REAL-TIMEMULTIMODALSENSINGINNANO/BIOENVIRONMENTByBoSongADISSERTATIONSubmittedtoMichiganStateUniversityinpartialtoftherequirementsforthedegreeofElectricalEngineering-DoctorofPhilosophy2016ABSTRACTREAL-TIMEMULTIMODALSENSINGINNANO/BIOENVIRONMENTByBoSongAsasensingdeviceinnano-scale,scanningprobemicroscopy(SPM)isapowerfultoolforexploringnanoworld.NeverthelesstwofundamentalproblemstacklethedevelopmentandapplicationofSPMbasedimagingandmeasurement:slowimaging/measurementspeedandinaccuracyofmotionorpositioncontrol.Usually,SPMimaging/propertiesmeasuringspeedistooslowtocaptureadynamicobservationonsamplesurface.Inaddition,BothSPMimagingandpropertiesmeasurementalwaysexperiencepositioninginaccuracyproblemscausedbyhysteresisandcreepofthepiezoscanner.ThisdissertationwilltrytosolvetheseissuesandproposedaSPMbasedreal-timemultimodalsensingsystemwhichcanbeusedinnano/bioenvironment.First,acompressivesensingbasedvideoratefastSPMimagingsystemisshownasantmethodtodynamicallycapturethesamplesurfacechangewiththeimagingspeed1.5frame/swiththescansizeof500nm500nm.Besidestopographyimaging,anewadditionalmodalofSPM:vibrationmode,willbeintroduced,anditisdevelopedbyustoinvestigatethesubsurfacemechanicalpropertiesoftheelasticsamplesuchascellsandbacteria.AfollowedupstudyofenzymatichydrolysiswilldemonstratetheabilityofinsituobservationofsinglemoleculeeventusingvideorateSPM.AfterthatwewillintroduceanothermodalofthisSPMsensingsystem:accurateelectricalpropertiesmeasurement.Inthiselectricalpropertiesmeasurementmode,acompressivefeedbacksbasednon-vectorspacecontrolapproachisproposedinordertoimprovetheaccuracyofSPMbasednanomanipulations.Insteadofsensors,thelocalimagesareusedasboththeinputandfeedbackofanon-vectorspaceclosed-loopcontroller.Afollowedupstudywillalsobeintroducedtoshowntheimportantroleofnon-vectorspacecontrolinthestudyofconductivitydistributionofmulti-wallcarbonnanotubes.Attheendofthisdissertation,somefutureworkwillbealsoproposedtothedevelopmentandvalidationofthisreal-timemultimodalsensingsystem.ACKNOWLEDGMENTSIwouldliketoexpressmymostsincereappreciationtomyadvisor,Dr.NingXi,andDr.LixinDongfortheirexpertguidance,generousencouragementandsupportformyresearch.Inaddition,IwouldliketothankallmyPhDcommitteemembers:Dr.HassanK.Khalil,Dr.DonnaH.WangandDr.XiaoboTan.Theymetimelyhelpandunfailingsupportthatimprovethetechnicalsoundnessandthepresentationofthisdissertation.Furthermore,Iwouldliketoexpressmygratitudetoallmycolleagues,especiallytoDr.KingWaiChiuLai,Dr.CarmenKarManFung,Dr.HongzhiChen,Dr.RuiguoYang,Mr.ZhiyongSun,Mr.LiangliangChen,Mr.AndyTomaswick,Dr.YongliangYang,Dr.JianguoZhao,andDr.YunyiJia,fortheirsupportintheexperimentsanddiscussion.Lastbutnottheleast,IwanttothankmywifeLinRen,mydaughterMeeyaSongandmyparents.Thisdissertationwouldnothavebeenpossiblewithouttheiryearsofencouragementandcontinuoussupport.Withloveandgratitude,Idedicatethisdissertationtothem.ivTABLEOFCONTENTSLISTOFFIGURES...................................viiiChapter1Introduction...............................11.1BackgroundandMotivation...........................11.1.1VideoRateImagingSystem.......................31.1.2SensingofElectricalPropertiesinNanoEnvironmentwithAccuratePositionControl..............................61.1.3SurfaceMechanicalPropertiesCharacterizationusingAFM111.2ObjectivesandChallenges............................141.3Contributions...................................151.4OutlineofthisDissertation...........................16Chapter2CompressiveSensingforReal-timeSensinginNano/BioEn-vironment.................................182.1Introduction....................................182.2TheoreticalFoundationofCompressiveSensing................212.2.1GeneralIdeaofCompressiveSensing..................212.2.2SignalSparseRepresentation......................232.3DesignofMeasurementMatrixforCompressiveScanninginReal-timeSensing242.4KnowledgebasedCompressiveSensing.....................272.4.1KnowledgebasedMeasurementMatrixDesign.............272.4.2ImageReconstruction...........................292.5SystemImplementationforSPM........................302.6ExperimentalTestingResults..........................302.6.1StaticObservation............................322.6.2DynamicObservationusingKnowledgebasedCompressiveScan...352.7Conclusions....................................36Chapter3SensingofMechanicalPropertiesinNano/BioEnvironment.383.1Introduction....................................383.2TheStateofArtofVibrationModel......................413.3MathematicModelforVibrationMode.....................423.4HardwareImplementationofVibrationModelonSPMSystem........503.5ExperimentalResult...............................523.5.1TopographyImageComparisonbetweenVibrationModeandConven-tionalTappingandContactModes...................523.5.2CompressiveSensingInvolvedTopographyandLocked-inAmplitudeImagingTestinVibrationMode.....................57v3.5.3SubsurfaceStructureorMechanicalPropertiesMeasurementUsingVi-brationMode...............................603.6Conclusions....................................63Chapter4VideoRateImaginginBiologicalEnvironment.........654.1Introduction....................................654.2VideoRateAFMImagingofCelluloseandCellulase(TrCel7A)Interaction674.3ExperimentalSetupandResults.........................684.3.1PreparationofCelluloseCrystalandTrCel7AforAFMImaging..................................684.3.2InSituVisualizationandImageAnalysis................694.4ResultsandDiscussion..............................704.4.1SizeandShapeofCelluloseNanoCrystalandTrCel7A.704.4.2TrCel7ABindstoCelluloseandMoves.................734.4.3Time-lapseofDensityandDistributionofTrCel7AMoleculesonCel-luloseSubstrate..............................744.4.4CelluloseSubstrateChangesIndicatesEnzymaticHydrolysisRate..794.4.5TheHydrolyticRateisDependentontheDensityofTrCel7AMoleculesontheCelluloseSubstrate........................814.5Conclusions....................................87Chapter5Real-timeSensingofElectricalPropertiesinNanoEnvironment885.1Introduction....................................885.2AccuratePositionControlinNanoEnvironment................925.2.1Non-vectorSpaceControlbasedonLocalImage............925.2.1.1EssentialsofMutationAnalysis................945.2.1.2MutationAnalysisforNanomanipulation...........965.2.2CompressiveSensingforVisualServoing................985.2.3Non-vectorSpaceControlbasedonCompressiveFeedback......1005.2.3.1ControllerDesignbasedonCompressiveFeedback......1015.2.3.2StabilityAnalysis........................1025.3ExperimentalImplementationandSetup....................1045.3.1ExperimentalImplementationonAFM.................1045.3.2ExperimentonNon-vectorSpaceControlwithCompleteImageasFeedback..................................1055.3.3ExperimentonCompressiveSensingwithRandomSampling.....1075.3.4ExperimentonCompressiveFeedbackNon-vectorSpaceController.1085.3.5ExperimentonTrackingSWNTbasedonCompressiveFeedbackNon-vectorSpaceController..........................1095.3.6PerformanceAnalysisofNon-vectorSpaceControllers.........1125.4CarbonNanotubeLocalElectricalPropertyCharacterization.........1135.5MeasurementResultsandAnalysis.......................1165.6ControllableElectricalBreakdownofMultiwallCarbonNanotubes......1175.6.1Introduction................................1175.6.2JouleHeatingandThermalDissipationofMWNTbasedCircuit...120vi5.6.3ExperimentalDetails...........................1235.6.4ResultsandDiscussion..........................1245.7Conclusions....................................130Chapter6ConclusionsandFutureWork....................1316.1Conclusions....................................1316.2FutureWork....................................1326.2.1QuantitativelyAnalyzeTrCel7AMoleculesInvolvedEnzymaticHy-drolysisProcess..............................1326.2.2SubsurfaceStructureorMechanicalPropertiesMeasurementUsingVi-brationModeforCellMigrationStudy.................133REFERENCES................................135viiLISTOFFIGURESFigure2.1Generalideaofcompressivesensing..................22Figure2.2RandomsamplingpointsandTSPtrajectory(800randompointsin5050pointsareawithtotaltraveldistance981.1645)........25Figure2.3Thehardwarearchitectureofthenanomanipulationsystem.....31Figure2.4StaticcompressivescanexperimentresultsonHaCaTcellssample(5050pixels)(a):OriginalAFMimage(scansize:55)(b):Reconstructedimagebyminimizingl1(c):Reconstructedimagebyminimizingtotalvariance........................32Figure2.5StaticcompressivescanexperimentresultsonDNAsample(5050pixels)(a):OriginalAFMimage(scansize:500nm500nm)(b):Reconstructedimagebyminimizingl1(c):Reconstructedimagebyminimizingtotalvariance........................33Figure2.6DynamicobservationofDNAonlooselyboundsurfaceusingknowl-edgebasedcompressivescan(5050pixels)(a):Firstframeimageobtainedbyconventionalscan(scansize:800nm800nm)(b)-(h):Reconstructedimageobtainedbyknowledgebasedcompressivescanwithminimizingtotalvariance.....................34Figure3.1SchematicofthesetupforthevibrationAFM............41Figure3.2SchematicofthesetupforthevibrationAFM............42Figure3.3Modelillustration............................44Figure3.4SchematicofthesetupforthevibrationAFM............51Figure3.5Topographyinformationofcalibrationgridformconventionaltapingmode(a):Topographyimgaeformconventionaltapingmode(b):cross-sectionanalysisfromtopographyimage.............53Figure3.6Topographyinformationofcalibrationgridformconventionalcontactmode(a):Topographyimageformconventionalcontactmode(b):cross-sectionanalysisfromtopographyimage.............53viiiFigure3.7Topographyinformationofcalibrationgridformvibrationmode(a):Topographyimageformvibrationmode(b):cross-sectionanalysisfromtopographyimage.........................54Figure3.8Amplitudeandphaseimagesofcalibrationgridformconventionaltapingmode(a):Amplitudeimageformtapingmode(b):Phaseimageformtapingmode........................54Figure3.9Topographyinformationofgoldandsilicondioxidemicro-electrodesformconventionaltapingmode(a):Topographyimageformconven-tionaltapingmode(b):cross-sectionanalysisfromtopographyimage55Figure3.10Topographyinformationofgoldandsilicondioxidemicro-electrodesformconventionalcontactmode(a):Topographyimageformcon-ventionalcontactmode(b):Cross-sectionanalysisfromtopographyimage...................................56Figure3.11Topographyinformationofgoldandsilicondioxidemicro-electrodesformvibrationmode(a):Topographyimageformvibrationmode(b):Cross-sectionanalysisfromtopographyimage..........56Figure3.12Amplitudeandphaseimagesofgoldandsilicondioxidemicro-electrodesformconventionaltapingmode(a):Amplitudeimageformtapingmode(b):Phaseimageformtapingmode...............57Figure3.13Mechanicalpropertiesmappingofvibrationmodeoncalibrationgrid(a):Lockedinamplitudeimage(b):espringconstantmap.58Figure3.14Mechanicalpropertiesmappingofvibrationmodeonmicrochip(a):Lockedinamplitudeimage(b):espringconstantmap...58Figure3.15Experimentalresultsofcompressivevibrationmodeleft:Vibrationlockedinamplitudeimagebyfullscan,middle:espringcon-stantmapcalculatedbyfullscandata,righespringconstan-tmapcalculatedbycompressivescanwithcompressionratioof(a)50%,(b)10%...............................59Figure3.16PDMScoatedmicroelectrodeschip..................60Figure3.17ExperimentalresultsofvibrationmodeonPDMScoatedmicrochipsample(a):Topographyimageusingconventionaltappingmode,(b)Vibrationamplitudeimage.......................61ixFigure3.18Experimentalresultforthemechanicalpropertiesmeasurementus-ingcompressivesensingbasedvibrationmode.(a)TopographyimageofsamplesurfacebeforePDMScoatingusingregulartappingmode.(b)TopographyimageofsamplesurfaceafterPDMScoatingusingregulartappingmode.(c)Tappingamplitudeimageofsamplesur-faceafterPDMScoatingusingregulartappingmode.(d)TopographyimagesofsamplesurfaceafterPDMScoatingusingcompressivesens-ingusingregulartappingmode.(e)MechanicalpropertiesimagesofsamplesurfaceafterPDMScoatingusingcompressivesensingbasedvibrationmode..............................62Figure3.19ExperimentalresultforthemechanicalpropertiesmeasurementofliveHacaTcellusingvibrationmode.(a)TopographyimageofliveHacaTcellusingregulartappingmode.(b)VibrationamplitudeimageofliveHacaTcellusingvibrationmode............63Figure4.1Visualizationofcellulosenanocrystal(a)Amplitudeimageofcellulosenanocrystal(scanbar:800nm),(b)Zoomedinamplitudeimageofcellulosenanocrystal(s-canbar:220nm),(c)Zoomedinamplitudeimageofcellulosenanocrystal(scanbar:100nm),(d)Heightanalysisofcellulosenanocrystal.........................71Figure4.2VisualizationofTrCel7Aenzyme.(a)and(b)AFMamplitudeimageofTrCel7Aoncellulosenanocrystalsurface(scanbar:70nm),(b)Amplitudeimageofcellulosenanocrystal(scansize:2.2m),(c)HeightanalysisofcellulosenanocrystalblackcurveforTrCel7Ainimage(a),redcurveforTrCel7Ainimage(b)....................................72Figure4.3InSituvisualizationofdynamicinteractionsofcellulaseandcellu-losemolecules,(a)TrCel7A(labeledwitharrows)boundtoCellulose(scansize:180nm500nm),(b)TimelapseamplitudeimagesofanindividualTrCel7Amovingontheasinglecellulosenanocrystal(scansize:180nm180nm)...............75Figure4.4Video-rateAFMObservationsofTrCel7A(50m)moleculesboundoncellulosesubstrate.(a)ContinuouslycapturedAFMframesofmovingTrCel7Aoncellulosesubstrate(twotlocations:(a1)and(a2))in50mMsodiumacetatewithpH5.0.Imagingframerate:0.5frames/s.(b)HistogramofaveragemovingvelocityofTrCel7A.ThevelocitieswerecalculatedbythemodistanceandbyPoissondistribution(Detailedinsupplementedmaterial).(c)TrCel7AmoleculescountingbasedonAFMimages.PositionsofeachTrCel7Amoleculearelabeledwitharrows......76xFigure4.5TimecourseofthesurfacedensityofactiveTrCel7A(50M)moleculesboundoncellulosesubstratein50mMsodiumacetatewithpH5.0at25C.ThesurfacedensityofactiveTrCel7Ahasbeencalcu-latedbyaobservationarea15050nm2.(A)ObservedsurfacedensityofactiveTrCel7AdecliningduringthecontinuouslyAFMob-servationandtheaveragenumbersofactiveTrCel7AwerecalculatedastheexpectedvalueofPoissondistribution(Eq.1and2).Errorbarsshowstandarddeviation(SD)fromthethreeindependentmea-surements.Theexperimentaldatawasbyanempiricaldecayfunction(Eq.3).(B)ExampleofAFMdynamicobservationsondif-ferentreactiontimepoints:3min(B1),23min(B2),46min(B3)and76min(B4),respectively.ThenumbersofactiveTrCel7AoneachAFMframewerecountedmanuallyandusedastherawdataforcalculatetheparameterofPoissondistribution..........80Figure4.6Timecourseofthedensity(number)ofthetopographicheightchangesofcellulosesubstrateinteractedwithTrCel7A(50M)in50mMsodi-umacetatewithpH5.0at25C.(A)Observedheightofcel-lulosesurfacedecliningduringthecontinuouslyAFMobservation.Errorbarsshowstandarddeviation(SD)fromthethreeindependentmeasurements.(B)and(C)ExampleofAFMdynamicobservationsoncellulosesurfacemonitoringduring480seconds.(B)isthecross-sectionof(C)atvarioustimespots.Thepositionofcross-sectionismarkedwithdashlineon(C)......................82Figure4.7TimecoursecomparisonofthesurfacedensityofactiveTrCel7Amolecules(A)andthetopographicheightchangesofcellulosesubstrate(B)dur-ingthecontinuousadditionofTrCel7A.50MofTrCel7Awasaddedattimepoint0min,120minand240min.Boththecellulosesubstrateandimaging(50mMsodiumacetatewithpH5.0at25C)werestayedthesamethroughoutthelengthofentiretimeperi-od.ThesurfacedensityofactiveTrCel7AhasbeencalculatedastheexpectedvalueofPoissondistribution(Eq.1and2).Errorbarsshowstandarddeviation(SD)fromthethreeindependentmeasurements.85Figure5.1Controldiagramofthenon-vectorspacecontrolsystemwithcom-pressivefeedback(AFMasanexample)................91Figure5.2Basicworkingapproachofnon-vectorspacecontrol.........93Figure5.3Experimentsetupandresultsofnon-vectorspacecontrolbasedoncompressivefeedback(a):Experimentalsetupforthenon-vectors-pacecontrol(b):Experimentresultsofnon-vectorspacecontrolwithimageasfeedback:Errorinxandydirections............106xiFigure5.4ExperimentresultsofAFMimagesreconstructionbasedoncompres-sivesensing(a):OriginalAFMimageof5050pixels(b):Recon-structedimageobtainedbycompressivesensing...........107Figure5.5Experimentsetupandresultsofnon-vectorspacecontrolbasedoncompressivefeedback(a):Experimentalsetupforthenon-vectors-pacecontrolbasedoncompressivefeedback(b):Experimentresultsofnon-vectorspacecontrolwithcompressivefeedback:Errorinxandydirections.............................110Figure5.6ExperimentresultsoftrackingSWCNTusingnon-vectorspacecon-troller,(a):OriginalAFMimageof10241024pixels,(b):Trackingpath,(c):Asequenceofimagefeedback,(d):Positionerrorduringtracking.................................111Figure5.7Testingplatform(A):I-Vcurveobtainbycurvetracer(B):Dimension3100AFM(C):Conductiveprobe...................115Figure5.8Schematicdiagramofexperimentalsetupforcharacterizinglocalcon-ductivity(a):experimentalsetup(b):Usingconductivetiptoprobelocalconductance(c):AFMimageoftestingsample.........116Figure5.9MWNTelectricpropertycharacteristics(a):I-Vcharacteristicsfromsourcetodrainelectrodes(b):Totalresistanceasafunctionofchan-nellength................................118Figure5.10DiagramofthermaldistributionofMWNTintconditions,(a)AsuspendedMWNT,(b)AnMWNTwithanduniformcon-tactwithsubstrate,(c)AnMWNTwithdefectcontactedanduniformlywithsubstrate,(d)AnMWNTwithnonuniformcontactwithsubstrate..............................122Figure5.11Experimentalsetup:MWNTonelectrodesandmoveableAFMprobeforconductancecharacterization....................123Figure5.12ElectricalbreakdownofanMWNTwithuniformconductancedis-tribution,(a)TheAFMimagesbefore(left)andafter(right)theelectricalbreakdown,(b)Thetotalresistancerespecttothechannellengthbeforeandaftertheelectricalbreakdown,measuringdirection:fromthebottomendtotheupperendoftheMWNTin(a)....125Figure5.13ElectricalbreakdownofanMWNTwithnonuniformconductancedistribution,(a)TheAFMimagesbefore(left)andafter(right)theelectricalbreakdown,(b)Thetotalresistancerespecttothechannellengthbeforeandaftertheelectricalbreakdown,measuringdirection:fromthebottomendtotheupperendoftheMWNTin(a)....126xiiFigure5.14ElectricalbreakdownofanMWNTwithnonuniformconductancedistributionandcontactconsition,(a)TheAFMimagesbefore(left)andafter(right)theelectricalbreakdown,(b)Thetotalresistancerespecttothechannellengthbeforeandaftertheelectricalbreak-down,measuringdirection:fromthebottomendtotheupperendoftheMWNTin(a)............................128xiiiChapter1Introduction1.1BackgroundandMotivationThenanoworldwasrevolutionizedtherecentadvancementoftechnology,enablingimag-ing,manipulationandmeasurementfromnanoandmolecularlevel.Targetednanoparticleimagingandsensinghaveintroducednanotechnologytothebiomedicine,materialscienceandphysicsstudies.Thelaboratory-leveltestingandexperimentofnanoscalerequiresin-strumentsthatcanprovidenanoscaleimagingandoperation.Asoneofthecenterpiecesinnanotechnology,Thescanningprobemicroscopy(SPM)isasuitablecandidateforsuchneedsasitcouldscanandmanipulatenanoparticlesorsinglemolecularatnanoscale.Thescanningprobemicroscopies(SPMs)suchasatomicforcemicroscopy(AFM)andscanningtunnelingmicroscopy(STM)havebeenfrequentlyusedtoimageandmanipulatenanomat-ters[1][2].Usuallythiskindofmicroscopyareequippedwithaprobewhichhasaverysharptip(tipapexisapproximately10nmorless)anditcandelicatelyscanontopofsamplesurfacetogetthetopographyimage.Besidesimaging,thesharptipcanbeconsideredasanendofnano-robotwhichiscapableofmanipulatingnano-objectsandmodifyingsamplesurfaces[3][4].AlthoughAFMhasmanyadvantagesinimaging,itstillhasaverytnegativepointandthatistheslowimagingspeed.ThisisduetotheworkingprincipleofAFM.UnlikeothermicroandnanolevelobserversuchasScanningElectronMicroscope(SEM),1AFMobtainstheimagesbyscanninglinebylineonthesurfaceofsample.Usuallyittakesseveralminutestoscanhundredslinestogenerateahighresolutionimage.Thereforetheframerateisabouttenframesperhour.However,withthedevelopmentofbiologyandphysic,moreandmoreresearchershavethewillingtoobservethedynamicchangeinsamplesuchasthedeformationchangeofcell,DNAshapechangeandsoforth[5][6].AlthoughthereareotheravailableobservationssuchasSEMwhichmayalsobeusedinmanyexperiments,itdemandsthevacuumworkingenvironmentwhichwouldmakethelivesamplessuchascelldead.AFMhasthenatureabilitytoworkinavacuumfreecondition,buttheissueisthelowimagingframerate.Therefore,thereisanincreasingdemandsontheAFMbasedfastimagingsystemthatcouldobservethecontinuallychangehappensinseconds.BesidesimagingAFMalsoplaysanimportantroleofprovidingaccuratetopographyimageandmechanicalpropertiesmeasurementinthenanoscale.AFMenablesthebiomedicalstudieshaveatremendousdevelopmentfrombullexperimenttosinglemoleculestudies.Mechanicalpropertiesofsinglecellhavebeenknownasanimportantindicatororreportertoestimateorpredictthestateofthecells.Numerousmethodshavebeenintroducedtoobtainsamplepropertiessuchaselasticity,viscosityandenergydissipation[7][8][9].Regularly,thecontactmodeinAFMisalsousedastheindentationmeasurementinthe"forcecurvefunction".Duringthismeasurement,awellcontrolledindentationisgeneratedbyAFMprobe,andthetip-sampleinteractionforceisrecordedthroughthePSDsensor.ThroughthecalculationbasedonHertzmodel,aneYoung'smodulescanbeestimateasthemechanicalpropertiesofthemeasuredmartial.Sincemechanicallyindentationisnec-essaryinthismode,themechanicaldamagemayhappenduringthemeasurementprocess.Inaddition,becausethetip-sampleindentationonlyemphasizethepropertiesofthematerial,theinternalmechanicalpropertiesareoutofscopeduringthetraditionalforce-2curvemeasurement.Thismaynotbeaseriousissueforhomogenousmaterial,however,forbiologicalsamplessuchascellandbacterial,theinternalstructuresarequitecomplicat-ed,andthepropertiesisverylikelytobettwiththeinternalones.Therefore,aandnoninvasivemechanicalmechanicalpropertiesmeasurementmethodisneededtotlymapthemechanicalpropertiesofsamples.Besidesimagingspeed,conventionalscanningprobemicroscopy(SPM)basednanoma-nipulationsalwayshavetofacescanneraccuracyproblemssuchashysteresis,nonlinearityandthermaldrift.Althoughsomescannersconsistofinternalpositionsensors,thesensitivi-tyisnothighenoughtomonitorhighresolutionnanomanipulations.Additionally,oncethescansizedecreasestonanolevelsuchaslessthan100nm,thenoisebroughtbysensorsislargeenoughtotheperformanceoftheclosed-loopmotioncontrolsystem.Inthisstudy,weproposedanovelsensingmethodinnano/bioenvironmentforAFM(whichisoneofmostusefulSPMswithatomicresolutionimagingandmanipulatingabilities)basedfastimagingandelectrical/mechanicalpropertiesmeasurement[3][4],whichaimstoprovidetheoperatorwithvideoratevisualizationinformationaboutsamplesurfacechangesinmolecularlevel,aswellastheabilitytopreciselycharacterizesurfacepropertieswithhighspatialaccuracy.Throughthismultimodalsystem,AFMcouldserveasamulti-functionalnanomanipulationsystem.Ithasmanyapplicationssuchasnano-surgeryonalivecell[2],nano-devicefabrication[10][11][12],fastimagingondynamicchange[13],andsoforth.1.1.1VideoRateImagingSystemIn1993,thescanspeedlimitofAFMwasdescribed[14].Althoughwefoundnopublications,somestudiesaimingatincreasingtheAFMscanspeedmusthavebeeninitiatedatleastbefore1995.Infact,westartedtodevelophigh-speedscannersin1994andsmallcantilevers3in1997.Hansmasgroupalsostartedtodevelopdevisesforhigh-speedAFMaround1995.Theypresentedthereportonshortcantilevers(23mby12m)in1996[15]andthenareportonfastimagingin1999,inwhichsmallcantileversandanopticaldetectordesignedforthesmallcantileverswereusedtotakeaDNAimagein1.7s.Nextyear,theyimagedtheformationanddissociationoftheGroES-GroELcomplexes[16].However,duetothelimitedfeedbackbandwidth,thismolecularprocesswastracedbyscanningthesamplestageonlyinthexandzdirections.Amorecompletehigh-speedAFMsystemwasreportedbyusin2001and2002[17],inwhichahigh-speedscannerandfastelectronicswereintroducedinadditiontosmallcantilevers(resonantfrequencies600kHzinwater)andanopticaldetectorforthesmallcantilevers.Theimagingrateof12.5frames/swasachievedandthereforetheswinginglever-armmotionofmyosinVmoleculeswasassuccessiveimageswithascanrangeof240nm.Thisstudyinspiredthestudyonhigh-speedAFMandseemedtobringaboutagroundswelltowardsthefull-scaledevelopmentofhigh-speedAFManditsapplicationtobiologicalissuesthatweretosolvebyothertechniques.DevicesforHigh-speedAFMA.SmallCantilevers:Foragivenspringconstant,theresonantfrequencyincreaseswithdecreasingmassofthecantilever.Thetotalthermalnoisedependsonlyonthespringconstantandthetemperature.Therefore,acantileverwithahigherresonantfrequencyhasalowernoisedensity.Intappingmode,thefrequencyregionusedforimagingistheimagingbandwidth(itsmaximumisthefeedbackbandwidth)centeredaroundtheresonantfrequency.Thus,acantileverwithahigherresonantfrequencyislessbythermalnoise.B.High-speedScanner:4Thescanneristhedevicemosttooptimizeforhigh-speedscanning.High-speedscanofmechanicaldeviceswithmacroscopicdimensionstendstoproduceunwantedvibrations.Threetechniquesarerequiredtominimizeunwantedvibrations;(a)atechniquetosuppresstheimpulsiveforcesthatareproducedbyquickdisplacementoftheactuators,(b)atechniquetoincreasetheresonantfrequencies.Theissuewassolvedbyacounterbalancingtechnique[17].Forexample,forthez-scannerthatmovesatmuchhigherfrequenciesthanthexandy-scanners,twoidenticalpiezoactuatorsareplacedtotheirsupportingbaseinthecounterdirectionsanddisplacedsimultaneouslywiththesamelength.AnalternativewayistosupportapiezoactuatoratboththeendswithThiswaywasappliedtothex-scannerandworkedverywell(unpublisheddata).Theresonantfrequencyofapiezoactuatorisdeterminedalmostsolelybyitsmaximumdisplacement(inotherwords,byitslength).However,itcanbeelyextendedbyaninversecompensationmethodasdescribedlater.ThestructuralresonantfrequencyisenhancedbytheuseofacompactstructureandamaterialthathasalargeratiooftheYoungsmodulustothedensity.However,acompactstructuretendstoproduceinterferencesbetweenthethree-scanaxes.Aball-guidestage[18]isonechoicetoavoidtheinterferences.Analternativewayistouse(bladesprings)thatareenoughtobedisplacedbutenoughinthedirectionsperpendiculartothedisplacementaxis[19].Itshouldbenotedthatthescannermechanicsexceptforpiezoacutatorshastobeproducedbymonolithicprocessinginordertominimizethenumberofresonantelements.Anasymmetricalx-yhasbeenemployedtogainahighresonantfrequencyforthex-scanner(thefastscandirection)[20].However,asymmetricalx-yhasanadvantageofbeingcapableofrotatingthescandirection[19].Asamaterialforthescanner,aluminum5orduraluminisoftenused.1.1.2SensingofElectricalPropertiesinNanoEnvironmentwithAccuratePositionControlWiththedevelopmentofsynthesistechniquesofnano-materials,includingnanotubsandnanowire[21],nanopolymers[22],quantumwellsandquantumdots[23],theelectricalchar-acterizationofthesematerials,albeitmorechallenging,attractedstrongattention.Nano-materialshaveuniqueelectricalpropertiesduetoquantumt.Notonlydotheelectricalcharacterizationsrevealtheunderlyingphysical,mechanical,andelectricalprop-ertiesofthenano-materials,buttheycanalsobeutilizedtofabricatehighperformancesensorsanddevices,suchastransistors(FETs)[24][25],infraredsensors[26],gassensors[27],andsolarcells[28].Theconventionalelectricalcharacterizationsetupfornanotubeswasmeasuringglobalresistancebyconnectingananotubetotwometals[29].However,suchasetupisonlycapabletomeasuretheoverallresistanceofthedevices,whichcannotdistinguishtheconductanceofcontactsandnano-materials.Whatismore,itlacksthecapabilitytoinvestigatethelocalconductance,whichunderlyingpropertiesofthenano-materials.SPMs,conventionalimagingtoolswithnanometer-resolution,havebeenproposedtostudythelocalconductanceofnano-materials.TheyemployedtheconductiveSPMprobeasamovableelectrodetoconductlocalconductancemeasurements[30][31][32][21].Despitethefeasibilityofthismeasurementtechnique,onlyafewattemptshavebeenimplemented,letalonethelowreliabilityandresolution.ThereasonistheinaccurateSPMtipmotionandforcecontrolduringthemeasurement.6AlthoughtheimagingprecisionwithSPMscanbeuptosubnanometer[33],itischal-lenging,ifnotimpossible,toachievesuchaprecisionfornanoscalemotioncontrolduetothespatialuncertaintyoftheprobe'stip[34].ThemainreasonforsuchaisthepiezoelectricactuationmethodforSPMsystems.Theinherentnonlinearitiesofpiezoactu-atorssuchashysteresis,creep,vibration,andthermaldriftmakeprecisepositioncontrol(inthenanometer)extremely[35].Additionally,themodelingerrorsincludeparametervariation,unmodeleddynamics,andcouplingalsoexertextrainpositioncontrol[36].Theaccuratepoint-to-pointpositioncontrolormotioncontrolinnanoscaleisacriticalrequirementforSPMbasednanomanipulationsbecausetheyrelyonpreciselymovingtheprobetipfromonepositiontoadesiredposition.Forexample,inAFMbasednano-sensorfabrication,carbonnanotubeswerepushedtoadesiredpositionbyanano-manipulatortoformphotodetectors[37].Thepositionaccuracyofthemanipulationshouldbewith-insub-10-nanometerstofacilitatetheintegrationtoanano-antennathathasagapof30nanometers[38,39].TheaccuracyofAFMmeasurementandmanipulationhighlydependsonaccuratemotioncontroloftheprobe(whichisequippedattheendofthepiezo-tubescanner).Thepiezo-tubescannerwithadvantagesofnanometerscaleresolution,highandfastresponse,hasbeenwidelyusedinnano-manipulationtocontroltherelativepositionbetweentheprobeandsamples.Nevertheless,thetdrawbackstheprecisionofpiezoactuatorsaretheinherenthysteresis,creepandsystemdriftcharacteristics[40].Thecreepcanthemagnitudeoftheoutputoftheactuatorswhichcanbecompensatedbythelinearmethod.Thehysteresisproblemisanonlinearonewhichcancauseseriouspositionerrorduringnanomanipulation.Thehysteresisproblemmightbesustainablefor7AFMimagingwithascanpattern.However,itisfatalforAFMbasedarbitrarymanipulation.Todate,thehysteresisandcreepproblemsinpiezoactuatorshavebeenstudiedbymanyresearchers,andvarioussolutionshavebeenproposed.TypicalcompensationmodelsuchasthePreisachmethod[41][42]whichincludeafeed-forwardcontrollerforsolvinghysteresisproblem.Itcannot,however,reducetheon-lineerrorbecauseoflackingfeedback.APreisachoperatorbasedhysteresiscompensatorwasdevelopedwithanindirectfeed-backadaptivecontrollerinordertoreducethepositioningerrorinAFMimagingsystem[43];acontrolstrategywhichintegratestheKalmanobserveraswellasavibrationcompensatorwiththeLQGcontrollerwasproposedtoalleviatethehysteresis,creep,vibrationandcrosscoupling[44].Thesemethodsabovebelongtothecategoryoffeedbackcontrollers,whichweredesignedtousesensorstocapturethereal-timeoutputinformationofthesystem.Basedontheinformation,spcontrolstrategiescanbedevelopedtoachieveprecisemotionpositioningduringnanomanipulations.However,theprecisionoftheclosed-loopscannerhasbeenlimitedbytheperformanceofthesesensors(suchasstraingauge[45],capacitivesensor[46],andopticalsensor[47]).Forsensors,highaccuracyandbandwidthusuallymakethemexpensiveandbulky.Moreover,integratedsensorsarehighlysensitivetonoises[48].ThisisthereasonwhyhighresolutionAFMsareusuallyequippedwithopen-looppiezotubescanners.Theyhaveseveraldrawbacksneededtobesolved.First,sensorsusuallyincreasethesystemnoise.Second,thedisplacementmeasuredbysensorsistheoutputofpiezo-tubewhichisnottheexactpositionofthetip(attheendofprobe),becausethecantileverofprobemightbebendingduringnanomanipulations.tfromthetraditionalapproaches,weproposeanimagebasedclosed-loopcontrol8methodtoaddressthenanoscalemotioncontrolproblem.Thetipcanbeconsideredasasinglepixelcamerawithtwotranslationaldegreeoffreedoms.Bymovingthetiplocallyinasmallarea,alocalscanimagecanbeobtained[49].Sincetheimageisobtainedfromthelocalscan,itcanaccuratelythetip'strueposition.Ifadesiredlocalscanimagearoundadesiredtippositionisgiven,thenacontrollercanbedesignedtosteerthetippositiontothedesiredpositionbasedontheimagefeedback.Theadvantageofsuchanimage-basedcontrolmethodisthatiteliminatesexternalsensorsforpositionfeedback.Theimagebasedcontrolmethodpresentedinthisresearchbelongstotheliteratureofvisualservoing,whichutilizesvisioninformationtocontrolthemotionofamechanicalsystem.Fortraditionalimagebasedvisualservoingmethods,prominentfeaturesareextractedfromtheimage,andthenacontrollerisdesignedtomakethevectoroffeaturepositionsconvergetoadesiredvalue[50].Twopossibleissuesassociatewiththisfeaturebasedvectorcontrolmethod.Ontheonehand,robustfeatureextractionandtrackingareinnaturalenvironments.Infact,mostvisualservoingexperimentsarebasedonmarkers[51].Ontheotherhand,featureextractionfrominformationlossbecauseonlythefeatureinformationisusedforcontrol.Recently,thedirectorfeaturelessvisualservoingmethodisproposedtoaddresstheabovetwoissues.Forsuchmethods,thefeatureextractionandtrackingareeliminatedbecausethecontrollersaredesigneddirectlybasedonalltheimageintensitiesinsteadofsomefeaturesextractedfromtheimage.Threevariationsexistforsuchdirectservoingmethods.Thevariationprocessestheoriginalimagewithaspatialsamplingfunctiontoderiveakernelmeasurement.Acontrollerisdesignedtomakethemeasurementerrorconvergetozero[52].Thesecondvariationformstheerrorastheofintensitiesbetweentwoimages,andthenmakesthiserrorapproachzero[53,54].Thethirdvariationemploys9aninformationtheoreticalapproachtocomparethedistributionoftheinformationbetweentwoimagesanddesignthecontrollawtomaximizethemutualinformation[55].Insuchacondition,theexperimentalresultsoflocalconductancemeasurementfrompreviousstudiesshowedalargemeasurementvariance[32][21],andthiswaspossiblyduetoinaccuratetippositioncontrolwhichmeansduringthemeasurement,theconductiveprobemaynotreachthedesiredmeasurementpoints.Next,thespatialresolutionofmeasurement(typical100nmintraditionalmeasurementmethods)isnotenoughtoinvestigatelocalelectricpropertiesinnanoscale[31].Additionally,contactresistancebetweenconductiveprobeandnanowiresisload-dependent[30].Inotherwords,inordertocharacterizethelocalconductanceuniformlyateachlocation,constantcontactforceshouldbemaintainedwhichisanotheryinpractice.Thenon-vectorspacecontrolstrategyhasthepo-tentialtoovercomethesebyimprovingthespatialresolutionofprobemotioncontrolthroughwhichthepositionerrorcanbecontrolledwithinseveralnanometers.Inaddition,contactforcebetweenconductiveprobeandsamplesurfacecanbecontrolledbytheforcefeedbacksystem[56]andthatensurestheconstantcontactresistancebetweentheprobeandsample.Therefore,thenon-vectorspacecontrolsystemhasthepotentialtocon-ductdelicateandcomplicatedmanipulationandmeasurement.Inthisstudy,weillustratetheofthenon-vectorcontrolstrategybyintegratingthenanomanipulationwithelectricalcharacterizationsystemtostudylocalelectricalpropertyofacarbonnanotube.101.1.3SurfaceMechanicalPropertiesCharacterizationusingAFMMorphologicalandmechanicalpropertiesanalysisinnanoscaleofcellisbecomingincreasing-lyimportantinvariousbiomedicalstudies.intopographyandbetweennormalandmaligncellswerefoundandestablishedasamarkerforthechangeinmetastaticpotential.Thechangesincellularandmorphologyalsorevealsthetstatusofcellmigration,whichbthestudiesoftheprogressionofvariousdiseasesincludingcancer,atherosclerosisandarthritis.Todate,ithasbeenextremelychallengingtostudythemorphologyofcellsbystandardlightmicroscopyinlivingcellsbecauseoftheirsmallsizeandcomplexstructure.Whileimmandelectronmicroscopyhaveprovidedinsightintothestructureofcelladhesionmolecules,amodelsystemforaddressingdynamicchangesduetophysiolog-icalmechanismshasbeenlacking.AFMtheadvantageofrequiringminimalsamplepreparation,sothatbiomolecularstructurescanbedirectlystudiedinsituonviablesamplesthatrecapitulatebiologicalconditions.AFMprovidesthree-dimensionalimagesofsurfacetopographyandquantitativemeasuresofbiologicalproperties(e.g.inunparalleledresolutionallowingfortheilluminationofstructuralmoafterantibodytreatmentatascalethatcannotberevealedbystandardlightmicroscopy.Regularcontactmodeandnon-contactmodeprovidetopographyimages,andnon-contactmodeisalsousedastheindentationmeasurementinthe"forcecurvefunction".Duringthismeasurement,awellcontrolledindentationisgeneratedbyAFMprobe,andthetip-sampleinteractionforceisrecordedthroughthepsdsensor.ThroughthecalculationbasedonHertzmodel,aneYoung'smodulescanbeestimateasthemechanicalprop-11ertiesofthemeasuredmartial.Sincemechanicallyindentationisnecessaryinthismode,themechanicaldamagemayhappenduringthemeasurementprocess.Inaddition,becausethetip-sampleindentationonlyemphasizethepropertiesofthematerial,theinternalmechanicalpropertiesareoutofscopeduringthetraditionalforce-curvemeasurement.Thismaynotbeaseriousissueforhomogenousmaterial,however,forbiologicalsamplessuchascellandbacterial,theinternalstructuresarequitecomplicated,andtheproper-tiesisverylikelytobettwiththeinternalones.RecentdevelopmentofultrasonicAFM(UAFM)seemsprovideanalternativewaytosolvethisissue.TheUAFMisamooftheoriginalAFMset-upworkingincontactmodeandconstantnormalforce[57].ThemainideaistoworkatfrequenciesfarabovethecantileverprimaryresonanceintheinertialregimeofanAFMcantileverandsensethenonlinearityofthetipsurfaceinter-action.Inpreliminarystudies,UFMhasalreadydemonstratedsensitivitytosurfaceelasticpropertiesofmaterialsandalsotosubsurfacedefects[58].UFMisbasedonastandardAFMoperatinginCMwiththeadditionalapplicationofanultrasonicvibrationtothesubstrate,wellabovetheAFMcantileverresonance.Inthisway,thefrictionforcecanbeeliminatedbecausethetip-samplecontactisbrokenseveraltimeswhilethetipislaterallymovedduringtheimagingprocess.Anypossibledamagetothesampleorthetipisthusminimized[59].Anotheralternativemethodtomeasuretheinternalstructureofsamplesisusingquartzcrystalmicrobalance(QCM).QCMisananogramsensitivetechniquethatutilizesacousticwavesgeneratedbyoscillatingapiezo-electric,singlecrystalquartzplatetomeasuremass.ThebasisofQCMoperationrelatestoquartz'sinherentpropertyofpiezoelectricity.QCMsbecamewidelyusedasmassbal-ancesonlyafterthetheoryandexperimentsrelatingafrequencychangeoftheoscillatingcrystaltothemassadsorbedonthesurfacewasdemonstratedbySauerbreyin1959[60].12LiquidapplicationofQCMtechnologyexpandedthenumberofpotentialapplicationsdra-maticallyincludingbiotechnologyapplicationsandinparticularbiosensorapplications.Inpracticalbiomolecularapplicationsthedissipationparameterandthesubsequentlyextractedviscoelasticparametersarecriticalformanyapplications.Incellularadsorptionapplication-s,thesimpleQCMfrequencyandSauerbreyrelationshipwouldgreatlyunderestimatetheadsorbedmassofcells,sincetheshearwaveoftheoscillatingquartzisdampenedoutbeforeevenreachingthemiddleofthecell.Thefrequencypenetrationdepth(inthezdirectionawayfromthesensorsurface)dependsonthematerialinquestionandtypicallyisontheorderof250nminwater(rigidmaterialsmaystronglycoupletothesensorsurfaceandthuspermitmonitoringthickerbutviscoelasticmaterialswillbelimitedtowithinthisrange).Whentheadsorbedmassisviscousandtlysoftthatitdoesnotfollowthesensoroscillationperfectly(suchasinthecaseofcelladsorption),thisleadstointernalfriction(duetothedeformation)intheadlayerandthustodissipation.Thismassisthedynamicmass(incorporatingassociatedwater)andnottherestmass.Themoreviscoustheadsorbatethemoretheoscillationwillinducedeformation,andthusthecoupledmasswilldeviatemoreandmorefromtherestmass.Therefore,monitoringcelladsorptionrequiresusingthedissipationparametertofullycharacterizetheadsorptionofaviscoelasticcellularstructure.Ontheotherhand,theadsorptionofasmall,rigidproteinmaybeaccuratelymeasuredbymonitoringonlyfrequencychangesandthesetotheSauerbreyrela-tion,althoughassociatedcoupledwatermayagaingiveanunderestimationoftheadsorbedmass.AlthoughtheQCMhastheabilityofmonitoringmass/adhesionchanges,thespatialdetectionisthemainlimitationofthistechniquewhichmakesthequantitativeanalysisisimpossible.131.2ObjectivesandChallengesTheobjectivesforthisdissertationaretodevelopamultimodalAFMsystemwiththeabilityofreal-timesensinginnano/bioenvironment.Themainchallengescanbesummarizedinthreeaspects.First,inordertomakethesystemhavethefunctionoffastimaging,avideo-ratefastscansystemisneeded.Thevideo-ratesystemshouldbeabletoworkattheaverageframerateof1frame/second,suchthattherapidchangesinbiomedicalsamplescanbecapturedininsituobservations.Second,TheaccuracyoftheAFMtipmotionandpositioningshouldbewellcontrolledwithincouplenanometers,whichassuretheaccuratemanipulationinnanoscaleandmolecularlevel.Thelastoneisthefunctionofsubsurfaceimaging/mechanicalpropertiesmappingability.Sincemostofreactionorinteractionofmoleculesinbiomedicalstudyhappensinsidethecellorbacteria,thereisanincreasingdemandsontheAFMwiththeadditionalfunctionofsubsurfaceimagingandmeasurementotherthanregulartopographyimagingandsurfacemechanicalpropertiescharacterization.Inordertomeetthechallengeabouttheimagingspeed,acompressivescanningisdevelopedbasedoncompressivesensingtheory.Thegoalistominimizescanningtrajec-tory/timebyeliminatingunnecessaryscanning.TherearethreemajorstepsinapplyingcompressivesensingtoAFMimaging:tomodelanimageforcompressivesensing,toob-taincompressivescanningpatternbyameasurementmatrixincompressivesensing,andtoreconstructoriginalimagebasedoncompressivedata.Forthesecondchallenge,anon-vectorspacepositioncontrolmethodispresentedinthisstudy.Thegeneralideaistoformasetfromanimageandformulatetheimagedynamicsinthespaceofsets.Thisspaceiscalledthenon-vectorspacebecausethelinearstructure14inthevectorspacedoesnotexist.Basedonthedynamicsformulation,acontrollercanbedesigneddirectlyontheimagesetsforvisualservoing.Thisnon-vectorspacecontrolmethodistfromexistingdirectvisualservoingmethodsbecausetheproblemformulationist.Forthelastchallenge,weplantouseaspecialdesigned"vibrationmode"AFMtosolvethecurrentissueofsubsurfacemeasurement.Thevibrationmodehasacombinationoftheadvantageofconventionaltappingmodeimagingwithnanoscaleresolution,andthenanomechanicalmappingusingtheadditionaldeformationinducedbyvibratingneartheresonancefrequencyofthemeasuredsampletorecoverythespringconstantmapoftheinternalstructureofthesample.1.3ContributionsThecontributionsforthisthesiscanbesummarizedintwoaspects:designanddevelopmentforreal-timemultimodalsensingsystem;followupapplicationresearchtostudythephysicsandmechanismsbehindthephysicalandbiomedicalphenomenalusingthissystem.First,acompressivesensingbasedvideoratefastAFMimagingsystemhasbeende-signedasantmethodtodynamicallycapturethesamplesurfacechangewiththeimagingspeed1.5frame/s.weproposedaconceptcalled"compressivescan",inwhichthecompressivesensingisusedtocompressthescantrajectoryandreconstructedoriginalAFMimageframes.ThevideoratefastAFMimagingsystemdoesnotrequireanyhardwareupgradesbutalsocanachievethehighimagingspeedwithcommerciallyfastscanAFMinthesamelevel.AfollowedupstudyofenzymatichydrolysisdemonstratedtheabilityofinsituobservationofsinglemoleculeeventusingvideorateAFM.Second,acompressive15feedbacksbasednon-vectorspacecontrolapproachwillbeproposedinordertoimprovetheaccuracyofAFMbasednanomanipulations.Insteadofsensors,thelocalimagesareusedasboththeinputandfeedbackofanon-vectorspaceclosed-loopcontroller.Thepositionerrorofthisnon-vectorspacesystemcanbecontrolledwithintwonanometers.Afollowedupstudywillalsobeintroducedtoshowntheimportantroleofnon-vectorspacecontrolinthestudyofelectricalbreakdownofmulti-wallcarbonnanotubes.Moreover,anewadditionalfunctionofthenanorobot:vibrationmode,willbeintroduced.twithconventionalpointandshootingsignalmeasurement,vibrationmeasurementisamoremethodtoevaluatethemechanicalpropertiesofinternalstructureofelasticmaterial.ThebasicideaofthismethodistovibrateverticallyusingtheAFMscannertodrivethemeasuredsamplevibrateupanddown.Theadditionalvibrationamplitudeontheuppersurfaceofsample,otherthanthedrivingvibrationcanbeconsideredastheresultofsampledeformationwhichdependsonthemechanicalproperties,suchasthespringconstant.Vibrationmodeispo-tentiallyausefulAFMfunctiontoinvestigatethesubsurfacemechanicalpropertiesoftheelasticsamplesuchascellsandbacteria.1.4OutlineofthisDissertationThedissertationcanbemainlydividedintotwoaspects:systemdesignandapplicationstudy.Chapter2,3discussthesystemdesignaboutvideorateAFMandreal-timesensingofelectrical/mechnicalproperties;Chapter4and5presentfollowupapplicationresearchusingthismultimodalsensingsystem.Chapter2presentsthetheoreticalfoundationofreal-timeimaging:compressivesensing.16Themathematicalmodelofcompressivesensingwillbediscussed.Afterthat,thedesignforthemeasurementmatrixandscantrajectorywillbeelaborated.Thenaknowledgebasedimagerecoveralgorithmtoobtainthebestreconstructedimages.Finally,wepresenttheimplementationdetailsandexperimentalresults.Chapter3introducesdesignanddevelopmentofvibrationmodeAFMwhichisusedformechanicalpropertiesmeasurementinnano/bioenvironment.Firstofall,wewillintroduc-tionofsubsurfaceimagingandmechanicalpropertiesmeasurement.Afterthat,amathe-maticmodelofelasticobjectisdiscussed.Finally,weusecompressivesensingtoincreasethesamplingtimetomeasurethesubsurfacemechanicalpropertiesmapusingvibrationmode.Chapter4discussesthefollow-upstudyusingvideorateAFMtoinvestigatesinglemoleculebehaviorofenzymatichydrolysis.First,insitusinglemoleculeobservationofcellulaseusingvideo-rateAFMispresented.Then,weperforminsituobservationofcellu-losesurfacechangesasanindicatorofhydrolysisrate.Finally,weplantodiscussthedataandinvestigatethemechanismofenzymaticinactivationduringhydrolysisinteraction.Chapter5introducesthereal-timesensingmethodforelectricalpropertiesmeasurementinnanoenvironment.Firstofall,anewtechniquenamed"non-vectorspacecontrol"isproposedinordertoincreasethespatialpositioningaccuracyofAFMprobingability.Af-terthatafollowedupstudyofcarbonnanotubelocalelectricalpropertycharacterizationexperimentisgiventobothvalidatethesystemandbetterunderstandingthemechanismofelectrontransportinmultiwallcarbonnanotube.Chapter6concludesthemainresultsandofthisstudyandproposalsthefuturework.17Chapter2CompressiveSensingforReal-timeSensinginNano/BioEnvironment2.1IntroductionAtomicForceMicroscopyisapowerfulinstrumentforstudyingandexploringnanoworld[61].AFMcanobtainultrahighresolutionimageinsub-nanoscale.ThebasicworkingprincipleofAFMisaccuratelyscanninglinebylineonthesamplesurface.AFMhasanoutstandingperformanceonimagingbothinairandliquid.Inaddition,withthehelpoftheAFMsharptip,itcouldalsobeservedasameasuringtooltomeasurethemechanicalpropertiessuchas,Young'smodulusandroughness[62][63].However,AFMhasaverysig-tnegativeaspect-theslowimagingspeed.ItisduetotheworkingprincipleofAFM.Usuallyitscanshundredslinestogenerateahighresolutionimage.Thereforetheframerateistlylowatetotenframesperhour.Thisisimpossiblefordynamicobservationinstudyingbiologicalandphysicalbehaviorssuchasthedeformationandroughnesschangeofcells,carbonnanotubeshapechangeandsoforth[5][6].Inaddition,forAFMbasedmanipulations,thelowframeratemakeittorealizearealtimevisualguidemanipu-lationsystem.Duetothelowimagingspeed,operatorsnormallyhastowaitseveralminutestovisualizethemanipulatingresults.AlthoughsomeothermicroscopessuchasSEMmightalsobeusedinmanyapplications,theydemandvacuumobservationenvironmentwhichis18notsuitableforlivesamplessuchascells.AFMnaturallysuitsforworkinginavacuumfreecondition,buttheissueisthetlowimagingframerate.Therefore,thereisanincreasingdemandsonfastimagingAFMsystemwhichcouldcapturethecontinuouslychangesoccurringinseconds.Inordertosolvetheproblemoflowframerate,hardwareupgradeisonepossibleoption.Usinguncoupledpiezoactuatorstodrivethemovementineachdirectionseparatelyisonewaytospeedupthescanspeed.Currently,afastscanimagingAFMnamedFastscanDimension(BrukerNano,SantaBarbara,CA)couldreachashighas3frameperminute.ForconventionalAFM,hardwareupgrademightnotbeanoption,thisisnotonlyeconomicproblembutthenewscannersandcontrollerscannotbedirectlyimplantedonaconventionalAFM.Anothersolutionforimagingspeedproblemisnotjustgearingupthescanspeedbutalsousenovelscanstrategy-compressivescan.ForconventionalAFM,thescannerscanstheentireareaforanimage,butforcompressivescan,arandomscanpatternisdelicatelydesignedtoachieveashorterscantrajectorywhichdecreasesthetimespentonscanning.OncetheAFMgetsthepartialtopographyinformation,anotherissueishowtousethiscompressivedatatoreconstructtheoriginalimage.Consideringacompressiblesignal(image),therearesomemethodstodirectlysamplethecompresseddatainsteadofthehugeonewithlessinformation.Compressivesensingcametosolvethisproblem.In2006,thefundamentalmathematicproofforrecon-structingsparsesignalusingfewermeasurementshadbeenestablished[64].Compressivesensingrealizescompressinginsamplingstep.Insteadofsamplingoriginalsignalpointbypoint,compressivesensingonlysamplesasumofrandomprojectionsfromoriginalsignaltoaprojectionmatrix(measurementmatrix).Afterafewmeasurementswhicharefewer19thantraditionalsamplingmethod,theoriginalsignalcanbereconstructedbysignalrecon-structionalgorithm[65].Becausethenumberofmeasurementsarefewerthanthedimensionoforiginalsignal,ifthesignalissparseandthemeasurementmatrixhasbeenwellselect-ed,thecompressivesensingcouldreconstructtheexactoriginalsignalwithoverwhelmingprobability.ForAFMbasedcompressivescan,itlargelydecreasesthetimespentonscanning,andthereconstructedimageisobtainedafterimagerecoveringalgorithmshavebeenapplied.Inaddition,inordertoobtainabetterreconstructedimagewithevenlessmeasurements,andrealizeAFMbaseddynamicobservation,aspecialcompressivescanbasedonpreviousknowledgeisproposed.Itcouldmergetheinformationobtainedbypreviousframeimageandthecompressivedataobtainedbycurrentframe.ThisapproachcouldlargelyincreasetheAFMimagingrate,enhanceimagequalityandrealizedynamicobservation.Inthisstudy,weproposeanewapproachforusingcompressivescantoachieveafastimagingAFM.Forthisapproach,therearefourstepsasfollows:(1)Theoreticalanalysisofcompressivescanbasedoncompressivesensing.(2)RandommeasurementmatrixdesignforAFMimplementation.BecauseoftheworkingprincipleofAFM,randommeasurementmatrixcannotbedirectlyapplied,themethodologytoimplementrandommeasurementmatrixintoAFMscantrajectorywillbediscussed.(3)Imagereconstructionalgorithmsinvestigation.Duetospecialdesignedmeasurementmatrix,timagereconstructionmethodswillbediscussed.(4)Inordertodynamicallycapturecontinuoussurfacechange,aknowledgebasedcompressivescanstrategyisdevelopedforAFMdynamicobservation.202.2TheoreticalFoundationofCompressiveSensingIntroducingcompressivesensingintoAFMimagingsystemisaconvenientandtwayforreducingtimespentonscanning.Thegoalistodecreasethescantrajectorywhichsam-plesfewerthanconventionalmeasurements.Therearethreemajorsectionsincompressivesensing:signalsparserepresentation,measurementmatrixdesignandsignalreconstructionalgorithms.Compressivesensingprefersthesparsesignal.Althoughmostsignalsarenotsparsenaturally,itisnottothetsparserepresentationmethods.ThetransformssuchaswaveletandFourierhavetheabilitytomakesignalsparsefromtimedomainintofrequencydomain.Inthissectionwewillintroducethebasicideaofcompressivesensingandthesignalsparsifyapproaches.Thedesignofmeasurementmatrixandsignalreconstructionalgorithmswillbediscussedinnextsections.2.2.1GeneralIdeaofCompressiveSensingGivenanunknownsignalxwhichx2RN,anduseMtimeslinearmeasurementstosampletheoriginalsignalx(asshowninFig.2.1).IfM=N,theoriginalsignalxwillbeperfectlycapturedbysolvingthelinearalgebraequations.However,itbecomesinterestingwhenM˝N,andinwordsfewermeasurementsmightbeenoughforsamplingandreconstructingtheoriginalsignal.y=x(2.1)whereiscalledmeasurementmatrix.Everymeasurementisasumoflinearprojectionfromtheoriginalsignalxtomeasurementmatrixyisthemeasurementresultswhichy2RM.Eq.(5.11)isobviouslyanunder-determinedequation.Thereisnouniquesolution21Figure2.1Generalideaofcompressivesensingforthisequation.Howeverifitisundersomeconstraintssuchasthattheoriginalsignalissparseandmeasurementmatrixisproperlydesigned,wecananoptimizationsolutionforxbysolvingtheminimizationl0problem[64].^x=argminjjxjj0s.t.x=y(2.2)Sincesolvingl0+minimizationproblemisaNP-hardquestion,peoplewouldliketousel1minimizationinstead[66].ThentheEq.(5.12)couldbemoas^x=argminjjxjj1s.t.x=y(2.3)where^xisthereconstructedsignal.222.2.2SignalSparseRepresentationAsignaliscalledsparseifonlyasmallamountofelementshavethetvaluewhilealltheothersarezero.HenceK-sparsemeansthesignalonlyhasKtvalues.Oneoftheassumptionsforthecompressivesensingisthattheobservedsignalmustbesparse.Actuallymostsignalsarenotsparseintimedomain.Thereforewemustthesignalsparserepresentationinotherdomainsorbasissuchasx=s(2.4)wheresisthesparserepresentationofsignalxinbasisManytransformbasissuchaswavelet,curveletandFourierhavetheabilitytomakesignalsparsebytransformingitfromtimedomaintothefrequencydomain.Underthesebasis,Eq.(2.4)becomesy=s(2.5)y=~s(2.6)Nownewmeasurementmatrixcanbeconsideredasandhereweuse~=todenotethisnewmeasurementmatrix.Thenunderthesamebasis,Eq.(5.13)becomes^s=argminjjsjj1s.t.s=y(2.7)where^sisthecotsunderbasisoftheoriginalsignal.Obviously,thetransformbasis=Iiftheoriginalsignalisalreadysparse.23Becausecompressivesensingcouldusefewermeasurementstoobtainahighqualityrecoveryimage,weareinterestedinintegratingcompressivesensingwithAFMscanningstrategytodecreasethetimespentonscanning.Thechallengeofintegrationishowtodesignapropermeasurementmatrix.UsuallyrandomGaussianandBernoullimatrixesaregoodchoicesbuttheyforapplyingtheserandommeasurementmatrixestoAFMisthattheAFMobtainsthetopographythroughscanninglinebyline.Itistosamplerandompointssimultaneously.Therefore,specialdesignedrandommeasurementmatriximplementationonAFMshouldbediscussed.2.3DesignofMeasurementMatrixforCompressiveScanninginReal-timeSensingForcompressivesensingthemeasurementmatrixisanessentialpartduetotherelationshipbetweenthemeasurementmatrixandmeasurement.Wellandproperlydesignedmeasurementmatrixusuallyleadtofewermeasurementsbuthighqualityreconstructionimage.HoweverthechallengeincompressivesensinginAFMishowtoimplementmea-surementmatrixontoAFMscantrajectory.ThephysicalmeaningofmeasurementmatrixinthisapplicationistheAFMtipscanningtrajectory.Inotherwords,givenadesignedmeasurementmatrix,thetipmovingandscanningtrajectoryisalsodetermined.BecauseofthespecialworkingprincipleofAFMwhichusesasharptiptoscanontopofsamplesurfacelinebyline,itisreallyhardtouseconventionalrandommeasurementmatrixwhichsamplesrandompointsintheentiresamplesurfacesimultaneously.Insteadofrandommea-surementmatrix,continueandsmoothAFMtrajectoryrepresentedbymeasurementmatrixmightbeabetterchoice.Thereforesomespecialdesignedmeasurementmatrixeshavebeen24studiedinpreviousresearch[13].Moreover,howtocontrolthemovementofAFMtipisanotherissue.Fortunately,thesystemwedevelopedforAFMbasednano-manipulation,hastheabilitytomakeAFMtipscanalongdesignedmeasurementmatrixandobtainthetopography.Duringthetestinpreviousstudy,althougheachoneofthesematrixeshasagoodperformanceondatasamplingandimagerecoveryfortheAFMsamplesurface,onepotentialproblemofthesemeasurementmatrixesisthatnoneofthemisrandom.FromtheviewoftheRestrictedIsometryProperty(RIP)[64],thesemeasurementmatrixescannotguaranteealltheinformationoforiginalimagetobetotallyreconstructed.Inthissection,were-designthemeasurementmatrixwhichisarandomsamplingmatrixwhenitassociateswithFourierorwaveletbasis,ittheconditionsofRIP.Theoriginalimagewillbefullyreconstructed.Figure2.2RandomsamplingpointsandTSPtrajectory(800randompointsin5050pointsareawithtotaltraveldistance981.1645)25Givenameasurementmatrix,thescanningtrajectoryisalsodetermined.Inthisresearchweprefertherandomsamplingintimedomain(asshowninFig.2.2).However,theworkingprincipleofAFMisusingasharptiptoscanlinebylineontopofsamplesurface.Thereforeacontinuoustrajectorywhichwillcoveralltherandompointsshouldbedeveloped.Itisthetypicaltravelingsalesmanproblem(TSP)whichisNP-hard.Beforesolvingthisproblem,severalconditionsmustbetipmustscaneachpointexactlyonceandreturntothestartingpoint.HereweuseGeneticAlgorithm(GA)whichisapopularcomputingparadigmbasedoncrossoverandmutationtothenearoptimalsolutionforthistrajectory[67].Thisalgorithmconnectseachofthetwopointsandthenrandomlychoosesonepositiontocuttheconnectionoftwopoints.Byusingprocessesofrecombination,mutationandselection,GAeventuallysearchesanewgenerationpointswhichisbetter(shorterdistance)thanitsformertrajectory.Herewesettheimagingareawiththesizeof5050pixelsandthetrajectoryisshowninFig.2.2.TheredlinedenotesthetrajectoryofAFMtipwhichwouldvisiteverypointonlyonce.Thetotaldistanceisaround989(thedistancebetweentwoneighborpointsissetasone)whichismuchshorterthanconventionalscanstrategy(totaldistanceis2500inrasterscan).Withshorterscantrajectory,wecandirectlysavethetimespentonscanningandincreasetheAFMimagingrate.Oneimportantthingshouldbenotedhere,forcompressivesensing,ithastwobasicconstraints:themeasurementmatrixshouldsatisfytheRIPcondition;second,theobservedsignalshouldbesparse.Forthisapplication,neitherofthemcouldbeGoodthingiswecanonebasiswhichcouldtransformthenon-sparsesignalintimedomainintofrequencydomain(asmentionedinprevioussection).Abouttheconstraint,onceweapplythebasisthenewmeasurementmatrixbecomes~=which26theRIPandimpliesthatwerandomlysampledintimedomainbutreconstructtheimageinfrequencydomainandtransferitbacktotimedomain.2.4KnowledgebasedCompressiveSensingIntheprevioussection,weproposedtherandommeasurementmatrixdesignforcompressivescan.Throughthetheoreticalanalysis,thissamplingmethodcoulddealwiththeconditionwhenthesignalissparseinfrequencydomain.Ifthesignalisnotsparseinfrequencydomain,inotherwords,iftheobservedimageissparseintimedomain,thissamplingmethodcouldnotguaranteetheobservedimagebewellsampledandexactlyreconstructed.Actually,forAFMbasedmanipulationsandobservations,theobservedimageisquitepossibletobesparseintimedomain.Accordingtouncertaintyprinciple,Ifthesignalissparseinfrequencydomain,itcannotbesparseattimedomain.Inthiscasetherandomsamplingintimedomainmightnotcoverallthetopographyinformation.Onesolutionofthisissueistobuildupaknowledgebasedcompressivescanstrategy.Inthedynamicobservation,AFMcontinuouslyscansandobservesthedynamicchangeofsamplesurface.Inthiscasewecandevelopanapproachtodesignthemeasurementmatrixbaseonlastframeinformation,andsimultaneouslyusetheinformationoflastframeasapartofcurrentmeasurements.Now,theproblembecomeshowtousethepreviousinformationandhowtodesignthenewmeasurementmatrixforthecurrentframe.2.4.1KnowledgebasedMeasurementMatrixDesignForcontinuouslyobservation,ifthecapturefrequencyishigherthannanoparticledynamicchangefrequency,wecanassumethattheimageintimetiissimilarwiththepreviousone27ti1kxtixti1k2(2.8)whereisapositivenumber.Inthiscase,wecanfurtherassumethatforcurrentframexti,itconsistsoftwopartsamongwhichoneisfrompreviousframexti1andtheotheroneisfromcurrentsamplingtixti.xtiˇti1xti1tixti=xti(2.9)whereti1andtiarethemeasurementmatrixesofxti1andxtirespectively.Inwords,theycouldbeconsideredastheprojectionmatrixeswhichti2RMN:RN!RMandti12R(NM)N:RN!R(NM)InEq.(2.9),tixtiistherandomsamplingresultsofcurrentframeimage.BecausethelengthofthismeasurementsisMwhichM<N,itstillneedstheinformationabouttheotherNMelementsinformationtoconstructcurrentframeimage.Forthesemissingelements,weusepreviousframeinformationtointheblankstogeneratexti.However,thisxticouldnotbeuseddirectlyasthecurrentframeimage,andthisisbecausethesetwopartsofdatafromtframescannotmergethemselvesautomatically.Anothercompliantandpredictprocessisneededforfurtherestimatingthecurrentframeimagexti.Here,thecompressivesensingbasedonBernoullirandommeasurementmatrixandminimizationtotalvariationalgorithmareusedtoestimatethexti.282.4.2ImageReconstructionyti=Bernoullixti(2.10)^xti=argminTV(xti)s.t.yti=Bernoullixti(2.11)whereTV(x)=Pi;jq(xi+1;jxi;j)2+(xi;j+1xi;j)2.Afterthefurthersamplingandreconstructionprocess,therecoveredcurrentframeimage^xtihasbeenobtained.Becauseofapplyingtheminimizationtotalvariationalgorithm,therecoveredimagecouldachieveagradientcontinuous.Inthiscasethe^xticouldbecomesharpandsmooth.Twoimportantthingsshouldbenotedhere.Firstoneisthephysicalmeaningof^xti.Here^xtiisreconstructedbyboththecurrentframextiandpreviousframexti1.Therefore,therecoveredcurrentframeimage^xtirepresenttheframebetweenti1andti.Hereweusethisinter-frametoapproximatethecurrentframeimage.Consideradynamicallycontinuousobservation,assumethattheframeofimagewehavealreadygotandthroughaboveapproachwerandomsampledattimeti,wherei=1;2;;nandrecoveredtheimagesatthetimeti,wherei=1;2;;nandˆ(0;1).Thevalueofparameterdependsonthenumberofrandomsampling.Inotherwords,ifrandomsampleshaveN/2measurements,thevalueofshouldaround0.5.SecondoneisabouttherandommeasurementmatrixestixtiandBernoulli.Bothofthemshouldberedesignedforeachframe.Theseprocessestrytoachieveanindependentanduniformsamplingwhichwillcovertheentireimageacrossseveralframes.292.5SystemImplementationforSPMIntheprevioussections,weproposedaknowledgebasedcompressivescanapproachforAFMdynamicimaging.ThismethodologyisusedforincreasingtheimagingspeedofAFMinordertoachieveafastimagingsystem.Byintroducingcompressivesensing,acompressivescanstrategyhasbeendeveloped.Inordertodealwiththesmallparticlesonsamplesurfacewhichmightbelostbyrandomsampling,webuildupaknowledgebasedcompressivescansystemwhichcouldreconstructimagesbetter.Inordertotesttheperformanceofcompressivescanandknowledgebasedcompressivescanstrategies,severalexperimentswerecarriedouttoprovetheabilityofthisfastimagingsystem.Inordertotesttheperformanceofcompressivescanstrategy,weimplementthismethod-ologyintoourAFMmanipulationsystem(asshowninFig.2.3).AnMultimode(BrukerInc.)AFMwithanopen-loopscannerisusedinthisexperiment.Thenano-manipulationsoftwareisrunonthemaincomputerwithahapticjoystick.Inaddition,areal-timeLinuxsystem(RT-Linux)withDAQcardsisusedforcontrol.WealsodevelopedaboxnamedSignalAccessandControlBoxforapplyingthecontrolsignalintotheAFMcontrolleraswellasreadingthesignaloftopographyofsamplesurface.2.6ExperimentalTestingResultsThesampleswechosefortheseexperimentsareHaCaTcellsandDNA.TheHaCaTcellisatypeofhumanskincell.TheHaCaTcellsweregrowninDMEM(Gibco-Invitrogen,Carlsbad,CAUSA.)medium,andsupplementedwithtenpercentsfetalcalfserum(GeminiBio-products,WesrSacramento,CAUSA.)[2].DNAsampleismadefromLambdaPhageDNA,methylated,fromEscherichiacoilhoststrainW3110(Sigma-Aldrich.Co).DNAsolutionwas30Figure2.3Thehardwarearchitectureofthenanomanipulationsystem31dilutedinto1:1000withDIwateranddroponlooselyboundmicasurface.2.6.1StaticObservation(a)(b)(c)Figure2.4StaticcompressivescanexperimentresultsonHaCaTcellssample(5050pixels)(a):OriginalAFMimage(scansize:55)(b):Reconstructedimagebyminimizingl1(c):ReconstructedimagebyminimizingtotalvarianceBeforecompressivescan,weuseconventionalAFMtogetalocalimagewiththescansizeof55onHaCaTcells(showninFig.2.4(a)).FirstlytheAFMimageswereobtainedforseveralminutes.Theninthesamearea,weusethecompressivescanmethodtore-scanandusecompressivesensingimagereconstructionalgorithmstorecovertheimage.TherecoveredimagesareshowninFig.2.4(b)and(c).Theimagereconstructionalgorithmswe32usedherearel1asEq.(2.7)theminimizationtotalvariationalgorithmasEq.(5.14).ForDNAsample,thescansizeis500nm500nmwhichismuchsmallerthanpreviousexperiment.Thisexampletriestoillustratetheimagingperformanceofcompressivescanonverysmallarea.TheresultsareshowninFig.2.5(a)(b)(c)Figure2.5StaticcompressivescanexperimentresultsonDNAsample(5050pixels)(a):OriginalAFMimage(scansize:500nm500nm)(b):Reconstructedimagebyminimizingl1(c):ReconstructedimagebyminimizingtotalvarianceFromthestaticexperimentresults,itiscleartovisualizethebetweenthesetwosamples.FortheHaCaTcellsimages,boththeimagereconstructionalgorithmshavethegoodperformance-bothofthemaresimilartooriginalimage(asshowninFig.2.4(a)).Althoughthel1algorithmsseemsnotasgoodastheminimizationtotalvariationalgorithm,33(a)(b)(c)(d)(e)(f)(g)(h)Figure2.6DynamicobservationofDNAonlooselyboundsurfaceusingknowledgebasedcompressivescan(5050pixels)(a):Firstframeimageobtainedbyconventionalscan(scansize:800nm800nm)(b)-(h):Reconstructedimageobtainedbyknowledgebasedcompres-sivescanwithminimizingtotalvariancethereconstructedimagesareapproximatetotheoriginalAFMimage.Minimizationtotalvariationalgorithmcalculatesthesparsestsolutioningradientlevelandthisisthereasonwhyitsimageslookmoresmooth.However,theDNAimages(asshowninFig.2.5)arequitet.Neitherofthesetwoimagereconstructionalgorithmscouldprovideclearimages.Bothreconstructedimageslooklike\partialimages"whichlosssomeinformation.Evenifapplyingtheminimizationtotalvariationalgorithm,theimagestillcouldnotbecomesmooth.Thereasonforthisphenomenonistheimagespasifyingproblem.Asthediscussioninprevioussections,thecompressivescanapproachcoulddealwiththesparsesignalinfrequencydomain.ForHaCaTcellsexampletheimageissparseinfrequencydomainandafterthesparsifybasis-wavelethasbeenapplied,theimagescouldbewellreconstructed.However,onceapplyingthesameprocessontotimedomainsparseimage-DNAexampleinthisexperiment,itdidnotwork.ThisisbecausetheDNAimageis34notsparseinfrequencydomain,andthecompressivescanfailedtocaptureandreconstructtheentireimages.Inordertosolvethisproblem,wedevelopedaknowledgebasedcompressivescanstrategy.Thismethodcanintegratetheinformationofcurrentframeimage(gotbycompressivescan)andlastframeimagetogethertoreconstructaframeimagewhichisclosetocurrentimage.2.6.2DynamicObservationusingKnowledgebasedCompressiveScanInthissection,wevalidateourknowledgebasedcompressivescanstrategyfordynamicobservation.Inthisexperiment,weuseAFMtocontinuouslyobservethedynamicchangeofDNAinliquidonlooselyboundsurface.FirstwegetanlocalareaAFMimagewiththescansizeof800nm800nm(5050pixels).Thisimageissetattheframe.Thenweusethecompressivescanstrategytocontinuouslyscanthisareaandusetheminimizationtotalvariationalgorithmtoreconstructedeachframe.Notethat,eachframeissampledandreconstructedbybothitscurrentframeinformationanditspreviousframeinformation.TheexperimentresultsareshowninFig.2.6ofwhichtimeintervalbetweentwoneighborframesisonesecond.Inthisdynamicobservation,thetotalcapturetimeissevenseconds(oneframepersecond).Fig.2.6(a)istheinitialframegotbyconventionalscanmodewhichscantheentirearea.Fromframe(b)to(h)thecompressivescanhasbeenappliedtopartialscanthearea.Ineachframethesamplingratio(thenumberofsamplestothelengthofsignal)is0.3whichlargelydecreasethetimespentonscanning.Inthisexperiment,themovingspeedofDNAiscontrolledbyadjustingtheconcentrationofionintheimagingForknowledge35basecompressivescan,oneassumptionisthatthechangeorbetweentwoframesshouldbesmalljustlikeconventionalvideoframes.Inordertosatisfythisassumption,aproperDNAmovingspeedhasbeenadjustedforthisexperiment.FromthissequenceofframesitiscleartoseethedynamicmovingofDNA.ComparingtheimageinFig.2.6withtheoneinFig.2.5whichonlyusescompressivescantosampleandreconstructimage,thereconstructedimageusingknowledgeoneismuchbetterandsharperthantheonewithoutpreviousknowledge.2.7ConclusionsInthisstudy,acompressivescanbasedAFMimagingstrategyisproposedforimprovingtheAFMimagingspeedtoreachahighimagingframerate.Throughintroducingcompressivesensing,AFMscannerhastheopportunitytoavoidrasterscanstrategywhichscanstheentireareawithhundredsofscanlines,andbecomeacompressivescanwhichonlyrandomlysamplespartialtopographyinformation.Inaddition,Theentireimageofpartiallyscannedareacouldbewellreconstructed.Thiscompressivescanstrategyprefersthesparsesignalinfrequencydomain.However,iftheimageissparseintimedomain,thismethodmightnotworkbecauseoflostofdetailinformation.Inordertosolvethisproblem,apreviousknowledgebasedcompressivescanisdevelopedinthisresearch.Wedesignedamethodologytomergetheinformationinlastframeandpartialinformationincurrentframetogethertogenerateaframewhichapproximatestocurrentframeintimedomain.Thisapproachcouldbedirectlyappliedontotheareaofdynamicobservation.ForAFMapplication,theinitialframecouldbewellscannedbyconventionalscanstrategytogetahighresolutionimage.Thenfromsecondframethecompressivescanstrategycouldbeappliedtolargelydecrease36totimespentonscan.Withthedatagotbycompressivescanandtheinformationinlastframeanapproximatedcurrentframeimagecouldbewellreconstructed.Theresultsfromstaticanddynamicexperimentsshowedgoodperformanceonimagingwithlessscantime.ThiscompressivescanstrategypotentiallycouldbeappliedtootherscanningmicroscopiessuchasSEM,STM,andsoforth.37Chapter3SensingofMechanicalPropertiesinNano/BioEnvironment3.1IntroductionDuringrecentseveraldecades,AFMplaysanimportantroleofprovidingaccuratetopog-raphyimageandmechanicalpropertiesmeasurementinthenanoscale.AFMenablesthebiomedicalstudieshaveatremendousdevelopmentfrombullexperimenttosinglemoleculestudies.Mechanicalpropertiesofsinglecellhavebeenknownasanimpor-tantindicatororreportertoestimateorpredictthestateofthecells.Numerousmethodshavebeenintroducedtoobtainsamplepropertiessuchaselasticity,viscosityandenergydissipation[7][8][9].Regularcontactmodeandnon-contactmodeprovidetopographyimages,andnon-contactmodeisalsousedastheindentationmeasurementinthe"forcecurvefunction".Duringthismeasurement,awellcontrolledindentationisgeneratedbyAFMprobe,andthetip-sampleinteractionforceisrecordedthroughthepsdsensor.ThroughthecalculationbasedonHertzmodel,aneYoung'smodulescanbeestimateasthemechanicalprop-ertiesofthemeasuredmartial.Sincemechanicallyindentationisnecessaryinthismode,themechanicaldamagemayhappenduringthemeasurementprocess.Inaddition,becausethetip-sampleindentationonlyemphasizethepropertiesofthematerial,theinternal38mechanicalpropertiesareoutofscopeduringthetraditionalforce-curvemeasurement.Thismaynotbeaseriousissueforhomogenousmaterial,however,forbiologicalsamplessuchascellandbacterial,theinternalstructuresarequitecomplicated,andthepropertiesisverylikelytobettwiththeinternalones.RecentdevelopmentofultrasonicAFM(UAFM)seemsprovideanalternativewaytosolvethisissue.TheUAFMisamooftheoriginalAFMset-upworkingincontactmodeandconstantnormalforce[57].ThemainideaistoworkatfrequenciesfarabovethecantileverprimaryresonanceintheinertialregimeofanAFMcantileverandsensethenonlinearityofthetipsurfaceinteraction.Inpreliminarystudies,UFMhasalreadydemonstratedsensitivitytosurfaceelasticpropertiesofmaterialsandalsotosubsurfacedefects[68][58].UFMisbasedonastandardAFMoperatinginCMwiththeadditionalapplicationofanultrasonicvibrationtothesubstrate,wellabovetheAFMcantileverresonance.Inthisway,thefrictionforcecanbeeliminatedbecausethetip-samplecontactisbrokenseveraltimeswhilethetipislaterallymovedduringtheimagingprocess.Anypossibledamagetothesampleorthetipisthusminimized[59].Anotheralternativemethodtomeasuretheinternalstructureofsamplesisusingquartzcrystalmicrobalance(QCM).QCMisananogramsensitivetechniquethatutilizesacousticwavesgeneratedbyoscillatingapiezoelectric,singlecrystalquartzplatetomeasuremass.ThebasisofQCMoperationrelatestoquartz'sinherentpropertyofpiezoelectricity.QCM-sbecamewidelyusedasmassbalancesonlyafterthetheoryandexperimentsrelatingafrequencychangeoftheoscillatingcrystaltothemassadsorbedonthesurfacewasdemon-stratedbySauerbreyin1959[60].LiquidapplicationofQCMtechnologyexpandedthenumberofpotentialapplicationsdramaticallyincludingbiotechnologyapplicationsandin39particularbiosensorapplications.Inpracticalbiomolecularapplicationsthedissipationparameterandthesubsequentlyextractedviscoelasticparametersarecriticalformanyapplications.Incellularadsorptionapplications,thesimpleQCMfrequencyandSauerbreyrelationshipwouldgreatlyunderes-timatetheadsorbedmassofcells,sincetheshearwaveoftheoscillatingquartzisdampenedoutbeforeevenreachingthemiddleofthecell.Thefrequencypenetrationdepth(inthezdirectionawayfromthesensorsurface)dependsonthematerialinquestionandtypicallyisontheorderof250nminwater(rigidmaterialsmaystronglycoupletothesensorsurfaceandthuspermitmonitoringthickerbutviscoelasticmaterialswillbelimitedtowithinthisrange).Whentheadsorbedmassisviscousandtlysoftthatitdoesnotfollowthesensoroscillationperfectly(suchasinthecaseofcelladsorption),thisleadstointernalfriction(duetothedeformation)intheadlayerandthustodissipation.Thismassisthedynamicmass(incorporatingassociatedwater)andnottherestmass.Themoreviscoustheadsorbatethemoretheoscillationwillinducedeformation,andthusthecoupledmasswilldeviatemoreandmorefromtherestmass.Therefore,monitoringcelladsorptionrequiresusingthedissipationparametertofullycharacterizetheadsorptionofaviscoelasticcellularstructure.Ontheotherhand,theadsorptionofasmall,rigidproteinmaybeaccuratelymeasuredbymonitoringonlyfrequencychangesandthesetotheSauerbreyrelation,althoughassociatedcoupledwatermayagaingiveanunderestimationoftheadsorbedmass.AlthoughtheQCMhastheabilityofmonitoringmass/adhesionchanges,thespatialdetectionisthemainlimitationofthistechniquewhichmakesthequantitativeanalysisisimpossible.Inordertoaddresstheseissues,wepresentamethodcalledvibrationmodeforthestudyofinternalmechanicalpropertiesofbiomedicalsamples.Thevibrationmodehasacombinationoftheadvantageofconventionaltappingmodeimagingwithnanoscale40resolution,andthenanomechanicalmappingusingtheadditionaldeformationinducedbyvibratingneartheresonancefrequencyofthemeasuredsampletorecoverythespringcon-stantmapoftheinternalstructureofthesample.Oneoftheofthistechnologyisthenon-invasivemeasurement.TheAFMtipisnotmechanicallytouchedwiththesamplesurface,whichassuretheaccuracyofthemeasurementbymeansofrulingoutthebythetip-surfaceinteractionswhicharethebiggestissueforthenano-indentationmeasure-ment.3.2TheStateofArtofVibrationModelFigure3.1SchematicofthesetupforthevibrationAFMtwithconventionalpointandshootingsignalmeasurement,vibrationmeasure-mentisamoremethodtoevaluatethemechanicalpropertiesofinternalstructureofelasticmaterial.ThebasicideaofthismethodistovibrateverticallyusingtheAFMscannertodrivethemeasuredsamplevibrateupanddown.Theadditionalvibrationam-41Figure3.2SchematicofthesetupforthevibrationAFMplitudeontheuppersurfaceofsample,otherthanthedrivingvibrationcanbeconsideredastheresultofsampledeformationwhichdependsonthemechanicalproperties,suchasthespringconstant(asshowninFig.3.1).However,thespringconstantandadditionaldeformationhasnodirectlylinkbetweeneachother.Wehavetobuildamathematicmodeltoconnecttheestimatedspringconstantwiththemeasuredamplitude.3.3MathematicModelforVibrationModeThesimplestmathematicmodelwhichcandescribethevibrationsystemisthetraditionalspring-massmodel.Asecondordersystemcanbeusedtobuildthedynamicmodelofthevibrationsystemasfollows:mx+k(xAdcos!dt)=0(3.1)42Herewemaketheassumptionthatthemasshasuniformlydistributionofsample.Al-thoughthedrivingsignalhasbeenappliedinthetimedomain,theanalysisatfrequencydomaincanprovidemoreinformationtodecodethespringconstantmap.AfterFouriertrans-fer(atfrequency!=!d),Eq.(3.1)canbewroteasm!2x(!)+k(x(!)Ad)=0(3.2)andthenwehavek=x(!)!2x(!)Ad(3.3)Eq.(3.3)istheeasiestwaytocalculatethespringconstantofthemeasuredsample.IfthemeasuredsampleisquitEq.(3.3)canbedirectlyappliedtothecalculationprocess,however,ifthesampleiselasticsuchascellsandbacterial,theconventionalsecondordermassandspringsystemmaynotworkproperly.Thisisbecausethemodelabovedoesnotconsidertheinnerconnectionofeachindividualpointswhichwillcompromisethemeasurementaccuracy.Inordertosolvethisissue,weusedathreedimensionalspring-massnetwork(asshowninFig.1)tomodeltheelasticsample.Thesecondordertialequationwasalsousedtomodelthebehaviorofelasticsample.Beforethemodeling,severalassumptionshavebeenmade:themassofeachtest-ingpointhasuniformlydistribution,however,theverticalandhorizontalspringconstanthasvariousdistributions.Thenthespring-massnetworkunderconstantvibrationcanbemodeledasfollowingequation:43Figure3.3Modelillustrationmxi;j+ki;j(xi;jAdcos!t)+gi;j(xi;jxi+1;j)+gi;j1(xi;jxi1;j)+gi;j(xi;jxi;j+1)+gi;j+1(xi;jxi;j1)=0(3.4)wherexi;jistheamplitudeofatpositionof(i;j);Adand!arethedrivingamplitudeandangularfrequency,respectively;ki;jandgi;jaretheverticalandhorizontalspringconstantsofthematerialatpositionof(i;j),respectively;misthemassatpoint(i;j).AfterFouriertransfer,Eq.(3.4)canbewroteasm(2ˇf)2Ai;j+ki;j(Ai;jAd)+gi;j(Ai;jAi+1;j)+gi;j1(Ai;jAi1;j)+gi;j(Ai;jAi;j+1)+gi;j+1(Ai;jAi;j1)=0(3.5)44whereAi;jistheamplitudeofatpositionof(i;j)afterfrequencylock-inatdrivingfrequencyf.IfwewritetheEq.(3.5)intomatrixformm(2ˇf)226666666666666411...11377777777777775266666666666664A1;1...Ai;j...An;n377777777777775+266666666666664AdA1;1...AdAi;j...AdA(n;n377777777777775266666666666664k1;1...ki;j...kn;n377777777777775+2666666666666642A1;10A2;10.........A2;1.........An;n1.........0An;n10An;n377777777777775266666666666664g1;1...gi;j...gn;n377777777777775=0(3.6)45Aftermatrixmanipulations,Eq.(3.6)changesintofollowingform.266666666666664m(ˇf)2m(ˇf)2...m(ˇf)2m(ˇf)2377777777777775266666666666664A1;1...Ai;j...An;n377777777777775=266666666666664AdA1;102A1;10A2;1...0.........AdAi;jA2;1.........An;n1............00AdAn;nAn;n102An;n3777777777777752666666666666666666666666666666664k1;1...ki;j...kn;ng1;1...gi;j...gn;n3777777777777777777777777777777775(3.7)46Afterfurthermanipulation,wetransferredthematrixasfollowinglinearform.266666666666664A1;1...Ai;j...An;n377777777777775=1m(ˇf)2266666666666664AdA1;102A1;10A2;1...0.........AdAi;jA2;1.........An;n1............00AdAn;nAn;n102An;n3777777777777752666666666666666666666666666666664k1;1...ki;j...kn;ng1;1...gi;j...gn;n3777777777777777777777777777777775(3.8)However,weEq.(3.8)isanunderdeterminedequation,whichmeansadditionmeasurementmaybeneeded.Ifwecanmakeafurtherassumptionthatthespringconstantinhorizontaldirectionhasauniformdistribution.Wemaysimplifytheequation.ThentheEq.(3.8)changesinto47266666666666664A1;1...Ai;j...An;n377777777777775=2666666666666644K+m(ˇf)20k04K+m(ˇf)2......k.........k......4K+m(ˇf)20k04K+m(ˇf)23777777777777751266666666666664AdA1;1...AdAi;j...AdAn;n377777777777775266666666666664k1;1...ki;j...kn;n377777777777775(3.9)TheEq.(3.9)canbewrittenasfollows:[A]=[Know]1[PartialKnow][K]=1]12][K]=[K](3.10)whereAisthemeasurementresults,isthemeasurementmatrixandKistheoriginalsignal.Whenweconducttheamplitudemeasurement,wecanobtaintheamplitudeAi;jatthespposition(i;j).Ifwewanttodirectlyappliedthecompressivesensingtothesemeasurement,wehavetoknowtheexactlyformofmeasurementmatrix.Itisnotabletodirectlyobtainthismeasurementmatrix,untilanadditionalcompressivesensingisapplied.Therearetwostepsofcompressivesensingneededinthisspringconstantmeasurement,Inthestep,weusethepartialmeasurementresultstorecoverthemeasurementmatrix,andinthesecondstep,weusethereconstructedmeasurementmatrixtorecoverytheoriginal48signal.Inthestep,wearegoingtorecoverthe2matrix.Inthismatrix,theoriginalsignalisAandwealsocanobtainpartialvalueofsomeA,inthiscasewecanusethecompressivesensingusedintopographyimagetogetanentiremapofA.Y=A(3.11)isthemeasurementmatrixwhichisdesignedaccordingtothemeasurementtrajectory(theonewedesignedwithTSP).Inthiscase,oncethemeasuringpointsarethemeasurementmatrixisobtained.Yistheamplitudemeasurementsresults.InthiscasewecanrecovertheA(theamplitudeofeverymeasurementpoint).[A]=1]12][K]=[K](3.12)Nowwegotthe2whichisgeneratedbytheamplitudeofeverymeasurementpoint.isan2n2matrixwhichisafullrankmatrix.Ifwewanttousethecompressivesensing,wehavetoasubsetofasthemeasurementmatrix.Inthisapplication,becauseeachrowincorrespondingtoeachA,wecanchoosetherowwithknownmeasuredpoints.Now,themeasurementequationchangestobe[A]=[K]=2666664Ameasured...Ameasured3777775=26666643777775266666666666664k1;1...ki;j...kn;n377777777777775(3.13)49Inthiscase,thedimensionofAism1,andthedimensionofismn2thedimensionofKisn21.Nowthemeasurementmatrixisadenserandommatrix(includesotherpointsinformationwithinonemeasurement)whichRIP.Now,wecanusecompressivesensingtosampleandrecoverythespringconstant.Compressivesensingrealizescompressinginsamplingstep.Insteadofsamplingoriginalsignalpointbypoint,compressivesensingonlysamplesasumofrandomprojectionsfromoriginalsignaltoaprojectionmatrix(measurementmatrix).Afterafewmeasurementswhicharefewerthantraditionalsamplingmethod,theoriginalsignalcanbereconstructedbysignalreconstructionalgorithm.Becausethenumberofmeasurementsisfewerthanthedimensionoforiginalsignal,ifthesignalissparseandthemeasurementmatrixhasbeenwellselected,thecompressivesensingcouldreconstructtheexactoriginalsignalwithoverwhelmingprobability.InthisapplicationwecanusethemeasurementmatrixandimagereconstructiondesignedinSectionII.3.4HardwareImplementationofVibrationModelonSPMSystemTheexperimentalset-upforthevibrationmodeimagingisshowninFig.3.4.Forvibrationmodeimaging,thebeamisbiasedtoanopticallysensitiveposition,thez-piezoisactuatedbyamodulatedtappingsignal.ThecarrierfrequencyistheorderresonancefrequencyoftheAFMprobeandthemodulatedfrequencyisthevibrationfrequencyat50Hzto100Hz.Carrierfrequencyworksforthetappingsignalfortopographyimage.Additionalmodulatedsignalworksforverticalvibrationgeneratingsignal.Sincetheentiresystememploysthetappingmodefortopographyimage,themodulatedtappingsignalisusedboth50forthetopographyfeedbackandAFMstagevibratingsimultaneously.Sincethecarrierfrequencylockedatresonancefrequencyoftheprobe,andtappingsignalisusedforconstantdistancebetweentheAFMtipandsamplesurface,theinteractionforcealsomaintainsaconstantvalue.Thedeformationcontributedbyvibrationshowsthemechanicalpropertiesinformationsuchasspringconstant.Simultaneouslywithtopographyimaging,thevibrationamplitudeimagealsoisshownintheAFMcomputerafterpassingtolock-inThelock-inlocksthefrequencyofmodulatedsignal.Asaresult,theoutputofthez-drivesignalservesasimagingchannelforboththetopographyandamplitude.Inotherwords,onecanobtaintopography(heightsignals)andcorrespondingmechanicalpropertiessignal(amplitude)foreverypixeloftheimage.Figure3.4SchematicofthesetupforthevibrationAFM513.5ExperimentalResultInthisexperiment,wevalidatetheideaofvibrationmodeandtestitsperformancecomparedwithconventionaltappingmodeandcontactmodeimaging.Inthisexperiment,westartedwiththeknownpatternsamplesuchascalibrationgridandmicro-electrodechip.Thegoalofthesetestingistoverifytheheight(topography)imagehasthesameimagingabilitywithtappingmodeorcontactmode.Afterthatwewillswitchtothesoftandelasticsamplessuchascells.3.5.1TopographyImageComparisonbetweenVibrationModeandConventionalTappingandContactModesTheexperimentstatedwithcalibrationgridwiththestandardpitchdepthandheight.BecausetheAFMhasbeencalibrateditsx,yandzdirectionusingthestandardcalibrationgrid(BrukerNano,SantaBarbara,CA,US),wecanassumethepositionerrorofconventionaltappingmodeimageissmallenoughtobeusedasastandardtoevaluatetheimagingabilityofvibrationmode.TheTopographyimageanditscross-sectionanalysisareshowninFig.3.5.Throughthecross-sectionanalysis,thedepthandstepofthepitchare4.994mand0.467m,respectively.Thetopographyimagescross-sectionanalysisfromcontactmodeandvibrationmodeforthesameareaareshowninFig.3.6and3.7withthethedepthandstepofthepitchare4.735mand0.434m(contactmode),and4.926mand0.473m(vibrationmode)respectively.Thetopographyimagesfrombothtappingmodeandvibrationmodehavethesimilarmeasurementvalueinverticalandhorizontaldirectionsandthesmallmaycomefromtheuniformfabricationaccuracyofcalibrationgrid.Afterthetestingincalibrationgrid,afreshfabricatedgoldandsilicondioxidemicro-52(a)(b)Figure3.5Topographyinformationofcalibrationgridformconventionaltapingmode(a):Topographyimgaeformconventionaltapingmode(b):cross-sectionanalysisfromtopogra-phyimage(a)(b)Figure3.6Topographyinformationofcalibrationgridformconventionalcontactmode(a):Topographyimageformconventionalcontactmode(b):cross-sectionanalysisfromtopog-raphyimage53(a)(b)Figure3.7Topographyinformationofcalibrationgridformvibrationmode(a):Topographyimageformvibrationmode(b):cross-sectionanalysisfromtopographyimage(a)(b)Figure3.8Amplitudeandphaseimagesofcalibrationgridformconventionaltapingmode(a):Amplitudeimageformtapingmode(b):Phaseimageformtapingmode54electrodesmicrochipwasusedasthesampletotesttheperformanceofourvibrationmode.twiththecalibrationgrid,themicrochiphasboththetopographychangesandmaterialchanges.Themechanicalpropertiesofsilicondioxideisquittwiththegoldandwhichmayresultintvibrationamplitudeinthevibrationmode.TheexperientialresultsareshowninFig3.9to3.12(a)(b)Figure3.9Topographyinformationofgoldandsilicondioxidemicro-electrodesformconven-tionaltapingmode(a):Topographyimageformconventionaltapingmode(b):cross-sectionanalysisfromtopographyimageThetopographyhasthesimilarresultswiththeelectrodeexperiment.Thetopographyimagesfrombothtappingmodeandvibrationmodehavethesimilarmeasurementvalueinverticalandhorizontaldirections.However,thevibrationlockedinamplitudeimageinthevibrationmodeprovideusmoreinformationotherthantopography.Fig3.13(a)and3.14(a)showthevibrationlockedinamplitudeimagesofcalibrationgridandmicrochip.Fig3.13(b)and3.14(b)arethespringconstantmapofthesetwosamplesbyEq.(3.3).Forthecalibrationgridsample,theespringconstanthasanonuniformdistribution,althoughthecalibrationgridhasbeenmadebysilicon.Thereasonforthatcouldbethe55(a)(b)Figure3.10Topographyinformationofgoldandsilicondioxidemicro-electrodesformcon-ventionalcontactmode(a):Topographyimageformconventionalcontactmode(b):Cross-sectionanalysisfromtopographyimage(a)(b)Figure3.11Topographyinformationofgoldandsilicondioxidemicro-electrodesformvi-brationmode(a):Topographyimageformvibrationmode(b):Cross-sectionanalysisfromtopographyimage56(a)(b)Figure3.12Amplitudeandphaseimagesofgoldandsilicondioxidemicro-electrodesformconventionaltapingmode(a):Amplitudeimageformtapingmode(b):Phaseimageformtapingmodesurfacecontainments.Thetopographyimageshouldbequiteifthereisnosurfacecontainments,however,thetopographyimageinFig3.5(a)showsthisheightchangesonthesurfaceofcalibrationgridwhichreferstothecontainments.SincethecontainmentsaremuchsofterthathesiliconsurfaceandthatisthereasonintheFig3.13(b),theespringconstantofcontaminatedareaissmallerthantheonewithoutcontaminated.3.5.2CompressiveSensingInvolvedTopographyandLocked-inAmplitudeImagingTestinVibrationModeInthissection,wetestedtheperformanceofcompressivesensingbasedvibrationmode.twiththecompressivesensingstrategyinChapter3,thecompressivesensingappliedtothevibrationmodehastheadvantageofsamplingcoupledinformationwithinonepointmeasurement.ThemeasurementmatrixismuchdenserthanthemeasurementmatrixinChapter3.Fromthetheoryofcompressivesensing,wemayachievehighercompressionrate57(a)(b)Figure3.13Mechanicalpropertiesmappingofvibrationmodeoncalibrationgrid(a):Lockedinamplitudeimage(b):espringconstantmap(a)(b)Figure3.14Mechanicalpropertiesmappingofvibrationmodeonmicrochip(a):Lockedinamplitudeimage(b):espringconstantmap58duringthemeasurement.Inthisexperimentwetestedtheimagingabilityofcompressivevibrationmadebycalibrationgrid.Fig.5.4showstheexperimentalresultsofthecompressivevibrationmodewithtcompressionrate.Therecoveredimageslookssimilarwiththefullscanimage.Evenifthecompressionratedecreasedinto10percents,therecoveryimageinFig.3.15(b)stillshowsthemajorinformationofspringconstantmap.(a)(b)Figure3.15Experimentalresultsofcompressivevibrationmodeleft:Vibrationlockedinamplitudeimagebyfullscan,middle:espringconstantmapcalculatedbyfullscandata,righespringconstantmapcalculatedbycompressivescanwithcompressionratioof(a)50%,(b)10%593.5.3SubsurfaceStructureorMechanicalPropertiesMeasure-mentUsingVibrationModeVibrationmodemeasurementisnaturallysuitabletoevaluatethemechanicalpropertiesofinternalstructureofelasticmaterial.Ifthesampleishomogenous,thevibrationamplitudesignalshouldbethesameonthetopofsamplesurface.However,ifthereissomedefectsorothermaterialsinsidethesample,thesubsurfacestructureshouldbeabletobedetectedbecauseofthevibrationamplitudechangesonthesurface.Inordertotesttheperformanceofsubsurfacemeasurement,wefabricateaPDMScoatedmicroelectrodeschipasshowninFig.3.16Figure3.16PDMScoatedmicroelectrodeschipWeusedthevibrationmodetoscanonthetopofPDMScoatedmicrochipsampleandobtainedthetopographyimageandvibrationlockedinamplitudeimagesasshowninFig.3.17.ThetopographyimageshownothingbutauppersurfaceofPDMS.However,thevibrationlockedinchannelshowsaquitetimagewiththetopographychannel.ThetwoelectrodesberriedbyPDMSweremeasuredandthevibrationlockedinamplitudeimagealsoshowedthetspringconstantoftheelectrodeareaandsilicondioxidearea.It60(a)(b)Figure3.17ExperimentalresultsofvibrationmodeonPDMScoatedmicrochipsample(a):Topographyimageusingconventionaltappingmode,(b)Vibrationamplitudeimageshouldbenotedthattheinspringconstantisnotcausedbythetmaterialssuchasthegoldandsilicondioxide.ThetlockedinvibrationamplitudeiscausedbytheinPDMSdepth.ThedepthofPDMSinthesilicondioxideregionisthickerthanthegoldelectroderegion,andtheseadditionalPDMScontributetheofthevibrationlockedinamplitudesignal.Basedontheseweareabletodetectthesubsurfacestructureoftheelasticsamples.Inordertofurthertesttheperformanceofvibrationmodeintheaspectofmechanicalpropertiesmeasurement,wedesignedaPDMScoatingsamplewithtdepthofthefeatures(holes)(asshowninFig.3.18).TheDepthofeachfeatureare:75nmforupanddown,150nmforleftandright.Afterdegasprocess,thePDMSfullyinsidethisfeatureswitharelativeuppersurface.Bothheightandamplitudechannelsofthevibrationmodewereusedtorecordtheinformationofthissample.Theheightchannelhasnoinformationotherthanasurface.However,themechanicalpropertieschannel61Figure3.18Experimentalresultforthemechanicalpropertiesmeasurementusingcompres-sivesensingbasedvibrationmode.(a)TopographyimageofsamplesurfacebeforePDMScoatingusingregulartappingmode.(b)TopographyimageofsamplesurfaceafterPDMScoatingusingregulartappingmode.(c)TappingamplitudeimageofsamplesurfaceafterPDMScoatingusingregulartappingmode.(d)Topographyimagesofsamplesurfaceaf-terPDMScoatingusingcompressivesensingusingregulartappingmode.(e)MechanicalpropertiesimagesofsamplesurfaceafterPDMScoatingusingcompressivesensingbasedvibrationmode62indicatedthat,thereareforfeatureswithtmechanicalproperties.Fig.3.18)(e)showsthespringconstantofeachfeatureisproportionaltoitsdepthwhichisthesameasweexpected.Inaddition,thecompressivesensingbasedcompressivescanwasalsousedinthisexperiment.Theexperimentalresults(Fig.3.18)(e))showsthat30%ofscanrateisenoughtodistinguishthisinmechanicalproperties.OtherthanPDMScoatingsample,livecells(HacaT)werealsousedasatestingsampleforvibrationmode.Theresult(Fig.3.19)fromvibrationmodeshowsboththespringconstantdistributioninformationaswellastheheightinformationsimultaneously.(a)(b)Figure3.19ExperimentalresultforthemechanicalpropertiesmeasurementofliveHacaTcellusingvibrationmode.(a)TopographyimageofliveHacaTcellusingregulartappingmode.(b)VibrationamplitudeimageofliveHacaTcellusingvibrationmode3.6ConclusionsInthisstudy,weutilizedestablishedandnovelnoninvasiveAFMmeasurementmethod,called"vibrationmode",tovisualizesampleandmapitsdistributionatthenanoscale,63andtodeterminedetailednanostructuralandnanomechanicalproperties.Ourexperimen-talresultsshowthat,comparedwithconventionalAFMbasedimagingandmeasurements,vibrationmodecanprovidefasterimagingspeed,andmulti-channelinformationfromnon-invasivebiologicalpropertiesmeasurements.64Chapter4VideoRateImaginginBiologicalEnvironment4.1IntroductionAtomicForceMicroscopy(AFM),asanimagingdevice,hasbeensuccessfullyappliedininvestigationsofnanoscaleinvariousareas[69][70][71].AFMisnaturallysuitableforimaginginliquidwithhighspatialresolution.However,itsimagingspeedistooslowtocapturetherelativemovementbetweencellulaseandcelllulosenanocrystal.Todate,imagingtheprocessofenzymatichydrolysisisstillachallengingworkandonlyafewattemptshavebeenmade[72].Inthispaper,weproposeanapproachforafastimagingAFM,basedonanewscanstrategy,compressivescantodynamicallyobservetheinteractionbetweencellulaseandcellulose.Inthismethodology,partialtopographyinformationiscollectedinsteadofscanningtheentirearea,andcompressivesensingisinvolvedtoincreasetheofscanningandreconstructtheimagesusingpartialinformation.Compressivesensingrealizescompressinginsamplingstep.Insteadofsamplingoriginalsignalpointbypoint,compressivesensingonlysamplesasumofrandomprojectionsfromoriginalsignaltoaprojectionmatrix(measurementmatrix).Afterafewmeasurementswhicharefewerthantraditionalsamplingmethod,theoriginalsignalcanbereconstructedbysignalreconstructionalgorithm[65].Becausethenumberofmeasurementsisfewerthan65thedimensionoforiginalsignal,ifthesignalissparseandthemeasurementmatrixhasbeenwellselected,thecompressivesensingcouldreconstructtheexactoriginalsignalwithover-whelmingprobability.TheAFMbasedcompressivescan,canlargelydecreasethetimespentonscanning,andthereconstructedimageisobtainedafterimagereconstructionprocess.Inaddition,inordertoobtainabetterreconstructedimagewithevenfewermeasurements,andrealizeAFMbaseddynamicobservation,aspecialcompressivescanbasedonpriorknowledgeisproposedinthispaper.Itcanmergetheinformationobtainedbypreviousframeimageandthecompressivedataobtainedbycurrentframe.ThisapproachcanlargelyincreasetheAFMimagingrate,enhanceimagequalityandrealizedynamicobservation.Inthepresentstudy,thiscompressivescanstrategyisusedtodynamicallyobservetheinteractionbetweenTrCel7AandcellulosenanocrystalCellulose,astructuralcomponentofthecellwallofplants,hasbeenwidelyconsideredasarenewablelignocellulosicbiomassfromwasteagriculturalproducts[73][74][75][76].However,thelowoftheenzymatichydrolysisofcellulosehasbeenseemedasthebottleneckinindustry.Therigidandcomplexitystructure(-1,4-glycosidiclinkagesandintraandintermolecularhydrogenbonds)ofcelluloseincreasesitsresistancetoenzymatichydrolysisandresultsinasluggishrateofhydrolyticbreakdownofcellulose[77].Althoughvariousmethodshavebeendevelopedtoincreasetheoftheenzymatichydrolysisofcellulose,suchaspretreatingtherawcellulosematerialandassemblingcellu-lase"cocktail",thereisstillnobreakthroughtotlyincreasethesluggishinteractionbetweenthecelluloseandcellulolyticenzymes.Therefore,thecellulosehydrolysisprocessisnotwellstudiedduetothetunderstandingofthemechanismsunderlyingenzymeactions[78][79].Theenzymatichydrolysisofcelluloseinvolvesofthreetenzymes:cellulases,cellobiohydrolases,and-glucosidases.Inthepresentstudy,wefocusedonthe66enzymeofcellulase-TrCel7A.TheTrCel7Aisanendo-actingenzymethatcanbreakthegly-cosidiccellulosechainstogenerateanewchainend,whichcanbeusedforcellobiohydrolaseaction[80].4.2VideoRateAFMImagingofCelluloseandCellu-lase(TrCel7A)InteractionIntroducingcompressivesensingintoAFMimagingsystemisaconvenientandtwaytoreducethetimespentonscanning.Thegoalistodecreasethescantrajectory,whichsamplesfewerthanconventionalmeasurements.Consideranunknownsignal(image)x,x2RN,y2RMisthemeasurementresultsofy=x,andisthemeasurementmatrix.IfM˝N,fewermeasurementsmightbeenoughforsamplingandreconstructingtheoriginalsignal.Therearethreemajorsectionsincompressivesensing:signalsparserepresentation,measurementmatrixdesignandsignalreconstructionalgorithms.Thedetailsofsignalsparserepresentationandreconstructionalgorithmscanbefoundinourpreviousresearch[81].Inthisresearch,themeasurementmatrixdesignistfromthepreviousone.Thenewmeasurementmatrixalsotakestheinformationofthepreviousframeintoaccount,andintegratesitwiththeinformationofthecurrentframetoassurethat,theoriginalimagecanbeaccuratelyreconstructed.Themainyincomprehendingthemechanismoftheinteractionbetweencel-lulolyticenzymesandcelluloseistheabsenceofquantitativeanalyticalmethods.Insituvisualizationispossibletobeanalternativemethodtostudythemechanismoftheinterac-tionbetweencellulolyticenzymesandcellulosenanocrystalInsituimagescanprovidespatialresolutioninnanoscale,andareabletocapturethesinglecellulasebound67onsurfaceofcellosecrystalTherecentintroductionofhigh-speedAFMbreaksthelimitationandcanvisualizethebehaviorofsinglemoleculesofTrCel7Aduringhydrolysisofcellulosewithoutenzymelabel-ingorsubstratemo[82][83].HighresolutionAFMimagingatvideo-ratecanhelpdirectlyvisualizetheactivesingleTrCel7AmoleculeoncelluloseIIsurfacewithenoughtem-poralresolutiontotrackitsmovement.TrCel7AisamajorcomponentofTrichodermareeseicellulolyticsystem,whichproducescellobioesefromthereducingendofcellulose[84],[85].TheTrCel7Amoleculecontainsanactivesitewhichresidesina40-50angstromlongtunnelandbindingsitesfor10glucoseunits[86].TrCel7Aisknowntohydrolyzethecrystallinecellulosechaininaprocessivemanner,makingconsecutivecutsofcellulosechainthroughthetunnel-shapedactivesites[82][87].4.3ExperimentalSetupandResults4.3.1PreparationofCelluloseCrystalandTrCel7AforAFMImagingPreparationofcellulosesolutionThecellulosesolution(0.01mg/ml)waspreparedbydis-solvingcelluloseinureasolution(12%wturea,7%wtNaOH).Thesolutionwasstoredin-20Cfridgesfor1hourwithstirringfromtimetotime[88][89].AnchoringmicasubstrateFreshclavemicawascutinto0.6cm0.6cmpieces.Micasubstrateswerewashedbyimmersingin10%NaOHsolution,followedbyrinsedwithDI-water,driedwithnitrogengas,andplacedinaUV/ozoneovenfor15min.3-Aminopropyltrimethoxysilane(APTS)wasadsorbedontothesilicasubstratesinordertoimprovethecoverageofthe68Washedsilicasubstrateswereimmersedinto1%v/vAPTS/toluenesolutionfor40min,rinsedwithtolueneanddriedinanovenat60Cfor30min.PreparationofcelluloseAddonedropofcellulosesolutiononmicasubstrates.After20min,raisedbyDI-wateranddriedwithnitrogengas.PreparationofTrCel7ATheTrCel7AwasagiftfromDr.JunXi'sgroupatDrexelUniversity.Forthepreparationofappropriatedilutions,theTrCel7Awasdilutedto50Menzymesolution.4.3.2InSituVisualizationandImageAnalysisAFMinsituimagingwasconductedusingacommercialAFM(Multi-Mode,BrukerNano,CA)withasignalaccessandcontrolbox,whichwasdevelopedbyourgrouptocontroltheAFMprobe.Siliconnitrideprobes(SNL-10,BrukerNano,CA)wereusedtoimagethecellulosenanocrystalandTrCel7AinimagingThecellulosesamplewasinitiallyobservedwithoutTrCel7Ain80lofimaging(50mMsodiumacetatewithpH5.0),followedbytheaddition5lof50Menzymesolution.Aspeciallydesignedscantrajectorywasusedtoperformacontinuousrandomsampling,andthepriorknowledgebasedcompressivesensingwasusedtodynamicallyobservethesamplesurfacechange.Atthebeginningofeachexperiment,anAFMimagewasobtainedbyconventionalrasterscanastheframe.Afterthat,priorknowledgescanstrategystartedtotakeovertheimagingworkofalltherestframes.StationarycrosssectionanalysiswasconductedbyAFMimageprocessingsoftware(NanoscopeAnalysis,BrukerNano,CA).694.4ResultsandDiscussion4.4.1SizeandShapeofCelluloseNanoCrystalandTrCel7AThecross-sectionanalysiswasconductedbyconventionalAFM.WechoseanareawithanumberofcellulosenanocrystalandusedAFMtoimagetheheightandamplitudechannels.Fig.4.1(a)istheamplitudeimageofcellulosesurface.Fig.4.1(b)and4.1(c)arethezoomedinimageinthesamelocation.Fig.4.1(d)isthecross-sectionofsinglecellulosenanocrystalThroughtheseimages,theshapeandcontoursofeachcellulosenanocrystalcouldbefound.Thesizeoftypicalcellulosenanocrystalweobservedis250nm(width)60nm(height),andthelengthinthemeasurementisvariousformonetotensofmicrometerswiththemostfrequencyof3.Accordingtothesizeofcellulose,thesamplelookslikeasmallbundleofcellulosenanocrystalThereasonforthesepresentedcellulosenanocrystalbundlesisbecausetheprocedureofourcellulosepreparationprocess.AfteradditionofTrCel7Aenzyme,individualTrCel7AboundwithcellulosenanocrystalwasimagedbyconventionaltappingmodeAFMinimagingThesingleTrCel7AboundoncellulosesurfacewascaptureasFig.4.2.Fig.4.2(a)and4.2(b)aretheamplitudeimagesofsingleTrCel7Aonthecellulosesurface,thescalebaris70nm.Cross-sectionalanalysiswasperformedtoquantifytheTrCel7A,whichhasaheightof4nmandis25nm15nminlengthandwidth,respectively.AccordingtopublishedresultsonstructuresoftheTrCel7Ainthecatalyticdomain(approximately6nm5nm4nm),andtheprojectionofaboundTrCel7Amoleculeawayfromthecellulosesurfacemaybe70(a)(b)(c)(d)Figure4.1Visualizationofcellulosenanocrystal(a)Amplitudeimageofcellulosenanocrystal(scanbar:800nm),(b)Zoomedinamplitudeimageofcellulosenanocrystal(scanbar:220nm),(c)Zoomedinamplitudeimageofcellulosenanocrystal(scanbar:100nm),(d)Heightanalysisofcellulosenanocrystal71(a)(b)(c)Figure4.2VisualizationofTrCel7Aenzyme.(a)and(b)AFMamplitudeimageofTrCel7Aoncellulosenanocrystalsurface(scanbar:70nm),(b)Amplitudeimageofcellulosenanocrystal(scansize:2.2m),(c)HeightanalysisofcellulosenanocrystalblackcurveforTrCel7Ainimage(a),redcurveforTrCel7Ainimage(b)72inferredtobebetween5and10nm[90],thenanoparticlesweobservedaremostlikelytobetheTrCel7A.4.4.2TrCel7ABindstoCelluloseandMovesInthepresentstudy,weperformedinsituAFMimagingofTrCel7Aboundoncellulosenanocrystalanddynamicallyobservedtherelativemovementsofthesetwonanostructures.Theenzymatichydrolysisofcellulosenanocrystalwasstudiedusingcellulosedepositedonfreshcleavedmicasubstratesin50mMsodiumacetatewithpH5.0atroomtemperature,211C.TrCel7AwasaddedtotheAFMcelltostudytheenzymatichydrolysisofcellulosesample.Fig.4.3showstheprogressionofthemovementofTrCel7Aonthecelluloseobservedoveraperiodof15seconds.Fig.4.3(a)istheamplitudeimagewiththescansizeof180nm500nmobtainedbyourpriorknowledgebasedfastimagingsystem.Inthisimage,itiscleartoseethreesingleTrCel7Asboundonthecellulosesurface.Fig.4.3(b)showsthedynamicobservationofasingleTrCel7Aonthesurfaceofthecellulosenanocrystalwiththetimeintervalof1.8seconds.Theimageswerecapturedandrecoveredbypriorknowledgebasedfastimagingsystemoveraperiodoftime(15seconds).TheballshapefeatureineachframecouldbeTrCel7Aenzymesbindingtothecellulosesurface(intheprocessofenzymatichydrolysis),accordingtothatthesemovingparticleswerenotseenintheabsenceoftheenzyme,weconcludethattheyareTrCel7AslidingoncrystallinecelluloseDuringtheobservation,mostofTrCel7Amoleculeswerefoundwithasimilarmovingvelocityonthecellulosesurface,andtheaveragerateofmovementwasestimatedtobe2:351:2nm/s(n=10).Comparedwiththemovementvelocityobtainedfromotherresearch(3:51:1nm/s)[82],ourmeasurementresultisinthesamelevel.Thefastimaging73AFMweusedinthisresearchcouldreachashighas1frame/second,however,thetime-resolutionisnothighenoughtocapturethedetailsofTrCel7Aenzymatichydrolysisofcellulose,andthatneedstofurtherincreasetheimagingrateofAFMinthefuture.4.4.3Time-lapseofDensityandDistributionofTrCel7AMoleculesonCelluloseSubstrateThedensityofTrCel7A(Fig.2C)onsubstrateisalsoimportantsinceitindicatestheeadsorptionofcellobiohydrolasesandismediatedbytheCBD[91].Theadsorptionofthefamily1CBDoncrystallinecelluloserequiresthreearomaticaminoacids,andthebindingsitestocellulosecrystals[92].Duetotheprocessivecharacteristicsofhydrolysis,thebindingofTrCel7Aandcellulosethehydrolysisrate.Generally,tenzymatichydrolysisrequireshighbindingdensity,highmovingvelocityandlowdissociationrate[93].Sincethehydrolysisisadynamicprocess,ateachmomenttherealwaysexistsanumberofactiveTrCel7Amoleculesboundoncellulosesurface.Atthatmoment,someoftheTrCel7Aonthesurfacewilldetachtothesolution,andsomenewbindingactivitiesofTrCel7Aappears.Consideringthestochasticnatureoftheprocess,weusedPoissonprocesstoestimatethemeanvalueofthedensityofactiveTrCel7A(Eq.1andEq.2).Duringtheobservation,wesetthetimeintervalas5minutes.WesettheAFMimagingspeedas0.6frame/sandgroupevery5framestocalculatetheexpectedvalueofthenumberofactiveTrCel7A.Wecouldcollectapproximately36expectedvaluesofthenumberofactiveTrCel7A,andusethesevaluestostatisticallyanalyzethemeanandvariancesofnumberofactiveTrCel7Awithinthe5minutesperiod.Figure2CshowsoneframeofthecontinuousobservationwiththenumberofactiveTrCel7A.74(a)(b)Figure4.3InSituvisualizationofdynamicinteractionsofcellulaseandcellulosemolecules,(a)TrCel7A(labeledwitharrows)boundtoCellulose(scansize:180nm500nm),(b)TimelapseamplitudeimagesofanindividualTrCel7Amovingontheasinglecellulosenanocrystal(scansize:180nm180nm)75Figure4.4Video-rateAFMObservationsofTrCel7A(50m)moleculesboundoncellulosesubstrate.(a)ContinuouslycapturedAFMframesofmovingTrCel7Aoncellulosesubstrate(twotlocations:(a1)and(a2))in50mMsodiumacetatewithpH5.0.Imag-ingframerate:0.5frames/s.(b)HistogramofaveragemovingvelocityofTrCel7A.ThevelocitieswerecalculatedbythemodistanceandbyPoissondistribu-tion(Detailedinsupplementedmaterial).(c)TrCel7AmoleculescountingbasedonAFMimages.PositionsofeachTrCel7Amoleculearelabeledwitharrows.76ThesurfacedensityofactiveTrCel7Aoncellulosesurfacedecreasesovertimeaftertheywereaddedontothecellulosesubstrate(Figure2A).RepresentativeframesforTrCel7Acountingareshownatthetimeofthestartpoint,20minutes,45minutesand75minutes(Figure3B),respectively,afterthereactionstarted.ThesurfacedensityofactiveTrCel7Adeclinedto50%ofinitialvalueafter10minutes,and10%40minutesafteraddingTrCel7A.ThedensityofactiveTrCel7Areachedasteadystateof5%after60minutes.Weusedanempiricalexponentialdecayfunction(Eq.3)totheexperimentaldata,andthedecayconstantisb=0.0592.WhilethenumberofactiveTrCel7Arapidlydecreasesovertime,theaveragemovingspeedofTrCel7Aoncellulosesubstrateonlydecreasedslightly(b=1.710-8inFig.3C),whichcouldbenegligible.ThisreductionofactiveTrCel7Acouldcausehydrolyticratedecliningduringhydrolysisinourresults(Fig.4).Fromtheperspectiveofenzymatichydrolysis,whenTrCel7Ahydrolyzecellulose,theenzyme-cellulosecomplexshouldconsistofthesolubleenzymesolutionandtheinsolublesubstratecellulose.TrCel7Aenzymeshavetoactatthesolid-liquidinterfaceduringhydrolyzingcellulose.TheCBDofTrCel7Aiseitherdeactivatedorattenuatedinthescaleofhours,whichresultsinthepercentageofactiveTrCel7Akeepdecreasingasthehydrolysisreactiongoingon.Inpreviousstudies,CBDwasknownforitsabilitytoenhancetheconcentrationofenzymesratherthanitsactiveroleincellulosehydrolysis.CBDcouldpenetratecellulosechainsandservetofeedchainintotheactivesitetunneloftheCD[94].ThebindingofindividualTrCel7Aoncellulosesurfacecouldbeintotwocategories:productivebinding(bindingbybothCDandCBD)andnon-productivebinding(bindingbyCBDonly).Forthesinglemolecularobservation,bothproductivebindingandnon-productivebindingwereobservedduringtheexperiment.SincetheTrCel7Abelongstothecategoryofmotorprotein,andthemotionenergycomesfromthehydrolysisofaglycosidicbondofcellulose(approximately-12.5kJ/mol)[82],theobserved77TrCel7Amoleculesthatareinmotioncanbeconsideredasactiveenzymesorproductiveenzymes;whilenon-productiveenzymecannotmovealongthesurfaceofcellulose,duetothelackofdrivingenergyfromhydrolysis[82].Therefore,themajorityofactiveTrCel7Amoleculesobservedinourstudycanbeconsideredastheproductiveenzymes,astheyweremovingalongthecellulosesurface.However,theactiveTrCel7Amaybetransformedfromtheproductivestateintonon-productivestate,suchasenzymejamming(Fig.S3).SurfacedefectscouldstackTrCel7Amoleculeswithinashortperiodoftime,andsubsequentlythejammingcouldbebrokenandnon-productiveTrCel7Amoleculescomebacktobeproductive.Inthisstudy,weconsideredthesetemporalnon-productivemoleculesasactiveTrCel7A.AlternativemethodswerealsousedtoestimatethequantityandactivityofactiveTr-Cel7A.Maetal.calculatedthequantityofactiveTrCel7Aasthebetweenthemassesofadsorbedandirreversible(deactivated)TrCel7A29.TheirresultsindicatedthattheactivityofactiveTrCel7Ahasnotchange,evenasthehydrolyticratedur-inghydrolysisdecreased.ThisresultechoedourthatthemovingvelocityofactiveTrCel7Ahadslowedonlyslightly.TheyalsofoundthatthenumberofactiveTrCel7Aex-periencednotchange,butwefoundthedensityofactiveTrCel7Awasreducedwithtime.ThebetweenourcurrentresultsanddatabyMaetal.maybeduetotheinexperimentdesignmethod.Theyusedbulksolutionwithwmethod,whileweusedsinglemolecularobservationtechnique,whichshouldbemoreaccurate.784.4.4CelluloseSubstrateChangesIndicatesEnzymaticHydroly-sisRateBesidescapturingthemovementandcalculatingthesurfacedensityofactiveTrCel7A,wealsomeasuredthetopographicinformationofcelluloseasanindicatorofhydrolysisrate[95].AFMimaging(well-tunedtappingamplitude)doesnotcausemechanicaldamagetocellulosesurface,thus,theobservedtopographicchangesincelluloseduringenzymatichydrolysiscanbeinterpretedastheresultofenzymaticaction.ThechainsofcelluloseIIusedinthisstudyhavealmostperfecttwo-foldsymmetryandarecompatiblewithoccurrenceoftwointermolecularhydrogenboundsbetweenconsecutiveresidues.Thecrystalstructureconsistsofanti-parallelchainswithtconformationsbutwiththehydroxymethylgroupsofbothchainsnearthegauche-transorientation[96].Normallythecrystallinehavethecrosssectionsof4-6nm.However,inthisstudy,mostofthetime,thehavebeenstackingtogetherwithcrosssectionsof0.5-5m.TheheightchangesofcelluloseafteradditionofTrCel7Awerecalculatedfromthetopographyimages(Fig.4C).Theaverageheightoftheerdecreasedto50%ofinitialheightat20minutesandfollowedby23.5%at40minutes,andthenleveledfortherestoftheobservation(Fig.4A).Arepresentativeofthetopographicchangesofselectedtargetcellulosewithin6minuteswasprovided(Figure4B)andFigure4Crepresentsthecrosssectionanalysisthesameposition.Weusedtheaverageheightoftheentirecrosssectiontoplottheheightchangescurve.Theresulteddatacombinetheheightchangeswiththewidthchangesofthecellulosetogenerateanormalizedvolumechangeswhichcouldbeconsideredastheresultofenzymatichydrolysis.Consideringthesmallexperimentalerrorof3.5nm,ourresults(Fig.4A)suggestthatthisdecayisrelatedwiththerapiddeclineofenzymatichydrolysis.Theheightchanges79Figure4.5TimecourseofthesurfacedensityofactiveTrCel7A(50M)moleculesboundoncellulosesubstratein50mMsodiumacetatewithpH5.0at25C.ThesurfacedensityofactiveTrCel7Ahasbeencalculatedbyaobservationarea15050nm2.(A)ObservedsurfacedensityofactiveTrCel7AdecliningduringthecontinuouslyAFMobser-vationandtheaveragenumbersofactiveTrCel7AwerecalculatedastheexpectedvalueofPoissondistribution(Eq.1and2).Errorbarsshowstandarddeviation(SD)fromthethreeindependentmeasurements.Theexperimentaldatawasbyanempiricaldecayfunc-tion(Eq.3).(B)ExampleofAFMdynamicobservationsontreactiontimepoints:3min(B1),23min(B2),46min(B3)and76min(B4),respectively.ThenumbersofactiveTrCel7AoneachAFMframewerecountedmanuallyandusedastherawdataforcalculatetheparameterofPoissondistribution80observedinthecurrentexperimentsareconsistentwiththepreviousresultsobtainedfrombulkbioanalyticalassays,whichmeasuredtheconcentrationofthehydrolysisproductandsuggestedthatthehydrolyticrateofTrCel7Ahadarapidexponentialdecayintheinitialbindingstage,andthattheseenzymesbecomeinactivateandreducedtheenzymatichy-drolysisrate[83][97][98].Infact,swellingalsoinducesthetopographychangesofcelluloseTheswellingeventisarelativelyslowprocessaswatermoleculespenetratethespacebetweenadjacentcellulosechains,causingaoftheintermolecularhydrogen-bondnetworkandresultingintheexpansionoftheHowever,itiswellestablishedthatthehydrolysisdominatesthetopographychangesattheinitialstage,andswellingcomesinatalaterstage[99].Theobservationtimecourseintheexperimentrunsfrom90to120minuteswhichcouldbeconsideredasaperioddominatedbyhydrolysis.Inaddition,TrCel7A(unlikeCel7B(alsoknownasendoglucanaseI(EGI)whichcancleaveinternalbondsandcreatenewchainends))isunlikelytointroducethewatermoleculesintotheexposedhydrophilicstructureoftheinnerpara-crystallinecellulosechains,whichmaytriggertheswellingofcellulosethustheheightchangescausedbyswellingisnegligiblewhenonlyTrCel7Ahasbeeninvolvedintotheenzymaticreaction.4.4.5TheHydrolyticRateisDependentontheDensityofTr-Cel7AMoleculesontheCelluloseSubstrateThisisthetimethatthewelldocumenteddropofhydrolysisrateisobservedatsinglemolecularlevel.Viavideo-rateAFM,weobservedthathydrolysisreactionreducestheheightofcellulosemolecules(Fig.4.6A).Consistentwiththedropofhydrolysisrate,theheightchangesofcellulosesubstrategetslowerduringthehydrolysisreaction.Weused81Figure4.6Timecourseofthedensity(number)ofthetopographicheightchangesofcellu-losesubstrateinteractedwithTrCel7A(50M)in50mMsodiumacetatewithpH5.0at25C.(A)ObservedheightofcellulosesurfacedecliningduringthecontinuouslyAFMobservation.Errorbarsshowstandarddeviation(SD)fromthethreeindependentmeasure-ments.(B)and(C)ExampleofAFMdynamicobservationsoncellulosesurfacemonitoringduring480seconds.(B)isthecross-sectionof(C)atvarioustimespots.Thepositionofcross-sectionismarkedwithdashlineon(C)82anempiricalexponentialdecayfunction(Eq.3)totheexperimentaldata,andthedecayconstantis0.0592.ThedensityofTrCel7Aoncellulosesubstratealsoreducesduringthehydrolysisreaction.Theexponentialdecayconstantis0.0503,atthesamescaleofthatofthereductionofheightchangesofthecellulosesubstrate,whichindicatesthehydrolysisreactionrate.WethushypothesizethattherapiddecliningofenzymatichydrolysisrateisrelatedwiththedensityofTrCel7Aonthecellulosesubstrate,andnextwewillcompareourresultsandtheonesexistedinliterature.(i)InhibitionofTrCel7Abyhydrolysisproduct:cellobiose[100].Inordertooutiftheproductinhibitionisadominatingfactorforhydrolysisratedeclining,wedesignedacontinuousexperimentusingthesamesubstrate(cellulose)andsamewithcontinuousadditionofTrCel7A.Duringtheobservation,weaddedTrCel7Aatthetimepointsof0minute,120minuteand240minute.ThesurfacedensityofactiveTrCel7AandheightchangesofsubstratehavebeenmeasuredusingAFMimagingframes.AfteraddingTrCel7Atotheimagingtheconcentrationofhydrolysisproductincreasesduringtheentireexperiment.However,thehydrolysisrate(celluloseheightchanges)andsurfacedensityofactiveTrCel7Aremainedthesametrends(Fig.4.7)asthoseinexperimentsdescribeinprevioussection.ThissuggeststhatthehydrolysisproductscannotinhibitthereactionofcelluloseandTrCel7Aoratleastisnotadominatingfactorfortheratedeclining.Inaddition,Converseetal.showedthatthehydrolysisrateremainedindecliningtrendwhentheproductswereremovedduringthereactions[101].(ii)Thecellobiohydrolasesbecomingstuckorjammingonthesubstratesurfaceduetoacrystallinedefect[102][103][104].Fromthetimecoursestudy,wedidobservetheTrCel7Amoleculesjamming.Sincethehydrolysisrateswereindependentofenzymetosubstrateratio(Fig.4.7),jammingofTrCel7Aoncellulosesurfaceisnotaprimaryreasonfordecreasing83hydrolysisrate.Inaddition,jammingofenzymemoleculeslastedonlyforashortperiodbeforeitwasbrokendownandTrCel7Amoleculescamebacktofreemovement.Theseresultssuggestedthattheenzymejammingisalocallytransientstateofenzymatichydrolysis,anditislesslikelytotheoverallhydrolysisrate.(iv)Non-productivebindingofadsorbedenzyme[98].BindingoftheintactTrCel7AonlythroughCBDresultsinanon-productivebinding,wherethecellulosechainisnotintheactivesite.Accordingtotheexperimentalresultsofthisstudy,thenon-productivebindingTrCel7Amoleculeswerealsoobservedasimmobilizedenzymes.However,comparedwithactiveTrCel7A,itonlyaccountedforlessthan5%ofthetotalnumberofobservedenzymemolecules.Basedonconcentrationanalysis,JalakandValjamae[98]suggestedthatthesurfacedensityofactive(productive)enzymesdidnotchangeduringthehydrolysisprocess,andsomeTrCel7Awasinactivatedonasubstratesurfacetobecomenon-productivebingingenzymeswhileotheractiveTrCel7Acouldproceedfreelyalongthecellulosesurface.Howev-er,inourresults,thesurfacedensityofactiveTrCel7Amoleculesdecreasedovertime.Thebetweentheirandourresultsislikelyduetothetobservationmethods.JalakandValjamae[98]usedpara-nitrophenol--D-lactoside(pNPL)asareportermoleculetomeasuretheconcentrationofnon-productiveTrCel7Amoleculesbybindingtotheirac-tivesites.However,sincethepNPLmoleculesisalsoinvolvedinthehydrolysisreaction,themeasuredconcentrationofproductive/non-productiveenzymescouldbeinterferedbyaddi-tionalpNPL.ItisnoteasytoruleoutthepossibilitythatpNPLmaythehydrolysisofcellulose.Moreover,itisknownthatthecellobiose,theproductofTrCel7Ahydrolysis,isastronginhibitorofthehydrolysisofpNPL[105],whichmakespNPLanunstablereportermoleculeduringtheTrCel7Ahydrolysisprocess.TheresultsproposedinthisstudytriedtousesinglemoleculeinsitutomeasuredirectlythehydrolysisbehaviorofTrCel7Awhich84shouldbemoreaccurate.(v)Inactivationofenzymethroughirreversiblebindingtocellulose[106].Theexperi-mentalresultsofthisstudysupportthishypothesisquitewell.ThetimecoursestudyofthesurfacedensityofactiveTrCel7A(Fig.4.5)andthehydrolysisratebyexaminingtheheightreduction(Fig.4.6)suggestedatemporalcorrelationofthedeclininginhydrolysisratewiththedecreaseofsurfacedensityofactiveTrCel7A.AdetailedanalysisofthedensityofactiveTrCel7Aandhydrolysisproductionshowedasimilartimeconstantinthetwodecaycurves(bTrCel7A=0:0592andbheight=0:0503).Figure4.7TimecoursecomparisonofthesurfacedensityofactiveTrCel7Amolecules(A)andthetopographicheightchangesofcellulosesubstrate(B)duringthecontinuousadditionofTrCel7A.50MofTrCel7Awasaddedattimepoint0min,120minand240min.Boththecellulosesubstrateandimaging(50mMsodiumacetatewithpH5.0at25C)werestayedthesamethroughoutthelengthofentiretimeperiod.ThesurfacedensityofactiveTrCel7AhasbeencalculatedastheexpectedvalueofPoissondistribution(Eq.1and2).Errorbarsshowstandarddeviation(SD)fromthethreeindependentmeasurementsBecausetheenzymatichydrolysisinvolvesthesolubleenzymeandinsolublesubstrate,85eachsingleenzymeshouldbeabletobindandactatthesolid-liquidinterface.CBDisthoughttoenhancethehydrolysisoftheinsolublesubstratesviaincreasingboundenzymeconcentrations[106].Enzymebindingreversibilityhasbeenthefocusofnumerousstudiesbuttheresultsareoftencontroversial.Insomestudiesfullreversibilitywasob-served[107][108],whichcanbetheadaptionoftheLangmuirmodel;whereasothersreportedtirreversibility[109][110].However,ourresultssuggestedatimevariationonthesurfacedensityofboundenzymethatoccurredduringtheenzymatichydrolysiswhichcon-tradictstheassumptionofLangmuirmodelofconstantequilibriumandadsorptioncapacity.Itmaycomeoutwiththeconclusion:forTrCel7A,eachbindingmaynotbeequivalentandtheremayexistsomeuncertaininteractionbetweenadsorbedmoleculesonadjacentsites.Someotherfactorssuchasenzymehalf-lifeperiodmayalsothehydrolysisrate.Thehalf-lifeparameterisrelatedtothetimeperiodthatsinglemolecularstaysonthesurfaceofcellulosesurface.Althoughthethermaldeactivation(whichthehalf-lifeperiodofprocessivehydrolysis)alsocontributestheslowhydrolysisrate,theenzymedeactivationislikelytobetheorderdecay[104].Comparedwiththedensityofactiveenzymemolecules,whichhasbeenshownasexponentialdecayinthisstudy,thehalf-lifeparameterislesslikelytobeadominatedfactorforrapiddecayofhydrolysisrate.Wedidnotobservetheinitialstateofbindingwithincreasingbindingandactivityincreasesimultaneouslyasreportedinsomeresearches[111],whileourresultsindicatedthatthedeclineofthesurfacedensityofTrCel7AstartedrightaftertheadditionofTrCel7A.ThisresultisconsistentwiththeexperimentalresultofMaetal.,whousedaUV-spectralmethodtoestimatetheadsorp-tionbehaviorofTrCel7A7.However,wecannotdiscountthesuggestionofinitialbindingincrease,sinceourtechniqueisnotenoughtoresolveatemporalphenomenonwithinseveraltensofsecondsaftertheonsetofreaction.864.5ConclusionsInthisresearch,westudiedtheenzymatichydrolysisofcellulosenanocrystalbyusinganAFMtodynamicallyobservetheenzymatichydrolysisprocess.Weusedascanstrategy{priorknowledgebasedcompressivescantoimprovetheimagingrateofAFMhighenoughtocapturethemovesofTrCel7Aoncellulosesurface.Duringtheenzymatichydrolysis,onlytheactiveTrCel7Acouldbeconsideredastheeenzyme",basedonthevisualizedinformationoftimecoursestudyonsinglemoleculeTrCel7A,thesurfacedensityofeenzymetlydecreasedalongwiththedecliningofhydrolysisrate,whichisalsoindependentoftheconcentrationofcelluloseandproducts,respectively.ThissuggestedthatthesurfacedensityofactiveTrCel7A,isthedominatefactorthatcausedtheinactivationofenzymeduringthehydrolysisprocess.Nevertheless,wedidnotruleoutthepossibilitythatthedeclinedhydrolysisratemayalsobecorrelatedwiththehalf-lifetimechangesoftheboundenzyme.Consideringthedramaticaldecliningofthedensityofactiveenzyme,enzymatichalf-lifetimechangesisunlikelytobethemainreasonthatcausedthedeclinedhydrolysisrate.FurtherimprovementonAFMwithfasterimagingspeedwouldbehelpfultoaccuratelyestimatethemovingvelocityofTrCel7Aandcalculatetheprocessiveparameterssuchaskon,koffandkcat,wouldbehelpfultohaveamorecomprehensiveunderstandingofenzymaticinactivation.OurresultsalsosuggestthattheactivationofCBDofTrCel7Aseemstobesuppressedduringthehydrolysis,whichmaybeanusefulinformationforproteinengineeringstudytoincreasetheofenzymatichydrolysisrate.87Chapter5Real-timeSensingofElectricalPropertiesinNanoEnvironment5.1IntroductionWiththedevelopmentofnano-materials,suchasnanotubesandnanowires,theelectricalcharacterizationofthesematerials,attractedstrongattentionbecauseoftheiruniqueelec-tricalandthermalpropertiesduetoquantumt[112][113].Asatypicalnanoma-terial,multiwallnanotubes(MWNTs)haveintrinsicthermalandelectricalproperties[114],whicharebeingconsideredaspotentialcandidatesforthenextgenerationofcircuitwiresandnanoelectronicdevicessuchasnanotransistors[115][116],andsensors[26][25][29].Thecarbonnanotubescanholdacurrentdensityashighas109A=cm2(whichismorethan1000timesgreaterthancopper)[117],andthethermalconductivitiesishigherthan3000Wm1K1[118].However,thethermalandelectricalpropertiesoftheMWNTsarenotfullyunderstood,especiallyfortheelectricalbreakdown.AnMWNTconsistsofmanylayersofsingle-wallnanotubes,andeachofthemhasavariousmechanical,electricalandthermalproperties.ElectricalbreakdownispossibletobewellcontrolledtopeeltheouterlayersofMWNTortailoritsstructure,inordertochangethepropertiesofMWNT[119].TheelectricalbreakdowndeterminesthemaximumcurrenttransportthroughtheMWNTscircuit,anditisalsoconsideredasanapproachto88fabricatehighperformancesensorsandtransistors.Itisessentialtounderstandtheelectronicpropertiesofthematerialpriortodesigningahighperformancenanodevice.Generally,theelectricalbreakdowniscausedbyJouleheatingproducedbytheelectronwinthelayersofMWNT[120][121].Inpractice,however,thereasonsforelectricalbreakdownbecomevariousifenvironmentalconditionsareconsidered,suchasenergydissipationtotheelectrodes,heatsinkofsubstrate,localheatingandoxidation.Althoughelectricalbreakdownisknownasanissuefortheapplicationsofinterconnects,italsocanbeconsideredasanapproachtochangelocalmechanicaland/orelectricalpropertieswhichcouldbemorevaluablethanregularMWNTsfortheapplicationsofMWNTsbasedsensorsandtransistors.IthasbeenwidelyacceptedthattheelectricalbreakdowniscausedbyJouleheating[122].Inwords,theelectricalbreakdownisexpectedtobehappenedinthecenterofasuspendedMWNT.However,somestudiesobservedconverseresults:electricalbreakdownsarenotalwayshappenedinthecenter,sometimeitlocatesapartquitalongdistancetothemid-dle[123].Insuchacondition,thestructuraldefectofMWNT(whichcouldreducethelocalconductivity)wasconsideredasthemajorreasonthatleadstotheelectricalbreakdown[124].Besidesstructuraldefect,localconductancechange,suchasdiametervariationfromoneendtotheother,alsodeterminesthepositionofelectricalbreakdown[125].Themotivationofpresentresearchistothecrucialfactorsthatelectricalbreakdown,andmaketheelectricalbreakdowncontrollable.Controllableelectricalbreak-downisstudiedutilizingatomicforcemicroscopy(AFM)basednanorobot.TheAFMbasednanorobotisaspecialandusefultechnologicaldevicetoimagethenanostructures,andtoconductlocalmanipulationsonnanomaterials[70][69][71].ThesharpAFMtip(apexisap-proximately10nmorless)canbeconsideredasanendofthenanorobot,whichcanmeasureandmanipulatesamplesinnanoscale.InthisresearchanAFMbasednanorobot89isusedtomeasurethelocalconductivityofMWNT,andmanipulateitsspatialstructuretocontrolthelocationoftheheatsink,whichmakeselectricalbreakdowncontrollable.Thenon-vectorspacecontrolcomesfromageneralframeworkcalledmutationanalysisforsetevolutions,whichisproposedbyAubin[126].Mutationanalysisprovidesanaturalwaytodescribevariousphysicalphenomenabecausesomeobjectssuchasshapesandimagesarebasicallysets.Sincetheintroductionofmutationanalysis,ithasbeeninvestigatedinboththeoryandapplications.Onthetheoryside,ithasbeenrecentlyextendedtoobtaintheviabilitytheoremformorphologicalinclusions[127]andthegeneralmorphologicalcontrolproblemswithstateconstraints[128].Ontheapplicationside,ithasbeenappliedtoimagesegmentation[129],visualservoing[130],andsurveillancenetworks[131].ThevisualservoingusingmutationalanalysisisproposedbyDoyenin[130].Nevertheless,possiblyduetoitsabstractnature,nofurtherextensionsareperformedafterwards.Inthisresearch,wetrytoextendtheresultsandapplythemethodtonanoscalemotioncontrol.Themajorextensioncanbesummarizedinthreeaspects.First,thegeneralframeworkforthenon-vectorspacecontrolisestablishedinthisresearchwhichisnotdiscussedinDoyen'swork.Second,theoriginalformulationonlydealswithbinaryimages,whileinthisresearch,grayscaleimagesareconsidered.Third,thecontrollerdesignisperformedforasystemdescribingthenanoscalemotioncontrol.Consequently,thecontrolleristfromtheonein[130].Inordertodesignasystemwhichcansolvetheissue:howtogetaccuratemotioncontrolwithoutintroducingextranoise,wedonotuseextrasensorsforgeneratingSPMscannerpositionfeedback.Insteadofsensors,weusetheSPMimagesasboththeinputandfeedbacktogenerateaclosed-loopcontrolfortipmotioncontrolinthenanomanipulationsystem.Inthisresearch,wedevelopedanovelcontrolstrategybyutilizingthefeedback/compressive90Figure5.1Controldiagramofthenon-vectorspacecontrolsystemwithcompressivefeedback(AFMasanexample)feedbackproducedbyimages/compressivedata.Becausetheimageorcompressivefeedbackisaset,notavector,fromwhichcomesthetermnon-vectorspacecontrol,andinaddition,thefeedbackcanbefulllocalimageorpartialimagethatcanbeconsideredascompressivedata,fromwhichcomesthetermcompressivefeedback.Insidethiscontrolsystem,boththecontrollerdesignandfeedbackarebasedonthenon-vectorspacefortipmotioncontroltoconductnanomanipulationonSPM(asshowninFig.5.1).Threecrucialstepsinthisstrategyareasfollows:(1)Designanon-vectorspacecontrollerinwhichthelocalimageisuseddirectlyasthefeedback.(2)Usingcompressivescanningtocompressedsampleandreconstructlocalimage.Compressivesensingisintroducedhereforreducingthescanningtimetoincreasethefeedbackrate.(3)Replacecompletefeedback(localimage)withcom-presseddatadirectlytogenerateacompressivefeedback(asshowninFig.5.1).Inthisstep,wedesignedanon-vectorspacecontrollerbasedoncompressivefeedback.Aftercompressivescanning,itisnotnecessarytorecoverthelocalimagethatcostsextratimeoncalculation.Thecompressivedataobtainedbycompressivescanningisuseddirectlyasthefeedbackof91thisnon-vectorspacecontroller.Thisisthechallenge.Insuchacasethecontrollermustensurethestabilitywhenthecompresseddataisusedasthefeedbackofclosed-loopcontrol.InthisresearchwewilluseAFMasaspexampletoilluminatehownon-vectorspacecontrollerworks.Inaddition,anAFMbasednanomanipulationapplications:carbonnan-otubeconductivitymappingusingnon-vectorspacecontrolwillbeintroducedattheendofthisreport.5.2AccuratePositionControlinNanoEnvironment5.2.1Non-vectorSpaceControlbasedonLocalImageAnon-vectorspacecontrolstrategybasedonlocalimageisproposedinthissection.Alocalimageisobtainedbyscanninglocally(thelocalscanonlysamplesasmallareaofinterestandsamplingtimecanbereducedsothatanacceptablefeedbackrateisachievable)[49].Intheconventionalvisualservoingapproaches,severaloffeaturesareextractedfromtheimagefollowedbyacontrollerwhichisdesignedtoconvergepositionerrorbetweendesiredandcurrentvectorsoffeaturestozero[50].Traditionalvisualservoingreliesonfeatureextraction,andinmostvisualservoingliteratures,severalmarkersareusedforfeaturessothatthetrackingofthemcanbeeasilyachieved[132].tfromtheabovetraditionalservoingmethods,wedevelopedafeaturelessmethodthatdirectlyusetheimageintensityinformation.First,ourmethodconsiderstheimageasaset.Second,wethebetweensetsastheerrorbetweenthedesiredandcurrentimageset.Finallyanon-vectorspacecontrollerisdesignedtoconvergethetozero[133].Thismethodisrecentlyappliedtonanomanipulations[134].Itshouldbenotedthatotherfeaturelessmethodsalsoexist,includingthekernelbasedmethod[52],thesum-of-92Figure5.2Basicworkingapproachofnon-vectorspacecontrolmethod[135][54],andtheentropybasedmethod[136].Butourapproachisfundamentallytfromthem.Althoughthecontrollerdesigninaboveapplicationswasperformedinnon-vectorspaceinwhichthelinearstructureinvectorspacedoesnotexist,thedynamicmodelsarestillinvectorspace.Itbroughtmoreinthetheoreticalanalysisanddesignworkofthecontrolsystems.Inourapproach,boththedynamicsmodelandthecontrollerdesignareinnon-vectorspace.Thebasicnon-vectorspacecontrolstrategyisshowninFig.5.2.First,alargeareaofinterestisscannedbySPM.Thenasmallimagepatchischosenasthedesiredimage(insidethelargeareaSPMimage).Thenthetipstartsthelocalscanningtoobtainthe93currentimage.Basedonthetwosetscorrespondingtothedesiredimageandcurrentimage,thenon-vectorspacecontrollercalculatesthemovingdirectionfortheSPMtip.Throughupdatingcurrentimages,eventuallythedesiredimageistotallythesamewithcurrentimage.Bythisway,thetipcanbesteeredtothedesiredpositionformanipulation.Thisstrategyiscompletelytfromcurrentvisualservoingmethodology.Thisisbecausethatalthoughimageisalsousedinvisualservoing,imageitselfisneithertheinputnorthefeedback.Invisualservoing,imageisusedforrecognizingfeaturesorlandmarkswhichareusedforlocatingtheposition.Someothermethodssuchasopticalw[137]whichcouldalsobeusedinvisualservoing.However,opticalwmethodologyworksinvectorspace,andinotherwordsimageisavector(notaset)toopticalwmethod.Inthiscase,thiskindofmethodalsoneeddedicatedcalibrationbeforeapplying,whichisveryinnanoworld.Inordertodesignsuchacontrolsystem(mentionedabove),twofundamentalissuesneedtobesolved:howtoa(distance)innon-vectorspace;howtobuildadynamicmodelinthenon-vectorspace.Thenon-vectorspacecontrollerisbasedontheset,andifwewanttosolvethetheseissues,mutationanalysisshouldbeusedtobuildthedynamicsmodelinnon-vectorspace[134].5.2.1.1EssentialsofMutationAnalysisInordertoformulatethebetweentwosets,thesetdistanceshouldbeAnysetdistanced(X;Y)betweensetsXandYmustsatisfyfollowingthreeconditions[138].(1)Non-negative:d(X;Y)>0ifXisnotthesamewithY;d(X;X)=0;(2)Symmetry:d(Y;X)=d(X;Y);(3)TriangularInequality:d(X;Z)(X;Y)+d(Y;Z)foranyothersetZ.94Anysetdistancewhichthesethreeconditionscouldbeappliedinnon-vectorspacecontrolsystem.Inthisresearchweusedistanceasanexampletodiscussthecontrollerdesignandstabilizationproblem.GivenasetofpointsP2Rn,thesetdistancebetweenthesetPandapointx2RnisdP(x)=miny2Pjjyxjj.TheprojectionfromxtoPisdenotedasP(x)=fy2P:jjyxjj=dP(x)g.ThedistanceoftwosetsPandQisas:dh(P;Q)=maxfmaxp2Pminq2Qjjpqjj;maxq2Qminp2Pjjqpjj)g(5.1)Followsaresomeextraforthesetdynamics.AtubeK(t)ˆRnisamapping:K:R+7!2Rn,where2RnisthepowersetofRn.Let':E7!RnwithEˆRnbeaboundedLipschitzfunction.DenotethesetofallsuchfunctionsasBL(E;Rn).Thetransitionfor'2BL(E;Rn)isas:T'(t;K0)=fx(t):_x='(x);x(0)2K0g(5.2)whichcanbeconsideredasatubeevolvingundertheruleof'.Thederivativeofthetube,basedonmutationanalysis,mustsatisfythefollowingcondition:limt!0+1tdh(K(t+t);T't;K(t)))=0(5.3)K(t)=f'(x)2BL(E;Rn):Eq.(5:3)isg(5.4)95Therefore,thesetdynamicsmutationequationisasfollows:'(x)2K(t)(5.5)Inaddition,thecontrolledmutationequation(letUbethesetofallthepossiblecontrolsu)isas:'(x(t);u(t))2K(t)withu(t)=(K(t))(5.6)where':EU7!BL(E;Rn)isamappingprocessfromastatetoaboundedLipschitzfunction.:2Rn7!UisthefeedbackmapfromcurrentsetK(t)tothecontrolinput.5.2.1.2MutationAnalysisforNanomanipulationMutationanalysisisanalternativewaytosolveavisualservoingproblem:designacontrolleru(t)=(K(t))basedoncurrentimages^K(t)sothatdh(K(t);^K)!0ast!1,whereK(0)and^Kareaninitialcurrent)andgoal(desired)imagesetsrespectively,Infact,ifthefunction'inEq.(5.6)islinearinu(t),wehavethefollowingtheorem[133,134]:ForthesystemdescribedbymutationequationL(x)u2K(t)withx2Rm,L(x)2Rmn,u2Rn,andK(t)ˆRm,thefollowingcontrollercanbelocallyexponentiallystabilizedat^K:u(t)=(K)=A(K)+V(K)(5.7)where>0isagainfactor.A(K)+istheMoore-PenrosepseudoinverseofA(K)2R1n96by:A(K)=ZKd2^K(x)mXi=1@Li@xidx+2ZK[x^K(x)]TL(x)dx2Z^K[xK(x)]TLK(x))dxwhereLi(i=1;2;:::;m)istheithrowvectorsinmatrixL.V(K)istheLyapunovfunctionas:V(K)=ZKd2^K(x)dx+Z^Kd2K(x)dx(5.8)Innanomanipulations,theSPMcanbeconsideredasanimagingdevicewithtwotrans-lationaldegree-of-freedom(verticalmotionisusedtoobtainthesampletopography).Ifthecontrolinputisu=[ux;uy]T,themutationdynamicequationis:Lu2K(t)(5.9)whereL=26666641001003777775isaconstantmatrix.Inthiscase,thecontrollercanbeobtainedfromEq.(5.7):u(t)=2fZK[x^K(x)]TLdx+Z^K[xK(x)]TLdxg+V(K)(5.10)975.2.2CompressiveSensingforVisualServoingInthenon-vectorspacecontrolsystem,SPMimagesareusedastheinput.Theinputimagehereisnottheentireimagewhichcoststoomuchtimeonscanningbutthelocalimagewhosedimensionismuchsmallerthantheentireimage.Thelocalscanstrategy[2]wedevelopedcouldmakethescannerscaninasmalllocalareaandgetitstopographyimage.However,itstilltakeseveralseconds(actualtimedependsonlocalimagesize)toobtainalocalimagewhichistooslowforprovidingfeedbackforthenon-vectorspacecontroller.Inordertosolvethelowfeedbackproblem,compressivesensingisintroduced.Consideringanunknownsignalx2RN,ifMlinearmeasurementsaretakenaccordingtoameasurementmatrix(asshowninEq.(5.11),inthecaseofM=N,theoriginalsignalxcouldbewellsampled.However,wearemoreinterestedintheconditionwhenM˝N:fewermeasurementsmightbeenoughforreconstructingtheoriginalsignal.y=x(5.11)whereisthemeasurementmatrixandyisthemeasurementresultswhichy2RM.Eq.(5.11)isanunder-determineequationifM˝N-impossibletoauniquesolution.However,ifaddingsomeconstraintsuchasthatxissparseandhasbeenproperlydesigned,theoptimizationsolutionofxcanbefoundbysolvingthe0-normminimizationproblem[64].^x=argminjjxjj0s.t.x=y(5.12)Becausesolvingthe0-normminimizationproblemisNP-hard[66,139],1-normmini-98mizationisusedtoinsteadof0-norm.ThentheEq.(5.12)couldbewrittenas^x=argminjjxjj1s.t.x=y(5.13)where^xisthereconstructedsignal.Besidesthe1-normminimizationalgorithm,minimizationtotalvariationmethod(Eq.(5.14))isusedforsignalreconstruction.Itcanthesparestsolutioninintensitygradientleveltoobtainacontinuousandsmoothreconstructedimage.^x=argminTV(x)s.t.x=y(5.14)whereTV(x)=Pi;jq(xi+1;jxi;j)2+(xi;j+1xi;j)2.Becausecompressivesensingcanfewermeasurements,wecanuseitassociatedwithourlocalscanstrategytoincreasethefeedbackratebyfurtherdecreasingthescanningtime.HowtodesignapropermeasurementmatrixisachallengefacingtotheimplementationofcompressivesensingintoSPM.UsuallycompressivesensingusesrandommeasurementmatrixessuchasrandomGaussianandBernoullimatrixes.ItistoapplytheserandommeasurementmatrixestoSPMduetothespecialworkingprincipleofSPM.TheworkingprincipleofSPMisusingatiptoscanontopofsamplesurfacelinebylinewhichisatimeconsumingwork.Themeasurementmatrixincompressivesensingisanessentialpartduetotherela-tionshipbetweenthemeasurementmatrixandmeasurement.AccordingtotheRestrictedIsometryProperty(RIP)[64],randommatrixesusuallyleadstothetotallyre-constructedoriginalsignal.InordertodesignarandommeasurementmatrixforSPM,thephysicalmeaningofthe99measurementmatrixinSPMimagingshouldbestudiedMeasurementmatrixistheSPMscanningtrajectory.Thetipscanningtrajectoryisdeterminedbymeasurementmatrix.However,becauseoftheworkingprincipleofSPM,wehavetoacontinuoustrajectoryforrandomsamplingpointswhichcanconnectallthepointsandonlyvisitonce.Thisisatypicaltravelingsalesmanproblem(TSP)whichisaNP-hardproblem.Inordertoanearoptimalsolutionforthistrajectory,theGeneticAlgorithm(GA)whichisaparadigmbasedoncrossoverandmutationisusedforsolvingthisproblem[67].Theworkingprincipleofthisalgorithmisthatitconnectseachofthetwopointsandthenrandomlyselectsthepositiontocuttheconnectionbetweentwopoints.Throughthemethodsofrecombination,mutationandselection,GAcouldsearchanewgenerationpointswhichisbetter(shortertravelingdistance)thantheformertrajectory.Forexample,wesetthelocalareawith5050points,andafterGAwasapplied,thetrajectoryisobtainedasshowninFig.2.2.TheredlinedenotesthetrajectoryoftheSPMtipwhichvisitseachpointonceandeventuallyreturnstotheinitialpointwiththetraveldistance981.1645(assumethedistancebetweentwoneighborpointsisone).Itismuchshorterthanrasterscanningtheentirelocalarea(totaldistanceis2500).Bymeansofcompressivesensing,wecandirectlysavethetimespentonscanningwhichcanincreasetheimagefeedbackrate.5.2.3Non-vectorSpaceControlbasedonCompressiveFeedbackAlthoughcompressivesensingdecreasesthetimespentonscanning,itstillneedsextratime(approximate0.5secondfor3030image)forimagereconstruction.Inordertofurtherin-creasethefeedbackrate,weextendedthenon-vectorspacecontrollertocompressivefeedbackcaseinsteadofcompleteimagefeedback.Thederivationissimilartothecaseofcompleteimagebasednon-vectorspacecontrol100methodologywhichusesregularstatefeedback.Theonlyfromtheapproachinsection5.2isthetypeoffeedback.Thefeedbackforformercontrollerisacompleteimagerecoveredfromcompressivescanning.Incontrast,forcompressivefeedback,thecompressivedataobtainedbycompressivescanningisuseddirectlyasthefeedbackwithoutrecoveringprocess.Inotherwords,theSPMscanneronlyscanspartialpointsoflocalarea.Basedonthiscompressivedata,acontrollerisdesignedtocontroltheSPM'stiptowardsthedesiredpositionwhichisachievableifthisprocessisperformedrepeatedly.Italsoshouldbenotedthatinsteadoftheprocessofimagerecovering,wedirectlyuseitforfeedbackwithoutrecovery.Inthiscase,thefeedbackratecanbeincreased.5.2.3.1ControllerDesignbasedonCompressiveFeedbackBecausethemutationequationisthesameandthecompressivefeedback(data)isalsoaset,thecontrollerinsection5.2stillworksanditcanbeslightlymoasfollows:LetKcand^Kcbethesetsobtainedbyrandomscanning/samplingfromthecurrentimageandthedesiredimagesetsK,^K,respectively.FollowingcontrollercanlocallyexponentiallystabilizeKcat^Kc.u(t)=2fZKc[x^Kc(x)]TLdx+Z^Kc[xK(x)]TLdxg+V(Kc)(5.15)whereV(Kc)=RKcd2^Kc(x)dx+R^Kcd2Kc(x)dx,andtheothervariablesarethesameasprevioussection.Thiscontrollermightnotmeetthegoalofdh(K;^K)!0ast!1.ItpossiblyexistsanotherseteKwhere^KcˆeK,ifthecardinalityof^Kcismuchfewerthanthatof^K.Topreventsuchcondition,wehavetoprovethatwhendh(Kc;^Kc)!0,dh(K;^K)!0,if101Kcsatisfysomecertainconstrains.Theseconstrainscomefromthecompressivesensingtechnique.Intuitively,thereshouldbeauniqueKgivenarandomlysub-sampledKcˆK.AssumethattheimageisSsparseinthefrequencydomain(Fourierdomaininthisresearch,thenumberofnonzerocotsisS).Ifwesampletheimagepixelintensityinuniformrandom,theimagecanbeexactlyreconstructedbyl1minimizationalgorithmifthenumberofsamplesisattheorderofO(Slogn).5.2.3.2StabilityAnalysisAssumethattheelementsofsetKisobtainedinorderfromtheimage.Forexample,forannnimage,thenelementsinKaretherow(orcolumn)oftheimage.Letxkbethek-thpixelofalltheintensitiesofimagesetK,andtheelementsinxkareobtainedusingthesameorderinK.Similarly,let^xk,xkc,and^xkcbethevectorofalltheintensitiesof^K,Kc,and^Kc,respectively.Thefollowinglemmaisusedtoprovethestabilityofthecontroller.Lemma1dh(K;^K)!0ifandonlyifjjxk^xkjj!0(1)Firstofall,let'sshowdh(K;^K)!0)jjxk^xkjj!0.Bytheofdistance,ifdh(K;^K)!0,thenforanyp=[p1;p2;p3]TinsetK,wehaveminq2^Kjjpqjj!0.Letq=[q1;q2;q3]Tbetheelementin^Kwhentheminimumisachieved,then(p1q1)2+(p2q2)2+(p3q3)2!0.Becausethetwocoordinatesinpandqarethepixelindices,(p1q1)2+(p2q2)2cannotapproachzeroiftheindicesaret.Therefore,p1=q1andp2=q2whichmeanstheorderofpandqarethesameinKand^K,respectively.Moreover,wehave(p3q3)2!0.Consequently,wehavejjxk^xkjj!0sincejjxk^xkjj2isthesumofallthesquareofintensityforthesamepixelindicessuchas(p3q3)2.102(2)Second,let'sshowjjxk^xkjj!0)dh(K;^K)!0.Letp=[p1;p2;p3]TinsetKandq=[q1;q2;q3]Tinset^Kbetwoarbitrarilyelementswiththesamepixelindices,i.e.,p1=q1andp2=q2.Sincejjxk^xkjj!0,wehave(p3q3)2!0.Thenforp2K,wehaveminq02^Kjjpq0jjjjpqjj!0.ForanyotherelementsinK,wealsohavesimilararguments.Therefore,maxp02Kminq02^Kjjp0q0jj!0.Similarly,wehavemaxq02^Kminp02Kjjq0p0jj!0.Therefore,dh(K;^K)!0.Besidesthelemma,anotherequation(RIP)fromthecompressivesensingliteratureisusedtoestablishourresult.Firstofall,weintroducetheRIPconditionforamatrixformally.1AmatrixA2RmntheRIPconditionoforderSifthereexistsaS2(0;1)suchthat:(1S)jjxjj22jjAxjj22(1+S)jjxjj22(5.16)foralltheSsparsevectorsx2Rn.TotestamatrixwhetherRIPconditionisaexponentialcomputationalcom-plexityproblem.ButrandommatriceshaveshowntosatisfytheRIPconditionwithveryhighprobability.Infact,wehavethefollowinglemma:Lemma2[140]Let2Rnnbethespikebasisand2RnnbetheFourierbasis.ThenthematrixA=R1whereR2Rmnextractsmrowsin1uniformlyinrandom.ThenAsatisfytheRIPconditionoforderSwithveryhighprobabilityifmCSlog4n,whereCisaconstant.Basedonthetwolemmas,wecanhavethefollowingpropositionwhichvthecor-rectnessofusingcompressivefeedback.103Proposition1Assumexk2Rnand^xk2RnareSsparseinthefrequencydomain,xkc2Rmand^xkc2RmbeobtaineduniformlyatrandomfromtheimagesetKand^K.Ifm2CSlog4n,whereCisaconstant.Thenwithhighprobability,wecanhavedh(K;^K)!0ifdh(Kc;^Kc)!0.Fromtherandomsampling,wehavexkc=Axkand^xkc=A^xk.Itisnotedthatbasedontheassumption,therandomsamplingmatrixisthesameasLemma2.Therefore,fromLemma2,A2RmntheRIPconditionwithorder2S.LettheRIPconstantbe2S.Usinglemma1,wehavejjxkc^xkcjj!0fromdh(Kc;^Kc)!0.FormtheRIPcondition,wehavejjxkc^xkcjj22=jjAxkA^xkjj22(12S)jjxk^xkjj22.Since12S>0,wehavejjxk^xkjj!0.BasedonLemma1again,wehavedh(K;^K)!0.ThispropositionsshowthatifcertainconditionsarethesamecontrollerinEq.(5.15)canbeusedunderthethecompressivefeedback.5.3ExperimentalImplementationandSetup5.3.1ExperimentalImplementationonAFMInordertovalidatethenon-vectorspacecontrollerdesignandtesttheperformanceofthiscontrolsystem,weimplementeditintoourAFMbasednanomanipulationsystem(asshowninFig.2.3).AnAFM(Multimode,Bruker-nano,CA)isusedinthisexperiment.Acomputerwithahapticdevice,areal-timeLinuxsystemandDAQcardsareusedinthisnanomanipulationsystem.Inaddition,asignalaccessandcontrolboxisdevelopedforacquiringthesignaloftopographyinformationandinputtingthecontrolsignalintothe104AFMcontroller.5.3.2ExperimentonNon-vectorSpaceControlwithCompleteImageasFeedbackInthisexperiment,wevalidatethenon-vectorspacecontrollerwithcompleteimageasfeedbackusingnanomanipulationsystem.Inthisexperiment,aconventionalAFMwasusedtoobtainanimageof10241024pixelsonsinglewallcarbonnanotube(SWNT)sample(scansizeis1.61.62).Thisistheworkingareaofthenon-vectorspacecontroller.WenamethisAFMimagewith"originalimage".ThenAFMscannedlocallytogetasmallpitchimageofcurrentposition.Afterthat,apositionclosetocurrentposition(approximate56nmaway)waschosenasthedesiredposition.Thedesiredimagecanbeeasilyselectedintheoriginalimage.Aftercalculationsthenon-vectorspacecontrollerprovidesthetranslationalvelocityuxanduy.Thecurrentanddesiredimages,withsizeof3030pixels,arelabeledinoriginalimageinFig.5.3(a).ResultsareshowninFig.5.3(b),wheretheiterationmeansthestepsthatAFMtiptravelstothedestination.Atapproximate50stepstheAFMtipeventuallyreachedthedesiredpositionwhenthedistanceapproachedzero.Anotherthingshouldbenotedhereisthattheerrorinsteadystate.Theoretically,theerrorshouldconvergetozeroastimegoingtohowever,inAFMapplicationbecausethethermaldriftandnoise,thenon-vectorspacecontrolhastominimizetheerrorprovidedbythermaldriftandnoise.Thisisthereasonforwhysteadystateerrordoesnotapproachzerobothinxandydirections.105(a)(b)Figure5.3Experimentsetupandresultsofnon-vectorspacecontrolbasedoncompressivefeedback(a):Experimentalsetupforthenon-vectorspacecontrol(b):Experimentresultsofnon-vectorspacecontrolwithimageasfeedback:Errorinxandydirections1065.3.3ExperimentonCompressiveSensingwithRandomSam-plingInthepreviousexperiment,non-vectorspacecontrolsystemobtainedtheimagefeedbackbyscanningtheentirelocalareawhichspentmuchtime.Inordertoreachahighersamplingrate,imagingspeedmustbegearedup.Thatisthereasonwhycompressivesensingisinvolved.TheexperimentresultsofcompressivescanningandimagereconstructionareshowninFig.5.4(a)(b)Figure5.4ExperimentresultsofAFMimagesreconstructionbasedoncompressivesensing(a):OriginalAFMimageof5050pixels(b):ReconstructedimageobtainedbycompressivesensingThesetwoimagesinFig.5.4are5050pixelsandthescansizeineachimageis112ofDNAsample.Aftercompressivesensingwasapplied,thescanningtimedecreasedinto1.25second(comparedwith6.98secondsinconventionalrasterscan).Compressivesensingcanlargelydecreasesthetimespentonscanning.However,forcompressivesensing,itstillconsumestime(approximate1secondsaccordingtoTV-normreconstructionmethod)107toreconstructtheoriginalimage.Inordertosolvethisnewissue,wegetridofimagereconstructionstep,andusethecompressivesamplingdataasthefeedbacktonon-vectorspacecontrollerdirectly.5.3.4ExperimentonCompressiveFeedbackNon-vectorSpaceCon-trollerFromthepreviousexperiment,itisshownthatcompressivesensingcouldincreasethesam-plingratewithoutlosingimportantdatainformation.However,itsdisadvantageisalsoobvious:compressivesensinghastoreconstructtheoriginalimage.Achallengecomesout-whetherwecandirectlyusethecompressivedatawhichisnotanimagebutasetofrandomchosendata(compressivedata)toserveasthefeedback.InSectionIV,weshowedthethe-oreticalproofofthisapplication.Inthissection,anexperimentwassetupfortestingtheperformanceofthiscontrolsystem.Theexperimentalprocedureissimilartotheexperimentwithcompleteimageasfeedback.Theonlybetweenthesetwoexperimentsisthatinthisexperimentweusesthecompressivedataobtainedbycompressivescanninginsteadofcompletelocalimageasthefeedback.Weusedthesameinitialanddesiredlocationswiththeexperiment.Thedistancebetweencurrentpositionanddesiredpositionis40nminverticaldirectionand-41nminhorizontaldirection.Thefeedbackusedinthisexperimentisasetof350elements(theonesinside3030pixelsasshowninFig.5.3(a)).Theexper-imentresultisshowninFig.5.5(b).Inthisexperiment,initialanddesiredpositionsarejustthesameastheexperiment,butthecalculationtimespentoncompressivefeedbackcontroller(0.152s)ismuchsmallerthantheoneusecompleteimageasthefeedback(0.322s)ineachstep.Thatmeansthenon-vectorspacecontrollerbasedoncompressivefeedback108canlargelyreducethetimespentonbothscanningandcalculating.5.3.5ExperimentonTrackingSWNTbasedonCompressiveFeed-backNon-vectorSpaceControllerThegoalofthisexampleisusingAFMtiptotrackalongSWNT.BeforewestartedtheAFMtipmotioncontrol,ahighresolutionAFMimageintheareaofinteresthadbeenscannedastheoriginalimage(asshowninFig.5.6(a))Thescansizeofimageis1.251.252andtheresolutionis10241024pixels.Oncethehighresolutionimagewasobtained,thepathplannermodulesstartedworking.TheoperatorcouldselecteitherautomaticallyidentifytheSWNTandgeneratethetippathormanuallydesignthearbitrarypath.Inthisexamplethepathwasselectedmanuallybyusingthehapticdevice,andthetrackingpathisshowninFig.5.6(b).Oncethepathwasselected,thesystemautomaticallygeneratedasequenceofimagesabouttheinterimstepsbetweenstartandendpoints(showninFig.5.6(c)).Withtheguidanceofnon-vectorspacecontrollertheAFMtiptrackstheSWCNTandeventuallyreachesthegoalposition.Inaddition,thepositionerrorisshowninFig.5.6(d).Theerrorishighlyrelatedtotheimagescansizeandresolution.Generally,thesmallerscansizewithhigherresolution,thelesspositionerror.Inordertoachieveultrahighaccuracypositionandmotioncontrol,wewanttomakethescansizeassmallaspossible.However,thisisachallengewhenthescansizedecreaseintohundredsnanometers,especiallyforthelocalimageorcompresseddatausedforfeedback.Inthiscasethenoiseinimagemighttheperformanceofcontroller.Typicaldistanceisverysensitivetothenoise;therefore,inthisapplication,weusemodistanceinstead.Themodistanceisasfollows.109(a)(b)Figure5.5Experimentsetupandresultsofnon-vectorspacecontrolbasedoncompressivefeedback(a):Experimentalsetupforthenon-vectorspacecontrolbasedoncompressivefeedback(b):Experimentresultsofnon-vectorspacecontrolwithcompressivefeedback:Errorinxandydirections110(a)(b)(c)(d)Figure5.6ExperimentresultsoftrackingSWCNTusingnon-vectorspacecontroller,(a):OriginalAFMimageof10241024pixels,(b):Trackingpath,(c):Asequenceofimagefeedback,(d):Positionerrorduringtracking111GivenasetofpointsP2Rn,thedistancebetweenapointx2RnandthesetisdP(x)=miny2Pjjyxjj.TheprojectionfromxtoPisthesetofpointsdenotedasP(x)=fy2P:jjyxjj=dP(x)g.ConsidertwosetPandQ,theMoDistance(MHD)isas:dh(P;Q)=1mXfmaxp2Pminq2Qjjpqjj;maxq2Qminp2Pjjqpjj)g(5.17)TheMHDisrobusttothenoise,whichissuitableinthisexample.AfterMHDwasappliedintothenon-vectorspacecontroller,theerrorrangewascontrolledwithin4nm.Themethodtoverifypositionerrorinallexperimentsisthetemplatematching.Becausethereisnopositionordisplacementsensorinthisopen-loopAFMscanner,thewaytocalculateabsoluteerrorisusingeachcurrentlocalimageasatemplatetomatchwithaccuratepositioninoriginalimage.Thisisthemethodtoverifyerrorbutnottheoneweusedinnon-vectorspacecontrolstrategywhichusedMHDtotheerrorbetweencurrentanddesiredimages.5.3.6PerformanceAnalysisofNon-vectorSpaceControllersCurrently,therearetwottypesofnon-vectorspacecontroller-imagefeedbackandcompressivefeedback.Fromtheexperimentalresultitshowsthatthesteadystateerrorofcompleteimagefeedbackcontrollerapproachestozero(errorisapproximate1nm)inbothinxandydirectionswhichprovesthatdh(K(t);^K)!0ast!1.However,inthecaseofcompressivefeedback,theerrorisnotalwaysconvergingtozero.ThisisbecauseoffollowingPropositionincompressivefeedbackcontroller.Proposition2Supposebothxand^xobeythepowerlawdecay.Withoutlossofgenerality,112assumeweusethelargestS=dn=2eelementstoapproximatetheoriginalsignals,whereistheceiloperator.IfmatrixARIPconditionwithorder2Sandconstant˙2S,thenwehavedh(K;^K)2R(p1+˙2S+p1˙2S)=pS(1˙2S)ifdh(Kc;^Kc)!0.Thispropositionindicatesthatifdh(Kc;^Kc)!0,thesetdistancebetweenthetwocom-pressivesetscanbebounded.Therefore,insteadofasymptoticalstability,onlythestabilitycanbeguaranteed(thedetailedproofcanbefoundin[141]).Inotherwordsthereexistsansteadystateerrorinthecompressivefeedbackcontroller.AsshowninFig.5.5(b)thesteadystateerrorisapproximate2nm.Althoughsteadysteaderrorexistsincompressivefeed-backcontroller,itsadvantageisstillobviouswhichislesscalculationtimeandhighfeedbackratewhichisusefulforrealtimecontrol.Itisnotedthattheaccuracyofthisnon-vectorspacecontrollerdependsontheoriginalimageresolutionandscansizewhichisusedforvisualservoing.Ifa10241024pixelsAFMimagewiththescansizeof600nmisused,theaccuracyofthisnon-vectorspacecontrolsystemwillreachashighas1nmaccordingtothisexperimentresult.5.4CarbonNanotubeLocalElectricalPropertyChar-acterizationFornanomanipulations,oneofthemostessentialpartsisthehighaccuracymotioncontrol.Withthehelpofnon-vectorspacecontroller,itenablesthenanomanipulationsystemtohavetheabilitytoconductdelicateandcomplicatednanoparticlesmanipulationandnanosurgery.Inthisresearch,anexamplesofthenanomanipulation:carbonnanotubelocalelectricalpropertycharacterizationbasedonnon-vectorspacemotioncontrolareprovided113toillustratetheapplicationofthiscontrolstrategy.Carbonnanotubeisaquasi-one-dimensionalmaterialwhichhasbeenfrequentlyusedforbuildingnanodevices.Itisessenstialtounderstandtheelectronicpropertiesofthiskindofbuildingblocksbeforedesignnanodevices.Allseveralmethodscanbeusedforstudyingthepropertiesofcarbonnanotube,employingaconductiveSPMprobeasamov-ableelectrodetoconductlocalconductivitymeasurementsisamosttanddirectapproach[30][31][32][21].UsingSPMconductiveprobetomeasuretheconductivitycanbeconsideredasmeasuringtransportpropertiesasafunctionofchannellength.Despitethismeasurementtechniqueissuitableforstudyingelectrontransportproperty,onlyafewat-temptsavebeenmadeinpractices.Thereasonforthatistheyinaccurateprobemotioncontrolduringthemeasurement.Thereisnosuitablewaytoaccuratecontrolcon-ductiveprobemotionuntilthenon-vectorspacecontrolstrategyhasbeenproposed.Inthissection,weuseAFMasaexampletoillustratetheapplicationofusingnon-vectorspacetomapmulti-wallcarbonnanotubelocalconductivity.Inthisexample,aMWNTlocatedontwoelectrodeswasusedasthesample.Thesamplewasfabricatedusingopticallithography.Here,ametalelectrodeconsistingofTi30nm/Au50nmlayerswasdepositedontopofanIn2O3nanowireusinganelectronbeamevaporator,followedbyaprocess.TheMWNTs,arepurchasedfromBuckyUSAinpowderyform.TheseMWNTshavediametersrangingfrom20to200nm,andlengthesfrom0.5to10m.TheSWCNTspowderwasputintoethanolalcoholtoformSWCNTssuspensionafter10-20minutesultrasonica-tion[142][143].AsingleSWCNTwasdepositedtodesiredlocationsusingdielectrophoresis(DEP)depositionsystem:adropletofSWCNTssuspensioninethanolalcoholwasdispersedbetweenpre-fabricatedelectrodes,andanACvoltageof1Vppand10kHzfrequencywas114Figure5.7Testingplatform(A):I-Vcurveobtainbycurvetracer(B):Dimension3100AFM(C):ConductiveprobeappliedtoattracttheSWCNTstothevicinityoftheAuelectrodes.TheAsymmetricAu-MWNT-Ausamplewasusedinthisexampleasakindofnanowirewhosediameterissmallenoughfortestingtheperformanceofnon-vectorspacemotioncontrol.Beforeconductivitymapping,ametallicI-Vcharacteristicwasobserved(asshowninFig.5.9(a)).ThetotalresistanceofthisMWNTis11.0kInordertolocallycharacterizetheelectricalproperties,thesamplesareplacedinanAFM(Dimension3100,Brukernano,CA)basednanomanipulationsystemoperatingatroomtemperature(asshowninFig.5.9.A115diamond-coatedconductiveprobe(DDESP-FM-10,Brukernano,CA)wasusedasamovabledrainelectrodewhenitwasphysicallycontactedwiththeMWNT(asshowninFig.5.7).ThechannellengthListhedistancefromtheconductivetiptothesourceelectrode.Webeginbyusingtheconductivetipasasourcecurrentcontact.Inthisexperimentwemeasuredthecurrenttransferthroughthechannelwith20nmintervalevenlybyplacingthetipabovetheMWNTatsplocationthroughnon-vectorspacecontrollerandthenlowereduntilthephysicalcontactwasbetweentipandMWNT.Thenthecurrentwsfromtheconductivetiptothedrainelectrodeisrecordbycurvetracer.Theresistancehasplotasafunctionofchannellength(asshownschematicallyinFig.5.9(b)).Figure5.8Schematicdiagramofexperimentalsetupforcharacterizinglocalconductivity(a):experimentalsetup(b):Usingconductivetiptoprobelocalconductance(c):AFMimageoftestingsample5.5MeasurementResultsandAnalysisInthisapplication,weusenon-vectorspacecontrolmethodtoprobeaccuratepositionofconductivetipasamovableelectrodetoinvestigatethescalingandelectrontransport116properties.TheseresultsareessentialforusesofMWNTintransistorapplications.BesidesMWNT,otherkindsofnanowirecanbealsousedassamples.Non-vectorspacecontrolmethodisatwaytoaccuratecontrolSPMtipmotionduringnanomanipulations.5.6ControllableElectricalBreakdownofMultiwallCar-bonNanotubes5.6.1IntroductionWiththedevelopmentofnano-materials,suchasnanotubesandnanowires,theelectricalcharacterizationofthesematerials,attractedstrongattentionbecauseoftheiruniqueelec-tricalandthermalpropertiesduetoquantumt[112][113].Asatypicalnanoma-terial,multiwallnanotubes(MWNTs)haveintrinsicthermalandelectricalproperties[114],whicharebeingconsideredaspotentialcandidatesforthenextgenerationofcircuitwiresandnanoelectronicdevicessuchasnanotransistors[115][116],andsensors[26][25][29].Thecarbonnanotubescanholdacurrentdensityashighas109A=cm2(whichismorethan1000timesgreaterthancopper)[117],andthethermalconductivitiesishigherthan3000Wm1K1[118].However,thethermalandelectricalpropertiesoftheMWNTsarenotfullyunderstood,especiallyfortheelectricalbreakdown.AnMWNTconsistsofmanylayersofsingle-wallnanotubes,andeachofthemhasavariousmechanical,electricalandthermalproperties.ElectricalbreakdownispossibletobewellcontrolledtopeeltheouterlayersofMWNTortailoritsstructure,inordertochangethepropertiesofMWNT[119].TheelectricalbreakdowndeterminesthemaximumcurrenttransportthroughtheMWNTscircuit,anditisalsoconsideredasanapproachto117(a)(b)Figure5.9MWNTelectricpropertycharacteristics(a):I-Vcharacteristicsfromsourcetodrainelectrodes(b):Totalresistanceasafunctionofchannellength118fabricatehighperformancesensorsandtransistors.Itisessentialtounderstandtheelectronicpropertiesofthematerialpriortodesigningahighperformancenanodevice.Generally,theelectricalbreakdowniscausedbyJouleheatingproducedbytheelectronwinthelayersofMWNT[120][121].Inpractice,however,thereasonsforelectricalbreakdownbecomevariousifenvironmentalconditionsareconsidered,suchasenergydissipationtotheelectrodes,heatsinkofsubstrate,localheatingandoxidation.Althoughelectricalbreakdownisknownasanissuefortheapplicationsofinterconnects,italsocanbeconsideredasanapproachtochangelocalmechanicaland/orelectricalpropertieswhichcouldbemorevaluablethanregularMWNTsfortheapplicationsofMWNTsbasedsensorsandtransistors.IthasbeenwidelyacceptedthattheelectricalbreakdowniscausedbyJouleheating[122].Inwords,theelectricalbreakdownisexpectedtobehappenedinthecenterofasuspendedMWNT.However,somestudiesobservedconverseresults:electricalbreakdownsarenotalwayshappenedinthecenter,sometimeitlocatesapartquitalongdistancetothemid-dle[123].Insuchacondition,thestructuraldefectofMWNT(whichcouldreducethelocalconductivity)wasconsideredasthemajorreasonthatleadstotheelectricalbreakdown[124].Besidesstructuraldefect,localconductancechange,suchasdiametervariationfromoneendtotheother,alsodeterminesthepositionofelectricalbreakdown[125].Themotivationofpresentresearchistothecrucialfactorsthatelectricalbreakdown,andmaketheelectricalbreakdowncontrollable.Controllableelectricalbreak-downisstudiedutilizingatomicforcemicroscopy(AFM)basednanorobot.TheAFMbasednanorobotisaspecialandusefultechnologicaldevicetoimagethenanostructures,andtoconductlocalmanipulationsonnanomaterials[70][69][71].ThesharpAFMtip(apexisap-proximately10nmorless)canbeconsideredasanendofthenanorobot,whichcanmeasureandmanipulatesamplesinnanoscale.InthisresearchanAFMbasednanorobot119isusedtomeasurethelocalconductivityofMWNT,andmanipulateitsspatialstructuretocontrolthelocationoftheheatsink,whichmakeselectricalbreakdowncontrollable.5.6.2JouleHeatingandThermalDissipationofMWNTbasedCircuitInthispaper,westudythedeterminantswhichcontrolthepositionofelectricalbreak-down.AfterhighbiasvoltageappliedonbothendofMWNT,itcanbebrokendownbyoxidationcausedbyJouleheating.Todate,muchattentionhasbeenpaidonsustainablemaximumcurrentdensitiesinnanotube,however,electricalbreakdownisamuchcompli-catedphenomenonbecauseofthenonuniformheatdistribution.JouleheatisgeneratedbythecurrentandthedissipatedbyheatexchangefromMWNTtotheair,electrodesandsubstrate.Thetemperature(T)distributionofMWNTcanbedescribedasfollowingonedimensional(alongxaxis)heattransportequation[144].d2Tdx2+T=q(5.18)whereisthethermalconductivityoftheMWNT,isthethermalcouplingwithsubstrateandenvironmentrespecttoposition,andqisthegeneratedheatperunitvolume[145].AssumedthatthepowerishomogeneouslygeneratedalongtheMWNT,q=jF(5.19)wherej=I=AiscurrentdensitythroughtheecrosssectionA,andFistheelectrical120FromEq.(5.18)and(5.19),itcanbefoundthat,thelocaltemperatureisdeterminedbyMWNTthermalconductivity,thermalcouplingwithsubstrateandthegeneratedheat.Inordertoillustratethat,wetaketheMWNTonelectrodesasanexample(asshowninFig.5.10).ConsideredasuspendedMWNTwithuniformresistancedistribution(uniformdiameterandnodefectinstructure),accordingtotheheattransportequation,thehigh-esttemperaturelocatesinthecenterofMWNT(asshowninFig.5.10(a)).However,inpractice,fortheMWNTbasedcircuitandsensors,wehavetotakesubstrateandnonhomogeneousMWNTstructureintoaccount.Therefore,thetemperaturedistributionisdeterminedbythelocalconductivityofMWNTandlocalcontactconditionbetweenMWNTandsubstrate.Inpresentresearch,werevealthatifMWNTshaveauniformandcontactwithsub-strate,localresistancedistributionisthedominantfactorforelectricalbreakdown.Insuchcondition,iftheMWNThasauniformconductancedistribution(asshowninFig.5.10(b)),thebreakdowncouldbehappenedrandomlyatanylocationalongtheMWNTsurface.Be-yondtheuniformconductancedistribution,electricalbreakdownhappensatthepositionwhichhasasuddenchangeoflocalresistance(asshowninFig.5.10(c)).ThisisbecausetheheatgeneratedinthisareaisbiggerthantheotherpartsofMWNT.However,iftheMWNTdoesnothavetheuniformcontactwiththesubstrate,theresistancedistributionofMWNTisnolongerconsideredasthecrucialofelectricalbreakdowncomparedwithheatexchangeInthiscondition,theheatexchangeisthedeterminatefortheelectricalbreakdown.Sincethesubstratecanbeconsideredasalargeheatsink,theJouleheatcanberapidlydissipatedtothesubstrateatthecontactarea,whileinotherareatheheatisslowlydissipatedtotheair.Therefore,electricalbreakdownismostlikelyhappenedattheposi-tionwithoutsubstratecontact.Inordertoverifyourelectricalbreakdowntheory,weused121(a)(b)(c)(d)Figure5.10DiagramofthermaldistributionofMWNTintconditions,(a)Asuspend-edMWNT,(b)AnMWNTwithanduniformcontactwithsubstrate,(c)AnMWNTwithdefectcontactedanduniformlywithsubstrate,(d)AnMWNTwithnonuniformcontactwithsubstrate122anAFMbasednanorobottomeasurethelocalconductivitydistributionandmechanicallychangethecontactbetweenMWNTandsubstrate.5.6.3ExperimentalDetailsFigure5.11Experimentalsetup:MWNTonelectrodesandmoveableAFMprobeforcon-ductancecharacterizationInordertocomparetheofthedeterminedbreakdownfactors,andwhichtheeoneis,wedesignaserialofcomparisonexperimentsoflocalconductivityandthermaldissipation.Thefabricationprocessofthetestingdevice(asshowninFig.5.11)startedfromfabricatingtwoAuelectrodesonthesubstratethroughphotolithography,ther-malevaporation,andAfterthat,asingleMWNTwasdepositedinthecentertobridgetwoelectrodesusingdielectrophoresis(DEP)depositionsystem:MWNTpowder,purchasedfromBuckyUSA,wasimmersedintoethanolandultrasonicated10-20minutestoformMWNTsuspension;adropletofthesuspensionwasdispersedbetweentheelectrodes,andanACvoltageof1Vppand10kHzfrequencywasappliedtoattractanMWNTtobridgetheelectrodes.AuniformPMMAlayerwasspin-coatedontopofthedevice.ThePMMAbetweentwoelectrodeswasremovedafterelectronbeamexposureandphotoresist123development,andtwostripsofthePMMAatthecontactswaslefttopinanMWNTonthesubstrate.Beforeconductinglocalconductancemeasurement,theglobalI-Vcharacteristicsofthedevicesweremeasuredbyapplyingbiasesbetweentheelectrodes,andthecurrentwasmea-suredusingasemiconductorparameteranalyzer(4156c,AgilentTechnologies,CA).Acom-puterwithahapticdevice,areal-timeLinuxsystemandDAQcardsareusedinthisnanoma-nipulationsystem.Inaddition,asignalaccessandcontrolboxisdevelopedtoacquirethesignaloftopographyinformationandinputthecontrolsignalintotheAFMcontroller.Inordertolocallycharacterizetheirelectricalproperties,sampleswereplacedinanAFM(Dimension3100,Brukernano,CA)basedcompressivefeedbackbasednon-vectorspacenanomanipulationsystemintegratingwithanelectricalmeasurementsystem.Adiamond-coatedconductiveprobe(DDESP-FM-10,Brukernano,CA)wasusedasamovabledrainelectrode(asshowninFig.5.11).ThechannellengthListhedistancefromtheconductivetiptothesourceelectrode.5.6.4ResultsandDiscussionTheresistancedistributionofMWNT,whichisakeyparameterofelectricalbreakdown,wasaccuratelymeasuredbyanAFMbasednanorobotandanon-vectorspacecontrolstrategywereused,andthepositionerrorinthemeasurementwascontrolledwithinseveralnanometers.Intheexperiment,thelengthdependentlocalconductanceoftheMWNTwasmeasuredwithalengthincrementof20nm.TheconductivetipofthenanorobotwaspositionedabovetheMWNTatasplocation,andfollowedbyloweringthetiptocontactwiththeMWNT.Thecurrentwsfromtheconductivetiptotheelectrodewererecorded,andthetotalresistancewasplottedasafunctionofchannellength.124Intheexperiment,weusedanMWNTwithuniformconductancedistribution(whichwaspre-selectedaccordingtotheresistancedistribution)asshowninFig.5.12(a).Fromtheresistancemap(Fig.5.12(b)),itcanbefoundthat,theresistanceincreasesgraduallyandcontinuouslywiththeincensementofthelengthofMWNT,andthatmeanstheconductanceofthisMWNThasauniformdistribution.Afterthat,weusedthenanorobottomakeMWNTandsubstratehaveacontact(Fig.5.12(a)).ThecontactwasdoublecheckedbyusingAFMtopographyimage.TheMWNTsweusedinthisexperimenthasbeencarefullyexaminedbyscanningelectronmicroscopy(SEM),tomakesureeachonehastheuniformdiameterdistribution.(a)(b)Figure5.12ElectricalbreakdownofanMWNTwithuniformconductancedistribution,(a)TheAFMimagesbefore(left)andafter(right)theelectricalbreakdown,(b)Thetotalresistancerespecttothechannellengthbeforeandaftertheelectricalbreakdown,measuringdirection:fromthebottomendtotheupperendoftheMWNTin(a)125Insuchacondition,afterbridgedontwoelectrodes,topographychangesthethreedimensionalstructureofMWNT.Thelocationwithhigherpositioninverticaldirection(respecttotheplaneofsubstrate)meansthat,atthispoint,MWNTisapartfromthesubstrate.FortheMWNTintheexperiment,becausethetopographyhasnotchange,thecontactbetweenMWNTandsubstratewasestablished.Inthiscondition,thebreakdowncouldhappenatanylocationrandomly,andasaresult,thebreakdownhappenedatthelocationoftheupperpositionoftheMWNT(circledwithgreencolorinFig.5.12(a)(right)).(a)(b)Figure5.13ElectricalbreakdownofanMWNTwithnonuniformconductancedistribution,(a)TheAFMimagesbefore(left)andafter(right)theelectricalbreakdown,(b)Thetotalresistancerespecttothechannellengthbeforeandaftertheelectricalbreakdown,measuringdirection:fromthebottomendtotheupperendoftheMWNTin(a)126Inthenextexperiment,wechoseanMWNTwithdefect,whichmeansthelocalcon-ductancecouldhaveasuddenjumpataspposition.WefoundthissuddenjumppositionaftercarefullymeasuringtheresistancedistributionusingourAFMsystem(theresistancedistributionisshowninFig.5.13(b)).AccordingtoEq.(5.18)and(5.19),inthiscase,thegeneratedheathasanonuniformdistribution:themaximumtemperaturelocatesatthepositionwithasuddenjumpofconductance,wherethebiggestlocalresistancewasfound.Wepredictedthat,thebreakdownwouldhappenatthepositionwherethebiggestlocalresistancewasfound.Thisissupportedbytheexperimentalresults(thelocationofbreakdownislabeledbygreencircleintherightimageofFig.5.13(a),whichisthepositionwithasuddenjumpofresistance).Fromtheanalysisabove,wemayconcludedthat,fromtheviewofheatgeneration,localresistancedistributionisthekeyparameterfortheelectricalbreakdown,ifthethermaldissipationisnottakenintoaccount.However,inpracticeofMWNTbasedcircuitwireortransistorsystem,thethermaldissipationisamoreessentialparametercomparedwiththelocalconductancedistribution.Inordertotheevidencewhichcansupportthetheoryabove,inthelastexperiment,wechoseanMWNTwithnonuniformconductancedistribution(asshowninFig.5.14(b)).AftermeasuringtheresistancedistributionofthisMWNT,weusedtheAFMprobetopushoneendofthisMWNT(theotherendisbyathinlayerofPMMA)tomakesomepartsofthisMWNTapartfromthesubstrate.Afterthat,wecoveredthepushingendofthisMWNTwithPMMAtomaintainitsthreedimensionstructure,andatopographyimagewasobtainedusingAFM(asshowninFig.5.14(a)left).Fromthetopographymap,wepredictedthatelectricalbreakdownisverylikelytobehappenedatthehighestposition(theplacehasthemaximumverticaldistancefromthe127(a)(b)Figure5.14ElectricalbreakdownofanMWNTwithnonuniformconductancedistributionandcontactconsition,(a)TheAFMimagesbefore(left)andafter(right)theelectricalbreakdown,(b)Thetotalresistancerespecttothechannellengthbeforeandaftertheelectricalbreakdown,measuringdirection:fromthebottomendtotheupperendoftheMWNTin(a)128substrate).ThepredictionismadeaccordingtoEq.(5.18)and(5.19),thetemperatureisdeterminedbyboththeconductivitydistributionandthenonuniformthermaldissipation.Fromtheexperimentalresults,thebreakdownismostlikelytobehappenedatthepositionwhichhasafurthestdistanceapartfromthesubstrate(labeledbygreencircleinFig.5.14(a)right)withtheminimumthermaldissipation.Fromtheresistancemeasuringandbreakdownresultswecanthat:althoughthemaximumconductancechangelocatedinthelowerpartofthisMWNT,theelectricalbreakdownhappenedintheupperpartoftheMWNT,wheretheMWNThastheminimumthermaldissipation.Wemayconcludethat,thethermaldissipationisthedominateparameterforMWNTbasedcircuitwire.AlthoughinEq.(5.18)and(5.19),conductancechangeisalsoapa-rameterregradingtothermalgenerating,sincetheconductancedistributioninMWNTisunlikelytohavesuchatchangethatgeneratingenoughthermalenergyforbreak-down.Therefore,comparedwithconductancedistribution,thermaldissipation(thecontactconditionbetweenMWNTandsubstrate)isthemostimportantparameterforelectricalbreakdown.Ingeneral,fromtheviewofnanocircuit,contactbetweenMWNTandsubstratecanassurearapidthermaldissipationfromMWNTtothesubstrate,whichworksasaheatsink.Insuchacondition,theMWNTcanholdlargerelectrondensityandre-ducetheprobabilitythatelectricalbreakdownhappened.FromtheperspectiveofMWNTengineering,theelectricalbreakdowniscontrollablebymeansofcontrollingthecontactconditionbetweenMWNTanditssubstrate.ThisisanalternativewaytotailortheMWN-Tandchangeitslocalmechanicalandelectricalpropertiestofabricatehighperformancetransistorsandsensors.1295.7ConclusionsFromafundamentalperspective,thenon-vectorspacecontrolmethodhastheabilitytomakehighaccurateSPMbasednanomanipulationseasier,andsimultaneouslythecompres-sivefeedbackcanmakeareal-timenanomanipulationpossible.TheintegratingofthesetwoapproachescanachieveahighaccuracyandhighspeedmotioncontrolforSPMbasednanomanipulation.Furthermore,thetheorydevelopedinthisresearchcanbeappliedtonanoassembly,nanoimaging,nanomanipulationandsoforthwhicharetheareawewillconsiderinthefuture.Asanapplicationresearch,westudiedtheparameterswhichcontrolthelocationwheretheelectricalbreakdownofMWNThappened.Thecontactconditionwastookintoconsiderationasadominateparametertowardselectricalbreakdown.Weconcludethatcomparedwiththermalaccumulation(forsuspendedMWNT),resistancedistribution(thestructuraldefect),thethermaldissipation:thecontactconditionbetweenMWNTandsubstrate,contributesmoreinthermaldynamicsintheprocessofelectricalbreakdown.Theexperimentalresultswellsupportthisconclusion.Theelectricalbreakdowncouldbemechanicallycontrolledbyanadditionalheatsink,whichcouldbethesubstrateofMWNTdevice.Therefore,theelectricalbreakdownprocessiscontrollablethroughcontrol-lingJouleheatingandthermaldissipation.ManipulatingthethreedimensionalstructureofMWNTtochangethepositionofheatsinkisanalternativewaytocontrolthelocationthatelectricalbreakdownhappened.Moreover,theconclusionofthisresearchalsoprovidesasuggestionforthefabricationofnanocircuit,contactbetweenMWNTandsubstrateassuresthattheMWNTcanholdlargerelectrondensityandreducetheprobabilitythatelectricalbreakdownhappened.130Chapter6ConclusionsandFutureWork6.1ConclusionsInthisstudy,weproposedasystematicmultimodalsensingapproachinthenano/bioen-vironment.WeusedcompressivesensingtechniquetoincreasetheimagingrateofSPM/AFMtomakeitsuitabletodynamicallyobservethesamplesurfaceinreal-time.Afollowedupapplicationstudyshowsthat,thisfastimagingtechniquecanleadbetterunder-standingofenzymatichydrolysisprocess.OurexperimentalresultandanalysissuggestthatthesurfacedensityofactiveTrCel7A,isthedominatefactorthatcausedtheinactivationofenzymeduringthehydrolysisprocess,whichmaybeanusefulinformationforproteinengineeringstudytoincreasetheofenzymatichydrolysisrate.Wealsoproposedabrandnewmechanicalpropertiesmeasurementmethodcalled"vibra-tionmode".twithconventionalpointandshootingsignalmeasurement,vibrationmeasurementisamoremethodtoevaluatethemechanicalpropertiesofinternalstructureofelasticmaterial.Thebasicideaofthismethodistovibrateverticallyandtheadditionalvibrationamplitudeontheuppersurfaceofsample,otherthanthedrivingvibrationcanbeconsideredasthesampledeformationwhichdependsonthemechanicalproperties.Ourexperimentalresultsshowthat,vibrationmodecanprovidefasterimagingspeed,andmulti-channelinformationfromnoninvasivebiologicalpropertiesmeasurementsthanconventionalAFMbasedimagingandmeasurements.131OtherthanimprovingtheperformanceofSPMimagingandmeasurement,wealsopro-posedanewcontrolmethodcalled"non-vectorspacecontrol"toincreasethepositioningaccuracyofSPMbasedmanipulationandmeasurement.IthastheabilitytorealizehighaccurateSPMbasednanomanipulationsandsimultaneouslythecompressivefeedbackcanmakeareal-timenanomanipulationpossible.Furthermore,thetheorydevelopedinthisresearchcanbeappliedtonanoassembly,nanoimaging,nanomanipulationandsoforth.Inafollowupapplicationresearch,westudiedtheparameterswhichcontrolthelocationwheretheelectricalbreakdownofMWNThappened.Thecontactconditionwastookintoconsiderationasadominateparametertowardselectricalbreakdown.Weconcludethatcomparedwiththermalaccumulation(forsuspendedMWNT),resistancedistribution(thestructuraldefect),thethermaldissipation:thecontactconditionbetweenMWNTandsubstrate,contributesmoreinthermaldynamicsintheprocessofelectricalbreakdown.6.2FutureWork6.2.1QuantitativelyAnalyzeTrCel7AMoleculesInvolvedEnzy-maticHydrolysisProcessThedensityofTrCel7AonsubstrateisanimportantsinceitindicatestheeadsorptionofcellobiohydrolasesandismediatedbytheCBD.Theadsorptionofthefamily1CBDoncrystallinecelluloserequiresthreearomaticaminoacids,andthebindingsitestocellulosecrystals.Duetotheprocessivecharacteristicsofhydrolysis,thebindingofTrCel7Aandcellulosethehydrolysisrate.Generally,tenzymatichydrolysisrequireshighbindingdensity,highmovingvelocityandlowdissociationrate.Inthefuture,weplanto132useramanmicroscopyandHPLCtoquantitativelyanalyzetheparametersofenzymatichydrolysisprocess,suchastheconcentrationofsubstrate,enzymeandtheproduct,andassociatedwithourprevioussinglemoleculeexperimentalresulttobuildakinematicmodeltobettertheunderstandingtheslowrateofhydrolysis.6.2.2SubsurfaceStructureorMechanicalPropertiesMeasure-mentUsingVibrationModeforCellMigrationStudyVibrationmodemeasurementisnaturallysuitabletoevaluatethemechanicalpropertiesofinternalstructureofelasticmaterial.Previoussectionillustratestheideaofsubstructuremechanicalpropertiesmeasurementworkingprinciple.Inthefuturewewilluseourvibrationmodetostudythemechanicalpropertieschangesduringthecellmigration.Cellmonolayermigrationisanimportantphysiologicalphenomenoninvolvedinembry-odevelopment,woundhealing,andcancerinvasion,butitsgoverningprincipleisastillmystery.Themonolayermigrationdynamicsisrelatedwithsubstrateviscosity,topography,cellulartractionforce,freespaceandcelldamageandthegeometryofcellmonolayer.Atindividualcelllevel,cellularstronglyimpactscellularinvasionandintegrityinkeratinocytes.Thus,thereisacriticalneedtoestablishtheroleofcellularnessincollectivecellmonolayermigration.Withoutthisknowledge,thegoverningprincipleofcollectivecellmigrationmaybemisunderstood,thushinderdevelopingnewtherapiesforwoundhealingandcancermetastasis.Insuchacondition,ourvibrationmodemechanicalpropertiesmeasurementsystemwillbeaperfectcandidatetostudythemechanicalprop-ertieschangesduringthecellmigration,andusethe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