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Applied
Surface
Science
j o ur na l ho me pa g e :w w w . e l s e v i e r . c o m / l o c a t e / a p s u s c
Analysis
of
amplitude
modulation
atomic
force
microscopy
in
aqueous
salt
solutions
Pınar
Karayaylalı
a,
Mehmet
Z.
Baykara
a,b,∗aDepartmentofMechanicalEngineering,BilkentUniversity,Ankara06800,Turkey
bUNAM-InstituteofMaterialsScienceandNanotechnology,BilkentUniversity,Ankara06800,Turkey
a
r
t
i
c
l
e
i
n
f
o
Articlehistory:
Received13November2013
Receivedinrevisedform15January2014 Accepted6February2014
Availableonline19February2014 Keywords:
Atomicforcemicroscopy Imagingofbiomaterials Electrostaticdoublelayerforces
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Wepresentanumericalanalysisofamplitudemodulationatomicforcemicroscopyinaqueoussalt solu-tions,byconsideringtheinteractionofthemicroscopetipwithamodelsamplesurfaceconsistingofa hardsubstrateandsoftbiologicalmaterialthroughHertzandelectrostaticdoublelayerforces.Despitethe significantimprovementsreportedintheliteratureconcerningcontact-modeatomicforcemicroscopy measurementsofbiologicalmaterialduetoelectrostaticinteractionsinaqueoussolutions,ourresults revealthatonlymodestgainsof∼15%inimagingcontrastathighamplitudesetpointsareexpected undertypicalexperimentalconditionsforamplitudemodulationatomicforcemicroscopy,togetherwith relativelyunaffectedsampleindentationandmaximumtip–sampleinteractionvalues.
©2014ElsevierB.V.Allrightsreserved.
1. Introduction
Sinceitsinventionmorethantwodecadesago,atomicforce microscopy(AFM)hasbecomethemostwidelyutilizedmember ofthescanningprobemicroscopyfamilyinresearchandindustrial laboratoriesaroundtheworld[1,2].Akeyfactorinthewidespread useofAFMisitsabilitytoimagematerialsurfaceswith(sub)-nm resolutioninalargenumberofenvironmentalconditions,ranging fromultrahighvacuum(UHV)toambientandliquids.While imag-inginUHVusingcertainoperationalmodesofAFMhasallowed atomic-resolutionimagingofatomicallyflatandcleansurfaces[3], themainmotivationbehindoperatinginliquidshasbeenthegoal ofhigh-resolutionimagingofbiologicalmaterialsuchascell mem-branes,DNA, and variousfibrous andglobular proteinsin their naturalstates,withoutstructuraldeformationscausedbyvacuum conditionsneededfortransmissionelectronmicroscopy(TEM),the traditionalmethodofchoiceforhigh-resolutionimagingof bioma-terials[4–6].
AFMhasbeeninitiallyusedinthecontact-modeinliquidsto imagebiomaterialssuchaspurplemembraneand DNA[7,8].In thiscommonmodeofAFM,amicro-machinedcantileverwitha sharptip[9]isbroughtintosoftcontactwiththesamplesurface underinvestigation(withcontactforcesontheorderofafewnN) andscannedlaterallywithpmprecisionwhileverticaldeflections
∗ Correspondingauthorat:DepartmentofMechanicalEngineering,Bilkent Uni-versity,Ankara06800,Turkey.Tel.:+903122903428.
E-mailaddress:mehmet.baykara@bilkent.edu.tr(M.Z.Baykara).
ofthecantilevercausedbytopographicalfeaturesofthesample surfaceare detected,mostly byusingthelaserbeamdeflection (LBD)method[10].Thus,highresolutionmapsofbiological mate-rialsmaybeobtainedinliquidssuchaspurewaterorphosphate buffersolution(PBS).Onemajordrawbackofcontact-mode imag-ingofbiologicalmatteristheoccurrenceoflateralforcesbetween theprobetipandthesampleduringimaging,frequently damag-inganddisplacingthesoftbiologicalmatterunderinvestigation [4].To circumventthis problem, Mülleret al.have successfully demonstratedtheuseofrepulsiveelectrostaticinteractionforces occurringbetweentheprobetipandthesamplesurfacein aque-oussaltsolutionsduetoaccumulatedsurfacecharges[11].Thus, attractiveinteractionforcesactinglocallybetweenthetipapexand sampleatcloseseparationsareelectrostaticallybalancedand sam-pledeformationissignificantlyreducedwithanoticeableincrease inresolution.
Analternativemethodtoreducetheinfluenceoflateralforces on biological material during imaging in liquids is to employ dynamic imaging modes of AFM [12,13]. In dynamic AFM, the cantilever with the probe tip is oscillated at or near its reso-nance frequency using various actuation methods [14–16] and changesinitsoscillationcharacteristics(suchasamplitude,phase orfrequency)duetotip–sampleinteractionsarerecorded.While frequencymodulationatomicforcemicroscopy(FM-AFM,where the oscillation amplitude is kept constant during imaging and changesinoscillationfrequencyaredetected)hasrecentlybeen employedtoperformmolecularresolutionimagingofbiomaterials inliquidsthankstoseveraladvancesininstrumentation[17–21], amplitudemodulationatomicforcemicroscopy(AM-AFM,where http://dx.doi.org/10.1016/j.apsusc.2014.02.016
Fig.1.Schematicdescribingthemodelusedinthenumericalsimulations.The can-tileverisoscillatingwithanamplitudeofAwhileitsbaseislocatedadistanced abovethehardsubstrate.Theheightofthesoftislandistakentobe2nm.
the excitation frequency is kept constant during imaging and changesinoscillationamplitudearedetected)isusuallypreferred duetoitsrelativetechnicalsimplicity[22].Accordingly,AM-AFM (oftenreferredtoastapping-modeAFM)hasbeenusedtoimage anumberofbiomaterialsinliquidsinthepast[23,24].Itshould beindicatedthatthemainexperimentalchallengeassociatedwith AM-AFMimaginginliquidsisthesignificantlyreducedQ-factorof thecantilever,leadingtolowsignal-to-noiseratios[25].Assuch, attemptstoimprovetheeffectiveQ-factorsuchasthemethodof Q-Controlhavebeenemployedinthepast,leadingtoimproved imagingcontrast,aswellasreducedsampledeformationand inter-actionforces[26,27].
Beinginspiredbytheadvancesin AFMmeasurementof bio-materialsinliquidssummarized above,wehave investigatedin thiscontributiontheeffectofoperatinginaqueoussaltsolutions onAM-AFMimagingofamodelbiologicalsampleusing numer-icalsimulations.Contrarytocontact-modeoperation,ourresults indicateverymodestgainsinimagingcontrastduetoelectrostatic interactionsathighamplitudesetpoints,accompaniedbyrelatively unaffectedsampleindentationandmaximumtip–sample interac-tionvalues.
2. Theoreticalconsiderationsandmodeling
AM-AFMoperationinliquidconditionshasbeennumerically and theoretically analyzed in a number of studies in the past [27–30].Mostcommonly,theequationofmotionfortheoscillating cantileverisconsideredtobeinthefollowingform:
m¨z(t)+2f0m
Q ˙z(t)+k(z(t)−d)=kAextcos(2fextt)+Ftotal(z(t)) (1) where m is theeffective mass of the cantilever, z(t) the posi-tionoftheoscillatingtipofthecantileverrelativetothesample surface at time t, f0 theresonance frequency of the cantilever (f0=1/2
k/m),Qthequalityfactor,kthespringconstantand dthedistanceofthecantileverbasetothesamplesurface.The cantileverisoscillatedmechanically(e.g.,usingapiezoelectric ele-ment)withaconstant drivingamplitudeofAext anda constant drivingfrequencyoffext.Ftotal(z(t)) isthetotalinteractionforce actingbetweenthetipandthesamplesurfaceatpositionz(t).AsamodelsamplesystemappropriateforsimulatingAM-AFM experimentsinliquidsonbiologicalmaterial,wehaveconsidered asoft(Es,soft=1GPa)islandof2nmheightontopofahard sub-strate(Es,hard=130GPa),inaccordancewithpreviousstudies[27] (seeFig.1).Theheightofthesoftislandroughlycoincideswith thatofDNA,whiletheelasticmodulusofthesubstratefollowsthat ofsilicon(Si),basedonthefactthatDNAadsorbedonSiormica
substratesarefrequentlyusedastestsamplesforliquidAM-AFM experiments[4].
When performing AFM measurements in deionized liquids, attractiveinteractionsincludingvanderWaals’forcesaregreatly reducedduetoscreening[27,31,32]andthemaininteractionforce isduetotheelasticcontactbetweentheprobetipandthe sam-plesurfacewhichisappropriatelydescribedbyHertziancontact theory[33]asfollows:
FH(z)= 4 3E
√R(z0−z)3/2 (2)
whereEisaparameterderivedfromYoung’smodulusand Pois-son’sratiovaluesforthetipandsample(Et,Es,t,s)suchthat E=
(1−2s)/Es+(1−2t)/Et
−1, R the radius of the AFM tip modeledasasphereandz0aconstantvaluedescribingtheheight ofthesamplesurface(forourmodelsamplesystem,z0=2nmfor thesoftislandandz0=0forthehardsubstrate).Naturally, repul-sivecontactforcesdescribedbyFH affectcantilevermotiononly whencontactbetweentipandsampleoccurs(i.e.,(z0−z)>0).For noncontactconditions((z0−z)≤0),FHbecomeszero.Itshouldbe notedherethattheaccuracyofHertziancontactforcescalculatedin oursimulationsarelimitedbyassumptionsinvolvinglinear elastic-ity,isotropyandhomogeneity,amongothers.Whilelinearlyelastic conditions may not always be satisfiedduring actual AM-AFM measurementsperformedonbiologicalmaterial,Hertziancontact theoryhasbeenusedintheliteraturetosuccessfullyestimate con-tactforcestoafirstapproximationinsuchcases[22,27].Thus,it hasbeenemployedinthepresentdiscussionaswellforreasonsof comparability.Moreover,hydrodynamicreactionforceswhichare comparablysmallfortypicalcantilevertipdimensionsaswellas solvationforceshavebeenneglectedinouranalysisinaccordance withpreviousAM-AFMsimulationworkinliquids[22,27].
WhenperformingAM-AFMmeasurementsinaqueoussalt solu-tions,boththeAFMtipandthesampledevelopanetsurfacecharge, basedonvariousmechanismssuchasthedissociationofcertain surfacegroupsandadsorptionofionsontothematerialsurface [34].Duetotheelectrostaticinteractionbetweenthecharged sur-facesandtheionsinthesaltsolution,aconcentrationgradient calledtheelectrical doublelayer (EDL)existsneartheimmersed surfaces.Anelectricaldoublelayerforce(FEDL)basedonmutually attractiveorrepulsiveelectrostaticinteractionsisthusobserved betweensampleandtipwhenthedistancebetweenthemisonthe orderofafewtensofnanometers.WhilethePoisson–Boltzmann theoretical framework provides an accurate description of the potential that develops between such surfacesand the associ-atedinteractionforces[35],itinvolvesthenumericalsolutionofa secondordernonlineardifferentialequation,complicatingits use-fulness.Alternatively,anapproximateformoftheEDLforcethat developsbetweenaplanaranda sphericalsurface(suchasthe sampleandthetipsurfacesinanAFMexperiment)maybeused as[36] FEDL(z)=
4Rst ε0ε ıexp z0−z ı (3) for (z0−z)≤0, where s andt are surface chargedensities of sampleandtip,respectively,ε0thepermittivityofvacuum,εthe dielectricconstantoftheliquidandıtheDebyelength,described by: ı= ε0εkBT e2iciZi (4) wherekBistheBoltzmannconstant,Tthetemperature,ethe elec-troniccharge,citheconcentrationoftheithtypeofioninthesalt solutionandZithevalencevalueforthesameiontype.Whileit shouldbeindicatedthattheapproximateformoftheEDLforce
providedbyEq.(3)isoflimitedaccuracyoncethedistancebetween thesurfacesisbelowtheDebyelength,it hasbeensuccessfully implementedinanumberofAFMstudiesinthepast,andhasthus beenadoptedforthepresentdiscussionaswell[36–38].Finally, combiningtheHertziancontactforceandtheEDLforce,thetotal tip–sampleinteractionforceisobtainedas
Ftotal=FEDL(z)=
4Rst ε0ε ıexp z0−z ı when z≥z0 (5) Ftotal=FH(z)+FEDL(0)= 43E√R(z0−z)3/2+4Rst ε0ε ı when z<z0 (6)Experimentally appropriate parameters used in the simula-tionsfortheabovedescribedmodelsamplesurfaceandatypical Sicantileverareasfollows:Et=130GPa,t=s,soft=s,hard=0.3, t=s,hard=−0.012C/m2, s,soft=−0.04C/m2, T=293K, ε=80.2, R=10nm,f0=20kHz,Q=5,k=1N/m,fext=f0=20kHz.Aextis cho-sensuchthatthecantileverundergoesafreeoscillationamplitude ofA0=10nmfarfromthesamplesurfacewhentip–sample interac-tionsarenegligible,similartoearliersimulationwork[27].Please notef0=20kHzcorrespondstothewetresonancefrequencyofthe cantileverintheliquidmedium[30]anddoesnotimplyunusually largedimensions.Itshouldbenotedthatwhileithasbeenrecently demonstratedthatatomic-resolutionimagingofmineralsurfaces
suchasmicaismadepossiblebyasignificantreductionof oscilla-tionamplitudeinliquids[39],andtheuseofsmall,high-frequency cantileversinconjunctionwithhigh-speedAFMleadstoimpressive results[40,41],typicalexperimentalparametersforimaging bio-materialsusingAM-AFMremainsimilartothevaluesemployedin oursimulations.Tipandsurfacechargedensityvaluesforourmodel system–whichgenerallydisplayaratherweakdependenceonsalt concentrationdownto1mM[35]andhavethusbeentakentobe constantinthisstudy–havebeendeterminedbasedon experi-mentalworkintheliterature[35,36]andresultinanetrepulsive EDLforce.AllresultspresentedinSection3havebeenobtainedby numericallysolvingEq.(1)forthevariablez(t)byapplyingafourth orderRunge–Kuttamethodforsetvaluesofd,representingfixed distancesbetweenthecantileverbaseandsamplesurface.
3. Resultsanddiscussion
In typical AM-AFM operation, the cantilever is driven with a fixed driving amplitude (Aext)and a fixed driving frequency (fext),whileshiftsintheoscillationamplitude(A)withdecreasing tip–sample distance due to increasing force interactions are detected.Imagingisusuallyperformedatafixedamplitude set-point(usually10%to20%lowerthanthefreeoscillationamplitude A0)bytheutilizationofafeedbackloop.Assuch,theimaging con-trastbetweendifferentregionsofasamplesurfacearedetermined by thevertical displacementof the cantileverbase required to keeptheamplitudesetpointconstantduringimaging.Therefore,
Fig.2.Comparisonofamplitudevs.distancecurvesforthehardsubstrateandthesoftislandatvaryingsaltconcentrationsof0mM(a),100mM(b),10mM(c)and5mM (d).Imagingcontrastisonlymarginallyaffectedbychangesinsaltconcentration,withanincreaseofabout15%atanamplitudesetpointof9nmforaconcentrationof5mM (d0mM=0.88nmwhiled5mM=1.02nm).Pleasenotethatthed0mMvalueof0.88nmreportedhereislowerthanthecorrespondingcontrastvaluepresentedinRef.[27]
itwouldbeappropriatetocompareamplitudevs.distance(Avs.d) curvesforthehardsubstrateandthesoftislandemployedinour modelsamplesurfaceforvaryingsaltconcentrationstoinvestigate theeffectofoperatinginaqueoussaltsolutionsonimaging perfor-manceofAM-AFMinliquids.Accordingly,numericallyobtained Avs.dcurvesformonovalentsaltconcentrationsof0mM,5mM, 10mM,and100mMareprovidedinFig.2foradistance(d)regime of7–13nm.Thereasonfortheconsiderationofmonovalent(e.g., NaCl,KCl)insteadofdivalent(e.g.,MgCl2,CaCl2)saltspeciesinthe presentcalculationsisthattheEDLforcescausedbyequal concen-trationsofmonovalentsaltsarefoundtobesignificantlyhigher thandivalentsalts,basedonhigherDebyelengths[35].Assuch, monovalentsaltspeciesaremoreusefulforassessingtheeffects ofelectrostaticinteractionsonAM-AFMoperationinliquids.Let usnoteherethatasaltconcentrationof0mMcorrespondstothe completelydeionizedcasewheretheEDLcontributiontothetotal forceinteractioniszero.
ComparingtheplotsinFig.2,twomainconclusionsaremade: (1)Asexpectedfromexperimentalworkintheliterature[11,35],
theeffect ofsalt solutions onAvs. dcurves is strongest at lowsaltconcentrationssuchas5mMduetoincreasedDebye lengths.Consequently,theeffectof saltsolutionsonAvs.d curvesarenegligibleathighconcentrationssuchas100mM. (2)Evenforlowsaltconcentrationsof,e.g.,5mM,theeffectofEDL
forcesonAvs.dbehaviorissmall,resultinginanincreaseofonly about15%inheightcontrast(d)betweenthehardsubstrate andthesoftislandatarelativelyhighsetpointamplitudeof A=9nm.Asexpected,themodestincreaseincontrastduetothe earlieronsetofEDLforcesforthesoftisland(bothduetothefact thatthesoftislandisclosertothetipthanthehardsubstrateby 2nmandthefactthatthesurfacechargedensityishigheron thesoftisland)diminisheswithincreasingsaltconcentration. Comparedtotheincreaseinheightcontrastofmorethan60% providedbythemethodofQ-Controlonaverysimilarsample system[27],itisclearthatoperationinaqueoussaltsolutions doesnotleadtoasignificantimprovementinimagingcontrast forAM-AFM,despitethefactthatdifferencesinsurfacecharge densityhaveresultedindetectabledifferencesinthephaseshift signalinanearlierstudyintheliterature[42].
ThereasonforthemarginaleffectofEDLinteractionson AM-AFMimagingbecomesclearwhenthemaximumcontributionsof theEDL(FEDL)andHertz(FH)interactionstothetotaltip–sample interaction(Ftotal)arecomparedforthesoftislandinourmodel samplesystem.Evenforarelativelylowsaltconcentrationof5mM, themaximumvalueforFEDL(∼0.4nN)ismorethananorderof mag-nitudelowerthanthatobservedforthecontactforceFH(∼10nN) intheinvestigateddistanceregime.Assuch,thetip–sample inter-action is mainly dominated by contact forces during AM-AFM operationinaqueoussaltsolutions,limitingtheeffectof electro-staticinteractionsonimaging.Itshouldbenotedthatthecalculated maximumvaluesfortheEDLinteractionareingoodquantitative agreementwithexperimentalresultsreportedintheliteraturefor monovalentsalts(takingintoaccountthedifferencesintipradius andsamplesurfacechargedensity)[35]despitetherelativelybasic natureofourmodelsamplesystemandcalculations.
Anotheraspectthat needstobeconsideredwhenevaluating AM-AFMmeasurements in liquidson biological materialis the issueofsampledeformation.Sincetypicallythebiological mate-rialtobeimagedismechanicallymuchweakerthanthesubstrate itis adsorbedon, low interactionforcesand indentationvalues aredesirable.Theresultsofthepresentnumericalanalysis indi-catethatmaximumtip–sampleinteractionforcesonlymarginally increase(againdue tothesignificantlylowermagnitudeofEDL forceswhencomparedtocontactforces)whilesampleindentation
Table1
Comparisonofmaximuminteractionforceandsampleindentationvaluesforthe softislandinourmodelsamplesystematvaryingsaltconcentrations(d=7nm). Itisreadilyobservedthatsampleindentationvaluesareessentiallyunaffectedby changesinsaltconcentration,whilemaximuminteractionforcesonlymarginally increasewithdecreasingsaltconcentrationwhencomparedtothedeionizedliquid.
Saltconcentration(mM) Maximuminteraction force(nN) Sampleindentation (nm) 0 10.2 1.7 100 10.2 1.7 10 10.4 1.7 5 10.5 1.7
valuesremainrelativelyunchangedwithdecreasingsalt concentra-tion(seeTable1)whencomparedtoimagingindeionizedliquids.
4. Conclusions
Insummary,wehaveperformedamodelnumericalanalysisof amplitudemodulationatomicforcemicroscopyonsoftbiological materialsadsorbedonhardsubstratesinaqueoussaltsolutions. Despitethesignificantadvantagesprovidedbyrepulsive electro-staticinteractionsincontact-modeimagingofsimilarsamples[11], ourresultsindicatethatonlymodestgainsinimagingcontrastat highamplitudesetpointsare expectedforAM-AFMunder typi-calexperimentalconditionsrepresentedbyoursimulations,while sampleindentationandmaximumtip–sampleinteractionvalues remainrelativelyunaffected.
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