A self-amplifying dielectric-elastomer-amplified piezoelectric for motion-based energy harvesting

Abstract

The dielectric elastomer generator is a stretchable generator that converts low-frequency motions into electrical output, with excellent impedance matching capabilities. However, the dielectric elastomer requires an external high-voltage priming source to initialize its operation. We previously proposed a piezoelectric generator as the priming source, and demonstrated a net amplification of specific output energy of 1.8 times by the dielectric elastomer generator, as compared with that of the piezoelectric working in isolation. We termed our prototype the dielectric-elastomer-amplified piezoelectric (DEAmP). In this version, we introduce a self-priming circuit that will progressively charge up the dielectric elastomer generator to a much higher potential, thereby allowing the system to approach its optimized operating voltage. We term this the DEAmPx generator, with the letter “x” denoting progressive voltage/charge amplification by the self-priming circuit. The DEAmPx attained an output voltage of about 2000 V in 18 cycles and generates a dielectric elastomer generator–specific energy output of 3.1 mJ/g per cycle—19 times higher than that of the piezoelectric generator working in isolation. The system-specific energy output of DEAmPx is 0.49 mJ/g, with just a single layer of elastomer film. With this significantly larger output, we demonstrate the capability of a single-layer DEAmPx to power dielectric elastomer actuators.

Keywords

Dielectric elastomer self-priming circuit piezoelectric energy harvesting

1. Introduction

Low-power sensors and actuators could be autonomously powered by harvesting energy from ambient motion sources. Traditional motion–based energy harvesters use electromagnetic or piezoelectric generators to harvest ambient motions and convert them into electrical outputs. All of them, however, require ambient motions to be regular and fast in speed, in order for usable power to be harvested. The dielectric elastomer generator (DEG) is an emerging technology that is capable of harvesting low-frequency and low-speed ambient motion like sea waves (Kornbluh et al., 2011; Moretti et al., 2018) and human footfall (Kornbluh et al., 2002; Paradiso and Starner, 2005). Dielectric elastomers (DEs) are stretchable capacitors that consist of an elastomeric membrane sandwiched by compliant electrodes. When a low-voltage (Φ) charge is placed on a stretched elastomer prior to contraction, the contraction work against the Maxwell pressure increases the potential of the charge (Φ′, where Φ′ > Φ), thus generating a surplus amount of energy (Figure 1) (Kornbluh et al., 2002; Pelrine et al., 2001). The most common elastomers used for DEGs are acrylics (Huang et al., 2013; Koh et al., 2011a; McKay et al., 2010b; Pelrine et al., 1997; Shian et al., 2014), silicones (Madsen et al., 2016; Skov and Yu, 2017), and natural rubber (Kaltseis et al., 2014; Koh et al., 2011a). The most commonly used electrodes are carbon-based and are classified into three categories, carbon powder, carbon grease, and conductive rubber (Rosset and Shea, 2013). High specific energies of up to 0.78 J/g (Shian et al., 2014), at least 10 times that of existing technologies like piezoelectric and electromagnetic systems, have been reported for DEGs (Kornbluh et al., 2002, 2012). DEGs offer many advantages over conventional generators. They are low cost, light weight, operates noise-free, resists corrosion, and present good impedance matching to many low-frequency ambient sources (Kornbluh et al., 2002; Pelrine et al., 2001; Suo, 2010). However, DEGs require an external high-voltage source to initialize energy conversion.

Figure 1.

Working principle of the dielectric elastomer generator (DEG). The DE membrane is stretched mechanically and pre-charged with Φ. When the DE membrane is relaxed, the work done by the membrane against the Maxwell pressure, hence increasing the voltage of the charge to Φ′ (Φ′ > Φ).

Currently, there are two approaches to free the DEG from an external high-voltage electrical source: one, by coupling it with another motion-based energy harvester or two, to use an initial charge source with a self-priming circuit (SPC) that enables the DEG to prime itself so as to progressively amplify its voltage on each cycle (Ikegame et al., 2017; Illenberger et al., 2017; 2018; McKay et al., 2010a, 2010b, 2012; Mathew and Koh, 2018; Zanini et al., 2016). Electrets (Jean-Mistral et al., 2012, 2014; Lagomarsini et al., 2017; Vu-Cong et al., 2013a, 2013b) and piezoelectric generators (Alexandru et al., 2016; Clara et al., 2018; Mathew et al., 2019) are considered for the first approach. However, as electrical energy input scales with the square of the electric field ( $~ ε E^{2}$ where $ε$ is the permittivity of the DE), these motion-based energy harvesters cannot supply a high enough electric field that will optimize the energy output (Mathew et al., 2019). The SPC introduced by McKay et al. consists of capacitors and diodes arranged as shown in Figure 2(a). Prior to the onset of a self-primed DEG (SP-DEG) cycle, a low-voltage charge source is used to prime the capacitors in the SPC and the DEG. Once the SP-DEG cycle starts, the charge source is disconnected via switch “S.” The charge flows from SPC to DEG while the DEG is being stretched and from DEG to SPC while the DEG is being relaxed. By the virtue of the arrangement of diodes in SPC, while the electric charges are being transferred from the DEG to the SPC (charge flows from A → B), the SPC capacitors assume a series configuration which stores the electric energy in high-voltage form. While the charges are being supplied back to the DEG (charge flows from B → A), the SPC capacitors assume a parallel configuration which stores the energy in high-charge form. The interaction between a cyclically stretching and relaxing DEG and the SPC therefore progressively steps up voltage and charge on the DEG, allowing it to operate at high electric fields. Due to the SPC switching between high-voltage form and high-charge (low-voltage) form, the DE must be sufficiently deformed so that its capacitance ratio (maximum to minimum capacitance of the DE during the operation) bridges the gap between the high-voltage and the high-charge forms in the SPC. With insufficient DEG capacitance ratio, charge will not flow between the SPC and the DEG. For an SPC consisting of only two capacitors switching between its series and parallel configuration (first-order SPC), the minimum capacitance ratio required of the DEG is 2, which we shall show later. In order to narrow this gap, higher order SPCs are also introduced (Figure 2(b)) to reduce the capacitance swing required of the DE (McKay et al., 2010b, 2012). McKay et al. (2010a) presented a modification to the SPC known as the integrated SPC (I-SPC), in which two DEGs are oscillated 180° out of phase to eliminate the need of external rigid capacitors of the SPC. Further modifications on the I-SPC are made to replace the rigid diodes with DE switches, thereby making the generator completely composed of DE (McKay et al., 2011). Self-priming of the DEG has been proven to be an attractive proposition in making the DEG free from an external high-voltage source. However, the SP-DEG still requires a charge source for the initial cycle to make it truly autonomous.

Figure 2.

(a) Basic circuit of a self-primed dielectric elastomer generator (SP-DEG). A first-order self-priming circuit is inscribed in a dashed rectangle. When charge flows from point A to B, the SPC capacitors assume a series configuration (high-voltage form) and when the charge flows from point B to A, the SPC capacitors assume a parallel configuration (high-charge form). DEG is represented as a variable capacitor (C_D). Switch “S” is kept ON for the initial priming of SP-DEG via a low-voltage source Φ_in. (b) nth-order SPC.

Anderson et al. used the SPC with microbial fuel cells (MFCs) or solar cell arrays as the charge source (Anderson et al., 2010, 2011; McKay et al., 2012). The physical process of energy conversion of MFCs or solar cell arrays is dissimilar to DEGs. Hence, they cannot be easily integrated to produce small-scale motion-based energy harvesters. Illenberger et al. (2018) used an electret as a charge source for the SP-DEG instead. Electrets are readily available but are expensive to purchase or produce. They require periodic priming from plasma discharge as its charges will eventually be depleted. In this work, we use a commonly available lead–zirconate–titanate (PZT) piezoelectric diaphragm as the initial charge source for the SP-DEG system. We term this the DEAmPx generator, where DEAmP refers to dielectric-elastomer-amplified piezoelectric (DEG coupled with a piezoelectric generator), previously proposed by the authors (Mathew et al., 2019), and the letter “x” denotes the progressive voltage amplification by the SPC.

Connecting the DEAmPx to an electrical load or a storage unit allows it to transfer a part of its internal energy to do useful work or to store the output charges. With the objective of quantifying this energy output, we analyzed a DEAmPx connected to an output capacitor. Our analysis suggests that the voltage boost per cycle of the system increases with the DEG capacitance ratio. For a space-constrained design, a DE deformation mode, namely, the ripple mode was introduced (Mathew et al., 2019) to induce a large capacitance ratio for the DEG (Figure 3). Based on our analysis, we present a fully autonomous generator prototype that integrates these three components: an SPC that is electrically connected with the DEG, the DEG deformed in ripple mode, and a PZT diaphragm as a charge source. Our compact design makes it suitable to be used as a small-scale energy harvester where the ambient motion source is of a compressive nature, like that of a human heel strike during walking. Experiments are carried out to characterize the energy harvesting capability of the prototype connected to a constant voltage output reservoir, which is a special case of a biased output capacitor where the output capacitance tends to infinity. Finally, we demonstrate the capability of our prototype to power two types of DE actuators (which essentially are output capacitors), which was previously suggested, but not demonstrated, by Anderson et al. (2012). Our demonstration allows safe and untethered operation of the DE actuator (DEA) that requires very large voltage to operate.

Figure 3.

Cross-sectional view of the ripple mode of deformation for DEG. The top and bottom rigid structures (blue and red) deform the DE film (black) out of plane resulting in a ripple shape.

2. State and process modeling of DEAmPx

The electrical voltage source with switch “S” shown in Figure 2(a) is replaced with a rectified piezoelectric (Figure 4). An output capacitor $(C_{out})$ is connected in series with a diode to prevent charge back flow when the voltage of SP-DEG system drops during the cycle. For a linear dielectric, we have $Q_{D} = C_{D} Φ_{D}$ , where $Q_{D}$ is the charge, $Φ_{D}$ is the voltage, and $C_{D}$ is the capacitance of the DEG. The SPC takes on either a series or a parallel configuration depending on the direction of charge flow. We define $Φ_{SS}$ and $Q_{SS}$ as the voltage and charge of the SPC in the series configuration and $Φ_{SP}$ and $Q_{SP}$ for the parallel configuration. The series and parallel capacitance of an nth-order SPC are given by $C_{SS} = nC / (n + 1)$ and $C_{SP} = (n + 1) C / n$ , here C is referred to the highest capacitance of an nth-order SPC (Figure 2(b)). From energy conservation, the series and parallel voltage of the SPC are related by $Φ_{SS} = (1 + (1 / n)) Φ_{SP}$ (Illenberger et al., 2017; Mathew and Koh, 2018). We define the voltage of the output capacitor as $Φ_{out}$ .

Figure 4.

Circuit diagram of DEAmPx connected to an output capacitor via a diode.

For the analytical model, we assume an ideal electrical circuit with zero resistance. We further assume no losses in the diodes and rigid capacitors, and that the DEG consists of electrodes that are perfect conductors and a dielectric that is a perfect insulator. Hence, energy losses within the electrical circuit and its components, and the dissipative processes in the DE such as leakage current and viscoelasticity (Chiang Foo et al., 2012a, 2012b; Zhao et al., 2011) are ignored for the analysis. The operation of the DEAmPx is as follows: the DEG is stretched from a state of minimum capacitance $(C_{D_MIN})$ to a state of maximum capacitance $(C_{D_MAX})$ . The piezoelectric is then deformed to charge the DEG, the SPC (in series configuration) and the output capacitor $(C_{out})$ simultaneously by a voltage $Φ_{P_in}$ . As the SPC, DEG, and the output capacitor are connected in parallel, their total capacitance is the sum of their individual capacitances $(C_{D} + C_{SS} + C_{out})$ . Hence, the relaxation of the DEG will result in an overall decrease in total capacitance, leading to a voltage boost. Equating the total electric charge prior to $(Φ_{P_{in}} (C_{D_{MAX}} + C_{SS} + C_{out}))$ and after DEG relaxation $(Φ_{i} (C_{D_MIN} + C_{SS} + C_{out}))$ , we derive the voltage on the DEG, SPC $(C_{SS})$ , and output capacitor as

Φ_{i} = Φ_{P_in} \frac{\frac{n}{n + 1} C + C_{D_MAX} + C_{out}}{\frac{n}{n + 1} C + C_{D_MIN} + C_{out}}

(1)

2.1. Analytical modeling of SP-DEG with an output capacitor

The SP-DEG cycle commences when $Φ_{D} = Φ_{SS} = Φ_{out} = Φ_{1}$ , where $Φ_{1} = Φ_{i}$ as shown in equation (1), in the first SP-DEG cycle and $C_{D} = C_{D_MIN}$ . We define this as state 1. As the DEG is stretched, the electric current flow within the circuit takes place in five processes, straddling six states, as shown in Figure 5. When the voltage of the SP-DEG is higher than the open-circuit voltage of the piezoelectric, the diodes of the rectifier circuit (Figure 4) become reverse-polarized. Hence, even if the piezoelectric is deformed, it does not participate in the charging process once the SP-DEG cycle kicks in.

Figure 5.

Current flow paths as DEG undergoes one cycle of deformation. (a) Process 1 → 2: DEG stretched from C_D_{_MIN}, Φ_D > Φ_SP, no current flow (open-circuit). (b) Process 2 → 3: DEG is further stretched so that Φ_D = Φ_SP, charge flows from SPC to DEG until DEG attains C_D_{_MAX}. (c) Process 3 → 4: DEG is relaxed from C_D_{_MAX}, Φ_D < Φ_SS, no current flow (open-circuit). (d) Process 4 → 5: DEG is further relaxed so that Φ_D = Φ_SS, charge flows from DEG to SPC. (e) Process 5 → 6: DEG is further relaxed so that Φ_D = Φ_SS = Φ_out, charge flows from DEG to SPC and output capacitor, until DEG attains C_D_{_MIN}.

We develop the equations-of-state for the circuit as follows:

For the process 1 → 2, the DEG is stretched from $C_{D_MIN}$ and its capacitance increases, and hence $Φ_{D (1 \to 2)} < Φ_{1}$ . We have $Φ_{SP (1 \to 2)} < Φ_{D (1 \to 2)} < Φ_{SS (1 \to 2)} = Φ_{1}$ . The diodes in the SPC will prevent charge flow from SPC (in series configuration) to DEG. With that, no charge transfer will take place in the entire circuit, giving an open-circuit condition (Figure 5(a)). Assuming no charge loss, from equation (1), we have

Φ_{D (1 \to 2)} = \frac{C_{D_MIN}}{C_{D (1 \to 2)}} Φ_{1}

(2a)

Q_{D (1 \to 2)} = C_{D_MIN} Φ_{1}

(2b)

While the voltage of the SPC in parallel configuration, is given as

Φ_{SP (1 \to 2)} = (\frac{n}{n + 1}) Φ_{1}

(2c)

Comparing (2a) and (2c), as long as $(C_{D_MIN} / C_{D (1 \to 2)}) > (n / (n + 1))$ , no charge will be transferred from the SPC (in parallel configuration) to the DEG. Once $Φ_{D (1 \to 2)}$ and $Φ_{SP (1 \to 2)}$ become equal, the SP-DEG system arrives at state 2. For charge transfer to take place from SPC to DEG, the following condition must be satisfied

C_{D_MAX} \geq (\frac{n + 1}{n}) C_{D_MIN}

(3)

where the pre-factor $(1 + (1 / n))$ provides the minimum capacitance ratio that the DEG must match in order for charge interchange to take place between the SPC and the DEG. From state 2, the DEG is further stretched and $C_{D}$ is further increased. Once $Φ_{SP (2 \to 3)} = Φ_{D (2 \to 3)}$ , the SPC will begin to charge the DEG (Figure 5(b)). The total charge in the SPC (in parallel configuration) and DEG at state 2 is given by $Q_{SP 2} + Q_{D 2} = (C + C_{D_MIN}) Φ_{1}$ . During process 2 → 3, the total charge is conserved between the SPC and DEG. Hence, we have

Φ_{D (2 \to 3)} = Φ_{SP (2 \to 3)} = \frac{C + C_{D_MIN}}{\frac{n + 1}{n} C + C_{D (2 \to 3)}} Φ_{1}

(4a)

Q_{D (2 \to 3)} = C_{D (2 \to 3)} Φ_{D (2 \to 3)}

(4b)

At state 3, the DEG is maximally stretched with its capacitance at $C_{D_MAX}$ . Substituting $C_{D (2 \to 3)} = C_{D_MAX}$ in (4a), the voltage of DEG at state 3 is

Φ_{3} = \frac{C + C_{D_MIN}}{\frac{n + 1}{n} C + C_{D_MAX}} Φ_{1}

(5)

For the process 3 → 4, DEG is relaxed and its capacitance reduces in an open-circuit condition, leading to a voltage increase in the DEG. We have $Φ_{3} = Φ_{SP (3 \to 4)} < Φ_{D (3 \to 4)} < Φ_{SS (3 \to 4)}$ . No current flow will take place, and we have a second open-circuit condition (Figure 5(c)). The voltage and charge in the DEG are given as

Φ_{D (3 \to 4)} = \frac{C_{D_MAX}}{C_{D (3 \to 4)}} Φ_{3}

(6a)

Q_{D (3 \to 4)} = C_{D_MAX} Φ_{3}

(6b)

While the voltage of the SPC in series configuration is given as

Φ_{SS (3 \to 4)} = \frac{n + 1}{n} Φ_{3}

(6c)

At state 4, $Φ_{D 4}$ and $Φ_{SS 4}$ equilibrates. The DEG will begin to charge the SPC which is in series configuration (Figure 5(d)). A further relaxation of the DEG will lead to a smaller $C_{D}$ and a larger $Φ_{D}$ . Again, assuming voltage equilibrium and charge conservation, we have

Φ_{D (4 \to 5)} = Φ_{SS (4 \to 5)} = \frac{C + C_{D_MAX}}{\frac{n}{n + 1} C + C_{D (4 \to 5)}} Φ_{3}

(7a)

Q_{D (4 \to 5)} = C_{D (4 \to 5)} Φ_{D (4 \to 5)}

(7b)

At state 5, the voltage of DEG becomes $Φ_{1}$ (voltage of the output capacitor $Φ_{out} = Φ_{1}$ ). As the DEG relaxes further, charge flows from DEG to SPC in series configuration and the output capacitor simultaneously. From voltage equilibrium and charge conservation, we get

Φ_{D (5 \to 6)} = Φ_{SS (5 \to 6)} = Φ_{out (5 \to 6)} = \frac{C_{out}}{C_{out} + \frac{n}{n + 1} C + C_{D (5 \to 6)}} Φ_{1} + \frac{(C + C_{D_MAX})}{C_{out} + \frac{n}{n + 1} C + C_{D (5 \to 6)}} Φ_{3}

(8a)

Q_{D (5 \to 6)} = C_{D (5 \to 6)} Φ_{D (5 \to 6)}

(8b)

At state 6, the capacitance of the DEG becomes $C_{D_MIN}$ . Substituting $C_{D (5 \to 6)} = C_{D_MIN}$ and $Φ_{3}$ from equation (5) in equation (8a), the voltage of DEG at state 6 is given by

Φ_{6} = \frac{C_{out} (\frac{n + 1}{n} C + C_{D_MAX}) + (C + C_{D_MAX}) (C + C_{D_MIN})}{(C_{out} + \frac{n}{n + 1} C + C_{D_MIN}) (\frac{n + 1}{n} C + C_{D_MAX})} Φ_{1}

(9)

The cycle restarts with the value of $Φ_{1}$ same that of the value of $Φ_{6}$ of the previous cycle. We define voltage boost per cycle $(G)$ as follows

G = \frac{Φ_{6}}{Φ_{1}} = \frac{C_{out} (\frac{n + 1}{n} C + C_{D_MAX}) + (C + C_{D_MAX}) (C + C_{D_MIN})}{(C_{out} + \frac{n}{n + 1} C + C_{D_MIN}) (\frac{n + 1}{n} C + C_{D_MAX})}

(10)

Energy transferred from SP-DEG system to the output capacitor is given by

Ω_{out} = \frac{1}{2} C_{out} (Φ_{6}^{2} - Φ_{1}^{2}) = \frac{1}{2} C_{out} (G^{2} - 1) Φ_{1}^{2}

(11)

We shall now consider two limiting cases of $C_{out} = 0$ and $C_{out} \to \infty$ . The former case denotes a circuit with no output capacitor—the SP-DEG simply exchange charges among themselves. Hence, there exists zero output yield, as suggested by equation (11). Substituting $C_{out} = 0$ in equation (10), we get the voltage boost per cycle for an SP-DEG circuit operating in isolation

{G |}_{C_{out} = 0} = (\frac{C + C_{D_MAX}}{\frac{n}{n + 1} C + C_{D_MIN}}) (\frac{C + C_{D_MIN}}{\frac{n + 1}{n} C + C_{D_MAX}})

(12)

Equation (12) recovers the same equations derived in existing works (Illenberger et al., 2017; Zanini et al., 2016). For the case of $C_{out} \to \infty$ , equivalent to an infinite output reservoir, equation (9) suggests that the voltage at the final state of the cycle is the same as that of the initial state ( $Φ_{6} = Φ_{1}$ or ${G |}_{C_{out} = \infty} = 1$ ). Physically, an infinite capacitance reservoir is equivalent to a battery of voltage rating $Φ_{1}$ connected to the SP-DEG system as a storage device. A closed-circuit between the DEG and the battery will make process 5 → 6 a constant voltage process $(Φ_{D (5 \to 6)} = Φ_{1})$ during charge transfer. The electrical energy output to the storage reservoir is given as

{Ω_{out} |}_{C_{out} = \infty} = Φ_{1} (Q_{D 5} - Q_{D 6}) = Φ_{1}^{2} (C_{D 5} - C_{D_MIN})

(13a)

where $Q_{D 5}$ and $Q_{D 6}$ are the charges on the DEG at states 5 and 6, respectively, and $C_{D 5}$ is the capacitance of the DEG at state 5. One may solve for $C_{D 5}$ by substituting equation (5) into equation (7a) and solving equation (7a) for $C_{D (4 \to 5)}$ by setting $Φ_{D (4 \to 5)} = Φ_{1}$ . Substituting $C_{D 5}$ into equation (13a), the net output yield is obtained as follows

{Ω_{out} |}_{C_{out} = \infty} = \frac{C (n C_{D_MAX} - (n + 1) C_{D_MIN})}{(n + 1) ((n + 1) C + n C_{D_MAX})} Φ_{1}^{2}

(13b)

Table 1 provides the summary of the equation of states.

Table 1.

Summary of the equation of states.

Process	Description of the process	Governing equations
1 → 2	DEG is stretched from $C_{D_MIN}$ in open-circuit condition.	$Φ_{D} = \frac{C_{D_MIN}}{C_{D}} Φ_{1}$ , $Q_{D} = C_{D_MIN} Φ_{1}$ , $Φ_{SP} = (\frac{n}{n + 1}) Φ_{1}$ $C_{D}$ increases from $C_{D_MIN}$ to $(\frac{n + 1}{n}) C_{D_MIN}$ and $Φ_{D}$ decreases from $Φ_{1}$ to $(\frac{n}{n + 1}) Φ_{1}$
2 → 3	DEG is further stretched so that $Φ_{D} = Φ_{SP}$ , charge flows from SPC (parallel configuration) to DEG until DEG attains $C_{D_MAX}$ .	$Φ_{D} = Φ_{SP} = \frac{C + C_{D_MIN}}{\frac{n + 1}{n} C + C_{D}} Φ_{1}$ or $Φ_{D} = Φ_{SP} = \frac{- Q_{D}}{\frac{n + 1}{n} C} + \frac{C + C_{D_MIN}}{\frac{n + 1}{n} C} Φ_{1}$ , $Q_{D} = C_{D} Φ_{D}$ $C_{D}$ increases from $(\frac{n}{n + 1}) C_{D_MIN}$ to $C_{D_MAX}$ and $Φ_{D}$ decreases from $(\frac{n + 1}{n}) Φ_{1}$ to $Φ_{3}$
3 → 4	DEG is relaxed from $C_{D_MAX}$ in open-circuit condition.	$Φ_{D} = \frac{C_{D_MAX}}{C_{D}} Φ_{3}$ , $Q_{D} = C_{D_MAX} Φ_{3}$ , $Φ_{SS} = (\frac{n + 1}{n}) Φ_{3}$ $C_{D}$ decreases from $C_{D_MAX}$ to $(\frac{n}{n + 1}) C_{D_MAX}$ and $Φ_{D}$ increases from $Φ_{3}$ to $(\frac{n + 1}{n}) Φ_{3}$
4 → 5	DEG further relaxed so that $Φ_{D} = Φ_{SS}$ , charge flows from DEG to SPC (series configuration) until $Φ_{D} = Φ_{1}$ .	$Φ_{D} = Φ_{SS} = \frac{C + C_{D_MAX}}{\frac{n}{n + 1} C + C_{D}} Φ_{3}$ or $Φ_{D} = \frac{- Q_{D}}{\frac{n}{n + 1} C} + \frac{C + C_{D_MAX}}{\frac{n}{n + 1} C} Φ_{3} = Φ_{SS}$ , $Q_{D} = C_{D} Φ_{D}$ $C_{D}$ decreases from $(\frac{n}{n + 1}) C_{D_MAX}$ to $C_{D 5}$ and $Φ_{D}$ increases from $(\frac{n + 1}{n}) Φ_{3}$ to $Φ_{1}$
5 → 6	DEG further relaxed so that $Φ_{D} = Φ_{SS} = Φ_{out}$ , charge flows from DEG to SPC (series configuration) and output capacitor until DEG attains $C_{D_MIN}$ .	$Φ_{D} = Φ_{SS} = Φ_{out} = \frac{C_{out}}{C_{out} + \frac{n}{n + 1} C + C_{D}} Φ_{1} + \frac{(C + C_{D_MAX})}{C_{out} + \frac{n}{n + 1} C + C_{D}} Φ_{3}$ or $Φ_{D} = Φ_{SS} = Φ_{out} = \frac{- Q_{D}}{C_{out} + \frac{n}{n + 1} C} + \frac{C_{out} Φ_{1} + (C + C_{D_MAX}) Φ_{3}}{C_{out} + \frac{n}{n + 1} C}$ , $Q_{D} = C_{D} Φ_{D}$ $C_{D}$ decreases from $C_{D 5}$ to $C_{D_MIN}$ and $Φ_{D}$ increases from $Φ_{1}$ to $Φ_{6}$
5 → 6 for $C_{out} = 0$	DEG further relaxed so that $Φ_{D} = Φ_{SS}$ , charge flows from DEG to SPC until DEG attains $C_{D_MIN}$ .	$Φ_{D} = Φ_{SS} = \frac{C + C_{D_MAX}}{\frac{n}{n + 1} C + C_{D}} Φ_{3}$ or $Φ_{D} = \frac{- Q_{D}}{\frac{n}{n + 1} C} + \frac{C + C_{D_MAX}}{\frac{n}{n + 1} C} Φ_{3} = Φ_{SS}$ , $Q_{D} = C_{D} Φ_{D}$ $C_{D}$ decreases from $C_{D 5}$ to $C_{D_MIN}$ and $Φ_{D}$ increases from $Φ_{1}$ to $Φ_{6}$
5 → 6 for $C_{out} \to \infty$	DEG further relaxed so that $Φ_{D} = Φ_{SS} = Φ_{out} = Φ_{1}$ , charge flows from DEG to output capacitor until DEG attains $C_{D_MIN}$ .	$Φ_{D} = Φ_{SS} = Φ_{out} = Φ_{1}$ , $Q_{D} = C_{D} Φ_{D}$ $C_{D}$ decreases from $C_{D 5}$ to $C_{D_MIN}$

DEG: dielectric elastomer generator; SPC: self-priming circuit.

$Φ_{3} = \frac{C + C_{D_MIN}}{\frac{n + 1}{n} C + C_{D_MAX}} Φ_{1}$ , $Φ_{6} = (\frac{C_{out} + C + C_{D_MAX}}{C_{out} + \frac{n}{n + 1} C + C_{D_MIN}}) Φ_{3}$ , and $C_{D 5} = \frac{n (n + 1) (C C_{D_MIN} + C_{D_MAX} C_{D_MIN}) + nC C_{D_MAX}}{(n + 1) ((n + 1) C + n C_{D_MAX})}$ .

Subscripts indicating processes are omitted for simplification.

2.2. Graphical illustrations for state processes of SP-DEG

To illustrate operation states and processes of the DEAmPx, we consider an arbitrary example, with operating parameters as follows: $C_{D_MAX} / C_{D_MIN} = 6$ , $C / C_{D_MIN} = 4$ , $C_{out} / C_{D_MIN} = 2$ , and $n = 1$ . We assume a linear capacitance change of the DEG with respect to time, in order to simply our illustration. We write the variation of DEG capacitance with time over one period of operation as follows

C_{D} (t) = {\begin{matrix} C_{D_MIN} + \frac{2 t}{T} (C_{D_MAX} - C_{D_MIN}) for 0 \leq t < T / 2 \\ 2 C_{D_MAX} - C_{D_{MIN}} - \frac{2 t}{T} (C_{D_MAX} - C_{D_MIN}) for T / 2 \leq t < T \end{matrix}

(14)

where t is the time and T is the time period for one stretch cycle of DEG.

Figure 6 shows the capacitance change for the DEG (Figure 6(a)) and the corresponding voltage on the DEG, SPC, and the output capacitor (Figure 6(b)) over one period of an SP-DEG cycle. Figure 7 shows the states of the DEG and the SPC plotted on a non-dimensionalized voltage–charge plane. We plot the processes of our example described above, against references of extreme output capacitances of $C_{out} / C_{D_MIN} = 0$ and $C_{out} \to \infty$ . The voltage boost per cycle $(G)$ , written by equation (11) is graphically represented in Figure 7, by the ratio of voltages at states 6 and 1. One may observe from the plots that as the capacitance of the output capacitor increases, the voltage boost per cycle decreases. From equations (11) and (13b), however, one may calculate that the energy transferred per cycle to the output capacitor increases with its capacitance.

Figure 6.

(a) Capacitance change for the DEG versus time and (b) corresponding voltage on DEG (red line), SPC series configuration (green line), SPC parallel configuration (blue line), and output capacitor (magenta line). States of the system are separated by black dashed lines. C_D_{_MAX}/C_D_{_MIN} = 6, C/C_D_{_MIN} = 4, C_out/C_D_{_MIN} = 2.

Figure 7.

SP-DEG cycle (C_D_{_MAX}/C_D_{_MIN} = 6, C/C_D_{_MIN} = 4, and n = 1) in the voltage charge plane for different cases of output capacitor: (a) C_out = 0, (b) C_out/C_D_{_MIN} = 2, and (c) C_out → ∞. The area below the line 2 → 3 represents the non-dimensionalized energy transferred from SPC to DEG, the area below 4 → 5 is the energy transferred from the DEG to SPC, and the area below 5 → 6 represents the energy from the DEG to SPC and the output capacitor. For the case with no output capacitor, energy is transferred from DEG to SPC alone, and when C_out → ∞, all the energy represented by the area under 5 → 6 are transferred to the output capacitor. From geometry, this is equivalent to the area enclosed by the pentagonal cycle (1-2-3-4-5-1). The coordinates of state 6 are mathematically represented by equation (10). Energy transferred to the output capacitor (Ω_out) for each case is shown on the plots.

2.3. Optimal voltage boost

From equation (10), it is easy to see that ${G |}_{C = 0} = 1$ and ${G |}_{C \to \infty} = 1$ . Hence, there exist an optimal value for the SPC capacitance, C, that maximizes the DEG voltage boost. For a given SPC of order n, we differentiate equation (10) with respect to C and set it to zero $(\partial G / \partial C = 0)$ to obtain the value of C that maximizes $G$

C_{opt} = C_{D_MIN} \sqrt{β (1 + γ)}

(15)

where $β$ is the DEG capacitance ratio $(β = C_{D_MAX} / C_{D_MIN})$ and $γ$ is the ratio of output capacitance to the minimum capacitance of the DEG $(γ = C_{out} / C_{D_MIN})$ . A special case of equation (15) where $γ = 0$ (without an output capacitor) recovers identical equations as those in existing works (Illenberger et al., 2017; Zanini et al., 2016).

The minimum SPC order is determined by the inequality given in equation (3). When $n \to \infty$ , we have $C_{SS} \to C_{SP}$ , implying that the SPC simply acts like a capacitor with a fixed capacitance connected in parallel with the DEG. Hence, there exists an optimal SPC order that maximizes the voltage boost. As the order of the SPC is an integer, its optimal value $(n_{opt})$ is found by solving $G (n_{opt} - 1) \leq G (n_{opt}) \geq G (n_{opt} + 1)$ as suggested by Illenberger et al. (2017).

Using equations (10), (15), and the optimal SPC order, the optimal voltage boost per cycle $(G)$ versus DEG capacitance ratio is plotted in Figure 8. The plot shows that the voltage boost per cycle increases with $β$ . Equation (11) suggests that the energy output per cycle scales with $G^{2}$ . Hence, it is very advantageous for the DEG to have a large capacitance ratio during the deformation. DEG capacitance ratios of up to 625 can be achieved for a DE deformed in equal biaxial mode (Mathew et al., 2019). For a small-scale DEG, it is challenging to have an equal biaxial mode of deformation. In our previous work, a ripple mode of deformation as shown in Figure 3 was introduced to have a large $β$ (up to 60) in a constrained space (Mathew et al., 2019). Hence, we adopted the ripple mode to have a large voltage and energy boost per cycle.

Figure 8.

Optimal voltage boost per cycle versus DEG capacitance ratio (β) for different output capacitance ratios (γ). β = C_D_{_MAX}/C_D_{_MIN} and γ = C_out/C_D_{_MIN}.

3. DEAmPx prototype

A prototype as shown in Figure 9 is designed to follow the operation of DEAmPx described in section “State and process modeling of DEAmPx.” On the downward stroke, the top ripple structure deforms the DE film attached to the bottom ripple structure. The restoring elasticity of the DEG pushes the top ripple structure back upward. Ambient compressive motion and the restoring elasticity of the DE hence facilitate the cyclical deformation of the DEG between its maximum and minimum capacitances in the ripple mode, facilitating the continuous transfer of charges across all components in the DEAmPx. The PZT diaphragm is placed at the bottom of the ripple structure so that a compression load on the prototype will deform the piezoelectric only when the DEG attains its maximum capacitance, $C_{D_MAX}$ . The deformation of the piezoelectric supplies the priming voltage, $Φ_{P_in}$ . The diodes in the rectifier circuit (Figure 4) ensure that the piezoelectric element is active only when the voltage of the SP-DEG drops lower than the open-circuit voltage of the piezoelectric. Once the SPC and the DE film are primed by the piezoelectric, the SP-DEG cycle kicks in, resulting in voltage and energy amplification on every cycle. We reserved a space termed the SPC block in Figure 9(a), to organize the components of the bridge rectifier and SPC according to the electric circuit shown in Figure 4. A photograph of the three-dimensional (3D)-printed prototype of diameter 10 cm and a maximum deformed height of 2 cm is shown in Figure 9(b).

Figure 9.

(a) Schematic of the DEAmPx prototype. (b) Photograph of the fully assembled prototype attached to a linear actuator. Photograph of the PZT diaphragm is shown at the top right.

The DE film is made by pre-stretching an acrylic-based elastomer, VHB 4905, equal-biaxially by about 1.8 times and securing the pre-stretch using a 3D-printed frame. Carbon grease is used as the compliant electrode. The capacitance of the DEG prior to deformation $(C_{D_MIN})$ and at maximum deformation $(C_{D_MAX})$ of the prototype is measured to be 1.26 and 9.22 nF, respectively, giving a capacitance ratio $β = 7.31$ . In the next section, we demonstrate the energy harvesting capability of DEAmPx connected to a constant high-voltage $(Φ_{out} >> Φ_{P_in})$ output reservoir. This particular energy harvesting process has two phases where in the first phase, the voltage of the DEG is boosted from the input priming voltage to the output voltage, and in the second phase, the excess charge on the DEG is transferred to the output voltage reservoir (Ikegame et al., 2017; Mathew and Koh, 2018). The voltage-boost phase is equivalent to the special case of the output capacitor where $C_{out} = 0$ , and the energy harvesting phase is equivalent to the special case of the output capacitor where $C_{out} \to \infty$ . For maximum voltage boost in the first phase, a first-order SPC with an SPC capacitance $(C)$ of 3.3 nF was used. The value of $C$ is close to the optimal value given by equation (15) for the special case of $C_{out} = 0$ : $C = 1.26 \sqrt{7.31} = 3.41 nF$ . High-voltage diodes (model: GP02-40) are used for the SPC circuit. A commonly available buzzer-type PZT diaphragm is used as the piezoelectric element. It has an active diameter of 20 mm and a thickness of 0.25 mm.

4. Energy-harvesting performance

We use the circuit as shown in Figure 10 to characterize energy output of the DEAmPx. A voltage divider (R₁ and R₂) was used to measure the voltage of the DEG $(Φ_{D} = Φ_{R 2} (R_{1} + R_{2}) / R_{2})$ . Zener diodes (20 × 100 V) were used to release the boosted charges at a prescribed voltage of $Φ_{out} = 2000 V$ , simulating a constant output voltage reservoir (Mathew and Koh, 2018; Shea et al., 2016). When the DEG attains $Φ_{out}$ after the SPC boosting process, the excess current $(i_{out})$ flows through the electrical load R₃ $(i_{out} = Φ_{R 3} / R_{3})$ . The prototype is deformed using a linear actuator (YAMAHA T9H10-250) as shown in Figure 9(b) to realize a low-frequency motion (∼1 Hz, the stroke length of 2 cm) reminiscent to that of a human heel strike. The data are captured using a Data Acquisition (DAQ) (NI USB-6356).

Figure 10.

Characterization circuit for DEAmPx. The values of the resistors used are indicated in the figure.

Our experimental results are shown in Figure 11. At the start of the first cycle, when the DEG is fully stretched, the piezoelectric is deformed to prime the DEG and the SPC in series configuration with an input voltage $(Φ_{P_in})$ of 53 V. By the end of the first cycle, the voltage of the system is boosted to $Φ_{i} = 209 V$ . The SP-DEG cycle commences at this point. The voltage-boost phase of the prototype took 18 cycles to attain a voltage of 1950 V (Figure 11(a)). The output voltage is measured to be slightly lower than 2000 V due to leaked charges in the Zener diodes. The energy harvesting phase starts when the voltage reaches 1950 V. The output current is shown in Figure 11(b).

Figure 11.

(a) DEG voltage versus time. (b) Output current versus time.

The mean experimental voltage boost per cycle can be calculated by $G_{\exp} = (Φ_{out} / Φ_{i})^{1 / k}$ , where $Φ_{i}$ is the voltage of the DEG at the start of the SP-DEG cycle (indicated in Figure 11(a), $Φ_{i} = 209 V$ ) and k is the number of cycles it took for the SP-DEG to boost the voltage from $Φ_{i}$ to $Φ_{out}$ . Substituting the values of $Φ_{i}$ , $Φ_{out}$ , and k, we obtain $G_{\exp} = 1.13$ . The theoretical value of voltage boost per cycle calculated using equation (12) is 1.23. The theoretical value hence provided an 8% over-estimate to the experimental voltage boost per cycle. We attribute it to losses from the mechanical system, the circuit, and the DEG. The sliding contact between the interlocking ripple structures and the DE film may cause disconnection of the carbon grease on the surface of DE film leading to a lower maximum capacitance $(C_{D_MAX})$ . The viscoelasticity of VHB (Chiang Foo et al., 2012a, 2012b; Li et al., 2012; Zhao et al., 2011) and actuator-like behavior (Zanini et al., 2015) of the DEG at high voltages causes the capacitance ratio of the DEG to decrease $(β < 7.31)$ during the operation. Charge leakage of the DE film also increases with the operating voltage (Chiang Foo et al., 2012b; Gisby et al., 2010; Kaltseis et al., 2011). These factors combine to give a lower experimental value of the voltage boost than that predicted from theory. The energy output per cycle is calculated by integrating the voltage, $Φ_{D}$ , with respect to the charge transferred to the output reservoir over one cycle. The charge transferred is found by a time integral of the output current (Figure 11(b)). Taking the average of five cycles, the output energy $(Ω_{out})$ is calculated as 2.3 mJ. The theoretical value of output energy calculated using equation (13b) is 2.66 mJ/g. Using the density of VHB 4905 (960 kg/m³) from datasheet, the mass of the active part of the DE film (m_D) is calculated as 0.74 g. Hence, the intrinsic (material only) specific energy output of the DEG (experimental output energy/mass of DE) is 3.1 mJ/g. The mass of the piezoelectric diaphragm (m_P) used in the prototype is measured to be 2.7 g. The mass of the SPC circuit components (m_S) is measured to be 1.2 g. Hence, the system-specific energy output of the DEAmPx $(Ω_{out} / (m_{D} + m_{P} + m_{S}))$ is 0.49 mJ/g.

In our previous work, we found that the piezoelectric generator working in isolation produces an intrinsic specific energy output of 0.16 mJ/g per cycle under the same loading conditions (Mathew et al., 2019). Our DEAmPx hence demonstrates a net intrinsic specific energy gain of 19 times over that of the piezoelectric working alone (3.1 mJ/g ÷ 0.16 mJ/g), with a system-specific gain of the DEAmPx at three times (0.49 mJ/g ÷ 0.16 mJ/g). The rather small number is a consequence of a very large proportion of mass is taken up by passive piezo and SPC (84%). One may attempt to theoretically scale-up the prototype by inserting more layers of DEGs to allow the system-specific output performance to approach the intrinsic output performance. Assume that the same piezoelectric primes have N number of DE layers. N layers of the DE film electrically connected in parallel will have a capacitance of $N C_{D}$ . Hence, the SPC capacitance $C$ must also be scaled accordingly. However, commercial capacitors (capacitors used for SPC) of similar masses can have capacitance in the range of nF to μF. Hence, the net weight of the DEAmPx system with multilayered DEG becomes Nm_D + m_P + m_S. N layers of the DE film operating in a similar experimental condition will generate N times the output energy of a single layer. Hence, the system-specific energy of a DE-multilayered DEAmPx is given by $N Ω_{out} / (N m_{D} + m_{P} + m_{S})$ . For a large value of N, this will converge to the intrinsic specific energy of 3.1 mJ/g as shown in Figure 12.

Figure 12.

DEAmPx specific energy versus number of layers of DE.

In our previous work, we estimated the mechanical input of DEAmP prototype, which excludes the SPC component, as 860 mJ (Mathew et al., 2019). Taking the ratio of the net electrical energy output (2.3 mJ) of the DEAmPx prototype to the net mechanical energy input of DEAmP prototype, we estimate an approximate value of the efficiency of the DEAmPx prototype as 0.26%. The low value of the conversion efficiency is mainly attributed to the viscoelastic loss of VHB (Mathew et al., 2019). Substituting VHB with an elastomer of lower viscoelastic loss may significantly increase the prototype efficiency. In our experiments, we applied a low-frequency (1 Hz) motion to match with that of a human heel strike. Operating the prototype at very low frequencies may lead to charge loss that may hinder the voltage boost and reduce the output energy. At high frequencies, a highly viscoelastic material may not get sufficient time to retract back to the undeformed state $(C_{D_MIN})$ . This reduces the effective value of DEG capacitance ratio $(β)$ and hence reduces the voltage boost and the energy output. Hence, depending on the dissipative performance of the elastomer used, there exist an optimal operating frequency that maximizes the net energy output and efficiency of the prototype. As a dynamic analysis including the dissipative process of the DEG is required to estimate this value, we shall leave it to a separate study.

5. Single-layer DE generator powering DE actuator systems

DEAmPx produces outputs with high voltage (in the order of kV) and low current (in the order of µA). Hence, the generator must ideally find applications that match its output. A most direct application would be to use it to power a DEA. A DEA requires voltage in the order of kilovolts to achieve observable voltage-induced deformation (Huang et al., 2012; Lu et al., 2012; Pelrine et al., 2000). Subject to an electric field, the DEA experiences electrostatic force of attraction (Maxwell stress) that thins down the membrane and expands its area (Pelrine, 2000; Pelrine et al., 2000). The high electric field is supplied using an external high-voltage source, which is in general, bulky, and expensive. Anderson et al. (2012) proposed the coupling of the DEG and the DEA due to the similarity of their physical processes in terms of energy transduction. However, they have yet to demonstrate a working system of their proposal. Here, we demonstrate the actuation of DEAs using the DEAmPx prototype, making it free from an external high-voltage source. Two configurations of the DEA are chosen for the demonstration: a circular DEA (Koh et al., 2011b) and a DE minimum energy structure (DEMES) (Kofod et al., 2006) in the form of a flapping wing.

A circular DEA consists of an electrode active area at the center of a pre-stretched elastomer membrane, secured by a rigid ring (Figure 13(b)) (Koh et al., 2011b). To obtain a visible actuation strain for the DEA within the voltage range of the DEAmPx prototype (0 to ∼2000 V), we applied an equal-biaxial pre-stretch of four times on VHB 4905 and secured using a 3D-printed frame. The diameter of the active area and inactive area was 1.5 and 8 cm, respectively. Carbon grease is used as the electrode material. The electrical connection is identical to that is shown in Figure 4, where the output capacitor is the DEA. However, since the DEA deforms with voltage, the output capacitance is now a function of voltage $C_{out} (Φ)$ .

Figure 13.

(a) Voltage across the circular DEA powered by DEAmPx. (b) Uncharged DEA at 0% area strain. (c) DEA at 1800 V, 34.55% area strain. (d) DEA at 2250 V, 49.48% area strain.

Figure 13(a) plots the voltage across the circular DEA powered by the DEAmPx prototype. At the beginning of the operation, the voltage across the DEA is zero. It takes 25 cycles for the voltage to reach a maximum value of ∼2250 V. Our loss-free voltage plot, Figure 6(b), suggests that the voltage across the DEA $(C_{out})$ remains constant during states 1–5 and increases during the process 5 → 6 in an SP-DEG cycle. However, the experimental data show that the voltage on the DEA first drops due to its parasitic resistance and then increases (Figure 13(a)). The voltage of the DEA peaks at around 2250 V due to the charge leakage and the actuator behavior of the DEG (Zanini et al., 2015). After the peak voltage is reached, the voltage of DEA fluctuates between $Φ ~ 1800 V$ and $Φ ~ 2250 V$ in every cycle. Figure 13(b) to (d) shows the images of the DEA at three different voltages as indicated in Figure 13(a).

We demonstrated the actuation of a circular DEA using DEAmPx and achieved areal strains up to 50%. We now demonstrate another type of DEA with a bending characteristic, DEMES. We prepare DEMES as follows: VHB 4905 is pre-stretched equal-biaxially by four times and adhered to a triangular shaped thin plastic frame (∼150 μm) as shown in Figure 14. The excess elastomer is cut off to achieve a final shape where it becomes a self-organized minimum energy structure (Figure 14) (Kofod et al., 2006). When a voltage is applied, the introduction of Maxwell stress reduces the mechanical stress within the DEA which allows the DEMES to change its shape in response to the voltage. The diode that is used in series with the circular DEA for the previous demonstration (Figure 4) was removed to allow a larger voltage swing for the DEMES (Figure 15(a)). The high-voltage swings on the DEA result in a wider motion sweep which is suitable for a flapping mechanism. In the absence of the diode, the DEA is connected in parallel with the DEG. Hence, the new minimum capacitance of the DEG becomes $C_{D_MIN} + C_{DEMES}$ and the new maximum capacitance of the DEG becomes $C_{D_MAX} + C_{DEMES}$ , where $C_{DEMES}$ is the capacitance of the DEMES. Note that as the DEMES is constrained to expand, its capacitance does not change with the applied voltage. The value of $C_{DEMES}$ used in our experiments is measured to be about 0.4 nF. With the new DEG capacitance, we ensured that the minimum DEG capacitance ratio condition given in equation (3) to be true. Figure 15(b) shows the actuation of the DEMES between two levels of voltage $Φ_{H} = 1950 V$ and $Φ_{L} = 600 V$ . $Φ_{H}$ is limited using Zener diodes. The continuous deformation of the DEMES resembles the flapping motion in nature, which we demonstrate using an origami bird in Figure 15(c).

Figure 14.

Schematics of the preparation method and photograph of the final shape of the DE minimum energy structure (DEMES). The dimensions of the DEMES are taken arbitrarily.

Figure 15.

Demonstration of DEMES powered using DEAmPx. (a) Voltage versus time for the DEMES showing a large voltage swing between Φ_H and Φ_L. (b) Close-up view of a flapping mechanism using DEMES. (c) Flapping mechanism attached to an origami bird.

6. Conclusion

A piezoelectric element is used as the initial charge source for the self-primed DE to create a truly autonomous self-amplifying dielectric-elastomer-amplified piezoelectric (DEAmPx) generator. Ignoring the dissipative processes, a simplified analysis of the system attached to an output capacitor was performed to predict the states of the components (DEG, SPC, and output capacitor) during the mechanical deformation of DEAmPx. From analysis, we found that the voltage boost per cycle of the SP-DEG increases with the DE capacitance ratio $(β)$ . To achieve a large $β$ in a constrained space, the ripple mode of deformation was used. Integrating all the components (a commonly available PZT diaphragm, pre-stretched DE film, the mechanism to deform the DE in ripple mode and SPC), a compact DEAmPx prototype is designed to harvest energy from a low-frequency compressive mechanical source like a human heel strike. The prototype demonstrated a high-voltage boost per cycle of 1.13 times (0–2000 V in 18 cycles) and a DEG-specific energy output of 3.1 mJ/g per cycle, which is 19 times higher than that of a piezoelectric operating under similar mechanical loading. High-voltage application of the prototype is demonstrated by powering two different configurations of DEA: a circular DEA and a DEMES. It is hoped that the theory, prototype, and demonstration of DEAmPx will inspire more applications in the field of autonomous energy harvesting using DEs.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported through funding from the first grant call under the Joint Science and Technology Research Cooperation between the Department of Science & Technology (DST), Govt. of India and the Agency for Science, Technology and Research (A*STAR), and from the NUS MOE strategic grant for Composites Engineering and Research. S.J.A.K. wishes to acknowledge the A*STAR-DST grant no. R-265-000-524-305 (SERC 142 520 3140) for funding this research. Anup Teejo Mathew and Vo Tran Vy Khanh wish to acknowledge the NUS Research Scholarship for their PhD study in NUS from August 2015 to August 2019. Financial support for Liu Chong from NUS MOE strategic grant R-265-000-523-646 is gratefully acknowledged.

ORCID iD

Anup Teejo Mathew

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