Electrode interface polarization formation in dielectric elastomer actuators

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Sensors and Actuators, A: Physical

Citation (APA)

Iannarelli, A., Ghaffarian Niasar, M., & Ross, R. (2020). Electrode interface polarization formation in

dielectric elastomer actuators. Sensors and Actuators, A: Physical, 312, [111992].

https://doi.org/10.1016/j.sna.2020.111992

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SensorsandActuatorsA312(2020)111992

ContentslistsavailableatScienceDirect

Sensors

and

Actuators

A:

Physical

jo u r n al hom e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / s n a

Electrode

interface

polarization

formation

in

dielectric

elastomer

actuators

Alessandro

Iannarelli

∗

,

Mohamad

Ghaffarian

Niasar,

Rob

Ross

DCSystems,EnergyConversionandStorage,FacultyofElectricalEngineering,MathematicsandComputerScience,DelftUniversityofTechnology, Mekelweg4,2628CDDelft,TheNetherlands

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received23December2019

Receivedinrevisedform31March2020 Accepted31March2020

Availableonline5May2020 Keywords:

DIelectricelastomeractuators Dielectricspectroscopy Electrodepolarization Reliability Spacecharges Interfacepolarization Electroactivepolymers

a

b

s

t

r

a

c

t

Dielectricelastomeractuators(DEAs)areaclassofelectrostaticactuatorsthathavepromising applica-tionsinfieldslikesensors,soft-robotics,microfluidics,andenergyharvesting.Thecrucialpointsinthe workingprincipleofDEAaretheapplicationofhighelectricfieldandtheuseofcompliantelectrodes. Theseelectrodesaretypicallycomposedofamixtureofasoftpolymerbasefilledwithhighlyconductive particles.Inthiswork,weshowthatthechargedimpurities,possiblypresentintheelectrodes com-posite,incombinationwithahighelectricfieldcancausetheformationofpolarizationinterfacelayers betweentheelectrodesandtheinnerdielectric.Theselayerscan,inthelongterm,diminishtheactuation performanceoftheDEA.

1. Introduction

Dielectricelastomeractuators(DEAs)areaspecificclassof elec-troactivepolymer(EAP)transducersthatexploitstheelectrostatic forceexertedbetweentwoconductorstoperformadisplacement. Becauseoftheirpliability,highefficiency,noiselessoperation,and fastelectromechanicalresponse[1–4]theyaresuitablefor vari-ousapplicationsuchasartificialmuscles,robotics,optics,sensors, microfluidics,andenergyharvesting[5–14]andreceivedattention incommercialapplications[15].

Despitetheirversatileproperties,DEAsexhibittwomain oper-ationaldisadvantages:theneedfor flexibleelectrodesand high electricfields[16].Manufacturingelectrodeswithhighcompliance andconductivityrepresentsachallengingtaskasthetwo proper-tiesareoftenmutuallyexclusive[17].Whereas,theintrinsically lowpermittivityεofelastomersmakesnecessarytheuseofa rel-ativelylargeelectricfieldEzforasufficientactuationforceFz.This

followsfromtherelation:

Fz=εAEz2=εA(V

d)

2

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∗ Correspondingauthor.

E-mailaddress:a.iannarelli@tudelft.nl(A.Iannarelli).

whereAistheelectrodearea.Intheright-handsideoftheequation, theﬁeldEzisre-writtenintermsoftheappliedvoltageVandthe

elastomerthicknessd.Ahighelectricﬁeldcan,thus,beobtained eitherbyreducingthedielectricthicknessorusingasubstantial voltagepotential[18].

Toovercomethesedisadvantages,compliantelectrodesare typ-icallypreparedwithhighlydopedelastomercomposites[19–24] andinorganicﬁllersareusedtoartiﬁciallyaugmentthedielectric’s permittivity[25–31]aswellasthechemicalfunctionalizationof theelastomer[32].

Despitetheefforts,stilltypically highelectricfield strengths needtobeinvolvedforasignificantactuationdisplacement.The influenceofhighelectricfields(orvoltages)onthedielectric prop-ertiesofDEAsystemisscarcelyinvestigatedasmostoftheresearch isperformedatlowvoltages[33].Inthepresenceofstrong elec-tricfields,newphenomenacanestablishanddrasticallyimpactthe dielectricproperties.Adistinctiveexampleisgivenbythe forma-tionofspacecharges(SC)atlow-frequencyhighfields[34,35].

Space charges formation in dielectrics exposed to high DC voltages is a known effect for polymeric materials used in DEAs fabrication [36–40]. However, the evolution of SC at the electrodes–dielectricinterfacesanditsconsequencesontheDEA actuationperformancearemuchlessstudied.

Ourresearchinvestigatesthedielectricphenomenaatthe inter-faces.Speciﬁcally,westudiedthroughdielectricspectroscopy(DS)

https://doi.org/10.1016/j.sna.2020.111992

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Fig.1.Schematicrepresentationofthespacechargeformationattheinterface.(a)Samplepanview.Intheinset,theformationoftheelectrodepolarizationlayershappens attheelectrode-dielectricinterfaces(b)Consequencesofelectrodepolarizationlayersonrealcapacitanceanddielectriclosses(tanı)spectrum.Theselayersresultina parasiticcapacitanceCpol,thataddstoandmodifythepre-existingdielectriccapacitanceCPDMS.

howthechargedimpuritiesmigratingfromthedopedelectrodes (forcedby thehighelectric ﬁeld employed)canform polariza-tionlayersattheelectrodes/dielectricinterfaces.Successively,we observedtheconsequencesofthesechargedlayersformationon themechanicalcapabilitiesoftheDEAsystembymonitoringits actuationperformanceovertime.

Theﬁrstpartof this workpresentsthe equivalentelectrical modelusedtodescribetheinterfacephenomenon.Thesecondpart addressestheresultsaboutspacechargemeasurementperformed withdielectricspectroscopyandtheperformancecharacterization overtimeofDEA.

2. DielectricphenomenaatinterfaceofDEAs

Compliant electrodes used in DEAs are typically composite materials.Theyarepreparedbyaddinghighlyconductivefillers (e.g.metalparticles,carbonblacks,ionicgels,dopants)toan elas-tomerbase material until the percolation threshold is reached [22,19].Dependingonthefabricationmethodused,these compos-itescancontainionicimpuritiesaswellasfreeionsresultingfrom residualcatalysts,solventsorthefillerthemselves[41,42].Under theinfluenceofasufficientlyhighelectricfield,theseimpurities arepushedacrosstheelectrode-dielectricinterface(seeFig.1(a)) leadingtothedevelopmentofachargedaccumulationlayer[43]. Thisphenomenonisknownaselectrodepolarization(EP)[44].The resultantcapacitanceoftheseparasiticlayerssuperimposestothe realsamplecapacitance.Becauseofthelargeinertiaofthe impu-rities,theeffectisdominantatlowfrequency,i.e.whentheyare slowlyacceleratedandexposedtoaunipolarfieldforalongertime. Asaresult,thecapacitancesuperimpositioncanbeobservedvia dielectricspectroscopy asa low-frequencysignalenhancement, Fig.(1(b)).

Whenanexternalvoltageisapplied,thepresenceofthe para-siticlayermodifiestheinternalelectricfielddistribution.Apartof theappliedelectricfieldconcentratesnexttotheinterfacesandthe remainingpartinthebulk.Thisunwantedeffectisacommon prob-leminelectrochemistryfield[45]becauseitdisguisesthedielectric contributionoftheactualsample.InthecaseofDEA,however,its presencecanbeusedtoassesstheactuatorperformanceovertime anditsreliability.

Fig.2.Total impedanceZTOT modelofDEA usinglumpedelements. Boththe

interfacesandthedielectricbulkaredescribedbytheconstantphaseelements impedancesCf,polandCf,PDMSinparallelwiththerespectiveresistiveelementsRpol

andRPDMS.TheelectrodesaremodeledastwopureresistiveelementsRser.Due

tosymmetry,theequivalentcircuitcanbere-writteninareducedform(bottom equation).

2.1. Interfacemodeling

To investigate the formation of the space charges at the interface,weconstructanequivalentelectricalcircuittoﬁtthe experimental impedance spectra obtained via dielectric spec-troscopy, Fig. 2 [46]. We emulate the parasitic and sample capacitances using constant phase elements (CPE). The CPE is speciﬁcallysuitabletodescribeinterfaceeffects[47,48].Itis char-acterizedbythetwoparameters˛andCCPE

ZCPE=

1 (jω)˛·CCPE

, ˛≤1 (2)

Herej2=−1istheimaginaryunitandωistheanglularfrequency oftheappliedsignal.TheparameterCCPE hastheunitof[CCPE]=

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A.Iannarelli,M.GhaffarianNiasarandR.Ross/SensorsandActuatorsA312(2020)111992 3

Fig.3. Minimalisticrepresentationofthedielectricspectrumanalyzer.The gener-atedsignalandtheresultingcurrentaremeasured.Theimpedanceiscalculatedas teratioofthetwocomplexquantitiesU(voltage)andi(current).

F·s˛−1.When˛=1,CCPEisacapacitance.Inthiswork,weaddress

totheCPEsimplyasamodiﬁedcapacitiveelementwithunit ˜pF= pF·s˛−1_.

3. Experimental

3.1. Dielectricspectroscopy

Dielectric spectroscopy (DS)measurements were performed usingaMeggerIdax300InsulationAnalyzerunitincombination withtheMeggerVax020HighVoltageAmplifier,Fig.3.Thetests weredonein normal environment conditions (20◦C an1 atm). Acustomrigwasusedtoholdthesamplesinplaceduringthe test. DS wasperformed onthesamplesin three stages: firstly, low-voltage (V_peak(LV )=10 V,corresponding toa field E_peak(LV )=0.19 kV/mm)DSwasperformedintherangefrom10mHzto10kHz toassessthecapacitancebaselineofnewDEAsamples.Inthe sec-ondstage,theDSwasexecutedathighvoltage(V_peak(HV )=1980V, henceE(HV )_peak ₌37.2kV/mm)inareducedfrequency-rangefrom10 mHzto2kHz.Thehighvoltageinthisstagehasatwofoldfunction: itisneededfortheDSspectrummeasurementatahigher elec-tricfield,anditsimultaneouslyforcesthemigrationofthecharged particlesat theinterfaces.In thethird and laststage,the sam-plesweresuccessivelyre-testedwithlowvoltageatdefinedtime intervals.

ThereducedfrequencyrangeoftheHVtestisduetothe limi-tationoftheamplifier.Itisworthmentioningthatthefrequency sweepwasperformedfromhightolowfrequenciesinallcases. Fromnon-reportedtests,however,wefoundthatthesweeporder won’tinfluencethefinalresults.

3.2. Samplepreparation

Thesamplesinthisanalysiswerepreparedusingcommercially availableWackerElastosilFilm2030polydimethylsiloxane(PDMS) ﬁlms.The100␮mthicksiliconesheetswerecutindiscsof50mm diameter.Aradialstretchofr=1.5wasimposedonthe

result-ingmembranesbytheOpen-SourceRadialStretchingSystem(RSS) [49].Toholdthemembranestensioned,thesewereanchoredto rigidring-shapedpolymethylmethacrylate(PMMA)framesof34 mminnerdiameterand2mmthickness.Adouble-sidedpolyamide siliconeglue tape wasused as fastenlayerbetween thePDMS andthePMMA.Theelectrodeswerethenpatternedonbothsides ofthemembranesusingthespray-painttechnique.Aconductive andelasticink[50]wassprayedwithanairbrushthroughshadow masksofpropershape.Theinkwaspreparedbydispersingthrough ahigh-speed mixer(ThinkyARE-250) carbonblackﬁllers (Cabot BlackPearl2000)intoanuncuredsiliconebase(NusilMED-4901). Isopropyl-alcoholandiso-octanewereusedasthinnerforthis

pro-Fig.4.RealpartoftheDEAcapacitanceresultingfromtheﬁrstdielectric spec-troscopystageperformedatlowvoltage,V(LV )

peak=10V.Thehigh-frequencydecrease

isduetotheelectrodeshighresistivity,whichmakesthesystemactasanRCﬁlter. Theerrorbarsrepresentthemeasurementsstandarddeviationover5samples.

cess.Thepainteddeviceswerecuredinaventilatedovenat50◦C for40min.Afterthistime,contactswereaddedtotheelectrodes bypaintingtwosilverinkpads(RSPROSilverConductivePaint). Thedevicewasthenputbackintotheovenforalastcuringstepof 12hat50◦C.Theresultingelectrodeshaveacircularshapeof12 mmdiameterandanaveragethicknessof10␮m,measuredusing thesurfaceproﬁlometerDektak150.

ThesamplespreparationwasperformedinanISO7controlled environmenttoavoidexternalparticulatecontamination.

4. Resultsanddiscussion

4.1. Interfacepolarization

4.1.1. Dielectricspectroscopyatlowvoltage

Thedielectricspectroscopyperformedon5newDEAsamples atlowelectricfield(lowvoltage)showstheexpectedbehaviorof aparallelplatecapacitor,Fig.(4).Therealpartofthecapacitance isapproximatelyconstantinthewholemeasuredfrequencyrange. Inthehighfrequency(f>2kHz)tail,theresistiveeffectofthe elec-trodesbecomespredominant.Inthisregion,thesystembehavesas anRCfilterattenuatingtheflowingcurrentandalteringthevoltage distributionalongtheelectrodesurface[51].Theelectrostatic com-pressionforthislowvoltageisnegligible,andthereisnovaluable capacitancechangeresultingfromitinthedielectricspectroscopy. Themeasuredcapacitanceintherangefrom0to500Hzhasan averagevalueofCLV=50.26±0.09pF.

4.1.2. Dielectricspectroscopyathighvoltage

TheDSissuccessivelyperformedathighvoltageV_peak(HV )(E_peak(HV )) onthesamesamplespreviouslytestedatLV.Signiﬁcantchanges appearinthedielectricresponseoftheDEAs,Fig.5.Fortheir anal-ysis,itisconvenienttodividethespectrumintwoadjacentregions delimitedbythecentralvaluef∗=10Hz.Thelowfrequencyrange

FLFcontainsfrequenciesfrom10mHzuptof∗=10Hz,whereas

thehighfrequencyrangeFHFcontainstheremainingfrequencies

abovef∗.

Followingthefrequency-sweepdirection,i.e.fromhightolow, itisobservedacapacitanceincreasewithdecreasingfrequencyof about1pFintheFHFrangewithrespecttothepreviouslowvoltage

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enhance-Fig.5. RealpartoftheDEAcapacitanceresultingfromtheseconddielectric spec-troscopystageperformedathighvoltage,i.e.V(HV )

peak=2kV.Anoticeableincreaseof

capacitanceisvisibleforfrequencieslowerthanf∗=10Hz.Theerrorbars repre-sentthemeasurementsstandarddeviationover5samples.Thelowvoltageaverage value(dashedline)isalsoreportedforreference.

Fig.6. tanımeasurementoftheseconddielectricspectroscopystageperformed

atV_peak(HV )=2kV.Thepeakislocatedaround1.45Hz.Theerrorbarsrepresentthe

measurementsstandarddeviationover5samples.Itisvisiblethelargedifference withthelowvoltagelosses(dashedline).

mentoftheoriginalcapacitance.Thevaluesinthis rangeshow small scattering and hence a uniform change for all the sam-ples.

Continuing on the lower frequencies of f∗, instead, a steep capacitanceincreaseappears.Thecapacitancevalueskeep mono-tonicallyincreasing withdecreasingfrequencies, with a milder slopefrom500mHzto10 mHz.Thescatteringofthevalues is largerinthisrange,withastandarddeviationofLF,HV=2.2pF.

Largevariationsarepresentinthemeasurementoftanı,i.e.the medium’sdielectriclosses,Fig.6.Morethananorderofmagnitude ofadditionallossesaremeasuredforfrequencieslowerthanabout 100Hz.Allthemeasurementsshowapeakvalueofaround1.45 Hz.

Athigherfrequencies,thetanıbehaviorisdominatedbythe contributionoftheresistiveelectrodesused.Incontrast,forlower

Fig.7.Realpartcapacitanceevolutionovertimemeasuredinthethirdstageof dielectricspectroscopy.Thehighvoltage(dashedredline)andlowvoltage(dashed blackline)arereportedforcomparison.Allthetestsareperformedatthelow

volt-ageV_peak(LV )=10V.Novoltageisappliedtothesamplesbetweentwoconsecutive

measurements.

frequencies,weobservethecontributionofthePDMSandits inter-faceswiththeelectrodes.

ThecapacitanceenhancementrecordedinFHF,isexplainedby

themembranethinning,whichresultsfromtheelectromechanical actionoftheelectrodes.Inthepresenceofhighelectricﬁelds,the electrostaticforcecausesasigniﬁcantcompression.Fromthewell knownparallel-platecapacitorrelation

C= ε0εrA

d (3)

(whereAistheareaoftheelectrodes)itisreadilyunderstoodthat adecreaseinthicknesscausesacapacitanceincrement.In princi-ple,thissameargumentcouldbeusedtoexplainthebehaviorin

FHF.Itcouldbearguedthatatlowfrequency,thesamplecan

com-pressmore,becauseofalessviscoelasticeffectandtherefore,an evenmoreconsiderablecapacitanceincreasecouldfollow.Thelast hypothesisisprovedtobecontradictedbytheoutcomesofthenext Section4.1.3.

4.1.3. Dielectricspectroscopyevolutionovertime

TheDSwasrepeatedonthesamesamplesatlowvoltageafter theHVinvestigation,Fig.(7).Apersistentcapacitanceincreasefor frequencyintherangeFLFisstillmeasured.Suchatrendwasnot

encounteredinthepreviouslowvoltagemeasurementsshownin Fig.(4).But,itwasrecordedfortheﬁrsttimeunderhighvoltage conditions,Fig.(5).

Thecompressionargumentexploitedtoexplainthecapacitance increaseinFHF(Section4.1.2),cannotholdinthiscasebecausethe

induceddisplacementatlowvoltageisreasonablynegligible.Also, thecapacitancemeasuredinFHF areinthiscaselowerthanthe

baselinebyapproximately2pF.

Thetwophenomenatogetherindicatethatthehighelectricﬁeld imposedduringthehighvoltageDSchangedtheDEAsproperties undertest.Theseresultsshowedtobereproducibleforallthe sam-plestestedinacoherentmanner.Thesampleswereleftapartin controlledtemperatureconditions(20degreeCelsius)andwere re-testedwithlowvoltageatsuccessivetimeintervalstoassessthe stabilityofthechanges.ThecurvesinFig.7showthetimeevolution oftheobservedcapacitanceforarepresentativespecimen.

Rightafterthehighvoltageapplication,thelowvoltageDSstill registershighcapacitancevaluesintheFLF range.Thesevalues

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Fig.8.Evolutionoftanıovertimemeasuredatthethirdstagedielectric spec-troscopyatlowvoltage.Thecentralpeakshiftsleftwardsovertimebecauseofthe gradualreductionofthepolarizationlayersinabsenceofanexternalelectricﬁeld.

at50◦Cfortwohoursandtestedagainoncecooleddowntoroom temperature.After42hnodifferenceinthecurveswasnoticeable anymore.

Anequivalenttimeevolutioncanbeobservedalsoforthetanı measurement,asshowninFig.8.Thecentralpeak(fpeak(t=0)=

3.6Hz),whichappearedwiththehighvoltageapplication,shiftsto lowerfrequencywiththetimepassing.Afterthe42hoursperiod, itstabilizestoitsﬁnalposition(f_peak(t₌42h)₌7.5mHz). 4.1.4. Inceptionthreshold

TheDSwasperformedatsuccessivelyhighvoltagelevelson untestedsamplestomeasuretheelectricﬁeld thresholdforthe inceptionofthepolarizationeffect.Namely,thisisthethreshold abovewhichapermanentdielectricchangeisobservableinthe DEAsystem.

Tenvoltage-peaklevelslogarithmically-spacedbetween198V and1980Vwerechosenforthetest.InFig.9,sixofthese volt-agelevelresultsarereported.Amildcapacitanceincreasedueto polarizationisvisibleatlowervoltagesforfrequencieslessthan 100mHz.Forvoltagesupto711V(about13kV/mmnominal elec-tricfield),therealpartofthecapacitancestaysnearlyunchanged, Fig.9(a).Asthevoltagereachesaround918Vpeak(orabout16 kV/mmnominalelectricfield),asuddenincreaseisobservedwhich persistsforhighervoltages(electricfields).Ananalogouschangeis observedinthedielectriclossesinvestigationforthesame volt-age,Fig.9(b).Inthisfigure,theformationofahumpisobserved betweenthetwovoltages918Vand1187V.Thephenomenoncan alsobeobservedinaNyquistplotforthecapacitancevalues.When thepolarizationsets,therespectivecurvesbendtillforming arc-likecurvesatlowerfrequencies,ascanbeobservedinthecurves inFig.9(c).

ThevalueEth=16kV/mmisthereforeconsideredtheelectric

ﬁeldthresholdfortheinjectionofpermanentpolarizationlayerfor thisspeciﬁcsystem.

4.1.5. Lumpedmodelﬁtting

Thepermanentdielectricvariationisexplainedbytheformation ofspacechargesattheinterfacesduringthehighvoltagestageof DS.Theimpuritiescontainedintheelectrodes,movedtowardsthe interface,creatingastablepolarizationlayer.

Thepolarizationlayersareschematizedusingthelumpedmodel presentedinSection2.1andshowedinFig.2.BoththePDMSbulk andtheinterfacesaremodeledwiththeCPEelementsCf,PDMSand

Cf,pol.ParalleltotheCPEs,theparasiticresistancesRPDMSandRpol

areincludedtoaccountforthematerialandinterfacelosses, respec-tively.

Thetotal impedance ZTOT measuredthroughdielectric

spec-troscopyinSection4.1.3hasbeenﬁttedwiththislumpedmodel usingtheMEISP3.0(MultipleElectrochemicalImpedanceSpectra Parameterization)softwarebyKumhoChemicalLaboratories.The resultsareshowedinFig.(10).Theevaluatedﬁtparametersofthe impedancedatatotheequivalentcircuitarereportedinTable(1). Wecantrackthetimeevolutionofthechargedinterface: ini-tially,asthepolarizationlayerisformed,itischaracterizedbya largecapacitanceCf,pol.Atthesametime,alargecapacitanceCf,PDMS

relativetothePDMSbulkismeasured.Comparingthisvaluetothe initialC0,LVisevidentalargeenhancement.Thisisexplainedbythe

reducedPDMSeffectivethickness ˜d.Overtime,thevalueofCf,pol

graduallydecreases:theformedchargesstartdiffusingand recom-bining,shrinkingtheinterfacelayerdepth.ThePDMScapacitance Cf,PDMSdiminishesaccordingly:theeffectivePDMSthickness ˜d is

nowincreasing.

Wecanﬁnallycomparetheevolutionofthetanıpeakswhich appearintheFLFrange.Accordingtotheproposedlumpedmodel

thisareroughlyproportionaltotheratio ∝_C 1

˛,1·Rpol

Wecomparedthesevalueswiththeonesactuallymeasuredover thetimeevolution,andwereportedtheminTable(2).Inallthe casesthereisadirectproportionalitykbetweentheestimated val-uesbythemodelandtheactualmeasuredones.Thisisafurther conﬁrmationofthevalidityofourﬁt.

4.1.6. Comparisonwithothermaterialsandconditions

Thethree-stages-dielectric-spectroscopytestwasperformedon differentmaterialstoassesstheformationofpolarizationlayers. Tworigidpolymersfilms,namelylow-densitypolyethylene(LDPE) andpolyvinylchloride(PVC),weretestedusingthesamesample preparationmethodexploitedinthePDMScase.Duetothe stiff-nessofLDPEandPVC,nopre-stretchwasappliedtothesesamples. Themeasuredfilmthicknesseswere103␮mand160␮mforthe LDPEandPVC,respectively.ThehighvoltageV_peak(HV ) usedforthe high-voltagedielectricspectroscopystagehasbeenchosentohave theresultingrespectiveelectricfieldE,suchthatE>E_th.Thevalue Eth=16 kV/mmis theelectricfieldthreshold measuredfor the

PDMS-basedDEA.

AscanbeseenfromFig.11,thesematerialsshowsimilar behav-iortothePDMScase.Atlowvoltage,bothLDPEandPVCexhibit onlybulkpolarization[52].DuringthesecondstageDS,performed underthehighelectricﬁeldE,theEPsettlesandpersistsevenafter thehighvoltageisremoved.Thepolarizationpersistencecanbe observedinthethirdandlaststageofDS,whichisperformedagain atlowvoltage.

AﬁnaltestwasconductedonPDMSusingnon-compliant,pure aluminiumelectrodes.Therigidaluminiumpreventsthepresence ofimpuritiesorfreeionsthatcanformtheEPlayer,likeinthe caseofthecarbon-siliconecomposite.Thepeakvoltagewas grad-uallyincreaseduptoV_peak(HV )=1980Vandthenrevertedbacktolow voltage.Theresults(seeFig.12)showthat,withthisconﬁguration, nopermanentpolarizationlayerisformedduringtheHVphase. Aminorcapacitanceincreasealloverthespectrumisexplained bytheelectrostaticforcesqueezingthesiliconelayer,thus reduc-ingitsthickness,Eq.(3).Whenre-testingatlowvoltage,thesample recoversitsoriginalcapacitanceshowingtheabsenceofpermanent EP.

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Fig.9. Polarizationinjectionstudycomparedwiththelowvoltagebaselinemeasurement.(a)Capacitancefrequency-sweeps.(b)tanıdielectriclossmeasurement.(c)Nyquist plotofthecapacitance,thearrowindicatesthedirectionofincreasingfrequencyω;theformationofanewarcinthecurvesisnoticeableasthepolarizationsettles.

Table1

Timeevolvingﬁt-parametersresultingfromthelumpedmodelfortheDEAactuator.

Time Rser() Cf,pol( ˜pF) ˛pol Rpol() Cf,PDMS( ˜pF) ˛PDMS RPDMS()

t0 11.64×104 401.7 0.9984 1.14×107 60.17 0.99 1.86×1014 t1 11.16×104 395.1 0.9983 1.59×108 59.72 0.99 1.85×1014 t2 11.79×104 331.5 0.9961 1.00×109 59.22 0.9941 1.85×1014 t3 11.92×104 318.6 0.9962 3.83×109 58.07 0.9964 1.85×1014 t4 11.93×104 315.1 0.9941 3.80×109 58.23 0.9968 1.85×1014 t5 12.03×104 321.5 0.9957 4.19×109 58.25 0.9965 1.8×1014

TheteststogethershowthatthemeasuredEPisindependent bychoice ofthe dielectric medium,but rather depends onthe electrodesused.Explicitly,it conﬁrmsthatahighconcentration ofimpurities orunbonded chargescontainedin theconductive carbon-siliconecompositesusedaselectrodescanpromotetheEP formation.

Finally,theseresultsencouragetheuseofpuremetalelectrodes forthefuturedevelopmentofinterface-polarization-freeDEAs.For example,ithasbeenrecentlyshown[53]thatgoldcancovalently bondtothiol-functionalizedsilicone(SH-PDMS)surfacetoforman ions-freecompliantconductivelayer.

4.2. Actuationeffects

Thepolarizationeffectsweremeasuredontheactuation perfor-manceoftheDEAovertime.Twosetsofsampleswerecontinuously actuatedwith1HzsquareandsinewaveAC4kVpeakvoltage,

respectively.FromresultsofSection4.1.4,thisvoltageensuresthe creationofpolarizationatinterfaces.Bothsetswerevideo-recorded fortheentirelengthofthetest.Afterwards,theinformationabout theradiuschangewasextrapolatedfromtherecordingswiththe aidofcustomMATLABcode.

Fig.13(a)showshowtherelativeactuationstrokes%(t)deﬁned

as

s%(t)=100×

rON(t)−rOFF(t)

r_ON(0)−r(0)_OFF

(4) whereristhemeasuredradius,diminishesovertime.The ON-(OFF-)radiusisdeﬁnedasthemaximum(minimum)radiusmeasured overavoltagecycle.

Thehighestperformanceloss(intermsofactuationstroke)is measuredfortheACsinewavecase.Theformedchargedlayers, concentratetheelectricﬁeldattheinterfacesattenuatingthebulk electricﬁeldresponsibleforthecompression.Asaconsequence,

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Fig.10.FittingofthetimeevolvingtotalcapacitanceC=C₊_iC_and_impedance_Z₌_Z₊_iZ_with_the_proposed_lumped_model_including_constant_phase_elements._(a–c)

Realandimaginarycapacitancefitting.(b–d)Realandimaginaryimpedancefitting.Solidlinesrepresentthefittingofthedatapoints,representedbythemarkers.

Fig.11. CapacitancemeasurementsresultingfromthethreestagesdielectricspectroscopyperformedonLDPE(left)andPVC(right).Theinitiallow-frequencycapacitance enhancementforthelowvoltagecurvesisduetothebulkpolarizability.

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Fig.12.CapacitancemeasurementonPDMSﬁlmusingrigidaluminiumelectrodes. TheelectrodesradiusisinthiscaseslightlylargerthantheCB-PDMSandahigher capacitanceisthusrecorded.AreversiblebulkpolarizationofthePDMSisvisible forlowerfrequencies.

theavailableelectrostaticpressureinthebulkisreducedaswellas theresultingdisplacement.

TheON-radiusreducesovertimebecausethebulkelectricﬁeld, whichcausesthecompression,reduceswiththechargedinterface formation,Figs.13(b)-(c)(darklines).

Similarly,intheOFFstate,thegrowingpermanentpolarization chargessettleanelectricﬁeldthatholdsthecompressionand pre-ventstheDEAtorecovertoitsinitialunperturbedstatefully.This explainstheincreasingradiusintheOFFstate,Figs.13(b)-(c)(bright lines).

Thisstudyaimedtoassess thepolarizationchargescreation at the electrodes-insulator interface and to measure its effects ontheactuationperformance ofa dielectricelastomeractuator (DEA)systems.Dielectricspectroscopy(DS)wasperformedonthe sampleinthreestages.Asystematicandpermanentcapacitance increase was measuredwhen exposing thesample to low fre-quency(<10Hz)andhigh-intensityelectricﬁelds(>16kV/mm). Theresultwasattributedtothecreationofspacechargesat inter-faces.Anequivalentcircuitwasmodelledtoquantifytheinterface polarizationmechanism,anditsuccessfullyﬁttedtheexperimental data.

Theeffectsofthepolarizationchargeswerestudiedonthe actu-ationstrokeovertime.Itwasgenerallyobservedastrokereduction over timecaused bythe formationof polarizationcharges.The worstperformancewasmeasuredinthecaseofACsinedriving signal.

Fig.13.(a)Relativestrokereductionovertimeforthetwodifferentinvestigatedwaveforms.In(b)and(c)itisshowedhowtheradiusrONincreasesovertimewhereasrOFF

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A.Iannarelli,M.GhaffarianNiasarandR.Ross/SensorsandActuatorsA312(2020)111992 9 Spacecharges(interfacepolarization)canexplainthesevere

reductionofactuatorperformanceovertime.Itistherefore sug-gested tomakea deliberatechoiceof thematerialusedduring electrodesfabrication,and,inparticular,itissuggestedtoavoid theuseofmaterialwithsigniﬁcantimpuritiesorionscontent.

CreditAuthorStatement

AlessandroIannarelli:Conceptualization,Methodology, Soft-ware, Validation, Formal Analysis, Investigation, Data Curation, Writing-Originaldraftpreparation.

MohamadGhaffarianNiasarh.:Investigation,Data Curation, Resources,Writing-Review&Editing.

RobRoss:Visualization,Supervision,Writing-Review& Edit-ing,Projectadministration

Acknowledgements

This work was possible thanks to the ﬁnancial of Marie Sklodowska-CurieInnovativeTrainingNetwork (MSCA-ITN-2014-ETN)grant641822.

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