CPCscanbeusedforapplications,suchasEMI shiel-ding, antistatic and electrostatic painting, due to their
Please cite this article in press as: Deng H, et al. Progress on the morphological control of conductive network conductivity. Moreover, these composites can also be
used for smart applications, including strain [21,22, 24,26,155–158] and damage sensing [23,63,159–165], vapour/liquidsensing [22,27–30,166–168]and tempera-turesensing[32,169,170].TheoverallconductivityofCPCs dependsheavilyonthetunnellingbetweenlocal conduc-tivenetworks;therefore,achangeinthelocaltunnelling distance could lead toa significant changein the con-ductivity.Outer-stimuli-inducedchangesinthetunnelling distancecouldresultinasignificantchangeinthe conduc-tivity.Therefore,thesechangescanbemonitoredandused forsensingpurposes.Furthermore,theelectrical conduc-tivityofCPCscanalsoresultsinotherfunctionalities,such asaflexibleconductor,electroactiveshapememoryand thermoelectricproperties.
5.1. Strainanddamagesensing
Awiderange ofapplicationshavebeenproposedfor strain sensing,includingsmart textiles,health monitor-ing,wearableelectronicsandmovementsensors[124,171].
For human motion, wearable, stretchable and sensitive devicesarerequiredtodetectresistivitychangesduring movement. Severalconductivefillers, suchas CB,CNTs, graphene and metal particles, can beincorporated into aninsulating polymermatrix tofabricate strainsensors [21,158,172–175].
The sensitivity of these strain sensors is thought to be one of the most important issues because different applicationsoftenrequiredifferentstrainsensitivities.The processingconditionsandmaterialproperties,suchasthe weightfraction,diameterandconductivityofthe conduc-tivefillers,theprocessingtemperatureandthetunnelling barrier height of thepolymer matrix, all play a role in determining the sensitivity [176]. To modify the strain sensitivity, severalmethods have been reported. Muru-garajetal.observedthatanarrowdistributionoftunnel gaps between overlapping nanochannels was beneficial for a highsensitivity in theirCPCs [177]. Hwang et al.
reported that the sensitivity strongly depended on the concentrationofpoly(3-hexylthiophene-2,5-diyl)(P3HT), which were wrapped around CNT bundles [24]. Dang etal.observedthataCNTwithahigheraspectratiowas preferredfor a highersensitivity inCNT/siliconerubber nanocomposites[22].Recently, ourgroupdemonstrated thatmixedfillerscontainingCNTsandmetallicparticles in different volume ratioscouldbe usedto modifythe strainsensitivityofCPCsfibres[158].Itwasalso demon-stratedthatthestrainsensitivitywasindependentofthe fillerconcentrationforthesamefillercomposition.This resultagreeswellwiththereportedstudybyZhangetal., inwhichauniversallogarithmicresistivity-strainrelation independent of theCNT concentrationin thermoplastic polyurethane(TPU)wasreported[26],asshowninFig.12.
Theauthorsdemonstratedthatastrain-inducedresistivity changecouldbeintroducedintothefluctuation-induced tunnelling(FIT)modelviaanincreaseinthetunnellinggap widthduetothemacroscopicseparation ofCNTsunder strain.
Fig.12.Theresistivity-strainbehaviorofTPU/MWNTcompositesata rangeoffillercontents,showinganuniversallogarithmicresistivity-strain relationshipindependentofCNTconcentration.[26],Copyright2007.
ReproducedwithpermissionfromAmericanPhysicalSociety.
TheFITmodel[178]isexpressedatacertain tempera-tureasfollows[26],assuminganimageforcecorrectionto arectangulartunnelbarrier:
d(lnp)
ds =c+f(T0,T1) (5)
cisanadjustableconstant,sisthestrain,T1isa mea-sureoftheenergythat isrequiredtomoveanelectron acrosstheinsulatinggapandT0isthetemperaturebelow whichtheresistivityreducestotemperature-independent tunnelling.Thevaluesf(T0,T1)exhibitinsignificant vari-ationscomparedwithc,thus,auniversalresistivity-strain behaviourisobservedatarelativehighstrainforeach com-positesystemthatcontainsthesametypeoffillers.
Iftheconductionissimpletunnelling,itiseasytoverify that∼exp(Bω)andd(ln)/ds=Bω,whereBisa numer-icalconstant.Theproductωonlydependsontheheight, shapeandwidthofthetunnellingbarrier[42].Asreported intheliterature[179–181],metalsandalloys(suchasthe nickel,tinandbismutheutecticalloythatwasusedinthis study)generallyhaveahighertunnellingbarrierthanCNTs becausethechargingenergyplaysamoreimportantrolein thetunnellingthatinvolvesametalparticle[182].Hence, asshowninFig.13,ahighervolumefractionofmetalinthe conductivefillerscontributestoahigherresistance-strain sensitivity.
Amodel thatwasderivedfromtunnelling theoryby Simmons[183][184]canbeusedtofurtherunderstand themechanismofstrainsensing.TheoverallresistanceR ofthecompositescanbecalculatedusingEq.(6)andEq.
(7).
R=
LN
8nhs
2a2e2
exp (s) (6)
= 4
2mϕ
h (7)
Listhenumberofparticlesthatformasingle conduc-tivepath,Nisthenumberofconductingpaths,hisPlank’s
Please cite this article in press as: Deng H, et al. Progress on the morphological control of conductive network Fig.13.(Top)ResistivityversusstrainforMWNTandhybridfiller
contain-ingMWNTandmetalindifferentratiosinTPUcomposites.(Bottom)SEM imagesof(a–c)PU-5Cand(d–f)PU-1.5C-15A,at(a,d)atzerostrain,(b,e) 10%strainand(c,f)100%strain.Thesamplesweredrawnalongthearrow direction.Thescalebarsare1m.[158],Copyright2013.Reproducedwith permissionfromtheSocietyoftheChemicalIndustry.
constant,s is thesmallestdistancebetweenconductive particles,a2 istheeffectivecross-sectional area,eisthe electroncharge,mistheelectronmass,ϕistheheightof thepotentialbarrierbetweenadjacentparticlesandnis thetotalnumberofconductiveparticles.
WhenCPCsareunderstrain,theresistancechangesdue tochangesintheparticleseparation.Themorphological observationofconductivenetworksunderdifferentstrains (0%,10%and100%)isshowninFig.13.Foralowstrain (<10%),itisassumedthattheparticleseparationchanges proportionaltotheincreasedstrainfroms0tos,theheight ofthepotentialbarrierchangeslinearlywiththeapplied strain,fromϕ0toϕ,andthenumberofconducting path-waysdecreaseslinearlywithstrain.
s=s0(1+Cε) =s0
1+C
ll0
(8)
s=ϕ0(1+Dε) =ϕ0
[1+D
ll0
(9)
N=N0(1−Eε) =N0
1−E
ll0
(10)
whereN0istheinitialconductingpathnumber,ϕ0is theinitialpotentialbarrierwhennostrainisapplied,i.e.,
thetensilestrainoftheelastomermatrix, listhe defor-mationofthecompositesamples,l0istheinitiallengthof thesampleandC,DandEareconstants.Thesubstitution ofEq.(7)–(9)intoEq.(6)yieldsthefollowing:
R=
B(1+Cx)
√1+Dx(1−Ex)2exp[A(1+Cx)(1−Ex)−0.5
(11)
wherex=ε,A=0S0andB= 28nhs0
0N02a2e2.
Foralargestrain(>10%),itisassumedthatfurther par-ticleseparationhasnoapparenteffectonthebarrierheight andthattheparticleseparationchangesproportionaltothe increasedstrainfroms0tos.Thefollowingexpressioncan thenbeobtained:
s=s0(1+Cε)=s0
1+C
ll0
(12)
Dueto therelativelyhighrateof resistivityincrease underalargestrain,itisassumedthatthenumberof con-ductingpathwayschangesatamuchhigherrateandcan beexpressedasfollows[184]:
N= N0
exp(Mε+Nε2+Uε3+Vε4) (13) whereM,N,UandVareconstants.
ThesubstitutionofEq.(11)and(12)intoEq.(6)yields thefollowing:
R=B(1+Cx)exp[A+(2M+AC)x+2Nx2+2Ux2+2Vx2] (14)
wherex=ε,A=SandB=28Nnhs2 0 0a2e2.
Intheliterature,suchanapproachwasutilisedto ana-lysethestrainsensingbehaviourofvariousCPCs[158,184].
Itwasconcludedthat,ofthedifferentfactors,includingthe tunnellingdistance,tunnellingbarrierheightandnumber ofconductingpathways,ahighertunnellingbarrierheight candirectlyresultinahighersensitivity.Thisresult pro-videsaguidelineforthepreparationofhigh-performance flexiblestrainsensorsfromCPCs.
In terms of damage sensing, composite materials often suffer from damage that is caused by live loads, accidents,mechanical fatigueand various environment-relatedissues.Itisextremelyimportanttomonitordamage topreventahazard,andrepair,replacementoran opera-tionadjustmentcanbeperformedoncedamageisdetected.
Incontrasttooccasionalmonitoring,real-timemonitoring isparticularlyinterestingbecauseitenablesdamagetobe detectedassoonasitoccurs[63].Aconventionalmethod forthismonitoringinvolvestheuseofembeddedsensors (suchasfibre-opticorpiezoelectricsensors)inacomposite structuretomonitordamage.Suchamethodsuffersfrom poordurability,highcost,lossinmechanicalpropertiesand difficultyofrepairingthesensors.
To avoid the use of an embedded sensor, a com-posite structure can be used for damage sensing. The composite structure hastheadvantage of low cost and durabilitycomparedwithconventionalsensors.Moreover, theentirevolumeofacompositestructureiscapableof sensing, incontrast withthelimited sensingvolume of
Please cite this article in press as: Deng H, et al. Progress on the morphological control of conductive network Fig.14.Changeofstressandresistanceduringthedeformationofglass
fiberreinforceepoxycompositescontainingCNTs.Insetsfigures demon-stratetheillustrationofcrackaccumulationstages:microcrackinitiation (Stage1),transversecracking(Stage2),andplydelamination(Stage3).
[160],Copyright2009.ReproducedwithpermissionfromWiley-VCH.
conventional embedded sensors [23,25,63,160,162,163].
Self-sensinghasbeensuccessfulwiththeaidofdirect cur-rent(DC)electricalresistancemeasurementsofglassfibre polymermatrix compositesthatcontaineda conductive nanofiller[160].AsshowninFig.14,Gaoetal.reported thattheuseofCNTconductivenetworksinaglassfibre compositeenabledadamagesensingcapabilitythatcould beutilisedtotrackthenatureandextentofmicrostructural damagewithinthecomposites[160].Generally,damagein theformofcrackingorthedisruptionoftheconductive networkscontributes toan increaseinresistance. How-ever, despitetheadvances that havebeen madein the areaofdamageself-sensinginpolymercomposites, dam-ageself-sensinghasyettobespatialresolved,tothebestof ourknowledge.Becauseapracticalstructuralcomponent tendstobelargeinsize,itsdamageisusuallylocalised.The locationofthedamageisessentialforrepairpurposes.
5.2. Stretchableconductor
Stretchableconductorscanmaintaintheirhigh electri-calconductivitywhenhighlystretched.Researchinthis areahascreatedexcitingopportunitiesandhasattracted intensiveinterestinrecentyears[33–36].Thisspecialtype of CPC is desirablefor applications inrobot arm joints, wearabledisplays,flexibleelectronics,dielectricelastomer actuatorsandstretchablesolarcells,aswellasin medi-calimplantsforhealthmonitoring,diseasediagnosticsand biologicalactuation[34](seeFig.15).AsshowninFig.15, Someya and co-workers [34] have demonstrated thata large-areastretchableactivematrixcanbefabricatedfor organictransistorsusingastretchableconductor.
As indicated by the name, a combination of good mechanical stretchability and highelectrical conductiv-ityisrequiredforstretchableconductors.Inrecentyears,
manystudieshavebeendevotedtothispromisingfield.
Generally, stretchable conductors can berealised using three strategies:(1) theengineering of a new conduct-ingstructuralconfiguration,(2)theuseofaspecialnovel preparation method or (3) the compounding of differ-entconductivefillersintoa polymermatrix.In thefirst strategy,materialstructureswith‘wavy’layouts[185]are utilised.Systemsthatconsistofathinstifflayeronasoft substrateareoftenused[186–188].Whenacompressive stressisappliedtoanelastomericpolymersubstratethatis bondedtoarigidthinfilm,thesurfacestraincanbereleased bymechanical buckling,thereby significantlyimproving thestretchability[189].Moreover,two-dimensional(2D) horseshoeorthree-dimensional(3D)metalinterconnects canalsobeusedasawavystructuretoeffectivelysustain alargestrain(>100%)[33][190,191].
In the second strategy, stretchable conductors can bedevelopedbyintegratingconductivestringsor inter-connectsonto an elasticsubstrateusing high-definition printingtechnologies[192],filtratingalignedCNTforests thatweregrownoniron-catalyst-coatedsiliconinto elas-tomers [193] and casting a preformed conductor onto elastomer sheets [186–188]. However, the functional materialswere directly exposed toharmful strainsand environmentsinsomeoftheseapproaches;therefore,the conductivitywasnotstablewithincreasingstrain. More-over, some of the above methods are complicated and expensive,makingthemunsuitableforthefabricationof arbitrarilyshapedobjectsinlargescaleapplications.
The third method for obtaining stretchable conduc-tors is to compound a conducting polymer [194] (e.g., polyaniline,polypyrroleorhexylthiophene)orconducting fillers[34,188,195,196](e.g.,CB,CNTs,graphite,graphene ormetallicparticles)intoarubberymatrixtoform elas-tic CPCs. Composites witha low content of conducting fillerscanproducehighlyelasticconductorswithastrain higher than 100%, yet the conductivity is typically too low for use as a flexible conductor. Composites witha highconcentrationcanproduceconductorswitha high levelofconductivitybutwithpoorstretchabilitydue to thesegregationor agglomeration of the fillers. Stretch-able conductorsthat canwithstand a largestrain have beenfabricatedusingtensofmicron-tomillimetre-long bundles of SWNTs (see Fig. 15). A mixture of SWNTs andionicliquids(ILs)wasgroundinanagatemortaror stronglysonicatedtoproducechemicallystablebuckygels, whichwerethendispersedinelastomers,suchasa vinyli-denefluoride-hexafluoropropylenecopolymer[34],PDMS [196]orpolyurethane(PU)[195].Theas-prepared compos-itesexhibitedveryhighconductivitiesunderzerostrain and excellent ultimatestretchability. Theadvantages of usingthesematerialsasstretchableelectrodesaretheir excellentprintability andstretchability. However,many reportsencounteredthesameobstacleasabove,i.e.,the electrical conductivitydecreased significantly when the material wasstretched,even for a very highfiller con-tentor whenusinga verylargeaspectratio conductive filler[34,186,197–199].Toovercomethisobstacle, ultra-lightCNTaerogels[198]orpre-growngraphenenetworks [185]wereusedtoprovideanorderedstructurethatwas electricallystableunderanappliedpressure.However,the
Please cite this article in press as: Deng H, et al. Progress on the morphological control of conductive network Fig.15. SchematicsoflargeareastretchableactivematrixconsistingofprintedorganictransistorsandwiringusingSWNTelasticconductor.Thetransistors functionasactivecomponents,andtheSWNTelasticconductorfunctionsaswordlinesandbitlinesforinterconnectionbetweentransistors,andtheinset showstheconductivityasafunctionoftensilestrain.Strain-conductivitymeasurementswereperformedonthreedifferentspecimens:SWNTfilm(1), SWNTelasticconductor(2),andcommerciallyavailablecarbonparticlebasedconductingrubber(3).[34],Copyright2008.Reproducedwithpermission fromtheAmericanAssociationfortheAdvancementofScience.
electricalconductivityofthesematerialswastoolowfor useasastretchableconductor[34].
Toenabletheeasyfabricationofahigh-performance stretchableconductorwithanultrahighconductivityand alowstraindependence,fundamentalaspectsneedtobe consideredduringthepreparationofthisparticulartypeof CPC.Asdiscussedintheabovesections,theelectrical prop-ertiesofCPCsarecloselyrelatedtothemorphologyofthe conductivenetwork[15,32,73,200].Severalmethodshave beenreportedthatcancontrolthemorphologyof these networksand, thus, their electrical property. Neverthe-less,asystematicstudyontherelationbetweenthestrain sensitivityandthemorphologyofconductivenetworksin anelasticconductorstillneedstobeconducted.Thekey tothepreparationofflexibleconductorsistomaintaina stableconductivenetworkduringstretching.Inspiredby thestructureofaspringorawavystructure,whichcan berepeatedlystretchedandreleasedmanytimeswithout losingitsintegrity,itisdesirabletoachieveaconductive networkwithaspring-likestructureinCPCstofabricate a high-performanceflexible conductor. CNTs have been reportedasaflexible,strongandconductivematerial[201].
Themorphologyof CNTsthatareproducedbychemical vapourdeposition(CVD)oftenappearscurlyandexhibits moreorlessasimilarstructuretoaspring,andtheirshape aretunableviaprocessing[73,202].Ourrecentwork[203]
demonstratedthataninterface-mediatedmethod,which involvedpre-strainingandsubsequentthermalannealing, couldbeusedtoaligna randomlyorientedfillerduring the stretching and induced buckling of MWNTs during relaxation.AsshowninFig.16,furthermorphological stud-iesindicatedthepossibleformationofaCNTspring-like structureinducedbycyclicpre-straining.Subsequent ther-malannealingledtothecollapseoftheorientednetwork andtoanimprovementinthelocalcontactsbetweenthe
conductivenetworks.Byusingsuchasimple procedure, a conductivity of almost 1000Sm−1 and a stretchabil-ityof200%couldbeachievedforcompositescontaining 20wt% MWNT (see Fig. 16).These values, which were obtainedbysimplypre-strainingandthermallyannealing theas-preparedCPCs,arecomparabletothosethatwere obtainedfromcomplexandcostlymethods[34,185,198].
Thismethodcouldbeusedasageneralmethodfortheeasy fabricationof a high-performancestretchableconductor withanarbitrarilyshapeinlargescaleapplications.
5.3. Temperaturesensing
Duetothethermalexpansionormeltingofthepolymer matrixinCPCswithincreasingtemperature,achangeinthe conductivenetworkanditselectricalpropertycanoftenbe observed[32,87,170].CPCswithsuchacharacteristiccould serveastemperaturesensors,self-regulatedheatersand over-currentprotectors.
Positive temperature coefficient (PTC) and negative temperaturecoefficient(NTC)effectsareoftenobserved forCPCswithincreasingtemperature[87].ThePTCeffect is thought to be associated with the melting of the crystalline phase [87,123]. Because the transformation ofthecrystallineintoamorphousphase isaccompanied by a significantvolume expansion, which results in an increasedinter-particledistancebetweentheconductive fillers, it reducestheprobability of electronstunnelling betweennearbyconductiveregions.Conversely,theNTC effect isthoughttobedue tothere-aggregation ofthe conductive fillers in the polymer melt, as discussed in Section 4.3. Extensive literature can be found on this topic[31,87,169,170,204,205],andrecentstudieswillbe reviewedinthefollowingpart.Inastudythatwasreported byLiandco-workers[206],theNTCeffectwasobserved
Please cite this article in press as: Deng H, et al. Progress on the morphological control of conductive network Fig.16.(Left)SEMimagesshowthemorphologyofconductivenetworkforas-prepared(A)10wt.%MWNT/TPUCPCs,(C)Pre-strained,(E)Pre-strained
&annealed;(Right)SEMimagesinB,D,FshowthemorphologyofconductivenetworkfortheseCPCsshowsinA,C,E,respectively,under100%strain.
(Middle)Topstrain-resistivitycurvesshowdifferentbehaviorofCPCsatdifferentprocessingstages;bottomgraphshowsorientationstudyfromWAXD andRamanspectroscopyforTPUmatrixandMWNTs,respectively[203].
in a PU foam containing CNTs. The thermal expansion ofthegasthatwaswrappedinthecellularfoam struc-turewasthoughttoberelatedtotheobservedenhanced NTC effect. CPCs that were based on different conduc-tive fillers were alsoinvestigated by Deng et al. [207];
theauthorsdemonstratedthatthemoreentangledMWNT conductivenetwork,whichwascausedbythelargeraspect ratiooftheconductivefiller,gaverisetoadifferentPTC behaviourcomparedwiththelessentangledCB conduc-tivenetwork.Recently,Luetal.[208]demonstratedthat thePTC effectcanbeenhancedand thattheNTCeffect canbeeliminatedbytheselectivelydistributeofCBatthe interfaceofPA6/PSblends.WhenCBisdistributedatthe interfaceofinsitumicrofibrillarpoly(ethylene terephtha-late)(PET)/polyethylene(PE)composites[152],anunusual increaseintheresistivitywasobserveduponcooling. Ther-mallyinducedresidualstressesattheinterfacesbetween thePETmicrofibrilsandthePEmatrixwereresponsiblefor thiseffect.
WhilemostofthestudiesindicatedaPTCeffectnearthe softeningormeltingtemperatureofthepolymermatrix, Karet al. [169]reported a highly repeatablePTC effect belowtheglasstransitiontemperatureofapolymermatrix for CPCsthatwerebased onpoly(methylmethacrylate) (PMMA)andAg-coatedglassbeads.Theauthorsconcluded thatthemismatchofthethermalexpansioncoefficients betweenPMMA andtheglassbeadscausedadisruption inthecontinuousconductivenetworkstructure,evenat atemperaturewellbelowtheTgofPMMA.Inaseparate
WhilemostofthestudiesindicatedaPTCeffectnearthe softeningormeltingtemperatureofthepolymermatrix, Karet al. [169]reported a highly repeatablePTC effect belowtheglasstransitiontemperatureofapolymermatrix for CPCsthatwerebased onpoly(methylmethacrylate) (PMMA)andAg-coatedglassbeads.Theauthorsconcluded thatthemismatchofthethermalexpansioncoefficients betweenPMMA andtheglassbeadscausedadisruption inthecontinuousconductivenetworkstructure,evenat atemperaturewellbelowtheTgofPMMA.Inaseparate