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Quartzcrystalmicrobalance559●QQQCMquartzcrystalmicrobalanceQCNquartzcrystalmicrobalanceQuadraticmeanrootmeansquareQuantitationlimitlimitofquantitationQuartzcrystalmicrobalance—Thequartzcrys-talmicrobalance(QCM)ornanobalance(QCN)isathickness-shear-modeacousticwavemass-sensitivedetectorbasedontheeffectofanattachedforeignmassontheresonantfrequencyofanoscillatingquartzcrys-tal.TheQCMrespondstoanyinterfacialmasschange.TheresponseofaQCMisalsoextremelysensitivetothemass(density)andviscoelasticchangesatthesolid-solutioninterface[i–vi].Itisapiezoelectric(piezoelectricity)sensingdevicethatconsistofanoscillatorcircuitandacrystalwhichisincorporatedintothefeedbackloopofthecircuit.Thecrystalisthefrequency-determiningelement,asitsqualityfactorisveryhigh.Thepiezoelectriccrystalsarepatternedwithtwoexci-tationelectrodes(electronicsurfacefilms)ontheirop-positesides.Duetotheconversepiezoelectricityphe-nomenon,whenalternatingvoltageisappliedtotheattachedelectrodesmechanicaloscillationsoccurwithinthecrystallattice.Theseoscillationsarestableonlyatthenaturalresonantfrequencyofthecrystal.Thecrystalcutdeterminesthemodeofoscillations.ShearvibrationsaregeneratedifonelargecrystalfacemovesparallelwithrespecttotheunderlyingplanesasinQCMswithAT-cutα-quartzcrystals.Thiscrystalwaferispreparedbycuttingthequartzatapproximately.fromitsZ-axis.Atypicalcrystalplateisacylindricaldiskofadiametermmandthicknessabout.to.mmforresonantoperationinthetoMHzfre-quencyrange.Thistypeofcrystalsshowsweakdepen-denceoftheresonantfrequencyonthetemperatureandstressforroomtemperatureoperation.Thefundamentalresonantfrequency(fo)shiftswhenathinfilmisdepositedonthesurfaceofthequartzcrys-tal.Undertheassumptionthatthedensityandtheshearmodulusofthefilmarethesameasthoseofquartzandthatthefilmisuniform(constantdensityandthickness)andcoveringtheacousticallyactiveareaofthewholecrystal,theSauerbreyequation[iv]describestherela-tionshipbetweentheresonantfrequencyshift(Δf)andtheaddedmass(ΔM):Δf=fc−fo=−foΔMA(ρqμq)=−CfΔm,()wherefcistheresonantfrequencyofthecompositeoscillatorformedfromthecrystalandthefilmatthesurface,Aistheacousticallyactivesurfacearea,ρq=.gcm−andμq=.Nm−aretheden-sityandtheshearmodulusofquartz,respectively,Δmthechangeofthesurfacemassdensity,andCfisthein-tegralmasssensitivity.Sincefo=υqLq,()whereυq=μqρqisthewavespeedforquartz(νq=ms−)andLqisthethicknessofthequartz,inthiscasetheonlydifferencebetweenthefilm-coatedanduncoatedquartzistheaddedthickness(ΔLf).Thefilmshouldnotbetoothick,themassloadingshouldbelowerthan%ofthemassofthequartzplate,i.e.,typ-icallylowerthanμgcm−.Theremaybenon-mass-relatedfrequencychangesduetostress(e.g.,causedbyanimpropermounting)andtemperatureeffects[i,iii].Thevaluesoftheintegralmasssensitivityforthemostfrequentlyusedfo=MHzandMHzcrystalsareCf=.and.Hzcmg−,respectively.ItfollowsthatbyusingacrystalwithA=.cmsurfaceareaHzchange–whichcanbemeasuredeasilyandaccurately–correspondstongand.ng,respectively.Theuniformdistributionofthemassovertheactiveareaofthequartzplateisofimportancesincethedifferentialmasssensitivity(cf)variesacrossthisarea.Fortypicallyusedround-shapecrystals[i,vii]:Cf=πrcf(r)rdr.()Theresonantfrequencyalsodependsonthedensityandtheviscosityofthecontactingmedia.Thefrequencyshiftformeasurementinairvs.vacuumissmallerthanHz.However,thefrequencyshiftfromairtowateroraque-oussolution,foraMHzcrystalisabout–kHz.Themagnitudeofthisshiftcanbecalculatedbyusingthefol-lowingrelationship:Δf=−foρLηLπρqμq()560Quasielasticlightscattering(QELS)●QwhereρLandηLarethedensityandviscosityoftheliq-uidcontactingonesideofthecrystal.TheadditionalsurfacemasschangecanbemeasuredandcalculatedbyusingtheSauerbreyequationeveninthecasewhenthecrystalisincontactwithaliquid.Itmakesthein-situdetectionofthesurfacemasschangespossibleinthecourseofelectrochemicalexperimentsbyusinganelectrochemicalquartzcrystalmicrobal-ance(EQCM).AlackofconformancewiththeSauer-breyequationmaybetracedbacktohigh-massload-ing,surfaceroughness,surfacestress,interfacialslip-page,nonuniformmassdistribution,andviscoelasticef-fects.Inthelattercasethefilmdoesnotbehaveasarigidlayer,i.e.,thedeformationisnotpurelyelastic.Ithap-penswhenthefilmisthickanditsmorphologychangesdueto,e.g.,itsswelling.Thefrequencycanbemeasuredbythehelpofafre-quencycounterwithanaccuracyof.Hzandsamplingtime.–s.Refs.:[i]LuC,CzandernaAW(eds)()Applicationsofpiezoelectricquartzcrystalmicrobalances.Elsevier,NewYork;[ii]ButtryDA()Applicationsofthequartzcrystalmicrobalancetoelectrochemistry.In:BardAJ(ed)Electroanalyticalchemistry,vol..MarcelDekker,NewYork,pp–;[iii]BuckRP,LindnerE,KutnerW,InzeltG()PureApplChem:;[iv]SauerbreyG()ZPhys:;[v]But-tryDA,WardMD()ChemRev:;[vi]O’SullivanCK,Guil-bault()BiosensBioelectron:;[vii]BácskaiJ,LángG,InzeltG()JElectroanalChem:GIQuasielasticlightscattering(QELS)—fromthermallyexcitedcapillarywavesprovidesausefulinsightintodynamicsofliquidsurfaces[i]andinterfaces[ii]