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TRIBOLOGYOF GRAPHENE
TRIBOLOGYOF GRAPHENE SimulationMethods,
PreparationMethods, andtheirApplications
OLEKSIYV.PENKOV
ZJU-UIUCInstitute,InternationalCampus, ZhejiangUniversity
Elsevier
Radarweg29,POBox211,1000AEAmsterdam,Netherlands TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates ©2020ElsevierInc.Allrightsreserved.
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AbouttheAuthor
OleksiyV.Penkov iscurrentlyanassociateprofessorattheZhejiangUniversity/theUniversityofIllinoisatUrbana-ChampaignInstitute,Haining, China.HereceivedhisB.S.andM.S.degreesfromtheNationalTechnical University“KhPI”(Ukraine).In2007,hereceivedhisdoctoratedegreein physicsandmathematics,withaspecialtyinsolid-statephysics.Sincethen, hestayedinKoreaasapostdocandresearchprofessor.During2011–19,he wasaresearchprofessorattheCenterforNano-Wear,YonseiUniversity. HejoinedtheZJU-UIUCInstitutein2019.Hisresearchinterestscover severalareasofphysics,materialsscience,andmechanicalengineeringsuch asnano-layeredcoatings,tribology,andsurfaceengineering.
Preface
Frictionandwearareubiquitousfeaturesofmechanicalsystemshavingcontactbetweenmovingcomponents.Thesephenomenaareresponsiblenot onlyforthedegradationofmechanicaldurabilityandefficiencyduetoprogressivelossofmaterial,butalsoforexcessiveenergyconsumption.So,itis notsurprisingthatsignificanteffortshavebeendevotedtothecreationof effectivemethodsofcontroloftribologicalproperties.Oneofthe approachesistouseanothermaterialintheformofacoatingonslidingcomponentsthatprovideslowfrictionandwear.Thefabricationofintegral mechanicalcomponentsusingsuchmaterialsinthebulkformcouldbe complicatedandnotcosteffective,orevenimpossible.Acombinationof differentmaterialsforthebulkandsurfaceishighlyattractivebecauseit allowstailoringdifferentphysicalandmechanicalproperties.Inotherwords, surfacemodificationbycoatingscanprovideauniquecombinationofpropertiesandmultifunctionalityandoffersuperiortribologicalfeatures.
Tribologicalbehaviorisessentialonallscalesofmechanicalapplications, fromthenanotothemacro.Itplaysavitalroleintheperformanceofultraprecisionmechanicalsystemssuchasmicroelectromechanicalsystems (MEMS).DuetothesmallsizeandtighttoleranceofMEMSdevices,the effectivenessofmechanicalcomponentssuchasswitches,gears,andactuatorsisstronglydependentontheirfrictionalbehaviorwhilethewearresistancedeterminesthemechanicalandcommercialviabilityofthedevice. Furthermore,classicalmethodsforreducingfrictionwithlubricatingfluids cannotbeemployedinmicrosystemsbecauseofsignificantsurfacetension effects.Therefore,thetribologicalpropertiesofthecomponentsmustbe optimizedunderdryslidingconditionstoallowthedevelopmentofreliable microdevices.Differenttypesofthincoatingssuchassoftmetals,organic compoundssuchasself-assembledmonolayers,bilayerandmultilayerhard coatings,diamond-likecarbonfilms,andnanostructuredcoatingscanbe usedtoreducefrictionandwearinmicrodevices.
Nonetheless,despitereportsofnumerousproposedcoatings,auniversal methodforreducingthefrictionandwearofthesedeviceshasnotyetbeen identified.Thus,thediscoveryandinvestigationofnewmaterialsfornanoandmicrotribologicalapplicationsarestillongoing.Onesuchnewmaterial demonstratinghighpotentialfortribologicalpropertiesisgraphene.During thelastdecades,graphenehasattractedmuchattentioninthematerials
communityduetoitsexceptionalfeatures.Inadditiontoitsuniqueelectrical properties,themechanicalpropertiesofgraphenearealsoimpressive.Graphenehashighlevelsofstiffness,strength,andthermalconductivityandis alsoimpermeabletogas.Thecombinationoftheremarkablemechanical, thermal,chemical,andelectricalpropertiesofgraphenesheetsandtheirrelativelylowproductioncostdistinguishesthemfromothermaterialsusedfor nanoelectromechanicalapplications.Thus,graphenehasbeenconsidereda promisingmaterialforapplicationsinnanoelectronicsandminiaturized devices.
Moreover,duetoitssuperiorstrength,graphenehasexcellentpotential foruseasanultrathinprotectivecoatingforvariousmacroscalecomponents exposedtocontactstress.Graphenederivativessuchasfunctionalizationgraphenehaveopenednewperspectivesforuseinindustrialtribologicalapplicationsduetotheirrelativelylowprice.
Besidessolidlubrication,graphenematerialscanbeusedforthe improvementofvarioustypesofcompositematerialsfrompolymersto ceramics.Theyalsodemonstratedtheirperformanceasnanoadditivesfor differentkindsoflubricantssuchaswater,oils,greases,andionicliquids. Aminimalamountofgrapheneadditivecanenhancethedurabilityofcompositematerialsandtheperformanceoflubricants.
Inthisbook,advancementsmadeinthefabricationandapplicationsof graphenematerialsforthereductionoffrictionandweararereviewed.The aimistoprovideacomprehensiveoverviewofvarioustypesofgraphenebasedmaterialsfortribologicalapplicationsandgainabetterunderstanding oftheiradvantagesandlimitations. OleksiyV.Penkov
Acknowledgments
Firstandforemost,IwouldliketoexpressmysinceregratitudetoProf. Dae-EunKim(DepartmentofMechanicalEngineering,YonseiUniversity),whointroducedmetotribology.Hemotivatedmetowritemyfirst reviewpaper(TribologyofGraphene:AReview),whichfinallyevolvedinto thisbook.
Iamincrediblythankfultomyteachers,advisors,andformercolleagues fromtheNationalTechnicalUniversity“KharkivPolytechnicInstitute,” andespeciallytheX-rayopticslab.Thankallofyouforbringingmeto science.
Iacknowledgehundredsofresearcherscitedinthisbook.Thisbook wouldnotbepossiblewithouttheirfantastictheoreticalandexperimental work.
Imustalsorecordanotherspecialtributetomyfamily.Myparents,thank youforyourloveandconstantsupportasIsatisfymyowncuriosity.Mywife Evgeniya,thankyouforyourunfailinglove,sacrifice,andencouragement torealizemydreamaswellasyourconsiderationinmyeverydaylife.
OrganizationoftheBook
Thisbookisorganizedintoeightchapters,eachofwhichhasalistof references.
Chapter1 introducesthestructureofgrapheneanditsderivatives,basic definitions,andnomenclature.In Chapter2,theresultsofcomputersimulationsofthemechanicalandtribologicalperformanceofgraphenearediscussed. Chapter3 providesabriefoverviewofthepreparationand characterizationmethodsforgraphene,itsderivatives,andgraphene-based composites. Chapter4 evaluatesthetribologicalperformanceofgraphene fromthenano-tothemacroscale. Chapter5 discussesthepossibilityof replacinggraphenewithcheaperderivativesindifferenttribologicalapplications. Chapter6 isanoverviewoftheutilizationofgraphenereinforcementforimprovementofcompositematerials. Chapter7 discussesthe performanceofgraphene-basednano-additivesinlubricants,including water,oils,greases,andionicliquids. Chapter8 summarizestheoverallcontentofthebookanddiscussesthefuturedirectioninthetribologyof graphene.
Abbreviations
AFM atomicforcemicroscopy
AIREBO adaptiveintermolecularreactiveempiricalbondorderpotential
APCVD atmospheric-pressurechemicalvapordeposition
CMS computermodelingandsimulation
CNT carbonnanotube
CQD carbonquantumdots
CVD chemicalvapordeposition
DFT densityfunctionaltheory
DLC diamond-likecarbon
DV divacancy
EHL elastohydrodynamiclubrication
EHT epoxy-hydroxyl-terminatedrGO
EPD electrophoreticdeposition
ESCA electronspectroscopyforchemicalanalysis
ESD electrodynamicsprayingdeposition
FEM finiteelementsmethod
FG fluorinatedgraphene
fG functionalizedgraphene
fGO functionalizedgrapheneoxide
FTIR Fouriertransforminfraredspectroscopy
GIC graphiteintercalationcompound
GNP graphenenanoplatelet
GNR graphenenanoribbons
GNS graphenenanosheets
GO grapheneoxide
GONR grapheneoxidenanoribbons
HAADF high-angleannulardark-fieldimaging
HIP hotisostaticpressing
HOFG hydroxyl-functionalizedgraphene
HOPG highlyorderedpyrolyticgraphite
HRTEM high-resolutiontransmissionelectronmicroscopy
HT hydroxyl-terminatedrGO
IL ionicliquid
ISS internalshearstrength
LPCVD low-pressurechemicalvapordeposition
LST lasersurfacetexturing
MC MonteCarlo
MD moleculardynamics
MEMS/NEMS microelectromechanicalsystems/nanoelectromechanicalsystems
MG multilayergraphene
xviii Abbreviations
ML machinelearning
MSM molecularstructuralmechanics
NDP nanodiamondparticles
OFGR oxyfluorinatedgraphene
oWNC oxidizedwood-derivednanocarbon
PECVD plasma-enhancedchemicalvapordeposition
PGO pristinegraphiteoxide
PLD pulsedlaserdeposition
QCM Quartzcrystalmicrobalance
QC quantumchemistry
REBO reactiveempiricalbondorderpotential
rGO reducedgrapheneoxide
SAM self-assemblymonolayers
SEM scanningelectronmicroscopy
SPS sparkplasmasintering
STEM scanningtransmissionelectronmicroscope
STM scanningtunnelingmicroscopy
SW Stone-Walesdefect
TEM transmissionelectronmicroscopy
XPS X-rayphotoelectronspectroscopy
XRD X-raydiffractometry
Chemicalabbreviations
APS 3-aminopropyltriethoxysilane
APTES 3-aminopropyltriethoxysilane
APTMS 3-aminopropyltrimethoxysilan
BLG β-lactoglobulin
BMIMI 1-butyl-3-methylimidazoliumiodide
BScB bis(salicylate)borate
DDA dodecylamine
DDP alkylphosphate
DMF N,N-dimethylformamide
EC ethylcellulose
EMIM 1-ethyl-3-methylimidazolium
EP epoxy
ETA ethanolamine
GPTS 3-glycidoxypropyl-trimethoxysilane
HBPE hyperbranchedpolyamine-ester
MAC multiply-alkylatedcyclopentane
MC monomercastednylon
NBR acrylnitrilebutadienerubber
NMP N-methylpyrrolidone
ODA octa-decylamine
OHMimBScB 3-(hydroxypropyl)-3-methylimidazoliumbis(salicylate)borate
OL oleate
OTA octylamine
OTS hydroxylatedoctadecyltrichlorosilane
PAO polyalphaolephin
PA polyamide
PDA polydopamine
PDMS polydimethylsiloxane
PEEK poly(ether-etherketone)
PEG poly(ethyleneglycol)
PEI polyethyleneimine
PET polyethyleneterephthalate
PFDTS perfluorodecyltrichlorosilane
PFPE perfluoropolyether
PF phenol-formaldehyde
PI polyimide
PMMA poly(methylmethacrylate)
PPS polyphenylenesulfide
PSS poly(sodium4-styrenesulfonate)
PTFE poly(difluoromethylene)
PTFE polytetrafluoroethylene
PU polyurethane
PVC poly(vinylchloride)
PVDF polyvinylidenedifluoride
PVP poly(vinylpyrrolidone)
PWF polytetrafluoroethylenewax
SDBS sodiumdodecylbenzenesulfonate
TFSI bis(trifluoromethylsulfonyl)imide
UHMWPE ultrahighmolecularweightpolyethylene
ZDDP zinccialkylcithiophosphatelubricantadditives
Introductiontographene
1.1Introductiontographenestructure
Carbonisoneofthemostessentialmaterialsfororganiclife,and“graphene” isthenameofoneofthecarbonallotropes.Theword“graphene”consistsof theprefix“graph,”whichcomesfromgraphite,andthesuffix“ene,”which representsthecarbon/carbondoublebonds [1].Ingeneral,theword “graphene”referstoamonolayerofsp2-hybridizedcarbonatomspacked intoatwo-dimensional(2D)honeycombstructurethatispartiallyfilledwith π-orbitalsaboveandbelowthemonolayer [2].Thegraphenemonolayeris atomicallyflatwiththeVanderWaalsthicknessof 0.34nm.Thismonolayerrepresentsabuildingblockforallothergraphiticmaterials.Graphene canexistnotonlyintheformofthesinglemonolayer(sheet)butalsointhe multilayerformwhereseveralsheetsarestackedtogether,formingathreedimensional(3D)structure(Fig.1.1).Besidetheformingof3Dgraphite, graphenecanbewrappedupintozero-dimensional(0D)fullerenesorrolled intoone-dimensional(1D)nanotubes(Fig.1.2) [3]
Initially,itwasassumedthatgraphenecouldnotbestandalonebecauseof thepredictedthermodynamicinstabilityof2Dcrystals [2].Nonetheless,the theoreticalpredictionsaboutthismaterialbecamerealin2004whenitwas demonstratedthatisolated2Dstructurescannotonlybestableatroomtemperatureandintheair,butalsomaintainmacroscopiccontinuity [4].
Grapheneisafundamentalelementofalargegroupof2Dand3Dcarbon formsthatincludesmaterialswithverydifferentproperties,lateralsizes,and numberoflayers.Theterm“graphene”canbeprefixedby“bilayer,”“fewlayer,”or“multilayer.”Thisclassificationisessentialbecausetheproperties
TribologyofGraphene
2020ElsevierInc. https://doi.org/10.1016/B978-0-12-818641-1.00001-0
Fig.1.1 Formationof3Dgraphenefroma2Dbuildingblock threecommongraphite structureswithdifferentgraphenestackingarrangements:hexagonalstacking(AA), Bernalstacking(AB),andrhombohedralstacking(ABC).
Fig.1.2 A2Dgraphenesheetisthebaseforotherallotropes:0D(fullerene)and1D (carbonnanotube).
ofmono-,bi-andmultilayergraphenedifferfromthepropertiesofgraphite andeachother [1,2].Besides,differentnamescanbeusedforthesamestructures.Forexample,“multilayernanosheet”hasthesamemeaningas“fewlayernanoplate.”Themostcommonlyusedterminologyofgrapheneis summarizedin Table1.1
Table1.1 Nomenclatureofgraphenematerialsbasedontheirdimensions.
Parameter
Aspectratio A (length/width)Lateralsize D (nm) Range 1
Numberoflayers n
NomenclatureSingle-layer; monolayer Few-layer; multilayer GraphiteNanoMicro - Flake - Sheet - Plate - Platelet - Ribbon
Therearethreepossiblestackingconfigurationsoffew-layergraphene (Fig.1.1):Bernal(AB),hexagonal(AA),andrhombohedral(ABC) [5,6]. Thesestackingconfigurationsdifferintherelativeorientationofthegraphenelayerstacksthatmaybecrucialforsomeapplications.Forinstance, thestackingordersignificantlyaffectedtheelectronicstructureoffew-layer graphene [5].Amongthepossiblestackingconfigurations,theBernalconfigurationhastheloweststackingenergy [7].Thisconfigurationisformedby stackingtwographenesheetsrotatedby60degreesrelativetoeachother aroundthez-axis.Inthiscase,the3Dunitcellhasfouratoms,andathird basisvectorperpendiculartothegraphenelayerstacksis0.6672and 0.6708nmat4.2and297K,respectively [8].
InthecaseofAA-stackedgraphene,allcarbonatomsineverysheethave thesamexandycoordinates(Fig.1.1).IntheABCstructure,halftheatoms arelocateddirectlybelowatomsintheadjacentlayeranddirectlyabovethe hexagonalringcenterswhiletheotherhalfoftheatomsaredirectlyabove atomsanddirectlybelowhexagonalringcenters [9].EventhoughtheBernal stackingisthemostcommonconfigurationinsingle-crystalgraphite,itwas foundthat15%oftheexfoliatedmultilayergrapheneiscomposedof micrometer-sizeddomainsofrhombohedralstacking,ratherthantheusual Bernalstacking [10].Stackingordermaybecrucialforthemechanical behaviorofseveral-layergraphene,especiallyonthemacroscopiclevel. Forinstance,differentlengthsoftheupperandlowerlayersofgraphene inthecaseofABstackingledtoastressconcentrationattheboundaryof theshortlayersofgraphene [11]
Manypropertiesofgrapheneareaffectedbychiralityororientation. Becausegraphenehasahexagonallattice,therearetwotypesofedges,called zigzagandarmchair(Fig.1.3).Zigzagandarmchairedgesalsocouldbedrawn
Fig.1.3 Twotypesofedgesingraphene:(A)zigzagand(B)armchair.Theedgesare indicatedbyboldlines.
as“lateral”and“longitudinal”edges [12].Inthecaseofnanoribbons,“zigzag graphene”and“armchairgraphene”definitionscanbeused.Here,thename isdefinedbytheedgetypealongthelongestdimensionofananoribbon.
1.2Defectsingraphene
Varioustypesofstructuraldefectsmayappearduringthesynthesisofgraphene.Becausesp2-hybridizedcarbonatomscanrearrangethemselvesinto variouspolygonsandformdifferentstructures,theformationofnonhexagonalringsmayoccur [13].Suchnonhexagonalstructurescouldbeconsideredasstructuraldefectsoftheidealhexagonallattice.Dependingontheir configuration,nonhexagonalringscouldproducecurvatureofthegraphene sheetorleaveitflatifthearrangementofpolygonssatisfiescertainsymmetry rules.Suchbehaviorisattributedonlyto2Dstructuresandcouldnotbe foundinbulkcrystals [13].
Severalexperimentalstudiesreportedtheexistenceofeithernativeor physicallyintroducedstructuraldefectsingraphene.Thepresenceofdefects isessentialforthemechanicalandtribologicalpropertiesofgraphene materials.Defectsingraphenestructure arereferredtoasintrinsicorextrinsic,dependingontheirnature.Intrinsicdefectsresultedintheformof perturbationoftheoriginalcrystalstr ucturewithoutthepresenceofforeign atoms.Foreignatomsaredenotedasimpuritiesandconstituteextrinsic defects [14].Duetothereduceddimensionalityofgraphene,thenumber ofpossibledefectsisreducedincomparisonto3Dmaterials.The0Dpoint defectsingraphenearesimilartooneofthebulkcrystals,linedefectsare different,and3Ddefectsdonotexist.Graphenedefectshavecertain mobilityinthegrapheneplane.The migrationmobilityofvarioustypes ofdefectsisgovernedbytheiractivatio nenergyandexponentiallyincreases withtemperature [14].
Severalpointdefectsofgraphenesuchasmono-anddi-vacancies,adatoms,andStone-Wales(SW)defectsareknown.Defectsingrapheneare illustratedin Fig.1.4.Themonovacancyisthemissinglatticeatom;this isthesimplestpointdefectinagraphenestructure(Fig.1.4A).Theformationofthemonovacancyledtothecreationofnine-andfive-membered rings,alsocalledthe5-9cluster.Theformationenergyofthemonovacancy isabout7.5eV [15].Duetohavingadanglingbond,themonovacancyis highlyreactiveandcanbequicklydemolished.
Divacancy(DV)ingraphenehasnodanglingbond(Fig.1.4B).Dueto thelowerenergyofformation,itismuchmorestableandlessreactive [16].
Fig.1.4 Schematicsofpointdefectsingraphene.(A)mono-vacancy;(B)di-vacancy;and (C)Stone-Waledefect(SW);theboundaryofdefectsisindicatedbyboldlines.
Itcouldbeformedbythecoalescenceoftwomonovacanciesorbythe removingoftwoneighboringatoms.Thus,twopentagonsandoneoctagon arebuiltinsteadoffourhexagons,forminga5-8-5cluster [14].Theformationenergyofthedivacancyisveryclosetooneofthemonovacancies [15]. Butbecauseoftwomissingatoms,theenergyperatomwouldbesignificantlylower,makingtheformationofDVthermodynamicallypreferable [13].Besidethe5-8-5configuration,thereareseveralotherwaysforagraphenelatticetoaccommodatetwomissingatoms.Moreover,thisconfigurationisnotenergeticallypreferred.Otherarrangementssuchas555-777or 5555-6-7777havelowerformationenergy [14]
Theeliminationofmorethantwoatomsmaycausetheformationofa largerandmorecomplexconfigurationofdefects.Becauseanevennumber ofmissingatomsallowsthefullrecombinationofdanglingbonds,such defectsareenergeticallypreferableoverdefectshavinganoddnumberof missingatomsduetotheremainingoftheopenbond [14].Theformation oflargeholeswithunsaturatedbondsismorelikelyinthecaseofsimulations removingalargenumberofatoms.
Oneoftheexceptionalpropertiesofgraphenelatticeistheabilitytoreorderbyestablishingnonhexagonalringswithoutmissingatoms [14].ThesimplestexampleofsuchrearrangementistheformationoftheSWdefect (Fig.1.4C).Itformsduetoachangeofconnectivityoftwo π-bondedcarbon atoms,whichledtoa90degreein-planerotationofthebond [17].Fourhexagonsaretransformedintotwopentagonsandtwoheptagons,forminga so-called5-7-7-5cluster.Thus,theformationoftheSWdefectdoesnot involveanyremovedoraddedatom,andnodanglingbondsareintroduced [14].Theformationenergyofthe5-7-7-5defectisabout5eV [18]
Theformationofinterstitialatomsasoccurredinbulkcrystalsisnotpossibleingraphenebecauseaddinganatomtoanyin-planepositionsuchasthe
centerofahexagonwouldrequireexcessivelyhighenergy.Thus,ingraphene,adatomsarelocatedinthethirddimension.Theenergeticallypreferredpositionwouldbethetopofacarbon-carbonbond(thebridge configuration).Theformationofsuchastructureledtothechangingof hybridization.Duetotheappearanceofsomesp3 hybridization,theformationoftwocovalentbondsbetweentheadatomandtheunderlyingatomsin thegrapheneplanetakesplace [14]
One-dimensionaldefectssuchasdislocationsandgrainboundarieswere observedinseveralexperimentalstudiesofgraphene.Generally,these defectsaretiltboundariesseparatingtwodomainswithdifferentlatticeorientations.Suchdefectscouldbeimaginedasalineofpointdefectswithor withoutdanglingbonds [14].Theformationoflinedefectscanoccurinthe caseofsimultaneousnucleationofgraphenelayersindifferentlocationsfollowedbytheircoalescence.Thisprocessissimilartothecreationofgrain boundariesinbulkcrystals.
Thepresenceofatomic-scalestepsisaubiquitousfeatureofmultilayer graphene.Therearetwotypesofstepedges(Fig.1.5).Thefirsttypeisinternalorcoveredsteps,whichformedduringthegraphenegrowth (Section3.3).Thesecondtypeisexternal(uncovered)stepsusuallycreated duringthemechanicalcleavageofHOPG(Section3.1).Thepresenceof danglingbondsontheexposededgesmakesthemchemicallyactive. Ahigherworkfunctionwasobservedontheexternalstepscomparedwith otherinternalstepsduetostepdipolesandadsorbates [19]
1.3Derivativesofgraphene
Significantattentionwasfirstpaidtopristinegraphenebecauseofitsunique electronicproperties.Thismadegrapheneamodelsystemfortheobservationofanovelquantumphenomenonandthebuildingblockforfuture nanoelectronicdevices [3].Nevertheless,fromapracticalpointofview,
Fig.1.5 Coveredanduncoveredstepedgesofgraphene.
industrialapplicationsarerequiredtoproducegrapheneinsignificantlylarge quantiles.Oneoftheapproachestoincreasetheproductionrateofgraphene isfabricationbythereductionofgrapheneoxide(GO)becauseitdemonstratedthepotentialofcost-effective,large-scaleproductionofgraphenebasedmaterials [20].Sinceitwasfirstsynthesizedinthenineteenthcentury, GOhasbeenapopulargraphenederivative.GOisasingle-carbonmonolayerwithrandomlydistributedaromaticregions(sp2 carbonatoms)and oxygenatedaliphaticdomains(sp3 carbonatoms)containingcarbonyl,carboxyl,epoxy,andhydroxylfunctionalgroups(Fig.1.6).Thepresenceofthe functionalgroupsmakesGOhydrophilic [21].
GOissynthesizedbytheoxidationofgraphiteinthepresenceofastrong acidandanoxidizingagent.Theoxidationprocessleadstoapartialdisruptioninthesp2 hybridizedstructureofgraphiteandtoanincreaseofthedistancebetweenitscarbonlayers,leadingtofinalseparationtosheetsthatarea singlecarbonatomthick [21].Grapheneoxidesheetsarethickerthangrapheneduetothedisplacementofsp3 hybridizedcarbonatomsslightlyabove andbelowtheoriginalgrapheneplaneandthepresenceofcovalentlybound oxygenatoms [3].Theleveloftheoxidationcanbevarieddependingonthe method,thereactionconditions,andthegraphiteprecursor.Although extensiveresearchhasbeendonetorevealthechemicalstructureofGO, severalmodelsofthisprocessarestillbeingdebatedintheliterature [20] Reducedgrapheneoxide(rGO)isalsoa2Dsingle-atom-thickmaterial. Itislikegraphene,butithasextracarbonringdomains,defects,andremainingoxygen-containinggroups(-OH,-COOH,etc.)onthesurface (Fig.1.6).TheinitialgoalofreducingGOwastofabricategraphenematerialscomparabletothestructureandpropertiesofpuregrapheneachieved bymechanicalexfoliation.
Fig.1.6 Comparisonofthechemicalstructuresofgraphene,GO,andrGO.
1.4Mechanicalpropertiesofgraphene
Themechanicalpropertiesofgraphenearethemainreasonthatitisaprimarytribologicalmaterialofthefuture.Ithasthehigheststrengthandelastic modulusaftercarbonnanotubes.Theexceptionalmechanicalpropertiesof graphenearebasedonthestabilityofsp2 bondsformingthehexagonallattice.Thatallowsagraphenesheettoopposein-planedeformations [22].For thefirsttime,themechanicalpropertiesoffree-standingmonolayergrapheneweremeasuredbyLeeetal.usingthenanoindentationmodeof AFM [23].Itwasdemonstratedthatthemonolayergraphenemembrane hadaYoung’smodulusof 1TPa.Hoverer,differentstiffnessvalueswere obtainedinsomereports.Thisdifferencewasattributedtotheunrecordable crumplingofgraphenesheetsthatmayoriginatefrompointdefectsor unevenstressattheboundaries [22].Thetransferprocessusedafterthe CVDprocessalmostalwayscauseswrinklinganddamage,whichalso mayreducethemechanicalproperties.TheshearmodulusofCVD-grown monolayergraphene(Section3.3)wasmeasuredbyLuietal. [24].Avalueof 280GPawasobtained.
Defect-freemonolayergraphenewasconsideredbyHoneetal.tobethe mostdurablematerialevertested [23].Hoverer,themechanicalproperties ofgraphenecanbesignificantlyaffectedbydefects [25].Dependingonthe typeandconcentrationofdefects,suchasvacancytypeorsp3-type,the strengthandstiffnessofgraphenecanbereducedsignificantly,aswas observedforvacancies.Intheopposite,themechanicalpropertieswere maintainedevenathigherdensitiesofsp3-typedefects.
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CHAPTER2
Computersimulations andtheoreticalpredictions
2.1Simulationofmechanicalproperties
Foralongtime,graphenewasjustanidealmodelobject.Avarietyofcomputermodelingandsimulation(CMS)methodssuchasMonteCarlo(MC), moleculardynamics(MD),andquantumchemistry(QC)havebeenutilized fortheinvestigationofvariouscharacteristicsofgraphene,includingthermal conductivityandexpansion,surfacediffusion,andelasticmodulus [1].In general,CMSisapracticalapproachthatusescomputermodelstoinvestigatenotonlytheinteractionprocessbetweendifferentmaterials,butalso structuraltransformationsthatoccurredduringthisinteractionprocess [2].Theavailabilityofsimulationmethodsisespeciallycrucialforgraphene, whereexperimentsencounteredmanylimitationscausedbythenanoscale oftribologicalsystems.Butitshouldbenotedherethatduetothenatureof CMS,thescaleofsimulationsisusuallylimitedtoatenthsofnanometers. ThisisbecauseCMSmethodsdealwithindividualatomsandmolecules, andtheincreasingsizeofthemodelrequiressignificantcomputational resources.Inthecaseofsimulationoftribologicalphenomena,anotherlimitingfactorappears,whichisarequirementtohaveanadequatemodelto describeaninteractionbetweenindividualatomsofdifferentelements. Forinstance,inthetypicalMDsimulation,eachparticleisconsideredas
asingleentity,andtheinteractionsbetweenvariousparticlesaremodeled usingtheirreactionstopotentialfunctionsderivedfromclassicalphysics [2].Availablepotentialsdefinedavarietyofmaterialsthatcanbeusedinsimulations.Moreover,usingvariousreactivepotentialscouldgivesignificantly differentresultseveninsimilarmodels.
Historically,earlytheoreticalstudiesofgrapheneweremostlyfocusedon thesimulationofelectricalorthermalproperties.Later,manysystematic piecesofresearchwereperformedonthemechanicalpropertiesofgraphene. Forinstance,Young’smoduluswascalculatedusingvariousapproachesand simulationmethodssuchasMDandabinitioDFT [2].Dependingonthe reactivepotentialsusedinMDsimulations,thevaluesofYoung’smodulus reportedbyotherresearcherswereintherangefrom0.86to1.24TPa [3–5].Suchadifferencecanbeattributedtoseveralfactors.Thefirstfactor isaselectionofthereactivepotential.Forexample,AIREBO,Tersoff,Brenner,orbond-orderTersoff-Brennerpotentialswereusedindifferentstudies. Thesecondfactoristhesizeofasimulatedspecimen.Forinstance,increasing thespecimensizefrom0.1to0.35nmledtoanincreaseofYoung’smodulus from0.65to1.05Tpa,anditssaturation [6].Similarbehaviorwasobservedby Haoetal.forgraphenenanoribbons [4].Whenrelativelylargespecimens wereused(morethan2nm),themechanicalpropertieswerefoundtobe independentofthespecimensize [5].Thus,themodelusedinCMSshould belargeenoughtoavoidtheeffectsofitssize.
Manysimulationsdemonstratedasignificantdifferenceinthemechanical propertiesofgraphenedependingonthedirectionofdeformation.For instance,thezigzaggraphenestructurehada30%higherstrengthand60% higherfracturestrainthanthearmchairstructure [3].GaoandPeng [7] also reportedsimilarfailuremechanismsanddifferentmechanicalpropertiesofzigzagandarmchairgraphene.TheirMDsimulationshowedthatbothzigzag andarmchairgraphenebegantobreakattheoutermostcarbonatomiclayers.
Furthermore,Young’smoduluswasfoundtobeaffectedbytemperature.Raisingthetemperaturefrom100to500KincreasedtheYoung’s modulusofmonolayergraphenefrom0.94to1.1TPa [6].Dewapriya etal.alsoreportedthatYoung’smoduluswasslightlyaffectedbytemperatureintherangeof1–300K [8].Theyreportedvaluesof0.9and1.12TPa forarmchairandzigzagconfigurations,respectively.Thesmalldifferencein thetemperaturebehavioroftheYoung’smodulusofgrapheneagaincould beattributedtousingdifferentreactivepotentials.
Besidestheeffectsofchiralityandtemperature,themechanical propertiesofgrapheneareaffectedbythepresenceofstructuraldefects.
Thepresenceofdefectssignificantlyreducedthefailurestrainandthe inherentstrengthofsingle-layergraphenewhileithadasmalleffecton theYoung’smodulus [9].Theimpactofvariousdefectsonmechanical propertieswascarefullyassessedbyZandiatashbaretal. [10].Inthiswork, differenttypesofdefectshavingarangeofsizesweremodeledinasingle graphenesheetusingMDsimulation.Itwasdemonstratedthatboththe elasticmodulusandstrengthwerealmostinsensitivetodefects.Also,it wasconfirmedthatgraphenecanbecovalentlybondedtoapolymeric matrixwithoutlosingitsreinforcingproperties,whichisveryimportant forthedesignofgraphene-basedpolymers.
Asimulationofdefectsingrapheneusingamolecularstructuralmechanics(MSM)approachshowedthatSWdefectscausedasmallereffecton mechanicalpropertiesincomparisonwithvacancies [11].MSMisa continuum-basedmodelingtechniqueinwhichC Ccovalentbondswere replacedwithenergeticallyequivalentbeamelements.Aninvestigationof 100 100nm2 graphenesheetsrevealedthatmono-anddivacancyreduced theaxialstiffnessofgraphenesignificantly.Inthecaseofmonovacancy,it wasdroppedby 60%atthedefectconcentrationaround12%.Divacancies causedanevenhigherreductionofthestiffness.Moreover,vacancies—and especiallydivacancies—ledtoasignificantdeteriorationofmechanicalproperties.TheeffectofSWdefectswaslesssignificant.Thesameconcentration ofSWdefectsreducedtheaxialstiffnessbyseveralpercent.
ThefractureofgraphenesheetshavingSWdefectswasalsoinvestigated atdifferenttemperaturesusingMD [12].Itwasalsodemonstratedthatthe structuraldefectsandvacanciesingraphenecouldleadtoasignificantreductioninstrength.Inparticular,introducingfourvacancydefectsintoa 5 5nm2 graphenesheetcausedadecreaseoffracturestrengthfrom100 to60GPa.SWdefectscauseda 50%loweringoffracturestrength.Besides, itwasdemonstratedthatthefracturestrengthofgraphenewasdependenton temperatureandloadingdirection.Raisingthetemperaturefrom300to 900Kledtoa 20%dropofthefracturestrength.
Inthestudiesdiscussedabove,relativelysimplestretchingofgraphene wassimulated.FurtheradvancesinthedevelopmentofCMSmethods allowedperformingmorecomplicatedbutalsomorerealisticsimulations. Forexample,simulationoftheindentationofsuspendedgraphenemembraneswithatipbecameavailable.Kimetal. [13] performedasimulation ofsingle-andmultilayergraphenemembraneswitharoundedSitiphavinga diameterof5nm(Fig.2.1).Thewidthofthecirculargraphenelayerwas 17nm,whichallowedavoidingthesizeeffectmentionedabove.Itwas
