A loop-structured film-capacitor-based high-performance direct-current triboelectric nanogenerator with temporary charge accumulation

Abstract

Triboelectric nanogenerators (TENGs) are promising energy-harvesting devices that can reduce the carbon footprint and prevent global warming. Although extensive research has been conducted on TENGs, they have a serious limitation in that they can only generate a low peak current output. To overcome this limitation, direct-current TENGs (DC-TENGs) based on electrostatic discharge have been studied, which can increase the electrical output with an enhanced charge density or amplify the current output with an electron avalanche effect. However, these DC-TENGs can only generate short-duration peak outputs, where the integral of these outputs is low; thus, it is difficult to charge commercial capacitors or batteries, which narrows the application field of TENGs. In this regard, a loop-structured film-capacitor direct-current TENG (LFD-TENG) that can accumulate polarized charges inside the loop-structured film capacitor and harvest electricity from the discharge was fabricated. With the accumulated charges, the LFD-TENG can generate a long-duration high-peak output compared to general DC-TENGs, which significantly increases the peak voltage, root mean square voltage, and transferred charge. The high-performance LFD-TENG was demonstrated to power 3000 light-emitting diodes (LEDs), 11 5 W LEDs, and a continuously operated thermo-hygrometer.

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1. Introduction

As global warming has become a worldwide problem in recent years, energy harvesting is considered a promising technology that can contribute to reducing the carbon footprint. A triboelectric nanogenerator (TENG) is an energy-harvesting device that converts ambient mechanical energy into electricity via the triboelectric effect and electrostatic induction.^1–5 Extensive research has been conducted on TENGs owing to their various advantages such as simple structure,^6–9 low cost,^10–13 and high applicability.^14–18 However, a serious limitation of TENGs is that they can only generate a low peak current output of microampere scale due to their fundamental working mechanism; thus, several studies have focused on electrostatic discharge-based direct current TENGs (DC-TENGs) in various recent studies.^19–22 These DC-TENGs induce an electrostatic discharge directly inside the device; thus, these devices can increase the electrical output by enhancing the charge density by utilizing the air breakdown of the triboelectric layer^23–25 or by amplifying the output current with the electron avalanche effect of the electrostatic breakdown.^26–28 With these effects, several studies have reported DC-TENGs that can generate a milliampere or ampere range of peak current outputs.^29–32 However, even though the peak current output can be increased up to the milliampere or ampere range, it only generates an extremely short-duration peak output. In such cases, the integral of the output is low; thus, the total amount of transferred charge can still be low. Additionally, because of the low amount of charge transferred, it takes a longer duration to charge capacitors or batteries, which makes them difficult to use in real-life applications. Therefore, a new working mechanism for electrostatic-discharge-based DC-TENGs that can effectively increase the output duration and enhance the output performance should be developed to broaden the application field of TENGs.

In this study, we demonstrate a loop-structured film-capacitor direct-current TENG (LFD-TENG) that can effectively enhance both the peak output and transferred charge with temporary charge accumulation in a loop-structured film capacitor. The loop-structured film capacitor was first developed in this study; it has a continuous pattern inspired by the film capacitor structure, which can generate a high peak output with a long duration compared with the general DC-TENGs. Thus, the LFD-TENG generated 250.56% higher root mean square (RMS) voltage, 180.57% higher average peak voltage, and 97.49% higher transferred charge than the general DC-TENG without a loop-structured film-capacitor structure. In addition, the LFD-TENG was able to charge a commercial capacitor with about 1287% higher voltage in the same time period as the general DC-TENG without a loop-structured film-capacitor structure. Moreover, with the high output performance, the LFD-TENG can successfully power 3000 LEDs, 11 5 W LEDs, and a commercial thermo-hygrometer.

2. Results

Fig. 1 shows an brief explanation of the LFD-TENG. The two plates of the LFD-TENG are shown in Fig. 1a. The top plate of the LFD-TENG was constructed with a loop-structured film capacitor made of copper and dielectric films on a polymethyl methacrylate (PMMA) substrate, and the bottom plate of the LFD-TENG contains triboelectric layers and electrodes on the PMMA substrate. A detailed explanation of the loop-structured film capacitor is presented in Fig. 1b. The general film capacitor consists of a sandwich structure of electrode films and a dielectric film (Fig. 1b-i). Thus, with the polarization inside the dielectric film, opposite charges can be captured inside the electrodes. A loop-structured film capacitor is constructed as a general film capacitor, where each film capacitor is continuously connected to the others; however, each bottom electrode of the film capacitor is connected to the top electrodes of the next film capacitor. With this pattern, the loop-structured film capacitor structure shown in Fig. 1b-ii can be made in an endless length if made in a straight direction. The loop-structured film capacitor in the LFD-TENG is fabricated with this loop pattern; however, it is fabricated in a circular direction; thus, it can be fabricated with four other film capacitors, as shown in Fig. 1a and 1b-iii. Therefore, the four quadrant-circle-shaped film capacitors were connected, and the top electrodes were connected to the bottom electrodes. Through this structure, the induced charges from the triboelectric layers can accumulate inside the loop-structured film capacitor, and when the accumulated charges are discharged to the bottom electrode, the LFD-TENG generates a high peak output.

Fig. 1 Brief concept of the LFD-TENG. (a) Schematic illustration of the LFD-TENG. (b) Brief explanation of the (i) film capacitor, (ii) loop-structured film capacitor, and (iii) LFD-TENG. (c) Photograph of the rotator of the LFD-TENG (scale bar: 2 cm). (d) Photograph of the stator of the LFD-TENG (scale bar: 2 cm). (e) Voltage output of the LFD-TENG with a loop-structured film capacitor and the general DC-TENG without a loop-structured film capacitor.

Fig. 1c and d show photographs of the loop-structured film capacitors. As shown in Fig. 1c, four other quadrant circular film capacitors were connected to the loop pattern at the top plate. In addition, the top plate was the rotator that could be rotated by connecting it to a rotational input. The bottom plate was the stator, which was fixed and unable to move with the rotational input. This plate was constructed by attaching a PTFE film, a nylon film, and copper electrodes. Thus, the LFD-TENG generated an electrical output by sliding the top plate onto the bottom plate. Fig. 1e shows the voltage output of the DC-TENG with and without the loop-structured film capacitor. A DC-TENG without a loop-structured film capacitor was fabricated by attaching four quadrant circular copper films, as shown in Fig. S1.† With copper films, this device can generate the same electrical output with electrostatic discharge as a general DC-TENG.^33,34 The outputs of the DC-TENG with and without a loop-structured film capacitor are shown in Fig. 1e and S2† to compare their voltage and current outputs. As a result, the DC-TENG without the loop-structured film capacitor generated voltage and current outputs up to 340 V and 1.44 A, whereas the DC-TENG with a loop-structured film capacitor generated voltage and current outputs up to 1200 V and 6.32 A, respectively. Accordingly, the DC-TENG with a loop-structured film capacitor generated significantly higher voltage and current outputs than the DC-TENG.

The detailed working mechanism of the LFD-TENG is shown in Fig. 2a–c. Fig. 2a shows a schematic of the LFD-TENG variables, Fig. 2b shows an extended voltage graph of the LFD-TENG with and without a loop-structured film capacitor, and Fig. 2c shows the detailed working mechanism with a rotating rotator. The electrodes at the top of the loop-structured film capacitor are named E₁, E₂, E₃, and E₄. The electrodes connected to E₁, E₂, E₃, and E₄ were named , , , and , respectively (Fig. 2a). As the PTFE and nylon films on the bottom plate have triboelectric surface charge according to the triboelectric series, charges are induced inside the , , , and electrodes as shown in Fig. 2c. The negative charges were induced inside by the positive surface charges of the nylon film, and positive charges were induced inside the electrode by the negative surface charges of the PTFE film (Fig. 2c-i). With the induced charges and , the positive and negative charges were polarized inside E₁ and E₃, respectively, because both electrodes were connected to each other. In addition, with the polarization of the dielectric film inside the loop-structured film capacitor, negative and positive charges are induced in E₂ and E₄ by the charges of and , respectively. Moreover, and are connected to the electrodes on the bottom plate; thus, no charges are induced in and . With a loop-structured film capacitor, the top plate can accumulate more charge owing to the polarization effect of the dielectric film. When the top plate rotates (Fig. 2c-ii), the accumulated charges in and transfer to the electrodes on the bottom plate and generate high outputs. In this case, both and simultaneously discharge the accumulated charges, thus a large number of charges can be harvested. When the top plates rotate after discharge (Fig. 2c-iii), the positive and negative charges accumulate in and , respectively. Similarly, more charges can be accumulated by the polarization effect of a loop-structured film capacitor (Fig. 2c-i). When the top plate rotates (Fig. 2c-iv), the charges in and discharge to the electrodes on the bottom plate; thus, a high output can occur again. In addition, Fig. S3 and S4† show electrostatic discharge can be generated when the accumulated charges transfer to the bottom electrode. Fig. S3† shows the photograph of the LFD-TENG before rotating and after rotating which shows electrostatic discharge is generated during the operation. Moreover, Fig. S4† shows the expanded graph of one peak current output of LFD-TENG in 1.5 μs. As the current output is measured as an underdamping waveform, LFD-TENG generates high electric output with electrostatic discharge.³⁵ By this reason, even though the voltage output of LFD-TENG is measured as a DC output, the current output of the LFD-TENG can be measured as an alternating current output. Fig. 2c shows the working mechanism of the half cycle of the LFD-TENG; the LFD-TENG can generate four high-peak outputs in every cycle. The outputs of the LFD-TENG and the DC-TENG can be easily compared with Fig. 2b. The LFD-TENG generated a higher peak voltage of up to 870 V, whereas the DC-TENG generated a peak voltage of up to 300 V. Since the DC-TENG cannot accumulate charges, this device can more frequently generate a sharp peak voltage of 300 V. For better comparison, the integral areas of the peak outputs were calculated using the following formula:

where T_Q is the quarter cycle and V(t) is the voltage output over time. The integral area of one peak output of the LFD-TENG was 1.002, and the integral area of every peak of the TENG device in the quarter cycle was 0.219 (Fig. S5†). This result indicates that the electrical output of the LFD-TENG can be significantly enhanced compared to that of the DC-TENGs because of the increase of the accumulated charges inside the loop-structured film capacitor.

Fig. 2 Detailed working mechanism of the LFD-TENG. (a) Schematic illustration of variables of the LFD-TENG. (b) Extended voltage graph of the LFD-TENG with and without a loop-structured film capacitor. (c) Detailed working mechanism of the LFD-TENG when the top plate rotates. Comparison of (d) RMS voltage and average peak voltage, (e) transferred charge, and (f) stored energy in various capacitors of the LFD-TENG with and without a loop-structured film capacitor (temperature: 21.6 °C, humidity: 32%, rotational speed: 180 rpm).

Fig. 2d shows the RMS and average peak voltages of the LFD-TENG and DC-TENG for a better comparison. The RMS voltage was calculated using the following equation:

where T_T denotes total time. Using this formula, the average RMS voltages of the LFD-TENG and DC-TENG outputs measured for 4 seconds were calculated to be 24.74 and 7.058 V, respectively. In addition, the average peak voltages of the LFD-TENG and DC-TENG were calculated to be 875.0 and 311.9 V, respectively. From these results, the LFD-TENG could generate 250.56% higher RMS voltage within the same time and 180.57% higher average peak voltage than the DC-TENG.

For a better comparison of real-life applications, it is necessary to compare the transferred charge and stored energy in real capacitors. As shown in Fig. 2e, the transferred charges of the LFD-TENG and DC-TENG were measured using an electrometer and circuit (Fig. S6†). As shown in Fig. S4,† an inductor is used for smoothing the waveform of the LFD-TENG for accurate results.³⁶ At 9 s, 16.90 and 8.556 μC of transferred charges were measured with the LFD-TENG and the DC-TENG. Thus, 97.49% of transferred charge was increased in the loop-structured film capacitor. In addition, the energy stored in several capacitors with the LFD-TENG and the DC-TENG is shown in Fig. 2f and S7.† The stored energy was calculated after charging several capacitors, using the following formula:

where C is the capacitance and V is the voltage of the capacitor. As a result, the LFD-TENG charged 2.2, 20, 47, 100, 200, 330, 660, 1000, 1330, and 1660 μF capacitors in 4 s with the stored energy of about 126.4, 108.5, 83.44, 51.98, 20.98, 14.84, 7.861, 3.019, 2.803, and 2.296 μJ, respectively. With the same time, the stored energies in 2.2, 20, 47, 100, 200, 330, 660, 1000, 1330, and 1660 μF capacitors with the DC-TENG were 1.718, 0.3282, 0.1357, 0.03677, 0.05217, 0.01914, 0.02769, 0.0109, 0.01287, and 0.0106 μJ, respectively. These results indicate that the LFD-TENG has a higher charging capacitor performance than the DC-TENG, which is important for real-life applications.

In addition, to analyze the effect by the capacitance, the capacitances and RMS voltage of different sizes of LFD-TENG have been measured as shown in Fig. S8.† By measuring with a multimeter, the capacitances of LFD-TENG with diameters of 10 and 20 cm were measured as about 450 and 1500 pF, respectively. Moreover, the RMS voltage of LFD-TENG with diameters of 10 and 20 cm was measured as 25.74 and 92.44 V, respectively. This result indicates that the output can increase due to the higher capacitance of the loop structured film-capacitor.

The output performance of the LFD-TENG can be controlled by several parameters as shown in Fig. 3. Fig. 3a shows a schematic illustration of the bottom plate of the LFD-TENG, which shows that two other materials are used for the triboelectric layer; Fig. 3b and c show the measured voltage, calculated RMS voltage, and average peak voltage of the LFD-TENG at different rotational speeds. The RMS voltage was calculated based on the voltage measured for 4 seconds, and the charge was measured for 5 seconds. Fig. 3d–i show the voltage, RMS voltage, and transferred charge of the LFD-TENG when different materials were used for the triboelectric layer. These measurements were conducted while the LFD-TENG was rotated at a speed of 180 rpm. As shown in Fig. 3b, the voltage output of the LFD-TENG increased with the input rotation speed. The RMS and average peak voltage outputs at different input rotation speeds are shown Fig. 3c. When input rotation speeds of 30, 60, 120, and 180 rpm were applied to the LFD-TENG, the average peak voltages were 674.7, 739.6, 874.0, and 891.7 V, whereas the RMS voltages with 30, 60, 120, and 180 rpm of input rotation speed were 6.385, 11.46, 21.85, and 31.08 V, respectively. The current outputs of the LFD-TENG with different rpm inputs are shown in Fig. S9.† With a high-rotation-speed input, a high-frequency peak voltage was generated; thus, the RMS voltage significantly increased. This result indicates that the LFD-TENG can be utilized even with a high-rotation-speed input.

Fig. 3 Parametric studies on the LFD-TENG. (a) Schematic illustration of the triboelectric layer of the LFD-TENG. (b) Voltage outputs of the LFD-TENG with different input speeds. (c) RMS voltage and average peak voltage of the LFD-TENG with different input speeds. (d) Voltage outputs of the LFD-TENG with different materials when PTFE is used for Material A. (e) Voltage outputs of the LFD-TENG with different materials when nylon is used for Material A. (f) RMS voltage of the LFD-TENG with different materials. (g) Transferred charge of the LFD-TENG with different materials when PTFE is used for Material A. (h) Transferred charge of the LFD-TENG with different materials when nylon is used for Material A. (i) Transferred charge of the LFD-TENG with different materials (temperature: 21.2 °C, humidity: 32%, rotational speed: 180 rpm).

Additionally, the triboelectric layer of the bottom plate of the LFD-TENG is a major factor that determines the output performance. If the same material is used for the triboelectric layer as shown in Fig. S10,† only the induced charge from the triboelectric layer can be generated in the loop-structured film capacitor. As a result, this device can only generate the same output as the DC-TENG without the effect of the film capacitor. Thus, as shown in Fig. 3d–f, the voltage outputs were measured for different triboelectric materials. Fig. 3d and S11† show the voltage and current outputs of the LFD-TENG when Material A of the triboelectric layer of the bottom plate was fixed as PTFE and different materials were used for Material B. Consequently, high peak voltage was generated in the order nylon > PET > PI > PTFE. However, when the nylon film was used for Material A (Fig. 3e), higher peak voltages were generated in the order of PTFE > PI > PET > nylon. The current outputs of the LFD-TENG when the nylon film was used as Material A are shown in Fig. S12.†Fig. 3f shows RMS voltages of the results in Fig. 3d and e. When PTFE was used as Material A and PTFE, PI, PET, and nylon were used as Material B, the RMS voltages were measured as 1.668, 8.158, 16.36, and 24.17 V, respectively. When nylon was used for Material A and PTFE, PI, PET, and nylon were used for Material B, the measured RMS voltages were 23.01, 16.43, 8.052, and 0.5118 V, respectively. Moreover, the charges transferred with different materials were measured to obtain accurate results for optimizing the triboelectric materials of the LFD-TENG (Fig. 3g–i). When PTFE was used for Material A, higher transferred charges were measured in the order of nylon > PET > PI > PTFE. When nylon was used for Material B, higher transferred charges were measured in the order of PTFE > PI > PET > nylon. The accurately transferred charges for the different materials after 5 s are shown in Fig. 3i. The transferred charges when PTFE was used for Material A and PTFE, PI, PET, and nylon were used for Material B were measured as 0.1518, 5.848, 9.163, and 10.86 μC, respectively. When nylon was used for Material A and PTFE, PI, PET, and nylon were used for Material B, the transferred charges were 10.06, 7.305, 1.241, and 0.4273 μC, respectively. Based on these results, PTFE and nylon were selected as materials A and B, respectively, for the LFD-TENG and these results indicate that the loop structured film capacitor can enhance the LFD-TENG output by the capacitance.

To accurately demonstrate the performance of the LFD-TENG, several applications that can be powered with the LFD-TENG are shown in Fig. 4. Fig. 4a shows the circuit diagram for powering 3000 light emitting diodes (LEDs), charging capacitors, and an operating thermo-hygrometer using the rectified LFD-TENG output. A 10 mH inductor and capacitor were used to power the thermo-hygrometer with a high peak output of the LFD-TENG. As shown in Fig. 4b, 125 LEDs were connected in series in the same array, and 24 of these LED arrays were connected in parallel, resulting in 3000 LED modules. The LED modules were lit through the rectified electrical output generated by the LFD-TENG at an input rotational speed of 180 rpm (ESI Video 1†). In addition, it was experimentally confirmed that the LFD-TENG could stably power 11 5 W lamps connected in parallel. Fig. 4c is a graph showing the charging of a 100 μF capacitor for 40 s according to the LFD-TENG with a loop-structured film capacitor structure and the DC-TENG. Compared with the DC-TENG charging to 0.617 V for 40 s, the LFD-TENG charged to 8.465 V, which corresponds to 1287.10% of the charging amount of the DC-TENG. In addition to the 100 μF capacitor, the LFD-TENG charged 22, 47, and 330 μF capacitors at 18.539, 12.782, and 4.129 V for 40 s, respectively (Fig. 4d). Fig. 4e and f show the continuous operation of the commercial thermo-hygrometer by powering the LFD-TENG at 180 rpm. When the commercial thermo-hygrometer is connected after about 20 s of turning on the LFD-TENG, the charge of the 330 μF capacitor is maintained at about 1.5 V, and then decreases when the LFD-TENG is turned off (ESI Video 2†). From these experimental results, LFD-TENG showed high performance in powering several devices, indicating the potential to broaden the application fields of TENGs.

Fig. 4 Applications of the LFD-TENG. (a) Circuit diagrams of the LFD-TENG. (b) Experimental setup of the LFD-TENG to power 3000 LEDs and turned on LEDs with the LFD-TENG. (c) Charging graph of a 100 μF capacitor by the LFD-TENG with and without a loop-structured film capacitor. (d) Charging graph of various capacitors with the LFD-TENG. (e) Experimental setup for operating a thermo-hygrometer with the LFD-TENG. (f) Voltage graph of the capacitor while operating the thermo-hygrometer with the LFD-TENG (temperature: 21.9 °C, humidity: 33%, rotational speed: 180 rpm).

3. Conclusion

In this study, an LFD-TENG was fabricated that can generate a high peak output with a long duration compared with the general DC-TENGs with a loop-structured film-capacitor structure. The loop-structured film capacitor can accumulate polarized charges from the triboelectric layer and discharge them into the circuit; thus, the LFD-TENG can generate a high peak voltage output and high transferred charge. With the loop-structured film-capacitor, the LFD-TENG generated 250.56% higher RMS voltage, 180.57% higher average peak voltage, and 97.49% higher transferred charge than the general DC-TENG. With the high output of the LFD-TENG, 3000 LEDs and 11 5 W LEDs were powered and a commercial thermo-hygrometer was continuously operated. Although further studies are still necessary to apply the LFD-TENG in real-life applications, we believe that the LFD-TENG can overcome the existing limitations of general DC-TENGs and can lead to the broadening of new application fields of TENGs.

4. Methods

4.1 Fabrication of the LFD-TENG

The LFD-TENG is composed of two parts: a rotator with an attached loop-structured film capacitor (Fig. 1c) and a stator with triboelectric materials and two attached electrodes (Fig. 1d).

The rotator consists of three parts: a PMMA substrate, copper electrodes (DUKSUNG Hitech Co., South Korea) for the electrodes of the loop-structured film capacitor, and PET film (Goodfellow Co., United Kingdom) as a dielectric of the film capacitor (Fig. S13†). The PMMA substrate has a diameter of 10 cm and a thickness of 2 mm, the four copper electrodes were rectangular with a width of 5 cm and a height of 10 cm, and the four PET films were squares with a side length of 5 cm. To fabricate the loop-structured film capacitor, a PET film was first attached to one end of a copper electrode, with one side of the film aligned exactly with one edge of the electrode. That is, the PET film was positioned such that only half of the electrode was covered and the other half was not. The same process was repeated for the remaining three electrodes, with each film attached in a similar manner. Next, the PET film of one copper electrode was positioned by rotating it by 90° such that it aligned with the unattached part of the PET film from the other copper electrode (Fig. S13-i†). This process was repeated to connect all four copper electrodes (Fig. S13-ii and iii†). Finally, the part to which the PET film of the fourth electrode was attached was lowered below the first electrode and attached such that the four electrodes were interlocked (Fig. S13-iv†). The completed loop-structured film capacitor was attached to a PMMA substrate with its center aligned and cut into a circle to fit the shape of the substrate (Fig. S13-v and vi†).

The stator consists of the PMMA substrate, two electrodes, a nylon film (Goodfellow Co., United Kingdom), and PTFE tape (Chukoh Chemical Industries Co., Japan). The PMMA substrate had a diameter of 10 cm and a thickness of 2 mm, which is the same as that of the rotator. Two electrodes, each 2 mm wide, are placed along the diameter of the substrate and pass through its center. These electrodes are attached to the central area of the substrate, aligned symmetrically, and evenly spaced along the axis. PTFE is attached to the upper part of the electrodes and nylon is attached to the lower part. To ensure that the wires connected to measure the electrical output from the two electrodes are not mechanically affected while the LFD-TENG is operating, the two electrodes were cut to a length (more than 5 cm) that extends outside the substrate and attached, and the wires were connected to the ends of the electrodes.

4.2 Characterization and measurement

The output voltage and current were measured using a mixed-domain oscilloscope (MDO 3014, Tektronix Co., USA) with a high-voltage differential probe (THDP0200, Tektronix Co., USA) and a current probe (TCP0030A, Tektronix Co., USA). The transferred charge was measured using an electrometer (Model 6514, Keithley Co., USA). A DC motor (BXSD120-C, Oriental Motor Co.) provided the mechanical rotational input for operating the LFD-TENG. All experiments were conducted at a temperature of 21 ± 1 °C and a humidity of 32 ± 1%.

Data availability

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

Author contributions

S. C. and M. S. are the co-first author. S. C., M. S.: conceptualization, data curation, formal analysis, investigation, methodology, validation, visualization, writing – original draft, writing – review & editing. H. Y., H. R.: investigation, data curation. Y. J., J. H., S. L.: project administration, supervision.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We would like to thank Editage (https://www.editage.co.kr) for English language editing. This research was supported by the Chung-Ang University Research Scholarship Grants in 2023. This work was supported by the National Research Foundation of Korea (NRF) grant, funded by the Korean government (MSIT) (no. 2023R1A2C2006170) and Technology Innovation Program (RS-2022-00155791, Development of high power/high energy density supercapacitor technology for hybrid ESS for EV charging infrastructure) funded By the Ministry of Trade, Industry & Energy (MOTIE, Korea).

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ta09187f

‡ These authors contributed equally to this work.

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