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Strainengineeringofthermalconductivityingraphenesheetsandnanoribbons:ademonstrationofmagicflexibilityNingWei1,LanqingXu1,2,Hui-QiongWang1andJin-ChengZheng1*1DepartmentofPhysics,InstituteofTheoreticalPhysicsandAstrophysics,andFujianKeyLabofSemiconductorMaterialsandApplications,XiamenUniversity,Xiamen361005,People’sRepublicofChina2SchoolofPhysicsandOptoElectronicsTechnology,FujianNormalUniversity,Fuzhou350007,People’sRepublicofChina*correspondingauthor.Email:jczheng@xmu.edu.cn.AbstractGrapheneisanoutstandingmaterialwithultrahighthermalconductivity.Itsthermaltransferpropertiesundervariousstrainsarestudiedbyreversenonequilibriummoleculardynamics.Basedontheuniquetwo-dimensionalstructureofgraphene,thedistinctivegeometriesofgraphenesheetsandgraphenenanoribbonswithlargeflexibilityandtheirintriguingthermalpropertiesaredemonstratedunderstrains.Forexample,thecorrugationunderuniaxialcompressionandhelicalstructureunderlighttorsion,aswellastube-likestructureunderstrongtorsionexhibitenormouslydifferentthermalconductivity.Theimportantrobustnessofthermalconductivityisfoundinthecorrugatedandhelicalconfigurationsofgraphenenanoribbons.Nevertheless,thermalconductivityofgrapheneisverysensitivetotensilestrain.Therelationshipamongphononfrequency,strainandthermalconductivityareanalyzed.Asimilartrendlineofphononfrequencydependenceofthermalconductivityisobservedforarmchairgraphenenanoribbonandzigzaggraphenenanoribbon.Theuniquethermalpropertiesofgraphenenanoribbonsunderstrainssuggesttheirgreatpotentialsfornanoscalethermalmanagementsandthermoelectricapplications.1.IntroductionGrapheneisasinglelayeroftwo-dimensionalcarbonatomsinahoneycomblatticewithsp2bond.Ithasattractedmuchattentionduetoitsoutstandingelectronicandthermalproperties[1-5]whichwillleadtopotentialapplicationsinelectronicsandthermalmanagementdevices[6].Recently,grapheneisbeingconsideredasacandidatematerialforthepost-CMOS(complementarymetal-oxide-semiconductor)technology[7].Thermaldissipationhasbecomeoneofthemostimportantbarrierstobreakthrough[8]andhasstimulatedintensiveresearcheffortsonthisissue,bothexperimentally[9]andtheoretically[10,11].Toachieveenhancedfunctionalityofnanomaterialsbynanodesign,itisdesirabletotunethethermalconductivityaccordingtoapplicationrequirementsofthermoelectrics[12-15],thermalmanagement,andConfidential:notfordistribution.SubmittedtoIOPPublishingforpeerreview4January2011thermalrectification[16].Thethermalconductivityofgraphenenanoribbons(GNRs)canbemodifiedbydefects,impurity,tailoredgeometryshapes(sizeandasymmetry),andstrain，etc.Amongallthesemethods,straineffectscouldbeoneofthemostcompetitivecandidatestoexerciseforitscontinuoustunabilityanditseasinesstoperformevenatnanoscale.Straineffectsonthermalconductivityofbulkmaterialshavebeenstudiedfordecades[17-20].Forconventionalthree-dimensionalmaterials,compressivestrainenhancesthermalconductivitybystiffeningphononmodes,whereastensilestraindecreasesthermalconductivitybysofteningthephononmodes[19-22];apower-lawscatteringofthermalconductivityonstrainisobtainedusingPeierls-Boltzmannformulations[19].However,thislawisbrokeninlow-dimensionalmaterials,especiallyinone-dimensionalnanostructuressuchascarbonnanotube(CNT),becauselocalizedbucklingstructuresareformedundercompressivestrain,whichincreasephononscatteringandthuslargelyreducethermalconductivity[11,22].Uptonow,itisstillnotquiteclearhowthethermalconductivityofgraphenesheetsandGNRsresponsestoexternalstrains.Sincegraphenesheethastwo-dimensionalstructure,itsstrainresponseshouldbeverydifferentfromthree-dimenisonalbulkmaterialsorone-dimensionalCNT,becausethestrain-inducedstresscanbepartiallyreleasedinthedirectionperpendiculartothesheet.ForGNRs,besidesthedirectionoutoftheplane,theyhavetwoadditionaldegreesoffreedomtoreleasestress,thereforeGNRsareexpectedtoshowmuchmoreflexiblethermalresponsetostrains.Inthiswork,wehaveperformedcomputersimulationsbasedonreversenon-equilibriummoleculardynamics(RNEMD)[23],toinvestigatestraineffectsonthermalconductivityoftwotypesofGNRs,namely,zigzaggraphenenanoribbon(ZGNR)andarmchairgraphenenanoribbon(AGNR).Whentensilestrainsareapplied,GNRisfoundstabilizedintoplanargeometryanditsthermalconductivityisreducedduetothesofteningofthestretchingphononmodes,similartothatofCNT[22].Whereasforotherkindsofstrains,suchascompressivestrainsandtorsionalstrains,theresponseofthermalconductivityofGNRstostrainsaremuchmorecomplicatedthanthatofCNTs.Especially,theinfluenceofcorrugationofGNRsonthermalconductivityundercompressionisinvestigatedsystematically,becausecompressiondoesnotchangetheC-Cbond’sproperties(bondlengthorangle)butmainlytheradianofrippleinGNRs.Thisstrain-corrugationresponsebehaviorisonlyobservedintwo-dimensionalstructure.Undertorsionalstrain,GNRspresentinterestingtube-likestructure.Inordertounderstandtheoriginofstrain-inducedmodificationofthermalconductivity,weperformedthedetailedanalysesonbond-lengthandbond-angleunderstrainaswellasphononspectra.Therelationshipamongphononfrequencies,strainandthermalconductivityareobtained.Thephysicalinsightofstraine