PolymerPolymerMolecularweightsand高分子的Molecularweightsand1Molecularweightsandmolecularweightdistribution分子量與分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：熔體強度②高分子材料使用如：拉伸強度和沖擊強度與樣品中低分子量部分有較大關③溶液性如：溶液粘度④聚合反應機

纖 分子量分布宜

Molecular 聚丙烯腈試樣(三種Mw相同樣品a樣品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數量微分分布聚合物分子量化學或波譜方動力學方Dynamic

orendgroup滲透壓法OsmoticmethodUltracentrifugalsedimentationmethod及擴散法Diffusion凝膠滲透色譜法Gelpermeationchromatography(GPC) Determinationofthemolecularweight數均分子量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

：化學滴定法:縮聚產物如聚酯聚酰胺等放射化學法:末端具有放射性同位素波譜法:Colligative依數性方ThecolligativepropertiesBoilingpointMeltingpointVaporpressureOsmotic沸點升高Boilingpoint

RT2 Hv

Ac ingramspercubic

Latentheatsofvaporizationpergramofsolvent limlimcHvM1MM Kb iiMiKciiKciMKciciiNiiMniCryoscopic冰點降低zingpoint

flim ff

1 1 ingramspercubic

MnLatentheatsoffusionpergramofsolventVapor-phaseosmometry氣相滲透壓Vaporpressureofthe1P1X21VaporpressurethepureMoleofthe SchematicofSchematicofvapor-phaseTT1Acc2MKTMnMembrane膜滲透OsmoticlimlimcMnofanosmometerSchematicillustrationSchematicillustrationofthedependenceofosmoticpressureonconcentrationRT1AcAc2cM23若A1/1/21c2ccc02使聚合物分子不能透溶劑分子透過速率較不與聚合物和溶劑發生化學作(不適合未分級 低分子的聚合物若部分聚合物分子透過半透膜，所測分子量Comparisonofcolligative依數性方法的AAcomparisonofthecolligativesolutionpropertiesofa1%polymersolutionwithM=20,000g/molpressure1.3103pressure1.3103Boilingpoint4103Vaporpressurelargeenoughforfruitfulstudiesatthis15cmOsmoticzingpoint15cmOsmoticzingpoint2.5103 Light光散射Lightscattering光散射現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圖，可求得M

1 KciMi1

ciMiKc 22i

cii Kc i

12KcMLightscatteringoflargeparticle,dilute大粒子、稀溶11cos2KcRM12A2 1/(1x)1xx2 鏈（無規線團

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

h

...2A2c2 R的測定2 RR902 I90 R R90(benzene) I90 n(benzene)?n/?C的測定注意事項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測量重均分子量的其它 粘度Definitionof術語定粘粘粘RelativeRelative粘度比(相對粘度r0對數粘(比濃對數粘度cSpecificSpecific粘度相對增量(增比粘度0r0粘(比濃粘度cIntrinsic極限粘Intrinsic極限粘數(特性粘度crc0cThestressisidenticallyzeroatanyconstantstrain.Inliquids,thestressisdeterminedbydeformationrate.Therateofchangeofshearstrainwithtimeiscalledtheshearrate.d

unit:Pas=kgm-1s-Newton’slawofForsimpleliquids,theshearstressislinearlyproportionaltoshearrate,withtheconstantofproportionalitydefiningtheshearviscosity.Concentrationdependenceoftheviscosityofpolymersolutions高分子溶液粘度的濃度依賴性c(1kc(1k[]c)11k[]c c[]Huggins22r rcc1/ 1/lnln(1)SchematicofaSchematicofaplotofsp/candlnrel/cversusc,andextrapolationtozeroconcentrationtodetermine[]對于線型柔性鏈－良溶劑體 K>1/3, K<1/3,一點 [] c[]

(1特性粘度與分子量的av

KaFlory特性粘 hydrodynamicallyequivalentVhand

Rh的測定方法：動態光散射(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粘度法實AtBtrAtBt000t0tAtghR4tmVBAabDUbbelohde實驗注意事 GelPermeation凝膠滲透色另一名詞sizeexclusionchromatography體積排斥色濃度檢測濃度檢測Gelpermeationchromatography(GPC)makesuseofthesizeexclusionprinciple.Thesizeofthemolecule,definedbyitshydrodynamicradius,canorcannotentersmallporesinabedofcross-linkedpolymer.Thesmallermoleculescandiffuseintotheporesandaredelayed.Thelargermoleculespassbyandcontinueinthesolventphase.儀GPC濃度響濃度響淋出體積或淋出時

小GPC曲線就是聚合物的分子量分布Vi:載體內部的孔體

V0:載體的粒間體CalibrationlogMlogMA Ve與分子體積(流體力學體積)不同高分子Ve～M關系不同校正曲線GPC實驗確定分子量及其分布時,必須采用結Universalcalibration普適標η=limη=limc=AVhM []MVe[]KMKMaelog([]M)~Ve作圖，對所有聚TheTheuniversalcalibrationloglog[η1]M1=log[η2]M2[η][η]=KMa1111 =KMa2222logKlogK1+a1logM1logM1=logK2+a2logM2 1a1121+1log21+2K2Calculationofmolecularweight平均分子量的計MiMw iHiMn CalculationofmolecularweightaveragesfromGPC1Retention2Height3ChainLengthorMol42/ColCo5×Col6MnCol2/C