高物第五章高分子的分子量与尺寸

PolymerPolymerMolecularweightsand高分子的Molecularweightsand1Molecularweightsandmolecularweightdistribution分子量与分Characteristicsofpolymermolecular高分子的分子量的Themolecularweightsareveryhigh,rangingfromabout10,000to1,000,000g/molorhigher.Themolecularweightofordinarysizemoleculesisfixed(e.g.,benzenehasamolecularweightof78g/molregardlessofitssource).Mostpolymermolecularweights,ontheotherhand,varygreatlydependingonthemethodofpreparation.Mostpolymersarepolydisperse;thatis,thesamplecontainsmorethanonespecies.如：熔体强度②高分子材料使用如：拉伸强度和冲击强度与样品中低分子量部分有较大关③溶液性如：溶液粘度④聚合反应机

纤 分子量分布宜

Molecular 聚丙烯腈试样(三种Mw相同样品a样品b

acbM×10acb～Averagemolecularweight平均分子MolecularweightM1 Weightforeachchainm1

mminiMiMnMniniMiniNiMiiMwMw WiMim nMmiiniMiiZ-averagemolecularMMzini3iw2iini2i wiiiViscosity-averagemolecular Wiai1/MMnini103010 1010Mwn2i10ni103010104 znnM3i2i101010425.7iSchematicofasimplemolecularweightdistribution,Schematicofasimplemolecularweightdistribution,showingthevariousaveragesMz>Mw>M>Molecularweight分子量分Number-averagedistribution2nMM22MwnnMnMnWeight-averagedistribution2ww2w2MzwwMwMnMMw高分子分子量的多分PolydispersityNaturalAnionicRadicalStepCationicW(M)或W(M

N(MN(MM MMMM1M重量微分分布

M1M数量微分分布聚合物分子量化学或波谱方动力学方Dynamic

orendgroup渗透压法OsmoticmethodUltracentrifugalsedimentationmethod及扩散法Diffusion凝胶渗透色谱法Gelpermeationchromatography(GPC) Determinationofthemolecularweight数均分子量End- 端基分Manytypesofsynthesesleaveaspecialgroupononeorbothendsofthemolecule,suchashydroxylandcarboxyl.Thesecanbetitratedor instrumentallybysuchmethodsasNMR.Molecularweightdeterminedbyend-group isnumber-averagemolecularweightWM

Ni i presentintoolowaFormolecularweightsabovepresentintoolowaiOi O

hfm hfm

fn fn f

DPPCL2DPPEG[Ie/(IfIiDPPEGDPPEG3(IfIi)/4Igaae3chg

：化学滴定法:缩聚产物如聚酯聚酰胺等放射化学法:末端具有放射性同位素波谱法:Colligative依数性方ThecolligativepropertiesBoilingpointMeltingpointVaporpressureOsmotic沸点升高Boilingpoint

RT2 Hv

Ac ingramspercubic

Latentheatsofvaporizationpergramofsolvent limlimcHvM1MM Kb iiMiKciiKciMKciciiNiiMniCryoscopic冰点降低zingpoint

flim ff

1 1 ingramspercubic

MnLatentheatsoffusionpergramofsolventVapor-phaseosmometry气相渗透压Vaporpressureofthe1P1X21VaporpressurethepureMoleofthe SchematicofSchematicofvapor-phaseTT1Acc2MKTMnMembrane膜渗透OsmoticlimlimcMnofanosmometerSchematicillustrationSchematicillustrationofthedependenceofosmoticpressureonconcentrationRT1AcAc2cM23若A1/1/21c2ccc02使聚合物分子不能透溶剂分子透过速率较不与聚合物和溶剂发生化学作(不适合未分级 低分子的聚合物若部分聚合物分子透过半透膜，所测分子量Comparisonofcolligative依数性方法的AAcomparisonofthecolligativesolutionpropertiesofa1%polymersolutionwithM=20,000g/molpressure1.3103pressure1.3103Boilingpoint4103Vaporpressurelargeenoughforfruitfulstudiesatthis15cmOsmoticzingpoint15cmOsmoticzingpoint2.5103 Light光散射Lightscattering光散射现Thephenomenonoflight-scatteringiscausedbyfluctuationsintherefractiveindexofthemediumonthemolecularor

Sample pSchematicofSchematicoflightLightscatteringofpolymer高分子溶液的光散 Lightscatteringofsmallparticle,dilutesolution小粒子、稀溶液的

1cos2I n2 4r

c

RT1Acc2RT12Ac...2IIN42n22 1cos2Ac02sinM12A2Rayleigh因Rr2I0n2ncA4c1cos22sinM12A2 nK n2 AN4 cA

R

1 1cos21Rayleigh因

M

RR 11M2A22Kc12A2M作

~c图，可求得M

1 KciMi1

ciMiKc 22i

cii Kc i

12KcMLightscatteringoflargeparticle,dilute大粒子、稀溶11cos2KcRM12A2 1/(1x)1xx2 链（无规线团

1/(1x)1xx2RR21h2g61cos2Kc182n22sinRh2M22 2A2cIllustrationIllustrationofalight-scatteringZimm1cos2 1 2Zimm2sin M

h

...2A2c2 R的测定2 RR902 I90 R R90(benzene) I90 n(benzene)∂n/∂C的测定注意事项PS25C06.610-7.9410-9.5210-=546 R R90(ben)

I90 n(ben) nn(ben)n*Ccn06.610-7.9410-9.5210-1.00810- nK n(ben)2 AN4A

C

1.49792(0.106cm

/g)6.021023(5461071.8602106(cm2/g2Y1cos22sin Y值6.610-7.9410-9.5210-1.00810-Y=3.19461x10-6+6.52398x10Y=3.19461x10-6+6.52398x10-8 C

766540.10.20.30.40.50.60.70.882n2h2

9M

Rg=71

=30926Y=3.18235x10-6+0.64284x10-Y=3.18235x10-6+0.64284x10- c=10.88x10-c=9.52x10-c=7.94x10-0 08

6

A2=3.214x10-

-0

Othermethodstomeasure测量重均分子量的其它 粘度Definitionof术语定粘粘粘RelativeRelative粘度比(相对粘度r0对数粘(比浓对数粘度cSpecificSpecific粘度相对增量(增比粘度0r0粘(比浓粘度cIntrinsic极限粘Intrinsic极限粘数(特性粘度crc0cThestressisidenticallyzeroatanyconstantstrain.Inliquids,thestressisdeterminedbydeformationrate.Therateofchangeofshearstrainwithtimeiscalledtheshearrate.d

unit:Pas=kgm-1s-Newton’slawofForsimpleliquids,theshearstressislinearlyproportionaltoshearrate,withtheconstantofproportionalitydefiningtheshearviscosity.Concentrationdependenceoftheviscosityofpolymersolutions高分子溶液粘度的浓度依赖性c(1kc(1k[]c)11k[]c c[]Huggins22r rcc1/ 1/lnln(1)SchematicofaSchematicofaplotofsp/candlnrel/cversusc,andextrapolationtozeroconcentrationtodetermine[]对于线型柔性链－良溶剂体 K>1/3, K<1/3,一点 [] c[]

(1特性粘度与分子量的av

KaFlory特性粘 hydrodynamicallyequivalentVhand

Rh的测定方法：动态光散射(DLS)或粘度hollow solid4r2r 0

4/5 R

Rg

4/3R

3/h 4r2dr h0Forrandomcoiloflinearpolymer:Rg/Rh=1.5~Einstein粘 η=limsp= h

AMV 4R 4R23/ 3MRh

M1/3

3/NA h0M

M1/23令3/A2A

r23/2.54

Rh0

K

r

M =2.02.81023(mol-

(howaboutaundera[]KM1/ []/[]3ForgoodM0.1(Flory-Kringbaumtheory:5-3M0.5):from0.5(solvent)to0.8(goodForrigidrod-liker2M

R3 R3

M3 3aCis-1-Poly(ethylPoly(methylPoly(vinylEthylacetatehexaneCelluloseIntrinsicViscosity粘度法实AtBtrAtBt000t0tAtghR4tmVBAabDUbbelohde实验注意事 GelPermeation凝胶渗透色另一名词sizeexclusionchromatography体积排斥色浓度检测浓度检测Gelpermeationchromatography(GPC)makesuseofthesizeexclusionprinciple.Thesizeofthemolecule,definedbyitshydrodynamicradius,canorcannotentersmallporesinabedofcross-linkedpolymer.Thesmallermoleculescandiffuseintotheporesandaredelayed.Thelargermoleculespassbyandcontinueinthesolventphase.仪GPC浓度响浓度响淋出体积或淋出时

小GPC曲线就是聚合物的分子量分布Vi:载体内部的孔体

V0:载体的粒间体CalibrationlogMlogMA Ve与分子体积(流体力学体积)不同高分子Ve～M关系不同校正曲线GPC实验确定分子量及其分布时,必须采用结Universalcalibration普适标η=limη=limc=AVhM []MVe[]KMKMaelog([]M)~Ve作图，对所有聚TheTheuniversalcalibrationloglog[η1]M1=log[η2]M2[η][η]=KMa1111 =KMa2222logKlogK1+a1logM1logM1=logK2+a2logM2 1a1121+1log21+2K2Calculationofmolecularweight平均分子量的计MiMw iHiMn CalculationofmolecularweightaveragesfromGPC1Retention2Height3ChainLengthorMol42/ColCo5×Col6MnCol2/C