IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
vol. 60, no. 9,
September
2013
2013
Piezoelectric Polymer Multilayer on Flexible Substrate for Energy Harvesting Lei Zhang, Sharon Roslyn Oh, Ting Chong Wong, Chin Yaw Tan, Member, IEEE, and Kui Yao, Senior Member, IEEE Abstract—A piezoelectric polymer multilayer structure formed on a flexible substrate is investigated for mechanical energy harvesting under bending mode. Analytical and numerical models are developed to clarify the effect of material parameters critical to the energy harvesting performance of the bending multilayer structure. It is shown that the maximum power is proportional to the square of the piezoelectric stress coefficient and the inverse of dielectric permittivity of the piezoelectric polymer. It is further found that a piezoelectric multilayer with thinner electrodes can generate more electric energy in bending mode. The effect of improved impedance matching in the multilayer polymer on energy output is remarkable. Comparisons between piezoelectric ceramic multilayers and polymer multilayers on flexible substrate are discussed. The fabrication of a P(VDF-TrFE) multilayer structure with a thin Al electrode layer is experimentally demonstrated by a scalable dip-coating process on a flexible aluminum substrate. The results indicate that it is feasible to produce a piezoelectric polymer multilayer structure on flexible substrate for harvesting mechanical energy applicable for many low-power electronics.
I. Introduction
W
ith the decreasing power consumption in electronics, it is becoming more realistic to power electric circuits by harvesting ambient energy. By employing proper energy transducers, ambient energy such as solar energy, thermal energy, mechanical energy, and electromagnetic energy, can be converted to electric energy for practical use. Piezoelectric materials, which are capable of converting mechanical energy into electric energy, are suitable for mechanical energy harvesting. Various piezoelectric energy harvesters have been developed and reported in the literature [1]–[5]. One of the disadvantages of energy harvesting with piezoelectric materials is their high voltage output in conjunction with low current output. Typical piezoelectric energy harvesters can often produce voltage of up to several tens to hundreds of volts with current in the order of microamperes. To utilize the energy harvested by piezoelectric materials, the electric circuit usually needs transformers to reduce the output voltage, which increases the cost and dimensions of devices. In addition, the very high impedances of piezoelectric materials are usually not comparable with the load resistance. The impedance mismatch between the piezoelectric energy
Manuscript received April 10, 2013; accepted June 9, 2013. The authors acknowledge support through project IMRE/10-1C0109. The authors are with the Sensors and Transducers Program, Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology, and Research), Singapore ([email protected]). DOI http://dx.doi.org/10.1109/TUFFC.2013.2786 0885–3010/$25.00
harvester and the electric load leads to low efficiency of energy utilization. Multilayer piezoelectric materials structures are able to solve these problems. By using a piezoelectric multilayer structure, the output voltage and material impedance can be significantly reduced while the output current can be increased. Kim et al. [6] reported a lead zirconate titanate (PZT) multilayered cymbal transducer for energy harvesting. The piezoelectric energy harvester was used in the d31 extension mode, where stresses were applied to stretch the multilayer ceramics. The electrical impedance matching for the energy harvesting circuit was considered to allow the transfer of generated energy to a storage media. It was found that by using 10-layer ceramics instead of a single layer, the output current can be increased by 10 times. Song et al. [7] presented a design of energy harvester using piezoelectric ceramic multilayer bonded on a flexible substrate operating in bending mode. It was found that the piezoelectric multilayer energy harvester could be used directly for powering electrical devices without additional electric circuits. For piezoelectric multilayer-based energy harvesters, typical operation modes are extension mode, shear mode, or bending mode. A piezoelectric bending-mode energy harvester requires less mechanical input but can generate a large amount of electric charge through continuous vibration. Both piezoelectric ceramics and piezoelectric polymers can be used in bending-mode energy harvesters. Piezoelectric ceramics generally have large piezoelectric coefficients, but the brittleness of ceramics makes it difficult for them to sustain high mechanical strains. Piezoelectric polymers, on the other hand, have lower piezoelectric coefficients but are able to undergo larger mechanical strains, have much higher shock resistance, and can be produced at a much lower processing temperature. Poly(vinylidene fluoride) (PVDF) and copolymers of vinylidene fluoride and trifluoroethylene P(VDF-TrFE) are two typical piezoelectric polymers. PVDF is a low-cost piezoelectric polymer which has been used for energy harvesting. Granstrom et al. [3] demonstrated an energy harvesting system using PVDF-based shoulder straps on backpack. Sun et al. [4] proposed a respiration energy harvester by using PVDF micro-belts. Vatansever et al. [5] investigated the energy harvesting performance of a PVDF cantilever structure for rain drop and wind energy harvesting. To well utilize piezoelectric polymer multilayer structures for energy harvesting, the piezoelectric layer must be reasonably thin so that the impedance of the piezoelectric polymer multilayer can be effectively reduced. The thin-
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IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
ner the piezoelectric layer is, the lower is the electric impedance of the multilayer. However, thinner piezoelectric layers also mean that more layers are needed to achieve a certain energy level. In addition, because the stiffness of piezoelectric polymer multilayer is much smaller than metal electrode material, the effect of electrode stiffness must be considered in the design of piezoelectric multilayers for bending-mode energy harvesters. Although there are a few publications on piezoelectric multilayer structures for mechanical energy harvesting [6], [7], the material parameters that are critical to piezoelectric multilayer energy harvesting performance have not been systematically investigated. To clarify the effect of material parameters on the energy output, an analytical model must be developed for piezoelectric multilayer energy harvesters. In this paper, we propose a piezoelectric polymer multilayer structure on a flexible substrate for energy harvesting. To better understand the effects of material parameters on the energy harvesting performance, analytical and numerical models of the bending-mode piezoelectric polymer multilayer energy harvester are developed. Material parameters which are critical to the energy output are discussed. The remarkable effect of impedance matching between the piezoelectric polymer multilayer structure and the electric load is exhibited by comparison with a single-layer piezoelectric polymer of the same dimensions. A 10-layer P(VDF-TrFE)-based multilayer on a flexible Al substrate is demonstrated by using the dip-coating method, and the energy harvesting performance is evaluated. II. Analytical Model Fig. 1 illustrates an n-layer piezoelectric polymer [such as P(VDF-TrFE)] multilayer structure bonded on a metal (such as Al) substrate beam. The beam is in a cantilever configuration. The length of the beam is L, the width is b, and the thickness of the substrate is h. The length of the piezoelectric multilayer is Lp. The thickness of each piezoelectric layer is tp and the thickness of the electrode layer is te. The piezoelectric layers are alternatively polarized in the thickness direction and the alternate electrodes are connected. A vertical force of F is applied at the tip of the beam. The force F is removed after the beam achieves its maximum displacement. The beam will subsequently vibrate in the transverse direction, resulting in charge generation in the piezoelectric multilayer. To clarify the effects of material parameters on the energy harvesting capacity of the piezoelectric polymer multilayer, analytical formulations are developed and discussed. The constitutive equations of piezoelectric materials are
D 3 = ε 33E 3 + d 31T1 (1)
S 1 = d 31E 3 + s 11T1, (2)
where D3 is the electric displacement in the polarization direction, S1 is the strain in the axial direction, ε33 is the
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dielectric permittivity of piezoelectric material in the polarization direction at constant stress condition, E3 is the electric field in the polarization direction, T1 is the stress in the axial direction of the cantilever structure, d31 is the piezoelectric coefficient, and s11 is the compliance of piezoelectric material under constant electric field condition. For the ith piezoelectric layer, the electric displacement can be obtained from (1) and (2): D 3,i = d 31S 1,i /s 11 + ε 33E 3, (3)
2 2 2 where ε 33 = ε33(1 − k 31 ) and k 31 = d 31 /(ε 33s 11). Therefore, the charge generated in the ith piezoelectric layer can be calculated as
Qi =
∫ D 3,i dA = ∫ (d 31S 1,i/s 11 + ε 33E 3)dA, (4)
AP
where AP denotes the area in piezoelectric layers. The total charge generated in all n layers of piezoelectric materials can be expressed as n
Q =
∑
n
Qi =
i =1
∑ ∫ (d 31S 1,i/s 11 + ε 33E 3)dA. (5) i =1 AP
The axial strain in the ith piezoelectric layer can be determined by
S 1,i = µ 0 + κ 0(z i − z 0), (6)
where μ0 and κ0 are the axial strain and curvature of the beam at z0, respectively, for pure bending without external axial stresses, μ0 = 0; z0 is the location of natural axis with respect to global coordinates and zi is the location of the ith layer. The detailed calculation of neutral axis location can be found in Appendix A.
Fig. 1. Illustration configuration.
of
piezoelectric
multilayer
in
cantilever
zhang et al.: piezoelectric polymer multilayer on flexible substrate for energy harvesting
The curvature of the beam κ0 is defined by
κ0 =
w ′′ ≈ −w ′′, (7) [1 + w ′ 2]2/3
where w′ and w′′ are the first and second derivatives of w, which is the transverse displacement of the cantilever with respective to the length of the beam x. To determine the total charge generated in the piezoelectric multilayer during the vibration, the transverse displacement of the cantilever must be determined. The transverse displacement of the cantilever beam in vibration is governed by the equation of motion:
∂ 2w(x, t) ∂w(x, y) ∂ 4w(x, t) +λ +γ = 0, (8) 4 ∂t ∂x ∂t 2
where λ = ρA/YI is a coefficient related to the ratio of mass per unit length to the stiffness of the multilayer cantilever, ρ is the density of the multilayer beam, A is the cross-sectional area, Y is the Young’s modulus, I is the second moment of inertia, and γ is a damping coefficient. The boundary conditions for the cantilever configuration are
w(x, t) x = 0 = 0,
∂w(0, t) ∂ 2w(L, t) = 0, = 0. (9) ∂t ∂x 2
Prior to the start of the vibration, the cantilever beam has an initial displacement resulting from the external force F applied at the tip. According to the calculation in Appendix B, the initial condition is
w(x, 0) = ∆ L f (x ), (10) −((FL3)/(3YI))
((3x2)/(2L2)
where ΔL = and f (x) = − x3/(2L3)). The solution to (8) can be obtained by the method of separation of variables: ∞
w(x, t) =
∑ BmX m(x)Tm(t), (11)
m =1
where Bm is a constant, Xm(x) is a mode shape function, and Tm(t) is a time-dependent function. For the cantilever configuration, the mode shape function Xm(x) in (11) is
2015
The first five roots to (13) are kmL = 1.8751, 4.6941, 7.8548, 10.9955, and 14.1372. The wave number km is related to the natural frequency ωm by k m4 = λωm2 . The time-dependent function Tm can be determined by d Tm(t) = φ0 sin(ωm t + θm )e −ωmς mt, (14)
d where ϕ0 is a constant, ςm = γ/λ is a damping factor, ωm 2 = ωm 1 − ς m , and θm = tan( 1 − ς m /ς m ). With (12) and (14), (11) can be rewritten as ∞
w(x, t) =
∑ C mX m(x)φ0e −ω ς t sin(ωmdt + θm), (15) m m
m =1
where the term Cm = ϕ0Bm can be determined according to the initial condition in (10) as L
Cm =
∫0
∆ L f (x )X m(x )dx L
∫0
X m2 (x )dx
. (16)
The term Cm in (16) can be expressed in a simple form with initial tip displacement or the force applied at the tip as variables, C m = αm∆ L = −αm
L
FL3 , (17) 3YI
L
where αm = ∫ f (x )X m(x )dx /∫ X m2 (x )dx. 0 0 Thus, the solution of transverse displacement to (8) can be expressed as ∞
w(x, t) =
FL3
∑ −αm 3YI X m(x)ϕ 0e −ω ς t sin(ωmdt + θm). m m
m =1
(18) With the solution of transverse displacement w(x, t) in (18), the strains in the piezoelectric multilayer and the total charges can be calculated. According to (5)–(7) and (18), the total charge generated by the piezoelectric multilayer can be expressed as n n −w ′′(x, t)d ( z − z ) / s + ε E 31 i 0 11 33 3 dA i =1 i =1 AP (19)
Q =
∫
∑
∑
and the corresponding current Ic is X m(x ) = [cos(k mx ) − cosh(k mx )] dQ V cos(k mL) + cosh(k mL) Ic = − = , (20) − [sin(k mx ) − sinh(k mx )], R dt sin(k mL) + sinh(k mL) (12) where R is the external load resistance and V is the voltage across the external load resistance. where km is a wave number, which can be determined by Thus, the power of the load resistance R can be calcu cos(k mL) cosh(k mL) + 1 = 0. (13) lated using
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IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
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ceramic multilayers, whereas piezoelectric polymer multilayers can sustain large amplitude vibrations which are more suitable for bending-mode mechanical energy harvesting. n The term ∑i =1 (z i − z0) in (24) denotes the effect of the where ω is the frequency of electric output which is equivalent to the fundamental frequency of the cantilever beam, neutral axis on the maximum power output of the piezoi.e., ω = ω1d, and the term Λ(Lp, t) is electric multilayer on a flexible substrate. It is evident that if the position of the neutral axis z0 is fixed, more ∞ piezoelectric layers will lead to higher power output. On ∂X m(L p) d −αm φ0e −ωmς mt sin(ωm t + θm ), Λ(L p, t) = n ∂x the other hand, to obtain a higher value of ∑i =1 (z i − z0) m =1 (22) with fixed layer number n, the neutral axis should be as far as possible from the piezoelectric layers. To achieve From (21), the optimal load resistance Ropt and maximum that, the stiffness of piezoelectric multilayer, including the output power Pmax can be determined as internal electrode layers, must be substantially lower than that of the substrate beam so that the neutral axis is out 1 of the multilayer region. This will require using a much R opt = (23) 2 ω(1 − k 31 )C p stiffer substrate, such as hard metal, for piezoelectric multilayer ceramics or flexible piezoelectric polymer materials 2 3 n be FL with thin metal electrodes on flexible substrate. For the 31 3YI ∑i =1 (z i − z 0)Λ(L p, t) Pmax = , (24) 2 same substrate and dimensions, a piezoelectric polymer )C p 4ω(1 − k 31 n multilayer will have significantly higher value of ∑i =1 (z i where Cp = nε33ε0((bLp)/tp)) is the capacitance of the − z0) compared with a piezoelectric ceramic multilayer, piezoelectric multilayer and ε0 is the free space permit- meaning significantly higher power output. For a piezoelectric polymer multilayer, thinner electrodes will reduce tivity. the stiffness of the multilayer, which will keep the neutral axis farther from the multilayer. In addition, the thinner electrodes also mean lower stiffness of the multilayer. UnIII. Material Parameters Critical der constant force condition, the piezoelectric multilayer to Energy Harvesting with thinner electrodes will have larger bending displaceEq. (24) describes the maximum power output of a ment, which is desired for enhanced energy output. Thus, piezoelectric multilayer on flexible substrate for bending- then dual effects of thinner electrodes, i.e., increase of mode energy harvesting. It includes not only the mechani- ∑i =1 (z i − z0) and FL3/3YI, will result in higher energy cal and piezoelectric parameters, but also the effect of output. The preceding analyses show the opportunities for external force F and the effect of layer numbers. From the formulations in (24), the maximum power of piezoelectric polymer multilayers to offer competitive ena piezoelectric bending-mode energy harvester is propor- ergy harvesting performance compared with piezoelectric 2 2 tional to e 31 /[(1 − k 31 )C p ]. This relation indicates that the ceramic multilayers at constant force condition under higher the piezoelectric stress coefficient and the lower the bending mode. These clarified relationships provide guiddielectric permittivity are, the higher the power output ance for developing improved piezoelectric materials and will be. It is noted that larger electromechanical coupling for designing the right multilayer structure dedicated to 2 factor k 31 can lead to improved power generation. Howev- high-performance mechanical energy harvesting. The nu2 er, it could be neglected if k 31 is well below 1, which may merical simulation of the piezoelectric polymer multilayer in Section IV will validate the major conclusions. be true for many practical piezoelectric polymers. It is also noted that the maximum power output in (24) is proportional to the square of FL3/3YI. FL3/3YI represents the initial tip displacement of the multilayer IV. Numerical Simulation cantilever beam caused by the tip force F. It is obvious that under the same tip force F, piezoelectric ceramic mulNumerical simulation was carried out by using Ansys tilayers will have much smaller FL3/3YI because of their (version 12.0, Ansys Inc., Canonsburg, PA) software. The high bending stiffness YI as compared with piezoelectric piezoelectric layer was modeled by using the SOLID226 polymer multilayers. For example, the Young’s modulus coupled field element and the nonpiezoelectric layers were of a typical PVDF polymer is around 2 to 3 GPa, whereas modeled by using SOLID186. The model for simulation is the typical Young’s modulus of a PZT material is more shown in Fig. 1. The material properties and dimension than 60 GPa. Thus, piezoelectric ceramic multilayers will parameters are tabulated in Table I. have much smaller displacement at the same tip force. In The piezoelectric multilayer is based on P(VDF-TrFE) addition, the brittleness of piezoelectric ceramic materials polymer with a layer thickness of 20 μm and Al internal limits the maximum achievable FL3/3YI for piezoelectric electrode layers. To assess the effect of electrode layer on 2
be FL3 n (z − z )Λ(L , t) 31 3YI ∑i =1 i p 0 , (21) 2 P = I cR = (1/R + n ωε 33bL/t p)2R
∑
zhang et al.: piezoelectric polymer multilayer on flexible substrate for energy harvesting
2017
TABLE I. Material and Dimension Parameters for Simulation. Symbol
Value
Unit
s11 s12 s13 s22 s33 s44 s55 s66 d31 d33 d15 ε11 ε22 ε33 L h b Lp tp
3.32 −1.44 −0.89 3.24 3 94 96.3 14.4 10.7 −33.5 −36.3 7.4 7.95 11.3 50 0.4 30 45 20
10−10 m2/N 10−10 m2/N 10−10 m2/N 10−10 m2/N 10−10 m2/N 10−10 m2/N 10−10 m2/N 10−10 m2/N pC/N pC/N pC/N — — — mm mm mm mm μm
the total energy harvesting performance, the open circuit energy and peak voltage generated by the piezoelectric multilayer with different electrode thicknesses and layer numbers are calculated. Fig. 2 shows the effect of the electrode thickness on the open-circuit voltage and energy for different layer numbers at constant displacement and constant force conditions. It is observed from Fig. 2(a) that under constant tip displacement condition, both the peak voltage and output energy increase with the increase of layer numbers. The effect of electrode thickness becomes significant when the layer number is more than 20. Piezoelectric multilayers with thinner electrodes are capable of generating larger electric energy and peak voltage compared with piezoelectric multilayers with thicker electrodes. These results are in agreement with the discussion of material parameters in the previous section. For the constant force condition illustrated in Fig. 2(b), neither the peak voltage nor output energy monotonically increase with the layer numbers. There are optimal layer numbers for both the peak voltage and output energy. This reflects the tradeoff between the increase of piezoelectric layers and the increase of the bending stiffness. It is noted that in the constant force condition, the effect of electrode thickness is more significant than that under constant displacement condition. For a 26-layer piezoelectric multilayer with ideal near-zero electrode thickness, the output energy is more than 7 times larger than that of a piezoelectric multilayer with 2-µm-thick electrodes. These results show that the thickness of electrode layer is a critical factor to be considered for designing optimal piezoelectric multilayer structures for energy harvesting in bending mode. When the piezoelectric multilayer is connected to an electric load, the energy consumed by the load resistance is strongly dependent on the load resistance. There is an optimal load resistance for the piezoelectric multilayer in term of energy output. Fig. 3 gives the electrical output of
Fig. 2. Effect of electrode thickness and number of layers on the energy and voltage generation in P(VDF-TrFE) piezoelectric multilayer structure with a cantilever bending mode, under the condition of (a) constant displacement of 7 mm at the tip, and (b) constant force of 7 N at the tip. P(VDF-TrFE) thickness = 20 µm and Al substrate thickness = 0.4 mm.
a 20-layer P(VDF-TrFE) multilayer on flexible substrate with load resistance range from 1 to 30 kΩ. It is noted that the optimal load resistance is around 10 kΩ and the corresponding output voltage and energy are 169 μJ and −12.9 V, respectively. Based on the analytical solution of optimal load resistance in (23), the Ropt is calculated to be 9.4 kΩ, which is close to the 10 kΩ from the numerical result. The significant advantage of the P(VDF-TrFE) multilayer over a single layer for energy harvesting is shown in Fig. 4, which takes into account the impedance matching behavior of a piezoelectric multilayer structure compared with single-layer piezoelectric material with the same configuration and total thickness. It is observed that the energy output of the piezoelectric polymer multilayer is 5 to 400 times higher than that of a single-layer piezoelectric polymer for the load resistance range of 25 Ω to 100 kΩ. This result shows the dramatic enhancement in the performance for energy harvesting with a multilayer structure compared with a single-layer piezoelectric polymer.
2018
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
Fig. 3. Peak voltage and output energy of a 20-layer P(VDF-TrFE) multilayer in a cantilever configuration with load resistance ranging from 1 to 30 kΩ under 7 mm tip displacement with a subsequent release. Polymer layer thickness = 20 µm, Al electrode thickness = 0.2 µm, and Al substrate thickness = 0.5 mm.
V. Fabrication and Experimental Test of P(VDE-TrFE) Multilayer To demonstrate the fabrication and energy harvesting of piezoelectric polymer multilayer with thin electrode layers on a flexible cantilever substrate, a dip-coating process was used to fabricate a P(VDF-TrFE) multilayer with Al electrode layers alternately deposited by physical vapor deposition on a flexible substrate. To produce the piezoelectric polymer solution for the multilayer, P(VDF-TrFE) (70/30 mol ratio) was dissolved in methyl ethyl ketone (MEK) (17.5% by weight). 0.5-mmthick Al sheets were used as the flexible substrates. A 10-µm insulating layer was first formed on the Al substrates by dip coating in the P(VDF-TrFE) solution with withdrawal speed of 25 mm/min, followed by heating and annealing at 135°C for 2 h in an oven to increase the crystallinity [8], [9]. 0.2-µm-thick Al electrodes were then deposited through a shadow mask via e-beam evaporation (Edwards Ltd., Crawley, UK). The Al deposition was then followed by the dip coating of the first P(VDF-TrFE) active layer at withdrawal speed of 20 mm/min. After the samples were heated and dried, another dip-coating cycle was carried out under the same conditions, to increase the thickness of the P(VDF-TrFE) layer to approximately 20 µm. The samples were then annealed in an oven at 135°C for 2 h in an oven to increase the crystallinity of the P(VDF-TrFE). The dip-coating process of the polymer and the e-beam evaporation of Al are alternately repeated to build the piezoelectric polymer multilayer structures. Fig. 5 presents a scanning electron micrograph of a cross-section of a P(VDF-TrFE)/Al multilayer as obtained. A 10-layer P(VDF-TrFE) sample was fabricated with the previously described method and cut to a size of 3 × 5 cm. The thickness of the P(VDF-TrFE) layer is around 20 μm and the thickness of Al electrode is about 0.2 μm. This sample was clamped onto a metal block, as shown in
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Fig. 4. Comparisons of energy outputs of 22-layer P(VDF-TrFE) and single-layer P(VDF-TrFE) polymer with load resistance ranging from 25 Ω to 100 kΩ.
Fig. 6, for testing. A 7-mm deflection was applied at the tip of the sample with a subsequent release. The sample is electrically connected to an oscilloscope with which the electric outputs are measured and fed to a computer. Fig. 7 shows the test result of voltage and energy generated by a 10-layer P(VDF-TrFE) multilayer structure in comparison with simulation result. The fabricated 10-layer P(VDF-TrFE) is found to be able to generate 17 μJ at the optimal load resistance of 30 kΩ with single press. However, the output energy is considerably lower than the simulation result, where the output energy at 30 kΩ is expected to be more than 50 μJ. The main reason for the difference could be the many defects in the piezoelectric multilayer, as noted during the multilayer fabrication. In addition, as noted in Fig. 7(a), the damping behaviors of the simulated and experimental results are different. More precise damping models are needed to more accurately quantitatively simulate the energy output from the piezoelectric multilayer energy harvester. Nevertheless, the output of 17 μJ to the load as generated with a single press is adequate for many low-power electronics.
Fig. 5. Scanning electron micrograph of cross-section of P(VDF-TrFE)/ Al multilayer.
zhang et al.: piezoelectric polymer multilayer on flexible substrate for energy harvesting
2019
Fig. 6. Sample of a 10-layer P(VDF-TrFE) multilayer as fabricated for energy harvesting.
It is worth mentioning that the P(VDF-TrFE) material used in the piezoelectric multilayer structure can be replaced with PVDF homopolymer at much lower cost. Low-cost piezoelectric PVDF homopolymer can be produced from solution coating directly on a substrate without the conventional mechanical stretching to induce the polar phase [8], [10]. It is feasible to produce low-cost piezoelectric polymer multilayers for energy harvesting applications. VI. Conclusions A piezoelectric polymer multilayer structure formed on flexible substrate was investigated for mechanical energy harvesting under bending mode. Analytical and numerical models were developed to understand the effect of material parameters on the energy harvesting performance of the multilayer structure. It was shown that the maximum power is proportional to the square of the piezoelectric stress coefficient and the inverse of dielectric permittivity of the piezoelectric polymer. It was further found that a piezoelectric multilayer with thinner electrodes can generate larger electric energy in bending mode, especially under constant force condition. Compared with piezoelectric ceramic multilayers, piezoelectric polymer multilayers on flexible substrate are particularly advantageous under constant force condition. The effect of improved impedance matching in the multilayer on energy output is remarkable. A 5 to 400 times improvement on energy output was shown for a 22-layer P(VDF-TrFE) multilayer structure on flexible substrate compared with that of a single layer of the similar configuration with the load resistance range from 25 Ω to 100 kΩ. The fabrication of a 10-layer P(VDF-TrFE)-based multilayer structure was experimentally demonstrated by a scalable dip-coating process on a flexible Al substrate, with thin Al electrode layers prepared by physical vapor deposition method. The results indicate that it is feasible to produce piezoelectric polymer multilayer structures on flexible substrate for harvesting mechanical energy applicable for many low-power electronics.
Fig. 7. Comparison of simulation results with test results for 10-layer P(VDF-TrFE) multilayer (a) voltage output at 30 kΩ load resistance (b) energy output with load resistance ranging from 10 to 50 kΩ under 7 mm tip displacement with a subsequent release.
Appendix A Neutral Axis of Multilayer Cantilever Beam The coordinate of the neutral axis z0 from the bottom of the cantilever beam can be determined using 2n + 2
N =
∑ F1,i = 0, (A1) i =1
where F1,i is the axial force in the ith layer, i is the number of layers, and 2n + 2 is the total number of layers, including n layers of piezoelectric polymer, n + 1 layers of electrodes, and 1 layer of substrate beam. 2n + 2 h i,up
N =
∑ ∫ i =1
h i,low
−
bκ 0 z dz = 0 (A2) s 11,i
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IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
and hi,low and hi,up can be expressed as i
h i,up = z 0 −
∑
i −1
h j , h i,low = z 0 −
∑ h j . (A3) j =1
j =1
where hj is the thickness of the jth layer. Eq. (A2) leads to 2n + 2
∑ i =1
1 − z − s 11,i 0
2
i
h j − z 0 − j =1
∑
i −1
h j j =1
∑
2
= 0. (A4)
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current generation,” J. Electroceram., vol. 23, no. 2–4, pp. 301–304, 2008. [8] S. T. Chen, K. Yao, F. E. H. Tay, and L. L. S. Chew, “Comparative investigation of the structure and properties of ferroelectric poly(vinylidene fluoride) and poly(vinylidene fluoride-trifluoroethylene) thin films crystallized on substrates,” J. Appl. Polym. Sci., vol. 116, no. 6, pp. 3331–3337, 2010. [9] Y. J. Park, S. J. Kang, C. Park, K. J. Kim, H. S. Lee, M. S. Lee, U. Chung, and I. J. Park, “Irreversible extinction of ferroelectric polarization in P (VDF-TrFE) thin films upon melting and recrystallization,” Appl. Phys. Lett., vol. 88, no. 24, art. no. 242908, 2006. [10] X. He and K. Yao, “Crystallization mechanism and piezoelectric properties of solution-derived ferroelectric poly (vinylidene fluoride) thin films,” Appl. Phys. Lett., vol. 89, no. 11, art. no. 112909, 2006.
Thus, the position of neutral axis z0 can be expressed as
z0 = −
2n + 2 h i2 s 11,i
∑i =1
2n + 2 h i s 11,i 2n + 2 h i i =1 s 11,i
− 2∑i =1 2∑
i
∑ j =1 h j
. (A5)
Appendix B The Initial Curvature of the Multilayer Before the Start of Vibration To avoid the calculation resulting from the discontinuities in the bending stiffness, the difference in stiffness for regions 0 < x < Lp and Lp < x < L is neglected. Thus, the static bending of the cantilever beam caused by the tip force F can be determined by
YI
∂ 4w = −FL(1 − x /L). (A6) ∂x 4
The displacement can be solved as
w = ∆ L f (x ), (A7)
where ΔL = −(FL3)/(3YI) and f (x) = ((3x2)/(2L2) − x3/ (2L3)). References [1] S. R. Anton and H. A. Sodano, “A review of power harvesting using piezoelectric materials (2003–2006),” Smart Mater. Struct., vol. 16, no. 3, pp. R1–R21, 2007. [2] S. Priya and D. J. Inman, Eds., Energy Harvesting Technologies. New York, NY: Springer, 2009. [3] J. Granstrom, J. Feenstra, H. A. Sodano, and K. Farinholt, “Energy harvesting from a backpack instrumented with piezoelectric shoulder straps,” Smart Mater. Struct., vol. 16, no. 5, pp. 1810–1820, 2007. [4] C. Sun, J. Shi, D. J. Bayerl, and X. D. Wang, “PVDF microbelts for harvesting energy from respiration,” Energy Environ. Sci., vol. 4, no. 11, pp. 4508–4512, 2011. [5] D. Vatansever, R. L. Hadimani, T. Shah, and E. Siores, “An investigation of energy harvesting from renewable sources with PVDF and PZT,” Smart Mater. Struct., vol. 20, no. 5, art. no. 055019, 2011. [6] H. Kim, S. Priya, H. Stephanou, and K. Uchino, “Consideration of impedance matching techniques for efficient piezoelectric energy harvesting,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 54, no. 9, pp. 1851–1859, 2007. [7] H. C. Song, H. C. Kim, C. Y. Kang, H. J. Kim, S. J. Yoon, and D. Y. Jeong, “Multilayer piezoelectric energy scavenger for large
Lei Zhang received his bachelor’s degree in engineering from Shanghai Jiao Tong University (SJTU), China, in 2002 and his Ph.D. degree in mechanics from Nanyang Technological University (NTU), Singapore, in 2008. Currently, he is a research scientist at the Institute of Materials Research and Engineering (IMRE), A*STAR, Singapore. Prior to joining IMRE in January 2010, he worked at NTU from 2007 to 2009 as a research fellow. His research interests are in the area of modeling and simulation of smart materials and devices for sensor and transducer applications.
Sharon R. Oh is a researcher at the Institute of Materials Research and Engineering (IMRE) in Singapore. She is currently a Ph.D. candidate in the National University of Singapore. She received her B.S. degree in engineering physics in 1993 and her M.S. degree in applied science and technology in 2001, both from the University of California at Berkeley. Her research interests include: design, simulation, and fabrication of MEMS devices and micro- and nano-fabrication and their application to sensors and actuators.
Ting Chong Wong was born in Singapore in 1984. He received the B.Eng. degree in mechanical engineering from the National University of Singapore in 2009. From 2009 to 2012, he was a Research Specialist with the Institute of Materials Research and Engineering in Singapore. His research interests are in the area of polymeric piezoelectric materials and energy harvesting devices. He holds two patents on the subject.
Chin Yaw Tan was born in Singapore in 1973. He received his B.Sc. degree in physics and computational science in 1997 and his Ph.D. degree in physics in 2006, from the National University of Singapore. He worked on superconducting and ferroelectric microwave devices at the Centre for Superconducting and Magnetic Materials, National University of Singapore, from 2001 to 2006 as a research engineer, and from 2006 to 2007 as a research fellow. Since 2007, he has worked as a scientist at the Institute of Materials Research and Engineering, on the applications of piezoelectric materials for sensors and energy harvesting.
Kui Yao received his bachelor’s degree in electrical engineering and his Ph.D. degree in electronic materials and devices, both from Xi’an Jiaotong University, China, in 1989 and 1995, respectively; he received his master’s degree in technical physics from Xidian University, China, in 1992. Currently, he is a principal scientist, and the manager of Sensor and Transducer Program, in the Institute of Materials Research and Engineering (IMRE), A*STAR, Singapore. From 1998 to 1999, he worked in the Materials Research Laboratory at The Pennsylvania State University. Before that, he was a postdoctoral research fellow in the Microelectronics Center at Nanyang Technological University (NTU), Singapore, from 1995 to 1997. His research interests cover smart materials with signal and energy conversion and storage functions, including ferroic, piezoelectric, photovoltaic, and biochemical-sensing materials, and material-critical sensors, actuators, transducers, and their applications.
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Piezoelectric Polymer Multilayer on Flexible Substrate for Energy Harvesting Lei Zhang, Sharon Roslyn Oh, Ting Chong Wong, Chin Yaw Tan, Member, IEEE, and Kui Yao, Senior Member, IEEE Abstract—A piezoelectric polymer multilayer structure formed on a flexible substrate is investigated for mechanical energy harvesting under bending mode. Analytical and numerical models are developed to clarify the effect of material parameters critical to the energy harvesting performance of the bending multilayer structure. It is shown that the maximum power is proportional to the square of the piezoelectric stress coefficient and the inverse of dielectric permittivity of the piezoelectric polymer. It is further found that a piezoelectric multilayer with thinner electrodes can generate more electric energy in bending mode. The effect of improved impedance matching in the multilayer polymer on energy output is remarkable. Comparisons between piezoelectric ceramic multilayers and polymer multilayers on flexible substrate are discussed. The fabrication of a P(VDF-TrFE) multilayer structure with a thin Al electrode layer is experimentally demonstrated by a scalable dip-coating process on a flexible aluminum substrate. The results indicate that it is feasible to produce a piezoelectric polymer multilayer structure on flexible substrate for harvesting mechanical energy applicable for many low-power electronics.
I. Introduction
W
ith the decreasing power consumption in electronics, it is becoming more realistic to power electric circuits by harvesting ambient energy. By employing proper energy transducers, ambient energy such as solar energy, thermal energy, mechanical energy, and electromagnetic energy, can be converted to electric energy for practical use. Piezoelectric materials, which are capable of converting mechanical energy into electric energy, are suitable for mechanical energy harvesting. Various piezoelectric energy harvesters have been developed and reported in the literature [1]–[5]. One of the disadvantages of energy harvesting with piezoelectric materials is their high voltage output in conjunction with low current output. Typical piezoelectric energy harvesters can often produce voltage of up to several tens to hundreds of volts with current in the order of microamperes. To utilize the energy harvested by piezoelectric materials, the electric circuit usually needs transformers to reduce the output voltage, which increases the cost and dimensions of devices. In addition, the very high impedances of piezoelectric materials are usually not comparable with the load resistance. The impedance mismatch between the piezoelectric energy
Manuscript received April 10, 2013; accepted June 9, 2013. The authors acknowledge support through project IMRE/10-1C0109. The authors are with the Sensors and Transducers Program, Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology, and Research), Singapore ([email protected]). DOI http://dx.doi.org/10.1109/TUFFC.2013.2786 0885–3010/$25.00
harvester and the electric load leads to low efficiency of energy utilization. Multilayer piezoelectric materials structures are able to solve these problems. By using a piezoelectric multilayer structure, the output voltage and material impedance can be significantly reduced while the output current can be increased. Kim et al. [6] reported a lead zirconate titanate (PZT) multilayered cymbal transducer for energy harvesting. The piezoelectric energy harvester was used in the d31 extension mode, where stresses were applied to stretch the multilayer ceramics. The electrical impedance matching for the energy harvesting circuit was considered to allow the transfer of generated energy to a storage media. It was found that by using 10-layer ceramics instead of a single layer, the output current can be increased by 10 times. Song et al. [7] presented a design of energy harvester using piezoelectric ceramic multilayer bonded on a flexible substrate operating in bending mode. It was found that the piezoelectric multilayer energy harvester could be used directly for powering electrical devices without additional electric circuits. For piezoelectric multilayer-based energy harvesters, typical operation modes are extension mode, shear mode, or bending mode. A piezoelectric bending-mode energy harvester requires less mechanical input but can generate a large amount of electric charge through continuous vibration. Both piezoelectric ceramics and piezoelectric polymers can be used in bending-mode energy harvesters. Piezoelectric ceramics generally have large piezoelectric coefficients, but the brittleness of ceramics makes it difficult for them to sustain high mechanical strains. Piezoelectric polymers, on the other hand, have lower piezoelectric coefficients but are able to undergo larger mechanical strains, have much higher shock resistance, and can be produced at a much lower processing temperature. Poly(vinylidene fluoride) (PVDF) and copolymers of vinylidene fluoride and trifluoroethylene P(VDF-TrFE) are two typical piezoelectric polymers. PVDF is a low-cost piezoelectric polymer which has been used for energy harvesting. Granstrom et al. [3] demonstrated an energy harvesting system using PVDF-based shoulder straps on backpack. Sun et al. [4] proposed a respiration energy harvester by using PVDF micro-belts. Vatansever et al. [5] investigated the energy harvesting performance of a PVDF cantilever structure for rain drop and wind energy harvesting. To well utilize piezoelectric polymer multilayer structures for energy harvesting, the piezoelectric layer must be reasonably thin so that the impedance of the piezoelectric polymer multilayer can be effectively reduced. The thin-
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IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
ner the piezoelectric layer is, the lower is the electric impedance of the multilayer. However, thinner piezoelectric layers also mean that more layers are needed to achieve a certain energy level. In addition, because the stiffness of piezoelectric polymer multilayer is much smaller than metal electrode material, the effect of electrode stiffness must be considered in the design of piezoelectric multilayers for bending-mode energy harvesters. Although there are a few publications on piezoelectric multilayer structures for mechanical energy harvesting [6], [7], the material parameters that are critical to piezoelectric multilayer energy harvesting performance have not been systematically investigated. To clarify the effect of material parameters on the energy output, an analytical model must be developed for piezoelectric multilayer energy harvesters. In this paper, we propose a piezoelectric polymer multilayer structure on a flexible substrate for energy harvesting. To better understand the effects of material parameters on the energy harvesting performance, analytical and numerical models of the bending-mode piezoelectric polymer multilayer energy harvester are developed. Material parameters which are critical to the energy output are discussed. The remarkable effect of impedance matching between the piezoelectric polymer multilayer structure and the electric load is exhibited by comparison with a single-layer piezoelectric polymer of the same dimensions. A 10-layer P(VDF-TrFE)-based multilayer on a flexible Al substrate is demonstrated by using the dip-coating method, and the energy harvesting performance is evaluated. II. Analytical Model Fig. 1 illustrates an n-layer piezoelectric polymer [such as P(VDF-TrFE)] multilayer structure bonded on a metal (such as Al) substrate beam. The beam is in a cantilever configuration. The length of the beam is L, the width is b, and the thickness of the substrate is h. The length of the piezoelectric multilayer is Lp. The thickness of each piezoelectric layer is tp and the thickness of the electrode layer is te. The piezoelectric layers are alternatively polarized in the thickness direction and the alternate electrodes are connected. A vertical force of F is applied at the tip of the beam. The force F is removed after the beam achieves its maximum displacement. The beam will subsequently vibrate in the transverse direction, resulting in charge generation in the piezoelectric multilayer. To clarify the effects of material parameters on the energy harvesting capacity of the piezoelectric polymer multilayer, analytical formulations are developed and discussed. The constitutive equations of piezoelectric materials are
D 3 = ε 33E 3 + d 31T1 (1)
S 1 = d 31E 3 + s 11T1, (2)
where D3 is the electric displacement in the polarization direction, S1 is the strain in the axial direction, ε33 is the
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dielectric permittivity of piezoelectric material in the polarization direction at constant stress condition, E3 is the electric field in the polarization direction, T1 is the stress in the axial direction of the cantilever structure, d31 is the piezoelectric coefficient, and s11 is the compliance of piezoelectric material under constant electric field condition. For the ith piezoelectric layer, the electric displacement can be obtained from (1) and (2): D 3,i = d 31S 1,i /s 11 + ε 33E 3, (3)
2 2 2 where ε 33 = ε33(1 − k 31 ) and k 31 = d 31 /(ε 33s 11). Therefore, the charge generated in the ith piezoelectric layer can be calculated as
Qi =
∫ D 3,i dA = ∫ (d 31S 1,i/s 11 + ε 33E 3)dA, (4)
AP
where AP denotes the area in piezoelectric layers. The total charge generated in all n layers of piezoelectric materials can be expressed as n
Q =
∑
n
Qi =
i =1
∑ ∫ (d 31S 1,i/s 11 + ε 33E 3)dA. (5) i =1 AP
The axial strain in the ith piezoelectric layer can be determined by
S 1,i = µ 0 + κ 0(z i − z 0), (6)
where μ0 and κ0 are the axial strain and curvature of the beam at z0, respectively, for pure bending without external axial stresses, μ0 = 0; z0 is the location of natural axis with respect to global coordinates and zi is the location of the ith layer. The detailed calculation of neutral axis location can be found in Appendix A.
Fig. 1. Illustration configuration.
of
piezoelectric
multilayer
in
cantilever
zhang et al.: piezoelectric polymer multilayer on flexible substrate for energy harvesting
The curvature of the beam κ0 is defined by
κ0 =
w ′′ ≈ −w ′′, (7) [1 + w ′ 2]2/3
where w′ and w′′ are the first and second derivatives of w, which is the transverse displacement of the cantilever with respective to the length of the beam x. To determine the total charge generated in the piezoelectric multilayer during the vibration, the transverse displacement of the cantilever must be determined. The transverse displacement of the cantilever beam in vibration is governed by the equation of motion:
∂ 2w(x, t) ∂w(x, y) ∂ 4w(x, t) +λ +γ = 0, (8) 4 ∂t ∂x ∂t 2
where λ = ρA/YI is a coefficient related to the ratio of mass per unit length to the stiffness of the multilayer cantilever, ρ is the density of the multilayer beam, A is the cross-sectional area, Y is the Young’s modulus, I is the second moment of inertia, and γ is a damping coefficient. The boundary conditions for the cantilever configuration are
w(x, t) x = 0 = 0,
∂w(0, t) ∂ 2w(L, t) = 0, = 0. (9) ∂t ∂x 2
Prior to the start of the vibration, the cantilever beam has an initial displacement resulting from the external force F applied at the tip. According to the calculation in Appendix B, the initial condition is
w(x, 0) = ∆ L f (x ), (10) −((FL3)/(3YI))
((3x2)/(2L2)
where ΔL = and f (x) = − x3/(2L3)). The solution to (8) can be obtained by the method of separation of variables: ∞
w(x, t) =
∑ BmX m(x)Tm(t), (11)
m =1
where Bm is a constant, Xm(x) is a mode shape function, and Tm(t) is a time-dependent function. For the cantilever configuration, the mode shape function Xm(x) in (11) is
2015
The first five roots to (13) are kmL = 1.8751, 4.6941, 7.8548, 10.9955, and 14.1372. The wave number km is related to the natural frequency ωm by k m4 = λωm2 . The time-dependent function Tm can be determined by d Tm(t) = φ0 sin(ωm t + θm )e −ωmς mt, (14)
d where ϕ0 is a constant, ςm = γ/λ is a damping factor, ωm 2 = ωm 1 − ς m , and θm = tan( 1 − ς m /ς m ). With (12) and (14), (11) can be rewritten as ∞
w(x, t) =
∑ C mX m(x)φ0e −ω ς t sin(ωmdt + θm), (15) m m
m =1
where the term Cm = ϕ0Bm can be determined according to the initial condition in (10) as L
Cm =
∫0
∆ L f (x )X m(x )dx L
∫0
X m2 (x )dx
. (16)
The term Cm in (16) can be expressed in a simple form with initial tip displacement or the force applied at the tip as variables, C m = αm∆ L = −αm
L
FL3 , (17) 3YI
L
where αm = ∫ f (x )X m(x )dx /∫ X m2 (x )dx. 0 0 Thus, the solution of transverse displacement to (8) can be expressed as ∞
w(x, t) =
FL3
∑ −αm 3YI X m(x)ϕ 0e −ω ς t sin(ωmdt + θm). m m
m =1
(18) With the solution of transverse displacement w(x, t) in (18), the strains in the piezoelectric multilayer and the total charges can be calculated. According to (5)–(7) and (18), the total charge generated by the piezoelectric multilayer can be expressed as n n −w ′′(x, t)d ( z − z ) / s + ε E 31 i 0 11 33 3 dA i =1 i =1 AP (19)
Q =
∫
∑
∑
and the corresponding current Ic is X m(x ) = [cos(k mx ) − cosh(k mx )] dQ V cos(k mL) + cosh(k mL) Ic = − = , (20) − [sin(k mx ) − sinh(k mx )], R dt sin(k mL) + sinh(k mL) (12) where R is the external load resistance and V is the voltage across the external load resistance. where km is a wave number, which can be determined by Thus, the power of the load resistance R can be calcu cos(k mL) cosh(k mL) + 1 = 0. (13) lated using
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ceramic multilayers, whereas piezoelectric polymer multilayers can sustain large amplitude vibrations which are more suitable for bending-mode mechanical energy harvesting. n The term ∑i =1 (z i − z0) in (24) denotes the effect of the where ω is the frequency of electric output which is equivalent to the fundamental frequency of the cantilever beam, neutral axis on the maximum power output of the piezoi.e., ω = ω1d, and the term Λ(Lp, t) is electric multilayer on a flexible substrate. It is evident that if the position of the neutral axis z0 is fixed, more ∞ piezoelectric layers will lead to higher power output. On ∂X m(L p) d −αm φ0e −ωmς mt sin(ωm t + θm ), Λ(L p, t) = n ∂x the other hand, to obtain a higher value of ∑i =1 (z i − z0) m =1 (22) with fixed layer number n, the neutral axis should be as far as possible from the piezoelectric layers. To achieve From (21), the optimal load resistance Ropt and maximum that, the stiffness of piezoelectric multilayer, including the output power Pmax can be determined as internal electrode layers, must be substantially lower than that of the substrate beam so that the neutral axis is out 1 of the multilayer region. This will require using a much R opt = (23) 2 ω(1 − k 31 )C p stiffer substrate, such as hard metal, for piezoelectric multilayer ceramics or flexible piezoelectric polymer materials 2 3 n be FL with thin metal electrodes on flexible substrate. For the 31 3YI ∑i =1 (z i − z 0)Λ(L p, t) Pmax = , (24) 2 same substrate and dimensions, a piezoelectric polymer )C p 4ω(1 − k 31 n multilayer will have significantly higher value of ∑i =1 (z i where Cp = nε33ε0((bLp)/tp)) is the capacitance of the − z0) compared with a piezoelectric ceramic multilayer, piezoelectric multilayer and ε0 is the free space permit- meaning significantly higher power output. For a piezoelectric polymer multilayer, thinner electrodes will reduce tivity. the stiffness of the multilayer, which will keep the neutral axis farther from the multilayer. In addition, the thinner electrodes also mean lower stiffness of the multilayer. UnIII. Material Parameters Critical der constant force condition, the piezoelectric multilayer to Energy Harvesting with thinner electrodes will have larger bending displaceEq. (24) describes the maximum power output of a ment, which is desired for enhanced energy output. Thus, piezoelectric multilayer on flexible substrate for bending- then dual effects of thinner electrodes, i.e., increase of mode energy harvesting. It includes not only the mechani- ∑i =1 (z i − z0) and FL3/3YI, will result in higher energy cal and piezoelectric parameters, but also the effect of output. The preceding analyses show the opportunities for external force F and the effect of layer numbers. From the formulations in (24), the maximum power of piezoelectric polymer multilayers to offer competitive ena piezoelectric bending-mode energy harvester is propor- ergy harvesting performance compared with piezoelectric 2 2 tional to e 31 /[(1 − k 31 )C p ]. This relation indicates that the ceramic multilayers at constant force condition under higher the piezoelectric stress coefficient and the lower the bending mode. These clarified relationships provide guiddielectric permittivity are, the higher the power output ance for developing improved piezoelectric materials and will be. It is noted that larger electromechanical coupling for designing the right multilayer structure dedicated to 2 factor k 31 can lead to improved power generation. Howev- high-performance mechanical energy harvesting. The nu2 er, it could be neglected if k 31 is well below 1, which may merical simulation of the piezoelectric polymer multilayer in Section IV will validate the major conclusions. be true for many practical piezoelectric polymers. It is also noted that the maximum power output in (24) is proportional to the square of FL3/3YI. FL3/3YI represents the initial tip displacement of the multilayer IV. Numerical Simulation cantilever beam caused by the tip force F. It is obvious that under the same tip force F, piezoelectric ceramic mulNumerical simulation was carried out by using Ansys tilayers will have much smaller FL3/3YI because of their (version 12.0, Ansys Inc., Canonsburg, PA) software. The high bending stiffness YI as compared with piezoelectric piezoelectric layer was modeled by using the SOLID226 polymer multilayers. For example, the Young’s modulus coupled field element and the nonpiezoelectric layers were of a typical PVDF polymer is around 2 to 3 GPa, whereas modeled by using SOLID186. The model for simulation is the typical Young’s modulus of a PZT material is more shown in Fig. 1. The material properties and dimension than 60 GPa. Thus, piezoelectric ceramic multilayers will parameters are tabulated in Table I. have much smaller displacement at the same tip force. In The piezoelectric multilayer is based on P(VDF-TrFE) addition, the brittleness of piezoelectric ceramic materials polymer with a layer thickness of 20 μm and Al internal limits the maximum achievable FL3/3YI for piezoelectric electrode layers. To assess the effect of electrode layer on 2
be FL3 n (z − z )Λ(L , t) 31 3YI ∑i =1 i p 0 , (21) 2 P = I cR = (1/R + n ωε 33bL/t p)2R
∑
zhang et al.: piezoelectric polymer multilayer on flexible substrate for energy harvesting
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TABLE I. Material and Dimension Parameters for Simulation. Symbol
Value
Unit
s11 s12 s13 s22 s33 s44 s55 s66 d31 d33 d15 ε11 ε22 ε33 L h b Lp tp
3.32 −1.44 −0.89 3.24 3 94 96.3 14.4 10.7 −33.5 −36.3 7.4 7.95 11.3 50 0.4 30 45 20
10−10 m2/N 10−10 m2/N 10−10 m2/N 10−10 m2/N 10−10 m2/N 10−10 m2/N 10−10 m2/N 10−10 m2/N pC/N pC/N pC/N — — — mm mm mm mm μm
the total energy harvesting performance, the open circuit energy and peak voltage generated by the piezoelectric multilayer with different electrode thicknesses and layer numbers are calculated. Fig. 2 shows the effect of the electrode thickness on the open-circuit voltage and energy for different layer numbers at constant displacement and constant force conditions. It is observed from Fig. 2(a) that under constant tip displacement condition, both the peak voltage and output energy increase with the increase of layer numbers. The effect of electrode thickness becomes significant when the layer number is more than 20. Piezoelectric multilayers with thinner electrodes are capable of generating larger electric energy and peak voltage compared with piezoelectric multilayers with thicker electrodes. These results are in agreement with the discussion of material parameters in the previous section. For the constant force condition illustrated in Fig. 2(b), neither the peak voltage nor output energy monotonically increase with the layer numbers. There are optimal layer numbers for both the peak voltage and output energy. This reflects the tradeoff between the increase of piezoelectric layers and the increase of the bending stiffness. It is noted that in the constant force condition, the effect of electrode thickness is more significant than that under constant displacement condition. For a 26-layer piezoelectric multilayer with ideal near-zero electrode thickness, the output energy is more than 7 times larger than that of a piezoelectric multilayer with 2-µm-thick electrodes. These results show that the thickness of electrode layer is a critical factor to be considered for designing optimal piezoelectric multilayer structures for energy harvesting in bending mode. When the piezoelectric multilayer is connected to an electric load, the energy consumed by the load resistance is strongly dependent on the load resistance. There is an optimal load resistance for the piezoelectric multilayer in term of energy output. Fig. 3 gives the electrical output of
Fig. 2. Effect of electrode thickness and number of layers on the energy and voltage generation in P(VDF-TrFE) piezoelectric multilayer structure with a cantilever bending mode, under the condition of (a) constant displacement of 7 mm at the tip, and (b) constant force of 7 N at the tip. P(VDF-TrFE) thickness = 20 µm and Al substrate thickness = 0.4 mm.
a 20-layer P(VDF-TrFE) multilayer on flexible substrate with load resistance range from 1 to 30 kΩ. It is noted that the optimal load resistance is around 10 kΩ and the corresponding output voltage and energy are 169 μJ and −12.9 V, respectively. Based on the analytical solution of optimal load resistance in (23), the Ropt is calculated to be 9.4 kΩ, which is close to the 10 kΩ from the numerical result. The significant advantage of the P(VDF-TrFE) multilayer over a single layer for energy harvesting is shown in Fig. 4, which takes into account the impedance matching behavior of a piezoelectric multilayer structure compared with single-layer piezoelectric material with the same configuration and total thickness. It is observed that the energy output of the piezoelectric polymer multilayer is 5 to 400 times higher than that of a single-layer piezoelectric polymer for the load resistance range of 25 Ω to 100 kΩ. This result shows the dramatic enhancement in the performance for energy harvesting with a multilayer structure compared with a single-layer piezoelectric polymer.
2018
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
Fig. 3. Peak voltage and output energy of a 20-layer P(VDF-TrFE) multilayer in a cantilever configuration with load resistance ranging from 1 to 30 kΩ under 7 mm tip displacement with a subsequent release. Polymer layer thickness = 20 µm, Al electrode thickness = 0.2 µm, and Al substrate thickness = 0.5 mm.
V. Fabrication and Experimental Test of P(VDE-TrFE) Multilayer To demonstrate the fabrication and energy harvesting of piezoelectric polymer multilayer with thin electrode layers on a flexible cantilever substrate, a dip-coating process was used to fabricate a P(VDF-TrFE) multilayer with Al electrode layers alternately deposited by physical vapor deposition on a flexible substrate. To produce the piezoelectric polymer solution for the multilayer, P(VDF-TrFE) (70/30 mol ratio) was dissolved in methyl ethyl ketone (MEK) (17.5% by weight). 0.5-mmthick Al sheets were used as the flexible substrates. A 10-µm insulating layer was first formed on the Al substrates by dip coating in the P(VDF-TrFE) solution with withdrawal speed of 25 mm/min, followed by heating and annealing at 135°C for 2 h in an oven to increase the crystallinity [8], [9]. 0.2-µm-thick Al electrodes were then deposited through a shadow mask via e-beam evaporation (Edwards Ltd., Crawley, UK). The Al deposition was then followed by the dip coating of the first P(VDF-TrFE) active layer at withdrawal speed of 20 mm/min. After the samples were heated and dried, another dip-coating cycle was carried out under the same conditions, to increase the thickness of the P(VDF-TrFE) layer to approximately 20 µm. The samples were then annealed in an oven at 135°C for 2 h in an oven to increase the crystallinity of the P(VDF-TrFE). The dip-coating process of the polymer and the e-beam evaporation of Al are alternately repeated to build the piezoelectric polymer multilayer structures. Fig. 5 presents a scanning electron micrograph of a cross-section of a P(VDF-TrFE)/Al multilayer as obtained. A 10-layer P(VDF-TrFE) sample was fabricated with the previously described method and cut to a size of 3 × 5 cm. The thickness of the P(VDF-TrFE) layer is around 20 μm and the thickness of Al electrode is about 0.2 μm. This sample was clamped onto a metal block, as shown in
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Fig. 4. Comparisons of energy outputs of 22-layer P(VDF-TrFE) and single-layer P(VDF-TrFE) polymer with load resistance ranging from 25 Ω to 100 kΩ.
Fig. 6, for testing. A 7-mm deflection was applied at the tip of the sample with a subsequent release. The sample is electrically connected to an oscilloscope with which the electric outputs are measured and fed to a computer. Fig. 7 shows the test result of voltage and energy generated by a 10-layer P(VDF-TrFE) multilayer structure in comparison with simulation result. The fabricated 10-layer P(VDF-TrFE) is found to be able to generate 17 μJ at the optimal load resistance of 30 kΩ with single press. However, the output energy is considerably lower than the simulation result, where the output energy at 30 kΩ is expected to be more than 50 μJ. The main reason for the difference could be the many defects in the piezoelectric multilayer, as noted during the multilayer fabrication. In addition, as noted in Fig. 7(a), the damping behaviors of the simulated and experimental results are different. More precise damping models are needed to more accurately quantitatively simulate the energy output from the piezoelectric multilayer energy harvester. Nevertheless, the output of 17 μJ to the load as generated with a single press is adequate for many low-power electronics.
Fig. 5. Scanning electron micrograph of cross-section of P(VDF-TrFE)/ Al multilayer.
zhang et al.: piezoelectric polymer multilayer on flexible substrate for energy harvesting
2019
Fig. 6. Sample of a 10-layer P(VDF-TrFE) multilayer as fabricated for energy harvesting.
It is worth mentioning that the P(VDF-TrFE) material used in the piezoelectric multilayer structure can be replaced with PVDF homopolymer at much lower cost. Low-cost piezoelectric PVDF homopolymer can be produced from solution coating directly on a substrate without the conventional mechanical stretching to induce the polar phase [8], [10]. It is feasible to produce low-cost piezoelectric polymer multilayers for energy harvesting applications. VI. Conclusions A piezoelectric polymer multilayer structure formed on flexible substrate was investigated for mechanical energy harvesting under bending mode. Analytical and numerical models were developed to understand the effect of material parameters on the energy harvesting performance of the multilayer structure. It was shown that the maximum power is proportional to the square of the piezoelectric stress coefficient and the inverse of dielectric permittivity of the piezoelectric polymer. It was further found that a piezoelectric multilayer with thinner electrodes can generate larger electric energy in bending mode, especially under constant force condition. Compared with piezoelectric ceramic multilayers, piezoelectric polymer multilayers on flexible substrate are particularly advantageous under constant force condition. The effect of improved impedance matching in the multilayer on energy output is remarkable. A 5 to 400 times improvement on energy output was shown for a 22-layer P(VDF-TrFE) multilayer structure on flexible substrate compared with that of a single layer of the similar configuration with the load resistance range from 25 Ω to 100 kΩ. The fabrication of a 10-layer P(VDF-TrFE)-based multilayer structure was experimentally demonstrated by a scalable dip-coating process on a flexible Al substrate, with thin Al electrode layers prepared by physical vapor deposition method. The results indicate that it is feasible to produce piezoelectric polymer multilayer structures on flexible substrate for harvesting mechanical energy applicable for many low-power electronics.
Fig. 7. Comparison of simulation results with test results for 10-layer P(VDF-TrFE) multilayer (a) voltage output at 30 kΩ load resistance (b) energy output with load resistance ranging from 10 to 50 kΩ under 7 mm tip displacement with a subsequent release.
Appendix A Neutral Axis of Multilayer Cantilever Beam The coordinate of the neutral axis z0 from the bottom of the cantilever beam can be determined using 2n + 2
N =
∑ F1,i = 0, (A1) i =1
where F1,i is the axial force in the ith layer, i is the number of layers, and 2n + 2 is the total number of layers, including n layers of piezoelectric polymer, n + 1 layers of electrodes, and 1 layer of substrate beam. 2n + 2 h i,up
N =
∑ ∫ i =1
h i,low
−
bκ 0 z dz = 0 (A2) s 11,i
2020
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,
and hi,low and hi,up can be expressed as i
h i,up = z 0 −
∑
i −1
h j , h i,low = z 0 −
∑ h j . (A3) j =1
j =1
where hj is the thickness of the jth layer. Eq. (A2) leads to 2n + 2
∑ i =1
1 − z − s 11,i 0
2
i
h j − z 0 − j =1
∑
i −1
h j j =1
∑
2
= 0. (A4)
vol. 60, no. 9,
September
2013
current generation,” J. Electroceram., vol. 23, no. 2–4, pp. 301–304, 2008. [8] S. T. Chen, K. Yao, F. E. H. Tay, and L. L. S. Chew, “Comparative investigation of the structure and properties of ferroelectric poly(vinylidene fluoride) and poly(vinylidene fluoride-trifluoroethylene) thin films crystallized on substrates,” J. Appl. Polym. Sci., vol. 116, no. 6, pp. 3331–3337, 2010. [9] Y. J. Park, S. J. Kang, C. Park, K. J. Kim, H. S. Lee, M. S. Lee, U. Chung, and I. J. Park, “Irreversible extinction of ferroelectric polarization in P (VDF-TrFE) thin films upon melting and recrystallization,” Appl. Phys. Lett., vol. 88, no. 24, art. no. 242908, 2006. [10] X. He and K. Yao, “Crystallization mechanism and piezoelectric properties of solution-derived ferroelectric poly (vinylidene fluoride) thin films,” Appl. Phys. Lett., vol. 89, no. 11, art. no. 112909, 2006.
Thus, the position of neutral axis z0 can be expressed as
z0 = −
2n + 2 h i2 s 11,i
∑i =1
2n + 2 h i s 11,i 2n + 2 h i i =1 s 11,i
− 2∑i =1 2∑
i
∑ j =1 h j
. (A5)
Appendix B The Initial Curvature of the Multilayer Before the Start of Vibration To avoid the calculation resulting from the discontinuities in the bending stiffness, the difference in stiffness for regions 0 < x < Lp and Lp < x < L is neglected. Thus, the static bending of the cantilever beam caused by the tip force F can be determined by
YI
∂ 4w = −FL(1 − x /L). (A6) ∂x 4
The displacement can be solved as
w = ∆ L f (x ), (A7)
where ΔL = −(FL3)/(3YI) and f (x) = ((3x2)/(2L2) − x3/ (2L3)). References [1] S. R. Anton and H. A. Sodano, “A review of power harvesting using piezoelectric materials (2003–2006),” Smart Mater. Struct., vol. 16, no. 3, pp. R1–R21, 2007. [2] S. Priya and D. J. Inman, Eds., Energy Harvesting Technologies. New York, NY: Springer, 2009. [3] J. Granstrom, J. Feenstra, H. A. Sodano, and K. Farinholt, “Energy harvesting from a backpack instrumented with piezoelectric shoulder straps,” Smart Mater. Struct., vol. 16, no. 5, pp. 1810–1820, 2007. [4] C. Sun, J. Shi, D. J. Bayerl, and X. D. Wang, “PVDF microbelts for harvesting energy from respiration,” Energy Environ. Sci., vol. 4, no. 11, pp. 4508–4512, 2011. [5] D. Vatansever, R. L. Hadimani, T. Shah, and E. Siores, “An investigation of energy harvesting from renewable sources with PVDF and PZT,” Smart Mater. Struct., vol. 20, no. 5, art. no. 055019, 2011. [6] H. Kim, S. Priya, H. Stephanou, and K. Uchino, “Consideration of impedance matching techniques for efficient piezoelectric energy harvesting,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 54, no. 9, pp. 1851–1859, 2007. [7] H. C. Song, H. C. Kim, C. Y. Kang, H. J. Kim, S. J. Yoon, and D. Y. Jeong, “Multilayer piezoelectric energy scavenger for large
Lei Zhang received his bachelor’s degree in engineering from Shanghai Jiao Tong University (SJTU), China, in 2002 and his Ph.D. degree in mechanics from Nanyang Technological University (NTU), Singapore, in 2008. Currently, he is a research scientist at the Institute of Materials Research and Engineering (IMRE), A*STAR, Singapore. Prior to joining IMRE in January 2010, he worked at NTU from 2007 to 2009 as a research fellow. His research interests are in the area of modeling and simulation of smart materials and devices for sensor and transducer applications.
Sharon R. Oh is a researcher at the Institute of Materials Research and Engineering (IMRE) in Singapore. She is currently a Ph.D. candidate in the National University of Singapore. She received her B.S. degree in engineering physics in 1993 and her M.S. degree in applied science and technology in 2001, both from the University of California at Berkeley. Her research interests include: design, simulation, and fabrication of MEMS devices and micro- and nano-fabrication and their application to sensors and actuators.
Ting Chong Wong was born in Singapore in 1984. He received the B.Eng. degree in mechanical engineering from the National University of Singapore in 2009. From 2009 to 2012, he was a Research Specialist with the Institute of Materials Research and Engineering in Singapore. His research interests are in the area of polymeric piezoelectric materials and energy harvesting devices. He holds two patents on the subject.
Chin Yaw Tan was born in Singapore in 1973. He received his B.Sc. degree in physics and computational science in 1997 and his Ph.D. degree in physics in 2006, from the National University of Singapore. He worked on superconducting and ferroelectric microwave devices at the Centre for Superconducting and Magnetic Materials, National University of Singapore, from 2001 to 2006 as a research engineer, and from 2006 to 2007 as a research fellow. Since 2007, he has worked as a scientist at the Institute of Materials Research and Engineering, on the applications of piezoelectric materials for sensors and energy harvesting.
Kui Yao received his bachelor’s degree in electrical engineering and his Ph.D. degree in electronic materials and devices, both from Xi’an Jiaotong University, China, in 1989 and 1995, respectively; he received his master’s degree in technical physics from Xidian University, China, in 1992. Currently, he is a principal scientist, and the manager of Sensor and Transducer Program, in the Institute of Materials Research and Engineering (IMRE), A*STAR, Singapore. From 1998 to 1999, he worked in the Materials Research Laboratory at The Pennsylvania State University. Before that, he was a postdoctoral research fellow in the Microelectronics Center at Nanyang Technological University (NTU), Singapore, from 1995 to 1997. His research interests cover smart materials with signal and energy conversion and storage functions, including ferroic, piezoelectric, photovoltaic, and biochemical-sensing materials, and material-critical sensors, actuators, transducers, and their applications.
