USF Libraries
USF Digital Collections

Molecular simulations of Pd based hydrogen sensing materials

MISSING IMAGE

Material Information

Title:
Molecular simulations of Pd based hydrogen sensing materials
Physical Description:
Book
Language:
English
Creator:
Miao, Ling
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:

Subjects

Subjects / Keywords:
Palladium
Hydrogen sensor
Carbon nanotube
MD simulations
DFT
Dissertations, Academic -- Chemical and Biomedical Engineering -- Doctoral -- USF   ( lcsh )
Genre:
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: Hydrogen sensor technology is a crucial component for safety and many other practical concerns in the hydrogen economy. To achieve a desired sensor performance, proper choice of sensing material is critical, because it directly affects the main features of a sensor, such as response time, sensitivity, and selectivity. Palladium is well-known for its ability to sorb a large amount of hydrogen. Most hydrogen sensors use Pd-based sensing materials. Since hydrogen sensing is based on surface and interfacial interactions between the sensing material and hydrogen molecules, nanomaterials, a group of low dimensional systems with large surface to volume ratio, have become the focus of extensive studies in the potential application of hydrogen sensors. Pd nanowires and Pd-coated carbon nanotubes have been successfully used in hydrogen sensors and excellent results have been achieved. Motivated by this fact, in this dissertation, we perform theoretical modeling to achieve a complete and rigorous description of molecular interactions, which leads to the understanding of molecular behavior and sensing mechanisms.To demonstrate the properties of Pd-based sensing materials, two separate modeling techniques, but with the same underlying aim, are presented in this dissertation. Molecular dynamic simulations are applied for the thermodynamic, structural and dynamic properties of Pd nanomaterials. Ab initio calculations are utilized for the study of sensing mechanism of Pd functionalized single wall carbon nanotubes. The studies reported in this dissertation show the applications of computational simulations in the area of hydrogen sensors. It is expected that this work will lead to better understanding and design of molecular sensor devices.
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2006.
Bibliography:
Includes bibliographical references.
System Details:
System requirements: World Wide Web browser and PDF reader.
System Details:
Mode of access: World Wide Web.
Statement of Responsibility:
by Ling Miao.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 174 pages.
General Note:
Includes vita.

Record Information

Source Institution:
University of South Florida Library
Holding Location:
University of South Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 001936665
oclc - 226388725
usfldc doi - E14-SFE0001773
usfldc handle - e14.1773
System ID:
SFS0026091:00001


This item is only available as the following downloads:


Full Text

PAGE 1

MolecularSimulationsofPdBasedHydrogenSensingMaterial s by LingMiao Adissertationsubmittedinpartialfulllment oftherequirementsforthedegreeof DoctorofPhilosophy DepartmentofChemicalandBiomedicalEngineering CollegeofEngineering UniversityofSouthFlorida Co-MajorProfessor:BabuJoseph,Ph.D. Co-MajorProfessor:VenkatR.Bhethanabotla,Ph.D. VinayGupta,Ph.D. MartinM.Ossowski,Ph.D. BrianSpace,Ph.D. LiliaWoods,Ph.D. DateofApproval: August10,2006 Keywords:Palladium,hydrogensensor,carbonnanotube,MD simulations,DFT c r Copyright2006,LingMiao

PAGE 2

c r CopyrightbyLingMiao2006 Allrightsreserved

PAGE 3

Dedication ToSukit,withoutyourconstantloveandsupport,noneofthis wouldhavebeenpossible.

PAGE 4

Acknowledgments Theworkcontainedinthisdissertationwouldnotbepossibl ewithouttheintellectual supportofmyadvisers,professors,andfellowstudents.Iw ouldliketothankProfessor BabuJosephandProfessorVenkatR.Bhethanabotlafortheirgui danceandsupportthat ledtoabetterunderstandingofthisstudy,andmycommittee members:ProfessorsVinay Gupta,BrianSpace,LiliaWoodsandDr.MartinM.Ossowski.Ia malsogratefulforthe insightprovidedbymyclassmatesandfriendsduringthecou rseofmystudiesatUSF.I wouldalsoliketoacknowledgethecomputationalresources providedbyUSFAcademic Computing.Asoneoftheusersoftheirsystems,anunlimitedt imewasgrantedforusage andagreatsupportwasprovidedforanytechnicialproblems ,withoutwhich,noneof thisdissertationwouldbepossible.Andlastbutnotleast, Ialsothankmyparents.Your constantloveandsupportareappreciatedandIowemuchofmy successtoyou.

PAGE 5

TableofContents ListofTables iv ListofFigures v Abstract viii ChapterOneIntroduction 1 1.1MotivationandGoal 2 1.2OrganizationoftheThesis 3 ChapterTwoHydrogenSensorandSensingMaterials5 2.1WhatIsASensor? 5 2.2HydrogenSensors 7 2.2.1ChemiresistorSensor 7 2.2.2FETSensor 8 2.2.3SAWSensor 8 2.3HydrogenSensingMaterials 10 2.3.1CatalysisandSensing 10 2.3.2PalladiumBasedSensor102.3.3IntroductiontoCarbonNanotubes112.3.4IntrinsicCarbonNanotubeBasedSensor132.3.5FunctionalizedCarbonNanotubeBasedSensor14 ChapterThreeMolecularDynamicsSimulation16 3.1EquationsofMotionfortheAtomicSystems163.2IntegratingtheEquationsofMotion173.3TheForceCalculation 18 3.4SimulationConvergence 20 3.5Constraints 20 3.5.1ThermodynamicEnsembles203.5.2TemperatureControl 21 3.6PropertiesMeasurement 21 3.7DL POLYPackage 22 i

PAGE 6

ChapterFourMeltingofPdClustersandNanowires:AComparison Study UsingMolecularDynamicsSimulations23 4.1Abstract 23 4.2Introduction 24 4.3PotentialModelandComputationalMethod264.4ResultsandDiscussion 28 4.5MeltingModelComparison 47 4.6Conclusions 50 ChapterFiveMolecularDynamicsSimulationsofGraphiteSup portedPdNanoclusterMelting 52 5.1Abstract 52 5.2Introduction 52 5.3PotentialModelandComputationalMethod535.4ResultsandDiscussion 55 5.5Conclusions 61 ChapterSixDensityFunctionalTheoryandthePseudopotenti alMethod63 6.1DensityFunctionalTheory 63 6.1.1TheHohenberg-KohnPrinciple636.1.2TheSelf-ConsistentKohn-ShamEquations646.1.3Approximationsfor E xc [ n ( r )] :LDAandGGA65 6.2Plane-WaveBasisSetandPseudopotential686.3TheVienna Ab-initio SimulationPackage70 ChapterSevenInteractionsofHydrogenwithPdandPd/NiAllo yChainFunctionalizedSingleWalledCarbonNanotubesfromDensityFunc tionalTheory 71 7.1Abstract 71 7.2Introduction 72 7.3MethodofCalculations 74 7.4AtomicChainStructures 75 7.5ChainsonSWNTs 79 7.5.1PurePdChainonSWNT797.5.2Pd/NiAlloyChainonSWNT85 7.6H 2 InteractionswithChain-FunctionalizedSWNTs89 7.7Conclusions 96 ChapterEightDFTStudyofPdFunctionalizedCarbonNanotubes asHydrogenSensors 98 8.1Abstract 98 8.2Introduction 98 8.3MethodofCalculations 100 ii

PAGE 7

8.4ResultsandDiscussion 100 8.5Conclusion 110 ChapterNineConclusionsandProposedFutureWork112 9.1Conclusions 112 9.2MajorContributions 114 9.3FutureWork 114 9.3.1SensorPoisoning 114 9.3.2MultipurposeGasSensor1159.3.3 Abinitio MDSimulations115 References 117 Appendices 133 AppendixA:DL POLYPrograms 134 A.1TheInputFiles 134 A.1.1TheCONTROLFile 134 A.1.2TheCONFIGFile 136 A.1.3TheFIELDFile 164 A.2TheOutputFiles 166 AppendixB:VASPPrograms 167 B.1TheInputFiles 167 B.1.1TheINCARFile 167 B.1.2ThePOSCARFile 169 B.1.3ThePOTCARFile 172 B.1.4TheKPOINTSFile 172 B.2TheOutputFiles 173 B.3CalculateBandStructure 173 AbouttheAuthor EndPage iii

PAGE 8

ListofTables Table4-1.Sutton-ChenpotentialparametersforPd.27Table4-2.ThermodynamicpropertiesforPdbulk,clusteran dnanowire.31 Table4-3.Bond-orientationalorderparametersforanumber ofsimpleclustergeometries. 43 Table7-1.BindingenergyofPdatomsperunitcellontwoSWNTs. 82 Table7-2.Calculatedbindingenergies,chargetransfer,an dmagneticmomentfor Pd/Nichain-SWNTsystem. 86 Table8-1.H 2 adsorptionenergies E ad ,averagedatomicdistances d ,averagednearestneighbordistances nn ,chainangles ,andmagneticmoment for Pdradialchain-functionalizedSWNT(10,0)systemswithdif ferentH 2 coverage. 104 iv

PAGE 9

ListofFigures Figure2-1.Schematicdiagramofsensorprinciple.5Figure2-2.Schematicviewofachemiresistorsensor.8Figure2-3.SchematicviewofaFETsensorwithaSWNTtransduc ercontactedby twoelectrodes(sourceanddrain)andasiliconbottomgate. 9 Figure2-4.SchematicviewofaSAWsensor. 9 Figure2-5.Structureofamulti-walledcarbonnanotubemad eupofthreeshellsof differentchirality. 12 Figure2-6.IllustrationofzigzagandarmchairSWNTsbyroll ingagraphenesheet.13 Figure3-1.Thegeneralprocedureofleap-frogalgorithm.1 9 Figure4-1.PotentialenergyandheatcapacityofthePd(a)n anoclusterand(b) nanowire. 30 Figure4-2.Radiusofgyrationvs.temperatureforPdcluster andPdnanowirewith repeatingunitoflengthof5.6nm. 32 Figure4-3.Snapshotsofequilibratedatomicpositions,sh ownasprojectedcoordinatesinplanesparallel(upper)andperpendicular(lowe r)to(a)the nanowireaxis. 34 Figure4-4.Velocityautocorrelationfunctions(a)v and(b)v z foratomsindifferent shellsofthePdnanowireat800K.36 Figure4-5.Snapshotsoftheprojectedatomicpositionsoft he(a)456Pdatomclustersatdifferent T and(b)1,568atomPdnanowireprojectedontoa planeperpendiculartotheaxis. 37 Figure4-6.Self-diffusioncoefcientforatomsindiffere ntradialshellsatvarious temperaturesfor(a)Pdclusterand(b)Pdnanowire.38 Figure4-7.ComparisonofPdatomicdistributionsofPdclust eralongaCartesian coordinate( z )atdifferenttemperatures.41 v

PAGE 10

Figure4-8.ComparisonofPdatomicdistributionalongaCarte siancoordinate( z ) inthePdnanowireat(a)600K,(b)1100K,(c)1190K,and(d)12 00K.42 Figure4-9.Temperaturedependenceofaveragebond-orient ationalorderparametersfor(a)theatomsinPdnanowireand(b)thePdclusterwit h456 atomsandPdnanowirewith1,568atomsduringheating.44 Figure4-10.Correlationplotforbond-orientationalorder parameters ˆ W 6 asafunctionof Q 6 47 Figure5-1.Potentialenergyandheatcapacityunsupported andgraphite-supported Pdclustersvs.temperature( d = 2.3nm).54 Figure5-2.Atomicdistributionfunctionalong z coordinateperpendiculartothe graphitesubstrate. 55 Figure5-3.Velocityautocorrelationfunctionsofthesupp ortedPdclusterat1000K.57 Figure5-4.Atomcoordinatesof(a)surfaceatoms(atomsins hell1and2asillustratedinFigure5-3(d))and(b)inneratoms(atomsinshell3 ,4and5) ofgraphite-supportedPdclusterat1000K(bluedots)and11 00K(red dots). 59 Figure5-5.(a)Radialdistributionfunctionand(b)angular correlationfunctionfor Pdclusters. 60 Figure6-1.Schematicow-chartforself-consistentdensi tyfunctionalcalculations.66 Figure7-1.CalculatedbindingenergyofPdandPd/Nichainat omsperunitcellas functionoflengthofunitcell d 76 Figure7-2.Spin-polarizedbandstructureandDOSofthePdc hains(a-c)andPd-Ni chains(d-f). 78 Figure7-3.Schematicdrawingoftopviewsoffourpossibles itesforsinglePdatom adsorptiononSWNT(6,6)andSWNT(10,0).80 Figure7-4.3DviewofequilibriumgeometriesofthePdchain SWNTstructures.81 Figure7-5.Spin-polarizedbandstructureandDOSof(a)SWNT (6,6)and(b)Pd narrowanglechainadsorbedSWNT(6,6).83 Figure7-6.Spin-polarizedbandstructureandDOSof(a)SWNT (10,0),(b)Pdwide anglechainadsorbedonthebridge-1sitesofSWNT(10,0),and (c)Pd wideanglechainadsorbedonthebridge-2siteofSWNT(10,0). 84 Figure7-7.3DviewsofequilibriumgeometriesofthePd/Nic hain-tubestructures.87 vi

PAGE 11

Figure7-8.Spin-polarizedbandstructureandDOSof(a)Pd/ Ninarrowanglechain functionalizedSWNT(6,6),and(b)Pd/Niwideanglechainfun ctionalizedSWNT(10,0). 88 Figure7-9.Atomprojecteddensityofstate(PDOS)from(a)P datomwithtwonearestCatomsand(b)NiatomwithtwonearestCatoms,onbridge2site functionalizedSWNT(10,0). 88 Figure7-10.Contourplotoftotal(spin-upandspin-down)va lencechargedensity onthreeplanesforPd/NichainfunctionalizedSWNT(10,0)(u pper)and Pd/NichainfunctionalizedSWNT(6,6)(lower).89 Figure7-11.Contourplotofmagnetizationdensity(spin-up andspin-down)ontwo planesthroughPdorNiandthetubeforthesamesystemsasinF igure710. 90 Figure7-12.3DviewsofequilibriumgeometriesoftheH 2 adsorbedPdandPd/Ni functionalizedSWNTs. 93 Figure7-13.BandstructureandDOSforthefoursystemsshown inFigure7-12.94 Figure8-1.EquilibriumgeometriesofPdradialchain-func tionalizedSWNT(10,0).101 Figure8-2.Spin-polarizedbandstructureof(a)bareSWNT(1 0,0)and(b)Pdradial chain-functionalizedSWNT(10,0).101 Figure8-3.3Dviewsofequilibriumgeometriesofhydrogena dsorbedPdradial chain-functionalizedSWNT(10,0).103 Figure8-4.Spin-polarizedbandstructureofhydrogenadso rbedonPdradialchainfunctionalizedSWNT(10,0). 105 Figure8-5.3DviewsofequilibriumgeometryofPdfullycoat edSWNT(10,0).107 Figure8-6.Bandstructureandtotalspinpolarizeddensityo fstates(DOS)ofaPd fullycoveredSWNT(10,0). 109 Figure8-7.LocaldensityofstatesoftwoPdatomsinthefull ycoatedSWNT(10,0).111 vii

PAGE 12

MolecularSimulationsofPdBasedHydrogenSensingMaterial s LingMiao ABSTRACT Hydrogensensortechnologyisacrucialcomponentforsafet yandmanyotherpractical concernsinthehydrogeneconomy.Toachieveadesiredsenso rperformance,properchoice ofsensingmaterialiscritical,becauseitdirectlyaffect sthemainfeaturesofasensor,such asresponsetime,sensitivity,andselectivity.Palladium iswell-knownforitsabilityto sorbalargeamountofhydrogen.MosthydrogensensorsusePd -basedsensingmaterials. Sincehydrogensensingisbasedonsurfaceandinterfaciali nteractionsbetweenthesensing materialandhydrogenmolecules,nanomaterials,agroupof lowdimensionalsystemswith largesurfacetovolumeratio,havebecomethefocusofexten sivestudiesinthepotential applicationofhydrogensensors.PdnanowiresandPd-coate dcarbonnanotubeshavebeen successfullyusedinhydrogensensorsandexcellentresult shavebeenachieved.Motivated bythisfact,inthisdissertation,weperformtheoreticalm odelingtoachieveacomplete andrigorousdescriptionofmolecularinteractions,which leadstotheunderstandingof molecularbehaviorandsensingmechanisms. TodemonstratethepropertiesofPd-basedsensingmaterial s,twoseparatemodeling techniques,butwiththesameunderlyingaim,arepresented inthisdissertation.Molecular dynamicsimulationsareappliedforthethermodynamic,str ucturalanddynamicproperties ofPdnanomaterials. Abinitio calculationsareutilizedforthestudyofsensingmechanis m ofPdfunctionalizedsinglewallcarbonnanotubes.Thestud iesreportedinthisdissertation showtheapplicationsofcomputationalsimulationsinthea reaofhydrogensensors.Itis viii

PAGE 13

expectedthatthisworkwillleadtobetterunderstandingan ddesignofmolecularsensor devices. ix

PAGE 14

ChapterOne Introduction Duetotheunusualpropertiesofnanomaterialsandtheirext raordinaryperformancein variousapplications,nanotechnologyanditsmanydiffere ntbrancheshavebecomeavery promisingareaforresearchinphysics,chemistry,biology andmaterialsscience.Nanocluster,nanowire,andcarbonnanotubeconstituteanewclassof matterintermediatebetween atoms/moleculesandcondensedmatter.Theyarecurrentlyt hefocusofintensiveresearch duetobothtechnologicalandtheoreticalinterest.Newdev elopmentsinexperimentaltechniqueshavemadeitpossibletoprobethepropertiesofnanom aterialsviahighresolution spectroscopy.Theoretically,diverseclassesofstudyran gingfrom abinitio calculations throughclassicalsimulationstorigorousquantumdynamic alinvestigationshaveprovided awealthofinformationconcerningtheelectronicstructur es,spectroscopicaswellasdynamicpropertiesofavarietyofnanoparticles. Amongnanomaterials,carbonnanotubesandnanowiresarepa rticularlyinteresting frombothfundamentalandpracticalpointsofview,because oftheiruniquegeometric structuresandremarkablemechanical,chemical,electron ic,magnetic,andtransportproperties.Theirsmalldiameterandlonglengthleadtosuchlar geaspectratiosthattheyboth actasidealone-dimensionalsystems.Allthesecharacteri sticsmakecarbonnanotubesand nanowiresthefocusofextensivestudiesforpotentialappl icationsinvarioussensordevices. Ahydrogensensorisessentialformanypurposes,suchasind ustrialprocesscontrol, combustioncontrol,andinmedicalapplications.Pd(Palla dium)isanidealhydrogen sensingmaterial,becauseofitsuniqueadsorptivecapacit yforhydrogen.Sincechemical 1

PAGE 15

sensingisbasedonsurfaceandinterfaceinteractionsbetw eentheanalytemoleculesand thesensingmaterial,Pdnanomaterialswithalargesurface /bulkatomicratio,suchasPd nanowiresandPdfunctionalizednanotubes,arepotentiall yveryefcienthydrogensensing materials.HydrogensensorsfromhighlycrystallinePdnan owirearraysorPdfunctionalizedcarbonnanotubethinlmshaveattractedmuchintere strecently,anditisbelieved thatarraysofthousandsofthenanowiresornanotubescould beultimatelyused,eachtailoredtoreacttoaspecicspeciesinambientgases.Therefo reaclearunderstandingof theinteractionbetweensensingmaterialandgasmolecules atmolecularlevelisessential tounravelthesensingmechanismandtoimprovetheperforma nceofthesensor,which wouldultimatelyleadtodesignofmoreefcient,novelgass ensors. Computationalmodelingisaveryusefultoolininterpreting experimentaldataandpredictingthematerialbehaviorthroughtheuseoftechniques thatconsidersmallreplications ofthemacroscopicsystemwithmanageablenumbersofatomso rmolecules.Amongallthe modelingapproaches,MolecularDynamics(MD)methodisacl assicsimulationtechnique thatcalculatesthe“real”dynamicofthesystem,fromwhich timeaveragesofproperties canbecalculated.DensityFunctionalTheory(DFT)methodi saquantumapproachforthe studyofstructural,electronicpropertiesinmaterialssc ience.Bothofthemarevaluable meansforsimulationsintheeldofchemistryandphysicsan dhavegreatlycontributedto theunderstandingofvariouspropertiesofnanomaterials.1.1MotivationandGoalThisdissertationisfocusedoncharacterizingnanoscaled materialsandprobingtheirapplicationsintheeldofhydrogengassensorusingbothclassic alMDsimulationmethodand quantummechanicalDFTcalculations.Thisresearchaimsto unravelthetraditionalgap betweentheatomicandthemacroscopicworldinmechanicsan dmaterialsbyexplaining, 2

PAGE 16

exploringandpredictingchemicalandphysicalphenomenaw ithaidofthecomputational tools. ThegoalofthisresearchistostudyPdbasednanomaterialsa shydrogensensingmaterialsusingbothclassicalandquantumcomputationalmetho d.Thedissertationisdivided intotwoparts.First,themeltingandthermaldynamicprope rtiesofPdnanoclustersand nanowiresarestudiedusingMDsimulations,withfocusonth edynamicsandstructural evolutionduringtheheatingofthesystems.Thispartofwor kissignicantforthecharacterizationofsuchmaterials.Inthesecondpart,themechan ismofPdfunctionalizedsingle walledcarbonnanotubeandhydrogeninteractionsareinves tigatedusingDFTmethod, wheresensingmechanismisdiscussedandpossiblesensingm aterialdesignissuggested. 1.2OrganizationoftheThesisThisdissertationisorganizedasfollows: Chapter2providesintroductiontohydrogensensorsandhydr ogensensingmaterials, whichincludesgeneralinformationofsensor,recentexper imentalstudiesandan introductiontocarbonnanotubes. Chapter3describestheMDsimulationmethodusedinthisstud y.Thetheoryofthe methodandthedevelopmentofcomputationalalgorithmsemp loyedherearebriey mentioned. Chapter4discussesthecomparisonstudyofthermodynamic,s tructuralanddynamic propertiesofPdnanowireandnanocluster.Simulationsinv estigatethesimilarityand differenceofthetwosystemsinthemeltingprocess. Chapter5studiesthemeltingandstructuralevolutionofagr aphitesupportedPd nanocluster. 3

PAGE 17

Chapter6introducesDFTandpseudopotentialplanewavemeth od,aswellasthe simulationpackageused. Chapter7detailstheelectronicstudyofPdandPd/Nialloyfu nctionalizedSWNTs andtheirinteractionswithhydrogenmolecules. Chapter8extendsthestudyintheChapter7,wheredifferentwa ysoffunctionalization,includingfullcoatingareproposed,andthehydro gensensingmechanismis explored. Chapter9summarizesthestudycontainedinthisdissertatio nandsuggestspossible futurestudies. 4

PAGE 18

ChapterTwo HydrogenSensorandSensingMaterials 2.1WhatIsASensor?Asensorisadeviceorsystemthatproducesanoutputsignali nresponsestosomeinput quantity,asindicatedschematicallyinFigure2-1.Theinp utquantitycanbephysical, chemicalorbiochemicalproperties,andtheoutputsignali susuallyelectrical.Sensorsare comprisedoftwobasicparts:asensingelementandatransdu cer.Thesensingelementis theprimarypartofasensor.Itinteractswiththeenvironme nt,generatesaresponse,and determinesthenature,selectivityandsensitivityofthes ensor.Thetransducerisadevice whichreadstheresponseofthesensingelementandconverts itintoaninterpretableand quantiableterm,suchasavoltagesignal.Sensorsaimatim provingthereliabilityand efciencyofindustrialoperationsbyprovidingfaster,mo reaccuratefeedbackregarding productquality,andalsoatimprovingthequalityofhumanl ifethroughbetterinformation oftheenvironment. Sen sing material (gen er at e resp on se) Tra nsduc er (c on vert r es pons e to elec tr ical s ig na l) Outpu t qu ant ity: (e le ctr ica l ) Input qu ant ity: (c he mical, phy sic al, e tc ) Figure2-1.Schematicdiagramofsensorprinciple. 5

PAGE 19

Generally,sensorscanbeclassiedaccordingtothenature ofinteractionintothe groups[1]: 1.Physicalsensorsforpropertiesliketemperature,press ure,ow,orforce; 2.Chemicalsensorsforspecicchemicalsorclassesofchemi cals; 3.Biosensorsforbiologicallyactivesubstances. Anotherwayofclassicationistoconsiderthephyscialpri nciplesandoperationmechanismofthesensor,suchaselectrochemicalsensor,massse nsor,acousticwavesensor, andopticalsensor,etc.Therearevariouswaysofcharacter izingasensor[2,3].Some importantfeaturesinclude: Sensitivity:ameasureofmagnitudeoftheoutputsignalpro ducedinresponsetoan inputquantityofgivenmagnitude. Resolution:ameasureofminimumchangeofinputquantitytow hichthesensorcan respond. Responsetime:thelengthoftimerequiredfortheoutputtori setoaspeciedpercentageofitsnalvalue. Selectivity:thedegreetowhichthesensorcandistinguish oneinputquantityfrom another. Repeatability:theabilityofasensortoreproduceoutputre adingswhenthesame measuredvalueisappliedtoitconsecutively,undersameco ndition. Therapiddevelopmentofmicroelectronics,micromechanic s,andotherrelatedhigh technologiesenabledtheminiaturizationofsensorelemen ts,aswellasthephysicalintegrationofvariousfunctionsandsignal-processingelemen tsontothesamesubstrate.Nanotechnology,novelmaterialsandsmaller,smarter,andmor eeffectiveelectronicsystems 6

PAGE 20

areplayinganimportantroleinthefutureofsensors,where highersensitivity,greater selectivity,lowercostandfurtherminiaturizationhaveb ecomethenewwaveofsenor technology.2.2HydrogenSensorsHydrogenisanextremelycleanenergysourceformanypurpos es.Hydrogen'spotentialuse infuelandenergyapplicationsincludespoweringvehicles ,runningturbinesorfuelcellsto produceelectricity,andgeneratingheatandelectricityf orbuildings[4–6].However,itis explosivewhentheconcentrationisabovethelowerexplosi onlimitinairof4%.Therefore, safetyremainsatoppriorityinallaspectsofhydrogenener gy.Tofacilitatehydrogen safety,animportantresearchareaisthedevelopmentofhyd rogensensorstodetectleaks andmonitorgaspurity.Inaddition,ahydrogensensorisals oacriticalcomponentforother practicalconcernsintheproposedhydrogeneconomy. Hydrogensensorisatypicalchemicalgassensor,whichupon exposuretoagaseous chemicalcompound,altersoneormoreofitsphysicalproper ties(e.g.mass,electrical conductivity,orcapacitance)inawaythatcanbemeasureda ndquantieddirectlyorindirectly.Inthepastdecades,varioustypesofhydrogensen sorshavebeendeveloped[2]. Accordingtotheappliedsensingtechnologies,someofthec ommonsensorsforhydrogendetectionare:chemiresistorsensors[7,8],FET(eldeffecttransistor)sensors[9–11], SAW(surfaceacousticwave)sensors[12–14],andberoptic sensors[15]. 2.2.1ChemiresistorSensor Chemiresistorisoneofthesimplestsensorstructures.Thes chematicdrawingofachemiresistorisshowninFigure2-2.Itconsistsofasensingmateri alarrayorthinlmexposedto ambientgases.Theadsorptionanddiffusionofhydrogenint othesensingmaterialresultin 7

PAGE 21

Electro de Electro de Subst rate Sensing Mate rial Figure2-2.Schematicviewofachemiresistorsensor. thevariationofresistanceofthedevice.Thechangeinresi stanceisdirectlyrelatedtothe amountofhydrogenpresentintheambientgas. 2.2.2FETSensor Theeld-effecttransistorreliesonanelectriceldtocon troltheconductivityofasemiconductormaterial,orso-calledchannel.MostFETshavethree terminals,wheretheoutput currentowingbetweenthesourceanddrainterminalsiscon trolledbyavariableelectric eldappliedtothegate(thethird)terminal. Figure2-3givesaschematicdrawingofabottom-gatedcarbo nnanotubeFETgassensor.Thesensingmaterial,alsocalledchannel,isplacedbe tweentwometalelectrodes, calledsourceanddrain.Aninsulatinglayerisusedtosepar atesensingmaterialandthe silicongate,whichispatternedonanoxidizedSiwafer.The gatevoltagecanbeeither negativeorpositive,dependingonthenatureofthechannel ,inordertokeepthecurrent throughtransistorconstant.Inpractice,theresponseism easuredwhenthesource-drain current-gatevoltagecharacteristicsoftheFETdeviceshi ftsuponhydrogengas. 2.2.3SAWSensor ASAWdeviceconsistsoftwoIDTs(interdigitaltransducers )ofthinmetalelectrodesona polishedpiezoelectricsubstrateseparatedbyadelayline .ThespacingoftheIDTngers 8

PAGE 22

Sourc e Drain Substrate (S iO2) Gat e VgVsd Figure2-3.SchematicviewofaFETsensorwithaSWNTtransduc ercontactedbytwo electrodes(sourceanddrain)andasiliconbottomgate. INPUT OUTPUT Piezo elec tri c Su bstr ate Delay Li ne Figure2-4.SchematicviewofaSAWsensor. determinesthewavelength.Analternatingcurrentapplied tooneIDTcausesthesurfaceto expandandcontract.Thismotiongeneratessurfaceacousti cwaves,knownaspiezoelectric behavior,propagatingacrossthesubstrate.Hydrogenreac tionswithsensinglayerbetween twoIDTscauseafrequency,phase,oramplitudeshiftinthea cousticwavetravelingacross delayline.Thesechangesarereceivedandconvertedtoelec tricalsignalbytheotherIDT. ThebasicstructureoftheSAWsensorisshowninFigure2-4. Unliketheprevioustwotypesofsensors,whichisaffectedb yresistanceorconductance ofsensingmaterials,SAWsensorsaremostlybasedonmassch ange.However,duetothe factthatwavepropertiesdependonmanyparameters,SAWsen sorsarenotonlymass sensitivedevices,butalsoaffectedbytheelasticity,vis cosity,andotherpropertiesofthe sensinglayer. 9

PAGE 23

2.3HydrogenSensingMaterials 2.3.1CatalysisandSensing Hydrogendetectioninsolid-statechemicalsensorsisdire ctlyrelatedtothephenomenon ofcatalysis,whichinmostcases,aregovernedbytwoproces ses,namely,adsorptionand dissociationofmolecularhydrogenonthesolidsurfacelea dingtoformationofhydrogen atoms,anddiffusionofhydrogenatomsintothebulk.Theset woprocessesnotonlycontrol theresponsetime,butalsoaffecttheselectivityinhydrog endetection. Manygroup-VIIItransitionmetals,suchasNi,PdandPt,hav ebeenwidelyusedasin hydrogenationcatalyticreactions[16–18]aswellasinhyd rogensensors[19],duetothe activechemisorptionofhydrogenmolecules.Amongallthet ransitionmetals,Pdhasbeen usedasthesensingelementofavastmajorityofhydrogensen sors[2]. 2.3.2PalladiumBasedSensor Pdisanidealmaterialforhydrogensensingbecauseitisabl etoselectivelyabsorblarge quantitiesofhydrogengasandformsachemicalspeciesknow nasPdhydride[20].The measureddiffusivityofhydrogeninPdindicatesthatitiso rdersofmagnitudelargerthan diffusivitiesofothergases.Becauseoftheselectivitytoh ydrogenadsorption,Pdhasbeen employedasalterforhydrogenpurication,andalsohasbe enusedtoprovidehydrogen selectivityforvarioushydrogendetectors[20]. TheresponsetimeforaPdbasedhydrogensensorisdetermine dbytherateatwhich thePdelementequilibrateswithhydrogeninthecontacting gasphase[2].SincetheequilibrationofpurePdwithhydrogengasinvolvesthefastdiss ociativeadsorptionatthePd surfaceandrelativelyslowerdiffusionrate( 107cm 2 /s)[20]forhydrogenatomsintothe Pdlattice,thediffusionprocess,nottheadsorptionproce ss,tendstoberate-limiting.In principle,byreducingthethicknessorthedimensionofPds ensingmaterial,theequilibra10

PAGE 24

tiontimecanbereduced,andtheresponseofthesensortohyd rogenaccelerated.Therefore, toachieveafastresponsewhileincreasingthesensitivity ,nanometersizedPdmaterials, suchasPdthinlm,nanoclustersandnanowiresarecommonly appliedinthecurrentdevelopmentofhydrogensensors.Nanoclusterornanowireisa clusterofatoms/molecules oranextremelythinwirewithadiameterontheorderofafewn anometersorless.Due tothelowdimensionalityandspecialgeometry,theyhavela rgesurface/volumeratioand exhibitmanychemicalandphysicalpropertiesdifferentfr omthebulk.Hydrogensensors fabricatedfromthesematerialshaveshownasignicantimp rovementinresponsetime, aswellassensitivitycomparedtothecorrespondingconven tionalPdsensors[8,21–23]. Inaddition,usingnanomaterialsalsogreatlyfacilitates sensorminiaturizationandmeetthe requirementofanewgenerationhydrogensensorsthatusess mallestsampleandhaslowest weight,powerconsumptionandcost. 2.3.3IntroductiontoCarbonNanotubes Carbonnanotubeswerediscoveredin1991byIijimaduringthe directcurrentarchingof graphiteforthepreparationoffullerenes[24].Suchselfassemblednanoscaletubularstructuresofcarbonatomscanbeobtainedbyrollinggrapheneshe etswithvariouschiralities.A carbonnanotubecanbeeithersinglewalled(SW)ormultiwall ed(MW),forexample,doublewalledortriplewalledasshowninFigure2-5,depending onthenumberofgraphene layersthatisrequiredtorollupacarbontube[24,25]. ThechiralityanddiameterofasinglewalledSWNTareuniquel yspeciedbythevector c h showninEquation2-1, c h = n 1 a 1 + n 2 a 2 ( n 1 ;n 2 ) (2-1) 11

PAGE 25

Figure2-5.Structureofamulti-walledcarbonnanotubemad eupofthreeshellsofdifferent chirality.where n 1 n 2 areintegersand a 1 a 2 theunitvectorsofgraphite,asshowninFigure2-6. TheSWNTisformedbyconnectingtogetherthetwocrystallogr aphicallyequivalentsites onthe c h vector[26].Thetubediameter d isdenedbyEquation2-2. d = j c h j = = a q n 1 2 + n 1 n 2 + n 2 2 = (2-2) where a = 1.42 p 3 Aisthelatticeconstant. Accordingtoorientationforvector c h ,carbonnanotubescanbecategorizedintothree types: 1.armchairnanotubes:( n 1 n 2 ) = ( n ,0), n isaninteger. 2.zigzagnanotubes:( n 1 n 2 ) = ( n n ). 3.chiralnanotubes:allothers. Becauseofthesymmetryanduniqueelectronicstructureofgr aphene,thechiralityofa nanotubestronglyaffectsitelectricalproperties.Forag ivenSWNT( n 1 n 2 ),if2 n 1 + n 2 = 3 q 12

PAGE 26

a1 a2 (n,0) (n,n) (n1,n2) zigzag (10, 0) a rmch ai r (8,8) Figure2-6.IllustrationofzigzagandarmchairSWNTsbyroll ingagraphenesheet. thenthenanotubeismetallic,otherwiseitisasemiconduct or[26].Experimentally,carbon nanotubescanbesynthesizedbylaservaporization,electr icarcdischarge,hydrocarbon vaporgrowth,andothers[27].Carbonnanotubeshavemanyext raordinaryproperties, suchashighmodulusandstrength,highchemicalandthermal stabilities,andremarkable electronicandheatconduction[27].Theseproperties,tog etherwiththeone-dimensional charactermakecarbonnanotubestheperfectcandidatesfor variousnext-generationmicro electronicdevices. 2.3.4IntrinsicCarbonNanotubeBasedSensor Thediscoveryofcarbonnanotubeshasgeneratedkeenintere stamongresearcherstodevelopcarbonnanotubessensorsformanyapplications.Carbo nnanotubeshavebeendemonstratedtobepromisingnanoscalemolecularsensorsforde tectinggasmoleculeswithfast responsetimeandhighsensitivityatroomtemperature[28, 29].Uponexposuretogaseous molecules,suchasNO 2 ,NH 3 orO 2 ,theelectricalresistanceofthecarbonnanotubeis foundtodramaticallyincreaseordecrease,whichservesas thebasisfornanotubemolecu13

PAGE 27

larresistorsensor.Theseresponsewereattributedtochar getransferbetweensemiconductingSWNTsurfaceandgasmolecules. However,therangeofmoleculesthatcanbedetectedbyintri nsiccarbonnanotubesis verylimited[25,30–35].Manyimportantgases,suchasH 2 ,CO,CH 4 andH 2 Odonot adsorbonthecarbonnanotubesurface.Toovercometheselim itationsofintrinsiccarbon nanotubeasasensingmaterial,diverseexternalorinterna lfunctionalizationschemesare used. 2.3.5FunctionalizedCarbonNanotubeBasedSensor Theideaoffunctionalizingcarbonnanotubeisattractiveb ecauseitallowspersistentalterationofelectronicpropertiesofthetubes,aswellasto chemicallytailortheirsurface properties,wherebynewfunctionscanbeimplementedthatc an'totherwisebeacquired byintrinsiccarbonnanotubes.Functionalizationprocess introducesadditionalchemical elementsorgroupstointrinsiccarbonnanotubethroughdop ing,coatingorchemicalmodicationandsolubilization[36,37].Experimentally,fun ctionalizedcarbonnanotubescan becharacterizedbyvarioustechniquessuchasX-raydiffra ction,ultraviolet(UV)/infrared (IR)spectroscopy,Ramanspectroscopy,nuclearmagneticres onance(NMR),electronspin resonance(ESR),andsoon[37]. Themodicationofcarbonnanotubesidewallswithnanopart iclesmadeofsuitable metalshasshownpotentialapplicationsinsensors.In2001 ,Kong etal. showedthatexcellentmolecularhydrogensensorscanbeenabledbyelectr on-beamevaporationofPd nanoparticlesovertheSWNTsidewall[22].PdmodiedSWNTsam plesexhibitsignicantelectricalconductancemodulationuponexposuretosm allconcentrationofH 2 inair atroomtemperature,showingPdfunctionalizedSWNTsensorh ashighsensitivityandfast response.Followingthiswork,thePdlayerdepositedSWNTl mswerefabricatedand goodsensitivitytoH 2 withfastrecoveryandlowpowerconsumptionwerealsodemon 14

PAGE 28

strated[38,39].Inadditiontohydrogendetection,Pdcoat edSWNTshavebeenreported tobeusedassensitiveandrecyclablemethanesensor[40].I tisbelievedthatSWNTs canbedopedwithothercatalyticmetals,therebyextending therangeofgasesthesensor candetect.Furthermore,asensordevicecomprisingmoreth anonesuchSWNTdopedby differentchemicalsisexpectedtorespondtomultiplemole cularspeciesatthesametime. 15

PAGE 29

ChapterThree MolecularDynamicsSimulation Vastmajorityofexperimentaltechniquesmeasuremolecula rpropertiesasaverages, eithertimeaveragesorensembleaveragesorboth.Thuswese ekcomputationaltechniques capableofaccuratelyreproducingtheseaspectsofmolecul arbehavior.Thefocusofthis chapterisonthebriefoverviewofclassicalmoleculardyna mics(MD)simulationtechnique forthesimulationofrealsystems.3.1EquationsofMotionfortheAtomicSystemsClassicalmoleculardynamicssimulationisatechniqueforc omputingtheequilibriumand transportpropertiesofaclassicalmany-bodysystem,wher ethepositionsandvelocities ofatomsareallowedtoevolveaccordingtotheNewtonianequ ationofmotionshownin Equation3-1[41]. r i E p ( r 1 ; r 2 ;:::; r N )= m i d 2 r i dt 2 = m i d v i dt ;i =1 ; 2 ;:::;N (3-1) Here, r i v i m i andistheposition,velocityandmassofatom i E p isthepotentialenergy. Thetotalenergyisthesumofthepotentialenergy E p andkineticenergy E k .Thekinetic energyoftheatomsdeterminesthetemperatureofthesystem usingEquation3-2. h E k i = 3 2 ( N 1) k B T (3-2) 16

PAGE 30

where k B isBoltzman'sconstant.Theanglebracketsdenotetheensemb leaverageoverall atomsinthesystems. TodoaMDsimulation,threethingsarerequired:thepotenti al E p ( r i ) ,thepositions r i ,andthevelocities v i .Theparticleinitialpositionsshouldbechosencompatibl ewith thestructurethatisaimedtosimulate.Theinitialdistrib utionofvelocitiesareusually determinedfromarandomdistribution,forinstanceMaxwel l-BoltzmannorGaussiandistribution,withthemagnitudesconformingtotherequiredt emperatureandcorrectedso thereisnooverallmomentum.3.2IntegratingtheEquationsofMotionThedifferentialequationsofmotionareintegratednumeri callyaccordingtowhichtheparticlepositionsorbothpositionsandvelocitiesareupdate d.Thecommonlyappliedmethods areVerletalgorithm[42]anditsmodications[43].Verlet algorithmisacombinationof twoTaylorexpansionsforpositionfromtime t forwardorbackwardto t + t or t t accordingtoEquation3-3and3-4. r ( t + t )= r ( t )+ @ r ( t ) @t t + 1 2 @ 2 r ( t ) @t 2 t 2 + 1 3! @ 3 r ( t ) @t 3 t 3 + ::: (3-3) r ( t t )= r ( t ) @ r ( t ) @t t + 1 2 @ 2 r ( t ) @t 2 t 2 1 3! @ 3 r ( t ) @t 3 t 3 + ::: (3-4) Thenewpositions r ( t + t ) areobtainedbyaddingthesetwoexpansionsshowninEquation3-5. r ( t + t )=2 r ( t ) r ( t t )+ t 2 a ( t ) (3-5) 17

PAGE 31

where a areaccelerations.Thecurrentvelocitiesarethenderived fromtrajectoryofpreviousandnexttimestepsaccordingtoEquation3-6. v ( t )= r ( t + t ) r ( t t ) 2 t (3-6) Anotherequivalentschemeisso-calledhalfstepLeapFroga lgorithm.Inthisalgorithm, thestoredquantitiesarethecurrentpositions r ( t ) ,accelerations a ( t ) togetherwiththehalfstepvelocities v ( t 1 2 t ) .Thefuturepositions r ( t + t ) andthevelocitiesat v ( t + 1 2 t ) are calculatedfromEquation3-7and3-8. r ( t + t )= r ( t )+ t v t + 1 2 t (3-7) v t + 1 2 t = v t 1 2 t + t a ( t ) (3-8) ThecurrentvelocitiesarecalculatedusingEquation3-9. v ( t )= 1 2 v t + 1 2 t + v t 1 2 t (3-9) Thetermleap-frogreectsthepositionsbeingevaluatedat t andthevelocitiesat t 1 2 t .The generalprocedureofleap-frogalgorithmisshowninFigure 3-1 3.3TheForceCalculationNomatterwhichalgorithmisused,ateachstep,theforce F oneachatommustbecalculatedbydifferentiatingthepotentialfunction, E p ( r ) usingEquation3-10. F ( r )= dE p ( r ) d r (3-10) 18

PAGE 32

rv F t-1 t t+1t+2 rv F t-1 t t+ 1 t+ 2 rv F t-1 t t+ 1 t+ 2 rv F t-1 t t+1t+2 (a)(c) (b) (d) Figure3-1.Thegeneralprocedureofleap-frogalgorithm.Br iey,(a)knowingthepositions attimestep t ,onecomputesalloftheforces.(b)Equation3-8isthenused withtheknown forceatsteptandknownvelocitiesatstep t 1 2 t toadvancethevelocitytothenexthalf step t + 1 2 t .(c),(d)Equation3-7isthenusedtocomputethepositionat timestep t +1 andtheprocedurerepeats.Thepotentialenergyfunctiondecidesorapproximatesthei nteractionsbetweenallatoms inthesystem.Inprinciple,potentialfunctioncouldbesol vedfromtheelectronicstructure oftheatom,butifacomplexsystemisinvolved,theBorn-Oppe nheimerapproximationis appliedwhereonlynuclearmotionareconsidered[43].Thep otentialfunctionusedinthis researchwillbebrieyintroducedinthelaterchapter. Typicallypotentialenergiesdecayrapidlywithdistances ,thereforetheyaretruncated outsideaprimarycutoffradius, r c .InMDsimulations,asecond,largercutoffradius, r v isintroduced,andallneighborsseparatedbylessthan r v arestored.Thisneighborlist iscalledVerletlist[42],whichwillonlybeupdatedifthem aximumdisplacementofthe particlesislargerthan r v r c ,thusthecomputationaltimeissavedwhentheinteractions arecalculated. 19

PAGE 33

3.4SimulationConvergenceAftertheforcesarecomputed,thefuturepositionsaredete rmined,andthetrajectories areupdated.Inordertoknowwhetherthesystemisrunningwe ll,oneshouldcheckthat monitoredquantitiesareinfactevolvingintime.Theconve rgenceofthesimulationcanbe demonstratedbycalculationofenergy,root-mean-squared eviation(RMSD)orcorrelation functionbetweentwovariables[43,44].Ifthequantitiesa re“constant”overtimewithan acceptablysmalluctuation,thesystemisthenconverged, or,inotherword,equilibrated. Thermodynamicpropertiesandotherquantitiescanthenbec alculatedafterequilibration toanalyzetheresults.3.5ConstraintsTocomparesimulationsandexperiments,oneneedstocontro landmeasurethermodynamicproperties.Thecommonconstraintsarethermodynami cvariablesthatcanbecontrolledinphysicalexperiment,suchasnumberofparticles ( N ),temperature( T ),pressure ( P ),volume( V )andenergy( E ).Insimulation,thesevariablescanalsobecontrolled. Somemethodsusedinthisstudyareintroducedbelow. 3.5.1ThermodynamicEnsembles Anensembleisacollectionofallpossiblesystemswhichhav edifferentmicroscopicstates buthaveanidenticalmacroscopicorthermodynamicstate[4 5].Thereexistdifferentensembleswithdifferentcharacteristics.Forexample,cano nicalensemblehasconstant N V and T ,microcanonicalensemblehasconstant N V and E .Inthedissertation, NVT ensembleisemployed. N and V areeasilycontrolledinMDsimulationbyxingthenumber ofatomsandvolumeofthesimulationbox. T canbecontrolledbyapplyingathermostat toensuretheaveragesystemtemperatureismaintainedclos etothesettemperature. 20

PAGE 34

3.5.2TemperatureControl Thetemperaturecalculatedfromtheatomicvelocitiescanb econtrolledbytheBerendsen weakcouplingtechnique,wherethesystemiscoupledtoanex ternalheatbath[46].InMD simulations,thiscorrespondstoaddingfrictionaltermst otheequationofmotionshownin Equation3-11. m i d v i dt = F i + m i 2 T T 0 T 1 v i (3-11) T isthecouplingtimeconstantthatdeterminesthestrengtho fcouplingand T 0 istheset temperature[46].Bychoosingdifferentvaluesof T 0 ,thestrengthofthecouplingcanbe madesmallertominimizethedisturbancetothesystem,orit canbevarieddependingon theapplication.Thismethodalsohasanadvantageofmainta iningaMaxwelltypevelocity distribution.3.6PropertiesMeasurementThebasicthermodynamicpropertiescanbecalculatedastim eaverages h A i time fromMD simulationsafterthesystemisequilibrated.Thatis,thea veragevalueoftheproperty A overalltimestepsgeneratedbythesimulationintheproduc tiontimeaccordingtoEquation3-12. h A i time =lim x !1 1 Z x + t 0 t 0 A p N ( t ) ; r N ( t ) dt 1 M M X i =1 A i p N ( t i ) ; r N ( t i ) (3-12) where isthesimulationtime, M isthenumberoftimestepsinthesimulations,and A i is theinstantaneousvalueof A ,expressedasafunctionofthemomentum p ,andthepositions 21

PAGE 35

r ofthesystem.Theergodichypothesisassumes h A i time isindependentofchoiceof t 0 andequivalenttoensembleaverage h A i inmostmolecularsimulations[44]. 3.7DL POLYPackage AlltheMDsimulationsinthisdissertationareperformedby DL POLY,aparallelmolecularsimulationpackagedevelopedatDaresburyLaboratory[ 47].DL POLYincludesdensitydependentpotentialssuitableforcalculatingthepro pertiesofmetals,suchasSuttonChenpotentialusedinthecalculations[48].Theequationof motionintegrationalgorithms inDL POLYarebasedonVerletscheme.DL POLYalsoprovidesamultipletimestep algorithmtoimproveefciency[49].Abriefdescriptionof howtosetupaMDsimulation foroneparticularsystemusingDL POLYcanbeseeninAppendixA. 22

PAGE 36

ChapterFour MeltingofPdClustersandNanowires:AComparisonStudyUsing MolecularDynamics Simulations Aportionofthischapterhasbeenpublishedinthe PhysicalReviewB 72,134109,2005 4.1AbstractWepresentresultsfromamoleculardynamicssimulationstu dyofaPdclusteranda nanowire,usingtheSutton-Chenmanybodypotentialfunctio n.Changesinthermodynamicandstructuralpropertiesofthesetwosystemsduring heatingwerestudied.We foundthatthemeltingtemperatureofthePdnanowireof1200 Kislowerthanthesimulatedbulkvalue(1760K)buthigherthanthatoftheclustera t1090K.Meltingbehaviors werecharacterizedbyanumberofthermodynamic,structura landdynamicalparameters. Surfacepre-meltingatmuchlowertemperaturesthanthenea rrst-ordertransitiontemperaturesnotedabovewasobservedinbothPdsystems.Thesurfa cepre-meltingtemperature rangewashigherforthenanowirethanforthecluster.Surfa cemeltinginnanowiresmanifestsitselfaslargeamplitudevibrationsfollowedbyfree movementofatomsintheplane perpendiculartothenanowireaxis,withaxialmovementari singattemperaturescloserto thetransitiontemperature.Increaseinnanowirediameter aswellasshapechangeisseen toresultfromthisaxialmixing.Bond-orientationalorderp arametersindicatedthatthe nanoclusterretainedtheinitialfccstructureatlowtempe ratures.Thenanowires,however, wereseentobestableatasolidstructurethatwasclosetohc pasestablishedbybondorientationalorderparametercalculations.Meltingpoin tdepressionsinbothsystemsagree betterwithaliquid-dropmodelthanwithPawlow'sthermody namicmodel. 23

PAGE 37

4.2IntroductionStudiesofthemeltingprocessandthermodynamicsproperti esofparticlesatnanometer length-scaleshaveattractedboththeoretical[50,51],an dexperimental[51–53]interest becauseoftheirdramaticallydifferentbehaviorfrombulk materials[54].Forexample,it hasbeenknownthatthemeltingtemperaturedecreaseswithd ecreasingdiameterofclusters[55].Transitionandnoblemetal[56–58]oralloy[59,6 0]clustersandnanowiresare gettingmoreattention,mainlybecauseoftheirextensivea pplicationsincatalysisandin electronicandopto-electronicnanodevices.However,man ypropertiessuchassize,shape, andstructureofnanomaterialsaffecttheircatalytic,opt icalandelectronicpropertiesin waysthataredifculttopredict[61].Experimentally,the yhavebeenstudiedusingimaging[61–63]andspectroscopic[64,65]methods.Forexample ,recentadvancesinin-situ transmissionelectronmicroscope(TEM)techniqueshaveal loweddirectinvestigationof nanoparticlesunderrealisticreactionconditionsatatom iclevel[66].Theoretically,theuse ofmodelingandsimulationshasalsosubstantiallyimprove dourunderstandingofnanomaterialsinvariousapplications.Theoreticalinvestigati onsofthemeltingbehaviorofclusters andnanowireshavebeenmostlybymeansofMonteCarlo(MC)andM olecularDynamics (MD)computersimulationsandarefocusedonthefollowings aspects: 1.Investigationofthemeltingtemperatureandthermalsta bilityduringthemeltingprocess[67,68]. 2.Thestructuralevolutionsandmechanicalpropertiesdur ingheating[69]. 3.Relationshipofstructuralcharacteristicsandsizeeffe ctswithtemperature[50,70, 71]. Forexample,Wang etal. foundthatforTinanowiresthinnerthan1.2nm,thereisno clearcharacteristicofrst-orderphasetransitiondurin gthemelting,butacoexistenceof 24

PAGE 38

thesolidandliquidstatedoesexist[68].Liu etal. observedthreecharacteristictime periodsinthemeltingofgoldisomers:disorderingandreor dering,surfacemelting,and overallmelting[72].Leeandco-workersusedthepotential energydistributionofatoms inclusterstoexplainmanyphenomenarelatedtothephasech angesofclusters,andalso foundanewtypeofpre-meltingmechanisminPd 19 cluster[73]. Clustersareoftenconsideredasabridgebetweenindividual atomsandbulkmaterial. Recentexperimentalandtheoreticalstudiesdemonstratedt hatmetallicnanowireshavehelicalmulti-walledcylindricalstructureswhicharediffe rentfromthoseofbulkandclusters[74].However,atthesametime,nanowiresalsohavesom ethermodynamiccharacteristicswhicharesimilartoeitherclustersorbulk,because ofthelargesurface-to-volume ratiointhesenanostructures.Therefore,acomparisonofc lustersandnanowirescanprovideanopportunitytobetterunderstandtheirbehavior. Inthispaper,meltingcharacteristicsofpalladiumnanocl ustersandnanowiresofcomparablesizearedescribed.Pdnanoclustersandnanowiresh avebeenusedwidelyinthe designofhighperformancecatalysts[75,76]andnanoscale electronicdevices,suchas chemicalsensors[7,8,22].Severalexperimentsclearlyin dicatethatquantumbehaviorof metalnanoclustersisobservable,andismoststronglyexpr essedbetween1and2nm,therefore,particlesinthatsizeregionshouldbeofmostinteres t[77].Forexample,Volokitin et al. foundthat2.2nmPdclustersshowthemostsignicantdeviat ionsfrombulkbehavior atverylowtemperaturescomparedwiththoseof3.0,3.6and1 5nmdiameter[78].SimulationstudyofPdnanomaterialprovidesanopportunityforfu rtherunderstandingitsunique roleinexperimentalphenomena.Althoughthesizeofthemet allicclustersbeingstudied intheliteraturerangesfromtenstoseveralthousandatoms ,mosteffortshavebeenfocused onsizesbelow150atomsforbothPdandothermetals[79].Tof acilitatecomparisonwith experimentaldata,weinvestigatebothmeltingandstructu ralbehaviorofthePdcluster with456atomsandcomparable-sizednanowirewith1,568ato ms. 25

PAGE 39

4.3PotentialModelandComputationalMethodBecauseofthedelocalizedelectronsinmetals,thepotentia lfunctions,whichdescribethe interactionsofparticles,shouldaccountfortherepulsiv einteractionbetweenatomiccores aswellasthecohesiveforceduetothelocalelectrondensit y.Severalmany-atompotentialmodelsweredevelopedduringthe1980sbyvariousworke rs,suchastheEmbedded AtomModel[80],theGlueModel[81],Tight-bindingpotenti alwithasecond-momentum approximation(TB-SMA)[82],andSutton-Chenpotentialmode l[48],whichwasusedin ourMDsimulation.TheSutton-Chenpotentialcanbeusedtode scribetheinteractionof variousmetals,suchasAg,Au,Ni,Cu,Pd,Pt,andPb.Itisexpr essedasasummationover atomicpositionsusingEquation4-1. U = pp X 0@ 1 2 N X j 6 = i pp r ij n c p i 1A (4-1) where i = P Nj 6 = i pp r ij m isameasureofthelocalparticledensity.Here r ij istheseparationdistancebetweenatoms, c isadimensionlessparameter, pp istheenergyparameter, pp isthelatticeconstant,and m and n arepositiveintegerswith n>m .Thersttermof Equation4-1isapair-wiserepulsivepotential,andthesec ondtermrepresentsthemetallic bondingenergybetweenatomiccoresduetothesurroundinge lectrons.Therefore,ithas thesamebasisastheFinnis-Sinclairpotentialandintrodu cesanattractivemanybodycontributionintothetotalenergy.Thispotentialcanreprodu cebulkpropertieswithremarkable accuracy[83].Itprovidesareasonabledescriptionofsmal lclusterpropertiesforvarious transitionandnoblemetals[84,85].SCpotentialhasalsob eenappliedtomodeltheinteractionandstudythepropertiesofbimetallicalloysandmet al/substratesystems[60,86,87]. Recently,adsorbateeffectofsupportedPtnanoclusterswas studiedusingtheSCpotential anditwasfoundthatthepresenceofadsorbedatomsstabiliz esthesurfaceclusteratoms 26

PAGE 40

Table4-1.Sutton-ChenpotentialparametersforPd. ( A) ( 10 3 eV) cnm 3.89074.179108.27127 underaninertgasatmosphere[88].ValuesofSCparametersf orPdsimulationsinthis paperweretakenfromtheoriginalworkofSuttonandChen,asl istedinTable4-1[48]. MDsimulationswereperformedusingtheDL POLYpackage[47].Thesystemwas simulatedundercanonical( NVT )ensembleusingtheVerletleapfrogalgorithm[89].Periodicboundaryconditionswereappliedonlyintheaxialdi rectionofthenanowire.No boundaryconditionswereappliedtothecluster.Thebulksy stemswerestudiedwith3D periodicboundaryconditionsunderconstantpressureandt emperature( NPT ).Bothclusterandnanowirewerestartedfromface-centeredcubic(fcc )Pdbulkstructure.Acutoff diameterof2.3nmisusedtogenerateasphericalPdclustera ndcylindricalnanowire.This cutoffdiameterisnotthebestwaytospecifytheparticledi ameter.Forthesphericalcluster,theGuinierequationshowninEquation4-2providesame thodologyforestimatingthe actualradiusofthecluster[68]. R cluster = R g q 5 = 3+ R Pd (4-2) wherethersttermisderivedbyequatingtheRayleighequati onandanequationresulting fromtheGuinierapproximationforparticlescattering[90 ,91]. R g istheradiusofgyration, givenbyEquation4-3. R g = vuut 1 N X i ( R i R cm ) 2 (4-3) where R i R cm isthedistancefromcentertothecoordinationpoint,andth esumrunsover allparticles.Thesecondterminequation2ishalftheatomi cdistanceinthePdbulk, 27

PAGE 41

R Pd = 1.37 A.TheresultingdiametercalculatedfromEquation4-2isab out2.6nm,which istakentobethediameteroftheclusterinlatercalculatio ns.Thesame2.6nmistakento bethenanowirediameter. Inallthesimulationsreportedhere,atimestepof0.001psw asused.Theinitialsamples withatomsinidealfacecenteredcubic(fcc)positionswere rstrelaxedbysimplequenchingto0K.Eachsystemwasthenheatedwithatemperaturestep of50K.Thestep-size wasdecreasedto10Kwhenclosetothetransitiontemperatur e. 4.4ResultsandDiscussionThetemperatureofmeltingtransitioncanbeidentiedinma nyways.Werstemploy thevariationsoftotalpotentialenergyandheatcapacityd uringheating.Theyareshown inFigure4-1.Potentialenergiesincreaselinearlywithte mperatureintheearlystage,but deviatefromthelineardottedlinesathighertemperatures .Thesedeviations,associated withsurfacemeltingphenomena,willbediscussedlater.Whe nclosetothetransition temperature,simplejumpsintotalpotentialenergy,indic ativeofnearrst-ordertransitions, canbeeasilyobserved.Uponcooling,boththenanoclustera ndnanowireundergosharp liquid-solidtransitionsandshowratherstronghysteresi s.Thepotentialenergiesofthe newsolidsarenotverydifferentfromtheinitialones,thou ghstructuraldifferencesare boundtoprevail.Wefocusonthemeltingprocessinthiscont ribution,andtakethesharp jumpintheenergy(andthecorrespondingsharppeakinthehe atcapacity)torepresent themeltingtemperature.Consistentwithliterature,wede nedthemeltingpointasthe transitiontemperaturecorrespondingtothetemperatureo fobservedphasechangeinthe heatingrun,andthefreezingpointasthetemperatureofobs ervedphasechangeinthe coolingrun.Thepresenceofhysteresisinmelting/freezin gtransitionisnotunusualandis expectedboththeoretically[92,93]andexperimentally,a sreportedinthecasesofPb[94] andNa[51].Thestructuralchangesresultingfromcoolinga ndheatingalsoinuencethe 28

PAGE 42

phasetransitionandresultinhysteresisasreportedbyChau sakandBartellintheirstudy onfreezingofNi-Albimetallics[95].Fromthepotentialen ergycurve,weestimatethe meltingtransitionofPdclustertooccurat1090K,andthato fthePdnanowireat1200 K.Bothtemperaturesaremuchlowerthanthebulkmeltingtemp eratureof1760K(also obtainedfromsimulation). Theconstant-volumespecicheatcapacity C v iscalculatedbyastandardformula showninEquation4-4. C v = h ( E ) 2 i k b T 2 = h E 2 ih E i 2 k b T 2 (4-4) where E istotalpotentialenergyfromtheheatingcurveofFigure41, k b istheBoltzman constant,and T isthetemperature.Meltingpointisdenedasthetemperatu rewiththe maximumapparentheatcapacity.The C v curvesinFigure4-1(a)and(b)indicatethesame meltingtemperaturesasthosefrom E p curves.Comparedtothe C v curvebeforemeltingfor thePdcluster,thatofPdnanowireshowsmorestructure.Wea lsoobserveasmallupward jumpinthenanowireheatingcurve,afterwhichtheslopeinc reasesquicklyuntilthelarge jumpappears.Thisdeviationfromlinearityisaresultofsu rfacemelting[96]orsurface reconstruction[97],whichimpliesthatthemeltingproces stakesplaceintwostages,premeltingandhomogeneousmelting.Eventhoughthischangeis clearlyvisiblefromtheplot forthePdcluster,furthercharacterizationofthesurface meltingviadynamicalvariables suchasthediffusionbehaviorandvelocityauto-correlati onfunctionsrevealeddifferences inthedetailsofthepre-melting.Thesecharacterizations arediscussedlaterinthispaper. BasedonthedatashowninFigure4-1,wecanestimatethemelti ngtemperaturetobe1090 KforthePdcluster,and1200Kfortheinnitelylongnanowir e. Usingtheabovemeltingtemperatures,theheatoffusionofP dclusterandnanowire canbeobtainedusingEquation4-5. 29

PAGE 43

20 0 400600 800 100 01 200 1 400 -1 .66 -1 .64 -1 .62 -1 .60 -1 .58 -1 .56 -1 .54 -1 .52 -1 .50 -1 .48 Cv ( eV /K ) Ep ( Ke V)T (K ) he at in g c ool in g0. 00 0. 05 0. 10 0. 15 0. 20 0. 25 0.30 0.35 Cv 20 04 00 60080 0 100 01 20014001600 1 800 -5 .8 -5 .7 -5 .6 -5 .5 -5 .4 -5 .3 -5 .2 Cv (eV /K ) Ep (K eV )T (K ) he atin g co ol in g 0. 05 0. 10 0. 15 0. 20 0. 25 0. 30 0. 35 0. 40 0. 45 0. 50 C v (a) (b) Figure4-1.PotentialenergyandheatcapacityofthePd(a)n anoclusterand(b)nanowire. Heatingandcoolingdatapointsareontopofeachotherabove thetransitiontemperature, onlycoolingpointsarevisibleonthegraphs. 30

PAGE 44

Table4-2.ThermodynamicpropertiesforPdbulk,clusteran dnanowire. T m (K) H f (kJ/mol) r sv y (J/ m 2 ) Bulk(simulation)176016.83 Bulk(experiment)1825 a 16.70 b 1.808 a Pdcluster10906.711.328Pdnanowire12007.361.393 y ValuesmeasuredatT = 300K. a ValuesobtainedfromVanselowandHowe[98] b ValuesobtainedfromIidaandGuthrie[99] H f = H l H s (4-5) where l and s standfortheenthalpyoftheliquidandsolidphases.Thecal culatedvalueof theheatoffusion( H f )forbulk,clusterandnanowirearelistedinTable4-2.Thet otal potentialenergyperatomislargerindicatingtheexistenc eofasurfaceenergy[96],which canbecalculatedbyEquation4-6. r sv = E p nano E p bulk =A (4-6) where E p isthepotentialenergyofcluster,nanowireorbulk. A isthesurfacearea,calculatedassurfaceareaofperfectsphereorcylinder,which isapproximatelyequaltothe surfaceareaofclusterandnanowireat300K.ForthePdclust ersystem,thedifferenceof potentialenergyat300Kis29.873kJ/mol.Hence,weobtaina surfaceenergyof1.328 J/m 2 .Similarlyfornanowire,wehave r sv = 1.393J/m 2 .Therefore,weseethatthePd nanowirehaslargerenergyperunitsurfaceandhigherheato ffusionthanthecomparable Pdcluster,whichinturnimpliesthehighermeltingtempera ture. ShapechangesofthePdnanoclusterandnanowireweremonito redbycalculatingthe radiusofgyrationusingEquation4-3.Consideringthatthei nnitelylongnanowirein symmetricalaboutthe z -axis,andweareonlyinterestedintheshapevarianceinthe xy 31

PAGE 45

20040 06 0080 0 100 01 20 01 40 01 600 8. 2 8. 4 8. 6 8. 8 9. 0 9. 2 9. 4 9. 6 R g (A )T (K ) P d cl us te r P d nanow ir e Figure4-2.Radiusofgyrationvs.temperatureforPdcluster andPdnanowirewithrepeatingunitoflengthof5.6nm.plane,weuse2dimensional R g forthePdnanowire,whichistosayonlythedistancefrom eachatomtothe z -axisisutilized. Figure4-2showsthetemperaturedependenceoftheradiusof gyration R g ofthePd nanoclusterandnanowire.Inbothcases, R g hasanupwardjumpatthemeltingtransition, indicatingthatclusterandnanowirebehavesimilarlyinex pandingtoawidershape. Thestructuralfeaturesofthenanowireuponheatingwerefu rtherexploredbyvisualizationthroughsnapshotsandtrajectoryplotstoundersta ndthedifferencesinthesurface pre-meltingphenomenonbetweenthenanowireandcluster.F igure4-3(a)showssample projectedcoordinates,ontotheplaneparalleltothenanow ireaxis,ofeachatomattwo temperaturesof700Kand800K,asblueandreddots,aswellas adashedlineconnecting eachoftheatomicpositionsatthetwotemperatures.Whatisa pparentisanoscillatory motionintheplaneperpendiculartothenanowireaxis,with atomsmostlyretainingtheir positionsthroughthesimulationduration.Veryfewsurfac eatomsexhibitlargemovement alongthewireaxis,crossingdifferentplanes.Thissurfac eatomicmovementwasfoundto 32

PAGE 46

berarerattemperatureslowerthanthe700-800Kshowninthi sgure.Whileabitmore difculttoseefromFigure4-3(b),similarbehaviorisexhi bitedattheslightlyhighertemperaturesof900and1000K.ThetopviewinFigure4-3(b)show smoremovementatthe surfacethantowardsthecenterofthewire.Analysisofthes eandsimilarplotsalongwith trajectoryvisualizationshaveprovidedapictureofthesu rfacepre-meltingofonewherethe nanowireexhibitsincreasinglyfreermotionofthesurface atomsintheplaneperpendicular tothenanowireaxisattemperaturesmuchbelowthenearrst -ordertransitiontemperature, withthedegreeoffreedomparalleltothenanowireaxisavai lableathighertemperatures, closertothetransitiontemperature.Thesurfacepre-melt ingisfurthercharacterizedby ashrinkingsolid-likecoreofthenanowire,asthetemperat ureincreasestothetransition point.Thisphysicalpictureisconsistentwiththedeviati onofthepotentialenergycurve fromlinearityasshowninFigure4-1(b),however,thesedet ailsofthestructuralanddynamicalchangesarenotapparentfromthatplot.Indeed,the potentialenergycurveforthe near-sphericalnanoclustershowninFigure4-1(a)exhibit ssimilarbehavior,however,detailsofthesurfacepre-meltingarequitedifferent,adiff erencearisingfromthedifference inthegeometry.Itshouldbenotedherethatbothnanocluste rsandnanowiresofvarious metalshavebeensynthesizedbyavarietyoftemplatingando thersolutiontechniques,and itispossibletoexperimentallyobservethesedifferences inmeltingbehavioruponheating ofthesenanomaterials.Nosuchexperimentshavebeenrepor tedintheliteraturetoour knowledge. Componentsofthevelocityauto-correlationfunctionincyl indricalcoordinateswere calculatedasfunctionsofdistancefromthenanowireaxist ocharacterizeatomicmotion inthesurfacepre-meltingregime. v and v z characterizemovementinthe xy -planeand inthe z -direction.Figure4-4showsthecorrelationof v and v z withtimeat800K.The vecurvesinbothplotsrepresentcorrelatedatomsatdiffe rentdistancesfromthecenter with1beingtheclosestand5thefarthest.Thewirewasparti tionedintothese5shellswith 33

PAGE 47

(a ) (b) Figure4-3.Snapshotsofequilibratedatomicpositions,sh ownasprojectedcoordinatesin planesparallel(upper)andperpendicular(lower)to(a)th enanowireaxis.Bluedotsarefor 700Kandreddotsarefor800K,withthebluedashedlinesconn ectingthesameatomsat thetwotemperatures.Similarplotin(b)for900Kand1000K, respectively. dR = 2.77 Abasedontheinitialequilibriumatomicpositions(timeor iginsofthetimecorrelationfunctioncalculations),with dR chosentobeclosetotheinter-atomicdistance inbulksolidPdofabout2.75 A.Atomsstayedwithintheirshellsforthedurationofthe correlationtime,andbeyond,justifyingthesecalculatio nstofurtherunderstandthesurface meltingphenomenon. Bothcomponentsofthecorrelationfunctionsfortheinnersh ellsexhibitrebounding oscillationsthatdecaywithtime,indicativeoflocalizat ionatlatticesites.Comparingthe twoplots, v hasshortercorrelationtimeandmuchlargerdepthofthemin imathan v z whichimplieslargeramplitudetangentialvibrationsthan axial.Behaviorofatomsinthe outershells(especially,theoutermostshell)issignica ntlydifferent,atthistemperatureof 800K,withsurfacepre-meltingapparent.Nearlyliquid-li kemotionisinferredfromthe singledampedoscillationwithoneminimumbeforede-corre lationwithtimeoccurs.While resultsattheonetemperatureof800KareshowninFigure4-4 toillustratethesurfacepremeltingphenomenon, v and v z calculatedatothertemperaturecorroboratethearguments 34

PAGE 48

developedhere.Attemperatureshigherthan900K,axialmov ementislargerwhilethe tangentialoscillationsaredampened.Thewirediameterin creaseswithtemperatureasa resultofthesemovements. Surfacemeltingisobservedfrequentlyinsimulationsofna noparticles.Surfaceatoms meltattemperaturesbelowthetransitiontemperature,and thenthequasi-liquidskincontinuouslygrowsthickerasthetemperatureincreases.Thei nnerregionsstayordereduntil thetransitiontemperature.Thetemperatureatwhichthel mthicknessdivergestothe entiresystemsizeisthoughtofastheclustermeltingpoint .However,forultra-thingold nanowires,Wang etal. foundtheinteriormeltingtemperaturetobelowerthanthat of thesurface,indicatingthatthemeltingactuallystartsfr ominside,exhibitingnosurface meltingbehavior[74]. Snapshotsofatomicpositionsprojectedontoaplane(perpe ndiculartotheaxisinthe nanowirecase)areshowninFigure4-5.Theseprovideeviden ceforsurfacemeltingin boththePdclusterandnanowirecases. Furtherevidenceofsurfacemeltinginbothclusterandwire isobtainedfromselfdiffusioncoefcientscalculatedasfunctionsofradialdi stanceusingmean-squaredisplacements.Asinthecalculationofthevelocityauto-corr elationfunctions,theatoms wereassignedtobinsbasedontheirinitialpositionsatthe endoftheequilibrationperiod. Themean-squaredisplacementsforeachshellwerethengene ratedbyaveragingovera 25pstrajectorywithsamplingdoneevery0.1ps.Averagesta kenovera25pstrajectory withdifferentoriginsgavethesameresultwhichisindicat iveofasystemthatistrulyin equilibrium.Theself-diffusioncoefcientswerecalcula tedforeachradialshellatvarious temperaturesusingEquation4-7. D = 1 6 N lim t !1 d dt X i [ r i ( t ) r i (0)] 2 (4-7) 35

PAGE 49

-0 .6 -0 .4 -0 .2 0 0. 2 0. 4 0. 6 0. 8 1 00 .5 .5 t (p s)VA CF -T H sh e ll5 sh e ll4 sh e ll3 sh e ll2 sh e ll1 5 4 1 3 2 -0 .6 -0 .4 -0 .2 0 0. 2 0. 4 0. 6 0. 8 1 00 .5 .5t (p s)V ACF -Z sh e ll5 sh e ll4 sh e ll3 sh e ll2 sh e ll1 5 4 1 32(a) (b) 111 1 Figure4-4.Velocityautocorrelationfunctions(a)v and(b)v z foratomsindifferentshells ofthePdnanowireat800K.Shell1istheclosesttothewireax isandshell5isthefarthest. 36

PAGE 50

(a) (b) T=80 0 K T=1 000 K T=10 50 K T=1100 K T=90 0 K T=110 0 K T= 1200 K T= 1250 K Figure4-5.Snapshotsoftheprojectedatomicpositionsoft he(a)456Pdatomclustersat different T and(b)1,568atomPdnanowireprojectedontoaplaneperpend iculartothe axis. TheseareshowninFigure4-6.Inallthecases,wendthediff usivitiesofoutershells tobehigherthanthoseoftheinnerones.If D 1 D 5 denoteself-diffusioncoefcientsof theseshellsfrominnertoouter,wefoundthatatlowertempe ratures,bothclustersand nanowireshavesimilarself-diffusioncoefcientsoftheo rderof10 3 A 2 /ps.Atomsinthe outershellshavelargerdiffusioncoefcientthantheatom sclosertothecoreatoms.Asthe temperatureincreasesfurther,thediffusioncoefciento ftheoutermostshell, D 5 ,rststarts toincreaserapidly.Thisisfollowedbyanincreaseof D 4 ,while D 1 D 2 D 3 retaintheir valuesfromthelowertemperatures.Thisstateismaintaine duntilthemeltingtransition temperaturesareapproached.Thelargerdiffusioncoefci entsinoutershellsandrelatively staticstateofinnershellsattemperaturesbelowthetrans itiontemperaturessupportthe existenceofsurfacemeltinginbothPdclusterandnanowire .Atomsonthesurfacehave weakerrestrainingforcesthanthecoreatoms.Althoughsur facemeltinginsomesenseis 37

PAGE 51

20040 06 0080 01 00 01 20 01 40016001800 0 1 2 3 4 5 20 0 400 60 08 00 100 01 200 0. 0 0. 2 0. 4 0. 6 s he ll 1 sh e ll 2 sh e ll 3 shel l 4 sh e ll 5D (A 2 /p s)T (K ) 20 04 00 60 08 0010001200 1 400 -0 .0 5 0. 00 0. 05 0. 10 0. 15 0. 20 0. 25 0. 30 0. 35 0. 40 200400600 80 0 10001200 0.00 0.02 0.04 0.06 D (A 2 /ps)T (K ) sh e ll 1 sh e ll 2 sh e ll 3 s he ll 4 sh e ll 5 (a) (b) Figure4-6.Self-diffusioncoefcientforatomsindiffere ntradialshellsatvarioustemperaturesfor(a)Pdclusterand(b)Pdnanowire. 38

PAGE 52

notnecessarilyadiffusiveprocess,itcanbeconsideredac omplexphenomenoninvolving cooperativemotion[97].AccordingtotheLindemanncriter ion,thephasetransitionoccurs whenatomicmotionexceeds10-15%ofinter-atomicdistance .Fromthevariationofthe diffusioncoefcientsinvariousbins,wecaninferacontin uouslayer-by-layermeltingas theatomicdisplacementsmeettheLindemanncriterioninal ayer-by-layermanner,until, thecriterionismetfortheremainingsolidcoreallatonce, atthenearrstordertransition temperature.Fromthediffusionplots,togetherwiththeva riationsofpotentialenergiesand heatcapacitycurvesinFigure4-1,weestimatethesurfacem eltingregionsofthePdcluster andnanowiretostartatabout700-800K,and800-900K,respe ctively.Atmeltingpoints, diffusioncoefcientsofalltheshellsexhibitlargejumps ofsimilarmagnitude,indicating thephasetransitionsfromsolidtoliquid. Structuralpropertiesandchangesinthemduringheatingar eofinterestinunderstandingmechanicalandcatalyticpropertiesofmaterials.Expe rimentalobservationsinclude changesinthelatticeparameter,surfacecoordinationand structuraluctuations.Sometheoreticalcalculationsincludedetailedstudiesofthetopo logyandstructuralstability.Many smallclusters,withspecialnumbersofatoms,so-calledma gicnumbers,haveproventobe morestablethanothers[100].Thechangeincrystallograph icstructurecanbeattributedto surfaceenergy.IcosahedralPdclusterswith13,55,147ato msareexamples.Thegeometry oftheseextremelysmallclusterswithuniqueminimumenerg yhasbeenextensivelystudied[69,79].Inthiswork,wepayattentiontothetimeevolut ionofthestructuresduring heatingbyinvestigatingtwoparameters:atomicnumberdis tributionalongthe z -direction (aCartesiandirection,alongthewireaxisforthenanowire) andbond-orientationalorder parameters. Theatomicnumberdistribution N ( z ) foreachelementisdinedinEquation4-8. N ( z ) isagoodwaytolookatthestructuralfeaturesduringheatin gofthesphericalclusterand onedimensionalnanowireofsimilardiameter.PlotsinFigu re4-7showthedistribution 39

PAGE 53

ofPdatomsalong z -axisatdifferenttemperatures.Inthesolidphase,atomsh avehigher distributiononlyatcertaindistancesfromthecenter,for mingmanysharppeaks.Those peaksbecomewiderandshorteruponheating,andnallydisa ppearduetotheuniformly distributedatomsinliquidphase.Thisexpectedbehaviori n N ( z ) isseeninthePdcluster case,asshowninFigure4-7.Incontrast,Figure4-8forthen anowireexhibitscomplicated structuralfeatures.Longerwave-lengthvariationsinthe N ( z ) distributionareintroduced duetoincreasedamplitudesofoscillationsoftheatomsino rderedzones.Theordered zonesappeartomovealongthewireasweapproachthetransit ion,withthepossibilityof suchmovementwithtime,atasingletemperature.Whilethelo westtemperatureshown inFigure4-8is600K,wehaveseenthisbehavioratthelowest temperaturesimulated,of 100K.Thisextremelyinterestingbehaviorcouldbeanartif actoftheperiodicboundary conditions.Toexplorethisfurther,wehaverepeatedthesi mulationswithawirethatis twiceinlength.Resultsindicatedthatthelongerwave-leng thorderingofzonesispossible inthesurface-meltingregime,andisenhancedasthetransi tiontemperatureisapproached. However,theperiodicstructuresobservedinthelowtemper aturesolidstructuressuchas showninFigure4-8(a)havedisappeared.Noneofthemelting propertieswereportin thismanuscriptwereaffectedbythedoublingofthewire-le ngth.Weconcludethatthere existsthepossibilityoforderedzonesinPdnanowiresatcl ose-to-transitiontemperatures, andthatthisphenomenonshouldbeexploredwithsimulation sofmuchlongerwires,to eliminatealleffectsofperiodicboundaryconditions.Toe xplorethepossibilityoflower densityinthevalley(andconsequenthigherdensityinthep eaks)wehaveutilizedthe twodimensionalradiusofgyration,asdenedpreviouslyfo rthenanowire.Calculations oftheseradiiinthepeaksandvalleysyieldednearlythesam enumericalvaluesinthe solid-phase,indicatingthatthesefeaturesarecausedbyl argeramplitudeoscillationsofthe atoms. 40

PAGE 54

-2 015 -1 050 51 01 52 0 N(z)Z ( ) 400K 600K 800K 1000K 1100 K 1 200 K Figure4-7.ComparisonofPdatomicdistributionsofPdclust eralongaCartesiancoordinate( z )atdifferenttemperatures. N ( z )= X i ( z i z ) + (4-8) Thebond-orientationalorderparameters(BOP)methodwasap pliedtoquantifystructuralevolutionoftheclustersandnanowriescrystallogra phically,aswellastodistinguish betweenliquid-likeandsolid-likestates[101].Bondsared enedasthevectorsjoininga pairofneighboringatomswithaninter-atomicdistanceles sthanaspeciedcutoffradius. Thecutoffdistanceisusuallychosenasthepositionofthe rstminimuminthepaircorrelationfunction,whichisabout3.36 Aisthiscase.Associatedwitheverybondareasetof numberscalledlocalbond-orientationalorderparameters showninEquation4-9. Q lm ( r )= Y lm [ ( r ) ; ( r )] (4-9) where Y lm ( ; ) aresphericalharmonicsand ( r )and ( r )arethepolarangleandazimuthal anglesofvector r withrespecttoanarbitraryreferenceframe.Onlyevenl sphericalharmonicsareconsidered,whichareinvariantunderinversion .Aglobalbond-orientational 41

PAGE 55

-3 020 -1 00 102030N( Z)Z ( ) 60 0K-3 020 -1 00 1020 30N(Z )Z () 1100 K-3 020 -1 00 102030N( Z)Z() 11 9 0K-3 020 -1 00 10 2030N( Z)Z() 1200K(a ) (b ) (c ) (d ) Figure4-8.ComparisonofPdatomicdistributionalongaCarte siancoordinate( z )inthe Pdnanowireat(a)600K,(b)1100K,(c)1190K,and(d)1200K.orderparameter Q lm ( r )canbedenedbyaveraging Q lm ( r )overallbondsinthesystem usingEquation4-10. Q lm = 1 N b X Q lm ( r ) (4-10) where N b isthenumberofbonds.Tolet Q lm ( r )notdependonthechoiceofreference frame,asecond-orderinvariantisconstructedusingEquat ion4-11,andathird-orderinvariantisconstructedusingEquation4-12. Q l = 4 2 l +1 X Q lm 2 1 = 2 (4-11) W l = X m 1 ;m 2 ;m 3 0BB@ lll m 1 m 2 m 3 1CCA Q lm 1 Q lm 2 Q lm 3 (4-12) 42

PAGE 56

Table4-3.Bond-orientationalorderparametersforanumber ofsimpleclustergeometries. Geometry Q 4 Q 6 ^ W 4 ^ W 6 Icosahedra0.000000.663320.000000.16975 Fcc0.190940.574520.159320.01316 Hcp0.097220.484760.134100.01244 Bcc0.036370.510690.159320.01316 Liquid0.000000.000000.000000.00000 TheterminthebracketisaWigner-3jsymbol[102].Furtherm ore,areducedorderparameter ˆ W l isdenedinEquation4-13sothatitisnotsensitivetothepr ecisedenitionofthe nearestneighborofaparticle. ^ W l = W l = X Q lm 2 3 = 2 (4-13) Thevaluesofthesebond-orientationalorderparametersfo rsomecommoncrystalstructuresarelistedinTable4-3[101].Becauseofsymmetry,the rstnonzerovaluesoccurfor l =4intheclusterwithcubicsymmetryandfor l =6inclusterswithicosahedralsymmetry.Weusedthefourbond-orientationalorderparameter sQ 4 ,Q 6 ˆ W 4 ˆ W 6 togetherto identifystructures.Notethat Q isofthesameorderofmagnitudeforallcrystalstructures ofinterest,whichmakesitlessusefulfordistinguishingd ifferentcrystalstructurescomparedto ˆ W.ButQ 6 isusefultoidentifyphasetransitions,sinceithasalarge rvaluethan otherparametersanddecreasequicklytozerowhenthesyste mbecomesliquid.Consideringthesurfaceeffectinnanomaterialsandtogetmoreaccur ateanswerstomonitorglobal structuralchanges,wecalculatedbond-orientationalord erparametersforinternalatoms, surfaceatomsandallatomsinthesystems. Thetimeaveragedbond-orientationalorderparametersoft heinternalatoms,surface atoms,andtheentirePdnanowiresystemareplottedinFigur e4-9(a).Weseethatonly thesecond-orderinvariants( Q values)differwhenthesurfaceatomsareexcluded,while 43

PAGE 57

20 04 00600 80 01 000 120 01 40 01 60 0 -0 .1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 BO PT (K ) Q 4 Q 6 W 4 W 620 0 400 60 08 00100 0 1200 1 4001600180 0 -0. 15 -0. 10 -0. 05 0. 00 0. 05 0. 10 0. 15 0. 20 0. 25 0. 30 0. 35 0. 40 0. 45 BO PT (K ) Q4 Q6 W4 W6(a)(b) Figure4-9.Temperaturedependenceofaveragebond-orient ationalorderparametersfor (a)theatomsinPdnanowireand(b)thePdclusterwith456ato msandPdnanowirewith 1,568atomsduringheating.(a)Filled,unlledandunlled withacrosssymbolscorrespondtotheaveragebond-orientationalorderparametersf orinternalatoms,allatomsand surfaceatoms,respectively.(b)Filledandunlledsymbol srepresentclusterandnanowire, respectively. 44

PAGE 58

thethird-orderinvariants( ˆ Wvalues)arenotaffected.Thisisbecause Q ismoresensitive tothenumberofthenearestneighbors.Figure4-9(b)showst hebond-orientationalorder parametercomparisonbetweenthePdclusterandthePdnanow ire.Alltheparameters dropabruptlytozeroatthetransitiontemperature.Thesec hangesaremoreobviousin Q 6 EventhoughthePdclusterretainsthefccstructureatlower temperatures,thetimeaveragedglobalbond-orientationalorderparametersshowthat thePdnanowiremovesaway fromthestartingfccstructure,whichisconsistentwithwh atwehaveseeninthe N ( z ) plots.Thecorrelationplotfor ˆ W 6 asafunctionof Q 6 isshowninFigure4-10,wherethe reddotsarethevaluesforperfectcrystals.Weuse Q 6 becauseitchangessignicantlywith temperature.Weseefromthetimeaveragedbond-orientatio nalorderparametersthatat lowtemperature,thePdnanowirenolongerhasfccstructure ,insteaditformssomestructurebeyondregularcrystalgeometries.FromFigure4-10,w eobservethatthenanowire undergoesarapidstructuralchangeduringtheannealingpr ocess,afterthatitmaintainsa non-regularstructureatlowtemperaturesbeforethephase transition.Unlikethenanowire, theclustergoesthroughpossiblestructuralchangesinthe sametemperaturerange,reectedbythedecreasingrateofchangeof Q 6 .Calculatedvaluesof Q 6 aresensitivetothe numberandpositionsofthesurfaceatoms.Morerapidchange sinthenumberandpositionsofthesesurfaceatomsintheclustercomparedtothecy lindricalwirewithperiodic boundaryconditionscouldexplainthisbehaviorof Q 6 ˆ W 6 hasmoreuctuationsinthe nanowirethanthecluster,indicatingfrequentsymmetrych anges[101]. Inoursimulations,wehavechosenthebulk,fccstructurefo rthestartingcongurationsofthelowtemperaturesolidnanoclusterandnanowire .Itisdifculttoestablish thetruelowtemperaturesolidstructuresofthesenanomate rialsfrommoleculardynamicssimulations.Onecannotbecertainthatthebulkfccstru ctureisareasonablestarting structure,althoughotherstudieshaveutilizedbulkstruc turesforstartingcongurations ofnanomaterials[68,96,103].Someinsightscanbegainedb ystartingthesimulations 45

PAGE 59

fromotherhypotheticalstructures,suchasthehcp,andagl assystructurethatresultsfrom therstheating/coolingcycleofthefcc-startedsimulati on.Toestablishthereasonablenessofourfcc-startedsimulations,wehaverepeatedthehe ating/coolingsimulationswith anhcpinitialstructureandtheglassystructureobtaineda t300Kuponcompletionofthe rstfcc-startedMDrunafterafullheating/coolingcycle. Someexperimental[104]and simulation[67]evidenceforthepossibilityofhcpstructu resinnanoclustersexistsinthe literature,withlessknownaboutnanowires.Withminorvar iationsaccountedforbythe differencesinnumbersofatoms(mandatedbythedifference sinstartingcongurationsfor differentclosepackedstructuresofsamediameter),wehav efoundthatthemeltingpoints areessentiallythesameasthoseobtainedfromthefcc-star tedsimulation.Whilethehcpstartedclusterappearedtobestableatlowtemperatures,i tundergoesalesssharptransition (whileyieldingnearlythesamemeltingpoint),perhaps,du etostructuralrearrangementin thesolidsnearmeltingtemperatureand/orenhancedsurfac emeltingascomparedtothe fcc-startedcluster.Thehcp-startednanowire,ontheothe rhand,rapidlyrearrangedtoa less-orderedstructureatlowtemperaturesasinthefcccas e,andshowedasharpermeltingtransition,withanidenticalmeltingpointasthefcc-s tartedwire.Theannealedsolid structuresduringcooling,ofbothclusterandwire,didnot trackpotentialenergiesofthe heatingrun,indicatingthatthefccstartingconguration isperhapsclosertothetruestructureoftheboththeclusterandthewire.Nearlyidenticalme ltingpointsandpotential energycurveswerefoundfromthesecondheating/coolingcy cleofthefcc-startedcluster andwire,indicatingthatthecycle,includinghysteresis, isrepeatable.Thisgivesfurther supporttothechoiceofthefccstructureinourlowtemperat uresolidstartingcongurations.Coupledwiththeresultsforthebondorientationalor derparameterspresentedin Figure4-10,weconcludethatthechosenfccstartingcongu rationsarereasonableinthis study.Generally,priortomelting,bothsystemshavetrend stowardsdisorderasnumberof unclassiedbondorientationsincreases.Theclassicati onsoflocalatomsduringheating 46

PAGE 60

-0.1 0. 00 .1 0. 20 .3 0. 40 .5 0. 60 .7 -0 .1 8 -0 .1 6 -0 .1 4 -0 .1 2 -0 .1 0 -0 .0 8 -0 .0 6 -0 .0 4 -0 .0 2 0.00 0.02 0.04 0.06 0.08 ic os fc c hc p bc c liq ui d BO PW 6BOPQ 6 cl us te r nanow ir e pe rf ec t cryst al Figure4-10.Correlationplotforbond-orientationalorder parameters ˆ W 6 asafunctionof Q 6 .Symbolsareat100Kintervalsstartingat300K. canbeimprovedbystudyingCNA(commonneighboranalysis)si gnatures,asshowninthe workfromHendy etal. [105]. 4.5MeltingModelComparisonMeltingbehavior,especiallymeltingtemperature,ofclus tersandnanowireswilldepend ontheirsize.Thestudyofsizeeffectsonmeltingofmetalli cnanoparticleshasbeenexploredbothexperimentallyandtheoretically[52,106–108 ].Andalargenumberofdata havebeenestablished.Modelsforthesize-dependentmelti ngpointdepressionfordifferent materialshavebeenestablishedbasedonvariousassumptio ns,suchasmanyoutstanding classicthermodynamicsmodels[54,109–113]andothermode ls,likesurface-phononinstabilitymodel[114],bondorder-length-strength(OLS)m odel[36],andliquid-droplike model[115].Thegeneralresultofthesetheoriesisthatmel tingtemperatureofsmallparticlesdecreaseslinearlyorquasi-linearlywiththedecre asingoftheirdiameters.Inthis section,wecompareoursimulatedresultswithtwoofthemod els. 47

PAGE 61

ThethermodynamicsmodelwasrstproposedbyPawlowin1909 ,itisbasedonequatingtheGibbsfreeenergiesofsolidandliquidsphericalclu sters,assumingconstantpressureconditions,withtheresultingequation[109,110]. T b T c ( R ) T b = 2 s L b R 24 r sv s l 2 = 3 r lv 35 (4-14) where T b and L b arethebulkmeltingtemperatureandbulklatentheatofmelt ing, is themassdensity, r sv and r lv arethesolid-vaporandliquid-vaporbulkmaterialinterfa cial energies,respectively.Thesimulatedmeltingpointdepre ssion( T b T c (2.6nm))of670K ishigherthanthe278Kpredictedbytheabovemodel.Ithasbe enpointedoutinthe literaturesthatthe1/Rbehaviorisapproximatelycorrect forclustersofsufcientlylarge size[55,94]. Forananowire,asimilarprocedurecanbeappliedbyequatin gtheGibbsfreeenergies perunitlengthofsolidandliquidatconstanttemperaturea ndpressure.G ¨ ulserendeveloped amodelforthemeltingtemperature T nw ( R ) ofnanowiresusingEquation4-15[71]. T b T nw ( R ) T b = 1 s L b R 24 r sv s l 1 = 2 r lv 35 (4-15) Thesetwomodelshavebeenshowntoagreewithsimulationres ultsinG ¨ ulseren'sPbclustersandwiresconstructedfrom(110)planeswithmorethan1 ,100atomsinthesystems. FromEquation4-14and4-15,weseethatsince s / l iscloseto1,thedepressionof meltingtemperatureofasphericalclustershouldbeapprox imatelytwicethatofthecorrespondingamountforananowire.Using r sv =1.808J/m 2 r lv =1.480J/m 2 ; s =0.0681 atom/ A 3 l =0.0594atom/ A 3 ,and L b =16.69kJ/mole,thecalculateddepressionsofmeltingtemperaturesare160Kand278KforthePdnanowireandclu ster,respectively,giving aratioof1.7.However,oursimulationresultsyieldaratio of1.2.Thisdiscrepancymay beduetothemanyassumptionsinthemodelandthesimulation ,forexample,thesurface 48

PAGE 62

energyanisotropyofthesolidisnottakenintoaccount,and thepossibilityofinhomogeneousphasesisalsoneglectedinthemodel.Thesamediscrep anciesbetweenmodeland simulationresultsexistinotherpreviouswork[68,103].T heaccuracyofthesemodels appearstobebetterforlargerclustersandnanowiresthans imulatedhere.Itshouldalsobe notedthatsignicantvariationexistsintheliteraturefo rvaluesoftheinterfacialenergies. Also,usingthesimulatedinterfacialenergiesfortheclus tersandwires,andnotthebulk values,wouldimprovecomparisonwithPawlow'smodel. Theotherscalinglaw[115]forsize-dependentmeltingisba sedontheliquid-drop modelandempiricalrelationsbetweensurfaceenergy,cohe siveenergyandsize-dependent meltingtemperature.Accordingtothismodel,thecohesive energyofN-atomnanoparticles canberepresentedbyvolumeandsurfacedependentterms.Fo rasphericalnanoparticleof diameter d ,theexpressionforthecohesiveenergyperatomisshowninE quation4-16. a v;d = a v 6 v 0 r d (4-16) where a v;d and a v arethecohesiveenergyperatomintheclusterandinthebulk v 0 isthe atomicvolumeand r issurfaceenergyofsolid-vaporinterface.Usingempirica lrelations betweencohesiveenergyandmeltingtemperatureforbothbu lkandnanoparticles,the meltingtemperatureofnanoparticlescanbecalculatedbyE quation4-17. T c ( R ) T b =1 6 v 0 0 : 0005736 d r T b =1 d (4-17) where = 6 v 0 0 : 0005736 r T b .Thevalueof canbecalculatedfromtheknownvaluesof v 0 r ,and T b .UsingforPdinEquation4-17,wegetthemeltingpointdepre ssionofthePd clusterof669K,whichcompareswellwithoursimulatedvalu eof670K.Thisfavorable comparisonisconsistentwithotherworkmentionedpreviou sly[68,103].Usingthesame 49

PAGE 63

modelforthemeltingofthinwires,thesize-dependentmelt ingtemperatureofananowire canbedescribedbyEquation4-18[115]. T nw ( R ) T b =1 2 3 d (4-18) Fromthis,thedepressionofmeltingtemperatureofthenano wireis446K,smaller thanoursimulatedresultof560K.Thisrelationdescribedi nEquation4-18hassome similaritytothemodelofG ¨ ulseren,describedpreviously,exceptthatthedepression of meltingtemperatureofananowireis2/3ofthedepressionof thesphericalnanocluster. T b T c ( R ) T b T nw ( R ) =1 : 5 (4-19) TheresultobtainedfromEquation4-19isclosertooursimul ationresultof1.2thanthat fromPawlow'smodel.4.6ConclusionsThesimulationstudiesofthisworkindicatethatthePdnano wirehaslowermeltingtemperaturethanPdbulkbuthigherthanthesamediameterPdclu ster.BothPdnanowiresand nanoclustersexhibitsurfacepre-melting,thestructural anddynamicalnatureofwhichis somewhatdifferent.Thesedifferencesarefullycharacter izedbyseveralthermodynamic, structuralanddynamicvariablesinthisstudy.Thegeneral picturethatemergesisthatthe surfacepre-meltingbehaviorfortheclusterissimilartot hatofothernobleandtransition metalnanoclusters.Thenanowireexhibitsahigherpre-mel tingtemperaturerange,and dynamicalbehaviorcharacterizedbyincreasedmovementof atomsintheplaneperpendiculartotheaxisfollowedbyincreasedmovementacrossthese planes,asthetemperature approachesthetransitiontemperature.Aquasi-liquidski ngrowsfromthesurfaceinthe radialdirectionforbothclusterandwire,inthesurfacepr e-meltingregime,followedby 50

PAGE 64

thebreakdownoforderintheremainingsolidcoreatthetran sitiontemperature.Bondorientationalorderparametersindicatedthatthecluster retainstheinitialfccstructure, whereas,thenanowireappearsstableinastructurecloseto thehcp,inthesolidphase, beforemelting.Meltingpointsofstudiedclusterandwirew erecharacterizedparticularly wellbytheliquid-dropmodelforsize-dependentmelting. 51

PAGE 65

ChapterFive MolecularDynamicsSimulationsofGraphiteSupportedPdNa -noclusterMelting 5.1AbstractThethermalbehaviorofgraphitesupportedandunsupported palladiumnanoclusterswere studiedusingmoleculardynamicssimulations.Duetointer actionsbetweenPdandCinthe supportedenvironment,differencesinthermodynamic,geo metricandstructuralproperties wereobserved.Assuch,graphitesupportedPdnanoclusterh adhighermeltingtemperature thantheunsupportedcluster.Athightemperatures,themot ionandgeometryofsurface atomsarequantitativelydifferent.Radialandangularcorr elationfunctionsindicatevery similarstructuralevolutionofthetwosystems,butastron gerpositionalcorrelationwith thenearestneighborsofsupportedPdcluster.5.2IntroductionThestudyofmeltingprocessandthermodynamicpropertieso fmetallicclustersofnanometerlength-scaleshasattractedmuchtheoretical[50,51,1 16]andexperimental[52,53,117] interestmainlybecauseoftheirdramaticallydifferentbe haviorsfromthebulkmaterials[54].Transitionalandnoblemetal[56–58]oralloy[59, 60]clustersaregettingmore attention,duetheirextensiveapplications.Theoretical investigationsoftheirmeltingphenomenausingvarioussimulationmethodsarefocusedonthef ollowing: 1.Themeltingtemperatureanddetailsofthemeltingproces s[67]. 52

PAGE 66

2.Thestructuralevolutionsandmechanicalpropertiesdur ingheating[55,69]. 3.Theeffectofinitialstructureandsizeonthemeltingtem perature[50,106]. Pdhasbeenwidelyusedinheterogeneouscatalysisaswellas inmicroelectronicandoptoelectronicdevices[75,76].NormallyPdissupportedona graphitesubstratewhenitis usedascatalyst[118].Recently,thesignicanceofthesupp ortwasinvestigatedtoimprove thecatalyticpropertiesofPd[119].Thestructuralanddyn amicpropertiesofmetallicclustersongraphitesurfacehavealsoattractedmuchattention lately[120,121].Forexample, Bardotti et.al reportedrapidmovementoflargeantimonyclustersongraph itesurfaces, andpointedoutthatstudyoftheserapidmotionmechanismsl eadstoanunderstandingof theinteractionbetweennanoparticleandsubstrate[122]. Severalexperimentsindicatethatquantumbehaviorofmeta lnanoclustersisobservable,andstronglyexpressedbetween1and2nanometers.Hen ce,particlesinthatsize regionshouldbeofmostinterest[77,78].Simulationstudi esofPdnanoparticleprovidean opportunityforfurtherunderstandingitsuniqueroleinva riousapplications,andexplainingexperimentalobservations.Althoughthesizeofthemet allicclustersbeingsimulated rangedfromtenstoseveralthousandatoms,mosteffortshav ebeenfocusedonsizebelow 150atoms[79].Inthispaper,themeltingbehaviorsofunsup portedandgraphite-supported Pdclustersof2.3nmdiameter(456atoms)arestudied.Thesu pport-effectsofgraphiteon bothmeltingandstructuralpropertiesareinvestigatedin thisstudy. 5.3PotentialModelandComputationalMethodMDsimulationswereperformedusingtheDL POLYpackage[47].Thesystemwassimulatedunder NVT ensembleusingtheVerletleapfrogalgorithm[89].Atimest epof1 fswasusedandnoboundaryconditionwasapplied.Thecluste rswereconstructedfrom face-centeredcubicPdbulk,usingsphericalcutoffradiit ogetdesiredsize.Aclustersize 53

PAGE 67

200400600800100 0 12001400 -1.6 6 -1.6 4 -1.6 2 -1.6 0 -1.5 8 -1.5 6 -1.5 4 -1.5 2 -1.5 0 -1.4 8 Ep uns uppor te d Ep sup port edEp (Ke V)T (K ) 0.00 0.05 0.10 0.15 0.20 0.25 0. 30 0. 35 0.40 0.45 0.50 0.55 0.60 0.65 C v uns upporte d C v supp or te d Cv (eV/ K) Figure5-1.Potentialenergyandheatcapacityunsupported andgraphite-supportedPdclustersvs.temperature( d = 2.3nm). C v iscalculatedbyEquation4-4. of2.3nmwith456atomsisused.AtwolayerABstackedgraphit esubstratewithdimensionsof73.8 73.8 6.7 AwasusedtosupportPdclusters.Adistanceof2.0 Aissetasthe initialdistancebetweentheclusterandgraphite.SuttonChenpotential(SC)[48]shownin Equation4-1isusedtodescribethePdinteractions.ThePdgraphiteinteractionpotential wasdevelopedusingDFTcalculationwithLDAapproximation spreviously[123].Due tothemuchsmallerPd-carboninteractionforcescomparedt oPd-Pdforces,theLennardJones(LJ)potentialwasalsodeemedadequatetomodelthePd -Cinteractions.TheLJ well-depth andsize forCandPdarecalculatedtobe2.926 Aand0.0335eVusing theLorentz Berthelotmixingrules[41,124,125].Astaticgraphitesubs tratewithxed Catomicpositionsisusedtosaveacomputationaleffort.Th einitialclusterswererst relaxedbysimplequenching,followedbyannealingcycle.E achsystemwasthenheated withatemperaturestepof50K.Thestepsizewasdecreasedto 10Kwhenclosetomelting temperature. 54

PAGE 68

0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 3. 0 N(Z)Z (As t ro m) 800K 1000K me lt in g poi nt 05 10 15 20 25 da sh lines : su pp ort ed soli d l ines : u nsup por te d Figure5-2.Atomicdistributionfunctionalong z coordinateperpendiculartothegraphite substrate.5.4ResultsandDiscussionWerstcalculatethetotalpotentialenergy E p andheatcapacity C v atvarioustemperaturetoidentifythemeltingtemperatureforbothgraphitesupportedand-unsupportedPd cluster.AsshowninFigure5-1,thepotentialenergiesincr easenearlylinearlywithtemperature,whileheatcapacitiesremainmostlyconstantatlowt emperatures.Nearthemelting temperature,simplejumpsinboth E p and C v valuescanbeeasilyobservedasanindicative ofthephasetransition.AccordingtotheFigure5-1,weesti matethatthemeltingtemperatureoftheunsupportedandsupportedPdclusteroccurat109 0Kand1260K,respectively. Notethatbothclustershavemuchlowermeltingtemperature sthanthePdbulk,whichis 1760Kfromourprevioussimulations[116].Thehighermelti ngtemperatureofsupported PdclusterisduetotherestrainingmovementofPdatomsonth esubstrate,whichalso explainstheloweringofpotentialenergycomparedtotheun supportedcluster. Atomicdistributionfunction N ( z ) iscalculatedtoinvestigatetheorganizationofPd atomsintheclustersatvarioustemperatures.Figure5-2de scribesthedistributionofPd 55

PAGE 69

atomsalongtheaxisperpendiculartothegraphitesurface, where z = 0isthepositionof thegraphitesurface.Weobservethatinthesolidphase,ato mshavehigherdensityinthe centerarea,indicatedbysharppeaks.Thisisbecauseatlow temperatures,atomsoscillate aroundthelatticesitesandretainthecrystal-likestruct ure.Thepeaksbecomewiderand loweruponheating,andeventuallydisappear,leadingtoun iformlydistributedatomsinthe liquidphase.Adifferentsetof N ( z ) distributionsforthegraphite-supportedclusterwere observedatthesametemperatures.Weseethatalthoughthet emperatureiswellbelow meltingtemperaturethesupportedPdclusterhasgreatlych angeditsatomicdistribution withenhancedpeaksclosetothesubstrate(blackdashedlin es),indicatingsubstrateeffect isevidentevenintheweakeldofgraphite. ThesupportedPdclustercontinuestomaintainitscrystallikestructureatthehigher temperatureof1000K(reddashedlines),asatomiclayersse paratedbyunitcelllength canstillbeclearlyseen,andagraduallydecreasingdensit ydistributionwithincreasing z .Atthemeltingtemperature(bluedashedlines),theentire clustercollapsesintoawider ellipsoidalshape,spreadingoverthesubstratewiththede nsityreachingessentiallyzero at20 Aabovethesubstrate.Sharppeaksareevidentinthelowestf ewlayers,wherethe physicalstateisclearlyliquid-likeatthismeltingtempe rature.Similardensitydistributions areobservedathighertemperatures,withtheclusterseent ohaveessentiallymeltedinto aliquidbutlayeredagainstthesurface,asistypicallyobs ervedinsmallmolecularliquid physisorption.Onthecontrary,unsupportedclusterhasev enlyatomicdistributionimplied byasmooth N ( z ) curve. Wehavenoticedthattheshapechangeofsamesizedunsupport edPdclusterand graphitesupportedclusteraremuchdifferentduetotheexi stenceofthesubstrate.Inorder tocharacterizethesupporteffectofgraphitesubstrateon themotionofPdatomsandthe surfacemeltingphenomena,wecomputecomponentsofthevel ocityauto-correlationfunctionincylindricalcoordinatesforthelowestfourPdatomi clayers.Bothcomponentsofthe 56

PAGE 70

-0 .6 -0 .4 -0 .2 0 0. 2 0. 4 0. 6 0. 8 1 00 .511.5t (p s)VA CF Z 1 2 3 4 -0 .4 -0 .2 0 0. 2 0. 4 0. 6 0. 8 1 00 .5 11 .5t (p s)V ACF -T H 1 2 3 4 -0.6 -0.4 -0.2 0 0. 2 0. 4 0. 6 0. 8 1 00 .5 11 .5 2t (p s)VA C F sh e ll 1 sh e ll 2 sh e ll 3 sh e ll 4 sh e ll 5 (a) (b) (c) (d) Figure5-3.Velocityautocorrelationfunctionsofthesupp ortedPdclusterat1000K.(a)and (b)are v and v z componentcorrelationsforthebottomfourlayers.Layer1i stheclosest tographite,layer4isthefarthest.(c) v correlationsofdifferentshells.Shellpartitionis shownin(d).fromshell5to1arecolorred,green,yellow,li ghtblueandpurple.Thethree bottomlayersareexcludedintheshellpartition. 57

PAGE 71

correlationfunctionsexhibitreboundingoscillationsth atdecaywithtimeinFigure5-3(a) and(b).Comparingthetwoplots, v z haslongercorrelationtimeandmuchlargerdepthof theminimathan v ,whichimplieslargeramplitudetangentialvibrationstha n z axial.The correlationof v z oflowestPdlayerissignicantlydifferentfromtherestof threelayers duetothestronginteractionsbetweenPdandcarbon.Theint eratomicforcesinducedby carbonatomsrestrictthelargemovementofPdatomsalongth e z direction,forcingthem tostayclosetothegraphite.Thisforceisreducedwiththei ncreasein z distances,andhas almostnoeffectonthePdatomsabovethethirdlayer,wherew enoticethatthethirdand fourthlayerhavealmostthesamecorrelationson v z WeagainpartitionedPdatoms,excludingthebottomlayers, into5shells,asillustrated inFigure5-3,with r cut = 2.77 Abasedontheinitialequilibriumatomicpositions.The calculationofvelocitycorrelationforeachshellshowsth einnershells(shell1,2,3)exhibit reboundingoscillationsatlatticesitesthatdecaywithti me,whileoutershells(shell4and 5),havenearlyliquid-likemotionasinferredfromthesing ledampedoscillationwithone minimumbeforedecorrelatingwithtime. Fromvelocityauto-correlationcalculations,weobserved thatmanyPdsurfaceatoms (reddots)haveliquid-likebehaviorat1000K,becauseofth esmallerinteratomicforces fromneighboratoms.Thisisfurtherveriedinthetrajecto ryplotwhentemperature changesfrom1000Kto1100K.ThebluedashlinesinFigure5-4 indicatethatatoms onclosetothesurfacegenerallymovedownward,whileinner atomsjustexhibit xy planar oscillationwithoutmovingdowntowardgraphitesubstrate .Aclearchangeoftheheight ofclustercenterwithrespecttographitesubstrateathigh ertemperaturesindicatesthesupportedclustercollapsedfromanearlyballshapetoahalfsp herewithatbottomonthe substrate.Thisisquitedifferentfromunsupportedcase,w herethenearlysphericalcluster hasanisotropicexpansiontotheovalshape[116]. 58

PAGE 72

10 20 30 -1 5 -1 0 -5 0 5 4 6 8 10 12 14 16 18 20 x y z 10 20 30 -1 5 -1 0 -5 0 5 4 6 8 10 12 14 16 18 20 x y z (a) (b) Figure5-4.Atomcoordinatesof(a)surfaceatoms(atomsins hell1and2asillustrated inFigure5-3(d))and(b)inneratoms(atomsinshell3,4and5 )ofgraphite-supported Pdclusterat1000K(bluedots)and1100K(reddots).Bluedots areconnectedtothe correspondingreddotsbybluedashlinestoindicatethemov ementofeachPdatom. 59

PAGE 73

23456 7 RDF (no rmalized u nit )r () unsuppo rt ed 300 K s upported 300K unsuppo rt ed 1000K s upported 1000K unsuppo rt ed 1400 K s upported 1400K 0 20 40 6080 100120 140160 180 0 0.1 0.2 0.3 0.4 0.5 0.6 Angl e(deg)ACF (a) (b) Figure5-5.(a)Radialdistributionfunctionand(b)angular correlationfunctionforPd clusters. 60

PAGE 74

Radialdistributionfunctions(RDF)inFigure5-5(a)implies verysimilarstructuralevolutionsofPdclusterswithandwithoutsupport.Atroomtemp erature,theybothhavesharp periodicmultipeaks,whichisacharacteristicfeatureoff ccstructures,andaftermelting bothofthemalsoshowtheamorphousfeatureofadisordereds tructure.RDFofsupported Pdclusterhaverelativelyhigherandwiderpeakthanthecor respondingisolatedcluster,indicatingthatthepositionalcorrelationofatomsisstrong erwithinthenearneighborregion. Angularcorrelationfunctions(ACF)[126](Fig.5-4(b))are calculatedtofurtherillustrate thestructuralcharacters.ItisobviousthatPdclusterswe ntthroughalmostthesamestructuralevolutionprocess,showingthesupporthaslittleeff ectontheclusterinternalstructure changeduringtheheating.AsimpliedbytheACF,atlowertemp eratures,therearefour peaksat60 ,90 ,120 ,180 respectively,typicalbondanglesofregularfccstructure .At highertemperatures,thepeaksat90 ,180 graduallydisappear,whileothertwomajor peaksarestilllocatedat60 and120 ,showingahexagonalclosedpackedrelatedstructure[74,116].Aftertheentireclustermelts,thebroaddis tributionofACFat60 and116 demonstratenoncrystallinestructure.5.5ConclusionsThesimulationstudiesofthisworkindicatethatthefreePd clusterhaslowermeltingtemperaturethangraphitesupportedPdcluster.Surfacemelti ngisfoundinbothcases,while severalanalysisrevealsupportedPdclusterhasaverydiff erentgeometricevolutionduringheating.Thesupportedclusterisseentomelttoaliquid thatshowsliquidmulti-layer physisorbedstructure,withsharpdensitypeaksinthefewP datomiclayersneargraphite. Thisstructureisretainedwellintotheliquidphasepastth emeltingpoint.Adownward movementofsurfaceatomsofsupportedclusterisobservedi nthesurfacemeltingregime. Structuralanalysisimpliesbothunsupportedandsupporte dPdclustershaveverysimilar structuralevolutions,withaslightlymorestablecrystal linestructureforsupportedcluster 61

PAGE 75

athighertemperatures.Thisstudyissignicantfortheinv estigationofinteractionbetween Pdandsensorsubstrateunderdifferenttemperatures. 62

PAGE 76

ChapterSix DensityFunctionalTheoryandthePseudopotentialMethod Inprinciple,thecompleteknowledgeaboutasystemcanbeob tainedfromthequantum mechanicalwavefunction.ThisisobtainedbysolvingtheSc hr ¨ odingerequationofthe completemanyelectronsystem.However,inpracticesolvin gsuchamany-bodyproblem provestobecomputationallydifcult.Tomakeiscomputati onallyfeasible,itisnecessary tousedensityfunctionaltheorytomodeltheelectron-elec troninteractionsandpseudopotential(PP)theorytomodeltheelectron-ioninteractions .Inthischapter,theessential conceptsfortotalenergycalculationusingthesetechniqu esareintroduced. 6.1DensityFunctionalTheory 6.1.1TheHohenberg-KohnPrinciple DFTisbasedontheprincipleprovenbyHohenbergandKohnin1 964thatthetotalenergy, includingexchangeandcorrelation,ofanelectrongasisau niquefunctionaloftheelectron density n ( r ) [127].Theminimumvalueofthetotal-energyfunctionalist heground-state energyofthesystem,andthedensitythatyieldsthisminimu mvalueistheexactsingleparticleground-statedensity.TheHohenberg-Kohntheore mcanbestatedasfollows: Everyobservableofastationaryquantummechanicalsystem canbecalculatedfrom ground-statedensityalone,i.e.,everyobservablecanbewr ittenasafunctionalofthe ground-statedensity. 63

PAGE 77

6.1.2TheSelf-ConsistentKohn-ShamEquations KohnandSham,inthefollowingyear,showeditispossibleto replacethemany-electron problembyanexactlyequivalentsetofself-consistentone -electronequations[128]. AccordingtotheKohn-Shamapproach,thetotalenergyfunct ionalofelectronicstates i canbewrittenaccordingtoEquation6-1. E [ i ]= Z V ion ( r ) n ( r ) d 3 r + e 2 2 ZZ n ( r ) n ( r 0 ) j r r 0 j d 3 r d 3 r 0 + E xc [ n ( r )]+ T [ n ( r )] (6-1) where n ( r ) istheelectronicdensitygivenby n ( r )= P i j i ( r ) j 2 V ion isthestatictotalelectron-ionpotential, E xc istheexchange-correlationfunctionaland T isthekinetic energyfunctional. Thesetofwavefunction i thatminimizetheKohn-Shamtotalenergyfunctionalare givenbytheself-consistentsolutionstotheKohn-Shamequ ationsshowninEquation6-2 and6-3. h 2 2 m r 2 + V eff # i ( r )= i i ( r ) (6-2) V eff = V ion ( r )+ V H ( r )+ V xc ( r ) (6-3) where i istheKohn-Shameigenvalueofelectronicstate i V eff iscalledeffectivepotential expressedastotalofallthepotentialterms, V H ( r ) istheHartreepotentialoftheelectrons givenbyEquation6-4. V H = e 2 Z n ( r ) n ( r 0 ) j r r 0 j d 3 r 0 (6-4) 64

PAGE 78

V xc istheexchange-correlationpotentialgivenbytakingthef unctionalderivativewith respecttodensityshowninEquation6-5. V xc ( r )= E xc [ n ( r )] n ( r ) (6-5) Aschematicmapovertheiterativeprocesstoobtainself-co nsistencyisprovidedinFigure6-1.Ifthedensityequalstheinitialtrialdensity,the ntheself-consistencyisobtained. Otherwise,moreiterationwillbeperformeduntilasatisfa ctoryresultisreached. Ascanbeseen,theKohn-Shamequationsrepresentamappingo ftheinteractingmanyelectronsystemontoasystemofnoninteractingelectronsm ovinginaneffectivepotential duetoalltheotherelectrons.Iftheexchange-correlation energyfunctionalwereknown, theexchangeandcorrelationeffectswouldbeexactlyprovi ded. 6.1.3Approximationsfor E xc [ n ( r )] :LDAandGGA Thecommonlyusedmethodsofdescribingtheexchange-corre lationenergyarethelocal densityapproximation(LDA)andgeneralizedgradientappr oximation(GGA).InLDA,it isassumedthatexchange-correlationenergyofanelectron atpoint xc isequaltothatof anelectroninahomogeneouselectrongasofthesamedensity [128].Thus, E LDA xc [ n ( r )]= Z xc [ n ( r )] n ( r ) d 3 r (6-6) with xc [ n ( r )]= homxc [ n ( r )] .TheexchangepartiselementaryandgivenbyEquation67[128] x ( n ) 0 : 458 =r s (6-7) 65

PAGE 79

Up date t he geo me try Init ial gu es s ()n r ()()()ef fi on Hx c VV VV =+ + rr r Co m p ute Ef fe ct iv e Po te n tial ()()? ne w nn nd< rr Ou t p ut q uant itie s En er gy f orces stres s, eigenval u es … So lv e Kohn -S ha m e q uatio ns () ()2 2 ef f 2 ii i V mye y+ = rr Ca lcul ate ne w el ec tr on d ensi t y ()()2 i ne w i ny= rr Ye s Mi xing No h [] Figure6-1.Schematicow-chartforself-consistentdensi tyfunctionalcalculations. 66

PAGE 80

where r s istheradiusofaspherecontainingoneelectron.Thecorrel ationpartwasrst estimatedbyWignershowninEquation6-8[129]. c ( n ) 0 : 44 = ( r s +0 : 78) (6-8) andmorerecentlywithahighprecisionofabout 1%byCeperley[130],Ceperleyand Alder[131]. GGAgoesbeyond`local'densityapproximation.Theexchang e-correlationfunctional inGGAnotonlydependsondensity n ( r ) ,butalsoongradientofthedensity r n ( r ) in accountforthenon-homogeneityofthetrueelectrondensit y.Thesefunctionalscanbe generallywrittenaccordingtoEquation6-9. E GGA xc [ n ( r )]= Z f ( n ( r ) ; r n ( r )) d 3 r (6-9) Severalsuggestionsfortheexplicitdependenceoftheinte grand f ondensitiesand theirgradientsexist,includingsemiempiricalfunctiona lswhichcontainparametersthat arecalibratedagainstreferencevaluesratherthanbeingd erivedfromrstprinciples.In principle, E GGA xc isusuallysplitintoitsexchangeandcorrelationcontribu tionsshownin Equation6-10. E GGA xc = E GGA x + E GGA c (6-10) ThecommonlyusedexchangefunctionalsarefunctionalsB88a ndB86[132,133], P86[134],PW91[135,136],andPBE[137].Themostwidelyusedc orrelationfunctionals areP86,PW91,andLYP[138].Inprinciple,eachexchangefunc tionalcouldbecombined withanyofthecorrelationfunctionals,butonlyafewcombi nationsarecurrentlyinuse, 67

PAGE 81

forexample,BP86(Becke'sexchangefunctionalwithPerdew's correlationfunctional)and BLYP(Becke'sexchangefunctionalwithLYPcorrelationfunct ional). AnotherimprovementofLDAiscalledhybridapproximation, introducedbyBeckein 1996,wherethe E hybrid xc iscalculatedbylinearinterpolationoftheexchangeenerg ycalculatedwiththeexactKohn-Shamwavefunction E KS x andanappropriateGGA E GGA xc [139]. TheuseofGGAandhybridapproximationsinsteadoftheLDAha sreducederrorsofatomizationenergiesofstandardsetsofsmallmoleculesbyfa ctorsoftypically3 5[140]. Thisimprovedaccuracy,togetherwiththepreviouslyempha sizedcapabilityofDFTtodeal withsystemsofverymanyatoms,hasmadeDFTbecomethemetho dofchoiceforcalculatingelectrondensitiesandenergiesofmostcondensed-m attersystems,aswellaslarge, complexmoleculesandclusters.6.2Plane-WaveBasisSetandPseudopotentialPlanewaveshavemanyadvantagesoverothertypesofbasisse ts[141].SlaterorGaussian functionsaremathematicallysimpletoimplement,andthec onvergenceofthecalculationscanbeeasilycontrolledbyusingplane-wavemethod.T heplane-wavebasisisalso independentofatomicpositions,whichisveryconvenientf orcoding. AccordingtoBloch'stheorem,theelectronicwavefunctionc anbewrittenasasumof discreteplane-wavebasissetshowninEquation6-11[142]. i ( r )= X G C i; k + G exp [ i ( k + G ) r ] (6-11) where k iswavevector,and G isreciprocallatticevector.Theplane-wavebasissetcanb e truncatedtoincludeonlyplanewavesthathavekineticener gieslessthansomeparticular cutoffenergy, ( h= 2 m ) j k + G c j 2 ,toachieveanitebasisset.Howeverthebasissetwill stillbeintractablylargeforsystemsthatcontainbothval enceandcoreelectrons. 68

PAGE 82

Thepseudopotentialapproximationovercomesthisproblem byallowingthewavefunctionstobeexpandedinamuchsmallernumberofplane-waveba sisstates.Thisisbecause inthepseudopotentialapproximation,thecoreelectronsa reremovedandthestrongionic potentialisreplacedbyaweakerpseudopotentialthatacts onasetofpseudowavefunctionsratherthanthetruewavefunction[143–145].Thereis noneedforaverylargenumber ofplanewavestoexpandthetightlyboundcoreorbitalsandt ofollowtherapidoscillations ofthewavefunctionsofcoreelectrons.Thecalculationisp erformedwithalowcutoffenergyandsmalltheplane-wavebasisset.Beyondthecoreregio n,thepseudowavefunction andpseudopotentialareidenticaltotheactualvalencewav efunctionandpotential. Theconstructionofapseudopotentialisoverallmotivated bythefollowinggoals: 1.Thepseudopotentialshouldbeassoftaspossible,meanin gthatitshouldallowexpansionofthevalencepseudowavefunctionsusingasfewpla newavesaspossible. 2.Itshouldbetransferableaspossible,therebyhelpingto assurethattheresultswillbe reliableinsolidstateapplications. 3.Thepseudochargedensityshouldreproducethevalencech argedensityasaccurately aspossible. Thereareanumberofdifferentschemesforgeneratingapseu dopotential,twoofthe mostcommonlyusedincludingtheKleinman-Bylanderpseudop otential[146]andVanderbiltorultrasoftpseudopotential(US-PP)[147].Thelatte roneallowsthepseudopotential insidecoreregiontobeassoftaspossible,thusgreatlyred ucestheplane-wavecutoff neededincalculations.Despitethecomplicationofgenera tingtheUS-PP,thecomputationalcostisnegligiblecomparedwiththecostofthelarge scalecalculations.Inthis thesis,US-PPisusedinallDFTcalculations. 69

PAGE 83

6.3TheVienna Ab-initio SimulationPackage Thecalculationsinthefollowingchaptersareperformedwi ththeVienna Ab-initio SimulationPackage(VASP)[148–151].VASPisacomplexpackagef orperforming abinitio quantummechanical/moleculardynamics(QM/MD)simulatio nsusingpseudopotentialor theprojector-augmentedwavemethodandaplanewavebasiss et.Theexpression abinitio meansthatonlyrstprinciplesareusedinthesimulations, noexperimentaldataare needed. VASPhasalargeamountofsettingsandspecicationsavaila blefortailoringthecalculations.SomeofthefeaturesthatIhaveusedwillbebrieyd escribedintheappendixBas anexampleofhowtostartapseudopotentialplane-waveDFTc alculationforaparticular systemusingVASP. 70

PAGE 84

ChapterSeven InteractionsofHydrogenwithPdandPd/NiAlloyChainFuncti onalizedSingleWalled CarbonNanotubesfromDensityFunctionalTheory Acceptedbythe JournalofPhysicalChemistryB 7.1AbstractDensityfunctionaltheoryisemployedtostudyPdandPd/Nia lloymonatomicchainfunctionalizedmetallicsinglewalledcarbonnanotubesSWN T(6,6)andsemi-conducting SWNT(10,0),andtheirinteractionswithhydrogenmolecules .Thestablegeometriesand bindingenergieshavebeendeterminedforbothisolatedcha insandchainsonSWNTsurfaces.WefoundthatcontinuousPdandPd/NichainsformonSWN Tswithgeometries closetostablegeometriesintheisolatedchains.Nialloyi ngimprovesstabilityofthe chainsowingtoahigherbindingenergytobothPdandCatoms. Thephysicalpropertiesof SWNTsaresignicantlymodiedbychain-functionalization .SWNT(10,0)istransformed tometalbyeitherPdoralloychains,ortoasmallergapsemic onductor,dependingonthe Pdbindingsite.FromcalculationsforH 2 interactionswiththeoptimizedchainSWNT systems,theadsorptionenergyperHatomisfoundtobeabout 2.6timeslargerforPd/Ni chain-functionalizedSWNTsthanforpurePdchain-function alizedSWNTs.BandstructurecalculationsshowthattheSWNT(10,0)revertsbacktose miconductorandSWNT(6,6) hasreduceddensityofstatesatFermileveluponH 2 adsorption.Thisresultisconsistent withtheexperimentallyobservedincreaseofelectricalre sistancewhenPdcoatedSWNTs areusedasH 2 sensingmaterials.Finally,ourresultssuggestthatPd/Ni -SWNTmaterials arepotentiallygoodH 2 sensingmaterials. 71

PAGE 85

7.2IntroductionRecently,modicationsofsinglewalledcarbonnanotubes(S WNTs)haveattractedmuch interestbecausetheyallowcontrolofthepropertiesofbar etubes[36,37].Acarbonnanotubewithadsorbedmetalscansignicantlychangeitsphys icalproperties,therebyprovidingausefulmeansformanipulatingelectrontransport,whi chisofvalueinmicroelectronic devicedesign[152].Ourinterestisingassensingmaterial s.Forexample,Pdnanoparticle modiedSWNTbasedsensorsareshowntoexhibithighsensitiv ityandfastresponsetohydrogenatroomtemperature[22,39].PdcoatedSWNTshavealso shownsomeadvantages overconventionalsensorsformethanedetection,whilebar eSWNTsshownoresponseto methane[40].Itisexpectedthatadvancedgassensorscanbe constructedfromthesemetal functionalizedcarbonnanotubes.Thus,theoreticalstudi esofinteractionsofmetalatoms withSWNTsandtheirresponsetohydrogengasareusefultound erstandandevaluate theirpotentialforfabricatingmicroelectronicgassenso rdevices.Theinteractionofsingle metallicatomswithSWNTshasbeensystematicallystudiedla tely,usingdensityfunctional theory(DFT)[153,154].However,notmuchattentionhasbee ngiventothecontinuous metalatomfunctionalized,especiallymetalalloyfunctio nalizedSWNTs[155,156].Gas interactionswithmetalandalloyfunctionalizedSWNTshave alsoreceivedverylittletheoreticaltreatmentsofar.Suchstudieshavethepotentialo fnotonlyexplainingsensors mechanismsbutalsoofsuggestingimprovedsensingmateria ls.Issuessuchasthestabilityandstructureofsensingmaterialupongasadsorptio nandnatureofbondingcan beaddressedwithDFTcalculationsusingpseudopotentiala ndplanewavemethods.The pseudopotentialapproachisbasedonthediscriminationbe tweencoreandvalenceelectrons.Itconsidersthechemicallyinertcoreelectronstog etherwiththenucleiasrigidnonpolarizableioniccores,sothatonlythevalenceelectrons havetobedealtwithexplicitly, andtherebysignicantlyreducesthecomputationalcost[1 57].Thepseudopotentialplane 72

PAGE 86

wavemethodforDFTcalculationshasbeendevelopedandperf ectedovermanyyearsinto areliabletoolforpredictingstaticanddynamicpropertie sofmoleculesandsolids[158]. Thismethodhasbeenwidelyusedinthetheoreticalcalculat ionsofSWNTsystems,includingfunctionalizationsandinteractionswithgasmole cules[159–161]. Inthispaper,weuseDFTmethodstostudybothpurePdandPd/N ialloymonatomic chain-functionalizedSWNTsandtheirinteractionswithH 2 molecules,becausePdisawell knownelementusedinH 2 sensingmaterials[2,7,162].Priorresearchhasshownthep ossibilityofformingisolatedsingleatomicchains[163–170 ].ElectronbeamevaporatedPd andNiwereshowntocoatSWNTswithreasonableadhesion,indi catingthepossibilityof experimentallyrealizingchainandclusterfunctionalize dSWNTswiththesemetals[171]. Therefore,achain-functionalizationstudybyDFTcanbeus edtoexaminethestability ofchain-SWNTmaterialsaswellastodemonstrateahigherada tomcoverage,compared tosingleatomfunctionalization,thusbettermimickingsy stemsusedinexperiments.Ni isusedasPd-alloyingelementbecause,likePd,Nicanalsoq uicklyadsorbH 2 ,henceis widelyusedinhydrogenationcatalyticreactions[172].Mo reover,Nihasbeenshowntobe importantforhydrogensensorsforimprovingreliabilitya ndspeedofthesensorresponse indetectinghydrogen[173,174].Theoretically,Niisfoun dtoalsohavehigherbinding energyonSWNTthanPd[153].TheeffectofNiontheperformanc eofPdfunctionalized CNTsisthereforeofparticularinterest. Inthiswork,weperformDFTcalculationsonbothsemiconduc tingSWNT(10,0)and metallicSWNT(6,6),withsimilardiametersof7.83 Aand8.14 A.First,geometriesand stabilityoffreestandinginnitePdandPd/Nimonatomicch ainsareanalyzed.Then,Pd andPd/Nichainsareconstructedonthetubesurfacetoexami netheformationofchainfunctionalizedSWNTs.Finally,H 2 moleculesareaddedtostudytheinteractionsandsensingmechanisms.Ourprimarygoalistorevealthecharactera ndgeometriesofPdand 73

PAGE 87

Pd/Niatomicchain-functionalizedSWNTsandtounderstandt hehydrogeninteractions withthesematerials.7.3MethodofCalculationsTheVienna abinitio simulationpackage(VASP)[148–151]wasusedtoperformcal culationswithinthegeneralizedgradientapproximationofPW91 [136]usingoptimizedultrasoftpseudopotentials[147,175]andaplanewavebasisset. Theplanewavebasissetassumesasupercellgeometrythatisperiodicinallthreedire ctions.Thesingleatomicchains andSWNTswereconsideredtobeisolatedandinniteinlength ,withlateralseparation ofmorethan1nm.TheBrillouinzoneofthesupercellwassampl edbyMonkhorst-Pack special1 1 31k-points[176].StructuralcongurationsofisolatedSWN Tswerefully relaxed,andallatomicpositionsofadsorbateandadsorbin gSWNTswereoptimizeduntil residualforceswerewithin0.05eV/ A. Thebindingenergy E b ofchainatomsperunitcellcanbecalculatedintermsoftota l energyofisolatedatomandthechainformedbythesameatoms ,seeEquation7-1and7-2. E ( Pdchain ) b = E ( Pdchain ) T 2 E ( Pd ) T (7-1) E ( Pd=Nichain ) b = E ( Pd=Nichain ) T E ( Pd ) T E ( Ni ) T (7-2) E ( Pdchain + SWNT ) b = E ( Pdchain + SWNT ) T E ( SWNT ) T 2 E ( Pd ) T (7-3) Similarly,thebindingenergiesofchainatomsperunitcell onSWNTsarecalculated usingEquation7-3and7-4. E T isthegroundstatetotalenergyforthedifferentfullyrelaxedsystems,andthefactor2accountsforthenumberofP datomsintheunitcell.In 74

PAGE 88

allthesecalculations,therearetwoPdatomsoronePdandon eNiatomsperunitcell. Negativebindingenergiescorrespondtoenergeticallybou ndspecies. E ( Pd=Nichain + SWNT ) b = E ( Pd=Nichain + SWNT ) T E ( SWNT ) T E ( Pd ) T E ( Ni ) T (7-4) PdandNiadsorbedSWNTsystemshavebeenreportedashavingaz eroorverysmall magneticmoment[153,177].Evenso,weemployedfullyspinpolarizedDFTcalculationstoobserveanychangeinthemagneticmomentofPdandPd /Nichain-functionalized SWNTs.7.4AtomicChainStructuresWerststudiedthePdandPd/Nimonatomicchainstructures. Twocongurationsofchains werestudied,namely,linearchainandzigzagchains.Inthe alloychains,PdandNiatoms werelocatedalternately.ResultsareshowninFigure7-1,wh erethebindingenergyis plottedasafunctionofthechainunitcelllength d inthechaindirection.Thesecurvesshow thatPdandPd/Nichainsatlocalminimahavelarger-magnitu debindingenergiesthanin theirownbulksystems,whichisabout 0.7eV/bondforPdface-centeredcubic(fcc)bulk and 0.9eV/bondforNifccbulk,indicatingthemanyatomeffecti nthebulk[168].The largest-magnitudebindingenergyofPdlinearchainis 1.21eV/bond,closetothe 1.20 eV/bondcalculatedbyBahnandJacobsen[168].Thebindingen ergyofPd/Nilinearchain atlocalminimaiscalculatedtobelargerinmagnitudethant hatofthePdlinearchain, indicatingastongerbindingofPd-NithanPd-Pd. Weobservethatzigzagchainshavemuchstrongerbindingtha nthecorrespondinglinearchains,whichindicatesthatthepreferredgeometryofs ingleatomicchainisnotlinear. Thelargest-magnitudebindingenergyofPdzigzagchaincan befoundwhenPdbondsform 75

PAGE 89

2. 12 .2 2. 32 .4 2. 52 .6 2. 72 .8 -3.6 -3.4 -3.2 -3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 Eb ( eV )d( ) 1. 52 .0 2. 5 3.03.5 4. 04 .5 5. 0 5.5 -6. 5 -6. 0 -5. 5 -5. 0 -4. 5 -4. 0 -3. 5 -3. 0 -2. 5 -2. 0 -1. 5 -1. 0 -0. 5 0.0 Eb ( eV )d( ) d=4 .00 d=2 .55 2.65 2. 45 d=2 .49 2.46d=3 .70 2.45 d = 2.31 d = 2.45 (a) (b) Figure7-1.CalculatedbindingenergyofPdandPd/Nichainat omsperunitcellasfunction oflengthofunitcell d .Twogeometries:(a)straight,(b)zigzagchainsareshowna s functionsof d .Thestablenarrowangleandmetastablewideanglezigzagch ainsaremarked intherightgure.BlackandwhitelledcirclesareforPdand Pd/Nichains,respectively. Thebindingenergyiscalculatedfromtotalenergydifferen cebetweenatomicchainand isolatedatoms. 76

PAGE 90

anarrowangleof57.5 o ,with d = 2.55 A,correspondingtothePd-Pdnearestneighbor( nn ) distanceof r nn = 2.55 A,andPd-Pdnextnearneighbor( nnn )distanceof r nnn = 2.65 A. Theothermetastablestateislocatedat d = 4.00 A,correspondingtothePd-Pd nn distance of2.45 AandPd-Pd nnn distanceof4.00 A,withawidebondangleof109.1 o .Asseen inFigure7-1,thePd/Nilinearandzigzagchainshaveoveral llargerbindingenergiesthan thoseofpurePd.Thedifferencebetweenthebindingenergie sisabout0.25eVsmallerfor thezigzagthanforthelinearchains.TherstminimumforPd /Nizigzagchainappearsat d = 2.49 A,whichcorrespondstothePd-PdandNi-Nidistanceof2.49 A,andPd-Nidistanceof2.46 A.Thebondangleis60.5 o .Thesecondlocalminimumappearsfor d = 3.70 A,correspondingtothePd-PdandNi-Nidistanceof3.70 A,andPd-Nidistanceof2.45 A, withasmallerbondangleof98.1 o Tounderstandthestabilityandcharacterofbondingofthes ethreetypesofchains,we studiedtheirelectronicbandstructuresanddensitiesofs tates(DOS),whichareshownin Figure7-2.Accordingtothebandstructurecalculations,a llthreechains,linear,wideangle andnarrowangleofbothPdandPd/Nispecies,aremetallic.H owever,thechainsundergo largechangesintheirbandstructuresupongoingfromlinea r(Fig.7-2(a)and(d))towide angle(Fig.7-2(b)and(e)),tonarrowanglegeometry.Inpar ticular,thehighdensityof statesneartheFermileveldueto d bandsapproachingandcrossingtheFermilevelinthe linearPdchainsignicantlyreducesthemagnitudeofitsbi ndingenergyrelativetothose ofthezigzaggeometrieswhich,duetotheirlargeratomicse perations,andconsequently smaller d stateoverlap,donotformsuchbroad d bands.Asimilareffecthasbeenobserved bySen etal. [166]andSanchez-Portal etal. [167]formonatomicgoldwires.Thenarrower d bandsofmetastablebroadanglePdchainalsoapproachtheFe rmilevel,althoughtheydo soatthezoneboundaries.Finally,thebandstructureofthe narrowanglePdchainreveals at d bandslyingwellbelowtheFermilevel.Thisgeometry,which formsalmostequilateraltriangles,ischaracterizedby4nearestneighbors,as opposedto2nearestneighborsin 77

PAGE 91

0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz 0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz 0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 KzEnergy (eV) -5-4-3 -2 -1 012 0 5 10 15 20 25 30 -5-4 -3-2 -1 012 0 5 10 15 20 25 30 -5 -4 -3 -2 -1 012 0 5 10 15 20 25 30 DOS ( stat es/eV) 0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz 0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz 0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz -5-4-3-2 -1 012 0 5 10 15 20 25 30 Energy (eV) -5-4-3-2-1 012 0 5 10 15 20 25 30 -5-4-3 -2 -1 012 0 5 10 15 20 25 30 Energy (eV) Energy (eV) Energy (eV) Energy (eV) Energy (eV)DOS ( stat es/eV) DOS ( stat es/eV) DOS ( stat es/eV) DOS ( stat es/eV) DOS ( stat es/eV)Energy (eV) Energy (eV) Energy (eV) Energy (eV) Energy (eV)(a)(b) (c) (d) (e) (f) Figure7-2.Spin-polarizedbandstructureandDOSofthePdc hains(a-c)andPd-Nichains (d-f).Fromlefttoright:linearchains(aandd),narrowang lezigzagchains(bande),and wideanglezigzagchains(candf)showninFigure7-1.Bandsof linearchainsarefolded tocomparewiththezigzagstructures.Fermilevelissetatz eroenergy. 78

PAGE 92

thelinearandwideanglechains.Thisfactcontributestoth eincreaseinthemagnitudeof thebindingenergyinthenarrowanglePdchain.Asimilarpic tureemergesforthePd/Ni specieswithexceptionthatnowthenarrowanglechaindoesn othave d bandsapproachingtheFermilevel.Thismaybereectedbyitsshallowerloc altotalenergyminimumin Figure7-1comparedwiththatforthecorrespondingPdspeci es.Theoveralllowerlying energybandsinthePd/NisystemscomparedtothePdresultin thePd/Nispecieshaving relativelylarger-magnitudebindingenergy.Duringtheca lculation,wedidnotobserveobviousdimerizationeffects,suchasPeierlsdistortion[17 8].Thecalculationswererepeated withthefull-potentiallinearizedaugmentedplanewave(F PLAPW)method[179,180], andequivalentresultsforbandstructureswereobtained.7.5ChainsonSWNTs 7.5.1PurePdChainonSWNT ToformcontinuouschainsonisolatedSWNTs,eachsupercellc ontainstwometalatoms alongthetubedirection.Duetodifferentsymmetriesof(6, 6)and(10,0)tubes,thereare limitedpossibilitiesforplacingchainsontheSWNTs.Fours iteswereconsideredforPd adsorption,asshowninFigure7-3. Calculationsofadsorptionenergieshaveshownthatforthe( 6,6)tube,adsorptionon bridge-1siteisthestrongest,whileforthe(10,0)tube,th estrongestadsorptionsiteappears tobethebridge-2site.FromFigure7-1,weseethatthenarro wanglechainismoststable andawideanglechainismetastable.Basedonthis,wedecided toaddPdwideangle chainsonbothbridge-1andbridge-2sitesofthe(10,0)tube andPdnarrowanglechainson topsitesof(6,6)tube.Thebondlengthandbondangleofthec hainsareslightlychanged duetothecurvatureofthetubes.Inthecalculations,wedid notobservemagneticmoment inthePdchain-SWNTsystems. 79

PAGE 93

tu be a xi sto p b ridg e2 holl ow br id ge -1 t ube axi s ho ll ow to p bridge -1 b ri dge -2 Figure7-3.Schematicdrawingoftopviewsoffourpossibles itesforsinglePdatomadsorptiononSWNT(6,6)andSWNT(10,0).BrowndotsrepresentPda toms.Bridge-2site differsfrombridge-1siteinthattheC-Cbondisperpendicul artothetubeaxisatthissite. IntheSWNT(10,0)case,bridge-2siteislocatedonaC-Cbondpa ralleltothetubeaxis. ThePdchainsmaintaintheiroverallinitialgeometriesaft errelaxations.Theangle betweenPdatomson(6,6)tubeis53.0 o ,withthe nn distanceof d = 2.46 AasinFigure71.Thecurvatureofthe(6,6)tubeandthestrongerinteracti onsofPd-Pdatomsinduce unequalPd-Cdistanceof2.21 Aand2.26 AbetweenthePdatomsandtheirnearestcarbon atoms.ThesedistancesarelargerthanthePd-Cdistanceof2 .10 AformedbysinglePd atomonthetopsiteofthe(6,6)tube.Thebridge-1siteadsor bedPdatomson(10,0)tube formanangleof107.7 o with d = 4.26 A.Thisangleanddistance d areclosetothosefor theisolatedwideanglechain,showninFigure7-1(109.1 o and4.0 A).Wealsoobserved thatthePdadatomsriseabovethebridge-1site,withthePd Cdistanceof2.40 A.For the(10,0)tube,thedistancesbetweenthePdatomsandtheir nearestCatomsare2.13 A and2.12 A,whicharesmallerthanthe2.17 AobtainedforsinglePdatomadsorbedon thebridge-1site.ThePdchainonthebridge-2sitestabiliz esatabondangle 99 : 6 o and d =4 : 27 Ainitsmostenergeticallyfavorablegeometry.Unlikebrid ge-1siteadsorption, bothCatomsonbridge-2sitesofthis(10,0)tubeareonlysli ghtlyfurtheraway(2.18 A) fromthecarbonatomsthaninthecaseofsinglePdatomadsorp tion(2.14 A).Asalsocan beseenfromcrosssectionalviewsinFigure7-4,bothtypeso fSWNTshaveslightradial 80

PAGE 94

(a ) (b ) (c) Figure7-4.3DviewofequilibriumgeometriesofthePdchain SWNTstructures.(a)Pd narrowanglechainontopsiteofSWNT(6,6),(b)Pdwideanglec hainonbridge-1site ofSWNT(10,0),(c)Pdwideanglechainonbridge-2sitesofSWNT (10,0).Inallcases, changesinthetubeshapeareseenfromthecrosssectionalvi ews. distortionsfromcircularshapetoanellipticalshapewith majorandminoraxesof R 1 and R 2 ,respectivly.Wecalculatedradialstrainparametersusin gEquation7-5and7-6dened intermsofmagnitudeofchangesforthetubes. R 1 = R 1 R 0 1 R 0 1 (7-5) R 2 = R 2 R 0 2 R 0 2 (7-6) R 0 isradiusoftheundeformed(zero-strain)nanotubeintheab senceofPd.Itisfound thatthePdchainintroducestensionalstrainalong R 1 andcompressionalstrainalong R 2 ThePdwideanglechainsonthetwodifferentbridgesitesofS WNT(10,0)introducea differentradialstrainwithbridge-1siteproducingamuch largertensionalstrain(forwhich, R 1 =+ 0.052)andcompressionalstrain( R 2 = 0.020)thanbridge-2site( R 1 and R 1 are + 0.027and 0.003,respectively).ThePdnarrowanglechainhasaneglig ibleeffecton SWNT(6,6)with R 1 = 6.5 10 4 and R 2 = 0. Thecalculatedbindingenergiesperunitcellforthechaina tomsonSWNT(6,6)and SWNT(10,0)arelistedinTable7-1.Theadsorptionenergiesf orthesinglePdatomon 81

PAGE 95

Table7-1.BindingenergyofPdatomsperunitcellontwoSWNTs. d Pd C isthedistance betweenPdanditsnearestneighborCatom. Qistheelectronchargetransferfromtube toadatoms,wherepositiverepresentschargetransfertotu be. System E b (eV) d Pd C ( A) d Pd C ( A) Q(e) Pdchain+SWNT(6,6) 4.012.262.210.11 Pdchain+SWNT(10,0) y 3.752.132.120.20 Pdchain+SWNT(10,0) z 3.812.182.180.22 y Valuesmeasuredonbridge-1. z Valuesmeasuredonbridge-2. fourdifferentsitesrangefrom 1.20eVto 1.50eV,andtheaveragePd-tubedistancelengthisintherangeof2.10-2.18 A[181].InthiscaseofPdchainformationon carbonnanotube,duetothestrongPd-Pdbindinginthechain ,thebindingenergyperPd atomis 1.88eVto 2.00eV,muchlargerinmagnitudethanthatofthesingleatom adsorption.Thesevaluesarecomparedwiththebindingener gyofTichainonSWNTs, reportedas 3.24eVto 4.08eV[155].TishowsstrongerbindingwithSWNTsthan manyothermetals,andcanformcontinouswires.Fromresult softhiswork,weconclude thatPd/NichainformationonSWNTsisenergeticallyfavored .ThePdatomshavelarger bindingenergyonthe(6,6)tubethanonthe(10,0)tubeparti allybecauseofthestronger bindingofPdatomsinthenarrowanglegeometry.Comparingth etwostudiedwideangle chainsofsimilargeometryonbridge-1andbridge-2siteson the(10,0)tube,weseethatalthoughbridge-1sitechainiscloseringeometrytothemetastableisolatedchainstructure, thelarger-magnitudebindingenergyappearsforbridge-2s itebinding.Weattributethisto thelarger-magnitudeadsorptionenergyofPdatomonbridge -2sitethanonbridge-1site of(10,0)tubeasseeninourrecentcalculations[181]. TheelectronicstructuresofthebareaswellasPdchaindeco ratedSWNTsforboth the(6,6)and(10,0)tubesarepresentedinFigure7-5and7-6 ,respectively.Figure7-5(a) showsthebandstructureandelectrondensityofstateofa(6 ,6)tube.Theconductionband 82

PAGE 96

0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz 0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz -5 -4 -3-2-1 012 0 5 10 15 20 25 30 -5 -4 -3 -2-1 012 0 5 10 15 20 25 30 (a) (b)Energy (eV)DOS (states/eV)Ene rgy (eV )DOS (states/eV)Ene rgy (eV )Energy (eV) Figure7-5.Spin-polarizedbandstructureandDOSof(a)SWNT (6,6)and(b)Pdnarrow anglechainadsorbedSWNT(6,6).Fermilevelissetaszero. 83

PAGE 97

Energy (eV) 0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz 0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz 0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz -5-4-3-2-1 012 0 5 10 15 20 25 30 35 -5-4-3-2-1 012 0 5 10 15 20 25 30 35 -5-4-3-2-1 012 0 5 10 15 20 25 30 35 (a) (b) (c) DOS (states/eV)Ene rgy (eV )Energy (eV)Energy (eV)DOS (states/eV) DOS (states/eV)Ene rgy (eV ) Ene rgy (eV ) Figure7-6.Spin-polarizedbandstructureandDOSof(a)SWNT (10,0),(b)Pdwideangle chainadsorbedonthebridge-1sitesofSWNT(10,0),and(c)Pd wideanglechainadsorbed onthebridge-2siteofSWNT(10,0).Fermilevelissetaszero.andvalencebandmeetatFermilevelindicatingthatthetube ismetallic.Theseparation betweentwovanHovesingularitiesaroundFermilevelis3.6 5eV,whichisinagreement withresultsofReich etal. [182].Figure7-6ashowsthebandstructureandDOSofthe semiconducting(10,0)tube.Thebandgapbetweenthebottom oftheconductionband andtopofthevalencebandat pointisabout0.75eV,alsoinagreementwithprevious results[183]. Figure7-5(b),7-6(b),and7-6(c)showthatuponadsorption ofPdchains,theelectronic propertiesofbothSWNTsundergomanysignicantchanges.Th eoriginallydegenerated statesaresplitinbothvalanceandconductionbandsduetos ymmetrybreakingofthewave function.AsshowninFigure7-5(b),thePd-SWNT(6,6)system remainsmetallic.Infact, 84

PAGE 98

anincreaseindensityofstatesaroundFermilevelleadstoa higherelectricalconductivity ofthePd-SWNT(6,6)system.Thechargetransferstudy[184]s howsthereisabout0.1eV perunitcellelectrontransferredfromPdchaintothe(6,6) tube.AsshowninFigure7-6(b) and7-6(c),thebandstructuresof(10,0)tubeshowdifferen telectricalpropertychanges upontheadsorptionofPdchainsondifferentsites.Inthebr idge-1siteadsorption,band gapofthebaretubeissignicantlyreducedtoalow0.15eV.T heexistenceofthissmall gapsuggeststhatthesystemisanarrowgapsemiconductorma terial.However,whenPd chainisaddedonthebridge-2sites,metalliccharacteriso bservedthroughcrossingofthe Fermilevelnear point,withDOSattheFermilevelof4.5states/eV.Approxim ately0.20 and0.22electronstransferfrombridge-1andbridge-2site Pdchainstothe(10,0)tubes, respectivly.Allthissuggeststhatdifferentelectronicp ropertiesofacarbonnanotubecan beachievedthroughdecorationsofthetubebythesameeleme ntondifferentsites. 7.5.2Pd/NiAlloyChainonSWNT Pd/Nialloychain-functionalizedonthesametubeswerestu diedbysubstitutingalternate PdatomswithNiatoms,andthenrelaxingthesystems.Niatom isreportedtohavestronger bindingwithsemiconductingtube(8,0)thanPdatom[153],a ndNicanalsoimprovethe reliabilityofPdnanomaterials,especiallyinhydrogense nsingapplications[173,174]. Here,weusedthesameinitialcongurationsasthepurePdch ainsfunctionalizedSWNT systems,howeverwefoundthetotalenergywasnotconvergin gduringrelaxationofthe bridge-1siteadsorbedPd/Nichain+SWNT(10,0)system.Ther efore,inthestudyofPd/Ni alloychainsonSWNTs,weconsideredonlytwocongurations, namelythenarrowangle alloychainontopsiteofSWNT(6,6)andwideanglechainonbri dge-2siteofSWNT(10,0). TheirequilibriumgeometriesareshowninFigure7-7.Signi cantchangesinthecross sectionalshapeoftubesareobservedasshowninFigure7-7( b).SWNT(6,6)mostlyretains itscircularcrosssectionalgeometrybecauseoftheweaken edPd-Cinteractionsinducedby 85

PAGE 99

Table7-2.Calculatedbindingenergies,chargetransfer,an dmagneticmomentforPd/Ni chain-SWNTsystem. d Pd C isthedistancebetweenPdanditsnearestneighborcarbon atom. d Ni C isthedistancebetweenNianditsnearestneighborcarbonat om. Qis theelectronchargetransferfromtubetoadatoms,wherepos itivevaluemeanstubegains charge. System E b (eV) d Pd C ( A) d Ni C ( A) Q(e) ( B ) Pd/Nichain+SWNT(6,6) 4.982.361.970.180.76 Pd/Nichain+SWNT(10,0) y 4.342.241.990.300.08 y Valuesmeasuredonbridge-2. strongPd-Nicoupling.Again,radialstraincalculationsh owsanegligiblestraineffect introducedbyPd/NinarrowanglechainonSWNT(6,6).However thePd/Niwideangle chainproduces+0.056tensionalstrainalong R 1 and 0.037compressionalstrainalong R 2 ofSWNT(10,0),whicharebothmuchlargerthanforthepurePdw ideanglechainon thesamesiteshowninFigure7-4(c).Alargerbindingenergy wasobservedthaninthecase ofpurePdatomsonthesametubes,asshowninTable7-2.Inbot hcases,weobserveda muchsmallerdistancebetweenNiandCatomsthanbetweenPda ndCatoms.Thebond anglesofPd/Nichainon(6,6)tubeand(10,0)tubeare57.5 o and112.3 o ,respectively,very closetotheanglesof60.5 o and98.1 o intheirstablegeometriesasisolatedchains,asshown inFigure7-1. ThespinpolarizedbandstructuresshowninFigure7-8aresi milarinformtotheones obtainedforSWNT(6,6)andSWNT(10,0)decoratedwithPdchain s,cf.Figure7-5and76.However,wenowobservesplittingofthespinbands,mores ointhecaseofPd/Nichain adsorbedSWNT(6,6)thanincaseofPd/NiadsorbedSWNT(10,0). Wethereforeconclude thattheintroductionofNiatomsproducesmagneticmomenti nthesystems,higherinthe caseofmetallicSWNT(6,6).Table7-2listscorrespondingva luesfor Theadditionalbandsinthebandgapregionarerelatedtothe delocalizedstatesfrom thePd/Nichain.Forinstance,fromtheatomprojectedDOSin Figure7-9,wecanclearly 86

PAGE 100

(a ) (b) Figure7-7.3DviewsofequilibriumgeometriesofthePd/Nic hain-tubestructures.(a) Pd/NinarrowanglechainontopsiteofSWNT(6,6),(b)Pd/Niwi deanglechainonbridge2siteofSWNT(10,0).seethattheyarecontributedbythestatesfrombothNiandPd ,andtheneighboringC atoms.ThemajorbindingstateofPdandNiwiththeirnearest Catomsappearsatabout 0.75eVand 2.00eV,respectively.Thissuggestsastrongerbindingbet weenNiandC thanbetweenPdandC.Tofurtherexploretheelectronicinter actionsanddelocalizationof electronsbelongingtoPd,NiandSWNT,wehaveplottedthetot alelectrondensityacross variouscross-sectionsofthePd/NichainfunctionalizedS WNTsinFigure7-10.Asshown inFigure7-10,electronsintheareaunderchainsaredeloca lizedanddistributeonboth metalandcarbonatoms.ThechargetransfershowninTable72indicatesthatalarger numberofelectronsweretransferreduponalloying,moreon totheSWNT(10,0)thanonto theSWNT(6,6).Themagnetizationdensity,denedasthediff erencebetweenspinupand spindowndensity,showninFigure7-11showsthatastrongpo sitivemagnetizationdensity locatedonNiatom,indicatingthemagneticmomentismostly carriedbyNi,butnotby Pdortubes.Comparingthetwotubesystems,wenoticethatnom agnetizationdensityis foundatSWNT(10,0)Catoms,butalowmagnetizationisfoundd istributedontheCatoms ontheSWNT(6,6),showingthedelocalizationofthemagnetic moment.Thedistribution 87

PAGE 101

0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz 0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz -5-4-3-2-1 012 0 5 10 15 20 25 30 -5 -4-3-2-1 012 0 5 10 15 20 25 30 Energ y (eV)DOS (states/eV)Ene rgy (eV )Energ y (eV)DOS (states/eV)Ene rgy (eV ) Figure7-8.Spin-polarizedbandstructureandDOSof(a)Pd/ NinarrowanglechainfunctionalizedSWNT(6,6),and(b)Pd/Niwideanglechainfunctio nalizedSWNT(10,0).Fermi levelissetaszero. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 -5-4 -3 -2 -1 01 2 C Ni (a) (b) 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 -5 -4-3-2-1 01 2 C Pd Ene rgy (eV ) Ene rgy (eV )PDOS (st ates/eV) PDOS (st ates/eV) Figure7-9.Atomprojecteddensityofstate(PDOS)from(a)P datomwithtwonearestCatomsand(b)NiatomwithtwonearestCatoms,onbridge2sitefunctionalized SWNT(10,0). 88

PAGE 102

Figure7-10.Contourplotoftotal(spin-upandspin-down)va lencechargedensityonthree planesforPd/NichainfunctionalizedSWNT(10,0)(upper)an dPd/Nichainfunctionalized SWNT(6,6)(lower).Theplanesarethroughthecrosssectiono fthetubeanddifferent locationonthePd/Nichain.ofthemagnetizationdensityaroundtheNiatomresemblesdi fferentshapesintwochainSWNTsystems:a d -likeorbitalshapeon(10,0)tubeanda p -likeorbitalshapeon(6,6) tube.7.6H 2 InteractionswithChain-FunctionalizedSWNTs Experimentally,PdfunctionalizedSWNThavebeenstudiedas H 2 sensors,andgoodresponsehavebeenobservedthroughalargechangeinresistan ce[39].Theoretical[185,186] andexperimental[187,188],studieshaveshownthatmolecu larhydrogeninteractionwith barecarbonnanotubesisaweakphysisorptionprocess,with lowadsorptionenergy.The chemisorptionstatewithmoleculedissociationhasbeenfo undashydrogenmoleculeis veryclosetothetubesurface,howeverapproximateenergyb arriersof2.5eV[28,189] and3.4eV[190]areneededtobeovercomeforSWNT(6,6)and(10 ,0),respectively,to dissociativelychemisorbaH 2 moleculeontothetube.Inthissection,westudytheinteractionsbetweenH 2 moleculesandfunctionalizedSWNTsbyplacingoneH 2 moleculeon 89

PAGE 103

Figure7-11.Contourplotofmagnetizationdensity(spin-up andspin-down)ontwoplanes throughPdorNiandthetubeforthesamesystemsasinFigure7 -10. topofbothPdandNiatoms.Wehavetriedtwodifferentwaysof placingH 2 molecules bylettingH-Hbondeitherparallelorperpendiculartochai n-SWNTaxis.Afterrelaxing thesystems,wedidnotobserveanysignicantdifferencesi nnalgeometryorbinding energy.Theresultsshownherearefromtheinitialstructur eswhereH-Hbondsareparallel tothetubeaxisasshowninFigure7-12.Foracomparisonofth edifferentinteractions betweenpurePdchainandPd/NialloychainfunctionalizedS WNTs,westudyfouroutof vesystemsshowninFigure7-4and7-7,exceptforthebridge -1sitePdfunctionalized SWNT(10,0). ThedihydrogencomplexofH 2 andPdwasreportedtohaveanH-Hbondlengthof 0.86 A,andaPd-Hbondlengthof1.67 A[191].OurcalculationofafreePdH 2 gave thesameresult.IninvestigatingtheadsorptionofaH 2 moleculeonPdandPd/Nichain functionalizedSWNT(6,6)andSWNT(10,0),weobservedthedis sociationofH 2 .The distancebetweenthetwodissociatedHatomsis0.83 AonPdand0.86 AonNionboth 90

PAGE 104

typesofcarbonnanotubes,thereforeweconcludethatthen algeometryofindividualH 2 moleculeonPdisnotaffectedbythespeciesofitsneighbora toms.Wehavecalculatedthe adsorptionenergyofoneHatomwithrespecttotheH 2 moleculeaccordingtoEquation77. E ( H ) ad = 1 4 h E ( chain + SWNT +4 H ) T E ( chain + SWNT ) T 2 E ( H 2 ) T i (7-7) Weobtainedthebindingenergiesof-0.13eVand-0.33eVforp urePdfunctionalized SWNT(6,6)andSWNT(10,0),respectively,and-0.17eVand-0.4 8eVforthesamealloy functionalizedsystems.Thenegativevaluesofthesebindi ngenergiescouldbecompared withtheadsorptionenergyperHatom(energygainperHatomu ponadsorptionofaH 2 moleculeonthesurface)atlowtomediumhydrogencoverage( < 1)onPdsinglecrystal surfacesof0.45 0.5eV.[192,193]Differencesbetweenourcalculatedvalue sforthePdSWNTcasesandtheliteraturevaluesforthePdsurfacesarefr omthedifferencesinthe surfacecoordinationofadsorptionsitesinthesedifferen tsystems.Strongeradsorptionis seeninthealloyfunctionalizedsystems.Theadsorptionen ergydecreasesstronglywith increasinghydrogencoverage.[193,194]Forexample,at = 1.25,theadsorptionenergy canbeaslowasabouthalfoftheadsorptionenergyat = 1.OurresultsshowthataPd narrowanglechainfunctionalizedSWNT(6,6)hasmuchlowerH 2 adsorptionenergythan aPdwideanglechainfunctionalizedSWNT(10,0).Thisismain lybecauseofthehigherPd localdensityofthenarrowanglechain,whichprovidesless openspaceforH 2 adsorption. WealsondthatNialloyedPdchainfunctionalizedtubeshav ehigherH 2 adsorptionenergy comparedtothepurePdfunctionalizedtubes.Thisseemstoc onictwiththefactthat Ni-alloyingdecreasesH 2 sensitivityinsensorapplication.However,analloyingin duced sensitivitydecreaseisusuallyseenintheexperimentswhe relmthicknessisfromabout 50toabout2000nm.Inthatcase,aH 2 diffusionaltransportismainlyresponsibleforthe 91

PAGE 105

sensitivity,inotherwords,themagnitudeoftheresponse. Sincethediffusioncoefcient forHatomsinPdisabout 10 2 timeslargerthaninNiatroomtemperature[195],weusually seeadecreasedsensitivityofhydrogensensorswhenPdisre placedbyNi.Ifthehydrogen diffusionprocessisnotalimitation,suchaswhenanatomic allythinlmisused,then wewouldseeabetterH 2 sensitivityonNi,asNihasahigherH 2 adsorptionenergythan Pd[192,196,197].Thisisalsowhyweseelargeradsorptione nergywhenPd/Nialloy chainsaredecoratedonbothtypesofSWNTs. AdsorptionofH 2 moleculeschangesthegeometryofchainsonthetubesintwoa spects, asshowninFigure7-12:thebondangleofmetalchainsandthe distancebetweenmetal atomsandcarbonatoms.Fromthecalculations,wehaveseent heoverallbondanglesof atomicchainsdecreasewithanalmostunvaried d .Forexample,thebondangleofpure PdchainonSWNT(6,6)and(10,0)decreaseto49.3 o and97.6 o from53.0 o and99.6 o ,and alloychainsdecreaseto52.8 o and106.0 o from57.5 o and112.3 o .UponH 2 adsorption, thePdchainonSWNT(6,6)showsalargeexpansion,nearlysepa ratingthezigzagchain intolinearchains.Othersystemsalsohaveshowndifferent degreesofchainexpansion towardtwodifferentdirections.Thisismainlycausedbyth eHrepulsion,whichislarger onnarrowanglechains.Ontheotherhand,wendtheintroduc tionofH 2 molecules strengthensthemetal-carbonbindingbyloweringthechain sonthetubesurface.Wehave observedthatwithH 2 ,Pd CdistancesfrompurePdwideanglechain-SWNT(10,0)system increaseabout1.7%,butthePd CandNi CdistancesfromPd/Nichainonthesame (10,0)tubeshownolengthchange.Inthenarrowanglechain SWNT(6,6)systems,dueto thesignicantchangeofthechaingeometry,Pd-Cdistances haveaslightdecreaseof0.6% comparedtochain-SWNT(6,6)withoutH 2 ,whilePd-CandNi-Cdistancesinalloychain decreaseabout3.1%and2.2%,respectivelyafterH 2 isadsorbedonthe(6,6)tube.These observationsindicatethatthepresenceofH 2 affectsthechaingeometryandadatombinding withSWNTdifferently.Fordifferentsystems,largemorphol ogychangesareobservedin 92

PAGE 106

(a) (b) (c)(d) Figure7-12.3DviewsofequilibriumgeometriesoftheH 2 adsorbedPdandPd/NifunctionalizedSWNTs.Thecolorschemeissameaspreviousgures .Smallbrightbluedots arehydrogenatoms.(a)and(b)areSWNT(6,6)systems,(c)and (d)areSWNT(10,0) systems.narrowanglechain-tubesystems.AstrongNi-Pdbindingfro mNialloyingpreventsnarrow anglechainfromsplittingandpeelingfromtubesurfaceupo nexposuretoH 2 .Asforthe carbonnanotubegeometry,fromFigure7-12andaxialstrain parametercalculations,we ndthatH 2 produceslessstraintofunctionalized(10,0)tubes,where theinitialdistortion byPdandPd/Nifunctionalizationshownaremaintained.The largestH 2 inducedtube geometrychangeisobservedonpurePdchainfunctionalized (6,6)tubeduetothechain splitting,wheretensionalstrainalong R 1 is + 0.025andcompressionalstrainalong R 2 is 0.033. InFigure7-13,wepresentthebandstructureandDOSforthef oursystems.Wenote thattheadsorptionofhydrogenchangestheelectronicprop ertiesofchainfunctionalized SWNTs.Theelectrondensityofstatesofthe(6,6)tubesaroun dFermilevel(Fig.7-13(a) 93

PAGE 107

0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz 0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz(a) (b) 0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz 0 0. 1 0. 2 0. 3 0. 4 0. 5 -5 -4 -3 -2 -1 0 1 2 Kz(c) (d) -5 -4 -3-2-1 012 0 10 20 30 -5 -4 -3-2-1 012 0 10 20 30 -5 -4-3 -2-1 012 0 10 20 30 -5 -4-3 -2 -1 012 0 10 20 30 Energy (eV) Energy (eV) Energy (eV) Energy (eV)DOS (states/eV) DOS (states/eV) DOS (states/eV) DOS (states/eV) Figure7-13.BandstructureandDOSforthefoursystemsshown inFigure7-12. 94

PAGE 108

and7-13(b))decreasessignicantlycomparedtotheDOSofP d-chain-SWNT(6,6)(Fig.75(b))andofPd/Ni-chain-SWNT(6,6)(Fig.7-8(a)).InFigure 7-13(c)and7-13(d),wesee thebandgapof0.58eVand0.35eVatFermilevelinPdandPd/Ni chainfunctionalized (10,0)tubes,indicatingthesystemsaretransformedbackf rommetaltosemiconductor. BoththedecreaseofelectrondensityofstatesintheSWNT(6,6 )systemsandthebandgap openingintheSWNT(10,0)systemsimplyasignicantincreas eofelectricalresistanceof thematerial.Thisresultisconsistentwithexperimentalo bservationsfromothergroups, wherePdcoatedSWNTshavebeenutilizedinH 2 sensing[22,39].Intheseexperiments, anindividualPdcoatedsemiconductingSWNT[22]andaPdcoat edthin,uniformSWNT lm[39]wereused,respectively.Bothexperimentalresults showdramatic,reversibleincreaseofresistanceofthesensingmaterialsuponexposure tohydrogengasow,indicating PdcoatedSWNTshaveverygoodsensitivityforH 2 detection.ThesingletubesensorcongurationutilizedbyKong etal. [22]consistsofdiscretePdparticlesdecoratingthetube surface,whiletherandommatrixofsurface-dispersedSWNTs [39]wereconnectedwith amoreorlesscontinuousPdlm.Incomparison,ourcalculat ionsareforacontinuous monatomicwireontheSWNT.Boththeliteraturereportedexper imentalresultsandour DFTcalculationsshowthattheresistanceincreasesuponH 2 exposure.Ifweconstructa series-parallelarrayofresistancescomposedofmetaland SWNTsegmentsasanequivalentcircuit,thenourDFTcalculationscanbeinterpretedt oindicatethatbothcontinuous coatingbymetalanddecorationbydiscreteparticlesofbot hmetallicandsemi-conducting SWNTsleadtothesameresponseofincreasedresistanceinhyd rogensensorapplications. However,themagnitudesofresponsedependonthenatureoft hetube,beinglargerfor semi-conductingSWNTs.ChargetransferuponH 2 adsorptionwouldindicatewhetherthe resistancechangeisprimarilyinthetubeorcoating.Ouran alysisshowsthatHatomsare slightlynegativelychargedandtheoriginallynegatively chargedSWNTsgainmorecharge. PdandPd/NifunctionalizedSWNT(6,6)bothgain0.14e,andSWN Ts(10,0)gain0.03e 95

PAGE 109

and0.06e,respectively.Thus,uponH 2 adsorption,thetwofunctionalizedSWNT(6,6) gainabout0.1emorechargethanthetwofunctionalizedSWNT( 10,0).Pd/Nichainsdo notbringsignicantlylargeramountofchargetransfertob othtypesofSWNTsthanPd chains.TheextrachargetransferfromchainstoSWNTsisduet otheH 2 adsorption,which readjuststhepositionsofPdandNiatomsonthetubesurface andcausechargeredistributionsbetweenchainsandSWNTs.Thisisespeciallytruefor theSWNT(6,6),wherethe narrowanglegeometryyieldsalargechainexpansionorspli ttingafteradsorbingHand inducesasignicantchargeredistribution.Thesecharget ransferresultssuggestthatH 2 sorptionbringsmoreelectronstotheinitiallynegatively chargedSWNTfromthechain functionalization.Whilethismayindicateadecreaseintub eresistance,theoverallsystem resistanceisindicatedtoincreasefromthebandstructure andDOSresults.Hydrogenating ofthemetalappearstoincreaseresistancesignicantly. Finally,wenotethatafterH 2 adsorption,theinitialmagneticmomentcarriedbythe Pd/Nisystemsdisappearandthesystemsturnnonmagnetic.T hedemagnetizationofNi bulkandsurfacebyH 2 adsorptionwereunderstoodastheinvolvementoftheNi d -states withH s -state,whichtendstomake d -shellmorenearlyfullandasaconsequenceconsiderablyreducesthemagneticmoment[198,199].7.7ConclusionsInthiswork,wehavepresentedadetailedanalysisofformat ionofatomicPdandPd/Ni chainstructuresandtheirinteractionswithSWNT(6,6)andS WNT(10,0).Wefoundthat zigzagchainsareenergeticallymorefavorablethanlinear chains,andtheoverallbinding energyishigherinthePd/NialloychainsthaninthepurePdc hains.TheadditionofPd anditsalloychainsonthetubesurfacemodiestheelectron icstructureofbothtypesof SWNTs.Thechainshavesimilargeometryonthetubesurfaceas intheirisolatedstates, showingstablecontinuousPdandPd/Nimonatomicchainscan beformedonSWNTs. 96

PAGE 110

TheincreaseofelectrondensityofstatesaroundFermileve lenhancestheconductivity ofSWNT(6,6),whereastheadditionalstatesfromchainsatba ndgapregioneffectively transformsSWNT(10,0)intoametal.Chargetransferphenomen onisobservedfromchain tothetubeinallthecases,withalargeramountbeingtransf erredfromthealloychain. ThePd/Nichainalsoinducesamagneticmomentinthetube.We observethatthePd/Ni narrowanglechainfunctionalizedSWNT(6,6)hasmuchlarger magneticmomentthanthe wideanglechainfunctionalizedSWNT(10,0).Spindensitysh owsthemagneticmomentto bemostlyconcentratedonNiatomsbutondifferentorbitals determinedbytheinteractions betweenPdandNiinthechains. CalculationsofH 2 interactionswiththesemetalandalloychainfunctionaliz edSWNTs showdifferentdegreesofgeometricalchanges.Duetorepul sionbetweenHatoms,thePdchain-SWNT(6,6)showsthelargestexpansion.Ourresultssh owthatNicanimprovethe stabilityofPdchainontubesurface,aswellasincreasethe hydrogenadsorptionenergy. Theelectronicpropertycalculationsindicateadecreaseo felectrondensityofstatesat FermilevelinthefunctionalizedSWNT(6,6),andbandgapreo peninginthefunctionalized SWNT(10,0)whichturnsametallized(10,0)tubebacktosemic onductor.Theseelectronic propertychangescansignicantlyreducetheconductanceo fthetubes,whichexplains thereportedexperimentalobservationonPdfunctionalize dSWNTsinhydrogensensor applications. 97

PAGE 111

ChapterEight DFTStudyofPdFunctionalizedCarbonNanotubesasHydrogenS ensors 8.1AbstractDensityfunctionaltheoryisemployedtostudytheperforma nceofPdfunctionalizedsingle walledcarbonnanotubeashydrogensensors.Ourresultsdem onstratethataxiallydiscrete Pdmonatomiccoatingisabletometallizethesemiconductin gSWNT.Asignicantdecreaseofelectricalconductanceuponhydrogenadsorption isobservedduetotheelectron saturationofPd d state,whichbringsitbelowFermilevel.AnexaminationofS WNT fullycoatedwithPdindicatesPdatomsareabletodistribut eevenlyontheSWNTsurfacewithoutdestroyingthemorphologyofthetube.Itisexp ectedthatbothPdpartially functionalizedandfullycoatedSWNTscanbeusedashydrogen sensor. 8.2IntroductionRecently,greatadvanceshavebeenmadeindemonstratingthe viabilityofusingcarbon nanotubesasavaluableplatformforthedevelopmentofsens itivegasdetectors.Surface functionalizationofcarbonnanotubehasbeenofmuchinter estbecauseitenhancesthe propertiesofbareSWNTformanypurposes.Thefunctionaliza tionofcarbonnanotube offersfurtherscopeforimprovingthesensingperformance andfordetectingwiderange ofgasspeciesthatarenotdetectablebybarecarbonnanotub es[22,39,40,200–203]. Forexample,baresinglewalledcarbonnanotube(SWNT)hasno responsetohydrogen, however,PdnanoparticlemodiedSWNTsareshowntoexhibith ighsensitivityandfast 98

PAGE 112

responsetohydrogenatroomtemperature,seenbyasignica ntelectricalconductance dropuponexposuretosmallconcentrationsofH 2 [22,39].Eventhoughtheserecentwork haveshownthatfunctionalizedSWNTsachievemuchsuccessin gassensing,italsoraises manyunansweredquestions,suchas:whetherthesensingcap abilityispermanent[160]; howthegasinteractionaffectsthefunctionalizedcarbonn anotubeandiftheadvantagesof intrinsiccarbonnanotubemaintained;ifchargetransfert heorycanexplainfortheelectrical propertieschange;etc.Theoreticalstudiesoffunctional izedSWNTanditsinteraction withgasmoleculescanhelpdevelopabetterunderstandingo fthesensingmechanismand evaluatethepotentialforfabricatingmolecularsensorde vicesfromthesesensingmaterials. Inourpreviousstudy,wefoundaPdchainmetallizessemicon ductingSWNT(10,0). ThismetallicitydisappearuponH 2 adsorption,whichwouldimplyaconductancemodulationconsistentwithexperimentalobservations[22,39].I nthispreviousstudy,thecontinuousPdmonatomicchainwasplacedalongtheaxialdirection oftheSWNT.Bothofthe chainandtubewereconsideredtobeinnitelylong.Inthisp aper,westudyanotherclass ofchain-functionalizedSWNTsystems,wherePdatomsaredis tributeddiscretelyalong thenanotubeaxis,butformcontinuouslyalongthenanotube circumference. Inaddition,wealsostudyaSWNTfullycoatedwithPd.Experim entally,SWNTsfully coatedwithvariousmetalshavebeendemonstratedbyZhang etal. ,wherePdisshownto beabletoformasemicontinuouscoatingonSWNT[171].Theore tically,GaorTifully coatedSWNTsystemshavebeenstudied[204,205].Themetalat omsattachedoneach hollowsiteofSWNT(8,0)exhibitanonuniformdistribution. Theinteractionsbetween metalandcarbonnanotubewereseverelyweakenedandthetub ecrosssectionhadan obviousdeformationtoeitheranellipticalorsquare-like shape.Here,weshowthatPd monatomiclayercanbeformedevenlyonSWNT(10,0)withoutob viousdistortionofthe intrinsictube.ApotentialofusingfullycoatedSWNTandreg ionalfunctionalizedSWNT ashydrogensensorisalsodiscussed. 99

PAGE 113

8.3MethodofCalculationsTheVienna Ab-initio SimulationPackage(VASP)[148–151]wasusedtoperformcal culationswithinthegeneralizedgradientapproximationofP W91[136]usingoptimizedultrasoftpseudopotentials[147,175]andaplanewavebasiss et.ThefunctionalizedSWNT wasconsideredtobeisolatedandinniteinlength,withlat eralseparationofmorethan 1nm.TheBrillouinzoneofthesupercellwassampledbyMonkho rst-Pack[176]special1 1 31k-points.Structuralcongurationswereoptimizedunti lresidualforceswere within0.05eV/ A. 8.4ResultsandDiscussionInordertoconstructanaxiallynoncontinuousPdchain-fun ctionalizedSWNTsystem,the Pdmonatomicchain,containing20Pdatomspersupercell,is placedaroundcarbonnanotubeonbridge-2sites,asshowninFigure8-1.Twocarbonna notubeprimitiveunitcells containing80Catomsareusedineachsupercell.Eachradial chainisseparatedofabout 8 AontheSWNTsurface,thereforeisconsiderednoncontinuous alongnanotubeaxis.In thischapter,onlysemiconductingSWNT(10,0)isstudied.(A ccordingtoourprevious study,Pdchain-functionalizedSWNT(6,6)showsimilarbeha vioraschain-functionalized SWNT(10,0).)Semiconductingcarbonnanotubesaremorecomm onlyusedinconductivity basedhydrogensensorsratherthanmetalliccarbonnanotub es[22,28,206]. ThecalculatedelectronicbandstructuresnearFermilevel arepresentedinFigure82(a)and(b).AbareSWNT(10,0)isasemiconductorhavingaban dgapof0.75eV.Pd radialchainincreasestheFermienergyandyieldadditiona latspin-upandspin-down bandsinthebandgapofthebareSWNT.Thisagreeswiththecalc ulatedmagneticmoment of1.2 Bofthesystem.TheSWNT(10,0)ismetallizedupononPdadsorp tionintheform ofaradialchainbecausethebandscrosstheFermilevelduet oincreaseofFermienergy 100

PAGE 114

Figure8-1.EquilibriumgeometriesofPdradialchain-func tionalizedSWNT(10,0). 0 0.10.20.30.40.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6-0.4-0.2 0 0.20.4 0.6 0.6 1 0 2 4 6 8 10 Ener gy (eV) Ener gy (eV) Ener gy (eV)KzKz(a) (b)(c)DOS ( state/eV)-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 0.10.20.30.40.5* Figure8-2.Spin-polarizedbandstructureof(a)bareSWNT(1 0,0)and(b)PdradialchainfunctionalizedSWNT(10,0).(c)ThedensityofstatesofCato msinabareSWNT(10,0) andfunctionalizedSWNT(10,0)areshownassolidanddottedl ine,respectively.Fermi levelissetat0eV(horizontaldottedline). 101

PAGE 115

andthehybridizationbetweenC p statesandPd d states.Theoriginalgapbetweenthe SWNT(10,0)binding( )andanti-binding( )bandsreduceto 0.45eV.Thesummation ofDOSof80CatomsinFigure8-2(c)exhibitinghighdensitya tFermilevel,impliessuch atransformiscontributedbythecarbonnanotube.Chargetra nsferanalysisshowsatotal of2.1electronsweretransferredfromPdtotheSWNT,whichis accordancewiththeband structureandDOSresults. ThebindingenergyperPdatompersupercell,calculatedfro mEquation8-1,is 1.9 eV.ThisindicatesPdatomsinradialchain-functionalized SWNThavestrongerbinding energythanthatofasinglePdfunctionalizedSWNT,whichisk nowntobe 1.5eVfrom previouscalculations.Wenotethatthisvalueof 1.9eVisalmostsameasthebinding energyofPdinaaxialchain-functionalizedSWNT,implyingt hechaingeometryhasnegligibleeffectonbindingenergywhenthePdareplacedinthesa mesites,suchasthebridge-2 siteinthiscase. E ( Pd ) b = 1 N h E ( SWNT + NPd ) T E ( SWNT ) T NE ( Pd ) T i ;N =20 (8-1) Ashorteraverage nn Pd-Cdistanceof2.13 Aisobservedintheradialchain-SWNT, comparedtothecorrespondingdistanceintheaxialchain-S WNT.However,theaverage nnn Pd-Cdistanceincreases,namelyeachPdatomisnolongerequ allyboundedbythe twobridge-2Catomsasitisintheaxialchain.Theaveragean glebetweenPdatomsis 88.6 ,withtheaverage nn and nnn Pd-Pddistanceof2.72 Aand3.83 A.Thedecreases of nn and nnn distanceandchainanglecomparedtotheSWNTsupportedaxial chaincan beattributedtothecurvatureofthechaininducedbytheSWNT .Fromthecrosssectional viewinFigure8-1,thetubedoesnotappeartobedistortedas showninFigure7-4,where anellipticalshapewithamajoraxisunderPdchainisseen.T hemeasurementofradial distancealongthecircumferenceoftheSWNTindicatesthead sorptionofPdatomsslightly 102

PAGE 116

(a) (b)(c) Figure8-3.3Dviewsofequilibriumgeometriesofhydrogena dsorbedPdradialchainfunctionalizedSWNT(10,0).Fromtoptobottom: = 0.35,0.60,1.00. expandsthetubediameter,wherePdradialchainisplaced,b y 1%,whilethediameterof thecrosssectionnotadsorbedbyPdchainisnotaffected. NextwestudytheH 2 interactionswithPdradialchain-functionalizedSWNT.Dif ferent hydrogencoverages, ,( iscalculatedbytheratioofthenumberofH 2 moleculestoPd atoms)of35%,60%and100%,areused.Theirequilibratedstr ucturesareillustratedin Figure8-3. TheadsorptionenergyofoneHatomwithrespecttoH 2 moleculeiscalculatedby Equation8-2. 103

PAGE 117

Table8-1.H 2 adsorptionenergies E ad ,averagedatomicdistances d ,averagednearest neighbordistances nn ,chainangles ,andmagneticmoment forPdradialchainfunctionalizedSWNT(10,0)systemswithdifferentH 2 coverage. d nn and aremeasured forHadsorbedPdatomsonly.Theresultsareaveragedoverth enumberofadsorbedH 2 molecules. E ad (eV) d H H y d Pd H y nn Pd C y nn Pd Pd y z ( B) 0.00 2.132.7289.31.22 0.350.380.841.762.152.7988.50.960.600.370.841.772.152.7886.1 1.000.370.841.772.152.7986.30.00 y Valuesreportedinangstrom. z Valuesreportedindegree. E ad = 1 N E ( SWNT + chain + NH ) T E ( SWNT + chain ) T N 2 E ( H 2 ) T (8-2) whereNisthetotalnumberofHatoms.TheresultsofHadsorpt ionenergyareshownin Table8-1.Comparingwiththeaxialchain-functionalizedSWN T,H 2 hashigherdissociativeadsorptionenergyontheradialchain-functionalized SWNT.Thiscanbecontributedto thefactthattheradialchaingeometryhasasmallersurface relaxationuponH 2 adsorption. Thisisseenfromthecomparisonofaxialandradialchainstr ucturechangebeforeandafterH 2 adsorption.Table8-1indicatesthatthedistancebetweent wodissociatedHatoms andPd-Hbondlengtharenotaffectedbythecoverage,becaus eeveryH 2 isadsorbedon differentPdatoms. ForpartiallyadsorbedH 2 onradialchain-functionalizedtubes( = 0.35, = 0.60),the nn distanceofPdradialchaininthepartthatiscoveredbyhydr ogenislargerthanthepart thatisnotcovered,whichisaboutthesameas nn Pd Pd at = 0.Atthe = 1.00,the nn of thePdradialchainislargerthanthatoftheunabsorbedPdra dialchain-functionalizedtube. ThisismostlikelycausedbytherepulsionofHatomsasalsos eeninthepreviouschapterof axialchain-functionalizedtubes.Duetotheadsorptionof H 2 molecules,Pdatomsshowa 104

PAGE 118

0 0.10.20.30.40.5 -1 -0. 8 -0. 6 -0. 4 -0. 2 0 0.2 0.4 0.6 0.8 1 Kz 0 2 4 6 8 10 -1 -0 .8 -0. 6 -0. 4 -0. 2 00 .2 0. 40 .6 0. 81Ene rgy (eV )DOS ( sta tes/eV)= 0.35 = 0. 60 =1.00 (a)(b) (c) (d)Energy (eV)0 0.10.20.30.40.5 Kz 0 0.10.20.30.40.5 Kz -1 -0. 8 -0. 6 -0. 4 -0. 2 0 0.2 0.4 0.6 0.8 1Energy (eV)-1 -0. 8 -0. 6 -0. 4 -0. 2 0 0.2 0.4 0.6 0.8 1Energy (eV) Figure8-4.Spin-polarizedbandstructureofhydrogenadso rbedonPdradialchainfunctionalizedSWNT(10,0).From(a)to(c): = 0.35,0.60,1.00.(d)LocalDOSof Pdatomsatdifferent 105

PAGE 119

slightdisplacementontheSWNT(10,0),howeverthePd-C nn distancesincreaselessthan 1.0%withrespecttothecorrespondingdistancesbeforeH 2 adsorption.Thisobservationis differentfromtheaxialchain-functionalizedSWNT(10,0), wherealargerincreaseof1.7% ofPd-CdistanceswasseenuponH 2 adsorption.Pdatomsintheradialchainhaveless freedomofmotionthanintheonedimensionalaxialchainont heSWNT,andthisprevents thesePdatomsfrommovingonH 2 adsorption. UnlikePdaxialchain-functionalizedSWNT(10,0),Pdradial chain-functionalizedtube hasmagneticmomentof1.22 B.Theonsetofmagnetismisassociatedwiththeincreaseof densityofstatesatFermilevel,causedbythelocalsymmetr ychange,orbytheincreasing thepercentageofPdatoms,asdiscussedbySampedro etal. [207].Themagneticmoment carriedbythesystemdecreasesasthehydrogencoverageinc reases,asaresultsofthe lled-up4 d statesandtheconsequentreductionofdensityofstatesatF ermilevel[208]. Chargedensitycalculationsshow0.005electronsperHatoma retransferredfromPdto Hatoms.TheelectrondensityassociatedwiththePdfunctio nalizedSWNTincreasesby 0.2eVat = 1. Accordingtothebandstructure,thehydrogen-inducedband appears 8eVbelow FermilevelofthePd-SWNTsystem,inagreementwiththevalue reportedinthePd-H system[209,210].DuetothepresenceofHatomsinthePd,the Fermienergyisshifted upwardrelativetothe d bandofPd.PriortoH 2 adsorption,thePd d bandismostly lled.TheadsorptionofHatomsdrasticallyreducestheDOS attheFermilevelwitha correspondingdecreaseinthenumberofanti-bondingbands nearFermilevelasshown inFigure8-4(a)and(b).AthighHcoverage,the d bandbecomescompletelyoccupied, resultinginazeroDOSatFermilevel.Asaconsequence,theb andgapfromtheSWNT reappearsatFermilevel.ThegradualdecreaseofDOSofPdat omswithincreasing canbeclearlyseenfromthesummationoflocalDOSofeachPda tominFigure8-4(d). ThebandstructureandDOSchangeofPdduetoPdhydrideforma tionuponhydrogen 106

PAGE 120

Figure8-5.3DviewsofequilibriumgeometryofPdfullycoat edSWNT(10,0). adsorptionhasbeendiscussedbyChanandLouie[211].Asshow ninFigure8-4(a)-(c), themetallicnatureismaintainedat = 0.35,0.60,andbandgapof 0.48eVappears at = 1.00,indicatingthatthemetallicPdradialchain-functio nalizedSWNThasbeen transformedtoasemiconductor.Theresultingbandgapisab outthesamesizeasthe gapofPdfunctionalizedSWNTbeforeH 2 adsorptionasshowninFigure8-2(b),consistent withthechargepreservationofthetubeduringH 2 adsorption.Thereappearanceofthe bandgapwouldimplyasignicantresponseinthesensorappl ication.Sinceitisclearthat thePdatomsarediscretealongthetubedirection,ourDFTca lculationscanbeinterpreted toindicatethatbothcontinuousandnoncontinuousdecorat ionsbyPdofSWNT(10,0)lead tothesameresponseofincreasedresistanceinhydrogensen sorapplications.Thisisin agreementwithexperimentalobservationsofKong etal. [22]andSippel-Oakley etal. [39], whereanoncontinuousPdcoatedsemiconductingSWNTwereuse d[22]. Wenextinvestigatethepossibilityoffullycoatingthecar bonnanotubewithonePd atomiclayer.PreviousexperimentalresultsreportedbyZh ang etal. revealthatfora0.5nm Pdcoating,thediscontinuityinthecoatingisapparent[17 1].However,theyalsopointed outthatmetalcoatingonnanotubescouldbeinuencedbyvar iousdepositionconditions includingtemperature.OurcalculationsshowthataPdmona tomiclayercanbecoated uniformlyonSWNT(10,0)at0K. 107

PAGE 121

FullycoatedSWNTsystemshavebeenstudiedbyDurgun etal. whereGaorTiatoms attachedoneachhollowsiteofSWNT(8,0)exhibitnonuniform distribution[204,205].In thebothstudies,theinteractionsbetweenmetalandthetub ewereseverelyweakenedand thetubecrosssectionshowedanobviousdeformationtoeith eraellipticalorsquare-like shape.Here,aSWNT(10,0)fullycoatedwithPdisconstructed byplacingonePdatom oneachbridge-2site,namely,20Pdatomspercarbonnanotub eunitcell.Thesystem isrelaxedunderthesamecriteriaaspreviouscalculations forchain-functionalizedcarbon nanotubes.FromtheequilibratedstructureinFigure8-5,w eseethatPdatomsareable toformevenlyonthetubesurfacewithoutanytubedistortio n.Thebindingenergyper Pdatomis2.31eV,higherthanthatofchain-functionalized SWNT(10,0),owingtothe strongerPd-Pdcoupling.ThePd-Cdistancerangebetween2. 21 Aand2.24 A,indicating thatthePdisboundstronglywiththeCatoms.Theaverage nn distanceofPd-Pdis 2.87 A.Twobondanglesaredenedhere:axialbondangle, 1 ,equivalenttothebond angledescribedintheaxialchain,andcircumferentialbon dangle, 2 ,equivalenttothe bondangleofaradialchaindescribedinthischapter.Thetw oaveragebondanglesinthe PdfullycoveredSWNT(10,0)are 1 = 96.2 and 2 = 82.3 ,smallerthanthecorresponding individualbondanglesof99.6 and89.3 calculatedpreviously.Thus,webelievethatthe morphologyofPdatomsisaffectedbyboththecurvatureofth ecarbonnanotubeandthe numberofnearneighboratoms.Thechargetransferis0.06el ectronsperPdatomtocarbon nanotube,whichisaboutthesameasthechargetransferredi nPdchain-functionalized SWNTs. TheelectronicstructurehavingseveralbandcrossingtheF ermilevel,asshowninFigure8-6,indicatesthatPdfullycoatedSWNT(10,0)ishighlyc onducting.Theconductance associatedwiththeballisticelectrontransportofa1Dsys temisgivenbyLandauer'sequation,seeEquation8-3[212]. 108

PAGE 122

-1-0. 8 -0. 6 -0.4 -0. 20 0.2 0.40.60.8 1 0 20 40 60 0 0.1 0.2 0.30.4 0.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Kz Ener gy (eV) Ener gy (eV)DOS (st ate /eV ) Figure8-6.Bandstructureandtotalspinpolarizeddensityo fstates(DOS)ofaPdfully coveredSWNT(10,0).ZeroofenergyistakenasFermilevel. G = 2 e 2 h N X i T i (8-3) where 2 e 2 h = G 0 isthequantumunit,and T i isthetransmissionofeachcontributingsubband(conductionchannel)producedbytheconnementofthe electronsalongthecircumferenceofthecarbonnanotube.Inreality, T i isreducedduetothescatteringofcarriers fromtheabruptchangeofcrosssectionsandirregularities atthecontactstotheelectrodes andfromtheimperfections,impurities,andelectron-phon onscatteringinthetube.[205]. WenotethateventhoughthePdfullycoatedSWNT(10,0)showni nFigure8-5mayonly occurintheidealcondition,andathickandinhomogeneousc oatingintheexperiment maydecreasethechanneltransmission,Gisstillexpectedt obehighowingtothenew conductancechannelopenedatFermilevel.Thereforetheco nductanceofaPdcoated SWNT(10,0)canbeseveralG 0 WethenstudytheinteractionbetweenH 2 moleculeandaPdfullycoatedSWNT(10,0). WenoticethattheadsorptionenergyofeachHatomwithrespe cttotheH 2 moleculeis 109

PAGE 123

0.30eV,about0.3eVlowerthanH 2 adsorptionontheaxialchain-functionalizedtube and0.7eVlowerthanontheradialchain-functionalizedtub e.Thedistancesfromthe hydrogenadsorbedPdtoitsneighborPdatoms,aswellsastot henearestCatomincrease 3.8%and 1.3%respectively.Therelativelyweakerinteractionbetw eenPd-Pdand Pd-CallowsstrongerinteractionbetweenH 2 andPd,andhenceleadstoalargerH-H distanceof0.86 A.SimilarbehaviorhasalsobeenseeninthestudyofH 2 dissociation onsinglePtfunctionalizedSWNT[161].However,onecanexpe ctthatadetachment ofPdfromSWNTmayoccurifahighH 2 coverageisapplied.Whilethisisforeseen inafullycoatedPd-SWNTsystem,abettercontrolofPdpeelin gfromSWNTmaybe achievedbylocaldecorationsuchasradialchain-function alization,wherePdlocaldensity islower.TheH 2 adsorptiononaPdfullycoatedsemiconductingSWNTisalsoex pected toinducesignicantconductancechange.Thiscanbeseenby comparingthelocalDOSof PdatomindifferentlocationspresentedinFigure8-7.Figu re8-7indicatesthatsimilarto theradialchain-functionalizedSWNTcase,thePdthathasad sorbedH 2 hasmuchlower electrondensityofstatesthantheonewithoutH 2 ontheothersideofthefullycoated SWNT.Therefore,aswecanpredict,whenmoreH 2 moleculesappear,thetotalDOSof thesystemwillcontinuetoreduceandmostprobablywewills eeabandgapwhenallPd atomsareattachedbyH 2 8.5ConclusionDFTcalculationsonPdfunctionalizedSWNTsindicatethatad iscretePdmonatomiccoatingisabletometallizeasemiconductingSWNT.Thedramaticd ecreaseofelectricalconductanceuponH 2 adsorptiononthesePdatomscanbeattributedtothellingupofPd d state,whichbringsitbelowFermilevel.AstudyofSWNTfully coatedwithPdindicates thatthePdatomsareabletodistributeevenlyontheSWNTsurf acewithoutsignicantly alteringthemorphologyofthetube.BothPdpartiallyfuncti onalizedandfullycoated 110

PAGE 124

0 0. 2 0. 4 0. 6 -1-0 .5 00 .5 1 En ergy ( eV )DO S (s tate s/ eV )Pd 1 Pd 2 Pd 1 Pd 2 Figure8-7.LocaldensityofstatesoftwoPdatomsinthefull ycoatedSWNT(10,0).Pd1 andPd2arethetwoPdatomsasillustratedintheinsertedpic ture. SWNTsappeartobesuitableforhydrogensensingduetothein uenceofH 2 adsorption onthemetallicityofthePddecoratedcarbonnanotube. 111

PAGE 125

ChapterNine ConclusionsandProposedFutureWork 9.1ConclusionsClassicalMoleculardynamicssimulationsandquantumchemi cal abinitio methodswere usedtostudythepropertiesofPdbasedhydrogensensingmat erialsandtheirinteractions withhydrogengas.Therstpartinvolvedthecomparisonstu diesofthermodynamic,structuralanddynamicpropertiesofPdnanowireandnanocluster s.Thesimulationstudiesof thisworkindicatethatthePdnanowirehaslowermeltingtem peraturethanPdbulkbut higherthanthesamediameterPdcluster.BothPdnanowiresan dnanoclustersexhibit surfacepre-meltingwithdifferentthestructuralanddyna micalbehavior.Particularly,the nanowireexhibitsahigherpre-meltingtemperaturerange, anddynamicalbehaviorcharacterizedbyincreasedmovementofatomsintheplaneperpen diculartotheaxisfollowed byincreasedmovementacrosstheseplanesasthetemperatur eapproachesthetransition temperature.Aquasi-liquidskingrowsfromthesurfaceint heradialdirectionforboth nanoclusterandnanowire,inthesurfacepre-meltingregim e,followedbythebreakdownof orderintheremainingsolidcoreatthetransitiontemperat ure.Thenanoclusterretainsthe initialfccstructure,whereas,thenanowireappearsstabl einastructureclosetothehcpin thesolidphase.Meltingpointsofstudiedclusterandwirew erecharacterizedparticularly wellbytheliquid-dropmodelforsize-dependentmelting.A studyofgraphitesupported samesizedPdnanoclusterwasperformedinordertoexaminet hesubstrateeffects.SeveralanalysisrevealthatsupportedPdclusterhasverydiff erentgeometricevolutionduring 112

PAGE 126

heating.HoweverbothunsupportedandsupportedPdcluster sbehaveverysimilarinterior structuralevolutionsatlowertemperatures. Thesecondpartofthisstudyinvolvedquantummechanicalmo delingofPdfunctionalizedSWNTsandhydrogeninteractionsusing abinitio -DFTmethod.Adetailedanalysis offormationofatomicPdandPd/Nichainstructuresandthei rinteractionswithmetallic SWNT(6,6)andsemiconductingSWNT(10,0)wasconductedrst. Itwasfoundthatzigzag chainsareenergeticallymorefavorablethanlinearchains ,andtheoverallbindingenergy ishigherinthePd/NialloychainsthaninthepurePdchains. TheadditionofPdandits alloychainsonthetubesurfacemodiestheelectronicstru ctureofbothtypesofSWNTs. TheincreasedelectrondensityofstatesaroundFermilevel enhancestheconductivityof SWNT(6,6),whereastheadditionalstatesfromchainsatband gapregioneffectivelytransformsSWNT(10,0)intoametal.Alargermagneticmomentisobs ervedinthePd/Ni narrowanglechainfunctionalizedSWNT(6,6)thanthewidean glechainfunctionalized SWNT(10,0).Spindensitycalculationsshowedthatthemagne ticmomenttobemostly concentratedonNiatomsbutondifferentorbitalsdetermin edbytheinteractionsbetween PdandNiinthechains.Thestudyofhydrogeninteractionswi thchain-functionalized SWNTsshowtherearedifferentdegreesofchaingeometrychan gesonthetubesurfaces uponH 2 adsorption.TheresultsindicatethatNicanimprovethesta bilityofPdchainon tubesurface,aswellasincreasethehydrogenadsorptionen ergy.Itisfoundthatelectron densityofstatesdecreasedatFermilevelinthefunctional izedSWNT(6,6),andbandgap reopenedinthefunctionalizedSWNT(10,0),whichturnsamet allized(10,0)tubebackto semiconductor.Theseelectronicpropertychangescansign icantlyreducetheconductanceofthetubes,whichexplainsthereportedexperimenta lresultsonPdfunctionalized SWNTsinhydrogensensorapplications.Inaddition,weperfo rmH 2 interactionswith noncontinuousPdchain-functionalizedSWNT(10,0)inorder tofurtherclarifythesensingmechanism.WenotethatadiscretePdmonatomiccoatingi salsoabletometallize 113

PAGE 127

semiconductingSWNT.ByapplyingdifferentH 2 coverages,weconcludethatthelarge decreaseofelectricalconductanceuponH 2 adsorptionisduetothelling-upofPddstate, whichbringsitbelowFermilevel.AnexplorationofPdfullc oatingonSWNTindicatePd atomsareabletodistributeevenlyontheSWNTsurfacewithou tsignicantlyalteringthe structureofthetube.ThisshowsthatthePdfunctionalized SWNTsarehightlysuitedas hydrogensensingmaterials.9.2MajorContributionsThecontributionsofthedissertationtotheeldofsensorr esearcharemultifold.Itdevelopsafundamentalunderstandingofthesensingmaterialsan dunravelsthesensingmechanismofrecentlyproposedhydrogensensors.Thetheoretica lcalculationsfrommolecular simulationsinthisresearchwillnotonlybenettothedesi gnofnovelhydrogensensing materials,butalsoestablishesagoodplatformforthestud yofothergassensingmaterials. Thiswilleventuallyleadtoasuccessfulfabricationofhig hperformancebutlowcostgas sensors. Fromabroaderimpactperspective,thisdissertationcanhe lpimprovethequalityof humanlifethroughbetterinformationregardingthepollut antsandhazards.Inthearea ofnationalsecurity,thisresearchwillcontributetothed evelopmentofimprovedsensing capabilitytoguardagainstchemicalandbiologicalwarfar eagents. 9.3FutureWork 9.3.1SensorPoisoning Asaresultofconsiderableevidenceforhydrogengasinduce dsensorresponse,futurework shouldinvestigatehowtoprotectthesensorfrombeingpois onedbyharmfulspecies.This isbecauseinrealapplication,theenvironmentthatneedst obetestedisusuallyamulti 114

PAGE 128

componentgasmixture.Speciesotherthanhydrogenintheen vironmentmayinterfere withhydrogenuptakebyPdfunctionalizedSWNTs,thusadvers elyaffectingsensorperformance.ThereforetheinteractionsbetweenPdfunctiona lizedSWNTwithgasesthat frequentlyappearintheambientatmosphere,suchasCO,CH 4 ,SO 2 ,needtobestudied. Anadsorptionenergyofeachgasmoleculeonthefunctionali zedcarbonnanotubecanbe calculatedtodeterminethepoisoningeffectonthehydroge nsensor.Apossiblesolutionto thepoisoningphenomenonmaybealloyingPdwithambientgas activemetals. 9.3.2MultipurposeGasSensor ItisexpectedthatfunctionalizedSWNTscanbeusedasasenso rarraytodetectvarioustypesofgasessimultaneously[160].SWNTsfunctionaliz edbydifferentmetalscan formanarrayandthusfunctionasamulticomponentgasdetec tor.Bychoosingdifferent functionalmaterialsandcontrollingthecoatingamount,o necanmakethefunctionalized SWNTsexibleenoughtodetectawiderangeofmolecularspeci esandaswellasselectivetospecicmolecules.Hence,thefutureworkincludest hedesignofamultifunctional carbonnanotubesensorusing abinitio calculations. 9.3.3 Abinitio MDSimulations Althoughquantum-mechanical abinitio calculationsofelectronictotalenergyareextremelyusefultounderstandandtopredictcomplexchemica lreactions,itislimitedto zerotemperature. Abinitio MDtechniques[213]allowonetocalculateaccuratestructu ral anddynamicpropertiesatnitetemperaturebymeansofatom ictrajectoriesgeneratedby forcesobtaineddirectlyfromelectronicstructurecalcul ations,thereforenoempiricalmodelsareneeded. Abinitio MDhasbeensuccessfullyappliedtoawidevarietyofimporta nt problemsinphysicsandchemistry,aswellasinbiologyinth elastdecade.Innumerous studies,newphenomenahavebeenrevealedandmicroscopicm echanismselucidatedthat 115

PAGE 129

couldnothavebeenuncoveredbyusingempiricalmethods,le adingtonewinterpretations ofexperimentaldataandsuggestingnewexperimentstoperf orm[214].Therefore,another importantpartofthefutureworkistostudythesensingmate rialsandsensingreactions atnitetemperaturesusing abinitio MDtechniques.Thus,questionslikewhetherPd functionalizedSWNTsarestableatroomtemperatureorhight emperatures,willevendistributionofPdfullycoatedSWNTsobservedat0Kmaintainath ighertemperatures,and whatistheeffectoftemperaturetothesensorresponse,etc .canbeansweredthroughthese abinitioMDstudies. 116

PAGE 130

References [1]Stetter,J.R.,P.J.Hesketh,andG.W.Hunter.2006.Senso rs:Engineeringstructures andmaterialsfrommicrotonano. TheElectrochemicalSocietyInterface 15:66–69. [2]Christodes,C.,andA.Mandelis.1990.Solid-statesenso rsfortracehydrogengasdetection. JournalofAppliedPhysics 68:R1–R30. [3]Graber,N.,H.Ludi,andH.M.Widmer.1990.Theuseofchem icalsensorsin industry. SensorsandActuatorsB-Chemical 1:239–243. [4]North,D.C.1992.Aninvestigationofhydrogenasaninter nal-combustionfuel. InternationalJournalofHydrogenEnergy 17:509–512. [5]VanBlarigan,P.,andJ.O.Keller.1998.Ahydrogenfuelle dinternalcombustionenginedesignedforsinglespeed/poweroperation. InternationalJournalofHydrogen Energy 23:603–609. [6]Peschka,W.1998.Hydrogen:Thefuturecryofuelininter nalcombustionengines. InternationalJournalofHydrogenEnergy 23:27–43. [7]Favier,F.,E.C.Walter,M.P.Zach,T.Benter,andR.M.Penne r.2001.Hydrogen sensorsandswitchesfromelectrodepositedpalladiummeso wirearrays. Science 293:2227–2231. [8]Walter,E.C.,R.M.Penner,H.Liu,K.H.Ng,M.P.Zach,andF. Favier.2002.Sensorsfromelectrodepositedmetalnanowires. SurfaceandInterfaceAnalysis 34:409– 412. [9]Lundstrom,K.I.,M.S.Shivaraman,andC.M.Svensson.197 5.Hydrogen-sensitive Pd-gateMos-transistor. JournalofAppliedPhysics 46:3876–3881. [10]Lundstrom,I.,M.Armgarth,andL.G.Petersson.1989.P hysicswithcatalyticmetal gatechemicalsensors. CrcCriticalReviewsinSolidStateandMaterialsSciences 15:201–278. [11]Baranzahi,A.,A.L.Spetz,B.Andersson,andI.Lundstrom .1995.Gassensitiveeld-effectdevicesforhigh-temperatures. SensorsandActuatorsB-Chemical 26:165–169. 117

PAGE 131

[12]Anisimkin,V.I.,andE.Verona.1998.Newpropertiesof sawgassensing. IEEE TransactionsonUltrasonicsFerroelectricsandFrequency Control 45:1347–1354. [13]Jakubik,W.P.,M.W.Urbanczyk,S.Kochowski,andJ.Bodz enta.2002.Bilayer structureforhydrogendetectioninasurfaceacousticwave sensorsystem. Sensors andActuatorsB-Chemical 82:265–271. [14]Srinivasan,K.,S.Cular,V.R.Bhethanabotla,S.Lee,M.T. Harris,andJ.N.Culver. 2005.Palladiumnanoparticlecoatedtobaccomoasicviruss ensinglayerbasedsurfaceacousticwavehydrogensensors. In NanotechnologyandNanobiotechnology forSensorsI.The2005AnnualAICHEMeeting,Cincinnati,OH,7 4d. [15]Butler,M.A.,andD.S.Ginley.1988.Hydrogensensingwi thpalladium-coated opticalbers. JournalofAppliedPhysics 64:3706–3712. [16]Bond,G.C.1962.Catalysisbymetals.AcademicPress,NewY ork. [17]Anderson,J.R.1975.Thestructureofmetalliccatalysi s.AcademicPress,New York. [18]Cheng,Y.T.,Y.Li,D.Lisi,andW.M.Wang.1996.Preparat ionandcharacterization ofPd/Nithinlmsforhydrogensensing. SensorsandActuatorsB-Chemical 30:11– 16. [19]Armgarth,M.,D.Soderberg,andI.Lundstrom.1982.Pal ladiumandplatinumgate metal-oxide-semiconductorcapacitorsinhydrogenandoxy genmixtures. Applied PhysicsLetters 41:654–655. [20]Lewis,F.A.1967.Thepalladiumhydrogensystem.Acade micPress,London,New York. [21]DiMeoJr.,F.,andB.Chen.2000.MicrohotplatebasedH 2 gassensors. In Proceedingsofthe2000HydrogenProgramReview.U.S.DepartmentofE nergy,Golden, CO,VolumeII. [22]Kong,J.,M.G.Chapline,andH.J.Dai.2001.Functionali zedcarbonnanotubesfor molecularhydrogensensors. AdvancedMaterials 13:1384–1386. [23]Im,Y.,C.Lee,R.P.Vasquez,M.A.Bangar,N.V.Myung,E.J.M enke,R.M. Penner,andM.H.Yun.2006.InvestigationofasinglePdnano wireforuseasa hydrogensensor. Small 2:356–358. [24]Iijima,S.1991.Helicalmicrotubulesofgraphiticcar bon. Nature 354:56–58. [25]Iijima,S.,andT.Ichihashi.1993.Single-shellcarbo nnanotubesof1-nmdiameter. Nature 364:737–737. 118

PAGE 132

[26]Saito,R.,M.Fujita,G.Dresselhaus,andM.S.Dresselha us.1992.Electronicstructureofchiralgraphenetubules. AppliedPhysicsLetters 60:2204–2206. [27]Saito,R.,G.Dresselhaus,andM.S.Dresselhaus.1998.P hysicalpropertiesofcarbonnanotubes.ImperialCollegePress,London. [28]Kong,J.,N.R.Franklin,C.W.Zhou,M.G.Chapline,S.Peng, K.J.Cho,andH.J. Dai.2000.Nanotubemolecularwiresaschemicalsensors. Science 287:622–625. [29]Collins,P.G.,K.Bradley,M.Ishigami,andA.Zettl.2000 .Extremeoxygensensitivityofelectronicpropertiesofcarbonnanotubes. Science 287:1801–1804. [30]Dresselhaus,M.S.,G.Dresselhaus,andP.C.Eklund.199 6.Scienceoffullerenes andcarbonnanotubes.AcademicPress,SanDiego. [31]Dekker,C.1999.Carbonnanotubesasmolecularquantumwi res. PhysicsToday 52:22–28. [32]Treacy,M.M.J.,T.W.Ebbesen,andJ.M.Gibson.1996.Ex ceptionallyhigh Young'smodulusobservedforindividualcarbonnanotubes. Nature 381:678–680. [33]Wong,E.W.,P.E.Sheehan,andC.M.Lieber.1997.Nanobea mmechanics:Elasticity,strength,andtoughnessofnanorodsandnanotubes. Science 277:1971–1975. [34]Jhi,S.H.,S.G.Louie,andM.L.Cohen.2000.Electronicp ropertiesofoxidized carbonnanotubes. PhysicalReviewLetters 85:1710–1713. [35]Peng,S.,andK.J.Cho.2000.Chemicalcontrolofnanotube electronics. Nanotechnology 11:57–60. [36]Sun,C.Q.,Y.Wang,B.K.Tay,S.Li,H.Huang,andY.B.Zhang. 2002.Correlation betweenthemeltingpointofananosolidandthecohesiveene rgyofasurfaceatom. JournalofPhysicalChemistryB 106:10701–10705. [37]Xie,R.H.,J.Zhao,andQ.Rao.2004.Dopedcarbonnanotube s. Encyclopediaof nanoscienceandnanotechnology 2:505–535. [38]Sayago,I.,E.Terrado,E.Lafuente,M.C.Horrillo,W.K. Maser,A.M.Benito, R.Navarro,E.P.Urriolabeitia,M.T.Martinez,andJ.Gutiee rez.2005.Hydrogen sensorsbasedoncarbonnanotubesthinlms. SyntheticMetals 148:15–19. [39]Sippel-Oakley,J.,H.T.Wang,B.S.Kang,Z.C.Wu,F.Ren,A. G.Rinzler,and S.J.Pearton.2005.Carbonnanotubelmsforroomtemperatur ehydrogensensing. Nanotechnology 16:2218–2221. [40]Lu,Y.J.,J.Li,J.Han,H.T.Ng,C.Binder,C.Partridge,and M.Meyyappan.2004. Roomtemperaturemethanedetectionusingpalladiumloadeds ingle-walledcarbon nanotubesensors. ChemicalPhysicsLetters 391:344–348. 119

PAGE 133

[41]Frenkel,D.,andB.Smit.2002.Understandingmolecular simulation:Fromalgorithmstoapplications. 2 nd edition.AcademicPress,SanDiego. [42]Verlet,L.1967.Computer“experiments”onclassicalu ids.I.Thermodynamical propertiesofLennard-Jonesmolecules. PhysicalReview 159:98–103. [43]Allen,M.P.,andD.J.Tildesley.1989.Computersimulat ionofliquids.Oxford sciencepublications,ClarendonPress;OxfordUniversityP ress,OxfordEngland; NewYork. [44]Cramer,C.J.2004.Essentialsofcomputationalchemistr y:Theoriesandmodels. 2 nd edition.Wiley,Chichester,WestSussex,England;Hoboken, NJ. [45]Kittel,C.,andH.Kroemer.2000.Thermalphysics. 2 nd edition.W.H.Freemanand Co.,NewYork. [46]Berendsen,H.J.C.,J.P.M.Postma,W.F.Vangunsteren,A. Dinola,andJ.R.Haak. 1984.Molecular-dynamicswithcouplingtoanexternalbath JournalofChemical Physics 81:3684–3690. [47]Smith,W.,andT.R.Forester.1996.DL POLY2.0:Ageneral-purposeparallel moleculardynamicssimulationpackage. JournalofMolecularGraphics 14:136– 141. [48]Sutton,A.P.,andJ.Chen.1990.Long-rangeFinnisSincl airpotentials. PhilosophicalMagazineLetters 61:139–146. [49]Streett,W.B.,D.J.Tildesley,andG.Saville.1978.Mul tipletime-stepmethodsin molecular-dynamics. MolecularPhysics 35:639–648. [50]Ercolessi,F.,W.Andreoni,andE.Tosatti.1991.Melti ngofsmallgoldparticlesmechanismandsizeeffects. PhysicalReviewLetters 66:911–914. [51]Schmidt,M.,R.Kusche,W.Kronmuller,B.vonIssendorff, andH.Haberland.1997. Experimentaldeterminationofthemeltingpointandheatca pacityforafreecluster of139sodiumatoms. PhysicalReviewLetters 79:99–102. [52]Lai,S.L.,J.Y.Guo,V.Petrova,G.Ramanath,andL.H.All en.1996.Size-dependent meltingpropertiesofsmalltinparticles:Nanocalorimetr icmeasurements. Physical ReviewLetters 77:99–102. [53]Peters,K.F.,J.B.Cohen,andY.-W.Chung.1998.Meltingof Pbnanocrystals. PhysicalReviewB 57:13430–13438. [54]Couchman,P.R.1979.Lindemannhypothesisandthesizede pendenceofmelting temperatures.II. PhilosophicalMagazinea-PhysicsofCondensedMatterStruc ture DefectsandMechanicalProperties 40:637–643. 120

PAGE 134

[55]Borel,J.P.1981.Thermodynamicalsizeeffectandthest ructureofmetallicclusters. SurfaceScience 106:1–9. [56]Rey,C.,L.J.Gallego,J.Garciarodeja,J.A.Alonso,andM .P.Iniguez.1993. Molecular-dynamicsstudyofthebinding-energyandmeltin goftransition-metal clusters. PhysicalReviewB 48:8253–8262. [57]Longo,R.C.,C.Rey,andL.J.Gallego.2000.Moleculardynam icsstudyofthe meltingbehaviourofseven-atomclustersoffcctransition andnoblemetalsonthe (111)surfaceofthesamemetalusingtheembeddedatommodel SurfaceScience 459:L441–L445. [58]Li,T.X.,Y.L.Ji,S.W.Yu,andG.H.Wang.2000.Meltingp ropertiesofnoble metalclusters. SolidStateCommunications 116:547–550. [59]Shimizu,Y.,K.S.Ikeda,andS.Sawada.2001.Spontaneo usalloyinginbinarymetal microclusters:Amoleculardynamicsstudy. PhysicalReviewB 64:075412. [60]Huang,S.P.,andP.B.Balbuena.2002.Meltingofbimetall icCu-Ninanoclusters. JournalofPhysicalChemistryB 106:7225–7236. [61]Hansen,T.W.,J.B.Wagner,P.L.Hansen,S.Dahl,H.Topso e,andC.J.H.Jacobsen. 2001.Atomic-resolutioninsitutransmissionelectronmic roscopyofapromoterof aheterogeneouscatalyst. Science 294:1508–1510. [62]Kondo,Y.,andK.Takayanagi.2000.Synthesisandchara cterizationofhelicalmultishellgoldnanowires. Science 289:606–608. [63]Mikkelsen,A.,N.Skold,L.Ouattara,M.Borgstrom,J.N. Andersen,L.Samuelson, W.Seifert,andE.Lundgren.2004.Directimagingoftheatom icstructureinsidea nanowirebyscanningtunnellingmicroscopy. NatureMaterials 3:519–523. [64]Hendriksen,B.L.M.,andJ.W.M.Frenken.2002.COoxidati ononPt(110):Scanningtunnelingmicroscopyinsideahigh-pressureowreact or. PhysicalReview Letters 89:046101. [65]Wang,J.,H.F.M.Boelens,M.B.Thathagar,andG.Rothenber g.2004.Insitu spectroscopicanalysisofnanoclusterformation. Chemphyschem 5:93–98. [66]Helveg,S.,C.Lopez-Cartes,J.Sehested,P.L.Hansen,B.S .Clausen,J.R.RostrupNielsen,F.Abild-Pedersen,andJ.K.Norskov.2004.Atomic -scaleimagingofcarbonnanobregrowth. Nature 427:426–429. [67]Chushak,Y.G.,andL.S.Bartell.2001.Meltingandfreezi ngofgoldnanoclusters. JournalofPhysicalChemistryB 105:11605–11614. 121

PAGE 135

[68]Wang,L.,Y.N.Zhang,X.F.Bian,andY.Chen.2003.Melting ofcunanoclusters bymoleculardynamicssimulation. PhysicsLettersA 310:197–202. [69]Cleveland,C.L.,W.D.Luedtke,andU.Landman.1999.Melt ingofgoldclusters. PhysicalReviewB 60:5065–5077. [70]Valkealahti,S.,andM.Manninen.1992.Instabilityof cuboctahedralcopperclusters. PhysicalReviewB 45:9459–9462. [71]Gulseren,O.,F.Ercolessi,andE.Tosatti.1995.Preme ltingofthinwires. Physical ReviewB 51:7377–7380. [72]Liu,H.B.,J.A.Ascencio,M.Perez-Alvarez,andM.J.Yac aman.2001.Melting behaviorofnanometersizedgoldisomers. SurfaceScience 491:88–98. [73]Lee,Y.J.,E.K.Lee,S.Kim,andR.M.Nieminen.2001.Effe ctofpotentialenergy distributiononthemeltingofclusters. PhysicalReviewLetters 86:999–1002. [74]Wang,B.,G.Wang,X.Chen,andJ.Zhao.2002.Meltingbehav iorofultrathin titaniumnanowires. PhysicalReviewB 67:193403. [75]Schmid,G.,S.Emde,V.Maihack,W.MeyerZaika,andS.Pe schel.1996.Synthesis andcatalyticpropertiesoflargeligandstabilizedpallad iumclusters. Journalof MolecularCatalysisa-Chemical 107:95–104. [76]Blaser,H.U.,A.Indolese,A.Schnyder,H.Steiner,andM .Studer.2001.Supported palladiumcatalystsfornechemicalssynthesis. JournalofMolecularCatalysis a-Chemical 173:3–18. [77]Schmid,G.,M.Baumle,M.Geerkens,I.Helm,C.Osemann,an dT.Sawitowski. 1999.Currentandfutureapplicationsofnanoclusters. ChemicalSocietyReviews 28:179–185. [78]Volokitin,Y.,J.Sinzig,L.J.deJongh,G.Schmid,M.N. Vargaftik,andI.I.Moiseev. 1996.Quantum-sizeeffectsinthethermodynamicpropertie sofmetallicnanoparticles. Nature 384:621–623. [79]Westergren,J.,andS.Nordholm.2003.Meltingofpalla diumclusters-densityof statesdeterminationbyMonteCarlosimulation. ChemicalPhysics 290:189–209. [80]Foiles,S.M.,M.I.Baskes,andM.S.Daw.1986.Embeddedatom-methodfunctions forthefccmetalsCu,Ag,Au,Ni,Pd,Pt,andtheiralloys. PhysicalReviewB 33:7983–7991. [81]Ercolessi,F.,E.Tosatti,andM.Parrinello.1986.Au( 100)surfacereconstruction. PhysicalReviewLetters 57:719–722. 122

PAGE 136

[82]Tomanek,D.,A.A.Aligia,andC.A.Balseiro.1985.Calcula tionofelasticstrain andelectroniceffectsonsurfacesegregation. PhysicalReviewB 32:5051–5056. [83]Uppenbrink,J.,andD.J.Wales.1993.Structureanddyn amicsofmodelmetalclusters. JournalofChemicalPhysics 98:5720–5733. [84]Wales,D.J.,andL.J.Munro.1996.Changesofmorphology andcappingofmodel transitionmetalclusters. JournalofPhysicalChemistry 100:2053–2061. [85]Lloyd,L.D.,andR.L.Johnston.2000.Theoreticalanaly sisof17-19-atommetal clustersusingmany-bodypotentials. JournaloftheChemicalSociety-DaltonTransactions :307–316. [86]Nieminen,J.A.1995.Temperature-dependenceofsurfa cereconstructionsofAuon Pd(110). PhysicalReviewLetters 74:3856–3859. [87]Kaszkur,Z.A.,andB.Mierzwa.1998.Segregationinmode lpalladium-cobaltclusters. PhilosophicalMagazinea-PhysicsofCondensedMatterStruc tureDefectsand MechanicalProperties 77:781–800. [88]Lamas,E.J.,andP.B.Balbuena.2003.Adsorbateeffectso nstructureandshapeof supportednanoclusters:Amoleculardynamicsstudy. JournalofPhysicalChemistry B 107:11682–11689. [89]Allen,M.P.,andD.J.Tildesley.1989.Computersimulat ionofliquids.Clarendon Press;OxfordUniversityPress,Oxford;NewYork. [90]Glatter,O.,andO.Kratky.1982.SmallangleX-rayscat tering.AcademicPress, London;NewYork. [91]Miller,M.K.2000.Atomprobetomography:Analysisatt heatomiclevel.Kluwer Academic/PlenumPublishers,NewYork. [92]Reiss,H.,P.Mirabel,andR.L.Whetten.1988.Capillarityt heoryforthecoexistence ofliquidandsolidclusters. JournalofPhysicalChemistry 92:7241–7246. [93]Rethfeld,B.,K.Sokolowski-Tinten,andD.vonderLinde. 2002.Ultrafastthermalmeltingoflaser-excitedsolidsbyhomogeneousnucleat ion. PhysicalReviewB 65:092103. [94]Kofman,R.,P.Cheyssac,A.Aouaj,Y.Lereah,G.Deutscher ,T.Bendavid,J.M. Penisson,andA.Bourret.1994.Surfacemeltingenhancedbyc urvatureeffects. SurfaceScience 303:231–246. [95]Chushak,Y.G.,andL.S.Bartell.2003.FreezingofNi-Alb imetallicnanoclusters incomputersimulations. JournalofPhysicalChemistryB 107:3747–3751. 123

PAGE 137

[96]Qi,Y.,T.Cagin,W.L.Johnson,andW.A.Goddard.2001.Me ltingandcrystallizationinNinanoclusters:Themesoscaleregime. JournalofChemicalPhysics 115:385–394. [97]Calvo,F.,andF.Spiegelmann.2003.Mechanismsofphase transitionsinsodium clusters:Frommoleculartobulkbehavior. JournalofChemicalPhysics 112:2888– 2908. [98]Vanselow,R.,andR.Howe.1988.Chemistryandphysicsofso lidsurfacesVII. Springer-Verlag,Berlin;NewYork. [99]Iida,T.,andR.I.L.Guthrie.1988.Thephysicalpropert iesofliquidmetals.Clarendon,Oxford. [100]Echt,O.,K.Sattler,andE.Recknagel.1981.Magicnumb ersforspherepackingsexperimental-vericationinfreexenonclusters. PhysicalReviewLetters 47:1121– 1124. [101]Steinhardt,P.J.,D.R.Nelson,andM.Ronchetti.1983.Bo nd-orientationalorderin liquidsandglasses. PhysicalReviewB 28:784–805. [102]Sakurai,J.J.,andS.F.Tuan.1994.Modernquantummec hanics.Rev.edition. Addison-WesleyPub.Co.,Reading,Mass. [103]Wang,Y.T.,andC.Dellago.2003.Structuralandmorpho logicaltransitionsingold nanorods:Acomputersimulationstudy. JournalofPhysicalChemistryB 107:9214– 9219. [104]Jose-Yacaman,M.,R.Herrera,A.Gomez,andS.Tehuacan ero.1990.Decagonal andhexagonalstructuresinsmallgoldparticles. SurfaceScience 237:248–256. [105]Hendy,S.C.,andB.D.Hall.2001.Molecular-dynamicssi mulationsofleadclusters. PhysicalReviewB 64:085425. [106]Buffat,P.,andJ.P.Borel.1976.Sizeeffectonmeltingt emperatureofgoldparticles. PhysicalReviewA 13:2287–2298. [107]Castro,T.,R.Reifenberger,E.Choi,andR.P.Andres.1990. Size-dependentmeltingtemperatureofindividualnanometer-sizedmetalliccl usters. PhysicalReviewB 42:8548–8556. [108]Dash,J.G.1999.Historyofthesearchforcontinuousm elting. ReviewsofModern Physics 71:17371743. [109]Pawlow,P.1909.Meltingpointdependenceonthesurfa ceenergyofasolidbody. ZeitschriftfuerPhysikalischeChemie 65:1–35. 124

PAGE 138

[110]Pawlow,P.1909.Meltingpointdependenceonthesurfa ceenergyofasolidbody. ZeitschriftfuerPhysikalischeChemie 65:545–548. [111]Wronski,C.R.M.1967.Thesizedependenceofthemeltingp ointofsmallparticles oftin. BritishJournalofAppliedPhysics 18:1731–1737. [112]Vaneet,R.R.,andJ.M.Mochel.1995.Thermodynamicsof meltingandfreezing insmallparticles. SurfaceScience 341:40–50. [113]Sakai,H.1996.Surface-inducedmeltingofsmallpart icles. SurfaceScience 351:285–291. [114]Wautelet,M.1991.Estimationofthevariationofthem eltingtemperaturewiththe sizeofsmallparticles,onthebasisofasurface-phononins tabilitymodel. Journal ofPhysicsD-AppliedPhysics 24:343–346. [115]Nanda,K.K.,S.N.Sahu,andS.N.Behera.2002.Liquid-d ropmodelforthesizedependentmeltingoflow-dimensionalsystems. PhysicalReviewA 66:013208. [116]Miao,L.,V.R.Bhethanabotla,andB.Joseph.2005.Meltin gofPdclustersand nanowires:Acomparisonstudyusingmoleculardynamicssim ulation. Physical ReviewB 72:134109. [117]Schmidt,M.,R.Kusche,B.vonIssendorff,andH.Haberla nd.1998.Irregularvariationsinthemeltingpointofsize-selectedatomiccluster s. Nature 393:238–240. [118]Savoia,D.,C.Trombini,A.Umanironchi,andG.Verardo .1981.Activemetals frompotassium-graphite-palladium-graphiteascatalyst inthehydrogenationof nitro-compounds,alkenes,andalkynes. JournaloftheChemicalSociety-Chemical Communications :540–541. [119]Farkas,G.,L.Hegedus,A.Tungler,T.Mathe,J.L.Figu eiredo,andM.Freitas.2000. Effectofcarbonsupportpropertiesonenantioselectivehy drogenationofisophorone overpalladiumcatalystsmodiedwith(-)-dihydroapovinc aminicacidethylester. JournalofMolecularCatalysisa-Chemical 153:215–219. [120]Bazin,D.2002.Solidstateconceptstounderstandcata lysisusingnanoscalemetallic particles. TopicsinCatalysis 18:79–84. [121]Huang,S.P.,D.S.Mainardi,andP.B.Balbuena.2003.Str uctureanddynamicsof graphite-supportedbimetallicnanoclusters. SurfaceScience 545:163–179. [122]Bardotti,L.,P.Jensen,A.Hoareau,M.Treilleux,andB. Cabaud.1995.Experimentalobservationoffastdiffusionoflargeantimonyclus tersongraphitesurfaces. PhysicalReviewLetters 74:4694–4697. 125

PAGE 139

[123]Tomanek,D.,andW.Zhong.1991.Palladium-graphitei nteractionpotentialsbased on1st-principlescalculations. PhysicalReviewB 43:12623–12625. [124]Bhethanabotla,V.R.,andW.A.Steele.1990.Computer-si mulationstudyofmelting indenseoxygenlayersongraphite. PhysicalReviewB 41:9480–9487. [125]Agrawal,P.M.,B.M.Rice,andD.L.Thompson.2002.Predi ctingtrendsinrate parametersforself-diffusiononfccmetalsurfaces. SurfaceScience 515:21–35. [126]Ko,E.,M.Jain,andJ.R.Chelikowsky.2002.Firstprinci plessimulationsofsigefor theliquidandamorphousstates. JournalofChemicalPhysics 117:3476–3483. [127]Hohenberg,P.,andW.Kohn.1964.Inhomogeneouselect rongas. PhysicalReview 136:B864–71. [128]Kohn,W.,andL.J.Sham.1965.Self-consistentequati onsincludingexchangeand correlationeffects. PhysicalReview 140:A1133–38. [129]Wigner,E.1938.Thetransition-statemethod. TransactionsoftheFaradaySociety 34:29–41. [130]Ceperley,D.1978.Ground-stateofthefermionone-com ponentplasma-MonteCarlostudyin2and3dimensions. PhysicalReviewB 18:3126–3138. [131]Ceperley,D.M.,andB.J.Alder.1980.Ground-stateofth eelectron-gasbyastochasticmethod. PhysicalReviewLetters 45:566–569. [132]Becke,A.D.1988.Density-functionalexchange-energ yapproximationwithcorrect asymptotic-behavior. PhysicalReviewA 38:3098–3100. [133]Becke,A.D.1986.Densityfunctionalcalculationsofm olecular-bondenergies. JournalofChemicalPhysics 84:4524–4529. [134]Perdew,J.P.1986.Density-functionalapproximatio nforthecorrelation-energyof theinhomogeneouselectron-gas. PhysicalReviewB 33:8822–8824. [135]Wang,Y.,andJ.P.Perdew.1991.Correlationholeofthe spin-polarizedelectrongas,withexactsmall-wave-vectorandhigh-densityscalin g. PhysicalReviewB 44:13298–13307. [136]Perdew,J.P.,J.A.Chevary,S.H.Vosko,K.A.Jackson,M .R.Pederson,D.J.Singh, andC.Fiolhais.1992.Atoms,molecules,solids,andsurface s-applicationsofthe generalizedgradientapproximationforexchangeandcorre lation. PhysicalReview B 46:6671–6687. [137]Perdew,J.P.,K.Burke,andM.Ernzerhof.1996.General izedgradientapproximationmadesimple. PhysicalReviewLetters 77:3865–3868. 126

PAGE 140

[138]Lee,C.T.,W.T.Yang,andR.G.Parr.1988.Developmentof theColle-Salvetti correlation-energyformulaintoafunctionaloftheelectr on-density. PhysicalReview B 37:785–789. [139]Becke,A.D.1996.Density-functionalthermochemistr y.4.Anewdynamicalcorrelationfunctionalandimplicationsforexact-exchangemix ing. JournalofChemical Physics 104:1040–1046. [140]Kohn,W.1999.Anessayoncondensedmatterphysicsint hetwentiethcentury. ReviewsofModernPhysics 71:S59–S77. [141]SanchezPortal,D.,E.Artacho,andJ.M.Soler.1996.A nalysisofatomicorbital basissetsfromtheprojectionofplane-waveresults. JournalofPhysics-Condensed Matter 8:3859–3880. [142]Ashcroft,N.W.,andN.D.Mermin.1964.Solidstatephy sics.HoltRinehartand Winston,NewYork. [143]Phillips,J.C.1958.Energy-bandinterpolationschem ebasedonapseudopotential. PhysicalReview 1:685–695. [144]Yin,M.T.,andM.L.Cohen.1982.Theoryof abinitio pseudopotentialcalculations. PhysicalReviewB 25:7403–7412. [145]Yin,M.T.,andM.L.Cohen.1982.Theoryofstaticstruct ural-properties,crystal stability,andphase-transformations-applicationtoSia ndGe. PhysicalReviewB 26:5668–5687. [146]Kleinman,L.,andD.M.Bylander.1982.Efcaciousform formodelpseudopotentials. PhysicalReviewLetters 48:1425–1428. [147]Vanderbilt,D.1990.Softself-consistentpseudopot entialsinageneralizedeigenvalueformalism. PhysicalReviewB 41:7892–7895. [148]Kresse,G.,andJ.Hafner.1993. Abinitio molecular-dynamicsforliquid-metals. PhysicalReviewB 47:558–561. [149]Kresse,G.,andJ.Hafner.1994. Abinitio molecular-dynamicssimulationofthe liquid-metalamorphous-semiconductortransitioningerm anium. PhysicalReviewB 49:14251. [150]Kresse,G.,andJ.Furthmuller.1996.Efciencyof ab initio totalenergycalculationsformetalsandsemiconductorsusingaplane-wavebasi sset. Computational MaterialsScience 6:15–50. [151]Kresse,G.,andJ.Furthmuller.1996.Efcientiterat iveschemesfor abinitio totalenergycalculationsusingaplane-wavebasisset. PhysicalReviewB 54:11169– 11186. 127

PAGE 141

[152]Ciraci,S.,S.Dag,T.Yildirim,O.Gulseren,andR.T.Sen ger.2004.Functionalized carbonnanotubesanddeviceapplications. JournalofPhysics-CondensedMatter 16:R901–R960. [153]Durgun,E.,S.Dag,V.M.K.Bagci,O.Gulseren,T.Yildir im,andS.Ciraci.2003. Systematicstudyofadsorptionofsingleatomsonacarbonna notube. Physical ReviewB 67:201401. [154]Durgun,E.,S.Dag,S.Ciraci,andO.Gulseren.2004.Ene rgeticsandelectronic structuresofindividualatomsadsorbedoncarbonnanotube s. JournalofPhysical ChemistryB 108:575–582. [155]Yang,C.K.,J.J.Zhao,andJ.P.Lu.2002.Bindingenergie sandelectronicstructures ofadsorbedtitaniumchainsoncarbonnanotubes. PhysicalReviewB 66:041403. [156]Bagci,V.M.K.,O.Gulseren,T.Yildirim,Z.Gedik,andS .Ciraci.2002.Metal nanoringandtubeformationoncarbonnanotubes. PhysicalReviewB 66:045409. [157]Singh,D.J.1994.Planewaves,pseudopotentials,and theLAPWmethod.Kluwer AcademicPublishers,Boston. [158]Payne,M.C.,M.P.Teter,D.C.Allan,T.A.Arias,andJ.D. Joannopoulos.1992. Iterativeminimizationtechniquesfor abinitio total-energycalculations-moleculardynamicsandconjugategradients. ReviewsofModernPhysics 64:1045–1097. [159]Lee,E.C.,Y.S.Kim,Y.G.Jin,andK.J.Chang.2002.First -principlesstudyof hydrogenadsorptiononcarbonnanotubesurfaces. PhysicalReviewB 66:073415. [160]Peng,S.,andK.J.Cho.2003. Abinitio studyofdopedcarbonnanotubesensors. NanoLetters 3:513–517. [161]Dag,S.,Y.Ozturk,S.Ciraci,andT.Yildirim.2005.Ads orptionanddissociationof hydrogenmoleculesonbareandfunctionalizedcarbonnanot ubes. PhysicalReview B 72:155404. [162]Jakubik,W.P.,M.W.Urbanczyk,S.Kochowski,andJ.Bod zenta.2003.Palladium andphthalocyaninebilayerlmsforhydrogendetectionina surfaceacousticwave sensorsystem. SensorsandActuatorsB-Chemical 96:321–328. [163]Smit,R.H.M.,C.Untiedt,A.I.Yanson,andJ.M.vanRuiten beek.2001.Commonoriginforsurfacereconstructionandtheformationofc hainsofmetalatoms. PhysicalReviewLetters 87:266102. [164]Ohnishi,H.,Y.Kondo,andK.Takayanagi.1998.Quanti zedconductancethrough individualrowsofsuspendedgoldatoms. Nature 395:780–783. 128

PAGE 142

[165]Yanson,A.I.,G.R.Bollinger,H.E.vandenBrom,N.Agrait ,andJ.M.vanRuitenbeek.1998.Formationandmanipulationofametallicwireof singlegoldatoms. Nature 395:783–785. [166]Sen,P.,S.Ciraci,A.Buldum,andI.P.Batra.2001.Struct ureofaluminumatomic chains. PhysicalReviewB 64:195420. [167]Sanchez-Portal,D.,E.Artacho,J.Junquera,P.Ordej on,A.Garcia,andJ.M.Soler. 1999.Stiffmonatomicgoldwireswithaspinningzigzaggeom etry. PhysicalReview Letters 83:3884–3887. [168]Bahn,S.R.,andK.W.Jacobsen.2001.Chainformationofme talatoms. Physical ReviewLetters 87:266101. [169]Geng,W.T.,andK.S.Kim.2003.Linearmonatomicwires stabilizedbyalloying: Abinitio densityfunctionalcalculations. PhysicalReviewB 67:233403. [170]Nilius,N.,T.M.Wallis,andW.Ho.2004.Buildingalloy sfromsingleatoms:Au-Pd chainsonNiAl(110). JournalofPhysicalChemistryB 108:14616–14619. [171]Zhang,Y.,N.W.Franklin,R.J.Chen,andH.J.Dai.2000.M etalcoatingonsuspendedcarbonnanotubesanditsimplicationtometal-tubei nteraction. Chemical PhysicsLetters 331:35–41. [172]Marinas,J.M.,J.M.Campelo,andD.Luna.1986.Newsupp ortedmetallicnickel systems. StudiesinSurfaceScienceandCatalysis 27:411–457. [173]Hughes,R.C.,W.T.Schubert,andR.J.Buss.1995.Solid-st atehydrogensensorsusingpalladium-nickelalloys-effectofalloycompos itiononsensorresponse. JournaloftheElectrochemicalSociety 142:249–254. [174]Thomas,R.C.,andR.C.Hughes.1997.Sensorsfordetecting molecularhydrogen basedonPdmetalalloys. JournaloftheElectrochemicalSociety 144:3245–3249. [175]Raybaud,P.,G.Kresse,J.Hafner,andH.Toulhoat.1997 Abinitio densityfunctionalstudiesoftransition-metalsulphides:I.Crystalst ructureandcohesiveproperties. JournalofPhysics-CondensedMatter 9:11085–11106. [176]Monkhorst,H.J.,andJ.D.Pack.1976.Specialpointsf orBrillouin-zoneintegrations. PhysicalReviewB 13:5188–5192. [177]Yagi,Y.,T.M.Briere,M.H.F.Sluiter,V.Kumar,A.A.Fa rajian,andY.Kawazoe.2004.Stablegeometriesandmagneticpropertiesofsin gle-walledcarbonnanotubesdopedwith3dtransitionmetals:Arst-principless tudy. PhysicalReviewB 69:075414. [178]Peierls,R.E.1964.Quantumtheoryofsolids.Clarendon Press,Oxford. 129

PAGE 143

[179]Weinert,M.,E.Wimmer,andA.J.Freeman.1982.Totalenergyall-electrondensity functionalmethodforbulksolidsandsurfaces. PhysicalReviewB 26:4571–4578. [180]Blaha,P.,K.Schwarz,G.Madsen,D.Kvasnicka,andJ.Lu itz.2001.WIEN2k: AnAugementedPlaneWavePlusLocalOrbitalProgramforCalcu latingCrystal Properties.ViennaUniversityofTechnology,Vienna,Aust ria. [181]Miao,L.,V.R.Bhethanabotla,andB.Joseph.inprogress2 006. [182]Reich,S.,C.Thomsen,andP.Ordejon.2002.Electronicb andstructureofisolated andbundledcarbonnanotubes. PhysicalReviewB 65:155411. [183]Gulseren,O.,T.Yildirim,andS.Ciraci.2002.Systema tic abinitio studyofcurvatureeffectsincarbonnanotubes. PhysicalReviewB 65:153405. [184]Henkelman,G.,A.Arnaldsson,andH.Jonsson.2006.Af astandrobustalgorithmforbaderdecompositionofchargedensity. ComputatioinalMaterialsScience 36:254–360. [185]Zhao,J.J.,A.Buldum,J.Han,andJ.P.Lu.2002.Gasmole culeadsorptionin carbonnanotubesandnanotubebundles. Nanotechnology 13:195–200. [186]Tada,K.,S.Furuya,andK.Watanabe.2001. Abinitio studyofhydrogenadsorption tosingle-walledcarbonnanotubes. PhysicalReviewB 63:155405. [187]Dillon,A.C.,K.M.Jones,T.A.Bekkedahl,C.H.Kiang,D.S .Bethune,and M.J.Heben.1997.Storageofhydrogeninsingle-walledcarb onnanotubes. Nature 386:377–379. [188]Ahn,C.C.,Y.Ye,B.V.Ratnakumar,C.Witham,R.C.Bowman,andB.F ultz.1998. Hydrogendesorptionandadsorptionmeasurementsongraphi tenanobers. Applied PhysicsLetters 73:3378–3380. [189]Modi,A.,N.Koratkar,E.Lass,B.Q.Wei,andP.M.Ajayan .2003.Miniaturized gasionizationsensorsusingcarbonnanotubes. Nature 424:171–174. [190]Han,S.S.,andH.M.Lee.2004.Adsorptionpropertieso fhydrogenon(10,0)singlewalledcarbonnanotubethroughdensityfunctionaltheory. Carbon 42:2169–2177. [191]Balasubramanian,K.,P.Y.Feng,andM.Z.Liao.1988.El ectronicstatesandpotentialenergysurfacesofPdH 2 :ComparisonwithPtH 2 JournalofChemicalPhysics 88:6955–6961. [192]Conrad,H.,G.Ertl,andE.E.Latta.1974.Adsorptionof hydrogenonpalladium singlecrystalsurfaces. surfacescience 41:435–446. 130

PAGE 144

[193]Wilke,S.,D.Hennig,andR.Lober.1994. Ab initio calculationsofhydrogenadsorptionon(100)surfacesofpalladiumandrhodium. PhysicalReviewB 50:2548– 2560. [194]Behm,R.J.,K.Christmann,andG.Ertl.1980.Adsorptiono fhydrogenonPd(100). SurfaceScience 99:320–340. [195]Nowick,A.S.,andJ.J.Burton.1975.Diffusioninsolid s.AcademicPress,New York. [196]Christmann,K.,O.Schober,G.Ertl,andM.Neumann.197 3.Adsorptionofhydrogenonnickelsinglecrystalsurfaces. Thejournalofchemicalphysics 60:4528–4540. [197]Madix,R.J.,G.Ertl,andK.Christmann.1979.Pre-expon entialfactorsforhydrogen desorptionfromsingle-crystalmetal-surfaces. ChemicalPhysicsLetters 62:38–41. [198]Landolt,M.,andM.Campagna.1977.Demagnetizationof Ni(100)surfacebyhydrogenadsorption. PhysicalReviewLetters 39:568–570. [199]Muscat,J.P.,andD.M.Newns.1979.Natureofthebondi nhydrogenchemisorption onni,pd,andpt. PhysicalReviewLetters 43:2025–2028. [200]Wong,Y.M.,W.P.Kang,J.L.Davidson,A.Wisitsora-at ,andK.L.Soh.2003.A novelmicroelectronicgassensorutilizingcarbonnanotub esforhydrogengasdetection. SensorsandActuatorsB-Chemical 93:327–332. [201]Star,A.,T.R.Han,V.Joshi,J.C.P.Gabriel,andG.Grune r.2004.Nanoelectronic carbondioxidesensors. AdvancedMaterials 16:2049–2052. [202]Liang,Y.X.,Y.J.Chen,andT.H.Wang.2004.Low-resist ancegassensorsfabricatedfrommultiwalledcarbonnanotubescoatedwithathint inoxidelayer. Applied PhysicsLetters 85:666–668. [203]Bekyarova,E.,M.Davis,T.Burch,M.E.Itkis,B.Zhao,S.S unshine,andR.C.Haddon.2004.Chemicallyfunctionalizedsingle-walledcarbon nanotubesasammonia sensors. JournalofPhysicalChemistryB 108:19717–19720. [204]Durgun,E.,S.Dag,andS.Ciraci.2004.Theoreticalstu dyofGa-basednanowires andtheinteractionofGawithsingle-wallcarbonnanotubes PhysicalReviewB 70:155305. [205]Dag,S.,E.Durgun,andS.Ciraci.2004.High-conductin gmagneticnanowires obtainedfromuniformtitanium-coveredcarbonnanotubes. PhysicalReviewB 69:121407. [206]Peng,S.,andK.Cho.2002.Nanoelectromechanicsofsem iconductingcarbon nanotube. JournalofAppliedMechanics-TransactionsoftheAsme 69:451–453. 131

PAGE 145

[207]Sampedro,B.,P.Crespo,A.Hernando,R.Litran,J.C.S.Lop ez,C.L.Cartes, A.Fernandez,J.Ramirez,J.G.Calbet,andM.Vallet.2003.Fer romagnetisminfcc twinned2.4nmsizePdnanoparticles. PhysicalReviewLetters 91:237203. [208]Alefeld,G.,andJ.Vlkl.1978.Hydrogeninmetals.Top icsinappliedphysics;v. 28-29,Springer-Verlag,Berlin;NewYork. [209]Schlapbach,L.,andJ.P.Burger.1982.AnewXPSUPSstud yoftheelectronicstructureofPdH0.6. JournalDePhysiqueLettres 43:L273–L276. [210]Bennett,P.A.,andJ.C.Fuggle.1982.Electronic-struc tureandsurfacekinetics ofpalladiumhydridestudiedwithX-rayphotoelectron-spe ctroscopyandelectronenergy-lossspectroscopy. PhysicalReviewB 26:6030–6039. [211]Chan,C.T.,andS.G.Louie.1983.Self-consistentpseud opotentialcalculationof theelectronic-structureofPdHandPd 4 H. PhysicalReviewB 27:3325–3337. [212]Imry,Y.,andR.Landauer.1999.Conductanceviewedastr ansmission. Reviewsof ModernPhysics 71:S306–S312. [213]Car,R.,andM.Parrinello.1985.Uniedapproachformol ecular-dynamicsand density-functionaltheory. PhysicalReviewLetters 55:2471–2474. [214]Iftimie,R.,P.Minary,andM.E.Tuckerman.2005. Abinitio moleculardynamics:Concepts,recentdevelopments,andfuturetrends. ProceedingsoftheNational AcademyofSciencesoftheUnitedStatesofAmerica 102:6654–6659. 132

PAGE 146

Appendices 133

PAGE 147

AppendixA:DL POLYPrograms DL POLY 2requiresveinputlesnamedCONTROL,CONFIG,FIELD,TABLEan d REVOLD.Therstthreelesaremandatory,whileTABLEisusedo nlytoinputcertain kindsofpairpotential,andisnotalwaysrequired.REVOLDis requiredonlyifthejob representsacontinuationofapreviousjob.Inthefollowin gsectionsIdescribetheform andcontentoftheselesusedinthePdnanoclustersimulati ons. A.1TheInputFiles A.1.1TheCONTROLFile CONTROLledenesthecontrolvariablesforrunningaDL POLY 2job.TheCONTROLleissmallandeasytocheckvisually.AnexampleCONTRO LleforafccPd nanoclusterappearsbelow.DL_POLYCONTROLFILE:Pdnanoclustertemperature300.00pressure0.0000ensemblenvtber0.4integratorleapfrogsteps600000equilibration400000scale10print100stack10stats10rdf10timestep0.001cutoff6.878delrwidth1.000noelectrostaticszdentraj4000001001printrdf 134

PAGE 148

AppendixA(Continued)jobtime100000.00closetime500.00finishThemeaningofdirectiveslistedthisCONTROLleareasfollo ws: DL POLYCONTROLFILE:Thislineisaheadertoaididenticationo fthele. Thislineislimitedto80characters. temperature:Settherequiredsimulationtemperatureto30 0K pressure:Settherequiredsimulationpressureto0katm ensemblenvtber:SetNVTensemblewiththeBerendsenthermos tatwithcoupling timeconstant0.4 integrator:Selectleapfrogintegrationalgorithm steps:Runsimulationfor600,000timesteps equilibration:Equilibratesimulationforrst400,000ti mesteps scale:Rescaleatomicvelocitiesevery10timestepsduringe quilibration print:Printsystemdataevery100timesteps stack:Setrollingaveragestackto10timesteps stats:Accumulatestatisticsdataevery10timesteps rdf:Calculateradialdistributionfunctionsatevery10tim esteps timestep:Setsimulationtimestepto0.001ps 135

PAGE 149

AppendixA(Continued) cutoff:Setrequiredforcescutoffto6.8778 A delrwidth:SetVerletneighborlistshellwidthto0.55 A zden:Calculatethe z -densityprole traj:WritecoordinatesandvelocitiesoutputsintoHISTORY lestartingfromthe indicatedtimestep(400,000)atintervalof100timesteps printrdf:Printradialdistributionfunction jobtime:Settotaltimeallowedforthisjobto100,000ps closetime:SetthetimeDL POLYrequirestowriteandclosedatalesto500s nish:ClosetheCONTROLle A.1.2TheCONFIGFile TheCONFIGlecontainsthedimensionsoftheunitcell,theke yforperiodicboundary conditionsandtheatomiclabels,coordinates,velocities andforces.TheinitialCONFIG leofthesimulatedPdnanoclusterisgenernatedbytheFORT RANprogram.Boththe programandCONFIGleareshownbelow.CTHISPROGRAMGENERATEASPHERICALPdCLUSTERWITHACCUTOFFRADIUSOFRcCN--TOTALNUMBEROFPDATOMSCNC--NUMBEROFUNITCELLS INTEGERN,NCPARAMETER(NC=11,N=4 NC3) REALRX(N),RY(N),RZ(N)REALCELL1,CELL2 136

PAGE 150

AppendixA(Continued) REALRc,Ra,RsumNO=6OPEN(NO,FILE='OUTPUT') CCALCULATETHESIDEOFTHEUNITCELL CELL=3.8907CELL2=0.75 CELL CELL1=0.25 CELL CSUBLATTICEA RX(1)=CELL1RY(1)=CELL1RZ(1)=CELL1 CSUBLATTICEB RX(2)=CELL2RY(2)=CELL2RZ(2)=CELL1 CSUBLATTICEC RX(3)=CELL1RY(3)=CELL2RZ(3)=CELL2 CSUBLATTICED RX(4)=CELL2RY(4)=CELL1RZ(4)=CELL2 CCONSTRUCTTHELATTICEFROMTHEUNITCELL 137

PAGE 151

AppendixA(Continued) M=0DO99IZ=1,NC DO98IY=1,NC DO97IX=1,NC DO96IREF=1,4 RX(IREF+M)=RX(IREF)+CELL REAL(IX-1) RY(IREF+M)=RY(IREF)+CELL REAL(IY-1) RZ(IREF+M)=RZ(IREF)+CELL REAL(IZ-1) 96CONTINUE M=M+4 97CONTINUE98CONTINUE99CONTINUECSHIFTCENTREOFBOXTOTHEORIGIN S=0R=0Rsum=0DO100I=1,NRX(I)=RX(I)-0.5 CELL REAL(NC) RY(I)=RY(I)-0.5 CELL REAL(NC) RZ(I)=RZ(I)-0.5 CELL REAL(NC) 100CONTINUE Rc=13.2Do120J=1,N Ra=SQRT(RX(J)2+RY(J)2+RZ(J)2) IF(Ra.lt.Rc)THEN S=S+1R=R+(RX(J)2+RY(J)2+RZ(J)2) PRINT ,'Pd','',S,'','46' WRITE(6,110)RX(J),RY(J),RZ(J)Rsum=Rsum+(RX(J)2+RY(J)2+RZ(J)2) 110FORMAT(1x,F19.15,1X,F19.15,1X,F19.15) ENDIF 138

PAGE 152

AppendixA(Continued)120CONTINUE END DL_POLYCONFIGfile:Pdnanocluster 00 Pd146 -2.918099880218506-4.863500118255615-8.754300117492 676 Pd246 -0.972700595855713-6.808899879455566-8.754300117492 676 Pd346 0.972699642181396-4.863500118255615-8.7543001174926 76 Pd446 2.918099880218506-6.808899879455566-8.7543001174926 76 Pd546 4.863500118255615-4.863500118255615-8.7543001174926 76 Pd646 -6.808899879455566-0.972700595855713-8.754300117492 676 Pd746 -4.863500118255615-2.918099880218506-8.754300117492 676 Pd846 -2.918099880218506-2.918099880218506-10.69970035552 9785 Pd946 -0.972700595855713-0.972700595855713-10.69970035552 9785 Pd1046 -2.918099880218506-0.972700595855713-8.754300117492 676 Pd1146 -0.972700595855713-2.918099880218506-8.754300117492 676 Pd1246 0.972699642181396-2.918099880218506-10.699700355529 785 Pd1346 2.918099880218506-0.972700595855713-10.699700355529 785 Pd1446 0.972699642181396-0.972700595855713-8.7543001174926 76 Pd1546 2.918099880218506-2.918099880218506-8.7543001174926 76 Pd1646 139

PAGE 153

AppendixA(Continued) 4.863500118255615-0.972700595855713-8.7543001174926 76 Pd1746 6.808900356292725-2.918099880218506-8.7543001174926 76 Pd1846 -6.8088998794555662.918099880218506-8.7543001174926 76 Pd1946 -4.8635001182556150.972699642181396-8.7543001174926 76 Pd2046 -2.9180998802185060.972699642181396-10.699700355529 785 Pd2146 -0.9727005958557132.918099880218506-10.699700355529 785 Pd2246 -2.9180998802185062.918099880218506-8.7543001174926 76 Pd2346 -0.9727005958557130.972699642181396-8.7543001174926 76 Pd2446 0.9726996421813960.972699642181396-10.6997003555297 85 Pd2546 2.9180998802185062.918099880218506-10.6997003555297 85 Pd2646 0.9726996421813962.918099880218506-8.75430011749267 6 Pd2746 2.9180998802185060.972699642181396-8.75430011749267 6 Pd2846 4.8635001182556152.918099880218506-8.75430011749267 6 Pd2946 6.8089003562927250.972699642181396-8.75430011749267 6 Pd3046 -4.8635001182556154.863500118255615-8.7543001174926 76 Pd3146 -2.9180998802185066.808900356292725-8.7543001174926 76 Pd3246 -0.9727005958557134.863500118255615-8.7543001174926 76 Pd3346 0.9726996421813966.808900356292725-8.75430011749267 6 Pd3446 140

PAGE 154

AppendixA(Continued) 2.9180998802185064.863500118255615-8.75430011749267 6 Pd3546 -0.972700595855713-8.754300117492676-6.808899879455 566 Pd3646 -2.918099880218506-8.754300117492676-4.863500118255 615 Pd3746 2.918099880218506-8.754300117492676-6.8088998794555 66 Pd3846 0.972699642181396-8.754300117492676-4.8635001182556 15 Pd3946 4.863500118255615-8.754300117492676-4.8635001182556 15 Pd4046 -4.863500118255615-4.863500118255615-6.808899879455 566 Pd4146 -6.808899879455566-4.863500118255615-4.863500118255 615 Pd4246 -4.863500118255615-6.808899879455566-4.863500118255 615 Pd4346 -2.918099880218506-6.808899879455566-6.808899879455 566 Pd4446 -0.972700595855713-4.863500118255615-6.808899879455 566 Pd4546 -2.918099880218506-4.863500118255615-4.863500118255 615 Pd4646 -0.972700595855713-6.808899879455566-4.863500118255 615 Pd4746 0.972699642181396-6.808899879455566-6.8088998794555 66 Pd4846 2.918099880218506-4.863500118255615-6.8088998794555 66 Pd4946 0.972699642181396-4.863500118255615-4.8635001182556 15 Pd5046 2.918099880218506-6.808899879455566-4.8635001182556 15 Pd5146 4.863500118255615-6.808899879455566-6.8088998794555 66 Pd5246 141

PAGE 155

AppendixA(Continued) 6.808900356292725-4.863500118255615-6.8088998794555 66 Pd5346 4.863500118255615-4.863500118255615-4.8635001182556 15 Pd5446 6.808900356292725-6.808899879455566-4.8635001182556 15 Pd5546 8.754301071166992-4.863500118255615-4.8635001182556 15 Pd5646 -8.754300117492676-0.972700595855713-6.808899879455 566 Pd5746 -8.754300117492676-2.918099880218506-4.863500118255 615 Pd5846 -6.808899879455566-2.918099880218506-6.808899879455 566 Pd5946 -4.863500118255615-0.972700595855713-6.808899879455 566 Pd6046 -6.808899879455566-0.972700595855713-4.863500118255 615 Pd6146 -4.863500118255615-2.918099880218506-4.863500118255 615 Pd6246 -2.918099880218506-2.918099880218506-6.808899879455 566 Pd6346 -0.972700595855713-0.972700595855713-6.808899879455 566 Pd6446 -2.918099880218506-0.972700595855713-4.863500118255 615 Pd6546 -0.972700595855713-2.918099880218506-4.863500118255 615 Pd6646 0.972699642181396-2.918099880218506-6.8088998794555 66 Pd6746 2.918099880218506-0.972700595855713-6.8088998794555 66 Pd6846 0.972699642181396-0.972700595855713-4.8635001182556 15 Pd6946 2.918099880218506-2.918099880218506-4.8635001182556 15 Pd7046 142

PAGE 156

AppendixA(Continued) 4.863500118255615-2.918099880218506-6.8088998794555 66 Pd7146 6.808900356292725-0.972700595855713-6.8088998794555 66 Pd7246 4.863500118255615-0.972700595855713-4.8635001182556 15 Pd7346 6.808900356292725-2.918099880218506-4.8635001182556 15 Pd7446 8.754301071166992-2.918099880218506-6.8088998794555 66 Pd7546 8.754301071166992-0.972700595855713-4.8635001182556 15 Pd7646 -8.7543001174926762.918099880218506-6.8088998794555 66 Pd7746 -8.7543001174926760.972699642181396-4.8635001182556 15 Pd7846 -6.8088998794555660.972699642181396-6.8088998794555 66 Pd7946 -4.8635001182556152.918099880218506-6.8088998794555 66 Pd8046 -6.8088998794555662.918099880218506-4.8635001182556 15 Pd8146 -4.8635001182556150.972699642181396-4.8635001182556 15 Pd8246 -2.9180998802185060.972699642181396-6.8088998794555 66 Pd8346 -0.9727005958557132.918099880218506-6.8088998794555 66 Pd8446 -2.9180998802185062.918099880218506-4.8635001182556 15 Pd8546 -0.9727005958557130.972699642181396-4.8635001182556 15 Pd8646 0.9726996421813960.972699642181396-6.80889987945556 6 Pd8746 2.9180998802185062.918099880218506-6.80889987945556 6 Pd8846 143

PAGE 157

AppendixA(Continued) 0.9726996421813962.918099880218506-4.86350011825561 5 Pd8946 2.9180998802185060.972699642181396-4.86350011825561 5 Pd9046 4.8635001182556150.972699642181396-6.80889987945556 6 Pd9146 6.8089003562927252.918099880218506-6.80889987945556 6 Pd9246 4.8635001182556152.918099880218506-4.86350011825561 5 Pd9346 6.8089003562927250.972699642181396-4.86350011825561 5 Pd9446 8.7543010711669920.972699642181396-6.80889987945556 6 Pd9546 8.7543010711669922.918099880218506-4.86350011825561 5 Pd9646 -8.7543001174926764.863500118255615-4.8635001182556 15 Pd9746 -6.8088998794555664.863500118255615-6.8088998794555 66 Pd9846 -4.8635001182556156.808900356292725-6.8088998794555 66 Pd9946 -6.8088998794555666.808900356292725-4.8635001182556 15 Pd10046 -4.8635001182556154.863500118255615-4.8635001182556 15 Pd10146 -2.9180998802185064.863500118255615-6.8088998794555 66 Pd10246 -0.9727005958557136.808900356292725-6.8088998794555 66 Pd10346 -2.9180998802185066.808900356292725-4.8635001182556 15 Pd10446 -0.9727005958557134.863500118255615-4.8635001182556 15 Pd10546 0.9726996421813964.863500118255615-6.80889987945556 6 Pd10646 144

PAGE 158

AppendixA(Continued) 2.9180998802185066.808900356292725-6.80889987945556 6 Pd10746 0.9726996421813966.808900356292725-4.86350011825561 5 Pd10846 2.9180998802185064.863500118255615-4.86350011825561 5 Pd10946 4.8635001182556154.863500118255615-6.80889987945556 6 Pd11046 4.8635001182556156.808900356292725-4.86350011825561 5 Pd11146 6.8089003562927254.863500118255615-4.86350011825561 5 Pd11246 -4.8635001182556158.754301071166992-4.8635001182556 15 Pd11346 -2.9180998802185068.754301071166992-6.8088998794555 66 Pd11446 -0.9727005958557138.754301071166992-4.8635001182556 15 Pd11546 0.9726996421813968.754301071166992-6.80889987945556 6 Pd11646 2.9180998802185068.754301071166992-4.86350011825561 5 Pd11746 -4.863500118255615-8.754300117492676-2.918099880218 506 Pd11846 -6.808899879455566-8.754300117492676-0.972700595855 713 Pd11946 -2.918099880218506-10.699700355529785-2.91809988021 8506 Pd12046 -0.972700595855713-8.754300117492676-2.918099880218 506 Pd12146 -2.918099880218506-8.754300117492676-0.972700595855 713 Pd12246 -0.972700595855713-10.699700355529785-0.97270059585 5713 Pd12346 0.972699642181396-10.699700355529785-2.918099880218 506 Pd12446 145

PAGE 159

AppendixA(Continued) 2.918099880218506-8.754300117492676-2.9180998802185 06 Pd12546 0.972699642181396-8.754300117492676-0.9727005958557 13 Pd12646 2.918099880218506-10.699700355529785-0.972700595855 713 Pd12746 6.808900356292725-8.754300117492676-2.9180998802185 06 Pd12846 4.863500118255615-8.754300117492676-0.9727005958557 13 Pd12946 -8.754300117492676-4.863500118255615-2.918099880218 506 Pd13046 -8.754300117492676-6.808899879455566-0.972700595855 713 Pd13146 -6.808899879455566-6.808899879455566-2.918099880218 506 Pd13246 -4.863500118255615-4.863500118255615-2.918099880218 506 Pd13346 -6.808899879455566-4.863500118255615-0.972700595855 713 Pd13446 -4.863500118255615-6.808899879455566-0.972700595855 713 Pd13546 -2.918099880218506-6.808899879455566-2.918099880218 506 Pd13646 -0.972700595855713-4.863500118255615-2.918099880218 506 Pd13746 -2.918099880218506-4.863500118255615-0.972700595855 713 Pd13846 -0.972700595855713-6.808899879455566-0.972700595855 713 Pd13946 0.972699642181396-6.808899879455566-2.9180998802185 06 Pd14046 2.918099880218506-4.863500118255615-2.9180998802185 06 Pd14146 0.972699642181396-4.863500118255615-0.9727005958557 13 Pd14246 146

PAGE 160

AppendixA(Continued) 2.918099880218506-6.808899879455566-0.9727005958557 13 Pd14346 4.863500118255615-6.808899879455566-2.9180998802185 06 Pd14446 6.808900356292725-4.863500118255615-2.9180998802185 06 Pd14546 4.863500118255615-4.863500118255615-0.9727005958557 13 Pd14646 6.808900356292725-6.808899879455566-0.9727005958557 13 Pd14746 8.754301071166992-6.808899879455566-2.9180998802185 06 Pd14846 8.754301071166992-4.863500118255615-0.9727005958557 13 Pd14946-10.699700355529785-2.918099880218506-2.91809988021 8506 Pd15046 -8.754300117492676-0.972700595855713-2.918099880218 506 Pd15146-10.699700355529785-0.972700595855713-0.97270059585 5713 Pd15246 -8.754300117492676-2.918099880218506-0.972700595855 713 Pd15346 -6.808899879455566-2.918099880218506-2.918099880218 506 Pd15446 -4.863500118255615-0.972700595855713-2.918099880218 506 Pd15546 -6.808899879455566-0.972700595855713-0.972700595855 713 Pd15646 -4.863500118255615-2.918099880218506-0.972700595855 713 Pd15746 -2.918099880218506-2.918099880218506-2.918099880218 506 Pd15846 -0.972700595855713-0.972700595855713-2.918099880218 506 Pd15946 -2.918099880218506-0.972700595855713-0.972700595855 713 Pd16046 147

PAGE 161

AppendixA(Continued) -0.972700595855713-2.918099880218506-0.972700595855 713 Pd16146 0.972699642181396-2.918099880218506-2.9180998802185 06 Pd16246 2.918099880218506-0.972700595855713-2.9180998802185 06 Pd16346 0.972699642181396-0.972700595855713-0.9727005958557 13 Pd16446 2.918099880218506-2.918099880218506-0.9727005958557 13 Pd16546 4.863500118255615-2.918099880218506-2.9180998802185 06 Pd16646 6.808900356292725-0.972700595855713-2.9180998802185 06 Pd16746 4.863500118255615-0.972700595855713-0.9727005958557 13 Pd16846 6.808900356292725-2.918099880218506-0.9727005958557 13 Pd16946 8.754301071166992-2.918099880218506-2.9180998802185 06 Pd17046 10.699701309204102-0.972700595855713-2.918099880218 506 Pd17146 8.754301071166992-0.972700595855713-0.9727005958557 13 Pd17246 10.699701309204102-2.918099880218506-0.972700595855 713 Pd17346-10.6997003555297850.972699642181396-2.918099880218 506 Pd17446 -8.7543001174926762.918099880218506-2.9180998802185 06 Pd17546-10.6997003555297852.918099880218506-0.972700595855 713 Pd17646 -8.7543001174926760.972699642181396-0.9727005958557 13 Pd17746 -6.8088998794555660.972699642181396-2.9180998802185 06 Pd17846 148

PAGE 162

AppendixA(Continued) -4.8635001182556152.918099880218506-2.9180998802185 06 Pd17946 -6.8088998794555662.918099880218506-0.9727005958557 13 Pd18046 -4.8635001182556150.972699642181396-0.9727005958557 13 Pd18146 -2.9180998802185060.972699642181396-2.9180998802185 06 Pd18246 -0.9727005958557132.918099880218506-2.9180998802185 06 Pd18346 -2.9180998802185062.918099880218506-0.9727005958557 13 Pd18446 -0.9727005958557130.972699642181396-0.9727005958557 13 Pd18546 0.9726996421813960.972699642181396-2.91809988021850 6 Pd18646 2.9180998802185062.918099880218506-2.91809988021850 6 Pd18746 0.9726996421813962.918099880218506-0.97270059585571 3 Pd18846 2.9180998802185060.972699642181396-0.97270059585571 3 Pd18946 4.8635001182556150.972699642181396-2.91809988021850 6 Pd19046 6.8089003562927252.918099880218506-2.91809988021850 6 Pd19146 4.8635001182556152.918099880218506-0.97270059585571 3 Pd19246 6.8089003562927250.972699642181396-0.97270059585571 3 Pd19346 8.7543010711669920.972699642181396-2.91809988021850 6 Pd19446 10.6997013092041022.918099880218506-2.9180998802185 06 Pd19546 8.7543010711669922.918099880218506-0.97270059585571 3 Pd19646 149

PAGE 163

AppendixA(Continued) 10.6997013092041020.972699642181396-0.9727005958557 13 Pd19746 -8.7543001174926766.808900356292725-2.9180998802185 06 Pd19846 -8.7543001174926764.863500118255615-0.9727005958557 13 Pd19946 -6.8088998794555664.863500118255615-2.9180998802185 06 Pd20046 -4.8635001182556156.808900356292725-2.9180998802185 06 Pd20146 -6.8088998794555666.808900356292725-0.9727005958557 13 Pd20246 -4.8635001182556154.863500118255615-0.9727005958557 13 Pd20346 -2.9180998802185064.863500118255615-2.9180998802185 06 Pd20446 -0.9727005958557136.808900356292725-2.9180998802185 06 Pd20546 -2.9180998802185066.808900356292725-0.9727005958557 13 Pd20646 -0.9727005958557134.863500118255615-0.9727005958557 13 Pd20746 0.9726996421813964.863500118255615-2.91809988021850 6 Pd20846 2.9180998802185066.808900356292725-2.91809988021850 6 Pd20946 0.9726996421813966.808900356292725-0.97270059585571 3 Pd21046 2.9180998802185064.863500118255615-0.97270059585571 3 Pd21146 4.8635001182556154.863500118255615-2.91809988021850 6 Pd21246 6.8089003562927256.808900356292725-2.91809988021850 6 Pd21346 4.8635001182556156.808900356292725-0.97270059585571 3 Pd21446 150

PAGE 164

AppendixA(Continued) 6.8089003562927254.863500118255615-0.97270059585571 3 Pd21546 8.7543010711669924.863500118255615-2.91809988021850 6 Pd21646 8.7543010711669926.808900356292725-0.97270059585571 3 Pd21746 -6.8088998794555668.754301071166992-2.9180998802185 06 Pd21846 -4.8635001182556158.754301071166992-0.9727005958557 13 Pd21946 -2.9180998802185068.754301071166992-2.9180998802185 06 Pd22046 -0.97270059585571310.699701309204102-2.918099880218 506 Pd22146 -2.91809988021850610.699701309204102-0.972700595855 713 Pd22246 -0.9727005958557138.754301071166992-0.9727005958557 13 Pd22346 0.9726996421813968.754301071166992-2.91809988021850 6 Pd22446 2.91809988021850610.699701309204102-2.9180998802185 06 Pd22546 0.97269964218139610.699701309204102-0.9727005958557 13 Pd22646 2.9180998802185068.754301071166992-0.97270059585571 3 Pd22746 4.8635001182556158.754301071166992-2.91809988021850 6 Pd22846 6.8089003562927258.754301071166992-0.97270059585571 3 Pd22946 -4.863500118255615-8.7543001174926760.9726996421813 96 Pd23046 -6.808899879455566-8.7543001174926762.9180998802185 06 Pd23146 -2.918099880218506-10.6997003555297850.972699642181 396 Pd23246 151

PAGE 165

AppendixA(Continued) -0.972700595855713-8.7543001174926760.9726996421813 96 Pd23346 -2.918099880218506-8.7543001174926762.9180998802185 06 Pd23446 -0.972700595855713-10.6997003555297852.918099880218 506 Pd23546 0.972699642181396-10.6997003555297850.9726996421813 96 Pd23646 2.918099880218506-8.7543001174926760.97269964218139 6 Pd23746 0.972699642181396-8.7543001174926762.91809988021850 6 Pd23846 2.918099880218506-10.6997003555297852.9180998802185 06 Pd23946 6.808900356292725-8.7543001174926760.97269964218139 6 Pd24046 4.863500118255615-8.7543001174926762.91809988021850 6 Pd24146 -8.754300117492676-4.8635001182556150.9726996421813 96 Pd24246 -8.754300117492676-6.8088998794555662.9180998802185 06 Pd24346 -6.808899879455566-6.8088998794555660.9726996421813 96 Pd24446 -4.863500118255615-4.8635001182556150.9726996421813 96 Pd24546 -6.808899879455566-4.8635001182556152.9180998802185 06 Pd24646 -4.863500118255615-6.8088998794555662.9180998802185 06 Pd24746 -2.918099880218506-6.8088998794555660.9726996421813 96 Pd24846 -0.972700595855713-4.8635001182556150.9726996421813 96 Pd24946 -2.918099880218506-4.8635001182556152.9180998802185 06 Pd25046 152

PAGE 166

AppendixA(Continued) -0.972700595855713-6.8088998794555662.9180998802185 06 Pd25146 0.972699642181396-6.8088998794555660.97269964218139 6 Pd25246 2.918099880218506-4.8635001182556150.97269964218139 6 Pd25346 0.972699642181396-4.8635001182556152.91809988021850 6 Pd25446 2.918099880218506-6.8088998794555662.91809988021850 6 Pd25546 4.863500118255615-6.8088998794555660.97269964218139 6 Pd25646 6.808900356292725-4.8635001182556150.97269964218139 6 Pd25746 4.863500118255615-4.8635001182556152.91809988021850 6 Pd25846 6.808900356292725-6.8088998794555662.91809988021850 6 Pd25946 8.754301071166992-6.8088998794555660.97269964218139 6 Pd26046 8.754301071166992-4.8635001182556152.91809988021850 6 Pd26146-10.699700355529785-2.9180998802185060.972699642181 396 Pd26246 -8.754300117492676-0.9727005958557130.9726996421813 96 Pd26346-10.699700355529785-0.9727005958557132.918099880218 506 Pd26446 -8.754300117492676-2.9180998802185062.9180998802185 06 Pd26546 -6.808899879455566-2.9180998802185060.9726996421813 96 Pd26646 -4.863500118255615-0.9727005958557130.9726996421813 96 Pd26746 -6.808899879455566-0.9727005958557132.9180998802185 06 Pd26846 153

PAGE 167

AppendixA(Continued) -4.863500118255615-2.9180998802185062.9180998802185 06 Pd26946 -2.918099880218506-2.9180998802185060.9726996421813 96 Pd27046 -0.972700595855713-0.9727005958557130.9726996421813 96 Pd27146 -2.918099880218506-0.9727005958557132.9180998802185 06 Pd27246 -0.972700595855713-2.9180998802185062.9180998802185 06 Pd27346 0.972699642181396-2.9180998802185060.97269964218139 6 Pd27446 2.918099880218506-0.9727005958557130.97269964218139 6 Pd27546 0.972699642181396-0.9727005958557132.91809988021850 6 Pd27646 2.918099880218506-2.9180998802185062.91809988021850 6 Pd27746 4.863500118255615-2.9180998802185060.97269964218139 6 Pd27846 6.808900356292725-0.9727005958557130.97269964218139 6 Pd27946 4.863500118255615-0.9727005958557132.91809988021850 6 Pd28046 6.808900356292725-2.9180998802185062.91809988021850 6 Pd28146 8.754301071166992-2.9180998802185060.97269964218139 6 Pd28246 10.699701309204102-0.9727005958557130.9726996421813 96 Pd28346 8.754301071166992-0.9727005958557132.91809988021850 6 Pd28446 10.699701309204102-2.9180998802185062.9180998802185 06 Pd28546-10.6997003555297850.9726996421813960.9726996421813 96 Pd28646 154

PAGE 168

AppendixA(Continued) -8.7543001174926762.9180998802185060.97269964218139 6 Pd28746-10.6997003555297852.9180998802185062.9180998802185 06 Pd28846 -8.7543001174926760.9726996421813962.91809988021850 6 Pd28946 -6.8088998794555660.9726996421813960.97269964218139 6 Pd29046 -4.8635001182556152.9180998802185060.97269964218139 6 Pd29146 -6.8088998794555662.9180998802185062.91809988021850 6 Pd29246 -4.8635001182556150.9726996421813962.91809988021850 6 Pd29346 -2.9180998802185060.9726996421813960.97269964218139 6 Pd29446 -0.9727005958557132.9180998802185060.97269964218139 6 Pd29546 -2.9180998802185062.9180998802185062.91809988021850 6 Pd29646 -0.9727005958557130.9726996421813962.91809988021850 6 Pd29746 0.9726996421813960.9726996421813960.972699642181396 Pd29846 2.9180998802185062.9180998802185060.972699642181396 Pd29946 0.9726996421813962.9180998802185062.918099880218506 Pd30046 2.9180998802185060.9726996421813962.918099880218506 Pd30146 4.8635001182556150.9726996421813960.972699642181396 Pd30246 6.8089003562927252.9180998802185060.972699642181396 Pd30346 4.8635001182556152.9180998802185062.918099880218506 Pd30446 155

PAGE 169

AppendixA(Continued) 6.8089003562927250.9726996421813962.918099880218506 Pd30546 8.7543010711669920.9726996421813960.972699642181396 Pd30646 10.6997013092041022.9180998802185060.97269964218139 6 Pd30746 8.7543010711669922.9180998802185062.918099880218506 Pd30846 10.6997013092041020.9726996421813962.91809988021850 6 Pd30946 -8.7543001174926766.8089003562927250.97269964218139 6 Pd31046 -8.7543001174926764.8635001182556152.91809988021850 6 Pd31146 -6.8088998794555664.8635001182556150.97269964218139 6 Pd31246 -4.8635001182556156.8089003562927250.97269964218139 6 Pd31346 -6.8088998794555666.8089003562927252.91809988021850 6 Pd31446 -4.8635001182556154.8635001182556152.91809988021850 6 Pd31546 -2.9180998802185064.8635001182556150.97269964218139 6 Pd31646 -0.9727005958557136.8089003562927250.97269964218139 6 Pd31746 -2.9180998802185066.8089003562927252.91809988021850 6 Pd31846 -0.9727005958557134.8635001182556152.91809988021850 6 Pd31946 0.9726996421813964.8635001182556150.972699642181396 Pd32046 2.9180998802185066.8089003562927250.972699642181396 Pd32146 0.9726996421813966.8089003562927252.918099880218506 Pd32246 156

PAGE 170

AppendixA(Continued) 2.9180998802185064.8635001182556152.918099880218506 Pd32346 4.8635001182556154.8635001182556150.972699642181396 Pd32446 6.8089003562927256.8089003562927250.972699642181396 Pd32546 4.8635001182556156.8089003562927252.918099880218506 Pd32646 6.8089003562927254.8635001182556152.918099880218506 Pd32746 8.7543010711669924.8635001182556150.972699642181396 Pd32846 8.7543010711669926.8089003562927252.918099880218506 Pd32946 -6.8088998794555668.7543010711669920.97269964218139 6 Pd33046 -4.8635001182556158.7543010711669922.91809988021850 6 Pd33146 -2.9180998802185068.7543010711669920.97269964218139 6 Pd33246 -0.97270059585571310.6997013092041020.9726996421813 96 Pd33346 -2.91809988021850610.6997013092041022.9180998802185 06 Pd33446 -0.9727005958557138.7543010711669922.91809988021850 6 Pd33546 0.9726996421813968.7543010711669920.972699642181396 Pd33646 2.91809988021850610.6997013092041020.97269964218139 6 Pd33746 0.97269964218139610.6997013092041022.91809988021850 6 Pd33846 2.9180998802185068.7543010711669922.918099880218506 Pd33946 4.8635001182556158.7543010711669920.972699642181396 Pd34046 157

PAGE 171

AppendixA(Continued) 6.8089003562927258.7543010711669922.918099880218506 Pd34146 -4.863500118255615-8.7543001174926764.8635001182556 15 Pd34246 -0.972700595855713-8.7543001174926764.8635001182556 15 Pd34346 -2.918099880218506-8.7543001174926766.8089003562927 25 Pd34446 2.918099880218506-8.7543001174926764.86350011825561 5 Pd34546 0.972699642181396-8.7543001174926766.80890035629272 5 Pd34646 -8.754300117492676-4.8635001182556154.8635001182556 15 Pd34746 -6.808899879455566-6.8088998794555664.8635001182556 15 Pd34846 -4.863500118255615-4.8635001182556154.8635001182556 15 Pd34946 -6.808899879455566-4.8635001182556156.8089003562927 25 Pd35046 -4.863500118255615-6.8088998794555666.8089003562927 25 Pd35146 -2.918099880218506-6.8088998794555664.8635001182556 15 Pd35246 -0.972700595855713-4.8635001182556154.8635001182556 15 Pd35346 -2.918099880218506-4.8635001182556156.8089003562927 25 Pd35446 -0.972700595855713-6.8088998794555666.8089003562927 25 Pd35546 0.972699642181396-6.8088998794555664.86350011825561 5 Pd35646 2.918099880218506-4.8635001182556154.86350011825561 5 Pd35746 0.972699642181396-4.8635001182556156.80890035629272 5 Pd35846 158

PAGE 172

AppendixA(Continued) 2.918099880218506-6.8088998794555666.80890035629272 5 Pd35946 4.863500118255615-6.8088998794555664.86350011825561 5 Pd36046 6.808900356292725-4.8635001182556154.86350011825561 5 Pd36146 4.863500118255615-4.8635001182556156.80890035629272 5 Pd36246 -8.754300117492676-0.9727005958557134.8635001182556 15 Pd36346 -8.754300117492676-2.9180998802185066.8089003562927 25 Pd36446 -6.808899879455566-2.9180998802185064.8635001182556 15 Pd36546 -4.863500118255615-0.9727005958557134.8635001182556 15 Pd36646 -6.808899879455566-0.9727005958557136.8089003562927 25 Pd36746 -4.863500118255615-2.9180998802185066.8089003562927 25 Pd36846 -2.918099880218506-2.9180998802185064.8635001182556 15 Pd36946 -0.972700595855713-0.9727005958557134.8635001182556 15 Pd37046 -2.918099880218506-0.9727005958557136.8089003562927 25 Pd37146 -0.972700595855713-2.9180998802185066.8089003562927 25 Pd37246 0.972699642181396-2.9180998802185064.86350011825561 5 Pd37346 2.918099880218506-0.9727005958557134.86350011825561 5 Pd37446 0.972699642181396-0.9727005958557136.80890035629272 5 Pd37546 2.918099880218506-2.9180998802185066.80890035629272 5 Pd37646 159

PAGE 173

AppendixA(Continued) 4.863500118255615-2.9180998802185064.86350011825561 5 Pd37746 6.808900356292725-0.9727005958557134.86350011825561 5 Pd37846 4.863500118255615-0.9727005958557136.80890035629272 5 Pd37946 6.808900356292725-2.9180998802185066.80890035629272 5 Pd38046 8.754301071166992-2.9180998802185064.86350011825561 5 Pd38146 8.754301071166992-0.9727005958557136.80890035629272 5 Pd38246 -8.7543001174926762.9180998802185064.86350011825561 5 Pd38346 -8.7543001174926760.9726996421813966.80890035629272 5 Pd38446 -6.8088998794555660.9726996421813964.86350011825561 5 Pd38546 -4.8635001182556152.9180998802185064.86350011825561 5 Pd38646 -6.8088998794555662.9180998802185066.80890035629272 5 Pd38746 -4.8635001182556150.9726996421813966.80890035629272 5 Pd38846 -2.9180998802185060.9726996421813964.86350011825561 5 Pd38946 -0.9727005958557132.9180998802185064.86350011825561 5 Pd39046 -2.9180998802185062.9180998802185066.80890035629272 5 Pd39146 -0.9727005958557130.9726996421813966.80890035629272 5 Pd39246 0.9726996421813960.9726996421813964.863500118255615 Pd39346 2.9180998802185062.9180998802185064.863500118255615 Pd39446 160

PAGE 174

AppendixA(Continued) 0.9726996421813962.9180998802185066.808900356292725 Pd39546 2.9180998802185060.9726996421813966.808900356292725 Pd39646 4.8635001182556150.9726996421813964.863500118255615 Pd39746 6.8089003562927252.9180998802185064.863500118255615 Pd39846 4.8635001182556152.9180998802185066.808900356292725 Pd39946 6.8089003562927250.9726996421813966.808900356292725 Pd40046 8.7543010711669920.9726996421813964.863500118255615 Pd40146 8.7543010711669922.9180998802185066.808900356292725 Pd40246 -6.8088998794555664.8635001182556154.86350011825561 5 Pd40346 -4.8635001182556156.8089003562927254.86350011825561 5 Pd40446 -4.8635001182556154.8635001182556156.80890035629272 5 Pd40546 -2.9180998802185064.8635001182556154.86350011825561 5 Pd40646 -0.9727005958557136.8089003562927254.86350011825561 5 Pd40746 -2.9180998802185066.8089003562927256.80890035629272 5 Pd40846 -0.9727005958557134.8635001182556156.80890035629272 5 Pd40946 0.9726996421813964.8635001182556154.863500118255615 Pd41046 2.9180998802185066.8089003562927254.863500118255615 Pd41146 0.9726996421813966.8089003562927256.808900356292725 Pd41246 161

PAGE 175

AppendixA(Continued) 2.9180998802185064.8635001182556156.808900356292725 Pd41346 4.8635001182556154.8635001182556154.863500118255615 Pd41446 6.8089003562927256.8089003562927254.863500118255615 Pd41546 4.8635001182556156.8089003562927256.808900356292725 Pd41646 6.8089003562927254.8635001182556156.808900356292725 Pd41746 8.7543010711669924.8635001182556154.863500118255615 Pd41846 -2.9180998802185068.7543010711669924.86350011825561 5 Pd41946 -0.9727005958557138.7543010711669926.80890035629272 5 Pd42046 0.9726996421813968.7543010711669924.863500118255615 Pd42146 2.9180998802185068.7543010711669926.808900356292725 Pd42246 4.8635001182556158.7543010711669924.863500118255615 Pd42346 -4.863500118255615-4.8635001182556158.7543010711669 92 Pd42446 -2.918099880218506-6.8088998794555668.7543010711669 92 Pd42546 -0.972700595855713-4.8635001182556158.7543010711669 92 Pd42646 0.972699642181396-6.8088998794555668.75430107116699 2 Pd42746 2.918099880218506-4.8635001182556158.75430107116699 2 Pd42846 -6.808899879455566-2.9180998802185068.7543010711669 92 Pd42946 -4.863500118255615-0.9727005958557138.7543010711669 92 Pd43046 162

PAGE 176

AppendixA(Continued) -2.918099880218506-2.9180998802185068.7543010711669 92 Pd43146 -0.972700595855713-0.9727005958557138.7543010711669 92 Pd43246 -2.918099880218506-0.97270059585571310.699701309204 102 Pd43346 -0.972700595855713-2.91809988021850610.699701309204 102 Pd43446 0.972699642181396-2.9180998802185068.75430107116699 2 Pd43546 2.918099880218506-0.9727005958557138.75430107116699 2 Pd43646 0.972699642181396-0.97270059585571310.6997013092041 02 Pd43746 2.918099880218506-2.91809988021850610.6997013092041 02 Pd43846 4.863500118255615-2.9180998802185068.75430107116699 2 Pd43946 6.808900356292725-0.9727005958557138.75430107116699 2 Pd44046 -6.8088998794555660.9726996421813968.75430107116699 2 Pd44146 -4.8635001182556152.9180998802185068.75430107116699 2 Pd44246 -2.9180998802185060.9726996421813968.75430107116699 2 Pd44346 -0.9727005958557132.9180998802185068.75430107116699 2 Pd44446 -2.9180998802185062.91809988021850610.6997013092041 02 Pd44546 -0.9727005958557130.97269964218139610.6997013092041 02 Pd44646 0.9726996421813960.9726996421813968.754301071166992 Pd44746 2.9180998802185062.9180998802185068.754301071166992 Pd44846 163

PAGE 177

AppendixA(Continued) 0.9726996421813962.91809988021850610.69970130920410 2 Pd44946 2.9180998802185060.97269964218139610.69970130920410 2 Pd45046 4.8635001182556150.9726996421813968.754301071166992 Pd45146 6.8089003562927252.9180998802185068.754301071166992 Pd45246 -2.9180998802185064.8635001182556158.75430107116699 2 Pd45346 -0.9727005958557136.8089003562927258.75430107116699 2 Pd45446 0.9726996421813964.8635001182556158.754301071166992 Pd45546 2.9180998802185066.8089003562927258.754301071166992 Pd45646 4.8635001182556154.8635001182556158.754301071166992 TherstlineintheCONFIGlehasthesamedenitionasthatin theCONTROLle.The rstzerointhesecondlineindicateonlyatomiccoordinate sareincludedinthele.The secondintegeristheperiodicboundarykey,wherezeromean snoperiodicboundaries.If periodicboundaryconditionisused,athree-linecellvect orsneedstobedenedafterthe secondline,otherwisethe x y z coordinateswillbelistedwithoutthethreelines.Before eachatomiccoordinateline,atomname,atomindexandatomi cnumberarelistedinthe orderofincreasingindex. A.1.3TheFIELDFile TheFIELDlecontainstheforceeldinformationdeningth enatureofthemolecular forces.TheFIELDleusedforthesimulatedPdnanoclusteri sshownbelow. DL_POLYFIELDfile:Pdnanocluster 164

PAGE 178

AppendixA(Continued)unitsevmolecules1Palladiumnummols456atoms1Pd106.4200.0000finishvdw1PdPdstch0.0041793.8912.07.0108.27CloseTherstlinetheFIELDleisthetitle.Itmustbefollowedby theunits.Inoursimulations theenergyunitofeVisused.Linesfollowingthataremolecu lardetails.Therstlineinthe moleculardetailsspecifythenumberofdifferenttypesofm olecules.Thedetailsofeach typeofmoleculeincludethenameofthemoleculeandtotalnu mberofthismoleculein thesystem.Eachatomicinformationinthismoleculeisthen givenbyatomname,atomic massandatomiccharge.Adirectiveofnishisenteredtosig naltoDL POLY 2thatthe entryofthedetailsofamoleculehasbeencompleted.Theent riesforasecondmolecule maynowbeentered,andthecycleisrepeateduntilalltypeso fmoleculesindicatedbythe moleculesdirectivehavebeenentered.Sincetheinoursimu lationPdnanoclusterhasonly onetypeofmolecule/atom,therepeatingisnotneeded.Then on-bondedinteractionsare identiedbyatomtypes.TheSutton-ChenpotentialforPd-Pd interactionsissignaledby thedirectivestchwithcorrespondingparameters.Intheen d,theFIELDlemustbeclosed withthedirectiveclose. 165

PAGE 179

AppendixA(Continued)A.2TheOutputFilesDL POLY 2producesuptosevenoutputles:HISTORY,OUTPUT,REVCON,REV IVE, RDFDAT,ZDNDATandSTATIS,dependingonthedirectivesinthe CONTROLle.These respectivelycontain:adumpleofatomiccoordinates,vel ocitiesandforces;asummary ofthesimulation;therestartconguration;statisticsac cumulators;radialdistributiondata, Z -densitydataandastatisticalhistory.Theformatofeacho utputlecanbefoundinthe DL POLY smanual. 166

PAGE 180

AppendixB:VASPPrograms VASP4.6.28wasusedfortheDFTcalculationsinthisdissert ation.VASPusesarelativelylargenumberofinputandoutputles.Ashortdescrip tionofsomeoftheimportant lesaregivenintheexampleofPdfullycoatedSWNT(10,0)int hischapter. B.1TheInputFilesInordertorunaVASPjob,atleastfourinputlesareneeded. TheyareINCAR,POTCAR, POSCAR,andKPOINTSles. B.1.1TheINCARFile INCARisthecentralinputofVASP.Itdetermineswhattodoand howtodoit,andcontains arelativelylargenumberofparameters.However,sincemos toftheseparametershave convenientdefaults,INCARleisusuallysimply.AnINCARle forthetotalenergy calculationofPdfullycoatedSWNT(10,0)isgivenbelow.SYSTEM=PdfullycoatedSWNT(10,0)StartparameterforthisrunPREC=AccurateISPIN=2Electronicrelaxation1ENCUT=500NELMDL=-10EDIFF=1E-04VOSKOWN=1IronicrelaxationEDIFFG=1E-03NSW=0IBRION=-1ISIF=2ThemeaningofdirectiveslistedthisINCARleareasfollows : 167

PAGE 181

AppendixB(Continued) SYSTEMtagisfollowedbythetitlestringtohelpusertoiden tifythesystem. PRECtagdeterminestheenergycutoff,ifnovalueisgivenfor ENCUTintheINCAR.ForPREC=Accurate,ENCUTissettothemaximalENMAXvalueint he POTCARleplus30%.PREC=Accurateavoidswraparounderrorsan dusesan augmentationgridthatisexactlytwiceaslargeasthecours egridfortherepresentationofthepseudowavefunctions.PREC=Accurateincreasesth ememoryrequirementssomewhat,butitshouldbeusedifaccurateforcesande nergiesarerequired. ISPINdetermineswhetherspinpolarizedcalculationsarep erformed,where2isfor spinpolarizedcalculations. ENCUTisthecut-offenergyforplanewavesbasissetineV,asd iscussedinChapter Seven. NELMDLgivesthenumberofnon-selfconsistentstepsattheb eginning;ifoneinitializesthewavefunctionsrandomlytheinitialwavefunct ionsarefarfromanything reasonable.Avalueof-10resultsina10-stepdelayforthes tart-conguration. EDIFFSpeciestheglobalbreakconditionfortheelectroni cself-consistentloop. Therelaxationoftheelectronicdegreesoffreedomwillbes toppedifthetotal(free) energychangeandthebandstructureenergychange(“change ofeigenvalues”)betweentwostepsarebothsmallerthan1E-04. VOSKOWN=1turnontheVosko-Wilk-Nusairinterpolationform ulaforthecorrelationpartoftheexchangecorrelationfunctional.Thisusua llyenhancesthemagnetic momentsandthemagneticenergies.Itisdesirabletousethi sinterpolationwhenever thePW91functionalisapplied. 168

PAGE 182

AppendixB(Continued) EDIFFG=1E-03statesifthetotal(free)energybetweentwoi onicstepsissmaller than10-3,theionicrelaxationloopwillstop. IBRION=-1indicatesionswillnotbeupdatedormoved.IfIBRION= 2isdened, aconjugate-gradientalgorithmwillbeusedtorelaxtheion sintotheirinstantaneous groundstate. NSWdenesthenumberofionicsteps.ItshouldbezeroifIBRION =-1isdened inINCARle.Ifanionicrelaxationisperformed,i.e.IBRION=2,apositiveNSW shouldbeused. ISIFcontrolswhetherthestresstensoriscalculated.Inad dition,italsodetermines whichdegreesoffreedom(ions,cellvolume,cellshape)are allowedtochange. ISIF=2isadefaultsetforIBRION 6 = 0. B.1.2ThePOSCARFile Thislecontainsthelatticegeometryandtheionicpositio ns,optionallyalsostartingvelocitiesandpredictor-correctorcoordinatesforaMD-run .ThecoordinatesforSWNTs canbegeneratedusingTubeGenOnline.ThePOSCARofPdfullyc oatedSWNT(10,0)is shownbelow. CNT(10,0)-Pdfullcover 1.00000000000000019.112645654978930010.73303676374713000.00001491405 21125 0.0000580931183641-0.0001110915924111-4.29199682682 96320 -0.387884931888259922.13547344253870000.00058464694 32516 4020 Direct 0.57302354296751190.83309240870475780.1347674198436 266 169

PAGE 183

AppendixB(Continued) 0.42847960010679030.16689268718369730.8648536625587 369 0.42847969465123010.83307917088654190.8648512053138 973 0.57302511671323230.16702647187298680.1347684193137 511 0.44461671967712140.83319935553072360.1997764766189 718 0.55686384474138610.16694198550813870.7995882231241 254 0.55686419690220390.83299632104443330.7995886899596 130 0.44461696143713430.16696175480564790.1997742675413 647 0.30406766837030120.33317323314336280.1559314109024 541 0.69671908947979940.66684095462154860.8443979997476 063 0.69671907447452240.33312440621044460.8443985730891 725 0.30406977762287820.66698548423777030.1559307936110 770 0.38514326222836810.33315155609713540.2048413248878 092 0.61620264199571300.66689832030637320.7948968661175 968 0.61620362928457690.33304166129978090.7948961506890 768 0.38514388260144730.66701469496199910.2048413092415 728 0.29991632856820870.33306736933813850.0459241534056 574 0.70175544410953710.66697993798754850.9539516107590 060 0.70175415538475510.33304671963789900.9539527370850 251 0.29991759356792610.66701820461673120.0459247522986 814 0.67434843675703600.83310679772175430.0182293607363 064 0.32757892134191740.16688138797587730.9816675581370 617 0.32757996800512500.83316083781489430.9816672388197 674 0.67434845338259210.16695299372512550.0182288568258 002 0.62994235291132130.66697266195336620.0805259355444 719 0.37176619560260350.33301887948041300.9193130487637 688 0.37176502338135010.66698369903277670.9193131055507 777 0.62994271386912710.33312083010892480.0805271568464 931 0.50918217200000270.66698117524443030.1757417410070 019 0.49225303553198070.33314337535151850.8236259008850 624 0.49225297145979850.66680562606927650.8236246706400 081 0.50918130492844680.33316069912104500.1757424777175 132 0.33649794958093080.83307001347122880.1899805440847 686 0.66449650765554940.16695890422320050.8102118198415 553 0.66449650309484550.83299053434973300.8102124124881 627 0.33649659908407870.16709716809964450.1899817172593 217 0.29159477907410290.83322877278658320.1060628585158 980 170

PAGE 184

AppendixB(Continued) 0.70949809158837240.16683110564338220.8940258080240 611 0.70949891056162070.83316400682625160.8940259113864 570 0.29159367026576890.16690043191942290.1060641889645 453 0.25232883528202880.00008739565054580.2894911142560 943 0.32637722016514910.50009338736653320.3128480737465 154 0.20228545013843300.50006866962701930.2366363310640 125 0.18268266735068290.00004789734590100.1599514194914 278 0.19493398365057860.50002149810210030.0683297848739 883 0.41606779424925830.00009011428394250.3055335535651 835 0.51364162026223430.50008445375568300.2690563404465 109 0.61054522703317100.00007784345340410.2064733062026 534 0.69732661422141720.50005322114881070.1236357623665 469 0.76509508478624610.00003444160884670.0286964425642 751 0.80673883066422290.50001872638749490.9309400739388 991 0.81851255978697420.99999224652542300.8395361877630 307 0.79874805541845720.49997186917484270.7634748786246 206 0.74927400656837760.99995119452518820.7108216927405 806 0.67569843752349360.49994299747879010.6870073224369 904 0.58572838655271650.99994289421661620.6939589917366 931 0.48763431637628680.49994432271028440.7305789502648 068 0.39052322231830060.99995048843456400.7935228503093 086 0.30408097347999070.49998237202282070.8764144180255 471 0.23680569772235320.00000400642363020.9709818446001 535 Therstlineistreatedasacommentline,usuallyusedforth enameofthesystem.The secondlineprovidesauniversalscalingfactor,whichisus edtoscalealllatticevectors andallatomiccoordinates.Thenextthreelinesarethethre elatticevectorsdeningthe unitcellofthesystem.Thefthlinesuppliesthenumberofa tomsperatomicspeciesin asameorderastheincludedatomicspeciesinPOTCARle.Anop tionaltagofSelective Dynamicscanbeusedinthesixthlinetoallowforaselective atomrelaxation.Ifthistagis omitted,thesixthlinesuppliestheswitchbetweencartesi ananddirectlattice.Thedirect 171

PAGE 185

AppendixB(Continued)coordinatesisusedinthePOSCARle.Thenextlinesgivethet hreecoordinatesforeach atom. B.1.3ThePOTCARFile ThePOTCARlecontainsthepseudopotentialforeachatomics peciesusedinthecalculation.VASPissuppliedwithasetofstandardpseudopotent ial.AllsuppliedPP'swith VASPareoftheultrasofttype.Ifthenumberofspeciesinthe systemislargerthanone,a UNIXcommandcanbeusedtocombinethePOTCARofeachspeciesi ntoonePOTCAR le.ThePdfullycoatedSWNT(10,0)system'sPOTCARleismade bycatcommand: >catPOTCAR_CPOTCAR_Pd>POTCARNotethattheorderofeachspeciesinthePOTCARlehastobeco nsistentwiththatinthe POSCARle. B.1.4TheKPOINTSFile TheleKPOINTSmustcontainthek-pointcoordinatesandwei ghtsorthemeshsizefor creatingthek-pointgrid.Thek-meshcanbeeitherenteredb yhandorgeneratedautomatically.Inoursimulations,Monkhorst-packgridisusedtos ampletheBrillouinzone.The KPOINTleislikebelow:Monkhorstpack0MonkhorstPack 1131000 TheFirstlineistreatedasacomment.Thezeroonthesecondl ineactivatestheautomatic generationscheme.Theautomaticschemeisselectedbythet hirdline.Thefourthline 172

PAGE 186

AppendixB(Continued)denesthenumbersofsubdivisionsalongeachreciprocalve ctor.Thelastlineisoptional andsuppliesanadditionalshirtofk-mesh.Anzeroindicate snoshift. B.2TheOutputFilesVASPcangeneratemorethantendifferentoutputles,buton lysomeareusedinthisdissertationforelectronicpropertycalculations.Forexamp le,DOSCAR,CHGCAR,OUTCARandEIGENVALles.DOSCARcontainstheDOSandintegratedD OS.CHGCAR providesthetotalchargeontheFFT-grid.OUTCARcontainsin formationofself-consistent iterations,suchasforce,energy,stress,etc.EIGENVALsa vesKohn-Shameigenvaluesfor allk-pointsattheendofthesimulation.B.3CalculateBandStructureTocalculatethebandstructure,CHGCARlefromaprevioussel f-consistentrunisneeded asaninputle.TheINCARleisslightlydifferentfromthatf orthegroundstateenergy calculationasshowninthebeginningofthischapter,becau sethefollowingtagisneeded. ICHARG=11Thusthechargedensitywillbekeptconstantduringtheelec tronicminimization.The KPOINTSlealsoneedstobemodiedtogeneratestringsofkpointsconnectingspecic pointsofBrillouinzone.TheKPOINTSusedforbandstructure calculationforthePd functionalizedSWNT(10,0)isshownbelow,wherethethirdli nemuststartwithanLfor theline-modecalculation.k-pointsalonghighsymmetrylines20 173

PAGE 187

AppendixB(Continued)Linemoderec0.000000.000000.000000.000000.000000.50000AccordingtothisKPOINTSle,VASPwillgenerate20k-point sbetweentherstand secondsuppliedhighsymmetryk-pointsdenedinthefthan dsixthlines.Thesek-points aresuppliedinreciprocalcoordinatesbyusingarecinthef ourthline.Moreinterested k-pointscanbeaddedinpairintheendoftheleforcalculat ionsofbandstructurealong otherlines.AfterrunningVASPusingthemodiedINCAR,KPOIN TStogetherwiththe CHGCAR,POTCARandPOSCAR,anEIGENVALlethathasalltheneededin formation forbandstructureplotwillbegenerated.TheformatofEIGE NVALlecanbefoundinthe VASPmanual.AprogramcalledP4VASPcanbeutilizedforproc essingtheEIGENVAL leandforviewingthebandstructure. 174

PAGE 188

AbouttheAuthor LingMiaowasborninShanghai,China.SheattendedShanghaiK ongjiangmiddleand highschoolfrom1989to1996.ShestudiedherBachelor'sdegr eeinChemicalEngineering atShanghaiUniversityfrom1996to2000,whereshewasaward edtheoutstandingstudent scholarshipasoneofbeststudentsintheuniversityforfou rcontinuousyears.Afterthat sheworkedwithProfessorZhuongreentechnologyoptimumfo rbenzaldehydeproduction intheChemicalEngineeringDepartmentandcompletedherMas ter'sDegreeofApplied Chemistryin2002. ShebeganpursuingherPh.D.degreeintheChemicalEngineeri ngDepartmentatUniversityofSouthFloridain2002.DuringthestudyinUSF,She presentedherworkinmany conferencesandshewononegrandpriceandtwohonorablemen tionawards.Shehasone paperpublishedinPhysicalReviewBandoneacceptedinJourn alofPhysicalChemistry Bbeforecompletingthisdissertation.


xml version 1.0 encoding UTF-8 standalone no
record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd
leader nam Ka
controlfield tag 001 001936665
003 fts
005 20080430091928.0
006 m||||e|||d||||||||
007 cr mnu|||uuuuu
008 080430s2006 flu sbm 000 0 eng d
datafield ind1 8 ind2 024
subfield code a E14-SFE0001773
035
(OCoLC)226388725
040
FHM
c FHM
049
FHMM
090
TP145 (ONLINE)
1 100
Miao, Ling.
0 245
Molecular simulations of Pd based hydrogen sensing materials
h [electronic resource] /
by Ling Miao.
260
[Tampa, Fla] :
b University of South Florida,
2006.
3 520
ABSTRACT: Hydrogen sensor technology is a crucial component for safety and many other practical concerns in the hydrogen economy. To achieve a desired sensor performance, proper choice of sensing material is critical, because it directly affects the main features of a sensor, such as response time, sensitivity, and selectivity. Palladium is well-known for its ability to sorb a large amount of hydrogen. Most hydrogen sensors use Pd-based sensing materials. Since hydrogen sensing is based on surface and interfacial interactions between the sensing material and hydrogen molecules, nanomaterials, a group of low dimensional systems with large surface to volume ratio, have become the focus of extensive studies in the potential application of hydrogen sensors. Pd nanowires and Pd-coated carbon nanotubes have been successfully used in hydrogen sensors and excellent results have been achieved. Motivated by this fact, in this dissertation, we perform theoretical modeling to achieve a complete and rigorous description of molecular interactions, which leads to the understanding of molecular behavior and sensing mechanisms.To demonstrate the properties of Pd-based sensing materials, two separate modeling techniques, but with the same underlying aim, are presented in this dissertation. Molecular dynamic simulations are applied for the thermodynamic, structural and dynamic properties of Pd nanomaterials. Ab initio calculations are utilized for the study of sensing mechanism of Pd functionalized single wall carbon nanotubes. The studies reported in this dissertation show the applications of computational simulations in the area of hydrogen sensors. It is expected that this work will lead to better understanding and design of molecular sensor devices.
502
Dissertation (Ph.D.)--University of South Florida, 2006.
504
Includes bibliographical references.
516
Text (Electronic dissertation) in PDF format.
538
System requirements: World Wide Web browser and PDF reader.
Mode of access: World Wide Web.
500
Title from PDF of title page.
Document formatted into pages; contains 174 pages.
Includes vita.
590
Adviser: Babu Joseph, Ph.D.
653
Palladium.
Hydrogen sensor.
Carbon nanotube.
MD simulations.
DFT.
690
Dissertations, Academic
z USF
x Chemical and Biomedical Engineering
Doctoral.
773
t USF Electronic Theses and Dissertations.
4 856
u http://digital.lib.usf.edu/?e14.1773