高分子物理復(fù)旦大學(xué)chapter4高聚物分子量和分子量分布課件

Chapt4MolecularWeightandMolecularWeightDistributionofPolymers4.1高聚物分子量和分子量分布的表示方法4.2分子量的測定方法4.3分子量分布的測定方法4.2.1數(shù)均分子量的測定方法4.2.2重均分子量的測定方法4.2.3粘均分子量的測定方法MolecularweightandmolecularweightdistributionDistributionofmolecularweightsinatypicalpolymer4.1DefinitionsofAverageMWsandMWDistributionn:totalmolenumber;ni:molenumberofithmoleculewithmolemassofMi;Ni:molefractionofithmolecule;w:totalweightofthesample;wi:weightoftheithmolecule;Wi:weightfractionofithmolecule.(1)Number-averagemolecularweight(數(shù)均分子量):(2)Weight-averagemolecularweight(重均分子量):SchulzTungLogarithmnormaldistribution用簡化的函數(shù)擬合MWDistribution

Widthofmolecularweightdistribution(分子量分布寬度):Polydispersity(多分散系數(shù)):MWDistributionFunction實驗測量平均分子量分布寬度4.2MeasurementofMolecularWeight

Endgroupanalysis(端基分析)molecularweightdeterminationthroughgroupanalysisrequiresthatthepolymercontainaknownnumberofdeterminablegroupspermolecule.measurethenumber-averagemolecularweight,Mn

2.5104

Colligativeproperty(依數(shù)性)measurement:

measurethenumber-averagemolecularweightMnvapor-pressurelowingboiling-pointelevation(ebulliometry)freezing-pointdepression(cryoscopy)osmoticpressure(osmometry)DTb,DTf,andParetheboiling-pointelevation,freezing-pointdepression,andosmoticpressure.risthedensityofthesolvent.DHvandDHfaretheenthalpiesofvaporizationandfusion.

Vapor-phaseosmometry(VPO,氣相滲透法)Smalltemperaturedifferenceresultingfromdifferentratesofsolventevaporationfromandcondensationontodropletsofpuresolventandpolymersolutionmaintainedinanatmosphereofsolventvapor.MeasureMnthatistoolowerformembraneosmometrymethod.Calibratedwithlow-molecularweightstandards:arelativemethod.Quasi-steady-statephenomena.caremustbetakentostandarizesuchvariablesastimeofmeasurementanddropsizebetweencalibrationandsamplemeasurement.MeasurementchamberofVPO(Pasternak,1962).Dropletsofsolventandpolymersolutionareplaced,withtheaidofhypodemicsyringer,onthe“beads”oftwotheristorsusedastemperature-sensingelementsandmaintainedinequilibriumwithanatmosphereofsolventvapor.

Membraneosmometry(膜滲透壓法)DiagramoftheZimm-myersonosmometer(Zimm1946).Atypicaldiameterforthemeasuringandreference(solventcell)capillaryis0.5-1mm.Theclosureofthefillingtubeisa2-mmmetalrod.Amercurysealisusedatthetoptoensuretightness.TwomembraneareheldagainstaglasssolutioncellbymeansofperforatedmetalplatesTheassembledinstrumentissuspendedinalargetubepartlyfilledwithsolventThesuccessoftheosmoticexperimentdependsontheavailabilityofamembranethroughwhichsolventbutnotsolutemoleculescanpassfreely.Existingmembranesonlyapproximatelyidealsemipermeability.Measurablemolecularweight:2104<Mn<106.

Staticlightscattering(靜態(tài)光散射)Generalset-upofascattering(散射)experimentIncidentbeamIntensityI0ScatteredbeamIntensityI(q)DetectorSampleScatteringvector(散射矢量):where:wavelengthoftheradiationqTheoryofLightScatteringRandomPhaseApproximationbydeGennesForpolymer/polymermixtureForPolymerSoultiong:

StructurefactorofasinglechainA:PolymerB:Solvent(Rayleighratio)瑞利比(2)largeparticlesd>l/20qrI0II

μ(SAi)2q→0cY斜率2A2sin2q/2c1c2c3Ycq1q2q3YY斜率sin2q/2

TheZimm-Plot2A21/MwSmallanglelaserlightscatteringq?0用光陷阱扣除中心光的干擾Nomenclature(術(shù)語)ofsolutionviscosityhr:粘度比(相對粘度);hsp:粘度相對增量(增比粘度);hred:粘數(shù)(比濃粘度);hinh:對數(shù)粘數(shù)(比濃對數(shù)粘度);[h]:極限粘數(shù)(特性粘度)h:viscosityofpolymersolutionattemperatureTh0:viscosityofpuresolventatT.ViscositymeasurementThesmallmolecularliquidsanddilutepolymersolutionsareNewtonianflow:theviscositydoesnotchangewiththeshearstressandshearrate。Measurementsofsolutionviscosityareusuallymadebycomparingtheeffuxtimet(流出時間)requiredforaspecifiedvolumeofpolymersolutiontoflowthroughacapillary(毛細管)tubewiththecorrespondingeffuxtimet0ofthepuresolvent.IfB/tismuchsmallthanAtandr

r0

TreatmentofviscositydataHugginsequation:Ifhsp<1,hrcanbeexpressedbyTaylorseriesexpansion

Mark-Houwinkequation:Viscosity-averagemolecularweight(粘均分子量):MolecularWeightFractionations(分子量分級)ofPolymers

Columnelution(柱淋洗)Solvent-gradientelution(溶劑梯度淋洗)Thermal-gradientelution(溫度梯度淋洗)HighTemp.LowTemp.GoodSolventPoorSolvent

Gelpermeationchrom