Intermolecular and Surface Forces - UW Courses Web Server：表面与分子间的力-威斯康星大学课程的Web服务器

2.1IntermolecularandSurfaceForces ChemE554/ovePAGE21IntermolecularandSurfaceForces2.1.1 Overview:TypesofSurfaceForcesTherearethreeaspectsthatareofparticularimportanceforanyinteraction:(a)itsstrength,(b)thedistanceoverwhichitacts,and(c)theenvironmentthroughwhichitacts.Strengthsanddistancesforthemostcommonintermolecular"bonds"areasfollows: NatureofBondTypeofForceEnergy(kcal/mol)DistanceIonicbondCoulombicforce180(NaCl)240(LiF)2.8Å2.0ÅCovalentbondElectrostaticforce(wavefunctionoverlap)170(Diamond)283(SiC)N/AMetallicbondfreevalencyelectronseainteraction(sometimesalsopartiallycovalent(e.g.,FeandW)26(Na)96(Fe)210(W)4.3Å2.9Å3.1ÅHydrogenBondastrongtypeofdirectionaldipole-dipoleinteraction7(HF)VanderWaals(i)dipole-dipoleforce(ii)dipole-induceddipoleforce(iii)dispersionforces(chargefluctuation)2.4(CH4)significantintherangeofafewÅtohundredsofÅ Theintegralformofinteractionforcesbetweensurfacesofmacroscopicbodiesthroughathirdmedium(e.g.,vacuumandvapor)arenamedsurfacesforces.Table1providesanoverviewofthetypesofsurfaceforces.Onedifferentiatesbetweenshortrange(e.g.,VanderWaalsinteraction)andlongrangesurfaceforces(e.g.,electromagneticinteractions).CombinationsofinteractionsleadtonewforcessuchastheDLVOforces. Invacuum,themaincontributorstolong-rangesurfaceinteractionsaretheVanderWaalsandelectromagneticinteractions.Atseparationdistance<2

nmonemighthavealsotoconsidershortrangeretardationduetocovalentormetallicbondingforces.VanderWaalsandelectromagneticinteractionscanbeboth,attractiveorrepulsive.Inthecaseofavaporenvironmentasthethirdmedium(e.g.,atmosphericaircontainingwaterandorganicmolecules),onehasalsotoconsidermodificationsbythevaporduetosurfaceadsorptionorinteractionshielding.Thiscanleadtoforcemodificationoradditionalforcessuchasthestrongattractivecapillaryforces.

Source:HandbookofMicro/Nanotribology,ed.BharatBhushan,CRCPress

CovalentBond:Thestandardexampleforacovalentbondisthehydrogenatom.Whenthewave-functionoverlapisconsiderable,theelectronsofthehydrogenatomswillbeindistinguishable.Thetotalenergywillbedecreasedbythe"exchangeenergy",whichcausestheattractiveforce.Thecharacteristicpropertyofcovalentbondsisaconcentrationoftheelectronchargedensitybetweenthetwonuclei.TheforceisstronglydirectedandfallsoffwithinafewǺngstroms.IonicBonds:ThesearesimpleCoulombicforceswhicharearesultoftheelectrontransfer.Forexampleinlithiumfluoridethelithiumtransfersits2s-electrontothefluorine2p-state.Consequentlytheshellsoftheatomsarefilledup,butthelithiumhasanetpositivechargeandthefluorineanetnegativecharge.TheseionsattracteachotherbyCoulombicinteractionwhichstabilizestheioniccrystalintherock-saltstructure.MetallicBondsandInteraction:Thestrongmetallicbondsareonlyobservedwhentheatomsarecondensedinacrystal.Theyoriginatesfromthefreevalencyelectronseawhichholdstogethertheioniccores.Asimilareffectisobservedwhentwometallicsurfacesapproacheachother.Theelectroncloudshavethetendencytospreadout,inordertominimizethesurfaceenergy.Thusastrongexponentiallydecreasing,attractiveinteractionisobserved.2.1.2 CapillaryForces Capillaryforcesaremeniscusforcesduetocondensation.Itiswellknownthatmicro-contactsactasnucleiofcondensation.Inair,watervaporplaysthedominantrole.Iftheradiusofcurvatureofthemicro-contactisbelowacertaincriticalradiusameniscuswillbeformed.ThiscriticalradiusisdefinedapproximatelybythesizeoftheKelvinradiusrK=l/(l/rl+1/r2)whererlandr2aretheradiiofcurvatureofthemeniscus.TheKelvinradiusisconnectedwiththepartialpressureps(saturationvaporpressure)bywhereListhesurfacetension,Rthegasconstant,Tthetemperature,Vthemolvolumeandp/pstherelativevaporpressure(relativehumidityforwater).ThesurfacetensionLofwateris0.074N/m(T=20°C)leadingtoacriticalVanderWaalsdistanceofwaterofLV/RT=5.4

Å.Consequentially,weobtainforp/ps=0.9aKelvinradiusof100Å.Atsmallvaporpressures,theKelvinradiusgetscomparabletothedimensionsofthemolecules,andthus,theKelvinequationbreaksdown. Themeniscusforcesbetweentwoobjectsofsphericalandplanargeometrycanbeapproximated,forD«R,as:whereRistheradiusofthesphere,dthelengthof,seeFig.1,Dthedistancebetweenthesphereandtheplate,andthemeniscuscontactangle.Fig.1:CapillarymeniscusbetweentwotwoobjectsofsphericalandplanargeometryThemaximumforce,foundatatD=0(contact),is.CapillaryNeckinNanocontactsThemediumforcapillaryinteractionisthecapillaryneck.Structuredbulkwaterstronglyaffectsthesurfacetensionofthewater-airinterface,i.e.,themechanicalpropertiesofneckside-walls.Atthewater-solidinterface,thewaterexperiencessurfaceadhesionthatcompeteswiththemolecularself-associationofbulkwater.Atsufficientlylowhumidity,i.e.,inaspatiallyconfinedliquidfilmofonlyafewmolecularlayers,itcanbeexpectedthattheinterfacialinteractionispowerfulenoughtodistortthebulkstructure.Salmeronandco-workersemployedSFMadhesionmeasurementsonmicasurfacesasafunctionofthehumidityandnoticedthattherearethreedistinctforceregimesasillustratedinFig.2(experimentalconfirmationprovidedinFig.3).InRegimeI,themeasuredpull-offforcesaredepressedifcomparedtotheforcesinRegimeIIandIII.ThequalitativeforcebehaviorfromregimeItoIIhasbeenconfirmedbyotherswithhydrophilicSFMtipsonmica.ADDINEN.CITE<EndNote><Cite><Author>Thundat</Author><Year>1993</Year><RecNum>271</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>Thundat,T.</AUTHOR><AUTHOR>Zheng,X-Y</AUTHOR><AUTHOR>Chen,G.Y.</AUTHOR><AUTHOR>Warmack,R.J.</AUTHOR></AUTHORS><YEAR>1993</YEAR><TITLE>Roleofrelativehumidityinatomicforcemicroscopyimaging</TITLE><SECONDARY_TITLE>Surf.Sci.Lett.</SECONDARY_TITLE><VOLUME>294</VOLUME><PAGES>L939-L943</PAGES></MDL></Cite><Cite><Author>Yang</Author><Year>1996</Year><RecNum>173</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>Yang,G.L.</AUTHOR><AUTHOR>Vesenka,J.P.</AUTHOR><AUTHOR>Bustamante,C.J.</AUTHOR></AUTHORS><TITLE>Effectsoftip-sampleforcesandhumidityontheimagingofDNAwithascanningforcemicroscope</TITLE><SECONDARY_TITLE>Scanning</SECONDARY_TITLE><VOLUME>18</VOLUME><NUMBER>5</NUMBER><YEAR>1996</YEAR><PAGES>344-350</PAGES><KEYWORDS><KEYWORD>scanningforcemicroscope.DNA.humidity.tip-sampleforce.</KEYWORD><KEYWORD>aqueous-solutions.air.water.resolution.molecules.artifacts.surfaces.adhesion.strands.mica.</KEYWORD></KEYWORDS></MDL></Cite></EndNote>(10,14)Inordertoreflectonthepossibilitythatthequalitativetransitionbehaviorresemblesstructuralchangeofwater,ithasfirsttobediscussedonhowastructuralchangewouldaffecttheobservableforce.Fig.2:Genericsketchofthefunctionalrelationshipbetweenthepull-offforceandtherelativehumidity(RH).RegimesI,IIandIIIrepresentthevanderWaalsregime,mixedvanderWaals–capillaryregime,andcapillaryregimedecreasedbyrepulsiveforces,respectively. Figure3showstheresultsofpull-offforcevs.RHmeasurementsconductedwithahydrophilictiponasiliconsample.AtlowRH(40%),thepull-offforceisconstant.Inthemid-RHrange(40%RH70%),thepull-offforceincreaseswithincreasingRH.Apull-offforceRHhysteresisisnoticeableinthisregime.At40%RHaforcediscontinuityoccurs.Thetransitionseemstobemorepronouncedfordecreasinghumiditythanforincreasinghumidity,whichisaninstrumentalartifactduetoimprovedcontrolofRHfordecreasinghumidity.AtRHlargerthan70%,thepull-offforcedecreaseswithincreasinghumidity.ThetransitionRHdoesnotchangewithspringconstants.Fig.3:Pull-offforcevs.RHmeasuredbetweenahydrophilictipandaflatsiliconsample.measuredwhenincreasingRH,measuredwhendecreasingRH. Aqualitativeandquantitativesimilarresultswasfoundfora"macroscopic"silicaglassspherecantilever(microcontact).There,thepull-offforcesteppedupataround3040%RH..Typically,thecapillaryforceofbulkwaterisestimatedbythefollowingequation,assumingasphere-planegeometry(Fig.1), (1)(seederivativebelowfornanocontacts),whereRistheradiusofthesphere,dthelengthof,theliquidsurfacetension,andthemeniscuscontactangle.ADDINEN.CITE<EndNote><Cite><Author>Israelachvili</Author><Year>1992</Year><RecNum>270</RecNum><MDL><REFERENCE_TYPE>1</REFERENCE_TYPE><AUTHORS><AUTHOR>Israelachvili,JacobN.</AUTHOR></AUTHORS><YEAR>1992</YEAR><TITLE>Intermolecularandsurfaceforces</TITLE><PLACE_PUBLISHED>London</PLACE_PUBLISHED><PUBLISHER>AcademicPress</PUBLISHER><EDITION>2nd</EDITION></MDL></Cite></EndNote>(25)NotethatthecapillaryforcedescribedbyEq.(1)isonlydependentonthesurfacetensionofbulkwaterandthecontactangle,butisindependentofthesolid-liquidandsolid-solidinteractionparameters.Equation(1)predictsagradualchangeinthecapillaryforcewiththemeniscuscontactangle.Thisequationdoesnotexplaintheforcetransitionexperimentallyobserved(asdepictedinFig.2)Thedilemmaseemstobesolvedifoneassumesthattheforceinstabilityataround40%RHreflectsastructuraltransitionofwater,i.e.,isnotaconstant,butchangesat~40%RH.NotethatthethicknessofcondensedwatervaporfilmisstronglyrelatedtoRH,thusaboundaryregimeatthesolidsurfacecouldbedefinedinwhichwaterundergoesastructuralchange.Tthishypothesisisplausibleforahighlyorderedmicastubstrate,butraisessuspicioninthecaseofunstructuredsilicon-oxidesurface.Letusassumethatwaterundergoesaphasechangeat40%RHforhydrophilicsiliconsamples.Thisphasechangecanbeassumedtobeindependentofpressureconfinement,otherwisethetransitionforasharptipandamicrosphere,(Figs.3),wouldhaveoccurredatsignificantlydifferentRHvalues.ThethicknessofthewaterfilmonthesubstratesurfacedependsonRH.Thus,therestructuringtransitioninwateroccursinthevicinityclosesttothesiliconsubstrate,becausethewaterfilmisthinningwithdecreasinghumidity.Notethatonlyonehydrophilicsurfaceisnecessarytoformawaterfilm.Hence,thewaterrestructuringprocessanditsdetectioninpull-offforcemeasurementsshouldnotdependonthecantileverprobematerialaslongasthesampleishydrophilic.Forahydrophobictipcoatedwithn-octadecyltrichlorosilane(OTS),onthesamesiliconsubstrateasabove,oneobservedhoweverconstantpull-offforces(i.e.,forcesindependentofRH)intheentirerangefrom10%to80%RH(Fig.4).Consequentlythewaterstructuringmodelbasedonforce-distancecurvesisinconsistent.Amuchmorelikelyinterpretationfortheforceinstabilityat40%RHistheabilityorinabilityofthewaterfilmtoformaliquidjoiningneckbetweentheadjacentsurfacesathighandlowRH,respectively.Fig.4:Pull-offforcevsRHmeasuredbetweenasharpSFMtipcoatedwithOTSandaflatsiliconsample.Thepull-offforceisindependentofhumidity.Hence,basedontheaboveresults,thethreeregimesinpull-offforceSFMmeasurementsforadjacenthydrophilicsurfaces(Fig.3)canbeinterpretedasfollows:InregimeI,nocapillaryneckisdeveloped,andthepull-offforceisdominatedbyvanderWaalsinteractions.Acapillaryneckisformedatabout40%RH,whichcorrespondstotheforcediscontinuityobservedbetweenregimesIandII.Wecanunderstandthistransition-likebehaviorofthepull-offforcebyconsideringtheminimumthicknessrequirementofwaterprecursorfilmsforspreadingADDINEN.CITE<EndNote><Cite><Author>Bruinsma</Author><Year>1990</Year><RecNum>314</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>Bruinsma,R.</AUTHOR></AUTHORS><YEAR>1990</YEAR><TITLE>Slowspreadingofpolymermelts</TITLE><SECONDARY_TITLE>Macromolecules</SECONDARY_TITLE><VOLUME>23</VOLUME><PAGES>276-280</PAGES></MDL></Cite><Cite><Author>deGennes</Author><Year>1985</Year><RecNum>316</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>deGennes,P.G.</AUTHOR></AUTHORS><YEAR>1985</YEAR><TITLE>Wetting:statisticsanddynamics</TITLE><SECONDARY_TITLE>Rev.Mod.Phys.</SECONDARY_TITLE><VOLUME>57</VOLUME><NUMBER>3</NUMBER><PAGES>827-863</PAGES></MDL></Cite></EndNote>(28,29).Theheightoftheprecursorfilmcannotdropbelowacertainminimum,e,whichis;;. (2)wherea0isamolecularlength,ADDINEN.CITE<EndNote><Cite><Author>deGennes</Author><Year>1985</Year><RecNum>316</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>deGennes,P.G.</AUTHOR></AUTHORS><YEAR>1985</YEAR><TITLE>Wetting:statisticsanddynamics</TITLE><SECONDARY_TITLE>Rev.Mod.Phys.</SECONDARY_TITLE><VOLUME>57</VOLUME><NUMBER>3</NUMBER><PAGES>827-863</PAGES></MDL></Cite></EndNote>(29),Sthespreadingcoefficient,AtheHamakerconstant,SOthesolid-vacuuminterfacialenergy,andSLthesolid-liquidinterfacialenergy.Weproposethattheformationofthecapillaryneckalsorequiresaminimumheightofthewaterfilm.Nocapillaryneckformsbetweentwosurfacesuntilthewaterfilmthicknessreachestheminimumthickness.ThewaterfilmthicknesswasfoundtoincreasewiththeincreaseofRH(i.e.,p/ps).ADDINEN.CITE<EndNote><Cite><Author>Beaglehole</Author><Year>1992</Year><RecNum>290</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>Beaglehole,D.</AUTHOR><AUTHOR>Christenson,H.K.</AUTHOR></AUTHORS><YEAR>1992</YEAR><TITLE>Vaporadsorptiononmicaandsilica:entropyeffects,layering,andsurfaceforces</TITLE><SECONDARY_TITLE>J.Phys.Chem.</SECONDARY_TITLE><VOLUME>96</VOLUME><PAGES>3395-3403</PAGES></MDL></Cite></EndNote>(19),i.e.,thethicknessofthewaterfilmonthesiliconsurfaceistoothintoformacapillaryneckwiththeprobingtipforRHlessthan40%.Whenthewaterfilmthicknessreachestheminimumthicknessrequirementat40%RH,acapillaryneckformsbetweenthetipandthesubstratesurfaces,leadingtoasuddenincreaseofthepull-offforce.Themagnitudeofpull-offforcesmeasuredonhydrophilicsiliconsurfacesbelow40%RHis83nN(Fig.3and4).ForRHlargerthanthecriticalRH,inthemid-RHregimeII(Fig.2and3),thecapillaryforcedominatesthepull-offforceifbothsurfacesarehydrophilic.Thus,theSFMobservablethepull-offforceisnotadirectmeasureofthecapillaryforceonly.InregimeIIthepull-offforcecanbedescribedasthesumofthecapillaryforce(Fcap)andvanderWaalsinteractionforce(Fvdw),i.e., (3)InregimeI,thepull-offforceisrestrictedtovanderWaalsinteractionbetweenthecantilevertipandthesamplesurfaces.BothFcapandFvdwareattractive.InthehighRHregimeIII(Fig.2and3),thepull-offforcedecreaseswithincreasingRHforahydrophilictip.MateandBinggeliADDINEN.CITE<EndNote><Cite><Author>Binggeli</Author><Year>1994</Year><RecNum>250</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>Binggeli,M.</AUTHOR><AUTHOR>Mate,C.M.</AUTHOR></AUTHORS><YEAR>1994</YEAR><TITLE>Influenceofcapillarycondensationofwateronnanotribologystudiedbyforcemicroscopy</TITLE><SECONDARY_TITLE>Appl.Phys.Lett.</SECONDARY_TITLE><VOLUME>65</VOLUME><NUMBER>4</NUMBER><PAGES>415-417</PAGES></MDL></Cite></EndNote>(5)discussedthedecreaseastheinterplaybetweencapillaryforcesandtheforcesrelatedtothechemicalbondingoftheliquidinthegap.Thisleadstothefollowingexpressionforthepull-offforce:; (4)whereFchemADDINEN.CITE<EndNote><Cite><Author>Binggeli</Author><Year>1994</Year><RecNum>250</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>Binggeli,M.</AUTHOR><AUTHOR>Mate,C.M.</AUTHOR></AUTHORS><YEAR>1994</YEAR><TITLE>Influenceofcapillarycondensationofwateronnanotribologystudiedbyforcemicroscopy</TITLE><SECONDARY_TITLE>Appl.Phys.Lett.</SECONDARY_TITLE><VOLUME>65</VOLUME><NUMBER>4</NUMBER><PAGES>415-417</PAGES></MDL></Cite></EndNote>(5)istheforcerelatedtothechemicalbondingwithGtheGibbsfreeenergy,atheareaoftheliquidfilm,vthemolarvolume,thechemicalpotential.Measurementswithhydrophiliccantilevertipsonionicsurfaces,suchascalciumfluoride,CaF2,showasimilarqualitativetrendinthepull-offforceatlowRHasfoundaboveonsiliconsurfaces.AtintermediateRH,thepull-offforcecollapsesveryrapidlywithincreasingRH.Thiscanbeexplainedbyion-diffusionfromcalciumfluoridesurfaceintothewaterfilm,whichhasastrongaffectonthematerialpropertiessuchasthesurfacetension.Roughnesseffectscanexplainwhyforcevaluesforpresumablemicrocontacts(silicaglasssphere)atlowloadsaresignificantlysmallerthanexpectedfromEq.(1).Theroughnessofthesphereis10nmrmsdeterminedfroma2nd-orderflattenedAFMimageover1m2areaofthespheresurface.Atlowload,thespheremakescontactwithmultiplenanosizedasperities.Thisleadstoasignificantdecreaseinthepull-offforceinthevanderWaalsinteractionregimecomparedtoanatomicallysmoothsphere.Theargumentalsoholdsinthecapillaryregime.Theforceinstabilitymeasuredwithsilicaglassspheresiswidenedbytheasperitysizedispersion,andthemagnitudeofthepull-offforceisdeterminedbythenumberofasperitiesincontact.HalseyandLevinesuggestedthattheadhesiveforcebetweentworoughsphereswasdependentonthetotalamountofthefluidpresent.ADDINEN.CITE<EndNote><Cite><Author>Halsey</Author><Year>1998</Year><RecNum>315</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>Halsey,T.</AUTHOR><AUTHOR>Levine,A.</AUTHOR></AUTHORS><YEAR>1998</YEAR><TITLE>Howsandcastlesfall</TITLE><SECONDARY_TITLE>PhysicalReviewLetters</SECONDARY_TITLE><VOLUME>80</VOLUME><NUMBER>14</NUMBER><PAGES>3141-3144</PAGES></MDL></Cite></EndNote>(30)Capillaryforceequationfornano-contactsWederivedthecapillaryforceequationfornano-contactsfromthesphere-planeapproximation,foundinreferenceADDINEN.CITE<EndNote><Cite><Author>Israelachvili</Author><Year>1992</Year><RecNum>270</RecNum><MDL><REFERENCE_TYPE>1</REFERENCE_TYPE><AUTHORS><AUTHOR>Israelachvili,JacobN.</AUTHOR></AUTHORS><YEAR>1992</YEAR><TITLE>Intermolecularandsurfaceforces</TITLE><PLACE_PUBLISHED>London</PLACE_PUBLISHED><PUBLISHER>AcademicPress</PUBLISHER><EDITION>2nd</EDITION></MDL></Cite></EndNote>(25),withthedistinctionthatwedidnotrequirealargecontactarea,andthus,donotrestrictourcapillaryforceequationtolargesphereradii,R(Fig.2).Startingfromthesurfacefreeenergyofthesystem,W,ADDINEN.CITE<EndNote><Cite><Author>Israelachvili</Author><Year>1992</Year><RecNum>270</RecNum><MDL><REFERENCE_TYPE>1</REFERENCE_TYPE><AUTHORS><AUTHOR>Israelachvili,JacobN.</AUTHOR></AUTHORS><YEAR>1992</YEAR><TITLE>Intermolecularandsurfaceforces</TITLE><PLACE_PUBLISHED>London</PLACE_PUBLISHED><PUBLISHER>AcademicPress</PUBLISHER><EDITION>2nd</EDITION></MDL></Cite></EndNote>(25);;, (5)whereistheangleof,sthewettedsurfacearea,andcaconstant.Thecapillaryforcecanbeintroducedas. (6)whereDisthedistancebetweenthesphereandtheplane.ThedifferentialtermoftheanglewithDcanbeobtainedbyanisovolumeconsideration(dV/dD=0)ofasimplifiedmeniscusvolume(ABMQN),V,whichequalsthevolumeofthecylinderABMNminusthevolumeofthesphericalcapMNQ.Thesimplifiedmeniscusvolumeis (7)Equation(7)leadstothefollowingrelationship: (8)Thisequationisalsoapplicabletosmallcontacts.Thecapillaryforceisderivedbysubstitutingequation(8)intoequation(6),i.e., , (9)whichyieldsacapillaryforceatcontact(D=0) . (10)Equations(1)and(10)differbythegeometricalfactor (11)whichisimportantforsmallasperitycontacts,i.e.,largeanglesofFig.7).Equation(1)canbeappliedwitha20%uncertaintyforanangleoflessthan70.Yangandco-workersobservedlargepull-offforces(i.e.,100-200nN)onmicawithtypicalhydrophiliccantilevertips,ADDINEN.CITE<EndNote><Cite><Author>Yang</Author><Year>1996</Year><RecNum>173</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>Yang,G.L.</AUTHOR><AUTHOR>Vesenka,J.P.</AUTHOR><AUTHOR>Bustamante,C.J.</AUTHOR></AUTHORS><TITLE>Effectsoftip-sampleforcesandhumidityontheimagingofDNAwithascanningforcemicroscope</TITLE><SECONDARY_TITLE>Scanning</SECONDARY_TITLE><VOLUME>18</VOLUME><NUMBER>5</NUMBER><YEAR>1996</YEAR><PAGES>344-350</PAGES><KEYWORDS><KEYWORD>scanningforcemicroscope.DNA.humidity.tip-sampleforce.</KEYWORD><KEYWORD>aqueous-solutions.air.water.resolution.molecules.artifacts.surfaces.adhesion.strands.mica.</KEYWORD></KEYWORDS></MDL></Cite></EndNote>(14)whichweproposetoexplainwithalargeKfactor.NotethatEq.(10)isbasedonaverysimplifiedcylindricallyshapedgeometry.Moresophisticatedgeometriesarefoundintheliteratureformacrocontactsormicrocontacts,ADDINEN.CITE<EndNote><Cite><Author>Clark</Author><Year>1968</Year><RecNum>276</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>Clark,W.C.</AUTHOR><AUTHOR>Haynes,J.M.</AUTHOR><AUTHOR>Mason,G.</AUTHOR></AUTHORS><YEAR>1968</YEAR><TITLE>Liquidbridgesbetweenasphereandaplane</TITLE><SECONDARY_TITLE>Chem.Eng.Sci.</SECONDARY_TITLE><VOLUME>23</VOLUME><PAGES>810-812</PAGES></MDL></Cite><Cite><Author>Orr</Author><Year>1975</Year><RecNum>247</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>Orr,F.M.</AUTHOR><AUTHOR>Scriven,L.E.</AUTHOR><AUTHOR>Rivas,A.P.</AUTHOR></AUTHORS><YEAR>1975</YEAR><TITLE>Pendularringsbetweensolids:meniscuspropertiesandcapillaryforce</TITLE><SECONDARY_TITLE>J.FluidMech.</SECONDARY_TITLE><VOLUME>67</VOLUME><NUMBER>4</NUMBER><PAGES>723-742</PAGES></MDL></Cite><Cite><Author>Aveyard</Author><Year>1997</Year><RecNum>180</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>Aveyard,R.</AUTHOR><AUTHOR>Clint,J.H.</AUTHOR><AUTHOR>Nees,D.</AUTHOR></AUTHORS><TITLE>Theoryforthedeterminationoflinetensionfromcapillarycondensation</TITLE><SECONDARY_TITLE>JournalOftheChemicalSociety-FaradayTransactions</SECONDARY_TITLE><VOLUME>93</VOLUME><NUMBER>24</NUMBER><YEAR>1997</YEAR><PAGES>4409-4411</PAGES><KEYWORDS><KEYWORD>liquid.</KEYWORD></KEYWORDS></MDL></Cite><Cite><Author>Binggeli</Author><Year>1994</Year><RecNum>250</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>Binggeli,M.</AUTHOR><AUTHOR>Mate,C.M.</AUTHOR></AUTHORS><YEAR>1994</YEAR><TITLE>Influenceofcapillarycondensationofwateronnanotribologystudiedbyforcemicroscopy</TITLE><SECONDARY_TITLE>Appl.Phys.Lett.</SECONDARY_TITLE><VOLUME>65</VOLUME><NUMBER>4</NUMBER><PAGES>415-417</PAGES></MDL></Cite><Cite><Author>Adamson</Author><Year>1990</Year><RecNum>282</RecNum><MDL><REFERENCE_TYPE>1</REFERENCE_TYPE><AUTHORS><AUTHOR>Adamson,A.W.</AUTHOR></AUTHORS><YEAR>1990</YEAR><TITLE>PhysicalChemistryofSurfaces</TITLE><PLACE_PUBLISHED>NewYork</PLACE_PUBLISHED><PUBLISHER>JohnWiley&Sons,Inc.</PUBLISHER></MDL></Cite></EndNote>(5,20-23)andfornanocontacts.ADDINEN.CITE<EndNote><Cite><Author>Marmur</Author><Year>1993</Year><RecNum>248</RecNum><MDL><REFERENCE_TYPE>0</REFERENCE_TYPE><AUTHORS><AUTHOR>Marmur,A.</AUTHOR></AUTHORS><YEAR>1993</YEAR><TITLE>Tip-surfacecapillaryinteractions</TITLE><SECONDARY_TITLE>Langmuir</SECONDARY_TITLE><VOLUME>9</VOLUME><NUMBER>7</NUMBER><PAGES>1922-1926</PAGES></MDL></Cite></EndNote>(31)

2.1.3 VanderWaalsForcesPointInteractionVanderWaalsforcesexistbetweenatomsormoleculesandcanbedividedintothreegroups:Dipole-dipoleforce:Moleculeshavingpermanentdipoleswillinteractbydipole-dipoleinteraction.Dipole-induceddipoleforces:Thefieldofapermanentdipoleinducesadipoleinanon-polaratomormolecule.Dispersionforces:Duetochargefluctuationsoftheatomsthereisaninstantaneousdisplacementofthecenterofpositivechargeagainstthecenterofnegativecharge.Thusatacertainmomentadipoleexistsandinducesadipoleinanotheratom.Thereforenon-polaratoms(e.g.neon)ormoleculesattracteachother. TheattractivevanderWaalsforcebetweentheatomsisproportionalto1/r7,whereristhedistancebetweentheatoms.TheempiricalpotentialoftenusedistheLennard-Jones(LJ)potential:.Thepotentialisalsoreferredtoasthe6-12potentialbecauseofits(1/r)6and(1/r)12distance,r,dependenceoftheattractiveinteractionandrepulsivecomponent,respectively.Theempiricalconstantrepresentsthecharacteristicenergyofinteractionbetweenthemolecules(themaximumenergyofattractionbetweenapairofmolecules).,acharacteristicdiameterofthemolecule(alsocalledthecollisiondiameter),isthedistancebetweentwoatoms(ormolecules)for(r)=0.TheLJpotentialisdepictedbelow.ExamplesfortheLJparameters,and,areprovidedinTable2.LennardJones(6-12)potential(empiricalVanderWaalsPotentialbetweentwoatomsornonpolarmolecules).

Table2:Substance(Å)/kH2(lightelement)2.91538.0Ar(noblegas)3.418124PolyatomicSubstancesAir3.61797.0N23.68191.5HydrocarbonsCH43.822137n-C6-H145.909413k=1.38010-16ergmolecule-1K-1(Boltzmann'sconstant)MacroscopicBodyInteractionAboveafewÅngstromstohundredsofÅngstroms,vanderWaalsforcesaresignificant,particularlybetweenmacroscopicbodies.Theinteractionbetweendifferentgeometries,suchtwoplanes,asphereandaplane,ortwocrossedcylinders,canbecalculatedbyintegration.Forexample,theattractiveforcebetweenasphereandaplaneisF(D)

=

AR/6D2whereRistheradius,Dthedistancebetweenthesphereandtheplane.TheinteractionconstantA,iscalledHamakerconstant,definedasA=2CwhereCistheattractiveinteractionstrength(seeLJpotentialabove)andii=1,2,isthenumberdensityofthemoleculesinthesolid(1or2).ThefigurebelowandTable3providenon-retardedVanderWaalsinteractionfreeenergiesbetweenbodiesofdifferentgeometriesthatwerecalculatedon