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2024年12月29日发(作者:使用ajax技术能带来什么优势)
/NanoLett
GrapheneSurface-EnabledLithiumIon-ExchangingCells:
Next-GenerationHigh-PowerEnergyStorageDevices
,*
,†
ChenguangLiu,
†
DavidNeff,
†
ZhenningYu,
‡
,
‡
WeiXiong,
‡
and
ArunaZhamu*
,†,‡
†
NanotekInstruments,
‡
AngstronMaterials,Inc.,1242McCookAvenue,Dayton,Ohio45404,UnitedStates
SupportingInformation
b
ABSTRACT:Hereinreportedisafundamentallynewstrategyforthedesignof
proachisbasedonthe
exchangeoflithiumionsbetweenthesurfaces(notthebulk)oftwonanos-
tructuredelectrodes,completelyobviatingtheneedforlithiumintercalationor
electrodes,massivegraphenesurfacesindirectcontact
withliquidelectrolytearecapableofrapidlyandreversiblycapturinglithiumions
throughsurfaceadsorptionand/evices,based
onunoptimizedmaterialsandconfiguration,arealreadycapableofstoringan
energydensityof160Wh/kg
cell
,whichis30timeshigherthanthat(5Wh/kg
cell
)
ofconventionalsymmetricsupercapacitorsandcomparabletothatofLi-ion
ealsocapableofdeliveringapowerdensityof100kW/kg
cell
,
whichis10timeshigherthanthat(10kW/kg
cell
)ofsupercapacitorsand100timeshigherthanthat(1kW/kg
cell
)ofLi-ionbatteries.
KEYWORDS:Supercapacitor,battery,graphene,energydensity,functionalgroup
ithiumionbatteriesandelectrochemicalcapacitors(super-
capacitors),separatelyorincombination,arebeingconsid-
eredforelectricvehicle(EV),renewableenergystorage,and
smartgridapplications.
1À5
Amajorscientificchallengeisto
eithersignificantlyincreasetheenergydensityofconventional
supercapacitorsordramaticallyimprovethepowerdensityof
lithiumionbatteries.
2,3
Supercapacitorsworkontwomainchargestoragemechan-
isms:surfaceionadsorption(electricdoublelayercapacitance,
EDL)andredoxreactions(pseudocapacitance).
1,2
Compared
withbatteries,supercapacitorsdeliverahigherpowerdensity,
offeramuchhighercycle-life,needaverysimplechargingcircuit,
r,supercapacitorsexhibit
,5Wh/kg
cell
forcommercial
activatedcarbon-basedsupercapacitorsversus100À150Wh/
kg
cell
forthecommercialLi-ionbattery,allbasedonthetotalcell
weight).
2
Previousattemptstoincreasethegravimetricenergyof
supercapacitorshaveincludedtheuseofelectrodematerialswith
enhancedgravimetriccapacitances
6
orthepseudocapacitance
providedbynanostructuredtransitionmetaloxides.
7À9
How-
ever,theprohibitivelyhighcostofruthenium-basedoxidesand
thecyclinginstabilityofmanganese-basedoxides
9À11
have
impededthecommercialapplicationofthesesupercapacitors.
In2006,ourresearchgroupreportedgraphene-basedelectrodes
forbothEDLandredoxsupercapacitors,
12
whichhassincebecome
atopicofintensiveresearch.
13À19
Significantprogresshasbeen
,redoxpairsbetweengraphene
oxideÀMnO
2
16
orgrapheneÀpolyaniline
17,18
)andionicliquid
electrolytewithahighoperatingvoltage
13,19
forimprovedenergy
r,thesesupercapacitorshaveyettoexhibita
r
2011AmericanChemicalSociety
L
sufficientlyhighenergydensityorpowerdensityforEVand
renewableenergyapplications.
Lithium-ionbatteriesoperateonFaradaicreactionsinthebulk
lkstoragemechanismprovidesa
muchhigherenergydensity(120À150Wh/kg
cell
)ascompared
r,storinglithiuminthebulkofa
materialimpliesthatlithiummustleavetheinteriorofacathode
activeparticleandeventuallyenterthebulkofananodeactive
particleduringrecharge,e
oftheextremelylowsolid-statediffusionrates,theseprocesses
ult,lithiumionbatteriesdeliveravery
lowpowerdensity(100À1000W/kg
cell
),requiringtypically
hoursforrecharge.
Severaleffortshavebeenmadetoincreasethepowerchar-
acteristicsoflithium-ionbatteriesbyreducingthedimensionsof
lithiumstoragematerialsdowntothenanometerscale,which
wouldreducethelithiumdiffusiontime.
20À23
However,nanos-
,nanoparticlesof
lithiumtitanateanodeorlithiumironphosphatecathode)are
stillnotcapableofdeliveringapowerdensitycomparabletothat
ofsupercapacitorelectrodes.
Recently,Leeetal.
24
usedchemicallyfunctionalizedmulti-
walledcarbonnanotubes(MW-CNTs)toreplaceactivated
carbon(AC)asacathodeactivematerialandLi
4
Ti
5
O
12
asan
anodeactivematerialinalithium-ioncapacitor(LIC)
LICcell,theLi
4
Ti
5
O
12
anodestillrequireslithiumintercalation
Received:May31,2011
Revised:August1,2011
Published:August08,2011
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/10.1021/nl2018492
|
NanoLett.2011,11,3785–3791
NanoLetters
Figure
enabled,
1.(a)Upperportionshowsthestructureofafully
current
Liion-exchangingcellwhenitismade,containingan
surface-
anode
source
separator,
(e.g.,
collectorandananostructuredmaterialattheanode,aLiion
cathode.
liquid
pieces
electrolyte,
ofLifoilorsurface-stabilizedLipowder),aporous
fi
electrolyte
rstdischarge
Thelower
(Liis
left
ionized
portion
ananostructured
with
showsthestructure
functional
ofthis
material
cellafter
atthe
its
tured
portion
cathode
toreach
and
surface-borne
the
rapidlyreacting
functional
Liionsdiffusingthroughliquid
withthese
groups
groups).
inthe
Lower
nanostruc-
rapidly
showsthestructureofthiscellafterbeingrecharged(Liions
right
liquid
releasedfromthemassivecathodesurface,diffusingthrough
are
can
ions
serve
electrolytetoreachtheanodeside,wherethehugesurfaceareas
structure
canelectrodeposit
asasupportingsubstrateontowhichmassiveamountsofLi
provide
functional
accessibility
ofatreatedcarbon
concurrently,
byliquid
black
and(b)schematicoftheinternal
electrolyte
particlewith
in
poresorgatesopenedto
smallgraphene
groups
sheet
attached
canreadily
toanedge
react
or
with
surface
suchamannerthatthe
Liions.
ofanaromaticringor
intoandoutofthebulkofasolidparticle,whichremainsslow
andprovidesrelativelylowenergydensityandpowerdensity.
Leeetal.
24
alsoinvestigatedahalf-cellconfiguration,wherein
impressivepowerdensities,evenhigherthanthoseofsuper-
capacitors,r,theseexceptionalpower
densitiescouldonlybeachievedwithanelectrodethicknessof
0.3À3μmobtainedbythelayer-by-layer(LBL)approach.
Further,sincethespecificsurfaceareaofacurrentcollector
(typically,1m
2
/g)istoolowtoaccommodatemassive
amountsofreturninglithiumions,theoveralllithiumredeposi-
nfigurationis
alsoconducivetotheformationofdendritesuponrepeated
chargesanddischarges.
Anewparadigmishereinpresentedforconstructinghigh-
powerlithiumcells,whicharetotallygraphenesurface-mediated
orsurface-enabled,involvingexchangeofmassivelithiumions
betweentwonanostructuredgrapheneelectrodes.
AsillustratedinFigure1,boththecathodeandtheanodeare
porous,havinglargeamountsofgraphenesurfacesindirect
contactwithliquidelectrolyte,therebyenablingfastanddirect
surfaceadsorptionoflithiumionsand/orsurfacefunctional
group-lithiuminteraction,andobviatingtheneedforintercala-
ecellismade,particlesorfoiloflithiummetalare
implementedattheanode(upperportionofFigure1a),which
areionizedduringthefirstdischargecycle,supplyingalarge
onsmigratetothenanostruc-
turedcathodethroughliquidelectrolyte,enteringtheporesand
reachingthesurfacesintheinteriorofthecathodewithout
havingtoundergosolid-stateintercalation(lowerleftdiagramin
Figure1a).Whenthecellisrecharged,amassivefluxoflithium
ionsarequicklyreleasedfromthelargeamountofcathode
surface,gesurfaceareaof
thenanostructuredanodeenableconcurrentandhigh-rate
depositionoflithiumions(lowerrightportionofFigure1a),
re-establishinganelectrochemicalpotentialdifferencebetween
thelithium-decoratedanodeandthecathode.
Aparticularlyusefulnanostructuredelectrodematerialisthe
nanographeneplatelet(NGP),whichreferstoeitherasingle-
e-
layergraphenesheetisa2Dhexagonlatticeofcarbonatoms
covalentlybondedalongtwoplanedirections.
25À28
Inthisstudy,bothoxidizedandreducedsingle-layerand
multilayergraphenewerepreparedfromnaturalgraphite(N),
petroleumpitch-derivedartificialgraphite(M),micrometer-
scaledgraphitefibers(C),exfoliatedgraphite(GorEG),AC,
carbonblack(CB),andchemicallytreatedcarbonblack(t-CB).
ACandCBcontainnarrowergraphenesheetsoraromaticrings
asabuildingblock,whilegraphiteandgraphitefiberscontain
icrostructuresallmustbeex-
foliated(toincreaseintergraphenespacingingraphite)or
activated(toopenupnanogatesorpores,Figure1b)toallow
liquidelectrolytetoaccessmoregrapheneedgesandsurfaces
(experimentaldetailsprovidedinSupportingInformation).
Coin-sizecellswereconstructedtotestthesenanostructured
odeswerepreparedwith85%active
material,5%conductiveadditive,and10%swere
calculatedpertotalcathodematerialandpertotalcellweight
(approximatedascathodeweightÂ5).Thesampleswere
thermallyexfoliatedgraphite(CellG),graphenefromchemically
reducedgrapheneoxide(CellN),graphenefromoxidized
artificialmesophasegraphite(CellM),graphenefromoxidized
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Figure2.(a)AFMimageofsingle-layergrapheneoxidesheetsfromnaturalgraphite,(b)single-layergraphenesheetsstackedoverthesample-
supportingTEMmicrogrids,and(c)scanningelectronmicroscopyimageofexfoliatedgraphite.
carbonfiber(CellC),carbonblack(CellCB),oxidizedcarbon
black(t-CB),andactivatedcarbon(CellAC).Thesematerials
,>CdOandÀCOOH)that
-
phenoxidesheetsaremostlysingle-layered,basedontheresults
ofcombinedBrunauerÀEmmettÀTeller(BET)surfaceanalysis,
atomicforcemicroscopy(AFM)(Figure2a),andtransmission
electronmicroscopy(TEM)(Figure2b).Theconstituent
graphiteflakesinagraphitewormorexfoliatedgraphite
(Figure2c)remaininterconnectedasanetworkof3Delec-
tron-conductingpaths,andthemeso-andmacroscaledpores
betweenflakewallsareeasilyaccessibletoliquidelectrolyte.
TheGalvanostaticcharge/dischargecurvesandcyclicvoltam-
metry(CV)diagramsofCellsM,C,G,andNareshownin
Figure3a,b,rredoxpeakisobservedin
enotedthattheCVcurvesofboththe
conventionalpseudocapacitorsandlithium-ionbatteriestendto
exhibitastrongredoxpeakduetoslowerFaradaicredox
,
polyanilineinapseudocapacitor,lithiumtitanateinalithium-
ionbattery,andLi
x
C
6
O
6
inanorganicelectrodebattery
29
).The
lackofastrong,well-definedredoxreactionpeakintheCVsof
ourfullysurface-mediateddevicesandtheLBLCNTdeviceof
Lee,etal.
24
mightbeduetothefollowingreasons:(1)the
reactionbetweensurfacefunctionalgroupsandultrasmall
lithiumionsarerelativelyfastandoflowactivationbarrier
(Figure1b);
24,25,30À32
(2)fastadsorptionofLionabenzene
ringcenterofagraphenesheet;
33À35
(3)fasttrappingofLiions
ingraphenedefectsites;
36
and/or(4)electricdouble-layer
lelithium-capturingmechanismsofgraphene
surfacesarefurtherdiscussedinSupportingInformation.
,CellM)
withaspecificcapacityof127mAh/gatacurrentdensityof1A/g,
reachinganenergydensityof85Wh/kg
cell
(Figure3c)ata
currentdensityof0.1A/g,whichis17timeshigherthanthe
typically5Wh/kg
cell
ofcommercialAC-basedsymmetricsuper-
l-levelenergydensityandpowerdensitydata
presentedinFigure3c,dwereobtainedbydividingthecorre-
spondingvalues(basedonsingle-electrodeweight)inSupport-
ingInformationFigureS12andS13byafactorof5.
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Figure3.(a)Charge/dischargecurvesofthreesurface-enabledcells(M=NGPfrommesophasecarbon-derivedgraphite,C=NGPfromcarbonfibers,
G=fromexfoliatednaturalgraphite),andN=chargecurrentdensityis1A/g.(b)The
CVplotsofthesamecellsatthescanrate25mV/s,(c,d)RagoneplotsoftheseandCB,t-CB,andACcellswiththickcathodes.
Anothergraphenesurface-mediatedcell(CellN,Figure3d)
exhibitsanevenhigherenergydensityof160Wh/kg
cell
,
rgydensity
ofCell-Nmaintainsavalueover51.2Wh/kg
cell
evenata
currentdensityashighas10A/g,deliveringapowerdensityof
4.55kW/kg
cell
.ThepowerdensityofcommercialAC-based
symmetricsupercapacitorsistypicallyintherangeof1À
10kW/kg
cell
atanenergydensityof5Wh/kg
cell
,Thisimplies
that,comparedwithaconventionalsupercapacitoratthesame
powerdensity,thesurface-mediateddevicescandeliver>10
timestheenergydensity.
ThepowerdensityofCellNis25.6kW/kg
cell
at50A/gwith
anenergydensityof24Wh/kg
cell
.Thepowerdensityincreases
to93.7kW/kg
cell
at200A/gwithanenergydensityof12Wh/
kg
cell
(Figure3d).Thispowerdensityis1orderofmagnitude
higherthanthatofconventionalsupercapacitorsthatarenoted
fortheirhighpowerdensities,and2À3ordersofmagnitude
higherthanthat(typically0.1À1.0kW/kg
cell
)ofconventional
atahaveclearlydemonstratedthat
thesurface-enabledcellsareaclassofenergystoragecellsby
itself,distinctfrombothconventionalsupercapacitorsand
lithium-ionbatteries.
Figure3bcontainsacomparisonofCVdatashowingthatthe
carbonfiber-derivedgraphene(CellC)andmesophasecarbon-
derivedgraphene(M)havebetterperformancethanthermally
exfoliatedgraphite(G)in
linewiththeobservationthatCandMexhibitedsignificantly
higherÀCOOHandÀCdOcontents(Figure4b),whichare
capableofcapturingLiionsviaafastsurfaceredoxreaction.
Figure3dindicatesthattheenergydensityandpowerdensity
valuesofCBcanbesignificantlyincreasedbysubjectingCBtoa
treatmentthatinvolvesanexposuretoamixtureofsulfuricacid,
sodiumnitrate,
surfaceareawasfoundtoincreasefromapproximately122m
2
/g
toapproximately300m
2
/g,resultinginacapacityincreasefrom
8.47to46.63mAh/g).AlthoughAChasahighspecificsurface
area(1200m
2
/g),asignificantproportionoftheporesinACare
microscopicpores(<1nm)and,hence,arenotaccessibleto
,CellACdoesnotexhibithigher
powerandenergydensitiescomparedtoNGPcells.
ThecyclingperformanceforMcellisshowninFigure4aand
,NandAC)isinSupportingInformation
ementsweretakenonceevery100cycles
duringa0.1A/gchargeanddischarge,followingthesame
methodwithliterature
24
(forcomparisonpurpose).Allother
cycleswererunatanacceleratedrateof1A/1000cycles,
theretentionofcapacityremainsabove95%,whichillustratesthe
labilitycanbefurther
enotedthatmore
than30graphenesurface-enabledcellshavebeeninvestigatedfor
morethan2000cycles,andwehavefoundnoevidenceto
indicatetheinitiationofanydendrite-likestructure.
Thepresenceoffunctionalgroups,suchasÀCOOHand
>CdO,inchemicallypreparedgrapheneoxidehavebeenwell
documented.
37,38
Theformationofthesefunctionalgroupsisa
naturalresultoftheoxidizingreactionsofgraphitebysulfuric
,nitricacidandpotassium
permanganate).Bothunseparatedgraphitewormsandthe
separatedNGPshavesurface-oredge-bornefunctionalgroups.
Carbonylgroups(>CdO)inorganicandpolymericelectrodes
werefoundtobecapableofreadilyreactingwithlithiumionsto
formredoxpairs.
24,29
AccordingtoLeeetal.,
24
ÀCOOHgroups
onCNTsurfacesarecapableofreversiblyandrapidlyforminga
redoxpairwithalithiumionduringthechargeanddischarge
3788
/10.1021/nl2018492|NanoLett.2011,11,3785–3791
NanoLetters
Figure4.(a)ementsweretakenonceevery100cyclesduringa0.1A/gchargeand
ercycleswererunatanacceleratedrateof1A/ndofthetest,thecapacitywas95%entionmaybe
furtherimprovedwithoptimizationofthematerialpreparationprocedure.(b)FTIRspectraofthethreematerials,indicatingthatbothexfoliated
mesophasecarbon-andcarbon-fiber-basedelectrodes(MandC)exhibitmoreÀCOOHand>CdOgroupscomparedtotheexfoliatedgraphitesample
(G).(c)CyclicvoltammetryplotsofoxidizedMcellandapartiallyreducedMcell.(d)RagoneplotofoxidizedMcellandapartiallyreducedMcell,
indicatingsignificantlyreducedcapacity,energydensity,andpowerdensitywhenasignificantproportionofthefunctionalgroupswaseliminated.
(e)TheRagoneplotsofgraphenesurface-enabledLiion-exchangingcellswithdifferentelectrodethicknesses.
nceivablethatLiionsalsocanreactwith
the>CdOandÀCOOHgroupsonthegrapheneplanesor
edgesofseparatedgraphenesheets,theunseparatedgraphene
sheetsthatconstitutegraphiteworms,andthearomaticrings
(smallgraphenesheets)inACortreatedCB.
ThetypicalgravimetriccapacitanceofNGPelectrodesinthe
voltagerange3À4.2VversusLi(withacomparablevoltagescale
of0to∼1.2Vversusstandardhydrogenelectrode(SHE))is
150À350F/arbonyl(>CdO)groups,forinstance,can
bereducedbyLi
+
andreversiblyoxidized,capacitanceobtained
canbeattributedtotheFaradaicreactionsofoxygenonthe
grapheneedgeorsurface,illustratedasfollows
>CdO
graphene
þLi
þ
þe
À
T>CÀOLi
graphene
Onthebasisofelementalanalysis,theoxygencontentof
naturalgraphite-,artificialgraphite-,andcarbonfiber-derived
grapheneoxidesampleswere12.9,28.8,and20.8%,respectively.
TheFTIRspectraofthethreecathodematerials,shownin
Figure4b,indicatethatbothCellMandCellCexhibitmore
ÀCOOHand>
consistentwiththeobservationsthatCellsMandCexhibit
higherenergydensityandpowerdensitythanCellGprovided
thatLibondingwiththesefunctionalgroupsisaprimarylithium-
capturingmechanism.
Theroleofsurfacefunctionalgroupsinprovidinghigh
capacitancesingraphite-derivedgraphenewasfurtherillustrated
bycomparingthespecificcapacitanceofthegraphenematerial
beforeandafterexposuretoareductiontreatment(in4%H
2
and
96%N
2
at900°Cfor3h).AsshowninFigure4c,thegravimetric
currentofthegrapheneelectrodeinCellMdecreasedconsider-
ably(by65%)afterthisthermalreductiontreatmenttoreduce
acitanceofthereduced-
NGPcellis43mAh/gand50F/gatacurrentdensityof1A/g.
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Acomparisonoftheenergydensityandpowerdensitydatainthe
RagoneplotofFigure4dseemstosuggestthatthereductionin
oxygencontent(hence,thefunctionalgroupcontent)ledtoa
servationseemsto
beconsistentwiththeproposedlithiumstoragemechanismvia
thesurface-basedredoxreactionbetweenLiandfunctional
r,moreresearchisneededbeforeamore
definitivemechanismcanbevalidated.
ThesourceofextraLi
+
,Lipowder)implementedat
theanodeandtheLi
+
ions
+
pre-existinginliquidelectrolyte
providelargeamountsofLiionsthatcanbeshuttledbetween
twonanostructuredelectrodes,whicharefullycapableofcaptur-
themain
reasonwhythesurface-enabledcellsexhibitexceptionalenergy
densities.
Iftheseionscanmigrateatasufficientlyhighrate(short
migrationtimes),thentheultrahighpowerdensitywouldbe
brieflydiscussedbelow:Fordescribingtheion
transportinacell,theNernstÀPlanck(NP)equation(eqS4in
SupportingInformation)maybemoreaccurateascomparedto
theFick’equationprovidesthefluxofions
undertheinfluenceofbothanionicconcentrationgradientand
anelectricfiportingInformationprovidesseveral
significantobservations:
(1)Conventionallithiumionbatteriesfeaturingamicro-
meter-sizedgraphiteanodeandamicrometer-sizedLiFe-
PO
4
,7.29h)to
completetherequiredprocessesofintercalationinone
electrodeanddeintercalationintheotherelectrode
(SupportingInformationFigureS5a).Thisproblemof
alongdiffusiontimecanbepartiallyalleviatedbyusing
nanoscaledparticles.
(2)Forthefullysurface-mediatedcells,theelectrodethick-
tance,inthecaseof
usingfunctionalizedNGPastheelectrodes(Supporting
InformationFigureS8a),thetotalmigrationtimeofLi
ionsinliquidelectrolyteis1.27sifthecathodeandanode
areeach200μmthickandseparatoris100μ
migrationtimeisreducedto0.318siftheanode=
cathodethickness=100μmandseparatorthickness=
50μerimentalchargeanddischargetimedata
showninSupportingInformationFigureS9a,barecon-
llwithan
anodecenter-to-cathodecenterdistanceof250μm,an
ionmigrationtimeof0.88swasobtainedthrough
mentally,underhighcurrentdensity
conditionsthetotaldischargetimewasfoundtobe
between0.4and1.5s.
(3)Theaboveobservationsimplythatthesurface-enabled
cellsshouldhaveanextraordinarypowerdensity,parti-
er
densitiesobservedwithgraphene-enabled,fullysurface-
mediatedcells(withanelectrodethicknessof80μm,
Figure4e)arecomparableorslightlysuperiortothoseof
LBLf-CNT-basedbatteries
23
(thicknessof3μm)at
comparablecurrentdensities.
Therearegreatamountsofsuitablesitesavailableontheedges
ofagraphenesheet(inanNGP,AC,orCBnanostructure)ora
graphiteflake(inanexfoliatedgraphiteworm)toacceptfunc-
hlowercostofAC,CB,graphene,and
exfoliatedgraphite,andtheireaseofformingabulkelectrode
makethesenanocarbonsidealelectrodematerialsforthisnew
classofhigh-powerenergystoragecell.
Insummary,anewgenerationofenergystoragedeviceshas
beendevelopedwiththelithiumstoragemechanismandkinetics
ullysurface-enabled,lithiumion-exchanging
cellswiththeirmaterialsandstructuresyettobeoptimizedare
alreadycapableofstoringanenergydensityof160Wh/kg
is30timeshigherthanthatofconventionalelectric
cell
,
which
doublelayer(EDL)erdensityof
100kW/kg
cell
is10timeshigherthanthat(10kW/kg
EDLsupercapacitorsand100times
cell
)of
conventionalhigher
thanthat(1kW/kg
Figure4enicelydemonstrates
cell
)ofconventionallithium-ionbatteries.
thatthesurface-enabledcellsarea
classofenergystoragecellsbyitself,distinctfrombothsuper-
rkisneeded
tomoreclearlydifferentiatethedominantlithium-storage
mechanism(s)betweensurfaceredox,surfaceadsorption,
andsurfacedefecttrapping.
’
ASSOCIATEDCONTENT
b
SupportingInformation.
Descriptionofmaterialsand
terialisavailablefreeofchargeviatheInternet
at.
’
AUTHORINFORMATION
CorrespondingAuthor
*E-mail:(B.Z.J.)@;(A.Z.)
@.
’
ACKNOWLEDGMENT
chnologyInnovation
Program(TIP)Grant(ProgramManagers:Grinspon
u)isgratefullyacknowledged.
’
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Lett.
B
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