表面张力和接触角英文课件

2008讲稿-第6章Chapter6.SurfaceTensionand

ContactAngle6.1IntroductionSurfacetensionisaparametercanbeusedtocharacterizedpropertyofliquidsurface(interface)andmeasured.Contactanglecanbeusedmostlytocharacterizesurfacepropertyofasolidandmeasured.2008讲稿-第6章FocusofthisChapterConcerningtheequilibriumbehaviorofinterfacesbetween“pure”phases;Definitionsandreasons;Lapalceequation,thepressureacrossacurvedinterface;Tousesurfacetensionandcontactangledeterminingwettingphenomenaofsolid.2008讲稿-第6章6.2Surfacetension,surfaceworkand

surfacefreeenergySurfacetensionSurfacetension(γ)isaforcethatoperatesonasurfaceandactsperpendicular(垂直)andinwardfromtheboundariesofthesurface,tendingtodecrease

theareaoftheinterface.

F2008讲稿-第6章γ=F/2L(1)Characteristics:Acontractile(收缩)force，tendstoshrink(收缩)thesurface;Aforceofperunitlength,(Nm-1ordynescm-1)；Atwo-dimensionalpressure;2008讲稿-第6章（1）Reasonforproducing

surfacetensionAssumptionofvacantstateofsurface（表面层空位假说）:（Bakker，Davies，Fowkes，Ademson）Themoleculesinthesurfaceofliquidexchangeswiththemoleculesofitsvaporandtheliquid.2008讲稿-第6章Basedonkineticmoleculartheoryofgases(气体分子动力学理论)andtheoryofdiffusioninliquids(液体扩散理论),whentemperatureisin20˚C：Exchangerateofmoleculesbetweensurfaceandvaporis:2.9×1020/s.cm2Exchangerateofmoleculesbetweensurfaceandliquidis:1.7×1025/s.cm22008讲稿-第6章Inequilibriumthedistancebetweenthemoleculesonthesurfaceislargerthanthatinliquid,thereis“vacantposition”onthesurface.

Duetothedistancebetweenthemoleculesonthesurfaceislargerthanthatofthemoleculesinliquidthemoleculesinteractedattractivelyandinthestateoftension.Moleculesinliquid2008讲稿-第6章ThedistancebetweenthemoleculesonsurfaceislargerthatpredicatedbythisassumptionisagreewiththedistancecalculatedbyPrigogineandSaragawithstatisticsmethodbasedonamodelofsurfacethermodynamics.Thermodynamicfunctionsofliquefiedargon(液氩)(85K)2008讲稿-第6章（2）Mechanicalmodelofsurfacetension(表面张力的力学模型)Basedontheassumptionofvacantstateofsurface,surfacetensionofmattersisrelatedtotheforcesbetweenthemolecules.Surfacetension：Dispersionforce,Londonforce（d）(色散力);Hydrogenbonding(h)(氢键)Metallicbonding(m)(金属键)Interactionofelectrons(π)(电子相互作用)Interactionofions(i)(离子相互作用)2008讲稿-第6章SurfacetensiondefinedbyFowkes：

γ＝γd＋γh＋γm＋γπ＋γi

（6－1）Hydrocarbonliquids（H）：γH＝γHd

（6－2）Water（W）：γw＝γ

wd＋γ

wh

（6－3）Mercury(汞)(Hg)：

γHg＝γHgd＋γHgm

（6－4）Onlythedispersionforceexistinallmattersandthedistanceofthedispersionforceactonisthelongest(withinfewmolecules)。2008讲稿-第6章Surfacetensionofmatters2008讲稿-第6章（3）Surfacetensionandattractiveforce

Duetosurfacetensionisproducedbytheattractiveforcesbetweenmolecules,thevalueofinterfacetensionmeasurestheattractiveforcebetweenthemoleculesinliquidorthedifferenceoftheattractiveforce（∆f）

betweenagasandliquid.Planesurface

γ－surfacetension

f－attractiveforce(liquid)f’-attractiveforce(gas)

∆f=f－f’f’2008讲稿-第6章γ－Surfacetensionf－Attractiveforceofthemoleculesonthesurface;f΄΄－tangentialforceoff;f΄－radialforceoff;Thevalueofsurfacetensionisrelatedtof΄΄;Thetotaloff΄istheextraforceactonthemoleculeinthesurfacetowardstothecenteroftheliquiddrop.Curvedsurface2008讲稿-第6章（4）Directionofsurfacetension

Planesurface

：

Paralleltothesurface，contractileforce，tendstoshrinkthesurface

Curvedsurface

：2008讲稿-第6章（5）SurfacetensionandtemperatureorpressureγandTT↑→γ↓（densityofgas↑，⊿f↓；distanceofmoleculesinliquid↑，⊿f↓）

γandPP↑→γ↓（someofmoleculesingasphasegointoliquid，⊿f↓；densityofgas↑，⊿f↓）2008讲稿-第6章2．surfacework(表面功)Surfacetensionisacontractileforce,workcanbedonebytheforceundercertainconditions.

。

W＝2γLdx＝γdA

（6）Surfacework：Theworkdonebysurfacetensionwithreductionofsurfacearea.（J/m2）or（mJ/m2）2008讲稿-第6章WhentheforceFmakethewirethoughdx,theworkdoneonthesystem,andtheworkequalstotheworkperunitarearequiredtoproduceanewsurface.FTwoequivalentinterpretationofγ：Forceperunitlengthofboundaryofthesurface;Energyperunitareaofthesurface.2008讲稿-第6章3.surfacefreeenergy(表面自由能)Workdonebyreducingofsurfaceareapredictthatthesurfacehaveenergyandtheenergyisassurfacefreeenergy.Surfacefreeenergy：

Theenergyofthemoleculesonthesurfaceexcessintheenergyofthemoleculesinliquids.（mJ/m2）。

Surfacefreeenergyisan“excess”energy.2008讲稿-第6章Fromthermodynamics,foraequilibriumsystemoftwophasesintheprocessofequilibriumtheworkdonebythesystemincludespressure-volumework(膨胀功),chemicalwork(化学功)andsurfacework,then：

dU＝TdS－PdV＋γdA＋（6－5）

2008讲稿-第6章U－energyofthesystem；S－entropy(熵)；V－volume；T－temperature；P－pressure；μi－chemicalpotentialofi

component(成分)；

n－amountofsubstance(物质的量)；

γ－surfacefreeenergy；

A－areaofsurface.2008讲稿-第6章Surfacefreeenergyistheenergyofthesystemincreasedbyincreasingperunitareaofthesurfacewhenentropy,volumeandfractionsareconstant.Fromeq.(6-5)：2008讲稿-第6章Basedondefinitionsofenthalpy(焓),freeenergy(自由能)andGibbsfreeenergy:

（6－6）（6－7）（6－8）2008讲稿-第6章then：（6－9）（6－10）（6－11）Surfaceenergyisthechangeofenergyofthesystem,enthalpy,freeenergyandGibbsfreeenergybyincreasingperunitareaofthesurfaceundercertaincondition.2008讲稿-第6章Whysmalldropsofliquidalwaysbechangedintoalargeonespontaneously?dG＝γdA，whenγisconstant，A↓→G↓2008讲稿-第6章6.3Contactangleandwetting(润湿)WettingWettingisthedisplacement(置换)fromasurfaceofonefluid(流体)byanother.Wettinginvolvesthreephases,atleasttwoofwhichmustbefluids.Thewettingofagas(usuallyair)isdisplacedbyaliquidatthesurfaceofasolid.2008讲稿-第6章Whenadrysubstance→wetsubstancetheenthalpy(焓)ofthesubstanceischanged.∆Him＝Hwet－Hdry(6－12）∆Him

–heatofimmersion(浸泡)∆Him

<0，aprocessofreleasingheat(放热).Airisdisplacedbyaliquidatthesurfaceofsolidspontaneously,∆G<0.Enthalpyofwetting2008讲稿-第6章Forasolidsurfaceofunitareaiswettedbyaliquidthefreeenergyischangedas

－∆G＝γSA＋γLA－γSL＝WSL

（6－13）γSA－freeenergyoftheinterfacebetweenasolidandair;γLA－freeenergyoftheinterfacebetweenaliquidandair;γSL－freeenergyoftheinterfacebetweenasolidandaliquid;WSL－workofadhesion(粘附功)betweenasolidandaliquid.2008讲稿-第6章Workofadhesionmeasurestheattractionbetweenthetwodifferentphases.Therefore,WSLcanbeusedtomeasurethedegreeofwetting.

γSAandγSLareunabletobemeasured.

Contactangle(θ)isusedformeasuringthedegreeofwetting.2008讲稿-第6章Contactangle:Whenagas,aliquidandasolidareinequilibrium,theanglebetweentheinterfaceofsolidandliquidandatangentlineoftheinterfacebetweenthegasandliquidatthejunction(交点)ofthethreephases(当气、液、固三相平衡时，在固－液－气交点处作气液界面的切线，此切线与固液界线的夹角)2.Contactangle2008讲稿-第6章θ－Contactanglebetweenliquidandsolid;θ΄－Contactanglebetweengasandsolid;θ＋θ΄＝180˚（6－14）θ>90˚nowettableθ<90˚wettable(润湿)θ＝0˚wet(完全润湿)θ＝180˚完全不润湿Contactangleismeasuredintheliquid.2008讲稿-第6章Condition:1)Thesurfaceofasolidisperfectlysmooth;2)Thevapor,liquidandsolidareinequilibrium.γSA＝γSL＋γLAcosθ

（6－15）Taking（6－15）to（6－13）gives：

WSL＝γLA（1＋cosθ）（6－16）3.Young-Equatuin2008讲稿-第6章Forθ＝0˚，WSL＝2γLA（cohesionalworkofliquid,液体的内聚功）θ＝180˚，WSL＝0，完全不润湿。Noattractive(interaction)betweensolidandliquid.θ↓，WSL↑，θcanbeusedformeasuringdegreeofwetting.2008讲稿-第6章（1）contamination(污染)ofsubstance

Forliquidiscontaminated→γLA↓，

ForsurfaceofsolidiscontaminatedγSAandγSL↓.亲水表面4.Factorsaffectsthemeasurementofcontactangle亲油表面2008讲稿-第6章2）RoughnessofsolidsurfaceTherealsolidsurfaceisnotperfectlysmooth.

Roughnessfactor(粗糙度）（r）：

Ratioofthereal(真实)surfaceareaofasolidtotheapparent(表观)surfaceareaofthesolid.

r>12008讲稿-第6章Forasolidsurfacewithroughnessfactorr,theYoungequationisgivenr（γSA－γSL）＝γLAcosθ΄

（6－17）θ΄－apparentcontactangle，comparing（6－17）with（6－15）gives

（6－18）2008讲稿-第6章FromEq.(6-18)itwillbeA．Forθ<90˚，θ΄<θ，aroughsurfaceofasolidismorewettablethanasmoothsurfaceofthesolid.B．Forθ>90˚，θ΄

>θ，aroughsurfaceofasolidislesswettablethanasmoothsurfaceofthesolid.C．measurementofθisverydifficult.

θ↓

，errorsofmeasurement↑.2008讲稿-第6章5.Advancing(前进)andReceding(后退)ContactangleAdvancingcontactangle(θa):

largervalueRecedingcontactangle(θr):

smallervalueBothadvancingandrecedingcontactanglesshouldbemeasured.2008讲稿-第6章(θa)-

Thetilted(倾斜的)plateispushedintotheliquid.(θr)-

Thetiltedplateispulledoutfromtheliquid.2008讲稿-第6章6.4Cohesion(内聚),Adhesion(粘附)andSpreading(铺展)1.CohesionNosurface→2A(orB)SurfacesCondition:

Oneunitofsurfaceisaffectedbytheprocess.Theshapeoftheaffectedareaisimmaterial(非物质的).2008讲稿-第6章Workofcohesion:TheworkrequiredtopullapartacolumnofliquidAapart.∆G=2γA

=WAA(56)Itmeasurestheattractionbetweenthemoleculesoftwoportion.Surfacetensionmeasuresthefreeenergychangeinvolvedwhenmoleculesfromthebulkofasamplearemovedtothesurface.2008讲稿-第6章2.Adhesion1ABInterface→1A+1BSurfacesDifferencebetweenthefinalandinitialfreeenergiesforthisprocessyields∆G=WAB=γA+γB-γAB

(57)WABisworkofadhesionthatmeasurestheattractionbetweenthetwodifferentphases.2008讲稿-第6章TheworkofadhesionbetweenasolidandaliquidphasemaybedefinedWSL＝γLA（1＋cosθ）(60)Forθ＝0˚，

WSL＝2γLA

=WAAForθ＝180˚，WSL＝0，theliquidistangenttothesolidandthereisnointeractionbetweenthephases.2008讲稿-第6章3.Spreading∆G=

γAB+γB-γA

(61)DifferencebetweenthefinalandinitialfreeenergiesforspreadingBoverA(symbolizedB/A)weobtainThenegativeof∆GB/A

iscalledthespreadingCoefficientSB/A.2008讲稿-第6章ForSB/A>0，

BspreadsfreelyoverAandwetsit.BycombiningEq.(56),(57)and(61)thespreadingcoefficientcanalsobewritten

SB/A=WAB-WBB

(62)IfWAB>WBB

theA-BinteractionissufficientlystrongtopromotethewettingofAbyB.2008讲稿-第6章IfWAB<WBB

nowettingoccurs.SincetheworkrequiredtoovercometheattractionbetweentwoBmoleculesisnotcompensated(平衡)bytheattractionbetweenAandB.ForSB/A<0，BwillnotspreadoverA.

（《胶体化学基础》135页有误）2008讲稿-第6章6.5LaplaceEquationandCapillaryRiseTheLaplaceEquationObjective:Torelatethispressuredifferencetothecurvature(曲率)ofthesurface.Apressuredifferenceoperatesacrossacurvedinterface,andthegreaterpressureisontheconcave(凹)side.P1>P2.P1P2P12008讲稿-第6章TheLaplaceEquation（29）Eq.(29)isgeneralandappliesequallywelltogeometricalbodieswithradiiofcurvaturethatareconstantovertheentiresurfaceortomoreintricate（复杂的）shapesforwhichtheRi’schangefromplacetoplaceonthesurface.2008讲稿-第6章1．Forasphericalsurface，R1＝R2＝R，（30）2．

Foracylindricalsurface，R1＝∝，

(31)3．Foraplanarsurface，R1＝R2＝∝，∆P＝0（32）

Thepressuresinbothsidesofthesurfaceareequal.2008讲稿-第6章4．R1

andR2

↓，∆P↑；

5．Foragasbubble,6.Forasaddle(马鞍)shapedsurface,∆P＝0，

7.Itmaybealiquidoragasatbothsidesofthesurface.

2008讲稿-第6章

Thetotaloff΄istheextraforceactonthesurfacetowardstotheconcave

sideoftheinterface.Duetothevalueof∆Prelatetofandγrelatetof,therefore,γcanbeusedformeasuring

of

∆P。Whythereisapressuredifferenceoperatesacrossacurvedinterface?∆P＝P΄－PorP΄＝P

＋∆PPP’2008讲稿-第6章Condition:Thewallofcapillaryiswettablebyaliquid.（1）弯曲液面压差WhenacapillaryisjustpushedintowaterP1＝P2＝P3>P4Duetothepressureatpoint4islower，theliquidflowsfrompoint2towardpoint4andenterthecapillary.Atequilibrium:P5＝P1＝P2>P62.CapillaryRise2008讲稿-第6章R－radiusofthecurvedsurface；

r－radiusofcapillary;Forr＝Rcosθ，then，

Thedifferenceofpressureacrossthecurvedinterfacepushliquidflowsintothecapillary.（6-19）2008讲稿-第6章2．重力平衡（实验测定）Ifweimagine(设想)thesurfacetobe“hanging”fromthewallofthecapillaryandsupportedbytheverticalcomponent(γcosθ)ofthesurfacetension.《胶体化学基础》24页有误“表面张力将流体拉入毛细管”，表面张力的分力与重力平衡。2008讲稿-第6章《表面化学》，363页Pressuredifferenceacrossacurvedinterfaceas

（6－20）γLV－Surfacetensionbetweenliquidandvapor;r－Radiusofcapillary3．固－气、固－液界面张力差2008讲稿-第6章γSV－surfacetensionbetweensolidandvapor;γSL－surfacetensionbetweensolidandliquid；FromYoung-Equation（6－21）2008讲稿-第6章∆P＝2（γSV－γSL）/r（6－22）∆PonlydependonthedifferenceofγSVandγSL，andnotrelatedtoγLV.ForγSV－γSL>0，capillaryrise；ForγSV－γSL<0，capillarydepression“毛细下降”。TakingEq.6-21intoEq.6-20gives2008讲稿-第6章4．与表面张力反向力作用

《界面化学基础》，15页毛细管壁对液体的作用力将液体拉进毛细管。Itimagine

f＝γ，andfoppositefromγ.f2008讲稿-第6章Conclusionsforcapillaryrise：

1．ΔPor(γSV－γSL)isthedrivingforce;2．Foraspecifieds