Lowering of Electrostatic Actuator Driving Voltage and Increasing Generated Force Using Spontaneous Polarization of Ferroelectric Nematic Liquid Crystals

Abstract

Although electrostatic actuators have a simple structure and are lightweight, their range of application is limited because a high applied voltage of more than several kilovolts is required for practical use. Since the force acting between the electrodes of an electrostatic actuator is determined by the electric charge accumulated at the electrode/dielectric interface, the focus is on spontaneous polarization of ferroelectrics to increase the charge. As the ferroelectric material, a nematic liquid crystal material with a spontaneous polarization of 5 µC cm⁻² is used. It is demonstrated that a force of 1.3 N is generated at an applied electric field of 0.5 MV m⁻¹. This force is 1200 times higher than that for standard paraelectric materials with a dielectric constant of ten. Further, the generated force responds linearly to the applied voltage, whereas it is proportional to the square of the applied voltage for paraelectric materials. The actuator function of this ferroelectric is examined using a double‐helical coil electrode fabricated using a 3D printer. It can be successfully operated at a voltage of several tens of volts. Under an electric field of 0.25 MV m⁻¹, a remarkable contraction of 6.3 mm occurs, corresponding to 19% of the original length.

Introduction

As human life expectancy increases, the importance of health is becoming increasingly recognized.^[1,2] Age-related muscle deterioration reduces mobility.^[3,4] Many soft actuators have thus been developed to realize artificial muscles that can support walking and standing.^[5–7]

Materials used for soft actuators include gels,^[8] conductive polymers,^[9] ion-conductive polymers,^[10,11] carbon nanotubes,^[12] dielectric elastomers,^[13,14] polymer fibers,^[15] and liquid crystals.^[16–19] However, few materials meet the power-output, flexibility, and light-weight requirements to support human walking. Although electrostatic actuators are promising,^[19] their practical application has been limited because a high voltage is required to generate a sufficient force. They have thus been applied in fields such as microelectromechanical systems, where the processing size is on the order of micrometers,^[20–24] with few practical examples on a scale larger than millimeters. In addition, existing electrostatic actuators require a high voltage of several kilovolts to several tens of kilovolts, leading to concerns about the risk of electric shock when used on the human body. Thus, it is necessary to lower the driving voltage and increase the generated force.

The source of the generated force F in an electrostatic actuator is the electric charge Q accumulated at the electrode/dielectric interface. When an electric field E is applied to parallel-plate electrodes with a distance d between the electrodes, the generated force F acting between the electrodes can be expressed by 1 $$$\begin{equation}F = \frac{1}{2} QE = \frac{1}{{2d}} QV\end{equation}$$$

Therefore, to increase the generated force F without increasing the driving voltage V, it is necessary to increase the charge Q. For this purpose, it is effective to use the polarization phenomenon. Polarization, which refers to the electric charge per unit area, is classified into electron polarization, ion polarization, orientation polarization, and interface polarization, depending on its generation mechanism. The magnitude of polarization is determined by the magnitude and direction of the dipole moment per unit cell.

In ferroelectrics, it is known that a huge spontaneous polarization result from cooperative fluctuations of electrons, ions, and dipoles induced by an alternating electric field. It is thus expected that a huge generated force can be obtained if spontaneous polarization is used as the electrostatic actuator medium. For example, under the assumption that the spontaneous polarization P_s is 10 µC cm⁻², the distance d between electrodes is 100 µm, the electrode area S is 1 cm², and the applied voltage V is 20 V, the generated force can be as high as 1 N, as determined from Equation (1), indicating that the actuator has sufficient potential as a power source for an artificial muscle. For an ideal ferroelectric material, the polarization-voltage curve exhibits hysteresis, as shown in Figure 1a, suggesting that the generated force has a voltage dependence such as that shown in Figure 1b (obtained from Equation (1)). Except for nonlinear hysteresis characteristics near the coercive electric field E_c where the dipole direction reverses, the generated force has a linear response proportional to the applied voltage because the polarization is almost constant and independent of voltage.

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In contrast, for a paraelectric material, the accumulated charge is proportional to the applied voltage (Equation (2) and Figure 1c), 2 $$$\begin{equation}Q = CV = \frac{{{\varepsilon }_r{\varepsilon }_0S}}{d} V\end{equation}$$$where C is the capacitance, V is the applied voltage, d is the distance between electrodes, S is the electrode area, ε₀ is the dielectric constant of a vacuum, and ε_r is the relative dielectric constant. Substituting Equation (2) into Equation (1) gives 3 $$$\begin{equation}F = \frac{{{\varepsilon }_r{\varepsilon }_0S}}{2} {\left( {\frac{V}{d}} \right)}^2\end{equation}$$$

Equation (3) for the generated force is commonly used for electrostatic actuators with ordinary paraelectric media. The generated force is proportional to the square of the applied voltage (Figure 1d). Under the assumption that the relative dielectric constant for the paraelectric material is ten, the distance between electrodes is 100 µm, the electrode area is 1 cm², and the applied voltage is 20 V, as in the previous calculation, the generated force is only 0.2 mN.

This comparison indicates that ferroelectric media are superior to ordinary paraelectric media for use in electrostatic actuators in two respects. One is that the generated force is higher because a large polarization can be maintained even at low voltage, and the other is that the voltage response is almost linear, which gives good device controllability.

It is desirable to find soft ferroelectrics with large spontaneous polarization that can be applied to artificial muscles. Many inorganic materials that exhibit ferroelectricity have been reported. Some materials, such as BaTiO₃ and BiFeO₃, have been found to have a huge spontaneous polarization of 50 to 100 µC cm⁻² due to the presence of permanent dipoles caused by the asymmetrical atomic arrangement derived from the perovskite structure.^[25,26] However, such inorganic materials are so hard that they are unsuitable for actuators due to their small deformation in response to an applied voltage.

Organic materials are superior to inorganic materials, but few organic materials exhibit ferroelectricity.^[27–29] Among organic materials, liquid crystals are good candidates for soft ferroelectrics. Liquid crystal molecules can be easily designed so as to have a large dipole moment. Ferroelectricity results from the cooperative association of molecules into non-centrosymmetric packing. However, ferroelectric liquid crystals have been produced in only particular smectic phases, such as the chiral smectic C phase and the banana phase.^[30,31] Recently, ferroelectricity in the nematic phase, the most common phase in rod-shaped liquid crystals, has received interest. Theoretical studies by Lee et al. showed that the nematic phase becomes ferroelectric when a rod-shaped molecule has a large dipole moment that exceeds a certain critical magnitude along its long axis.^[32,33] This theoretical prediction is supported by the fact that nematic liquid crystals of aromatic polyesters and helical polypeptides with a large dipole moment along their long axis form ferroelectric nematic (N_F) phases via dipole–dipole interaction.^[34–36] Furthermore, more recent studies have indicated that low-molecular-weight liquid crystals with a dioxane group at the molecular end (referred to as DIO hereafter) exhibit a ferroelectric N_F phase and that their relative dielectric constant exceeds 10 000.^[37,38] Their fluidity and large spontaneous polarization of 4 µC cm⁻² make these liquid crystals suitable for soft actuators. The chemical structure and phase behavior of DIO are shown as No. 5 in Figure 2. It has been reported that a splay nematic phase is also ferroelectric.^[39,40] The discovery of these two molecular systems with a large dipole moment has stimulated a search for new ferroelectric N_F phase systems and an investigation of their polymerization.^[41–43]

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In the present study, we examine ferroelectric N_F liquid crystals as a medium for electrostatic actuators and apply them to a double-helical coil electrode (DHCE) device fabricated using a 3D printer and electroless resin plating.

Results and Discussion

Physical and Chemical Properties of Synthesized Liquid Crystals

Here, we considered applying the N_F phase of DIO as a medium for electrostatic actuators. However, the N_F phase of DIO is monotropic; it appears in the temperature range of 69–34 °C only on cooling and is easily crystallized if it is held at these temperatures for a prolonged time. Since room-temperature application is necessary, we first searched for new liquid crystal materials that can stably form the N_F phase at room temperature.

Material chemistry design principles for the ferroelectric nematic phase in rod-shaped liquid crystals have recently been established.^[44,45] A simple but essential guideline for synthesis is that the rod-like molecules must have a large dipole moment. The dipole moment can be increased by creating a relatively positive polarity employing an electron-donating group at one end of a rigid molecule and a relatively negative polarity employing an electron-withdrawing group at the opposite end. Note that the structure of DIO combines electron-donating and electron-withdrawing parts linked by an ester bond. Various combinations were explored by changing the raw materials for esterification based on quantum chemical calculations. As shown in Figures S1 and S2, Supporting Information, the dipole moments of the constituent parts of each electron-donating (vertical axis, 10 kinds) and electron-withdrawing (horizontal axis, 14 kinds) group, as well as the dipole moments of the combined molecules, were comprehensively calculated. Combinations with a maximum dipole moment of 14.50-D were found. Among them, ten compounds selected based on their dipole moment were synthesized. Their phase transition temperatures are summarized in Figure 2.

Most of the compounds in Figure 2 were crystalline at room temperature. However, DIO-CN (No. 6 in Figure 2), which has a huge dipole moment of 12.08-D, forms a liquid crystal at room temperature during the cooling process. Unfortunately, this material forms the ordinary paraelectric N phase, not the ferroelectric one. Although we failed to find a suitable material, we tried to mix the newly synthesized materials with DIO to lower the N_F temperature of DIO via eutectic depression of the crystal melting temperature. As a typical mixture, we selected a mixture of DIO and DIO-CN with a ratio of 50:50.

The transition temperatures and enthalpies during the cooling process for this equimolar mixture were as follows: Iso – 132 °C (0.47 kJ mol⁻¹) – N – 78 °C (0.01 kJ mol⁻¹) – SmZ_A – 52 °C (0.27 kJ mol⁻¹) – N_F – 22 °C (0.04 kJ mol⁻¹) − SmA (as shown later in Figure S5, Supporting Information). The ferroelectricity of the N_F phase was confirmed by the polarization switching behavior (as shown later in Figure 4). The spontaneous polarization P_s was about 5 µC cm⁻² in an electric field of 0.5 MV m⁻¹ at 30 °C and the relative dielectric constant ε′ in the ferroelectric N_F phase exceeded 10 000 (as shown in Figures S3 and S4, Supporting Information) and the dielectric anisotropy is positive.^[37] SmZ_A was an unidentified mesophase but was classified here based on a previous study.^[46] The sample was a slightly viscous fluid without elasticity. The breakdown voltage was about 15 MV m⁻¹.

It should be noted that the ferroelectric N_F phase is thermodynamically unstable, but remains in the ferroelectric N_F phase for a long time at room temperature due to supercooling. However, if a mechanical or electrical shock is applied, crystallization takes place. The melting temperature of the resulting crystal is around 50 °C.

Generated Electrostatic Force

Before the application of the liquid crystal to a device with a DHCE (described later), the force generation mechanism was examined using simple parallel-plate electrodes.

The electrical and optical properties of liquid crystals are often measured by filling a glass cell coated with transparent electrodes with the liquid crystal material. However, since measuring the generated force in a glass cell is difficult, we constructed an instrument using a universal tensile tester that can simultaneously measure the applied voltage, the current through the sample, the distance between electrodes, and the generated force (see Figure 3). A small heater was built into the base (Figure 3a) fabricated using a 3D printer and an aluminum plate (10 mm wide and 40–45 mm long) with a thin thermocouple attached to the top served as the electrode.

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A pair of electrode bases was placed at an angle 90° to each other. The effective electrode area was 1 cm² (Figure 3b). The small heater and thermocouples were connected to a temperature controller to heat the liquid crystals from room temperature to ≈100 °C, allowing the generated force in any liquid crystal phase to be measured. A signal source and a power amplifier were used to apply a triangular wave or other voltages to the electrodes, and a current amplifier was connected in series to measure the current flow. The lower chuck of the tensile tester was fixed whereas the upper chuck was movable in the vertical direction by the arm with a load cell (Figure 3d). The liquid crystal material was placed on the lower electrode and heated to a liquid crystal phase and was in direct contact with bare metal electrodes that have not been treated with rubbing or alignment layers. The distance between the electrodes was then adjusted by moving the arm up or down to measure the generated force at the desired gap (Figure 3b,c). The load cell was fixed during the measurement, so the distance between electrodes was kept constant.

Generated Force Calculated from Voltage versus Current Relationship

We first tried to estimate the expected electrostatic forces from the voltage versus current relationship (refer to Figure 1). Here, a triangular wave with an amplitude of 150 V_AC and a frequency of 10 Hz was applied by keeping the distance between the electrodes at 300 µm (0.5 MV m⁻¹). Figures 4a and 4e show the typical time response of the measured current to the applied voltage for the paraelectric N phase at 85 °C and for the ferroelectric N_F phase at 30 °C, respectively. Figure 4b,f shows Lissajous figures showing the applied voltage versus the measured current. Figure 4b shows the voltage–current characteristics of a typical paraelectric material and Figure 4f shows the polarization reversal current unique to ferroelectric materials.

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Figure 4c,g shows polarizations obtained using time integration after the removal of the conduction current component from Figure 4b,f. The observed spontaneous polarization of the ferroelectric N_F phase is 5 µC cm⁻². This value was compared with the calculated one, which is the product of the number of molecules per unit volume and the dipole moment. The molecular weight and dipole moment for DIO (No. 5 in Figure 2) are 510.4 and 9.33-D, respectively, and those for DIO-CN (No. 6 in Figure 2) are 423.4 and 12.08-D, respectively. If the specific gravity is assumed to be 1.1, the spontaneous polarization of the mixture of DIO and DIO-CN with a ratio of 50:50 is estimated to be 5.17 µC cm⁻², which is consistent with the observed value of 5 µC cm⁻².

The generated forces shown in Figure 4d,h were calculated from the polarization and the applied voltage according to Equation (1). These results were as theoretically expected, as shown in Figure 1b,d; the generated force is proportional to the square of the applied voltage in the paraelectric N phase, whereas it is almost proportional to the applied voltage in the N_F phase.

The magnitude of the force is different between the N and N_F phases. At 150 V and with a distance between electrodes of 300 µm, the generated forces expected for the paraelectric N and ferroelectric N_F phases were 0.28 and 1.3 N, respectively (see Figure 4d,h). Let us compare the magnitude of these generated forces with those for a conventional standard paraelectric such as insulating oil. For a standard paraelectric, under the assumption that it has a relative dielectric constant of ten, the generated force is estimated to be only 1.1 mN from Equation (3) under the conditions mentioned above.

Thus, the spontaneous polarization for the ferroelectric can generate a huge force that is ≈1200 times greater than that for a conventional paraelectric material. Of note, even in the paraelectric N phase of this system, a force 250 times greater than that for a conventional paraelectric material is generated. This is due to the fact that the paraelectric N phase has a large dielectric constant of more than 1000 at 10 Hz, which may be attributed to the cooperative fluctuation mode of a large number of associated dipoles (see Figures S3 and S4, Supporting Information).^[47–49]

Generated Force Measured Using a Load Cell

The generated forces in the N and N_F phases, measured directly by the load cell of the tensile tester shown in Figure 3, are shown in Figures 5a and 5e, respectively, and the corresponding Lissajous figures for the applied voltage versus the generated force are shown in Figures 5b and 5f.

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Note that the directly measured force responded to the applied voltage with a time delay that cannot be ignored. To estimate the time delay, the cross-correlation function for the generated force versus the absolute value of the applied voltage was calculated. The results are shown in Figure 5c,g. These figures show that the generated force had a time delay of 6–7 ms. Lissajous figures corrected for the time delay are shown in Figure 5d,h. A comparison of the Lissajous figures in Figures 5d and 5h with those in Figures 4d and 4h, respectively, indicates that the shapes and magnitudes of the forces measured using the load cell are in good agreement with those calculated from the current measurements. Thus, we can conclude that the charge accumulated at the electrode/dielectric interface is the source of the electrostatic force in both the ferroelectric and paraelectric media.

Finally, we report an exciting phenomenon that was visually observed through the phase transition of N to N_F. When observed from the side, after the application of a voltage of 200 V_DC, the liquid crystal material was stable from 85 to 50 °C (Figure 6a–d) due to the balance of surface tension between the upper and lower electrodes and the surrounding air. At 45 °C, the material began to separate into several columnar shapes. Further, it changed into many small columns below 40 °C and convection was observed within each column (Video S1, Supporting Information). At temperatures below 30 °C, the liquid crystal material began to crystallize. Some liquid crystals moved to the electrode edge and crystallized (see just below the red arrow in Figure 6h). Another interesting phenomenon was observed when the distance between the electrodes was increased at a rate of 1 mm min⁻¹ at 35 °C. As shown in Figure 6i (and Videos S2 and S3, Supporting Information), the columns extended to a length of more than 20 mm while decreasing in number. It should be noted that these thread-like columns immediately broke when the electric field was turned off.

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The observed convection is thought to be due to electrohydrodynamics.^[50] The dielectrophoretic force drives the dielectric material's electrohydrodynamics under a nonuniform electric field.^[51–53] Electrohydrodynamics in liquid crystals is widely known as an unstable phenomenon through characteristic patterns such as the Williams domain, cellular patterns, parallel striations, and chevrons that occur during this process.^[50] These 2D patterns are observed perpendicular to the glass cell with a gap of a few micrometers using polarized optical microscopy with the application of a high electric field. The liquid crystals investigated in the present study could be observed directly beside a pair of electrodes due to their huge polarization and dielectric constant, which allows the distance between the electrodes to be several hundred micrometers. The columnar structure and thread-like deformation are fascinating phenomena, the first time observed in ferroelectric nematic liquid crystals, and are considered to be a kind of liquid bridge that involves Maxwell stress and electrohydrodynamics.^[54–56] A detailed analysis is left for future research.

Double-Helical Coil Electrode Device

Since it was confirmed that a liquid crystal material with a huge spontaneous polarization is a promising medium for electrostatic actuators, the application of such materials to actual devices was examined.

For the development of device structures for electrostatic actuators, one must consider the reduction of the interelectrode distance and the wiring of the electrodes. An electrode structure that simultaneously solves these problems is the helical electrode. Carpi et al. reported a contraction ratio of 5% in an electric field of 14 MV m⁻¹ in a device in which a silicone rubber cylinder was cut into a helical shape and the electrodes were made of a material mixed with carbon black.^[57] We adopt the DHCE structure, which doubles the electrode area by using both sides of the helix. Because it is difficult to fabricate a double-helix structure with a large cross-sectional aspect ratio using metal processing, we used a 3D printing technique. To fabricate a DHCE electrostatic actuator with a large contraction ratio, a coil structure was printed using a UV-curable resin 3D printer and subjected to electroless plating.

Among various methods for 3D printing, including selective laser sintering, stereo lithography, and inkjet, we adopted the optical method,^[58,59] which is considered to be particularly suitable for high-definition output. The optical fabrication method uses a UV light source, usually with a wavelength of 365 or 405 nm, to irradiate the part of the shape to be formed by laser scanning or pattern projection using a digital micromirror device or an LCD mask panel to cure the resin and output a 3D model. Although there are differences depending on the projection method and the model, general-purpose machines can produce models with an in-plane resolution of lower than 50 µm and several tens of micrometers in the stacking direction. A high-end machine using the two-photon absorption method can produce models down to a submicron size.^[60]

Figure 7a shows the procedure used for rapid prototyping using a 3D printer. The spacer also has a double-helical coil structure to prevent short-circuiting of the electrodes. To prevent the coils from coming off the coaxial axis, a core rod with a threaded groove is passed through the center of the device. The entire device is tightened with a nut to allow the distance between electrodes to be freely adjusted.

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A liquid crystal material was dropped onto the electrodes of the device and a voltage was applied after the liquid crystal material was allowed to fill the space between the electrodes.

To measure the contraction ratio, the device core rod was suspended by a clip, as shown in Figure 7b, and a voltage was applied while the actuator could expand and contract freely. Before application of the voltage, the device length was 32.6 mm. When an electric field of 0.25 MV m⁻¹ (200 V/0.8 mm) was applied, the length decreased to 26.3 mm, resulting in a contraction of 6.3 mm and a contraction ratio of 19.3% (Figure 7b and Videos S4 and S5, Supporting Information). Visual observation showed that the device did not move at an applied voltage of 10 V but did move at 20 V (Video S6, Supporting Information). This means that the present actuator can be powered by a dry cell battery. When two 006P dry cell batteries were connected in series to create an 18-V power supply, the device moved, albeit slightly (Video S7, Supporting Information). These results indicate that a low driving voltage and a high-power electrostatic actuator can be realized using ferroelectric nematic liquid crystals as an electrostatic medium.

Although the soft material used in this study is a liquid crystal at room temperature, it is in a supercooled state. Hence, whenever the distance between the electrodes is narrowed by an AC electric field, the liquid crystal material is pushed out of the electrodes and sometimes crystallizes, which interferes with the movement of the electrodes. In addition, the viscoelasticity was not optimized, and thus there is room for improvement in terms of force transmission. If we can optimize the viscoelasticity of the liquid crystal material via gelation or polymerization into an elastomer,^[16,61–63] and integrate the material with the DHCE device, we will be able to realize an actuator with higher power and a wider range of motion.

Conclusion

Conventional electrostatic actuators have limited applications because a high applied voltage of several kilovolts to several tens of kilovolts is required for practical use. Air or ordinary paraelectric materials with a dielectric constant of about ten are typically used as the medium, leading to a weak generated force.

In this study, we proposed using the spontaneous polarization of ferroelectric materials to generate a large force with an electrostatic actuator. There are two advantages to using spontaneous polarization. First, the generated force is relatively high because spontaneous polarization is much larger than the dielectric polarization in paraelectric materials. Second, the generated force is almost proportional to the applied voltage because spontaneous polarization is independent of the applied voltage above the coercive electric field, which gives good device controllability.

As the ferroelectric material, we used a ferroelectric N_F phase with a spontaneous polarization of 5 µC cm⁻² formed at room temperature from an equimolar mixture of DIO and DIO-CN. The resulting force was found to be almost proportional to the applied voltage across parallel-plate electrodes and about 1200 times higher than that for a conventional paraelectric material with a relative dielectric constant of ten under the same driving conditions. Furthermore, the ferroelectric liquid crystal material was used as the medium for a DHCE electrostatic actuator fabricated using a 3D printer. It could be operated at a voltage of several tens of volts. When an electric field of 0.25 MV m⁻¹ was applied, the contraction was 6.3 mm, corresponding to 19% of the original length. Such a low-driving-voltage and high-power electrostatic actuator has promise for future applications.

Experimental Section

Quantum Chemical Calculations

The supercomputer TSUBAME3.0, developed and operated by the Tokyo Institute of Technology, was used for quantum chemical calculations. The software used for the quantum chemical calculations was Gaussian16 from Gaussian (USA) and Spartan'18 from Wavefunction (USA). The computational level of ωB97X-D/6-311G(d,p) was used for high-precision investigation.

Synthesis

The liquid crystal material used in this study was obtained via the esterification of carboxylic acid and phenol components. The carboxylic acid and phenol components, as well as other necessary reagents and solvents, were purchased from Sakai Kogyo, Tokyo Chemical Industry, and Kanto Chemical. The chemical structures of the carboxylic acid and phenol components are shown in Figure S1, Supporting Information (D01, D05, D07, D09, W01, W03, W06, and W10).

For the esterification synthesis, a carboxylic acid or phenol component (1 g) was used, and the counterpart component (1 mol equivalent), EDCI (1-ethyl-3-(3-dimethylaminopropyl)benzoic acid) as the condensing agent, and DMAP (4-dimethylaminopyridine) as the catalyst, respectively, were weighed in 1.1 mol equivalents in a flask, dissolved in dichloromethane or chloroform solvent (about 10 mL), and stirred at room temperature for more than 12 h. The product was purified by washing with NaCl solution and water, followed by the removal of the original component using a silica gel column in chloroform solvent. Further recrystallization was carried out with ethanol solvent if necessary.

Differential Scanning Calorimetry

The differential scanning calorimetry (DSC) measurement was performed using a DSC 8500 system (PerkinElmer Inc.). About 3 mg of the sample set in an aluminum sample pan was measured using an empty aluminum sample pan as a reference. The temperature rise and fall rates were set to 10 °C min⁻¹ and the phase transition temperature was read from the peaks of the second heating and second cooling.

Dielectric Constant

A frequency response analyzer (FRA51615, NF Corporation) was used for the dielectric constant measurements. A CR parallel circuit was assumed as the equivalent circuit of the sample. The capacitance C and parallel resistance R were measured by inputting the current flowing in the sample to the frequency response analyzer through a shunt resistor (100 Ω) built into a high-power impedance measurement adapter (PA-001-1841, NF Corporation). The measurement samples were injected into a glass cell with a transparent conductive electrode (EHC Co., Ltd.) using capillary action.

Because the electrode area and cell gap of the glass cell were known (typically, a cell without an alignment membrane with an electrode area of 10 mm × 10 mm and a cell gap of 10 µm was used), the complex dielectric constant was calculated from the capacitance C and parallel resistance R obtained using the frequency response analyzer. The measurement conditions were an applied voltage of 0.05 V_AC, a frequency range of 10 Hz–15 MHz (300 measurement points evenly distributed logarithmically), and an average number of additions of 20. The temperature was controlled by a microscope hot stage (METTLER TOLEDO HS82) equipped with a cooling mechanism based on liquid nitrogen. The temperature was decreased at a controlled rate of 5 °C min⁻¹. In some cases, however, the temperature was quenched in the temperature range where crystallization was likely to occur. The samples were allowed to stabilize at the target temperature for about 1 min before measurement.

Generated Force and Current Measurements

A 50-N load cell was attached to a compact table-top universal tensile tester (EZ-SZ, Shimadzu) for the force measurements, as shown in Figure 3d. A function generator (WF1943, NF Corporation) was used as a signal source. A voltage amplified by a bipolar power amplifier (HSA4051, NF Corporation) was applied to the sample. A programmable current amplifier (CA5351, NF Corporation) was connected in series to measure the current flow. A block diagram of the measurement system is shown in Figure S6, Supporting Information.

As shown in Figure 3a,c, a heater (4 mm in diameter, 100 V, 30 W) manufactured by Hakko Electric was embedded in a base jig for fixing electrodes made using a 3D printer. The electrode, which was cut from a 3-mm-thick aluminum plate, was fixed to the top of the jig. The gap between the heater and the electrode was filled and thermally bonded with heat-conductive grease (Shinwa Sangyo Ltd., SMZ-01R, 13.2 W m⁻¹ K⁻¹). A thermocouple (RKC Instrument Inc., ST-51SC, 180 µm in thickness) was fixed to the electrodes with Kapton tape and connected to a temperature controller (AS ONE, TJA-550K) to control the temperature of the electrodes.

The generated force and current were input to the universal tensile tester from a sensor I/O extension box (Shimadzu).

To avoid the influence of surface tension, the load cell was reset to zero before a voltage was applied and then the generated force was measured while a voltage was applied. The surface tension was ≈0.01 N. This resetting of the load cell did not significantly affect the measurement of the generated force by the electric field.

3D-CAD, Slicer Software, and 3D Printer

AUTODESK FUSION 360 was used as the 3D-CAD software. CHITUBOX 64 was used as the slicer software. A Mars UV Photocuring LCD MSLA 3D Printer and a Mars 2 Pro Mono LCD MSLA Resin 3D Printer, both made by ELEGOO, were used as photocuring 3D printers.

Statistical Analysis

The data shown in the Lissajous figures for current, polarization, and generated force in Figures 4 and 5 were superpositions of data recorded for 2 s. The input voltage was a 10-Hz triangular wave corresponding to 20 cycles (N = 20). Since the mean ± standard deviation fits within the line width, the 20-cycle superposition was displayed as was.

Acknowledgements

This work was supported by LG×JXTG Nippon Oil & Energy Smart Materials & Devices Collaborative Research Programs and by ENEOS Smart Materials & Devices Collaborative Research Programs. The authors would like to thank S. Kawauchi and Y. Hayashi for quantum chemical and molecular dynamics calculations using TSUBAME3.0, T. Kajitani for DSC analysis, and H. Hosoda, M. Sone, T. Seki, and K Toda for their kind support.

Conflict of Interest

The authors declare no conflict of interest.

Data Availability Statement

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

References

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