Optimizing energy harvesting performance of cone dielectric elastomer generator based on VHB elastomer

Journal Pre-proof Optimizing energy harvesting performance of cone dielectric elastomer generator based on VHB elastomer Yingjie Jiang, Suting Liu, Meilin Zhong, Liqun Zhang, Nanying Ning, Ming Tian PII:

S2211-2855(20)30164-6

DOI:

https://doi.org/10.1016/j.nanoen.2020.104606

Reference:

NANOEN 104606

To appear in:

Nano Energy

Received Date: 26 November 2019 Revised Date:

23 January 2020

Accepted Date: 10 February 2020

Please cite this article as: Y. Jiang, S. Liu, M. Zhong, L. Zhang, N. Ning, M. Tian, Optimizing energy harvesting performance of cone dielectric elastomer generator based on VHB elastomer, Nano Energy, https://doi.org/10.1016/j.nanoen.2020.104606. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

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Abstract

Optimizing energy harvesting performance of cone dielectric elastomer generator based on VHB elastomer Yingjie Jiang1, Suting Liu4, Meilin Zhong1 , Liqun Zhang1,2,3,Nanying Ning1,2,3* and Ming Tian 1,2,3* 1.State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China; 2.Beijing Advanced Innovation Center for Soft Matter Science and Engineering, Beijing University of Chemical Technology, Beijing 100029, China; 3.Key Laboratory of Carbon Fiber and Functional Polymers, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, China; 4 Department of Chemical Engineering, Weifang Vocational College, Weifang 262737, China. *Corresponding authors. E-mail addresses: [email protected] (N. Y. Ning), [email protected] (M. Tian)

Optimizing energy harvesting performance of cone dielectric elastomer generator based on VHB elastomer Yingjie Jiang1, Suting Liu4, Meilin Zhong1, Liqun Zhang1,2,3, Nanying Ning1,2,3* and Ming Tian 1,2,3* 1.State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China; 2.Beijing Advanced Innovation Center for Soft Matter Science and Engineering, Beijing University of Chemical Technology, Beijing 100029, China; 3.Key Laboratory of Carbon Fiber and Functional Polymers, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, China; 4 Department of Chemical Engineering, Weifang Vocational College, Weifang 262737, China. *Corresponding authors. E-mail addresses: [email protected] (N. Y. Ning), [email protected] (M. Tian)

Abstract：Dielectric Elastomer Generator (DEG) has been used to harvest energy from reciprocating mechanical motion due to its variable capacitance under tension, and thus it has attracted widespread attention in the last decade. In this study, a cone DEG based on VHB elastomer was developed and its energy harvesting performance was optimized by combining equibiaxial prestretching to cone stretching mode and then tailoring the variables such as the equibiaxial prestretch ratio, input bias voltage and cone displacement. The coupling relationship among these variables and their combined influences on generated energy, energy density and conversion efficiency were systematically studied for the first time. The results indicate that prestretching plays an important role in achieving the target energy harvesting performance at shorter displacement and lower bias voltage, which means lighter weight and portability of the device. More importantly, an up-to-date highest energy density of 130 mJ/g or a maximum electromechanical conversion efficiency of 40% could be obtained by optimizing the variables. In addition, the concept of "displacement 1

threshold" in DEG was firstly proposed and discussed based on leakage and viscoelastic. This work provides ideas for future applications of DEG on portable power and array power generators with high energy harvesting performance. Keywords: Energy harvesting, Sustainable energy, Prestretching, Dielectric Elastomer Generator, Energy density

1. Introduction Dielectric elastomer transducer (DET) is a soft/deformable elastomeric capacitor consisting of a thin dielectric elastomer (DE) film sandwiched between two compliant electrodes. [1-5] DET can be employed as dielectric elastomer generator (DEG) to transform an input mechanical energy into electrical energy, or as dielectric elastomer actuator (DEA) to produce force and displacement under electrical activation. DEA has been studied for decades, and its principle is to apply bias voltage in the longitudinal direction of the DE film, causing expansion on the plane direction due to Maxwell stress, i.e. the transformation of electrical energy into mechanical energy. [6-8] On the other hand, as a new type of generator, the electricity generation process of DEG can be considered as a reverse process of DEA, which can harvest energy through stretching-releasing cycles. [9, 10] DEG can be used for converting mechanical energy from natural motion sources, such as walking, waves, mechanical reciprocate etc. into electrical energy, and it has many attractive advantages over traditional generators with large volume and complicated structure, such as high energy density, light weight, changeable structure, soft/good impact resistance etc.. Thus, DEG has attracted much attention in the last decade [11-15]. Similar to triboelectric nanogenerators and piezoelectric nanogenerators, DEG also relies on charge separation and transfer in nanoscale to harvest electrical energy, and thus it can also be considered as nanogenerators [10, 16-27].

2

Scheme 1 Schematic Illustration of the Work Mechanism of a DEG: (a) A DE film sandwiched by two flexible electrodes is firstly stretched and charged with a low excited voltage. (b) When the DE film is released, the area of DEG decreases and the thickness increases, resulting in the improvement of charge density and energy density. DEG can convert mechanical energy into electrical energy based on the nanofarad-level capacitance difference between stretched and released states.[12] As illustrated in Scheme 1, electrical energy can be produced from a stretched, charged DEG by releasing its mechanical deformation while maintaining the charge on its electrodes. In the stretched state, the dielectric elastomer is firstly polarized at the atomic and molecular scales under the application of an external electric field, causing electrons, ions and intrinsic dipoles to induce dipole moments, thus forming bound charge, producing a macroscopic dipole moment with the same direction of the electric field, and finally resulting in charge accumulation on the surface of the DE film to store energy. In the releasing process, the thickness of the DE film increases, resulting in an increase in surface charge density as well as the potential. It can be considered that the conversion of mechanical energy to electrical energy is accomplished by nanogenerators composed of nano-capacitors in this process. Consequently, the electric energy stored in DE is raised, and the electric energy can be calculated according to the following equation by assuming that the charge is constant (Q=C1V1=C2V2) [11, 12, 28].

∆E = Eout − Ein =

C  1 1 C2V22 − C1V12 ) = C1V12  1 − 1 ( 2 2  C2  3

(1)

Where ∆E is the generated energy, Eout and Ein represent output electrical energy and input electrical energy in this process, respectively, C and V represent the capacitance and the voltage of DE, respectively, and the subscripts 1 and 2 represent the states of DE before relaxation and after relaxation, respectively. The capacitance of a planar capacitor can be calculated through the equation: C = ε 0ε r S / d

(2)

where ε0, εr, S, and d represent the vacuum permittivity, the relative permittivity, area, and thickness of the DE film, respectively. Thus, Eq. 1 can be rewritten as:

 1 ε 0ε r S1 2  S12  1 2  C1 ∆E = C1V1  − 1 = V1  2 − 1 2  C2  2 d1  S2 

(3)

where V1 is bias voltage, S1, S2 represent the area of DE film before releasing and after releasing, respectively, so S1/S2 is defined as the ratio of the change in size during a stretching−relaxation cycle. It can be concluded that the harvested energy of a DEG is determined by εr of the elastomer, the input bias voltage V1, and S1/S2 during a stretching−relaxation cycle. Therefore, the max energy output of a DEG with certain material is determined by its maximum stretching limit and electrical breakdown strength, which are usually called boundary conditions. [28, 29] There are several reports that optimized energy output based on boundary conditions by simulation calculation, [30, 31] but few of the experimental results under boundary condition were reported. Based on generated energy, two of the important properties for DEGs are their energy density and electromechanical conversion efficiency, which need to divide the generated energy by mass of film or input mechanical work, respectively. [32, 33] Lots of efforts have been focused on improving the energy generation performance of DEG by optimizing material properties of DE film, the DEG stretching modes and circuit design [31, 34-41]. DE materials employed for DEG are mostly acrylate elastomers and polydimethylsiloxane (PDMS) elastomers due to their stable performance and the ability to be highly stretched to provide large capacitance. The performance of DEG can also be tailored by stretching modes.[40] The most commonly used stretching 4

modes include cone stretching mode, inflated circular diaphragm mode, equibiaxial stretching mode and uniaxial stretching mode. [42-45]Although the equibiaxial stretching mode can achieve the highest energy harvesting performance in comparison with other modes, [29, 30, 46-48] its complex structure, the requirement of equibiaxial input source and high elongation of materials lead to its lack of practicability. [49-51] The structure of cone stretching mode can be extremely simple because of its requirement of linear motion, a fairly common form of motion. For example, there are many linear motion components in human motion. It has been reported that the array of cone DEGs mounted on the bottom of shoes uses repeated compression and releasing of shoes during walking. In addition, cone DEG can be directly applied to the motor or piston movement, so it may be the most promising mode for DEG application [37, 52]. However, the cone DEG has a relatively lower energy density, usually one or two orders of magnitude lower than that of the equibiaxial or inflated circular diaphragm of DEG, so improvement on its energy harvesting performance is necessary. Several studies have been completed to optimize the performance of cone DEG. Compared with the circuit design or fabrication of new DE materials, the combination of cone and equibiaxial stretching modes is a more effective way to improve the energy generation performance of cone DEG. [36-41] That is, the DE film is firstly prestretched in an equibiaxial way, then performed energy harvesting test by cone stretching mode under the fixed equibiaxial prestretching ratio. A simulation study that was focused on the failure mode of cone DEG at different equibiaxial stretch ratio reported the maximum energy density of 10.7 mJ/g and conversion efficiency of 26.1% under equibiaxial prestretch ratio of 125% and bias voltage of nearly 20kV. [31] An experimental research was focused on the influence of stretching rate on energy harvesting performance, and an improved energy density of 18.9 mJ/g and conversion efficiency of 18.3% under bias voltage of 1.2kV, equibiaxial prestretching ratio of 250% and cone displacement of 20 mm were reported. [37] Actually, the performance of cone DEG was affected by several variables including bias voltage, equiaxial prestretching ratio and cone stretch displacement, etc.. Nevertheless, these variables were studied 5

separately in previous studies [31, 37]. What is the coupling effect of these variables on energy harvesting performance remains unclear. Thus, the purpose of this study is to optimize the energy harvesting performance of cone DEG by combining equibiaxial prestretching to cone stretching mode and then tailoring the variables such as the equibiaxial prestretch ratio (λ), input bias voltage (V1) and cone displacement (Z). The coupling relationship among these variables and their combined influences on the energy generation performance of cone DEG were systemically investigated for the first time.

2. Materials and setup of cone DEG Equibiaxial and cone stretching device used in this work are shown as follows. The structure of homemade equibiaxial stretching device is given in Fig. S1, which has several symmetrical clamps to ensure the uniformity of stretching. The stretch ratio λ is used to describe the level of stretching, which can be adjusted by controlling the radii of the sample before and after stretching. Prestretch ratio can be calculated as

λ=R1/R0×100%, where R0 and R1 are radii before and after stretching, respectively. As shown in Scheme 2, the active working area of cone DEG is an annulus with inner-ring radius Rinner and the outer-ring radius Router in the initial state, which becomes the side of the frustum cone-like in the stretched state by fixing the outer ring of the annulus in vertical plane and stretching the inner ring in the horizontal direction. Due to the uneven thickness in the radial direction during cone stretching, the area-capacitance relationship does not follow the formula of the plate capacitor (Eq. 2). In the parallel plate capacitor model (equibiaxial stretching mode), the extent of stretch can be expressed by S1/S2 (area ratio), so Eq. 3 can be used to calculate generated energy of parallel plate capacitor model. Eq 2 and Eq 3 are used to help us understanding the "boundary conditions" including bias voltage and extent of stretch, and their influence on energy harvesting performance, rather than calculating the capacitance or energy of cone DEG. Therefore, another parameter of cone DEG, the displacement of inner clamps, Z was introduced to describe the extent of stretch. [31] Enlarging the Z value in cone DEG corresponds to increase the area ratio (S1/S2) before and after releasing 6

in plate/equibiaxial of DEG. We directly measured the capacitance values of cone DEG under different Z (see Fig. 4) by a digital multimeter. In this work, the DE film is first prestretched by an equibiaxial stretching device, and then the pre-stretching ratio of DE film is fixed by the outer clamps of cone DEG. After that, the film is transferred to the cone DEG device to complete the assembly of the cone DEG. Finally, energy harvesting test is performed by linear input source (cone DEG). Therefore, we use equibiaxial prestretching only for pretreatment. Our DEG device does not contain an equibiaxial device.

Scheme 2 Schematic structure of cone DEG: Orthogonality view of (a) initial state and (b) stretched state, lateral view of (c) initial state and (d) stretched state. Inner-ring radius Rinner and outer-ring radius Router are structure parameters of a cone DEG and displacement, Z is used to describe the extent of stretching. The DE film we used was a commercial polyacrylate elastomer film trademarked as 3M VHB4905 with a thickness of ca. 500 µm, which is widely used for DEA and DEG due to its low modulus, high elongation at break and stable dielectric properties. The microstructure and morphology characterization of the VHB4905 material is shown in Part III in Supporting Information. A relatively completed circuit shown in Fig. 1a was adopted according to Samuel Shian’s research, [53] The parallel transfer capacitors (CP) in this circuit can reduce the voltage rise caused by film releasing, so as to prevent the film from electrical 7

breakdown during the releasing process, and ensure the completion of the cycle. In the literature [53], CP was set as 1.3 times of the capacitance of elastomers at stretched state (C1), which can avoid electrical breakdown. In this study, CP was further increased to 9.5nF, which is about 1.5 times of the maximum C1 (6.2nF, see Fig. 4) to ensure that electric breakdown would not occur during the releasing process. A platform based on the circuit for testing DEG energy generation performance has been completed (see the scheme in Fig. 1b) in this study. As shown in Fig. 1c and Fig. S2, the annular DE film was fixed between two plastic disks with Rinner and Router are 20 and 30 mm, respectively. The plastic disk with a radius of 20 mm is connected to a force sensor (STC-50KG LASCAUX Co.Ltd.) on the front of a linear motor (Model E1100, Linmot Co. Ltd.) to apply cone stretching on DE film and record the stress and strain data. Conductive carbon grease was coated onto both sides of the annular DE film as compliant electrodes. And the compliant electrodes were then connected with external circuit by a pair of copper foil electrodes as shown in Fig. S2. Partial bare joints of the high-voltage lines were encapsulated by VHB4910, a high-insulation tape with a volume resistivity up to 1013 Ω•m and having sufficient electrical breakdown strength to retard the leakage of charge. An air conditioner and a rotary dehumidifier were used to control the experimental environment at 25℃, 30% RH. The excellent insulation and measurement accuracy of the device is obtained to cover the data under electrical or mechanical boundary conditions.

8

Figure 1 (a) The electric circuit employed for energy harvesting measurements, composed of a power supply, the elastomer (DEG), a transfer capacitor (CP), a diode, a charging switch (S1), harvesting switch (S2), and harvesting circuits , (b) Schematic and (c) Partial view of the experimental devices. As depicted in Scheme S1, the energy harvesting process was carried out through four subsequent steps: (i) The DE film was first prestretched by using a homemade equibiaxial stretching device (ii) Cone stretching under the fixed equibiaxial prestretching was performed on the DEG under a constant speed of 600 mm/min by using the linear motor to a preset displacement Z, (iii) closing switch 1 to charge the DEG for 10 s; (iv) opening switch 1 and releasing the DEG under a speed of 600 mm/min to Z0; and (v) closing switch 2 to measure the electrical energy stored in the DEG. The charging process does not complete in a second, but takes a few seconds to complete, so the too short charging time is not appropriate. On the other hand, the viscoelastic properties of the VHB4905 material leads to the occurrence of significant stress 9

relaxation. During the energy harvesting process, the film is charged under a stretching state, so a longer charging time means a longer relaxation time, resulting in a decrease in restoring force. So the too long charging time is also not appropriate. Taking the above two contradictory effects into consideration, we set the charging time to 10s. The input bias voltage (V1) was controlled by a high voltage DC source (Model DW-P803, Dongwen HV Source Co. Ltd.), the capacitance of elastomers at stretched state (C1) and the capacitance of elastomers at released state (C2) were measured by using a digital multimeter (Model DMM7510, Tektronix Co. Ltd.). The voltage of the DEG at relaxed state (V2) was recorded by the same digital multimeter. Note that a high-voltage dividers (Rdivider ~ 10 GΩ) were used to measure the high voltages with a low charge loss. The generated electric energy can be calculated by using Eq. 1. The input mechanical energy was recorded by the force sensor and linear motor. The electromechanical conversion efficiency can be obtained by dividing the generated electric energy by the input mechanical energy.

3. Working mechanism of our cone DEG and the variables setting Based on the energy generation principle described in the previous section, DEG can harvest energy through stretching-releasing cycles. Two types of energy are involved in the generation cycle, that is, an increase in electrical energy and the consumption of mechanical energy. The working mechanism of DEG includes a four-step cycle. It is firstly elastically deformed to increase the mechanical elastic energy and thus increase the capacitance C of the DE film by increasing the area S and reducing the thickness d, according to Eq. 2. Next, an applied voltage leads to the accumulation of charges Q at the interface between the DE film and the compliant electrodes. The DE film was then unloaded in step 3, reducing the elastic energy stored and thus leading to a reduction in area and an increase in thickness. Due to the resulting reduction in capacitance, there is an increase in voltage, according to Q = CV, and an increase in electrical energy, according to W = 0.5CV2. The final step discharges the electrical energy from the material, thereby harvesting the energy.

10

Figure 2 Voltage-Charge (V-Q) plot of an electrical cycle. State D’ is the actual physical states of the DEG, and state D is obtained by calculation under the assumption of constant charge. The CM and DN lines are perpendicular to the X-axis. SACM , SAND ,SDNMC represent the energy stored in DEG before releasing (input energy), the residual energy of DEG after releasing , and the energy increased in CP, respectively. A curve of electrical critical state based on measured value is added to represent the operation limitation. Fig. 2 describes the voltage-charge condition of DEG during the generation cycle. The cycle starts at the initial state A with the DE film not being charged. The DE film was then cone stretched to a preset displacement Z (A→B, these two points are coincident). The voltage and charge remain unchanged, but the capacitance of DE is increased from initial value C2 to a higher value C1 as calculated by Eq. (2). Once the DE has been stretched to a preset value, it is connected to a high-voltage power supply by activating switch S1. During the charging step, the DE changes from state B until the potential of DE and transfer capacitor CP equals to that of the power supply, and state C is reached (B→C). At this stage, a preset input bias voltage, V1 from the power supply is reached, the energy loss of high voltage power supply is as much as the 11

input energy. The charge and the voltage are related by the capacitance of the DE given by the state equation Q=CV. Then, in the next step, we disconnect the switch S1 to make DE and CP being an isolated system, and releases the mechanical loading (C→D). During this mechanical unloading, the thickness of the elastomer increases, and the elastic strain energy is converted into electrical energy by increasing the potential across the DE film. This, in turn, drives charge flows to the transfer capacitor CP. Since CP has a finite capacitance which is set as 9.5 nF, the additional charge increases the voltage across it. As the DE further relaxes, more charges on the DE transfer to CP and at the same time the potential of both DE and CP increase to output voltage V2. A small amount of leakage is inevitable in actual experiment, so we add point D’ to represent the measured value. The difference between the theoretical generated energy and the actual experiment is shown as the hatched area of the D-D’-C triangle in Fig. 2. The Final step is activating switch S2 to harvest the charge. The charge on the transfer capacitor CP and the remaining charge on the DE film was harvested by connecting to a storage device (D/D’→A). The total electrical energy generated during the conversion cycle is the area enclosed by A-C-D’. And energy density is the ratio of the generated energy to material’s mass. The output voltage in point D’ is measured as V2’. It should be mentioned that the charge leakage exists in the whole cycle as long as there is a voltage difference between two electrodes. However, the charge leakage before the DE film being fully charged is quite difficult to measure, and thus we did not calculate such charge leakage and the related energy, consistent with the calculation method reported by previous studies[53, 54]. We calculated the charge leakage starting from the completed charging state (C point) to the end of the releasing process (D’ point). In other words, only the charge leakage during the releasing process was calculated. Due to the addition of transfer capacitor CP that is parallel with DE capacitor, as shown in Eq. 4, the input energy is equal to the energy required to raise the potential of C1 and CP to the bias voltage; the output energy is the energy stored by C2 and CP at the measured voltage (V2’) after releasing. the generated energy in actual cycle can be rewritten by Eq. 1:

12

∆E = Eout − Ein =

1 ( C2 + C P ) V2’ 2 − ( C1 + C P ) V12  2

(4)

Thus, by choosing both the appropriate capacitance and input bias voltage, the magnitude of the system voltage can be controlled so that the DE is still operating below electrical breakdown voltage, while also optimizing the generated energy. To show more clearly the energy harvesting process, we added the CM and DN lines that perpendicular to the X-axis. The area of the input energy of DEG is SACM (the areas of the triangular ACM). During the releasing process, the capacitance of the DEG decreases, the voltage rises, and the charge flows from the DE film into the CP (the transfer capacitor). The increased energy in CP in this process is equal to SDNMC (the areas of the trapezoid DNMC). The derivation process is shown in Part I in Supporting Information. Therefore, the “output energy of DEG” in Fig. 2 is made up of two parts: residual energy after releasing (SAND , the areas of the triangular AND) and energy increased in CP (SDNMC，the areas of the trapezoid DNMC ). Compared to Eq. 4, the calculation method of generated energy (the area difference between blue and orange part) in Fig. 2 eliminates the initial input energy of the CP. Therefore, the area difference in Fig. 2 has the same meaning as the calculation result of Eq. 4, and both indicate the amount of generated energy.

Figure 3 Force-Displacement (F-Z) plot of a mechanical cycle. The area enclosed by the A-B-C-D-A curve (blue part) is the total input mechanical work of the DEG. 13

The input mechanical work during energy generation cycle is calculated according to the force-displacement curve recorded by the force sensor and linear motor. Fig. 3 gives the forces-displacement plots of the DEG during one stretching-releasing cycle. The cycle starts at state A where the DE hasn’t been stretched. The DE is then cone stretched to a preset displacement Z (A→B). After that, a bias voltage is applied to charge the DEG for a few seconds, which causes a decrease in tension due to Maxwell stress and the stress relaxation of DE film (B→C). Next, release the DEG to initial displacement (C→D). But because of the Maxwell stress and the stress relaxation, loss of restoring force occurs. The last step is returning to the state A by releasing the charge (D→A). The integral area of the enclosed graphic zone in Fig. 3, illustrated as shading area, is the mechanical work input Wmech (A→B→C→D→A) and can be calculated by Eq. 5. And energy conversion efficiency is the ratio of the generated energy to Wmech. Wmech = ∫

Z

Z0

( Fstretch − Frelease )dZ

(5)

Herein, we studied the energy harvesting performances of cone DEG including generated energy (ΔE), energy density (w) and energy conversion efficiency (η). Three variables are involved in the generation cycle, that is, equibiaxial prestretch ratio λ, input bias voltage V1, cone stretch displacement Z. It should be mentioned that a setup of Z0 was used to against the loss of tension during releasing process caused by the serious viscoelasticity of VHB4905.[37, 53] As shown in Scheme S2, sample without a prestretch or a Z0 setup would lead to loss of tension when the displacement returns to 10~20 mm during the releasing process, and the loss of tension will lead to wrinkles and adhesion of electrode, and finally result in mechanical and electrical instability. While this phenomenon does not occur in samples with a prestretch or a Z0 setup, so we set a Z0 of 20 mm for sample without prestretch (λ =100%) and Z0 of 0 mm for DEG of λ =150% and 200%. The values of Z were set from Z0 to Zmax with an increment of 10 mm and the displacements when DE film ruptured were 90 mm, 65 mm and 45 mm for DEG at λ=100%, λ=150% and λ=200%, respectively. To optimize the energy generation, we set Zmax slightly smaller than DE film’s rupture displacement, which were set as 80 mm, 60 mm and 40 mm under the equibiaxial prestretch ratio of λ=100%, 150% and 200%, 14

respectively. In addition, we found that during measurement, due to the electric leakage, when Z was too small (Z=30 mm for DEG at λ=100%, and Z=10 mm for DEG at λ=150%), the measured output voltage V2 was equal or even lower than input bias voltage V1, which means no energy was harvested in this cycle. Therefore, the data of these two groups (λ=100%, Z=30mm and λ=150%, Z=10mm) were drawn as dash lines that paralleled to X-axis in Fig. 7, indicating no energy generated due to the electric leakage. The bias voltage started from 0 kV with an increment of 0.5 kV until failure occurs. As shown in Fig. S3, electromechanical instability or electric breakdown occurs when the critical voltage is reached. The Critical State curve in Fig. 2 is based on several measured critical voltages. The maximum experimental voltage we chose was slightly less than the critical voltage. The ranges of variables are summarized in Table 1.

Table 1 Summary of experimental variables Displacement, Z/mm

Maximum experimental voltage /kV

10

20

30

40

50

60

70

80

(λ=100%)

-

-

-

5

4

3

2.5

2

(λ=150%)

-

4.5

4

3.5

3

2.5

-

-

(λ=200%)

6

4

3

2.5

-

-

-

-

4. Results and discussion 4.1 Capacitance-displacement relationship The change of capacitance can reflect the energy generation performance of the DEG. According to Eq. 1, under the same input bias voltage, the larger capacitance of the stretched DEG (C1) has the higher electric energy stored in the DEG, as well as the energy density, and thus higher energy could be generated in this cycle. Fig. 4 gives the relationship between capacitance and displacement (Z) of cone DEG under different equibiaxial prestretch ratios (λ). As expected by Eq. 2, the increasing in Z results in increased area and decreased thickness, which leads to enlargement in capacitance. The maximum capacitance increases from 6.2 nF (λ=100%) to 7.0 nF (λ=150%) and further increases to 7.3 nF (λ=200%). Another interesting phenomenon is that a sharp increase in capacitance is observed with the increase of λ at the same cone 15

displacement. For example, the capacitance of DEG under Z=40 mm increases from 1.6 nF at λ=100% to 3.3 nF at λ=150% and further increases to 6.2 nF at λ=200%. On the other hand, DEG under higher λ achieves the same capacitance under a quite smaller Z (see Fig. 4). For example, a capacitance value of 6.2 nF can be obtained under Z= 90 mm at λ=100% or Z= 40 mm at λ=200%. The smaller Z means smaller device structure and lower voltage source, which makes the entire unit lighter and benefits for application.

Figure 4 Capacitance-displacement (C-Z) relationships of the samples at different equibiaxial prestretch ratio (λ). Critical displacements (points outside the fold lines) is not used.

4.2 Optimization of generated energy and energy density Fig. 5 shows energy generated (∆E) of DEG in one work cycle at various bias voltages (V1) and cone stretch displacements (Z) at different equibiaxial prestretch ratio (λ). The generated energy shows a quadratic dependence on input bias voltage for all the DEGs as expected by Eq. 1. Also, the generated energy increases significantly with the increase in Z. For example, the generated energy increases from 1.5 mJ at Z=20 mm to 24.8 mJ at Z=60 mm under V1=2.5 kV for DEG at λ=150%. Although the growth in Z or

λ reduces the critical voltage, the generated energy under maximum voltage still increases greatly as a whole. The largest generated energy for DEG at λ=200% increases from 0.34 mJ (Z =10 mm, V1=6 kV) to 10.54 16

mJ (Z =20 mm, V1=4 kV) and further increases to 25.5mJ (Z =40 mm, V1=2.5 kV), increasing by 74 times. And importantly, as shown in Fig. 5d, generated energy significantly increases with the increase in λ. For example, the generated energy of DEG at λ=200% (25.5 mJ) is 3 times that at λ=150% (8.8 mJ) and 20 times that at λ=100% (1.2 mJ) under the same Z and V1 (Z=40mm, V1=2.5kV), which means that prestretching can help harvesting much higher energy.

Figure 5 Energy generated at various bias voltages (V1) and cone stretch displacements (Z) by DEG at different equibiaxial prestretch ratio: (a) λ=100%; (b) λ=150%; (c) λ=200%. (d) Generated energy at Z=40 mm, V1=2.5 kV for DEG at different equibiaxial prestretching ratio λ. Energy density (w) is the most important property to indicate the energy harvesting performance of DEG, which can be calculated by dividing generated energy by the mass of DE film. [11, 55] Therefore, the trend of its graphs is very similar to that of the generated energy, except that the scale of the ordinate is different. Fig. 6 shows the energy density (w) of the DEGs with equibiaxial prestretch ratio at λ=100% (Fig. 6a), λ=150% (Fig. 6b) and λ=200% (Fig. 6c) harvested in one work cycle at diffierent input bias voltages 17

and cone stretch displacements. It can be clearly observed that the energy density is remarkably improved as the bias voltage (V1) increases or as the cone stretch displacement (Z) increases. As shown in Fig. 6c, the harvested energy density of DEG at λ=150% is up to 71 mJ/g under the condition of V1 = 2.5 kV and Z = 60 mm, which is about 2 times higher than that under V1 = 2.5 kV and Z = 40 mm (25 mJ/g) and 5 times higher than that under V1 = 1 kV and Z = 60 mm (12 mJ/g). For comparison purpose, energy density at different λ under the same input bias voltage (V1 = 2.5 kV) and cone stretch displacement (Z = 40 mm) is plotted in Fig. 6d. We can find that the energy density increases significantly with the increase in λ. The energy density at λ = 200% is 130 mJ/g, which is 5 times that at λ = 150% ( 25 mJ/g) and 80 times that at λ=100% (1.6 mJ/g) under the same Z and V1 (Z = 40mm, V1 = 2.5 kV). The large increase in energy density caused by prestretching mainly comes from three factors. First, higher λ means smaller thickness d1, which can increase generated energy according to Eq. 3; Second, equibiaxial prestretch enables the high viscoelasticity VHB film to return to Z0 = 0 mm, which reduces the S2 and also increases the power generation (see Eq. 3); Third, the low thickness caused by the high λ can lead to a decrease in the quality of the working area. So the working mass of DEG at λ=200% is nine-sixteenths of that at λ =150% and a quarter of that at λ = 100%. It confirms that the equibiaxial prestretching of the cone DEG within λ = 200% can successfully enhance the ability to harvest electrical energy. This is quite different from a theoretical calculation result which shows that the energy density first increases and then decreases with the increase in equibiaxial prestretch ratio and it reaches a maximum value at λ=125% (10.7mJ/g). [31] The difference may come from the ignore of the charge leakage and material viscoelasticity in the theoretical model. Thus, the results obtained by the simplified model differs greatly from the experimental results. It is worth noticing that prestretching helps achieving the target energy harvesting performance at shorter displacement as well as bias voltage. The energy density of the sample without pre-stretch keeps at a low level and can only reach 13.8mJ/g at a relatively high voltage, whereas that of DEG at λ=150% reaches 71.1 mJ/g under the limited condition of Z=60 mm and V1=2.5 kV, and the maximum energy density reaches 130mJ/g at Z=40 mm, V1=2.5 kV, 18

which far exceeds that of other reported experimental results of cone DEG as shown in Table 2. This indicates that a high performance can be achieved under smaller device structure and lower input voltage source, which makes the entire device lighter and thus has a wider range of applications.

Figure 6 Energy density at various bias voltages (V1) and cone stretch displacements (Z) by DEG at different equibiaxial prestretching ratio: (a) λ=100%; (b) λ=150%; (c) λ=200%. (d) Energy density at Z=40 mm, V1=2.5 kV for DEG at different equibiaxial prestretching ratio λ.

Table 2 Summary and comparison of energy generation performance of cone DEGs Material PU+BT+DBP

[35]

NR+BT+DOP

[41]

[38]

PU+BT-MDI VHB4910

[45]

VHB4905 in McKay’s [36]

study

VHB4910

[37]

VHB 4905 in our study

Boundary condition

Circuit condition

Maximum energy density

Not considered

Simple circuit

1.7mJ/cm

Not considered

Simple circuit

0.71 mJ/cm

Not considered

Simple circuit

2.88 mJ/cm

Not considered

Simple circuit

~6 mJ/cm

~20%

Not considered

Designed circuit

10 mJ/g

12%

Not considered

Simple circuit

18.9mJ/g

18.3%

Considered

Designed circuit

130 mJ/g

25%

19

3

0.45% 3 3

3

Conversion efficiency

3.8% 1.56%

(maximum conversion efficiency in our study)

53.7mJ/g

40%

4.3 Optimization of conversion efficiency The corresponding electromechanical conversion efficiency (η) is shown in Fig. 7, which is determined by the ratio of harvested electric energy to consuming mechanical energy over a cycle, i.e., η=∆E/W×100%. In general, the electromechanical conversion efficiency increases with the increase in V1. Importantly, equibiaxial prestretching can significantly enhance the conversion efficiency. As shown in Fig. 7d, under Z=40mm, V1=2.5 kV, the conversion efficiency of DEG without prestretch (λ=100%) is 2.4%, whereas the conversion efficiency of DEG at λ=150% and λ=200% increases to 10.2% and 20.9%, respectively. Interestingly, the conversion efficiency of DEG overlaps with one another after a critical value. To further demonstrate this interesting phenomenon, two groups of data (λ=100%, Z=30mm and λ=150%, Z=10mm) were drawn as dash lines that parallel to X-axis, indicating that no energy generated due to the electric leakage as mentioned in Experimental Section. After considering these two lines, there exists a “displacement threshold”, after which the conversion efficiency is almost independent of Z and grows significantly with the increase in V1. As a result, the maximum conversion efficiency (40%, at λ=200%, Z=20mm and V1=4 kV) is obtained at the displacement threshold (Zthre) instead of Zmax (25%, at λ=200%, Z=40mm and V1=2.5 kV), because the critical voltage at threshold displacement is much higher. Based on the results above, energy harvesting performance can be optimized according to different DEG operational environments by tailoring Z, V1 and λ. For example, in the case of limited size of working environment of our cone DEG, we can obtain high conversion efficiency and good energy density at lower Z and higher V1. Moreover, in the case of low voltage limitation, we can choose materials with high elongation at break and increase Z as well as λ to obtain higher energy density and good conversion efficiency at safer voltage. Thus, we can propose optimization strategies for different operational environments.

20

Figure 7 Conversion efficiency at various bias voltages (V1) and cone stretch displacements (Z) by DEG at different equibiaxial prestretching ratio: (a) λ=100%; (b) λ=150%; (c) λ=200%.

(d) Conversion

efficiency at Z=40mm, V1=2.5kV for DEG at different equibiaxial prestretching ratio λ. The displacement threshold is Zthre=50 mm for DEG without prestretch (λ=100%) and then it decreases to Zthre=30 mm (λ= 150%) and further decreases to Zthre=20 mm (λ= 200%). This phenomenon was also observed in another report. [54] We propose and discuss the displacement threshold as follows to further understand the actual energy harvesting process.

4.4 Discussion on “displacement threshold” In DEG working cycle, the increase in electrical energy during the releasing process results from an increase in voltage caused by a decrease in DE capacitance. Under the assumption of constant charge, the amplitude of the voltage rise is equal to the capacitance ratio before and after the releasing (hereinafter referred to as “capacitance ratio”), that is, V2/V1=(C1+ CP)/(C2+ CP). In the case of a small amount of charge leakage, the actually measured output voltage (V2’) will be less than the theoretical output voltage (V2), i.e. 21

V2’< V2. From Eq. 4, the actual generated enregy (∆E) and the leakage-free generated energy (∆E*) can be given by following equations: 2 ’   1 2 C1 + CP  V2  ∆E = ( C1 + CP ) V1    − 1 2  C2 + CP  V2  

∆E ∗ =

C +C  1 ( C1 + CP )V12  1 P − 1 2  C2 + CP 

(6)

(7)

To explain the existence of the displacement threshold, we introduce two parameters including the capacitance ratio before and after releasing ((C1+CP)/(C2+CP)) and δ=(1-∆E/∆E*)*100%, which is the percentage of generated energy loss caused by charge leakage, and can be rewritten as follows.

      V ’ 2  1  1-  2   δ = 1+ C + C     V2   P 1  C + C -1    P  2

(8)

Then, we studied the effects of prestretch ratio (λ), displacement (Z) and bias voltage (V1) on these two parameters. Fig. 8a shows the relationship between the capacitance ratio and the displacement (Z) under different prestretch ratios (λ). The data is derived from the capacitance-displacement relationship in Fig. 4. Due to the setting of Z0, the data of the unprestretched sample (λ=100%) starts from Z=20 mm, and the prestretched sample (λ=150% and λ=200%) starts from Z=0 mm. Similar to the capacitance-displacement relationship in Fig. 4, the capacitance ratio increases with the increase in Z as a whole and higher λ causes a faster growth in the capacitance ratio. From Eq. 8, the increase in the capacitance ratio results in a decrease in δ, i.e. a decrease in generated energy loss caused by charge leakage. When the capacitance ratio is around 1, the δ value is very sensitive to the change of the capacitance ratio. As the capacitance ratio is far away from 1, the influence from the capacitance ratio δ becomes smaller, that is, the increase of the Z reduces the generated energy loss caused by charge leakage. It is worth noticing that the capacitance ratios at the displacement thresholds under different prestretch ratios are numerically close, which are 1.16 (λ=100%, Z=50mm), 1.20 22

(λ=150%, Z=30mm), 1.18 (λ= 200%, Z=20 mm), showing a good consistency. This means that the essence of the displacement threshold is the "capacitance ratio threshold" in practical circuits.

Figure 8 (a) The relationship between the capacitance ratio before and after releasing ((C1+CP)/(C2+CP)) and the displacement (Z) under different prestretch ratios. (b) The relationship between δ (the percentage of generated energy loss) and displacement (Z) and bias voltage (V1) under the condition of λ=200%. (c) The relationship between δ and the displacement (Z) under different prestretch ratios at V1=1 kV. (d) The relationship between the leakage-free conversion efficiency (∆E*/W) and displacement (Z) under different prestretch ratios (λ) at V1=1 kV. Fig. 8b shows the relationship between δ and displacement (Z) and bias voltage (V1) under the condition of λ=200%. δ is not sensitive to the bias voltage at a certain displacement value, but an increase in displacement leads to a rise in the capacitance ratio, which in turn greatly reduces the value of δ according to Eq. 8. It can be seen that the charge leakage causes more than 95% of the generated energy loss under a low displacement (Z=10 mm), and the energy loss of the sample with Z=20 mm rapidly reduces to about 35% 23

and the loss could be controlled below 10% under a much larger displacement of Z=40 mm. How the displacement (Z) and the prestretch ratio (λ) affect δ under V1= 1kV is shown in Fig. 8c. δ decreases with the increase in Z as a whole. Prestretching helps to achieve lower energy loss at lower displacements. For example, in order to reduce the δ to 20%, Z of sample with λ=100%, λ=150%, and

λ=200% needs to reach 70mm, 50mm and 30 mm, respectively. In addition, the prestretching greatly reduces the energy loss under the same Z. Under the condition of V1=1 kV and Z=40 mm, δ drops from 64.9% (λ=100%) to 26.0% (λ=150%) and further drops to 6.4% (λ=200%). And similar to the case of "capacitance ratio threshold" in Fig. 8a, the δ values at the displacement thresholds under different λ are also relatively close which are 40% (λ=100%, Z=50 mm), 28.1% (λ=150%, Z=30 mm), 35.9% (λ=200%, Z=20 mm). The conversion efficiency is the ratio of generated energy to mechanical work, so in addition to output generated energy, it is affected by input mechanical work. VHB4905 is a material with high viscoelastic effect, which causes stress relaxation within 10 s of charging the DEG and significantly reduces the releasing force and enlarge the difference between the stretch force and the releasing force. According to Eq. 5, the increasing in Z and enlarge of the difference between the stretch force and the releasing force cause more useless work be performed in the generation cycle, so as to enlarge the input mechanical work and reduce the conversion efficiency. Fig. 8d shows the relationship between the leakage-free conversion efficiency (∆E*/W) and displacement (Z) and prestretch ratio (λ) at V1= 1 kV. The values of ∆E*/W decreases with increase in Z in all λ conditions, which means that as Z increases, the rate of increase in mechanical work exceeds the rate at which the amount of leakage-free generated energy is increased. So under the assumption of constant charge, for severe viscoelastic DE materials, the increasing in Z leads to a reduction in conversion efficiency. This article considers that the displacement threshold is resulted from the viscoelasticity of DE film and the generated energy loss caused by a small amount of charge leakage in the actual circuit. In practice, a small amount of charge leakage leads to the smaller output voltage (V2’ ) than V2, so that the actual energy 24

generation is much lower than the leakage-free energy generation. A lower Z value result in a lower capacitance ratio (i.e. (C1+ CP)/(C2+ CP)≈1) and implies a lower voltage rise as well as a slight energy growth. In this case, the electrical loss can be the main factor controlling the conversion efficiency. As the Z value increases, the capacitance ratio continuously increases, the influence of electrical loss on generated energy is decreasing. After the capacitance ratio reaches a certain value, the influence of electrical loss on generated energy reaches quite a low level. We call the Z value at this point the “displacement threshold”, that is, the essence of the displacement threshold is the "capacitance ratio threshold". In this experimental environment, the displacement threshold is obtained when the capacitance ratio reaches about 1.16. When Z continues to increase, the high viscoelasticity of the DE film causes the increasing rate of mechanical work exceeding the increasing rate of leakage-free generated energy. On the other hand, the increase in Z further reduces the generated energy loss caused by charge leakage. Under these two effects, the growth rates of mechanical work and actual power generation are almost the same with the increase in Z. As a result, the conversion efficiency is not sensitive to Z at the same V1. So the efficiency-voltage curves at different Z appear to overlap with each other, as shown in Fig. 7.

5. Conclusions The energy harvesting performance including capacitance, generated energy, energy density and conversion efficiency of the cone DEG based on VHB elastomer was successfully optimized by combining equibiaxial prestretching to cone stretching mode followed by tailoring the variables such as the equibiaxial prestretch ratio (λ), input bias voltage (V1) and cone displacement (Z). As a whole, although the growth in displacement or equibiaxial prestretch ratio reduces the critical voltage, the energy harvesting performance still increases greatly. Prestretching plays an important role in achieving the target energy harvesting performance at shorter displacement as well as lower bias voltage. This means that a high performance can be achieved under smaller device structure and lower input voltage source, making the entire device lighter 25

and thus has a wider range of applications. By optimizing the variables above, an up-to-date highest experimental energy density of the cone DEG (130 mJ/g) accompanied with a relatively high conversion efficiency (25%) were obtained at λ=200%, V1=2.5 kV and Z=40 mm. In addition, the maximum conversion efficiency of 40% accompanied with a relatively high energy density (53.7 mJ/g) were obtained at λ=200%, V1=4 kV and Z=20mm. Moreover, the "displacement threshold" was firstly proposed and discussed based on the joint effect of leakage and viscoelastic. Our research reveals that combining equibiaxial prestretch and cone stretching mode is a feasible method to obtain DEG for both high energy harvesting performance and high practicality.

Conflicts of interest There are no conflicts to declare.

Acknowledgments We would like to thank the National Natural Science Foundation of China (Grant No. 51525301, 51473011), the Fundamental Research Funds for the Central Universities in China (buctrc201713) and a Project of Shandong Province Higher Educational Science and Technology Program(J18KA024) for financial supports.

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29

Highlights: The energy harvesting performance of a cone DEG was optimized. The key variables on energy harvesting performance of cone DEG were studied. An up-to-date highest energy density of cone DEG (130 mJ/g) was obtained. An up-to-date maximum electromechanical conversion efficiency of 40% was obtained. "Displacement threshold" in DEG was firstly proposed and discussed.

Y. J. Jiang is a Ph.D. candidate in Beijing University of Chemical Technology. He received his Bachelor’s degree in polymer material and engineering from the school in 2016. His research interests focus on the device and material design for dielectric elastomer generator.

S. T. Liu was born in Shandong, China in 1988. She received her B.S. degree in Polymer Material and Engineering from Qingdao University (China) in 2011, and her Ph.D. degree in Material Science and Engineering from Beijing University of Chemical Technology (China). Then she joined Weifang Vocational College as a Lecturer. Her research interests mainly focus on the design and preparation of elastomer composites for energy transformation applications.

M. L. Zhong was born in Yantai, Shandong Province in 1994. She received her B.S. degree in the Department of Polymer Science and Engineering, University of Science and technology Qingdao (China) in 2017. She is studying her M.S. degree in Materials Science and Engineering from Beijing University of Chemical Technology (China). Her research interests mainly focus on the preparation of novel dielectric

elastomer composites suitable for tapered tensile mode generator.

L. Q. Zhang is a professor of Beijing University of Chemical Technology. His research interests focus on rubber science and technology, polymer nanocomposites, bio-based polymeric materials and so on. He has received various awards such as Nation Outstanding Youth Foundation, Changjiang Scholar Professor of Ministry of Education of China, Sparks-Thomas sci-tech award of Rubber Division of American Chemical Society, Science of Chemical Engineering of Japan (SCEJ) Research award, Morand Lambla Award of International Polymer Processing Society. He has published over 300 peer-reviewed papers, (co-)authors of 8 books (chapters) and has given over 60 plenary/keynote/invited lectures in international conferences.

N. Y. Ning received her Ph.D degree in College of Polymer Science and Engineering, Sichuan University (China) in 2010. She is currently a Professor in College of Materials Science and Engineering, Beijing University of Chemical Technology. Her research interests focus on structure-performance

relationship of thermoplastic vulcanizate and dielectric elastomer materials. M. Tian is currently a Professor in College of Materials Science and Engineering, Beijing University of Chemical Technology.

He received National Science Fund for

Distinguished Young Scholars in 2015 and he was awarded as Changjiang Scholar Professor of Ministry of Education of China in 2017. His present research interests are special and functional elastomer materials.

Declaration of Interest Statement Declarations of interest: none