2010讲稿(第2章)-dzx

胶体的性质•界面性质：表面张力，表面压，润湿性•运动性质：沉降速度，扩散•平衡性质：沉降平衡，渗透压•流变特性•稳定性：双电层，电性质•光学性质Chapter2.Sedimentationanddiffusionandtheirequilibrium2.1Introduction1.Why?•Sedimentation（沉降）anddiffusion（扩散）affectmanycolloidalphenomena.•Basicprinciplesofsedimentationanddiffusionareessentialpartofcolloidscience.•ManyanalyticalandpreparativetechnologytakeadvantageofS&Dincolloidscience(biophysics,biochemistry).2.PurposeTointroducethebasicconceptsthatgovernS&Dofcolloidalparticles.•DiscussStokes’slawStokes’slawisakeyrelationshipinunderstandingthesedimentationrateofcolloidalparticles.•Fick’slawsFocusourattentiononthediffusioncoefficient.•Equilibriumbetweensedimentationanddiffusionofcolloidalparticles.•Brownianmotion（布朗运动）(randomwalks)anddiffusion2.2Sedimentation1.BasicconsiderationsFg:gravityforce(+),Fb:buoyantforceFv:viscousforcewhenρ2ρ1Sedimentationwhenρ1ρ2CreamingFv=fv(2)f:frictionfactor(kgs-1)v:stationarystatevelocity21netgbF=F-FVg(1)12(1-)g=vmfSincethenetforceofgravityandtheviscousforceareequalunderstationary（稳态）conditions.21netF=vVgf(3)Equation(3)mayalsobewritten(4)misthemassoftheparticle，visthestationarysettingvelocity.Thisequationhasthefollowingfeatures（特点）:•Itisindependent（无关）ofparticleshape;•Itassumes（假设）thatthebulkdensityofthepurecomponentsappliestothesettingunits(i.e.nosolvation（溶解）);•Itpermitstheevaluationofvforasituationinwhichthemass-frictionfactorration(m/f)isknown;•Itpermitstheevaluationof(m/f)inasituationforwhichvisknown.Problems:•Foraaggregates（聚集体）orsolvatedlyophilicparticles,thedensityofthesettingunitsisintermediated（居于中间）betweenthedensitiesofthetwopurecomponents.Densityforthesettingparticle?•visthefunction（函数）of(m/f),vshallbeverysmall?2.Stokes’sLawforSpheresVzDistortion（形变）offlowstreamlines（流线）aroundasphericalparticleItassumes（假设）that:•Thefluidislamina（层流）;•Theparticleisarigid（刚性的）sphere;•Thefluidiscontinuous（连续的）;•Nochangeofdensityandviscosityofthefluid.Boundary（边界）conditions（条件）:•Thethickness（厚度）ofeachsuccessive（连续的）layer（层）inthefluidistheinfinitesimalmathematicalincrementdr;•Velocityvariation（变化）inthefluidcanbedescribedbydv/dr;•Whenr=∞,thedisturbing（扰动）influenceoftheparticlehasbeendampedaway（消失）;•Whenr=Rs,thevelocityiszero.(nonslip没有滑动)Therateofenergydissipation（损耗）is2/6zsdEdtR(5)Therateatwhichworkisdoneonthefluidbytheparticleis26vzzsFvR(6)6sFRvTheforceactingonthefluidisgivenbyStokes’sLaw(7)3.SedimentationEquationForasphericalparticle,thefrictionfactorisgivenbyf=6πηRs(8)2134()6v3ssRgREquation(3)becomes(9)21229sRgv（10）4.EffectofnonsphericityandsolvationInactualcolloidstheparticlesinthecaseof•Polyhedron（多面体）•Solvated（溶解的）•Asymmetrical（非对称的）Equivalentsphere（等效球体）:Afictitious（虚拟的）particlewiththesamedensityastheunsolvatedparticlethatwiththesamevelocityastheexperimentalsystem.Actualparticlescandeviate（产生偏差）fromtheStokesmodelbybeingeithersolvated,asymmetricalorboth,inwhichcasefincreasessothataparticleofmassmwilldisplayasmallersedimentationvelocitythanitwouldifitwereanunsolvatedsphere.f/f0=(f/f*)(f*/f0)(14)•fisthefrictionfactoroftheactualparticle;•f0isthefrictionfactorforanunsolvtedsphereGivenbyStokes’sLaw(thelowestfrictionfactor);•Theratiof/f0measurestheamountbywhichtheactualfrictionfactorexceeds（超过）theminimumvalue;•f*isthefrictionfactorforasphericalparticlehavingthesamevolumeasthesolvatedparticleofmassm;•Theratiof*/f0measurestheincreaseinfduetosolvation;•Theratiof/f*measurestheincreaseinfduetoasymmetry.5.Centrifugalsedimentation（离心沉降）Ultracentrifuge（超级离心）•Thegravitational（重力）accelerationisincreasedbyafactorof105.Theparticlesizethatmaybestudiedbysedimentationisdecreasedbythesamefactor.•Ultracentrifugehasbeenusedextensivelyforcharacterization（表征）ofcolloidalmaterials,suchasproteins（蛋白质）,nucleicacids（核酸）andviruses（病毒）.2.3Diffusion（扩散）C2C1Diffusion:Atransport（运移）processofmatterfromahigh-concentrationregiontoalow-concentrationregionspontaneously.Diffusionisthetransportprocessofmattercausedbythedifferenceofconcentrationwithoutexternal（外加的）forces.Fundamentally,itisthesecondlawofthermodynamicsthatisresponsiblefortheuniform（均匀的）distributionofmatteratequilibriumsinceentropy（熵）ismaximumwhenthemoleculesaredistributed（分布）randomlythroughoutthespaceavailabletothem.Itissameforcolloidalparticles.1.Fick’sfirstlaw(/)dQAJdtQAJt(20)Q–theamountofmaterialthatflowthroughacrosssection（截面）ofareaA.J–theflux（通量）ofsoluteacrossA.TheamountofmaterialthatcrossesAinatimeinterval∆tis(21)Fick’sfirstlawequationdcJDdx(22)D–diffusioncoefficient（扩散系数）ofthesolute.(m2s-1)•Dmeasuresthediffusionabilityofthesolute.•Negativemarkpresentthesolutemigrates（迁移）fromhigh-concentrationregiontolow-concentrationregion.•Fick’sfirstlawgivestheconditionofdiffusionwilloccur（发生）andthedirectionofthesolutewillmigrate.•Condition?Differenceofconcentration.•Direction?Fromhightolowconcentrationregion.2.Fick’ssecondlaw22ccDtx(26)•ConditionsConsidertheconcentrationchangesthatoccurwithinazone（区域）ofcrosssectionA,whichhasathicknessof∆x.•Itassumethatthecrosssectionisuniformthroughoutthecompartment（单元）andthatDisindependentofsmallchangesofconc