膠體與界面化學(xué)英文5Static-and-Dynamic-Light-Scattering-and-Other-Radiation-Scattering-課件

1PrinciplesofColloid

andSurface/InterfaceChemistry

1PrinciplesofColloid

andSu2ContentsChapter1:ColloidandSurface/InterfaceChemistry—ScopeandVariablesChapter2:SedimentationandDiffusionandTheirEquilibriumChapter3:SolutionThermodynamics:OsmoticandDonnanEquilibiaChapter4:TheRheologyofDispersions2ContentsChapter1:Colloidan3Chapter5:StaticandDynamicLightScatteringandOtherRadiationScatteringChapter6:Surface/InterfaceTensionandContactAngle:ApplicationtoPureSubstancesChapter7:AdsorptionfromSolutionandMonolayerFormationChapter8:ColloidalStructuresinSurfactantSolutions:AssociationColloids3Chapter5:StaticandDynamic4Chapter9:AdsorptionatGas-SolidInterfacesChapter10:VanderWallsForcesChapter11:TheElectricalDoubleLayerandDouble-LayerInteractionChapter12:ElectrophoresisandOtherElectrokineticPhenomenaChapter13:ElectrostaticandPolymer-InducedColloidStability4Chapter9:AdsorptionatGas-5Chapter5Staticanddynamiclightscatteringandotherradiationscattering§5.1Introduction1.RadiationscatteringTheparticlesinteractwiththelightthatstrikesthemanddeflectsomeofthatlightsfromitsoriginaldirection.Awholeassortmentoftheopticalphenomenarelatedtothedeflectioniscalledaslightscattering.5Chapter5Staticanddyn6Theintensityofscatteredlightdependson:(1)Thewavelengthoftheincidentlight.(2)Thesizeandshapeofthescatteringparticles.(3)Theopticalpropertiesofthescatters.(4)Theangleofobservation.6Theintensityofscatteredli72.Staticlightscattering(SLS)Thetotalintensityoflightscattering(time-average)isafunctionofscatteringangle.Fromstaticlightscattering,wecanestablish:theinformationontheinternalstructureandshapesoftheparticlesandinterparticlestructurecanbededucedbymeasuringtheangledependenceoftheintensity.72.Staticlightscattering(S83.Dynamiclightscattering(DLS)Thetemporalvariationoftheintensityisobservedandmeasured.Fromdynamiclightscattering,wecanestablish:theinformationonthediffusioncoefficientsoftheparticles,particlesize,particlessizedistributionandetc.(Othername:intensityfluctuationspectroscopy,quasi-elasticlightscattering)83.Dynamiclightscattering(94.Focusofthischapter(1)Staticlightscattering(5)Dynamiclightscattering(2)TheoryofRayleighscattering(3)TheextensionofRayleightheory(4)Abrieftreatmentofscatteringbylarge,absorbingparticlesandtheconceptofabsorptionandscatteringcrosssections.94.Focusofthischapter(1)S10§5.2Interactionofradiationwithmatter1.ElementsofthetheoryofelectromagneticradiationElectromagneticradiationconsistsofoscillatingelectricalfieldandmagneticfield.Theyareperpendiculartoeachother,andperpendiculartothedirectionofpropagationofthewave.10§5.2Interactionofradiat11UndervacuumFrequencyv,andwavelength,andvelocityoftheradiationc.Underthemediumwiththerefractionindexn:or11UndervacuumFrequencyv,and12(1)Coulomb’slawTheinteractionbetweentwochargedparticles.(2)Electricfield12(1)Coulomb’slawTheinterac13Ordinarylightissaidtobeunpolarized,allformsofpolarizationarepresent,sotheindividualcancelout.Ifthephasedifferencebetweenthetwocomponentsofthefield(y-z)iszeroorsomeintegralmultipleof,theellipseflattenstoaline—asbeingplanepolarized.

(3)Polarizationoflight13Ordinarylightiss14Ifthephasedifferencebetweenthetwocomponentsofthefield(y-z)is/2

oranyoddintegralmultipleof/2andtheamplitudesofthetwocomponentsareequal,theellipseisroundedtoacircle—asbeingcircularlypolarized.

(4)Lightreflection14Ifthephasediffer152.Interactionbetweenanelectricfieldandachargeqequalsthemagnitudeofthecharge,apisitsperiodicacceleration,cisthevelocityoflight,risthedistancebetweenanelectricfieldandacharge,zistheanglebetweenthelineofsight–alongzaxes,0isthedielectricconstant.152.Interactionbetweenanel16Polarizability=E0Induceddipoleduetothefield:16Polarizability=E0Induc17§5.3Scatteringbysmallparticles:TheoryofRayleighscattering1.Scatteringbysinglemoleculesandgaseslighttransmittedlightscatteringlightabsorptionlight17§5.3Scatteringbysmall18(1)RayleightheoryA.Thescatteringcentersaresmallindimensioncomparedtothewavelengthoftheradiation(about1/20).C.Theparticlesmovesindependently(exp.gas).B.Therefractiveindexgradient(dn/dc)isnotverylarge.D.Theincidentlightisunpolarized.E.Thescatteringmoleculesarenotabsorbing.F.Scattersareisotropic.18(1)RayleightheoryA.Thesc19(2)Rayleighequationisistheintensityofthelightscatteredperunitvolumebyagasofmolecularweight.I0istheintensityofincidentlight.19(2)Rayleighequationisist20So,thebluecomponentofwhitelight,sunlight,isscatteredverymuchmorethethered.Theskyoverheadappearsblue.

Atsunset,weseemostlytransmittedlight.Sincethebluehasbeenmostextensivelyremovedfromsunsetlightbyscattering,theskyappearsredatsunset.TheRayleightheorydoesnotapplywhenthescatteringmoleculesareabsorbingortheatmospherecontainsdustparticles,waterdrops,orotherparticlewithdimensionsthatarelargerthanordinarygasmolecules.20So,thebluecomp212.Rayleighscatteringappliedtosolution:FluctuationsThemolecularmotioninsolutionresultsinsmallFluctuationsindensityatthemolecularlevel.Thescatteringmaybetracedtotwosources:fluctuationsinsolventdensityandfluctuationsinsoluteconcentration.Theintensityofscatteredlightinsolutiondependsonthesquareofpolarizability.212.Rayleighscatteringappli22AccordingtoRayleightheory,somekeysubstitutionsandjustificationsaremade.(dn/dc)—therefractiveindexgradient(/dc)0,T—theosmoticpressuregradientforanequilibriumsolutionatisothermalcondition.22AccordingtoRay23BecauseSo23BecauseSo24TheRayleighratioRisdefinedasTherefore24TheRayleighratioRisdef25OrThissuggeststhataplotof(Kc/R)versuscshouldbeastraightlineforwhichtheinterceptandslopehavethefollowingsignificance.Intercept=1/MSlope=2B25OrThissuggeststhat26

Comparingaboveequations,twoequationsrevealtheplots(straightline)haveidenticalintercept,atleastformonodispersecolloids,andtheslopesdifferby2,withthelight-scatteringresultshavingthelargerslope.26Comparingabovee27§5.4ExperimentalaspectsoflightScattering1.Somepreliminaryconsiderations(1)ConcentrationtermsA.Theconcentrationstermentersthelightscatteringexpressionsprimarilythroughtheequationsforosmoticpressure.So,thesameconditionsoftheconcentrationsapplyinthisapplicationasinosmoticpressure.27§5.4Experimentalaspects28B.Lightscatteringshouldbemeasuredunderisothermalconditions.(2)OpticaltermsBecauseKandRtermscontainthewavelength,wavelengthshouldbeconstant.(3)TherefractiveindexestermsBymeansofdifferentialrefractometer,therefractiveindexesandtherefractiveindexgradientsaremeasured28B.Lightscatteringshouldb292.IntensitymeasurementsTypicallightscatteringinstrument(Fig.5.5)292.IntensitymeasurementsTyp30Theanglecanbechangedandmeasured.Rtermsiscalculatedfromtheintensityofscatteringlightataangleandthedistancerbetweenthesampleandthelightscatteringphotometer.I0istheintensityofincidentlight.Ktermsisalsocalculated.30Theanglecanbechangeda313.RelatingintensitiestoabsorbanceandturbidityAbsorbanceabsIt=I0-Is313.Relatingintensitiestoa32ThequantityIsisnotthesameasthelightscatteringtoaparticularpoint(r,),butequalsthesummationofthesecontributions,totaloverallangles:Fromthefollowingequationtoaparticularpoint(r,)32ThequantityIsisn33ThereforeTheparameterHisdefinedtoequaltheclusterofconstants.33ThereforeTheparameterHis34Comparingisturbidity34Comparingisturbidity35P210example5.235P210example5.2364.Resultsfromlightscatteringexperiments:weight-averagemolecularweightsByosmometrymethods,wecanmeasurethenumber-averageweightforapolydispersecolloid.Inviewofthewaytheosmoticpressureentersthedevelopmentofthefollowingequation.Itappearsthatthesametypeofaverageisobtainedfromturbidityexperimentsalso.Thisisnotthecase.364.Resultsfromlightscatte37BecauseSoas37BecauseSoas38Theweightofparticlesinaclassgivestheweightingfactorfortheweight-averagemolecularweight.Forthisreason,theweightaverageisespeciallyinfluencedbythelargerparticlesinadistribution.Thereforetheweight-averagemolecularweightisalwayslargerthanthenumber-averagemolecularweight.38Theweightofpart39Note:(1)Fromfollowingthreeequations:Theslopeofalightscatteringplotistwicethevalueoftheslopeofacomparableplotfromosmometry.39Note:(1)Fromfollowingthre40Inadditiontothefactorof2,thereisamoresubtledifferencebetweentheslopesarisingfromadifferenceinthetwovaluesofthesecondvirialcoefficient.FromanotherequationinosmoticpressureThesecondvirialcoefficientisinverselyproportionaltothesquareofthemolecularweightofthesolute.40Inadditiontothe41Sincetheweight-averagemolecularweightislargerthanthenumberaverage,thesecondvirialcoefficientBwillbesomewhatsmallerasdeterminedbylightscatteringthanosmometryafterthefactorof2hasbeentakenintoaccount.(2)Theequationbylightscattering

Aboveequationdoesnotapplytochargedsystem.41Sincetheweight42Thereasonliesinthefactthatthechargeofmacroinsisalsoafluctuatingquantity,andthismustalsobeconsideredindevelopingascatteringtheoryforchargedparticles.TheresultinganalysisshowsthatitisaplotofHc/versusc1/2whichislinearinthiscase,withthelimitingslopeproportionaltoz2,theaveragevalueofthesquareofthecharge.Theslopeisalsopredictedtobenegativeinthissituation.42Thereasonliesin43§5.5ExtensiontolargerparticlesandtointraparticleinterferenceeffectReviewingtheassumptionsoftheRayleighmodel:(1)Thescatteringcentersareisotropic,dielectric,andnonabsorbing.(2)Thescattershavearefractiveindexthatisnottoolarge.(3)Theparticlesaresmallindimensioncomparedtothewavelengthoflight.43§5.5Extensiontolargerp44Ingeneral,inallradiationscatteringtechniques,theaboveassumptionsarealsosuitable.Therefore,developingmorecomplicatedtheoriesofscattering.Example,theDebyescatteringtheory,Miescatteringtheory,etal.1.TheDebyescatteringtheoryOvercomingtheapproximationinRayleightheorythatrestricttoparticleswithdimensionsthataresmallcomparedtothewavelengthoflight.44Ingeneral,inall45(1)TheDebyescatteringmodelA.Allowingtheparticlesapproximatethewavelengthofincidentlight.B.Theinterferencebetweenthewavesoflightscatteredfromdifferentpartsofthesameparticle.Fig.5.8Thelightscatteredfromthetwositeswillbeoutofphaseanddisplayinterference.45(1)TheDebyescatteringmod46Theinterferenceeffectmaybeconstructiveordestructive,dependingonthevalueof.Formfactor(ortheintraparticlestructurefactor),thecorrectionfactor,P(),correctsfortheinterferenceeffectsnotconsideredpreviously.C.Alargeparticledoesnotconsistofmerelytwoscatteringcenters,butmaybesubdividedintoseveralcenters,thenumberofwhichincreaseswiththesizeoftheparticle.46Theinterferenceeffe47(2)TheDebyescatteringequationTheRayleightscatteringequationTheDebyescatteringequation47(2)TheDebyescatteringequ482.ZimmplotsForsmallvaluesofsrij,theexpansionofsummatingtermatleftmaybelimitedtothefirsttwoterms:sisthescatteringvector,hasunitsof“1/length”.482.ZimmplotsFor49Becausethesquareoftheradiusofgyrationofaswarmofmasses(seep219)ThenSince49Becausethesquareofthera50

Threeimportantlimitingcasesfromaboveequation:(1)Inthelimitof=0,thereisnointerferenceeffectinthescatteringlight.50Threeimportantlim51(2)Inthelimitofc0,Kc/Risproportionaltosin2(/2).(3)Ifbothcandc0,Kc/Requalsto1/M.Theselimitssuggesthowexperimentaldatamightbecollected,plotted,extrapolated,andinterpreted.TheresultinggraphisknownasZimmplotafteritsoriginator.51(2)Inthelimitofc0,K52Fig.5.9Zimmplot52Fig.5.9Zimmplot53Therefore,wemustbeallunderstandtheZimmplot.SeeP221example5.3.53Therefore,wemust543.ThedissymmetryratioFromtheequationOnemeasuresofI/I0at=45o,and=135ofordispersionsatseveraldifferentconcentrationsmustbesame,butsoarenotinsomeactualcases,especiallyforgeometricaldimensionsofsomebodies..543.ThedissymmetryratioFrom55Therefore,anydeviationoftheratiooftheintensitieszfromunitymustmeasuretheratiooftheP()valuesatthesetwoangles(at=45oand=135o).So55Therefore,anydev56Thisiswhythecalculatedresults,experimentaldissymmetryratios,extrapolatedtoc=0toeliminatedtheeffectsofsolutionnonideality–canbedirectlyinterpretedintermsofRg.Fig.5.9Zimmplot56Thisiswhythec57WehavenotedpreviouslythatRgisrelatedtothegeometricaldimensionsofabodythroughexpressionsthatarespecificfortheparticleshape.Table5.4showsthatrelationshipsbetweentheradiusofgyrationandthegeometricaldimensionsofsomebodieshavingshapespertinenttocolloidchemistry.57Wehavenotedprevi58§5.6InterferenceeffectsandstructureofparticlesScatteringvectoris1.PhysicalsignificanceofthemagnitudeofthescatteringvectorIthasunitsof“1/length”,s-1isadimensionalquantity.58§5.6Interference59SuitablereferencedimensionLchisthecharacteristicdimensionthatrepresentsthesizeofthescatters.DimensionlessquantityQisdefinedbyLchisacharacteristiclengthsuitablefortheparticlesinthedispersion.WithLchandsdefinition,“small”and“l(fā)arge”simpliesQ=sLch

1orQ=sLch

1.59Suitablereferenc60Fig.5.12Fig.5.1360Fig.5.12Fig.5.13612.X-rayandneutronscatteringascomplementstolightscatteringlightscatteringisaconsequenceoftheinteractionofphotonswiththeelectronicstructureofatoms.X–raysarescatteredbyelectronclouds.Neutronsarescatteredbythenucleioftheatomsandbythemagneticmomentsoftheatoms.612.X-rayandneutronscatter62Table5.5indicatescomparisonofthewavelengthandtherangecoveredbyvariousradiationscatteringmethodsatTable5.5.MethodTypicalwavelength(nm)Rangeofs(nm-1)Laserlightscattering500110-3-410-2Small-anglex-rayscattering0.15210-2Small-angleneutronscattering0.4710-3-910-1wide-angleneutronscattering0.41101-510162Table5.5indicat63X-rayandneutronscatteringhavetwomajoradvantages:(1)TheparticlesandfluidareeffectivelytransparenttoX-rayandneutron,i.e.,theireffectiverefractiveindicesarenearlythesame.(2)TheverysmallvaluesofthewavelengthsofX-rayandneutronallowonetoreachlargevaluesoftheparameters.X-rayandneutronallowustoprobestructureatmuchshorterlengthscalesthanpossiblewithlight.63X-rayandneutro64§5.7Scatteringbylarge,absorbingparticles1.Scatteringandabsorption(1)AccountingforabsorptionthroughcomplexrefractiveindexThefirstfactoristhecasethatthematerialwouldbenonabsorbing.Itismodifiedbythesecondterm,whichisrealbutcontainstheimaginarypartoftheindexofrefraction.64§5.7Scatteringbylarge65(2)TheBeet-LambertformationTherelationshipoftheintensityofthetransmittedlightIt,withtheintensityoftheincidentlightI0maybewritten:65(2)TheBeet-Lambertformati66isturbiditycomparingtotheabsorbanceabs.absandscaarerespectivelytheefficiencyfactorforabsorptionandforscattering.andabsdescribetheattenuationoflightperunitopticalpathandhavetheunitslength-1.66isturbiditycomparingto672.TheMietheory:goldsolsMieassumption:AccordingtothevaluesfortheconstantsA1toA4inTable5.6,therelationshipsoftherefractiveindexorscatteringcoefficientswithwavelengthcanbedrawn(seeFig.5.14and5.15).672.TheMietheory:goldsols683.HigherorderTyndallspectra:MondisperseSulfursolsForuniformspheresoversomerangeofrefractiveindexandsize,differentcolorsoflightwillbescatteredindifferentdirections.Thesulfursolsdescribedherehavetherequiredpropertiestodisplaythiseffect.683.HigherorderTyndallspec69Therefore,ifabeamofwhitelightisshownthroughasampleofthedispersion,variouscolorswillbeseenatdifferentvalues.TheresultingarrayofcolorsisknownasthehigherorderTydallspectrum(HOTS).Redandgreenbandsaremostevidentinthesulfursols,andthenumberoftimesthesebandsrepeatincreasewiththesizeofthesulfurparticle.Therefore,thenumberandangularpositionsofthecoloredbandsprovideauniquecharacterizationoftheparticlesize.69Therefore,ifabeam70

ItwasoncethoughtthattheappearanceofHOTSwasevidenceinitselfforthepresenceofamonodispersesystem.70Itwasoncetho71§5.8DynamiclightscatteringDynamiclightscattering(DLS)istheclassoflightscatteringmethodsbasedonthetimedependenceofthescatteredlightintensity.Dynamiclightscatteringiscurrentlyaroutinelaboratorytechniqueformeasuringdiffusioncoefficients,particlesize,andparticlesizedistributionsincolloidaldispersions.71§5.8Dynamiclightsca721.IntensityfluctuationsandthesiegertrelationInatypicalscatteringexperiment,adetectormeasurestheintensityofthescatteredradiationoveraperiodoftime,indiscretestepsoft.Theintensityfluctuatesaroundanaveragevaluebecauseoftherandommotionsofthescatters.721.Intensityfluctuationsan73DynamicSinglePhotonCounterCorrelationFunctionParticleSize(0.001-5mm)Fig.5.16a73DynamicFig.5.16a74EncoderPhotomultipliertubePreamplifier/

DiscriminatorSteppingmotorMonitordiodeFocusLensDiodeLaserPumpedNd:YAGLaser

532nmWavelength400pin-holeCellhousingand

indexmatchingvatPosition-

sensitive

DetectorCuvettePhoton

CounterStatic,ClassicLLS

(timeaverageintensity)Dynamic,ModernLLS

(digitaltimecorrelator)RotatingArmSpectra-PhysicsHeliumNeonLaser

632.8nmWavelengthLaserLightScatteringSpectrometerLaserLaser74EncoderPhotomultipliertube757576h101000.004.008.0012.00

f(Rh)R/nm76h101000.004.008.0012.00f(Rh772.Applications(1)Monosizesphericalparticles:measuringdiffusioncoefficientandparticlesize772.Applications(1)Monosize78TheradiusRHmeasuredinthismannerisusuallyknownasthehydrodynamicradius.Disself-diffusioncoefficientoftheparticles.Seep239example5.5indetail.(2)Effectofpolydispersity:measuringsizedistribution78TheradiusRHmeasuredinth797980PrinciplesofColloid

andSurface/InterfaceChemistry

1PrinciplesofColloid

andSu81ContentsChapter1:ColloidandSurface/InterfaceChemistry—ScopeandVariablesChapter2:SedimentationandDiffusionandTheirEquilibriumChapter3:SolutionThermodynamics:OsmoticandDonnanEquilibiaChapter4:TheRheologyofDispersions2ContentsChapter1:Colloidan82Chapter5:StaticandDynamicLightScatteringandOtherRadiationScatteringChapter6:Surface/InterfaceTensionandContactAngle:ApplicationtoPureSubstancesChapter7:AdsorptionfromSolutionandMonolayerFormationChapter8:ColloidalStructuresinSurfactantSolutions:AssociationColloids3Chapter5:StaticandDynamic83Chapter9:AdsorptionatGas-SolidInterfacesChapter10:VanderWallsForcesChapter11:TheElectricalDoubleLayerandDouble-LayerInteractionChapter12:ElectrophoresisandOtherElectrokineticPhenomenaChapter13:ElectrostaticandPolymer-InducedColloidStability4Chapter9:AdsorptionatGas-84Chapter5Staticanddynamiclightscatteringandotherradiationscattering§5.1Introduction1.RadiationscatteringTheparticlesinteractwiththelightthatstrikesthemanddeflectsomeofthatlightsfromitsoriginaldirection.Awholeassortmentoftheopticalphenomenarelatedtothedeflectioniscalledaslightscattering.5Chapter5Staticanddyn85Theintensityofscatteredlightdependson:(1)Thewavelengthoftheincidentlight.(2)Thesizeandshapeofthescatteringparticles.(3)Theopticalpropertiesofthescatters.(4)Theangleofobservation.6Theintensityofscatteredli862.Staticlightscattering(SLS)Thetotalintensityoflightscattering(time-average)isafunctionofscatteringangle.Fromstaticlightscattering,wecanestablish:theinformationontheinternalstructureandshapesoftheparticlesandinterparticlestructurecanbededucedbymeasuringtheangledependenceoftheintensity.72.Staticlightscattering(S873.Dynamiclightscattering(DLS)Thetemporalvariationoftheintensityisobservedandmeasured.Fromdynamiclightscattering,wecanestablish:theinformationonthediffusioncoefficientsoftheparticles,particlesize,particlessizedistributionandetc.(Othername:intensityfluctuationspectroscopy,quasi-elasticlightscattering)83.Dynamiclightscattering(884.Focusofthischapter(1)Staticlightscattering(5)Dynamiclightscattering(2)TheoryofRayleighscattering(3)TheextensionofRayleightheory(4)Abrieftreatmentofscatteringbylarge,absorbingparticlesandtheconceptofabsorptionandscatteringcrosssections.94.Focusofthischapter(1)S89§5.2Interactionofradiationwithmatter1.ElementsofthetheoryofelectromagneticradiationElectromagneticradiationconsistsofoscillatingelectricalfieldandmagneticfield.Theyareperpendiculartoeachother,andperpendiculartothedirectionofpropagationofthewave.10§5.2Interactionofradiat90UndervacuumFrequencyv,andwavelength,andvelocityoftheradiationc.Underthemediumwiththerefractionindexn:or11UndervacuumFrequencyv,and91(1)Coulomb’slawTheinteractionbetweentwochargedparticles.(2)Electricfield12(1)Coulomb’slawTheinterac92Ordinarylightissaidtobeunpolarized,allformsofpolarizationarepresent,sotheindividualcancelout.Ifthephasedifferencebetweenthetwocomponentsofthefield(y-z)iszeroorsomeintegralmultipleof,theellipseflattenstoaline—asbeingplanepolarized.

(3)Polarizationoflight13Ordinarylightiss93Ifthephasedifferencebetweenthetwocomponentsofthefield(y-z)is/2

oranyoddintegralmultipleof/2andtheamplitudesofthetwocomponentsareequal,theellipseisroundedtoacircle—asbeingcircularlypolarized.

(4)Lightreflection14Ifthephasediffer942.Interactionbetweenanelectricfieldandachargeqequalsthemagnitudeofthecharge,apisitsperiodicacceleration,cisthevelocityoflight,risthedistancebetweenanelectricfieldandacharge,zistheanglebetweenthelineofsight–alongzaxes,0isthedielectricconstant.152.Interactionbetweenanel95Polarizability=E0Induceddipoleduetothefield:16Polarizability=E0Induc96§5.3Scatteringbysmallparticles:TheoryofRayleighscattering1.Scatteringbysinglemoleculesandgaseslighttransmittedlightscatteringlightabsorptionlight17§5.3Scatteringbysmall97(1)RayleightheoryA.Thescatteringcentersaresmallindimensioncomparedtothewavelengthoftheradiation(about1/20).C.Theparticlesmovesindependently(exp.gas).B.Therefractiveindexgradient(dn/dc)isnotverylarge.D.Theincidentlightisunpolarized.E.Thescatteringmoleculesarenotabsorbing.F.Scattersareisotropic.18(1)RayleightheoryA.Thesc98(2)Rayleighequationisistheintensityofthelightscatteredperunitvolumebyagasofmolecularweight.I0istheintensityofincidentlight.19(2)Rayleighequationisist99So,thebluecomponentofwhitelight,sunlight,isscatteredverymuchmorethethered.Theskyoverheadappearsblue.

Atsunset,weseemostlytransmittedlight.Sincethebluehasbeenmostextensivelyremovedfromsunsetlightbyscattering,theskyappearsredatsunset.TheRayleightheorydoesnotapplywhenthescatteringmoleculesareabsorbingortheatmospherecontainsdustparticles,waterdrops,orotherparticlewithdimensionsthatarelargerthanordinarygasmolecules.20So,thebluecomp1002.Rayleighsca