_{r}{\left(\displaystyle \frac{V}{t}\right)}^{2},\end{eqnarray} \tag{ 1 }$$

where ${\varepsilon }_{0},{\varepsilon }_{r},V,$ and $t$ are the vacuum permittivity, the dielectric constant, the applied voltage, and the DE membrane thickness, respectively. For a small actuation strain (at a strain typically below 20%), ¹⁹⁾ the relationship between the applied voltage and deformation in the thickness direction (S_z ) is expressed as

$$\begin{eqnarray}&&{S}_{z}\,=\,{\varepsilon }_{0}{\varepsilon }_{r}\displaystyle \frac{{V}^{2}}{Y{t}^{2}},\end{eqnarray} \tag{ 2 }$$

where Y is the elastic modulus of the DE membrane. From these equations, we can design low-voltage DEAs by reducing the thickness (t) of the DE membrane.

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A practical advantage of DEAs can be obtained when the DEAs can operate at low voltage. One possible application of low-voltage DEAs is as a haptic feedback device (HFD). ²⁰⁾ HFD usually has direct contact with the human body. In this case, low-voltage operations should ensure safe conditions for humans.

In HFD, DEAs should operate at a wide range of frequencies to provide multi-sensational feedback feeling when the device is utilized for a specific purpose. The current challenge of DEAs for HFD is the high driving voltage of DEAs that limits their application in the devices. In addition, cost, bulkiness, and electronics safety are also concerns. ²¹⁾ Electricity safety for humans is mandatory when designing an electromechanical actuator system. Our nanosheet-DEAs use a DC voltage source with a safety superior to that of an AC voltage source. The DC voltage does not have a definite shake-off threshold, which causes muscle pain and a spasm-like contraction. ²²⁾ Typically, DC electricity has a smaller electric shock accident risk than that of AC because shake off from the DC conductor is easier. Moreover, when the electric shock duration is higher than the cardiac cycle (around 800 ms), the ventricular fibrillation threshold of DC greatly exceeds that of AC. ²²⁾

There are three variables that affect the human body's response to electrical shock: the electrical resistance of the body, the amplitude of the applied voltage, and the amplitude of the current flowing through the body. ²³⁾ Considering these variables, the latest study about DC voltage to human health has found that a DC voltage less than 72 V will not cause skin scars, organ damage, or more dangerous injuries, ²²⁾ and when operated in a dry environment, it will not cause an unconscious cardiac muscle response. This value of DC voltage has also been confirmed as safe in medical treatments. ²⁴⁾

Much effort has been devoted to reducing the driving voltage of DEAs, for example, decreasing the film thickness, reducing the elastic modulus, ^11,25) and increasing the dielectric permittivity ²¹⁾ of the DE membrane. To design low-voltage DEAs, we must consider the electrical breakdown (E_B ) of DEAs. The E_B depends on both the thickness and the stretching ratio of the DE membrane. From the viewpoint of the E_B , reducing the membrane thickness is a reasonable approach to improve the electrical breakdown field. Previously, Gatti et al. ²⁶⁾ developed the empirical formula to model the E_B of PDMS-based DEAs, as shown in Eq. 3.

$$\begin{eqnarray}&&{E}_{B}\,=\,147\,{t}^{-0.23\,\pm \,0.02}\,{\lambda }^{1.77\,\pm 0.03\,},\end{eqnarray} \tag{ 3 }$$

where t is the initial elastomer thickness in μm, E_B is the electrical breakdown field strength in V μm^–1, and λ is the stretching ratio. Based on Eq. 3, minimizing the elastomer thickness can optimize the electrical breakdown field strength of the DE and reduce the driving voltage of DEAs at the same time.

The thickness of a DE membrane typically ranges from 20 to 100 μm. Recently, researchers fabricated a 3 μm thin silicone elastomer film for DEAs and reported a 7.5% lateral DE actuation strain at 245 V at a static test condition. ²¹⁾ Further reducing the DE membrane thickness enable DEA actuation in the hundreds of volt range. This approach is promising for low-voltage DEAs, but the fabrication process is challenging since attaching stretchable electrodes without damaging or adding additional stiffness to the DE membrane is difficult.

This study focuses on a simple fabrication of low-voltage DEAs capable of high-frequency operations by reducing the DE membrane thickness. We fabricate a PDMS nanosheet with three layers: PET (polyethylene terephthalate) film as the temporary supporting substrate, PVA (polyvinyl alcohol) membrane as the sacrificial layer, and PDMS (polydimethylsiloxane) as the nanosheet. The PDMS nanosheet can be released from the temporary substrate and easily transferred to any target surface. Herein we integrate 600 nm thick PDMS nanosheets and 200 nm thick stretchable electrodes composed of poly(3,4-ethylenedioxythiophene):poly(4-styrenesulfonate) (PEDOT:PSS) (PEDOT:PSS aqueous dispersion, Clevios PH1000 from H.C. Starck GmbH, Leverkusen, Germany) ²⁷⁾ ultrathin layer coated on a poly(styrene-b-butadiene-b-styrene) (SBS) nanosheet, which was fabricated using the roll-to-roll (R2R) process under the same conditions as in the previous report by Yamagishi, et al. ²⁸⁾ for low-voltage DEAs. Briefly, the nanosheet fabrication process began with the deposition of a polymer solution on the desired substrate using a gravure roll (Fig. S1(a) available online at stacks.iop.org/APEX/15/011002/mmedia) until the drying process. Then these nanosheets were used to create a single-layer low-voltage DEA.

To fabricate low-voltage DEAs, we first manually removed the nanosheet PDMS-PVA membrane from the hard PET membrane [Fig. 2(a)]. The removal technique was also applied to a PEDOT:PSS-SBS membrane since both nanosheet PDMS and PEDOT:PSS-SBS formed on a PVA coating with a PET roll substrate. Figures S1(b) and S1(c) show the layer arrangements of the PDMS nanosheet and final product, respectively.

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To remove the PVA layer from both nanosheets PDMS and PEDOT:PSS-SBS, we submerged the PDMS nanosheets into the NaCl–water solution with the PVA layer facing the liquid solution [Figs. 2(b) and 2(d)]. Figure S2 shows a detailed process of PVA removal. The liquid solution plays an essential role in the nanosheet stability condition. Hydrophilic polymers such as PVA absorb a lot of solvents. According to the Flory theory, ²⁹⁾ the thermal equilibrium state of the swelling polymers is fixed when the chemical potential of the solvent is equal inside and outside the polymer. (Figure S3 shows the expansion as a function of time for the nanosheet PDMS and excessive volume changes lead to the self-destruction of nanosheet PDMS [Fig. S4)].

Thus, the liquid solution becomes key in the PVA removal to prevent the self-destruction of nanosheet PDMS. Increasing the ionic strength of the liquid solution minimizes the osmotic pressure and controls the expansion of the nanosheet. Here, we used a NaCl–water solution to reduce the osmotic pressure. In NaCl–water solution the osmotic pressure can be easily controlled by adding or reducing the amount of NaCl in the solution.

Next, a rigid frame was applied to the nanosheet PDMS [Figs. 2(c) and S2)]. Then the electrodes (PEDOT:PSS-SBS) were applied to the PDMS nanosheet [Fig. 2(e)]. After the nanosheet PDMS sandwiched between the PEDOT:PSS-SBS (similar to the structure in Fig. 1), we left the nanosheet DEAs at room temperature until the nanosheet is fully dry (approximately 24 h). A pre-stretch of approximately 6% is acquired during the drying process since the PDMS nanosheet expands at 1.06 (Fig. S3) and shrinks at an initial size during the drying process. Finally, our low-voltage DEAs were connected with a wire using carbon ink [Fig. 2(f)]. We then operate the DEAs at room temperature conditions (20 °C and relative humidity of 50%).

Before connecting the nanosheet-DEAs to the DC voltage source, we analyzed the electric breakdown field (E_B ) strength limit using Eq. 3. To avoid breakdown during the dynamic test of nanosheet DEAs, we applied a DC voltage below the estimated breakdown field strength limit. Figure 3 shows the estimated breakdown strength limit of our nanosheet-DEAs. The safest operation condition should be between 33 and 150 mV nm⁻¹ since the calculated breakdown field limit is ∼165 mV nm⁻¹. The operation below the breakdown field limit should ensure the durability of the DEAs. ¹¹⁾ To perform a dynamic test on the nanosheet DEAs, we connected the DEAs [Fig. 2(f)] to DC voltage sources of 20, 50, and 90 V, which have calculated electrical fields of 33.3, 83.3, and 150 mV nm⁻¹, respectively. The cutoff frequency of the nanosheet DEAs was estimated using RC time constant ¹⁴⁾ analysis, which is given as

$$\begin{eqnarray}&&{f}_{c}=\displaystyle \frac{1}{2\pi RC}=\displaystyle \frac{t}{2\pi R\varepsilon A}\end{eqnarray} \tag{ 4 }$$

where f_c is the electric cutoff frequency, R is the resistance of the electrodes, C is the capacitance of the nanosheet-DEAs, ε is the dielectric permittivity of the membrane, and A is the active area of the nanosheet DEAs. Our nanosheet DEAs have a capacitance of 4.03 pF and the electrode total resistance is ∼326 kΩ. From the RC time constant (Eq. 4), the nanosheet DEAs can reach a cutoff frequency of ∼120 kHz. To vary the nanosheet DEAs operations, we used a signal generator, which produced a sine wave by repeatedly switching the DC voltage electric source on–off (pulse width modulation) with a frequency of 1–30 kHz. We used a laser Doppler vibrometer (Polytec OFV-505) to investigate the actuation performance of the DEAs (Fig. S6).

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Figure 4 shows the time history of the waveforms in the DE actuation. Figures 4(a)–4(c) depict the first 10 DEAs actuation cycles. In this experiment, the DEAs velocity response (Fig. S6) is defined as the time needed by the DEA surface to deform and relax cyclically. Surprisingly, the nanosheet DEA actuates at 50 V and covers a high frequency, including ultrasonic frequency. The low-voltage DEAs can respond with similar actuation characteristics when they are driven with a high-frequency DC voltage. The waveforms of the nanosheet-DEAs have identical sinusoidal shapes when operated at lower actuation frequencies [Figs. 4(a) and 4(b)], and at higher frequency operations of 30 kHz, the actuation is also close to sinusoidal shape [Fig. 4(c)]. This indicates that the low-voltage DEAs can handle operations at a wide range of frequency actuations. Moreover, Fig. 4 also indicates a repeatable high-frequency response of the nanosheet DEAs.

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Quantitatively in Fig. S7, we show the nanosheet DEAs characteristics of the frequency response in terms of velocity response and displacement response. Additionally, we also show the displacement of the nanosheet DEAs vs DC applied voltage in Fig. S8. We found that our nanosheet DEAs has approximately 1% actuation strain at 50 V and 2% at 90 V. Theoretically, in ideal DEAs (according to Eq. 2), the actuation of the nanosheet DEAs should be around 2% at 50 V and 7% at 90 V (Fig. S8). This difference in theoretical and experimental results is possibly due to the effect of the electrodes type ¹⁷⁾ since in Eq. 2 the actuation performance was defined by the dielectric elastomer without considering the stiffness of the electrodes of the DEAs. Furthermore, the response of the nanosheet DEAs in the thickness direction at high-frequency operation was confirmed by integrating the velocity response over time using a numerical integration Matlab toolbox (cumulative trapezoidal rule). Figure 5 shows the displacement of the nanosheet DEA membrane in the z-direction (Fig. S6 shows the nanosheet DEA actuation direction). The estimated displacement of the nanosheet DEA is several nanometers as shown in Fig. 5.

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Table I compares these DEAs operation results with previously reported devices. We successfully fabricated low-voltage DEAs, which can be actuated at a DC voltage below 70 V and over a wide frequency range. This device is the thinnest DEA reported to date.

In conclusion, The R2R method can effectively realize an ultrathin stretchable electrode and a DE membrane. We simultaneously employed PVA as a sacrificial layer and tools to pre-stretch the elastomer membrane. The optimized condition of the nanosheet PDMS was achieved using a 15 wt% NaCl–water solution. A nanometric elastomer membrane (600 nm thick) and electrodes (200 nm thick) enable low-voltage DEA operations. Low-voltage DEAs that can operate below 70 V increase the safety and decrease the complexity of the electric circuit required to drive the DEAs.

Our future challenges are to fabricate novel electrodes with a lower Young's modulus than that of the electrodes used in this study and to create a multi-stacking layer of ultrathin DEAs. Electrodes with a higher Young's modulus compared with the DE layer can suppress the displacement of DEAs. ¹⁷⁾ Generally, conducting polymers represented by PEDOT:PSS have Young's modulus of several GPa (e.g., 2.4 GPa ³⁰⁾). Hence, Young's modulus of PEDOT:PSS should impair the elasticity of an SBS nanosheet (i.e., 59 MPa ³¹⁾). According to our previous report, an ultrathin strain sensor consisting of PEDOT:PSS printed on the SBS nanosheet showed Young's modulus of 227 ± 32 MPa. ³²⁾ Utilizing other nanomaterials (e.g., carbon nanotube and metal nanowire) and the multi-stacking of DEAs should further reduce Young's modulus of the electrodes and improve the overall actuation performance. These improved low-voltage DEAs should realize new wearable device applications, including low-voltage DEAs for haptic device applications.

Acknowledgments