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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

, Mehmet Z. Baykara

aDepartmentofMechanicalEngineering,BilkentUniversity,Ankara06800,Turkey

bUNAM-InstituteofMaterialsScienceandNanotechnology,BilkentUniversity,Ankara06800,Turkey

a r t i c l e i n f o

Articlehistory:

Received13November2013

Receivedinrevisedform15January2014 Accepted6February2014

Availableonlinexxx

Keywords:

Atomicforcemicroscopy Imagingofbiomaterials Electrostaticdoublelayerforces

a b s t r a c t

Wepresentanumericalanalysisofamplitudemodulationatomicforcemicroscopyinaqueoussaltsolu- 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.Whileimag- inginUHVusingcertainoperationalmodesofAFMhasallowed atomic-resolutionimagingofatomicallyflatandcleansurfaces[3], themainmotivationbehindoperatinginliquidshasbeenthegoal ofhigh-resolutionimagingofbiologicalmaterialsuchascellmem- branes,DNA, and variousfibrous andglobular proteinsin their naturalstates,withoutstructuraldeformationscausedbyvacuum conditionsneededfortransmissionelectronmicroscopy(TEM),the traditionalmethodofchoiceforhigh-resolutionimagingofbioma- terials[4–6].

AFMhasbeeninitiallyusedinthecontact-modeinliquidsto imagebiomaterialssuchaspurplemembraneand DNA[7,8].In thiscommonmodeofAFM,amicro-machinedcantileverwitha sharptip[9]isbroughtintosoftcontactwiththesamplesurface underinvestigation(withcontactforcesontheorderofafewnN) andscannedlaterallywithpmprecisionwhileverticaldeflections

∗ Correspondingauthorat:DepartmentofMechanicalEngineering,BilkentUni- versity,Ankara06800,Turkey.Tel.:+903122903428.

E-mailaddress:mehmet.baykara@bilkent.edu.tr(M.Z.Baykara).

ofthecantilevercausedbytopographicalfeaturesofthesample surfaceare detected,mostly byusingthelaserbeamdeflection (LBD)method[10].Thus,highresolutionmapsofbiologicalmate- rialsmaybeobtainedinliquidssuchaspurewaterorphosphate buffersolution(PBS).Onemajordrawbackofcontact-modeimag- ingofbiologicalmatteristheoccurrenceoflateralforcesbetween theprobetipandthesampleduringimaging,frequentlydamag- inganddisplacingthesoftbiologicalmatterunderinvestigation [4].To circumventthis problem, Mülleret al.have successfully demonstratedtheuseofrepulsiveelectrostaticinteractionforces occurringbetweentheprobetipandthesamplesurfaceinaque- oussaltsolutionsduetoaccumulatedsurfacecharges[11].Thus, attractiveinteractionforcesactinglocallybetweenthetipapexand sampleatcloseseparationsareelectrostaticallybalancedandsam- 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

0169-4332/©2014ElsevierB.V.Allrightsreserved.

Fig.1.Schematicdescribingthemodelusedinthenumericalsimulations.Thecan- 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,aswellasreducedsampledeformationandinter- actionforces[26,27].

Beinginspiredbytheadvancesin AFMmeasurementofbio- materialsinliquidssummarized above,wehave investigatedin thiscontributiontheeffectofoperatinginaqueoussaltsolutions onAM-AFMimagingofamodelbiologicalsampleusingnumer- icalsimulations.Contrarytocontact-modeoperation,ourresults indicateverymodestgainsinimagingcontrastduetoelectrostatic interactionsathighamplitudesetpoints,accompaniedbyrelatively unaffectedsampleindentationandmaximumtip–sampleinterac- 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.,usingapiezoelectricele- ment)withaconstant drivingamplitudeofAext anda constant drivingfrequencyoffext.F_total(z(t)) isthetotalinteractionforce actingbetweenthetipandthesamplesurfaceatpositionz(t).

AsamodelsamplesystemappropriateforsimulatingAM-AFM experimentsinliquidsonbiologicalmaterial,wehaveconsidered asoft(E_s,soft=1GPa)islandof2nmheightontopofahardsub- strate(E_s,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 isduetotheelasticcontactbetweentheprobetipandthesam- plesurfacewhichisappropriatelydescribedbyHertziancontact theory[33]asfollows:

FH(z)= 4 3E^√

R(z0−z)^3/2 (2)

whereE^isaparameterderivedfromYoung’smodulusandPois- son’sratiovaluesforthetipandsample(Et,Es,t,s)suchthat E^=



(1−²s)/Es+(1−²_t)/Et



, R the radius of the AFM tip modeledasasphereandz₀aconstantvaluedescribingtheheight ofthesamplesurface(forourmodelsamplesystem,z0=2nmfor thesoftislandandz₀=0forthehardsubstrate).Naturally,repul- sivecontactforcesdescribedbyF_H affectcantilevermotiononly whencontactbetweentipandsampleoccurs(i.e.,(z0−z)>0).For noncontactconditions((z0−z)≤0),FHbecomeszero.Itshouldbe notedherethattheaccuracyofHertziancontactforcescalculatedin oursimulationsarelimitedbyassumptionsinvolvinglinearelastic- ity,isotropyandhomogeneity,amongothers.Whilelinearlyelastic conditions may not always be satisfiedduring actual AM-AFM measurementsperformedonbiologicalmaterial,Hertziancontact theoryhasbeenusedintheliteraturetosuccessfullyestimatecon- tactforcestoafirstapproximationinsuchcases[22,27].Thus,it hasbeenemployedinthepresentdiscussionaswellforreasonsof comparability.Moreover,hydrodynamicreactionforceswhichare comparablysmallfortypicalcantilevertipdimensionsaswellas solvationforceshavebeenneglectedinouranalysisinaccordance withpreviousAM-AFMsimulationworkinliquids[22,27].

WhenperformingAM-AFMmeasurementsinaqueoussaltsolu- tions,boththeAFMtipandthesampledevelopanetsurfacecharge, basedonvariousmechanismssuchasthedissociationofcertain surfacegroupsandadsorptionofionsontothematerialsurface [34].Duetotheelectrostaticinteractionbetweenthechargedsur- facesandtheionsinthesaltsolution,aconcentrationgradient calledtheelectrical doublelayer (EDL)existsneartheimmersed surfaces.Anelectricaldoublelayerforce(F_EDL)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,complicatingitsuse- fulness.Alternatively,anapproximateformoftheEDLforcethat developsbetweenaplanaranda sphericalsurface(suchasthe sampleandthetipsurfacesinanAFMexperiment)maybeused as[36]

FEDL(z)=



st

ε0ε



ıexp



0−z ı



(3) for (z0−z)≤0, where s andt are surface chargedensities of sampleandtip,respectively,ε0thepermittivityofvacuum,εthe dielectricconstantoftheliquidandıtheDebyelength,described by:

ı=



iciZi

(4)

wherekBistheBoltzmannconstant,Tthetemperature,etheelec- troniccharge,c_itheconcentrationoftheithtypeofioninthesalt solutionandZ_ithevalencevalueforthesameiontype.Whileit shouldbeindicatedthattheapproximateformoftheEDLforce

providedbyEq.(3)isoflimitedaccuracyoncethedistancebetween thesurfacesisbelowtheDebyelength,it hasbeensuccessfully implementedinanumberofAFMstudiesinthepast,andhasthus beenadoptedforthepresentdiscussionaswell[36–38].Finally, combiningtheHertziancontactforceandtheEDLforce,thetotal tip–sampleinteractionforceisobtainedas

Ftotal=FEDL(z)=



st

ε0ε



ıexp



0−z ı



when z≥z0 (5)

Ftotal=FH(z)+FEDL(0)= 4 3E^√

R(z0−z)^3/2+



st

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.Aextischo- sensuchthatthecantileverundergoesafreeoscillationamplitude ofA₀=10nmfarfromthesamplesurfacewhentip–sampleinterac- tionsarenegligible,similartoearliersimulationwork[27].Please notef₀=20kHzcorrespondstothewetresonancefrequencyofthe cantileverintheliquidmedium[30]anddoesnotimplyunusually largedimensions.Itshouldbenotedthatwhileithasbeenrecently demonstratedthatatomic-resolutionimagingofmineralsurfaces

suchasmicaismadepossiblebyasignificantreductionofoscilla- tionamplitudeinliquids[39],andtheuseofsmall,high-frequency cantileversinconjunctionwithhigh-speedAFMleadstoimpressive results[40,41],typicalexperimentalparametersforimagingbio- materialsusingAM-AFMremainsimilartothevaluesemployedin oursimulations.Tipandsurfacechargedensityvaluesforourmodel system–whichgenerallydisplayaratherweakdependenceonsalt concentrationdownto1mM[35]andhavethusbeentakentobe constantinthisstudy–havebeendeterminedbasedonexperi- 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.Imagingisusuallyperformedatafixedamplitudeset- point(usually10%to20%lowerthanthefreeoscillationamplitude A₀)bytheutilizationofafeedbackloop.Assuch,theimagingcon- 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]

duetoadifferenceintheYoung’sModuliofsubstratesemployedintherespectivesimulations.

itwouldbeappropriatetocompareamplitudevs.distance(Avs.d) curvesforthehardsubstrateandthesoftislandemployedinour modelsamplesurfaceforvaryingsaltconcentrationstoinvestigate theeffectofoperatinginaqueoussaltsolutionsonimagingperfor- 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 presentcalculationsisthattheEDLforcescausedbyequalconcen- 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].

ThereasonforthemarginaleffectofEDLinteractionsonAM- AFMimagingbecomesclearwhenthemaximumcontributionsof theEDL(FEDL)andHertz(FH)interactionstothetotaltip–sample interaction(F_total)arecomparedforthesoftislandinourmodel samplesystem.Evenforarelativelylowsaltconcentrationof5mM, themaximumvalueforFEDL(∼0.4nN)ismorethananorderofmag- nitudelowerthanthatobservedforthecontactforceF_H(∼10nN) intheinvestigateddistanceregime.Assuch,thetip–sampleinter- action is mainly dominated by contact forces during AM-AFM operationinaqueoussaltsolutions,limitingtheeffectofelectro- staticinteractionsonimaging.Itshouldbenotedthatthecalculated maximumvaluesfortheEDLinteractionareingoodquantitative agreementwithexperimentalresultsreportedintheliteraturefor monovalentsalts(takingintoaccountthedifferencesintipradius andsamplesurfacechargedensity)[35]despitetherelativelybasic natureofourmodelsamplesystemandcalculations.

Anotheraspectthat needstobeconsideredwhenevaluating AM-AFMmeasurements in liquidson biological materialis the issueofsampledeformation.Sincetypicallythebiologicalmate- rialtobeimagedismechanicallymuchweakerthanthesubstrate itis adsorbedon, low interactionforcesand indentationvalues aredesirable.Theresultsofthepresentnumericalanalysisindi- 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

valuesremainrelativelyunchangedwithdecreasingsaltconcentra- tion(seeTable1)whencomparedtoimagingindeionizedliquids.

4. Conclusions

Insummary,wehaveperformedamodelnumericalanalysisof amplitudemodulationatomicforcemicroscopyonsoftbiological materialsadsorbedonhardsubstratesinaqueoussaltsolutions.

Despitethesignificantadvantagesprovidedbyrepulsiveelectro- staticinteractionsincontact-modeimagingofsimilarsamples[11], ourresultsindicatethatonlymodestgainsinimagingcontrastat highamplitudesetpointsare expectedforAM-AFMundertypi- calexperimentalconditionsrepresentedbyoursimulations,while sampleindentationandmaximumtip–sampleinteractionvalues remainrelativelyunaffected.

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