Bubble Electret-Elastomer Piezoelectric Transducer

energies

Article Bubble Electret-Elastomer Piezoelectric Transducer

Ryszard Kacprzyk and Agnieszka Mirkowska *

Department of Electrical Engineering Fundamentals, Wroclaw University of Science and Technology, 50-377 Wroclaw, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-71-320-24-37

Received: 22 April 2020; Accepted: 3 June 2020; Published: 5 June 2020

Abstract: Ferroelectret-based piezoelectric transducers are, nowadays, commonly used in energy harvesting applications due to their high piezoelectric activity. Unfortunately, the processing properties of such materials are limited, and new solutions are sought. This paper presents a new solution of a piezoelectric transducer containing electret bubbles immersed in an elastomer matrix. Application of a gas-filled dielectric bubble as the fundamental cell of the piezo-active structure is discussed. A simplified model of the structure, containing electret thin-wall bubbles and elastomer dielectric filling, was applied to determine the value of the piezoelectric coefficient, d33. An exemplary structure containing piezo-active bubbles, made of an electret material, immersed in an elastomer filling is presented. The influence of the mechanical and electrical properties of particular components on the structure piezoelectric properties are experimentally examined and confirmed. The quasi-static method was used to measure the piezoelectric coefficient, d33. The separation of requirements related to the mechanical and electrical properties of the transducer is discussed.

Keywords: dielectric composites; dielectrics; energy harvester; ferroelectrets; piezoelectrets; piezoelectric materials

1. Introduction Energy harvesting from different renewable resources is presently broadly studied. One of the prospective solutions is energy harvesting from vibrations, based on the application of piezoelectric transducers [1,2]. Conventionally used piezoelectric transducers are based mainly on materials with spontaneous electric polarization, such as ceramics or polyvinylidene fluoride (PVDF) foils. The piezoelectric properties of structures are typically characterized by piezoelectric coefficient dij, which can be measured using different methods, such as quasi-static, dynamic, and other [3]. In the most popular lead zirconate titanate (PZT) ceramics and composites, the d33 component reaches 600 pC/N[4], while, in PVDF foils, d 30 pC/N is observed [5]. For well-known zinc oxide (ZnO), 33 ≤ the coefficient d33 reaches 12 pC/N[6,7], while, for lead-free (K,Na)NbO3 ceramics, it almost reaches 500 pC/N; however, to reach the highest values complex processing is required [8]. The piezoelectric phenomenon occurs due to different physical mechanisms. One of them is the generation of inhomogeneous strain in a dielectric containing a space charge density [9]. In practice, the requirement of inhomogeneous strain is realized by the application of layered dielectric structures containing layers exhibiting different mechanical properties (elasticity coefficient). Dielectrics possessing good electret properties (sufficiently long charge life-time), like poly(tetrafluoroethylene) (PTFE) or polypropylene (PP), simultaneously exhibit a relatively high Young’s modulus, which is usually of the order of 109 Pa [10]. This parameter seriously limits the direct application of such dielectrics in the construction of piezoelectric transducers. Models describing the piezoelectric properties of layered structures have shown that the presence of at least one dielectric layer with a relatively high elasticity (low value of Young’s modulus Y, which should be on the level of 105 Pa or lower) is one of

Energies 2020, 13, 2884; doi:10.3390/en13112884 www.mdpi.com/journal/energies Energies 2020, 13, 2884 2 of 11 the fundamental requirements [11–13]. This mechanical demand may be obtained by specific polymer processing, such as 3D printing [14], foaming, stretching, thermoforming, and others [15]. Structures made of different electret materials, such as polypropylene (PP) [16], cross-linked PP–XPP [17], poly(tetrafluoroethylene) (PTFE) [18], fluoroethylenepropylene (FEP) [19], poly(ethylene tetraphtalate) (PET) [20], poly(ethylene naphthalate) (PEN) [21], or cyclo-olefins polymers [22], have been investigated for many years. The mentioned polymers were used in a ‘dispersed’ form as gas-electret composites, so-called ferroelectrets. The name ‘ferroelectrets’ is associated with the fact that these gas-electret composites exhibit P–E (polarization-electric field intensity) hysteresis when submitted to high electric fields [23]. Ferroelectrets usually contain thin-wall, usually open, tubular gas channels or lens-like gas voids. Such a construction allows to obtain the effective Young’s modulus on the level of 105106– Pa, with preservation of charge-stability [24], and finally, receive the piezoelectric coefficient d33 exceeding 1000 pC/N[25]. Relatively high elasticity of ferroelectrets and their high d33 coefficient cause that ferroelectret materials are frequently applied in energy harvesters solutions [26–28]. Application of particular thin-wall electret elements in ferroelectrets is necessary due to two fundamental requirements: (1) the charge-storage abilities (the thinner the wall, the higher the surface charge density possible to deposit on the gas void surfaces), and (2) lowering of the effective Young’s modulus of the dielectric composite [11,29]. Ferroelectrets with a coefficient of d33 > 100 pC/N contain a great deal of gas inside thin-wall tube-like electret channels, which makes them very pliable to heavy strain. The piezoelectric properties of ferroelectrets can be determined using two-, three- or multi-layer models [11,12]. All of these leads to the conclusion that structures with a relatively high value of d33 can be obtained by: (1) increasing the surface charge density on the inner surface of gas voids, and (2) lowering of the effective Young’s modulus of the whole structure. Moreover, the technical application of ferroelectrets requires material property stability, such as charge or thermal stability in time. The charge stability depends highly on the temperature—the higher the temperature, the faster the charge decay. For PTFE, thermal stability reaches 130 ◦C[30]; the charge stability may last years, and chemical processing leading to improved charge stability is possible [31]. In addition, ferroelectret-based transducers are characterized by a low coupling factor, but the extremely low acoustic impedance of such materials compensate for this [32]. It should be noted that the number of electret materials (exhibiting a high value of Young’s modulus, Y) and their processing properties are limited, so new solutions are being explored. In this paper, a new solution of an electret-elastomer composite is discussed. In the case of thin-wall electret bubbles immersed in a non-conducting elastomer, the composite allows to separate the roles of the components, particularly, requirements related to their mechanical (Young’s modulus) and electrical (charge stability) properties. Stability of piezoelectric coefficient d33 is determined by the charge storage properties of the electret bubbles, and the mechanical strain (due to the external stress) is mainly determined by the properties of the used elastomer characterized by the value of Young’s modulus—Ye. The application of dielectric composites, containing electret bubbles immersed in an elastomer matrix widen the range of dielectric materials that can be applied in piezoelectric transducer constructions.

2. Structural Model The cross-section of the bubble electret-elastomer transducer is shown in Figure1. The piezoelectric transducer contains two essential layers: external elastomer ﬁlling as the forming layer (1), and an active electret layer consisting of gas bubbles with bipolar charge qs distributed on their inner surfaces ± of the thin electret “shell” (2). Also the two rigid metal electrodes were applied on the outside sides of the sample (3). Energies 2020, 13, 2884 3 of 11 Energies 2020, 13, x FOR PEER REVIEW 3 of 11

Figure 1. Bubble electret-elastomer transducertransducer with bi-polar charge qqss deposited on the inner surfaces of the the electret electret bubble, bubble, where where 1—forming 1—forming layer layer made made of dielectric of dielectric elastomer, elastomer, 2—electret 2—electret bubble, bubble, and and3—electrodes. 3—electrodes.

A simpliﬁedsimplified modelmodel ofof aa singlesingle electretelectret bubble bubble immersed immersed in in an an elastomer elastomer is is presented presented in in Figure Figure2. The2. The model, model, with with cylindrical cylindrical symmetry symmetry (structure (structure axis axis perpendicular perpendicular to tothe the layerslayers surface),surface), consists of three main layers: two A layers made of elastomer, characterized by elasticity coeﬃcient Y of three main layers: two A layers made of elastomer, characterized by elasticity coefficient Ye and ae and a thickness of x , and a non-uniform B-layer with a total thickness of x , made of an electret thickness of x1, and a1 non-uniform B-layer with a total thickness of x2, made of 2an electret bubble and bubble and elastomer surrounding characterized by the equivalent Young’s modulus, Y . The electret elastomer surrounding characterized by the equivalent Young’s modulus, Y2. The electret2 bubble has bubbleuniform has walls uniform with walls a thickness with a thickness of h and of hisand made is made of dielectric of dielectric characterized characterized by by its its Young’s Y modulus—Y1—and—and electric electric permittivity— permittivity—εε11. .The The properties properties of of the the gas gas layer layer are are given by gas-voidgas-void x bubble thickness xp and gas electric permittivity εp..

Figure 2.2. TheThe simplified simpliﬁed model model of a dielectric bubble immersed in an elastomer containing two

elastomer layers—A (with thicknessthickness xx11, electric permittivity of an elastomer εe andand Young’s Young’s modulus of an elastomerelastomer Yee)) and electret bubble-elastomer layer B with the totaltotal thicknessthickness ofof xx22 and eeffectiveﬀective Young’s modulusmodulus ofof thethe wholewhole layerlayer YY22.. The The area S2 isis the the area area of electret bubble (the propertiesproperties ofof electret wall areare givengiven byby hh—wall—wall thickness,thickness, YY11—Young’s modulusmodulus andand εε11—electric permittivity of electret material) and S2—the area of an elastomer in layer B. The properties of gas inside the bubble are given by gas electric permittivitypermittivity εεpp and gas void height xp..

The area of the elastomer part of layer B is given by S11,, which which is smaller than the area of electret bubble S2.. The The charge charge is is stored stored only only on area S2 on the inner surface of thethe bubble.bubble. Thus, eeffectiveffective charge qs is reduced by an S2//S ratio due to qs’0 possible to to store in the total area S.. Assuming that a bubble isis aa cylindrical cylindrical pastille, pastille, and and ignoring ignoring the edgethe edge effects, effects, the piezoelectric the piezoelectric properties properties of the B-layerof the canB-layer be determinedcan be determined using a 3-layerusing a dielectric3-layer dielectric model [ 29model]. Thus, [29]. the Thus,d33B thecoe ffid33Bcient coefficient is for the is B-layerfor the τ (FigureB-layer2 (Figure) only, and 2) only, for assumption and for assumptiontm >> τMe tm(measurements >> τMe (measurements carried outcarried for theout time for thetm muchtime tm shorter much τ thanshorterτMe than—the τMe Maxwell—the Maxwell time constant time constant for the for elastomer) the elastomer) it is given it is by given the followingby the following relation: relation: ! 2'2qqhxs0ε1εεεphxp 1 1 2'qhxspp1 11 d33B ==⋅−, (1) d33B 2 2· Y − Y , (1) 33B (()hhxεεεp ++xpε1) 2 YY2 1 ()hxpp1 YY21 where qs’ = qs S2/S and qs is the charge possible to store on the total area S of the sample. where qs’ = qs·S· 2/S and qs is the charge possible to store on the total area S of the sample. Assuming the adiabatic compression of the bubble with the initial pressure much lower than Y2 and for assumption Y2 << Y1, the d33B coefficient is:

Energies 2020, 13, 2884 4 of 11

Energies 2020, 13, x FOR PEER REVIEW 4 of 11 Assuming the adiabatic compression of the bubble with the initial pressure much lower than Y2 Y Y d and for assumption 2 << 1, the 33B coefficientεε is: 2'qhxspp1 1 ≅⋅ d33B 2qs0ε1εphxp 2 1 . (2) d ()hxεε+ Y. (2) 33B pp12 Y2 (hεp + xpε1) · 2 Considering, thickness h of a thin electret wall of the bubble (electret ‘shell’) filled with gas (air) Considering, thickness h of a thin electret wall of the bubble (electret ‘shell’) filled with gas (air) and satisfies the relation h << x2 and xp ≈ x2, Equation (2) can be rewritten as: and satisfies the relation h << x2 and xp x2, Equation (2) can be rewritten as: ≈ ε 2'qhsp 1 ≅⋅2q0εph d33B s 1 . (3) d33B ε xY. (3) ε1x122 · Y2 2

TheThe equivalent equivalent Young’s Young’s modulus, YY22 (for(for the the B-layer), B-layer), is is determined determined by by the the elasticity elasticity of of the the elastomerelastomer ringring (around(around the the bubble) bubble) and and was was determined determined using theusing model the shownmodel inshown Figure 3in. AssumingFigure 3. Assumingthat the B-layer that the strain B-layer is the strain same asis thethe strainsame ofas thethe elastomer strain of ringthe elastomer (Figure3b), ring and (Figure if Hook’s 3b), law and is inif Hook’spower, thelaw equivalentis in power, Young’s the equivalent modulus Young’sY2 is given modulus as: Y2 is given as: S = S1 1 YYY2 = Ye ,, (4) (4) 2 e SS wherewhere YYe eis isthe the Young’s Young’s modulus modulus of an ofelastomer, an elastomer, S1—surfaceS1—surface area of the area elastomer of the ring, elastomer and S = ring,S1 + Sand2—totalS = S surface1 + S2—total of the surfacelayer. of the layer.

FigureFigure 3. DeformationDeformation of of a) (a )plain plain elastomer elastomer layer layer and and b) (b )elastomer-ring, elastomer-ring, un underder external external stress stress FF, , wherewhere x isis thethe thicknessthickness of of both both layers, layers,Y eY—Young’se—Young’s modulus modulus of theof the plain plain elastomer elastomer layer layer with with the areathe areaS, Y2 S—e, Yﬀ2—effectiveective Young’s Young’s modulus modulus of the of elastomer the elastomer ring withring with the area the Sarea1. S1.

ConsideringConsidering the the charge charge stored stored on on the the inner inner surface surface of of the bubbles only (on the area ( S2)))) and and substitutingsubstituting Equation Equation (4) (4) into into Eq Equationuation (3) one can finally finally obtain: 2qsεph S2 1 d33B ε . (5) 2εqh1spx2 · SS1 · Ye1 d ≅⋅⋅2 . (5) 33B ε  The d33 coefficient measured on the electrodes12xSY for the 1 structuree as shown in Figure2 is reduced by the capacitances of A-layers (elastomer layers with thickness x1). The phenomenon can be described by The d33 coefficient measured on the electrodes for the structure as shown in Figure 2 is reduced the capacitive model shown in Figure4. Assuming S1 << S2, the capacitance Ce << Cb, where Ce is the by the capacitances of A-layers (elastomer layers with thickness x1). The phenomenon can be capacitance of the elastomer part, and Cb is the capacitance of the bubble (see Figure2). Hence, ignoring described by the capacitive model shown in Figure 4. Assuming S1 << S2, the capacitance Ce << Cb, the edge effects, the total capacitance of the B-layer (CB) is approximately equal to the capacitance of where Ce is the capacitance of the elastomer part, and Cb is the capacitance of the bubble (see Figure bubble Cb. The model allows to determine the d33 coefficient from the simplified relation: 2). Hence, ignoring the edge effects, the total capacitance of the B-layer (CB) is approximately equal to the capacitance of bubble Cb. The model allows to determineCA the d33 coefficient from the simplified d33 d33B , (6) relation: CA + CB where CA is the capacitance of both A-layers (in series) and CB is the capacitance of layer B. C dd≅ A , 33 33B + (6) CCAB where CA is the capacitance of both A-layers (in series) and CB is the capacitance of layer B.

Energies 2020, 13, x FOR PEER REVIEW 5 of 11

Energies 2020, 13, 2884 5 of 11 Energies 2020, 13, x FOR PEER REVIEW 5 of 11

Figure 4. Capacitance model of a layered dielectric structure, where CA is a parallel capacitance of

both A-layers, Ce is the capacitance of the elastomer ring, Cb is the capacitance of the bubble and CB is the capacitance of the whole B-layer.

Assuming that S1 << S, (or CB ≈ Cb), the final value for the d33 coefficient can be determined from Figure 4.4. CapacitanceCapacitance modelmodel of of a a layered layered dielectric dielectric structure, structure, where whereCA isCA a is parallel a parallel capacitance capacitance of both of the following relation: A-layers,both A-layers,Ce is C thee is capacitance the capacitance of the of elastomer the elastomer ring, ring,Cb is C theb is capacitance the capacitance of the of bubblethe bubble and andCB is C theB is capacitancethe capacitance of the of wholethe whole B-layer. B-layer. ≅⋅ 1 Assuming that S11 << S, (or CBB Cddbb), the final value for the d,3333 coefficient can be determined from Assuming that S << S, (or C ≈ C ),33 the final 33B value for theε d coefficient can be determined from ≈ x (7) the following relation: 12+⋅1 p 1x ε d33 d33B 2 ε ,e (7) · 1 + 2 x1 p x2 · εe where εp and εe are the electric permittivity of the gas and1 elastomer, respectively. According to ≅⋅ where εp and εe are the electric permittivitydd33 33 ofB the gas and elastomer,, respectively. According to Equation (7), when the thicknesses of layers A and B satisfy theε relation x1 << x2, the d33 coefficient is x1 p (7) Equation (7), when the thicknesses of layers A and12 B+⋅ satisfy the relation x1 << x2, the d33 coefficient is not practically reduced by capacitance CA of elastomer layer A.ε not practically reduced by capacitance CA of elastomer layerx2 A.e 3. Materials and Methods 3.where Materials εp and and εe Methodsare the electric permittivity of the gas and elastomer, respectively. According to Equation (7), when the thicknesses of layers A and B satisfy the relation x1 << x2, the d33 coefficient is 3.1. Sample Preparation 3.1.not practically Sample Preparation reduced by capacitance CA of elastomer layer A. TheThe electret electret bubbles bubbles were were thermoformed thermoformed from from a apolytetrafluoroethylene polytetrafluoroethylene (PTFE) (PTFE) electret electret tube. tube. 3. Materials and Methods TheThe PTFE PTFE polymer polymer was was chosen chosen due due to to its its good good charge charge and and thermal thermal stability stability [33]. [33]. The The tube tube with with inner inner   andand outer outer diameters diameters of 500500 ± 6060 m and m and 1200 1200200 ± m,200 respectively, m, respectively was flattened, was flattened and then and welded then at 3.1. Sample Preparation ± ± weldedequal intervals, at equal intervals, 4.5 0.3 mm.4.5 ± 0.3 The mm. electret The wallelectr thicknesset wall thickness after flattening after flattening was 200 was20 200µm, ± 20 and µm, the ± ± andheight theThe ofheight theelectret air of gapthe bubbles air was gap equalwere was to thermoformedequal 100 to20 100µm ± (see20from µm Figure a(see polytetrafluoroethylene 5Figurec,d). 5c, d). (PTFE) electret tube. ± ® TheThe PTFEThe pillow-shaped pillow-shapedpolymer was electretchosen electret duebubbles bubbles to its weregood were immersedcharge immersed and into thermal intoan elastomer—Gumosil anstability elastomer—Gumosil [33]. The tube AD-1. with® AD-1.innerThe prepared samples were dried for 24 hours in the air, at a temperature of 25 °C and humidity of RH = Theand preparedouter diameters samples of were 500 dried± 60 for m 24 and hours 1200 in the± 200 air, at m, a temperaturerespectively, of was 25 ◦flattenedC and humidity and then of 45%.RHwelded =The45%. at samples equal The samples intervals, with irregular with 4.5 irregular ± 0.3 (see mm. Figure (see The Figure 5a)electr 5anda)et and wallregular regular thickness (Figure (Figure after 5b)5b) flatteningbubble bubble distributions distributions was 200 ± 20 were were µm, prepared.prepared.and the height Finally, of the thethe air samples samples gap was were equalwere covered tocovered 100 by ± self-adhesive20 by µm self-adhesive (see Figure copper 5c, electrodes.copper d). electrodes. The final dimensionsThe final dimensionsof theThe bubbles–elastomer pillow-shaped of the bubbles–elastomer electret composite bubbles sample composite were were immersed sa equalmple towere into 20 equalan20 elastomer—Gumosil 2to mm 20 and× 20 the× 2 9 mm bubbles,® andAD-1. withthe The 9 a bubbles, with a total surface2 S2 = 90 mm2, were immersed in parallel.3.2.× × Sample charging totalprepared surface samplesS2 = 90 were mm dried, were for immersed 24 hours in parallel.the air, at a temperature of 25 °C and humidity of RH = 45%. The samples with irregular (see Figure 5a) and regular (Figure 5b) bubble distributions were prepared. Finally, the samples were covered by self-adhesive copper electrodes. The final dimensions of the bubbles–elastomer composite sample were equal to 20 × 20 × 2 mm and the 9 bubbles, with a total surface S2 = 90 mm2, were immersed in parallel.3.2. Sample charging

Figure 5. Electret-elastomer transducer: (a) electret pillow-shaped bubbles immersed in an elastomer Figure 5. Electret-elastomer transducer: (a) electret pillow-shaped bubbles immersed in an elastomer (irregular bubbles distribution), (b) cross-section of the whole sample (regular bubbles distribution), (irregular bubbles distribution), (b) cross-section of the whole sample (regular bubbles distribution), (c) cross-section perpendicularly to the bubble’s axis, and (d) back view of a pillow-shaped bubble. (c) cross-section perpendicularly to the bubble’s axis, and (d) back view of a pillow-shaped bubble.

Figure 5. Electret-elastomer transducer: (a) electret pillow-shaped bubbles immersed in an elastomer (irregular bubbles distribution), (b) cross-section of the whole sample (regular bubbles distribution), (c) cross-section perpendicularly to the bubble’s axis, and (d) back view of a pillow-shaped bubble.

Energies 2020, 13, 2884 6 of 11

Energies 2020, 13, x FOR PEER REVIEW 6 of 11 3.2. Sample Charging Energies 2020, 13, x FOR PEER REVIEW 6 of 11 Bi-polar charge distribution along the inner surfaces of bubbles were obtained using the Bi-polar charge distribution along the inner surfaces of bubbles were obtained using the corona-chargingBi-polar charge process distribution (Figure 6).along The highthe innervoltag surfacese needle electrodeof bubbles (1) werewas mounted obtained in using a distance the corona-charging process (Figure6). The high voltage needle electrode (1) was mounted in a distance of corona-chargingof 15 mm above processthe non-metalized (Figure 6). Theside high of a samplevoltage (2).needle The electrodesample was (1) placedwas mounted on a grounded in a distance metal 15 mm above the non-metalized side of a sample (2). The sample was placed on a grounded metal oftable 15 mm (3). aboveCorona the discharge non-metalized was carried side of out a sample under conditions:(2). The sample DC polarizationwas placed onvoltage a grounded Upol = +10 metal kV, tablepolarization (3). Corona time discharge tpol = 30 was s. A carriedTREK model out under 610E was conditions: used as the DC high polarization voltage DC voltage power supplyU = (4). +10 kV, table (3). Corona discharge was carried out under conditions: DC polarization voltage Upol = +10pol kV, polarizationpolarization time timetpol tpol= =30 30 s. s. AA TREK model model 610E 610E was was used used as the as thehigh high voltage voltage DC power DC power supply supply (4). (4).

FigureFigure 6. An 6. arrangementAn arrangement for for corona-charging corona-charging ofof samples,samples, where where 1—needle 1—needle electrode, electrode, 2—sample, 2—sample, 3—groundedFigure3—grounded 6. An table, arrangement table, and and 4—high 4—high for corona-charging voltage voltage power power supply. ofsupply. samp les, where 1—needle electrode, 2—sample, 3—grounded table, and 4—high voltage power supply. 3.3. Static3.3. Static Piezoelectric Piezoelectri Coec Coefficientﬃcient Measurement Measurement 3.3. Static Piezoelectric Coefficient Measurement MeasurementsMeasurements of theof the piezoelectric piezoelectric coefficient coefficient dd3333 werewere performed performed byby appl applyingying the thequasi-static quasi-static method [3,34]. The prepared arrangement is illustrated in Figure 7. The prepared sample (1) was method [Measurements3,34]. The prepared of the arrangementpiezoelectric coefficient is illustrated d33 were in Figure performed7. The by prepared applying sample the quasi-static (1) was placed betweenmethodplaced the between[3,34]. isolated The the rigid prepared isolated measuring rigidarrangement measuring electrode is electr (2)illust andratedode grounded, (2) in and Figure grounded, movable 7. The movableprepared electrode electrode sample (3) fixed (1)(3) towasfixed the pan (4). Theplacedto the cylindrical betweenpan (4). Thethe electrode isolated cylindrical with rigid electrode a measuring diameter with electr equal a diameterode to 20(2) mmand equal grounded, and to was20 mm applied. movable and was Voltageelectrode applied. measurements (3) Voltage fixed measurements were carried out using the electrometer (5) RFT-6302 with an attached measurement wereto carried the pan out (4). using The cylindrical the electrometer electrode (5) with RFT-6302 a diameter with equal an attached to 20 mm measurement and was applied. capacitor Voltage 1.5 nF (6). capacitor 1.5 nF (6). The total capacity of the voltage measurement system (including measurement The totalmeasurements capacity ofwere the carried voltage out measurement using the electrom systemeter (including (5) RFT-6302 measurement with an attached capacitor, measurement the cable and capacitorcapacitor, 1.5 the nF cable (6). Theand totalvoltmeter capacity input of capacithe voltagetances measurement and sample capacitance) system (including was equal measurement to CT = 1.65 voltmeternF. For input shielding capacitances from external and electric sample fields, capacitance) the whole was system equal was to placedCT = 1.65in a grounded nF. For shielding Faraday’s from capacitor, the cable and voltmeter input capacitances and sample capacitance) was equal to CT = 1.65 external electric fields, the whole system was placed in a grounded Faraday’s cage (7) The controlled nF.cage For (7) shielding The controlled from external stress was electric applied fields, to thethe sampleswhole system using wasthe weightsplaced in (8) a placedgrounded on theFaraday’s pan (4). stresscageMass was (7) appliedof The the controlled weights to the samples stresswas determined was using applied the using to weights the a samples quar (8)tz placed usingscale. the onThe theweights total pan mass (8) (4). placed Massof the on of movable the pan weights (4).part was determinedMasscontaining of usingthe the weights a electrode quartz was scale. (4) determined was The 134 total g. using mass ofa thequar movabletz scale. partThe containingtotal mass theof the electrode movable (4) part was 134 g. containing the electrode (4) was 134 g.

Figure 7. An arrangement for measuring the piezoelectric coeﬃcient d33 using a static method, where 1—sample, 2—isolated measuring electrode, 3—grounded electrode, 4—pan, 5—total capacitance CT, 6—electrometer, 7—Faraday’s cage, and 8—load. Energies 2020, 13, x FOR PEER REVIEW 7 of 11

Figure 7. An arrangement for measuring the piezoelectric coefficient d33 using a static method, where 1—sample, 2—isolated measuring electrode, 3—grounded electrode, 4—pan, 5—total capacitance CT, 6—electrometer, 7—Faraday’s cage, and 8—load.

Energies 2020, 13, 2884 7 of 11 The d33 coefficient was calculated using the relation: Δ⋅UC = T The d coeﬃcient was calculated using thed33 relation: , (8) 33 Δ⋅mg

∆U CT where CT = 1.65 nF is the total capacitance dof the= voltage· ,measuring system, ΔU is the voltage change (8) 33 ∆m g measured after application of the known stress (static· force) within time tm << τMe, Δm is the mass of the load, and g is the gravitational acceleration (9.81 m/s2). where CT = 1.65 nF is the total capacitance of the voltage measuring system, ∆U is the voltage change Assuming that the d33 measurement, using the described method, is carried out within time tm measured after application of the known stress (static force) within time tm << τMe, ∆m is the mass of τ the(equal load, to and a fewg is seconds) the gravitational and relation acceleration tm << Me, (9.81is satisfied, m/s2). the transient effects (in elastomer) should not affect the measured d33 value. Assuming that the d33 measurement, using the described method, is carried out within time tm (equal to a few seconds) and relation tm << τMe, is satisfied, the transient effects (in elastomer) should 4. Results not affect the measured d33 value.

4.4.1. Results Properties of Applied Materials The properties of the elastomer were examined using a 500 µm thick homogeneous sample. 4.1. Properties of Applied Materials After polymerization, the charge decay characteristic, electric permittivity εe and Young’s modulus wereThe determined. properties Approached of the elastomer value were of examinedMaxwell-time using constant a 500 µ mτMe thick was homogeneousdetermined from sample. the Afterequivalent polymerization, voltage Uz( thet) decay charge characteristic decay characteristic, (see Figure electric 6). The permittivity time te determinedεe and Young’s for |Uz/ modulusUz0| = 1/e werewas determined.assumed in Approachedthe first approximation value of Maxwell-time to be equal constant to τMeτ,Me wherewas determined Uz0 is the frominitial the value equivalent of the voltageequivalentUz(t )voltage decay characteristicjust after corona (see charging Figure6). [35]. The timeAccordingte determined to Figure for 8,|U thez/U timez0| = t1e /≈e wasτMe is assumed equal to inτMe the ≈ 100 ﬁrst ± approximation 10 s. to be equal to τMe, where Uz0 is the initial value of the equivalent voltage just after corona charging [35]. According to Figure8, the time te τ is equal to τ 100 10 s. ≈ Me Me ≈ ± |

z0 1.2 U / z

U 1.0

0.8

0.6

0.4

0.2

0.0

Relative quivalent voltage | voltage quivalent Relative 0 20 40 60 80 100 120 140 160 180 200 Time, s

Figure 8. An experimental charge decay for a 500-µm-thick Gumosil® layer. Figure 8. An experimental charge decay for a 500-µm-thick Gumosil® layer. The measured relative electric permittivity εe of elastomer was on the level 3.29–3.37 (20–50,000 Hz), so theThe value measuredεe = 3.3 relative (measured electric for 1 permittivity kHz) was assumed εe of elastomer for thecalculations. was on the level 3.29–3.37 (20–50,000 Hz),The so the Young’s value modulusεe = 3.3 (measured of elastomer for 1Y kHz)e was wa measureds assumed using for the calculations. setup presented in [29]. As the Young’sThe modulus Young’s of modulus elastomers of elastomer is pressure-dependent Ye was measured and usually using the non-linear setup presented [36], pressure in [29].p applied As the inYoung’s Young’s modulus modulus measurementsof elastomers wereis pressure-dependent the same as in piezoelectric and usually coeﬃ cientnon-linear measurements. [36], pressure Finally, p theapplied value ofin YeYoung’s= 86–98 kPamodulus was measured measurements (for pressure werep inthe a rangesame betweenas in 3.1piezoelectric and 8.7 kPa). coefficient Finally, Ymeasurements.e = 90 kPa was assumedFinally, the for value the calculations. of Ye = 86–98 kPa was measured (for pressure p in a range between 3.1 and 8.7 kPa). Finally, Ye = 90 kPa was assumed for the calculations. 4.2. Measurements and Calculations of d33 Coeﬃcient 4.2. Measurements and calculations of d33 coefficient Calculations of the d33B and d33 values were carried out using Equations (5) and (7), considering 4 the following data: Young’s modulus of an elastomer Ye = 9.0 10 Pa, electric relative permittivity · of an elastomer εe = 3.3 (measured at 1 kHz); the ratio (S /S ) = 0.3, thickness: h = 200 20 µm, 2 1 ± x = 750 20 µm, x = 500 20 µm (determined from observation of the bubble cross-sections under 1 ± 2 ± optical microscope). Energies 2020, 13, x FOR PEER REVIEW 8 of 11

Calculations of the d33B and d33 values were carried out using Equations (5) and (7), considering the following data: Young’s modulus of an elastomer Ye = 9.0·104 Pa, electric relative permittivity of an elastomer εe = 3.3 (measured at 1 kHz); the ratio (S2/S1) = 0.3, thickness: h = 200 ± 20 µm, x1 = 750 ± 20 µm, x2 = 500 ± 20 µm (determined from observation of the bubble cross-sections under optical microscope). Energies 2020, 13, 2884 8 of 11 The approached value of maximum surface charge density qsMAX possible to store in the inner parts of the bubble was determined using the relation [37]:

The approached value of maximum surface charge density qsMAX possible to store in the inner xp parts of the bubble was determined usingqE the relation=+εε [37 ε]: (9) sMAX01 p k 2h xp qsMAX = ε0 εp + ε1 Ek (9) where critical electric field Ek = 8.6 MV/m was calculated2h using Paschen’s law for the air gap thickness xp =100 µm. The calculated value of the qsMAX is on the level of 114 µC/m2. Results of where critical electric field Ek = 8.6 MV/m was calculated using Paschen’s law for the air gap thickness experiments have shown [29,37], that the real surface charge density q2s of the charge stored along the xp =100 µm. The calculated value of the qsMAX is on the level of 114 µC/m . Results of experiments have surface of the gas void is smaller than the value estimated using Equation (9). So finally for the d33 shown [29,37], that the real surface charge density qs of the charge stored along the surface of the gas calculations the value qs = 50 µC/m2 was assumed (according to [29]). Using the above data, the void is smaller than the value estimated using Equation (9). So finally for the d33 calculations the value values of d33B2 = 69 pC/N and d33 = 36 pC/N were finally determined using Equations (5) and (7). qs = 50 µC/m was assumed (according to [29]). Using the above data, the values of d33B = 69 pC/N For validation of the presented model, the measurements of the d33 coefficient were carried out and d33 = 36 pC/N were finally determined using Equations (5) and (7). on the described structures. Results obtained for freshly charged structure and structures stored in For validation of the presented model, the measurements of the d33 coefficient were carried out on thethe described air in temperature structures. of Results 25 °C obtainedand humidity for freshly RH = charged45% are structurepresented and in Figure structures 9. stored in the air in temperature of 25 ◦C and humidity RH = 45% are presented in Figure9.

30 pC/N , 25 33 d 20

10 15 min after charging 5 1 h after charging

Piezoelectric coefficient coefficient Piezoelectric 0 0 5 10 15 20 25 Pressure, kPa

Figure 9. The pressure dependence of static piezoelectric coeﬃcient d33 for an exemplary sample.

Figure 9. The pressure dependence of static piezoelectric coefficient d33 for an exemplary sample. The first measurement of d33 coefficient was carried out 900 s after the structure polarization, so the charges stored in an elastomer should not have been present (τMe 100 10 s), and only the The first measurement of d33 coefficient was carried out 900 s after the≈ structure± polarization, so charges deposited on the inner surfaces of bubbles were supposed to be responsible for the observed the charges stored in an elastomer should not have been present (τMe ≈ 100 ± 10 s), and only the quasi-piezoelectriccharges deposited phenomenonon the inner surf Theaces measured of bubbles static wered33 supposedcoefficient to is be in responsible the range offor 15–25 the observed pC/N, and it is almost constant in a pressure range between 2–24 kPa in contrast to ferroelectrets with open quasi-piezoelectric phenomenon The measured static d33 coefficient is in the range of 15–25 pC/N, voids,and it where is almostd33 isconstant decreasing in a withpressure applied range pressure between [37 2–24]. According kPa in cont torast the to fact ferroelectrets that charge with decay open of PTFE shows that the highest decrease of charge is observed in the first moments after charging [29,31], voids, where d33 is decreasing with applied pressure [37]. According to the fact that charge decay of thePTFE same shows results that may the behighest apparent decrease in the ofd 33chargerelation is observed due to time in the after first charging. moments As after is presented charging [29] in Figure9, the d coefficient decreases in time—lower values of d were obtained 1 h after charging in [31], the same33 results may be apparent in the d33 relation due 33to time after charging. As is presented comparison to values obtained 15 minutes after charging in the pressure range 8–24 kPa. in Figure 9, the d33 coefficient decreases in time—lower values of d33 were obtained 1 h after charging in comparisonThe first measurement to values obtained of d33 coe15 ffiminutescient was after carried charging out in 900 the s pressure after the range structure 8–24 polarization, kPa. so the charges stored in an elastomer should not have been present (τ 100 10 s), and only the The first measurement of d33 coefficient was carried out 900 s afterMe the≈ structure± polarization, so charges deposited on the inner surfaces of bubbles were supposed to be responsible for the observed the charges stored in an elastomer should not have been present (τMe ≈ 100 ± 10 s), and only the quasi-piezoelectric phenomenon. The dynamic piezoelectric coefficient measurements were also performed 3 hours after charging, using PM200 PiezoMeter System with a flat electrode with a diameter of 10 mm. The applied static force was Fstat = 10.5 0.1 N (corresponding to pressure p = 134 2 kPa), dynamic force F = 0.25 N, ± ± dyn measuring frequency f m = 110 Hz (parameters recommended by the producer). The measured dynamic coefficient d = 16.8 2.0 pC/N. 33d ± Energies 2020, 13, 2884 9 of 11

5. Discussion The simplified model describing the piezoelectric properties of the charged electret bubble-elastomer composite was presented in the paper. The presence of piezoelectric phenomena was confirmed experimentally for the exemplary structure. The obtained results illustrate the technological possibilities in obtaining the structures, where the mechanical properties and the geometrical stability of the whole structure are determined mainly by the elasticity of an elastomer—not by the elasticity of the electret material. The presence of upper and lower elastomer layers, with x1 thickness, always reduce the d33 coefficient, and that case was considered for a technological requirement only (see Figure5b). Thus, Equations (6) and (7) describe the worst situation ( x1 > 0) from the point of view of the d33 coefficient value. Moreover, Equations (4), (5) and (7) describe possibilities of obtaining composites with required d33 coefficient and the mechanical stiffness of the whole structure. Hence, it widens the range of technological applications for piezo-active composites. d33 values obtained from calculations (36 pC/N) were higher in comparison to those measured (15–25 pC/N). The difference may result from the assumption h << x2, which was not fulfilled in the experiment. Higher thickness of the bubble wall h leads directly to an increase of the value of effective Young’s modulus for the layer B and finally to a decrease d33 value. The differences in measured and calculated values of d33 may also result from the higher value of surface charge density qs assumed for calculation in comparison to the average charge density obtained (on the inner parts of the bubbles) experimentally. According to the presented model, the constructions of the piezo-active bubble electret-elastomer composites with higher piezoelectric coefficient d33 are possible to obtain. Using bubbles with smaller wall thickness h, reduction of A-layers during the processing of a composite or application of elastomer with lower Young’s modulus may lead to achieving transducers with higher piezoelectric coefficients, where the mechanical properties will be characterized by elastomer material. According to low Young’s modulus of elastomers, the acoustic impedance of presented composites might also be an interesting issue for further research. The further investigation and analysis of the charge storage properties of electret bubbles (charge density, surface distribution and influence of charging conditions) are recommended.

Author Contributions: Conceptualization, R.K.; methodology, R.K. and A.M.; validation, A.M.; formal analysis, R.K. and A.M.; investigation, A.M. and R.K.; resources, A.M. and R.K..; data curation, R.K. and A.M.; writing—original draft preparation, A.M..; writing—review and editing, R.K. and A.M.; visualization, R.K. and A.M.; supervision, R.K. and A.M.; project administration, R.K. and A.M.; funding acquisition, A.M. and R.K. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. This work was financed by a statutory activity subsidy from the Polish Ministry of Science and Higher Education (PMSHE) for the Department of Electrical Engineering Fundamentals of Wroclaw University of Science and Technology. Conflicts of Interest: The authors declare no competing financial interest. Patents: Kacprzyk R., Grygorcewicz A., Materiał kompozytowy o wła´sciwo´sciachpiezoelektrycznych, Eng. Composite material with piezoelectric properties, P422861, 14 April 2020.

References

1. Priya, S.; Song, H.; Zhou, Y.; Varghese, R.; Chopra, A.; Kim, S.; Kanno, I.; Wu, L.; Ha, D.S.; Ryu, J.; et al. A Review on Piezoelectric Energy Harvesting: Materials, Methods, and Circuits. Energy Harvest. Syst. 2017, 4, 3–39. [CrossRef] 2. Elahi, H.; Eugeni, M.; Gaudenzi, P. A Review on Mechanisms for Piezoelectric-Based Energy Harvesters. Energies 2018, 11, 1850. [CrossRef] 3. Hillenbrand, J.; Sessler, G.M. Quasistatic and Dynamic Piezoelectric Coeﬃcients of Polymer Foams and Polymer Film Systems. IEEE Trans. Dielectr. Electr. Insul. 2004, 11, 72–79. [CrossRef] 4. Gamboa, B.; Bhalla, A.; Guo, R. Assessment of PZT (Soft/Hard) Composites for Energy Harvesting Assessment of PZT (Soft/Hard) Composites. Ferroelectrics 2020, 555, 118–123. [CrossRef] Energies 2020, 13, 2884 10 of 11

5. Usher, D.T.; Cousins, K.R.; Zhang, R.; Ducharme, S. The promise of piezoelectric polymers. Polym. Int. 2018, 67, 790–798. [CrossRef] 6. Yoon, C.; Jeon, B.; Yoon, G. A Feasibility Study of Fabrication of Piezoelectric Energy Harvesters on Commercially Available Aluminium Foil. Energies 2019, 12, 2797. [CrossRef] 7. Novak, N.; Keil, P.; Froemling, T.; Schader, F.; Martin, A.; Webber, K.; Roedel, J. Influence of metal/semiconductor interface on attainable piezoelectric and energy harvesting properties of ZnO. Acta Mater. 2019, 162, 277–283. [CrossRef] 8. Zheng, T.; Wu, J.; Xiao, D.; Zhu, J. Giant d33 in nonstoichiometric (K,Na)NbO3-based lead-free ceramics. Scr. Mater. 2015, 94, 25–27. [CrossRef] 9. Hayakawa, R.; Wada, Y. Piezoelectricity and related properties of polymer films. In Fortschritte der Hochpolym; Springer: Berlin/Heidelberg, Germany, 1973; pp. 1–55. 10. Brown, E.N.; Rae, E.B.; Orler, G.T.; Gray, D.; Dattelbaum, M. The effect of crystallinity on the fracture of polytetrafluoroethylene (PTFE). Mater. Sci. Eng. 2006, 26, 1338–1343. [CrossRef] 11. Sessler, G.; Hillenbrand, J. Electromechanical response of cellular electret films. Appl. Phys. Lett. 1999, 75, 3405–3407. [CrossRef] 12. Kacprzyk, R.; Motyl, E.; Gajewski, J.B.; Pasternak, A. Piezoelectric properties of nonuniform electrets. J. Electrostat. 1995, 35, 161–166. [CrossRef] 13. Hennion, C.; Lewiner, J. A new principle for the design of condenser electret transducers. J. Acoust. Soc. Am. 1978, 63, 1229–1231. [CrossRef] 14. Palitó, T.T.C.; Assagra, Y.A.O.; Altafim, R.A.P.; Carmo, J.P.; Altafim, R.A.C. Hydrophone based on 3D printed polypropylene (PP) piezoelectret. Electron. Lett. 2019, 55, 203–204. [CrossRef] 15. Mohebbi, A.; Mighri, F.; Ajji, A.; Rodrigue, D. Cellular Polymer Ferroelectret: A Review on Their Development and Their Piezoelectric Properties. Adv. Polym. Technol. 2016, 1–16. [CrossRef] 16. Paajanen, M.; Lekkala, J.; Kirjavainen, K. ElectroMechanical Film (EMFi)—A new multipurpose electret material. Sens. Actuators A Phys. 2000, 84, 95–102. [CrossRef] 17. Xue, Y.; Zhang, X. Comparative Study of Transducers for Air-borne Sound based on Normal and Irradiation Cross-linked Polypropylene Piezoelectret Films. IEEE Trans. Dielectr. Electr. Insul. 2018, 25, 228–234. [CrossRef] 18. Xue, Y.; Zhang, X. Air-coupled Ultrasonic Transducers based on Laminated Fluorinated Ethylene Propylene and Porous Polytetrafluoroethylene Ferroelectrets. IEEE Trans. Dielectr. Electr. Insul. 2017, 25, 808–815. [CrossRef] 19. Zeng, H.; Liu, Z.Z.; De Medeiros, L.J.; Kamimura, H.A.S. Optimizing dimensions of unipolar Teflon-FEP piezoelectrets with micro-system-technology. J. Phys. Conf. Ser. 2018, 1052, 1–4. [CrossRef] 20. Zúñiga, V.T.; Carmona, S.G.; Saavedra, O.G.M. Electromechanical characterization of didactical piezoelectric sensors based on crystalline grade PET Electromechanical characterization of didactical piezoelectric sensors based on crystalline grade PET. J. Phys. Conf. Ser. 2019, 1221, 1–6. [CrossRef] 21. Fang, P.; Wirges, W.; Wegener, M.; Zirkel, L.; Gerhard, R. Cellular polyethylene-naphthalate films for ferroelectret applications: Foaming, inflation and stretching, assessment of electromechanically relevant structural features. e-Polymers 2008, 8.[CrossRef] 22. Li, W.; Duan, J.; Zhong, J.; Wu, N.; Lin, S.; Xu, Z.; Chen, S.; Pan, Y.; Huang, L.; Hu, B.; et al. Flexible THV/COC Piezoelectret Nanogenerator for Wide-Range Pressure Sensing. ACS Appl. Mater. Interfaces 2018, 10, 29675–29683. [CrossRef] 23. Gerhard-Multhaupt, R. Less can be more. IEEE Trans. Dielectr. Electr. Insul. 2002, 9, 850–859. [CrossRef] 24. Zhang, X.; Wu, L.; Sessler, G.M. Energy harvesting from vibration with cross-linked polypropylene piezoelectrets. AIP Adv. 2015, 5.[CrossRef] 25. Zhang, X.; Sessler, G.M.; Wang, Y. Fluoroethylenepropylene ferroelectret films with cross-tunnel structure for piezoelectric transducers and micro energy harvesters. J. Appl. Phys. 2014, 116, 074109. [CrossRef] 26. Fang, P.; Zhuo, Q.; Cai, Y.; Tian, L.; Zhang, H.; Zheng, Y.; Li, G.; Wu, L.; Zhang, X. Piezoelectrets for wearable energy harvesters and sensors. Nano Energy 2019, 65, 104033. [CrossRef] 27. Zhang, Y.; Bowen, C.R.; Ghosh, S.K.; Mandal, D.; Khanbareh, H.; Arafa, M.; Wan, C. Ferroelectret materials and devices for energy harvesting applications. Nano Energy 2019, 57, 118–140. [CrossRef] 28. Kayaharman, M.; Das, T.; Seviora, G.; Saritas, R.; Abdel-rahman, E.; Yavuz, M. Long-Term Stability of Ferroelectret Energy Harvesters. Materials 2019, 13, 42. [CrossRef] Energies 2020, 13, 2884 11 of 11

29. Kacprzyk, R.; Mirkowska, A. Piezo-tubes. IEEE Trans. Dielectr. Electr. Insul. 2018, 25, 759–765. [CrossRef] 30. Altafim, R.A.P.; Qiu, X.; Wirges, W.; Gerhard, R.; Altafim, R.A.C.; Basso, H.C.; Jenninger, W.; Wagner, J. Template-based fluoroethylenepropylene piezoelectrets with tubular channels for transducer applications. J. Appl. Phys. 2009, 106, 014106. [CrossRef] 31. Rychkov, D.; Yablokov, M.; Rychkov, A. Chemical and physical surface modification of PTFE films-an approach to produce stable electrets. Appl. Phys. A Mater. Sci. Process. 2012, 107, 589–596. [CrossRef] 32. Bovtun, V.; Döring, J.; Wegener, M.; Bartusch, J.; Beck, U.; Erhard, A.; Borisov, V. Air-coupled ultrasonic applications of ferroelectrets. Ferroelectrics 2008, 370, 11–17. [CrossRef] 33. Zhang, X.; Hillenbrand, J.; Sessler, G.M. Thermally stable fluorocarbon ferroelectrets with high piezoelectric coefficient. Appl. Phys. A Mater. Sci. Process. 2006, 84, 139–142. [CrossRef] 34. Fialka, J.; Beneš, P. Comparison of Methods of Piezoelectric Coefficient Measurement. In Proceedings of the 2012 IEEE International Instrumentation and Measurement Technology Conference Proceedings, Graz, Austria, 13–16 May 2012; pp. 37–42. [CrossRef] 35. Kacprzyk, R. Influence of discharge conditions on the charge decay characteristics. J. Electrostat. 2010, 68, 190–195. [CrossRef] 36. Bednarz, J. The New Methodology for Assessing of the Applicability of Elastomeric Materials in the Vibration Isolation Systems of Railway Lines. Arch. Acoust. 2016, 41, 573–578. [CrossRef] 37. Zhukov, S.; Eder-Goy, D.; Fedosov, S.; Xu, B.-X.; von Seggern, H. Analytical prediction of the piezoelectric d33 response of fluoropolymer arrays with tubular air channels. Sci. Rep. 2018, 8, 1–10. [CrossRef]

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