Dielectric Elastomers - Carnegie Mellon University

uid dielectric 11 mild dielectric didnot notfail failatatThe 11kV kVwhile while mildwrinkles wrinkles 0 bath,did 0 ¼ V tbath, , accordturn, the true electric field is calculateduid as E sion. areal actuation strains increase at a decreasing rate in Fig. appeared on the dielectric film (see image in Fig.2(b)). 2(b)). filed. The areal actuation appeared on the DEA dielectricwith film respect (see image 8,9,14,24,25 ing to Ref.wrinkles 7. As the voltagethat wasindicate ramped up during to the applied electric the loss of in the preInterestingly, asastension driving went beyond 11 Interestingly, drivingvoltage voltage went beyondindependent 11kV, kV,the theoiloilactivation, leakage current was monitored continuously strains are almost of the increasing electric field stretched dielectric film. Such pull-in instability was also al view) showing the experimental setup, which immersed DEA continued to work even though the wrinkles nal view) showing the experimental setup, which immersed DEA continued to work even though the wrinkles using a digital multimeter (Agilent 34410A) and a NI data above 400 MV/m because the active dielectric film, which ely immersed while the observed in test samples. The(see DEA sample, etely immersedinina asilicone siliconeoil oilbath bathour while theof DEA atat15 kV) totosevere (see the turned from mild image 15 kV) severe (see the turned from mild (see image tage. logger photographs forinthe DEA cappre-stretched,actuators lost tension andin buckled into wrinkles that oltage. which was tested air,activated nearly failed atwere 11 kV and it was exhibVerywhile high dielectric strength for dielectric elastomer atat18 kV). image 18 kV). image tured using ited a digital camera.electrode shape and irregular-pitch wrinkles were accompanied primarily by thickness reduction but little 0 0 a distorted measured asassAsA¼dielectric while the Figure 2(b) actuation ofofthe asasaafunction measured ¼AA A A0 0""1,1,or while theinstability liquid immersion Figure 2(b)isshowed showed actuation theDEAs DEAs function on how wrinkles affect Electromechanical pull-in of DEAs often areal expansion. Similar observation A ). On 0 0 near the defective spot as shown in Fig. 2(a) (images calculated as t ¼ t ðs þ 1Þ, on the of the applied electric filed. A similar trend of actuation was 192905-2 T.-G. La and G.-K. Lau Appl. Phys. Lett. 102, 192905 (2013) pre A calculated as tand ¼ tG-K ðs þ 1Þ, on the of the applied electric filed.the A similar trend of actuation was elastomer pre A T-G La Lau APL 102in192905 (2013) accompanied by thinning down thickness and severe areal actuation of dielectric was previously the other hand, the DEA sample, which was tested in the liqelectric ielectricfilm filmthat thatisisincompressible. incompressible.InIn observed observedfor forboth bothsamples samplestested testedinineither eitherair airororoil oilimmerimmer0 0 bath, did not fail at 11 kV while mild wrinkles 8,9,14,24,25 uid dielectric eld isiscalculated increase rate wrinkles that indicate the loss of tension in the preV t,0 ,accordaccord- sion. field calculatedasasEE 0¼¼V t sion.The Theareal arealactuation actuationstrains strains increaseatataadecreasing decreasing rate in Fig. 2(b)). appeared on the dielectric film (see image voltage was ramped up during DEA with respect to the applied electric filed. The areal actuation dielectric film.actuation Such pull-in instability was also voltage was ramped up during DEA with respect to the appliedstretched electric filed. The areal Interestingly, as driving voltage went beyondindependent 11 kV, the of oil-the increasing electric field urrent was monitored continuously strains are almost current was monitored continuously observed in our test of DEA samples. The DEA sample, strains are almost independent of the increasing electric field al setup, which immersed DEA continued to work even though the wrinkles eter (Agilent 34410A) and a NI data above 400 MV/m because the active dielectric film, which meter (Agilent 34410A) and a NI data above 400 MV/m becausewhich the active dielectric film, which was tested in air, nearly failed at 11 kV and it exhibbath while the at 15 kV) tolost severe (seeand the buckled into wrinkles that turned fromwere mild (see image phs for pre-stretched, tension aphs forthe theactivated activatedDEA DEA werecapcap- was was pre-stretched, lost tension buckled electrode into wrinkles thatand irregular-pitch wrinkles ited and a distorted shape image at 18 kV). mera. were by reduction but little A ). On amera. wereaccompanied accompaniedprimarily primarily bythickness thickness reduction butshown little in Fig. 2(a) (images near the defective spot as 1,orwhile theinstabilityFigure 2(b) showed actuation of the DEAs as aobservation function on how wrinkles affect pull-in of DEAs is often areal expansion. Similar al or pull-in instability of DEAs is often areal expansion. Similar observation on how affectwhich was tested in the liqthe other hand, thewrinkles DEA sample, þ 1Þ, down on the in thickness of the applied electric filed. A areal similar trend of of actuation waselastomer was previously ning nning down in thickness and and severe severe the the areal actuation actuation of dielectric dielectric elastomer was previously uid dielectric bath, did not fail at 11 kV while mild wrinkles pressible. In observed for both samples tested in either air or J. Zhou et oil al. /immerInternational Journal of Solids and Structures 45 in (2008) Fig. 3739–3750 2(b)). appeared V t0 , accordsion. The areal actuation strains increase at a decreasing rate on the dielectric film (see image Interestingly, as driving voltage went beyond 11 kV, the oilduring DEA with respect to the applied electric filed. The areal actuation FIG. 1. A schematic (sectional view) showing the experimental setup, which immersed DEA continued to work even though the wrinkles ontinuously strains are almost independent of the increasing field aelectric has a DEA sample completely immersed in a silicone oil bath while the at 15 kV) to severe (see the from mild (see image FIG. 2. Electromechanical activation of d a DEA NI data above MV/m because the active dielectric film, turned which X is activated by high400 voltage. 1at 18 kV). image DEAs in either the air or the oil immersion: Top view Top view A were capwas pre-stretched, lost tension0 and buckled into wrinkles that (a) Photographs showing expant0 . The areal were strainaccompanied is measured primarily as sA ¼ Aby Athickness the Figure 2(b) showed actuation of the DEAselectrode as a function 0 " 1, while reduction but little sion for a DEA when tested in air. Wrinkles 0 Φ was X3 electric filed. is calculated as t observation ¼ tpre ðsA þon1Þ, on wrinkles the ofaffect the applied A similar trend of actuation EAsactivated is often thickness areal expansion. Similar how and sparks at spot were observed on dielecthat is incompressible. In previously observed for both samples in either air breaks or oildown immerX2 tric tested film when the DEA at andassumption severe the the arealdielectric actuationfilm of that dielectric elastomer was 0 0 kV (orincrease 450 MV/m). (b) Photographs turn, the true electric field is calculated as E ¼ V t , accordsion. The areal actuation11 strains at a decreasing rate showing electrode a DEA ing to Ref. 7. As the voltage was ramped up during DEA with respect to the applied electric filed. expansion The arealforactuation when tested in the silicone oil immersion. Zhou, Hong, Zhao, activation, leakage current was monitored continuously strains are almost independent the increasing electric Wrinklesof appear changing from mildfield to Zhang, Suo, using a digital multimeter (Agilent 34410A) and a NI data above 400 MV/m because the undulated active dielectric film, severely and sagging as thewhich drivFIG. 2. Electromechanical activation of FIG. Electromechanical activation of increases ing voltage kV to 45 18 kV, IJSS 3739-3750 logger while photographs for the activated DEA were cap- DEAs was 2.pre-stretched, lost tension and buckledfrom into11wrinkles that DEAsinineither eitherthe theair airororthe theoil oilimmersion: immersion: but the oil immersed DEA did not break tured using a digital camera. were accompanied primarily by thickness reduction but little (a) expan(2008) (a)Photographs Photographsshowing showingelectrode electrode expandown. (c) A graph showing areal strain of for DEA ininair. Wrinkles Electromechanical or pull-in instability of DEAs is often sion areal Similar observation on how wrinkles affect sion fora aexpansion. DEAwhen whentested tested air.the Wrinkles activated DEAs as a function of electric and sparks atatspot were observed on dielecand sparks spot were observed on dielecfield until breakdown. accompanied by thinning down in thickness and severe the areal actuation of dielectric elastomer was previously Electromechanical Instability (Pull-In) tric tric film film when when the the DEA DEA breaks breaks down down atat 11 kV (or 450 MV/m). (b) Photographs 11 kV (or 450 MV/m). (b) Photographs showing showing electrode electrode expansion expansion for for a a DEA DEA when tested in the silicone oil immersion. when tested in the silicone oil immersion. Section Wrinkles Wrinkles appear appear changing changing from from mild mild toto severely undulated and sagging as the driv-

chanically constrained to avoid any movement during tests. A Electromechanical Instability (Creasing) mping voltage was applied between the rod and the substrate til electrical breakdown occurred. The breakdown voltages Electro-creasing instability in deformed polymers: re recorded to calculate the breakdown electric fields.27 To experiment and theory oid extremely high voltage, a thinner VHB film (50 mm) was Q. Wang, M. Tahir, L. Zhang, X. Zhao Soft Matter 7 6583 (2011) ed for the breakdown test of un-stretched film (i.e. lp ¼ 1). Results and discussion itical electric field for the instability e measured critical voltages Fc for the electro-creasing tability in films with various thicknesses H and shear moduli Fig. 1 Schematic illustrations of the current experimental setup for Schematic illustrations of the current experimental setup for studying the electro-creasing instability (a), a pattern of electro-creases ng the electro-creasing instability (a), a pattern of electro-creases (b), the electric fields in the polymers (c), and a cross-section of the e electric fields in the polymers (c), and a cross-section of the creased film (d). d film (d). quantitatively matched with predictions from a theoretical itatively model. matched with predictions from a theoretical . Many polymers under voltages are also mechanically ny polymers under voltages are also mechanically deformed in applications. For example, insulating polymers . 2 Schematic illustrations of the current experimental setup for med in carry applications. For example, insulating components polymers usually mechanical loads from surrounding 27 thickne 150 150Stylu Sty Follo Follow glassslid sli glass factoro a afactor (DuPon (DuPont conduc conducti adhered adhered topsurfa sur spe top conduc film conducti the film An the film’s the solu" the solut 10 electrod electrode mo deform deforma control thi controlla the cop 150 the copp rate of F rate of electroelectro-c was gla rec

The voltage is also limited by electrical breakdown: Internal electric field is so large that bound charge carriers get energized and mobilized The charges (electrons or ions) crash into neighbors and form a cascade of interactions Excited charges carry current through the dielectric and cause an electrical discharge (much like lightening in air) Dielectric momentarily acts like a conductor – can lead to permanent damage To prevent breakdown, E must remain less than the breakdown strength Eb E Φ Φ̂ µ Φ̂ µ Eb λ λt 0 λ ε Eb ε

1.5 E b 10 MV/m E b 100 MV/m λ 1 0.5 0 0 0.5 1 Φϵ 1/2 /t 0 µ 1/2 Typical values: µ 105 Pa ε 10-11 F/m Eb 107-108 MV/m Φ̂ µ 1 105 λ 8 Φ̂ Φ̂ 11 E b ε 10 10 1.5

Electrical Breakdown in Dielectrics REPORTS applied (Fig. 2). The expansion of the circle is equal in both x and y planar directions because there is no preferred planar direction for the film. By contrast, the linear strain tests used a high prestrain in one planar direction and little or no prestrain in the other planar direction. High prestrain effectively stiffens the film in the high-prestrain planar direction, which causes the film to actuate primarily in the softer, low-prestrain planar direction and in thickness. Figure 3 shows a linear strain test. The relative strain was measured in the central region of the elongated (black) active area, away from the edge constraints. The circular test results for three elastomers under different conditions of prestrain are given in Table 1. The peak relative area strain was measured directly, and the relative were performed, thickness strain was calculated from the con(uniaxial). In the stant volume constraint. The breakdown field ar active region (5 was calculated from the known voltage and d to decrease the the measured film thickness (corrected for the defect causing an given relative thickness strain). No attempt voltage. The film was made to minimize voltage with these the frame, and the relatively thick films, and voltages were typen a voltage was ically 4 to 6 1. kV.Circular Thinner films Table andgenerally linear yield strain lower but comparable performance at lower voltage. For example, preliminary measurest meaments showed 104% relative area strain at ctuated 980 V using a thinner acrylic film.Prestrain The eleclm. The Material tromechanical energy density e was(x, estimated pansion y) (%) e film. from the peak field strength (Eq. 1) and the relative thickness strain. The value 1 2e is listed in Table 1 for convenient comparison to conventional elastic energy densities availableHS3 for other actuator materials. (68,68) silicone As indicated by the values, the(14,14) VHB 4910 acrylic elastomer gave the highest perforCF19-2186 (45,45) mance in terms of silicone strain and actuation pres(15,15) sure. Extensive lifetime tests have not been made, but 4910 acrylicacrylic films have been operated VHB (300,300) continuously for several hours at(15,15) the 100% relative area strain level with no apparent degradation in relative High-speed electrically actuated elastomers with strain greaterstrain thanperformance. 100% test of HS3 HS3 the acrylic elastomer has(280,0) However, relatively ntal prestrainRon Pelrine, Roy Konbluh, Qibing Pei, Jose Joseph, Science vol. 287 (2000) highCF19-2186 viscoelastic losses that limit its half(100,0) ) with a field strain bandwidth which the VHB 4910 (the frequency at(540,75) e strain was strain is one-half of the 1-Hz response) to of (B). (C and test results. ww.sciencemag.org on March 26, 2012 he absolute strain in the film. The ed similarly, with cing length in the Fig. 3. (A and B) Linear strain test of HS3 silicone film with a high horizontal prestrain for the field off (A) and on (B) with a field of 128 V/"m; 117% relative strain was observed in the central region of (B). (C and D) Activation of acrylic elastomers, producing about 160% relative strain, for the field off (C) and on (D); the dark area in (C) indicates the active region. Actuated relative thickness strain (%) Actuated relative area strain (%) Circular strain 93 69 64 33 158 40 Linear strain 54 117 39 63 68 215 48 41 39 25 61 29 Field strength (MV/m) Effective compressive stress (MPa) Estima 1 2e (MJ/m 110 72 350 160 412 55 0.3 0.13 3.0 0.6 7.2 0.13 0.09 0.03 0.75 0.09 3.4 0.02 128 181 239 0.4 0.8 2.4 0.16 0.2 1.36

Energy Method When charge is the free variable, 1 u D E use the “internal electrical energy”: 2 The total electrical energy is calculated by integrating over the volume in the current placement: Γ #1 & B % 2 D E'( dV For a parallel-plate capacitor, E (F/h)e3 and D (q/A)e3 #1 & 1 * q -* Φ 1 Γ D E ' dV , /, / ( Ah ) qΦ B% ( 2 2 A . h . 2 q2 Noting that F q/C, Γ 2C Referring to the “spring analogy” F F, u q, and k C-1, the internal electrical energy has the same form as the elastic spring energy ku2/2. As with spring energy, an alternative way to derive G for a parallel plate capacitor is by integrating F for charge increasing from 0 to q: Γ q 0 q̂ dq̂ C

Example Consider the same Ogden solid as before: W & µ 4 µ# 2 4 4 4 λ λ λ 3 λ 3 ( ( 1 2 3 ) 4 % λ 2 ' 4 The total potential energy is Π WV0 Γ q 2 hq 2 λ 2 h 0 q 2 where Γ 2C 2εA 2εA 0 ( µ% 2 λ 2 t 0q 2 4 Π ' 2 λ 3* A 0 h 0 ) 4&λ 2εA 0 If q is prescribed as a fixed value, then Π is only minimized w.r.t. λ: 3 1' dΠ λt 0 q 2 µ & λ 3 ) A0t 0 0 % dλ λ ( εA 0 must solve numerically for λ.

Now suppose that Φ is prescribed/fixed and q is unknown. This is analogous to stretching a spring with a prescribed force F. In this case, the potential becomes Π WV0 Γ qΦ. The proof is similar to before. Applying a voltage Φ to the capacitor results in a charge q* CΦ at electrostatic equilibrium. Now suppose that the capacitor is loaded with additional charge δq. The electrostatic work required to elevate δq to a voltage Φ must be balanced by the change in internal electrical energy: δΓ q* δq q* Φdq Φδq δ ( Γ qΦ) 0 This implies that for variations in q, Γ must be replaced by Γ̂ Γ qΦ. Now, Π must be minimized w.r.t. λ and q: ' µ 2 λ 2 t 0q 2 4 Π & 2 λ 3) A 0 h 0 qΦ ( 4%λ 2εA 0 dΠ λ 2 t 0 q εA Φ 0 q 2 0 Φ dq εA 0 λ t0 1/6 2) 2 & εΦ dΠ 1' λt q λ '1 2 * µ & λ3 3 ) A0t 0 0 0 % dλ λ ( εA 0 ( µt 0

For cases when Φ is prescribed, a shortcut is to use the electrical enthalpy instead of internal energy. This is associated with a change of variables for Π: Π ( λ, Φ). Π Π ( λ, q ) Π Recall Π WV0 Γ qΦ WV0 qΦ q 0 Φdq̂ Performing an integration by parts (“Legendre Transformation”) WV qΦ qΦ Π 0 Φ 0 q dΦ̂ 1 WV0 CΦ 2 2 “Electrical Enthalpy” ' µ 2 εA 0Φ 2 4 Π & 2 λ 3) A 0 t 0 ( 4%λ 2λ 2 t 0 3 1' dΠ εA 0Φ 2 µ & λ 3 ) A0t 0 3 0 % dλ λ ( λ t0 1/6 & εΦ 2 ) λ '1 2 * ( µt 0

DEA Generator Dielectric starts out with a small voltage drop (Φin) and is partially stretched D Maintain charge (Qin) and let dielectric partially stretch (increase C à reduce Φ) A Maintain voltage (Φin) and stretch dielectric(increase C à increase Q) Current in (low voltage) B Maintain charge (Qhigh) and let dielectric partially relax (reduce C à increase Φ) C Voltage Φout B D Φin A Qlow Charge Q high C Maintain voltage (Φout) and let dielectric completely relax (reduce C à decrease Q) Current out (high voltage)

DEA Generator Harvest electrical energy from changes in fluid pressure Balloon Energy harvesting shoe Ocean waves R R1 R0 p p Φ i Compressed Air In ii Voltage Applied

Balloon Generator Kaltseis, Suo, Bauer, et al. APL (2011) membrane is connected to the input reservoir at voltage Uin . FIG. 2. (Color online) Rectangular energy conversion cycle operating between two charge reservoirs depicted in the work-conjugate (U,Q) plane. The cycle proceeds counterclockwise from state 1 to state 4. During the four steps of the cycle solid and dashed lines indicate the evolution of the balloon shape. In the constant voltage steps, 1 ! 2 and 3 ! 4, charges are taken from the low voltage reservoir and fed into the high voltage reservoir. In the constant charge steps 2 ! 3 and 4 ! 1, the voltage across the membrane is brought in line with the reservoirs. The area enclosed by the contour corresponds to the generated electrical energy DUDQ. Downloaded 03 Oct 2013 to 211.138.121.37. This article is copyrighted as indicated in the abstract. R

DEA Generator Iain Anderson (Univ. Auckland) 0.8 J per step Avg. Power 1 Watt Specific Energy: 0.3J/g 33% conversion

PolyWEC infer strains or stresses (i.e., displacements or forces). In generator mode, mechanical energy is converted into direct electricity via the variable–capacitance electrostatic generator principle. Properties of DEs which make them suited for transduction applications are: low mass density; large deformability; high energy density; rather good electromechanical conversion efficiency; moderate or low-cost; solid-state monolithic embodiment with no sliding parts; easy to manufacture, assemble and recycle; good chemical resistance to corrosive environments; and silent operation. Initially proposed as musclelike actuators for robots, DE are now receiving significant attention for energy scavenging applications [2–6]. Their intrinsically cyclical operation makes them particularly suited for the development of WEC [7–12]. Specifically, dielectric elastomer generators (DEG) are foreseen to replace the power take-off systems of traditional WEC, which are currently made of stiff, heavy, shock-sensitive, corrosion-sensitive, and costly (metallic and rare-earth) materials. Expected advantages of DEG power take-off systems are: ease of installation and maintenance; low capital and operating costs; shock and corrosion wave-induced pressure oscillations at the underwater interface cause the reciprocating motion of the water column, with a Polymeric Wave Energy Converter EU funded project (2012-2016; 2mil. euros) Lead: Marco Fontana (SSSA) Partner: Univ. of Edinburgh 1 Corresponding author. Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 14, 2014; final manuscript received September 3, 2014; published online November 12, 2014. Assoc. Editor: Ryan L Harne. Journal of Vibration and Acoustics C 2015 by ASME Copyright V Fig. 1 Poly-OWC WEC FEBRUARY 2015, Vol. 137 / 011004-1 Downloaded From: me.org/ on 02/23/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use

The circular test results for three elas-tomers under different conditions of prestrain are given in Table 1. The peak relative area strain was measured directly, and the relative . Very high dielectric strength for dielectric elastomer actuators in liquid dielectric immersion T-G La and G-K Lau APL 102 192905 (2013) t0. The areal strain is .