高分子物理课件(复旦大学)chapter4-5

1、Chapt 4 Molecular Weight and Molecular Weight Distribution of Polymers4.1 高聚物分子量和分子量分布的表示方法高聚物分子量和分子量分布的表示方法4.2 分子量的测定方法分子量的测定方法4.3 分子量分布的测定方法分子量分布的测定方法4.2.1 数均分子量的测定方法数均分子量的测定方法4.2.2 重均分子量的测定方法重均分子量的测定方法4.2.3 粘均分子量的测定方法粘均分子量的测定方法Molecular weight and molecular weight distributionDistribution of mole

2、cular weights in a typical polymer4.1 Definitions of Average MWs and MW DistributioniinniiNnn1iiNwwiiiiWww1iiWn: total mole number; ni: mole number of ith molecule with mole mass of Mi; Ni: mole fraction of ith molecule; w: total weight of the sample; wi: weight of the ith molecule; Wi: weight fract

3、ion of ith molecule.(1) Number-average molecular weight (数均分子量数均分子量): (2) Weight-average molecular weight (重均分子量重均分子量): 1d diiiiiiiiiiiiiinin MN MnNN M M MN MwwMW MMMW MMdMdMW MwMMndM 22 d ddiiiiiiiiiiiiiiiwin Mn MN M MMwMWMwWW M M MW M dN MMMMMiiiwn MwnMM(3) Z-average molecular weight (Z均分子量均分子量):

4、(4) Viscosity-average molecular weight (粘均分子量粘均分子量): 223232 ddiiiiiiziiiiiiiiiiiz MMzwMwMW Mn Mn MN M MMMW M MdMN M M dMM11/1/11/1 aaiiiiiaaaaiiiiiiaaMn Mn MwMwN M MdMN MM MM MWdzwnMMMMSchulzTungLogarithm normal distribution用简化的用简化的函数拟合函数拟合MW Distribution222220()()nnnnnnMMMMN M dMMM222dd/dd/nwnN M M

5、MN M MMN M dMN M M MN M M MN M dMMMM221nwnnMMMwnMdM Width of molecular weight distribution (分子量分布宽度分子量分布宽度): Polydispersity (多分散系数多分散系数):MW Distribution Function/, /, iiiiiiiiiiiiiiiiiinnwMN MnnwMwwn MW Mwwn M实验测量实验测量平均分子量平均分子量分布宽度分布宽度4.2 Measurement of Molecular Weight End group analysis (端基分析端基分析)

6、 molecular weight determination through group analysis requires that the polymer contain a known number of determinable groups per molecule. measure the number-average molecular weight, Mn 2.5 104 Colligative property (依数性依数性) measurement:measure the number-average molecular weight Mn vapor-pressure

7、 lowing boiling-point elevation (ebulliometry) freezing-point depression (cryoscopy) osmotic pressure (osmometry)D DTb, D DT Tf, and P P are the boiling-point elevation, freezing-point depression, and osmotic pressure. r r is the density of the solvent. D DHv and D DHf are the enthalpies of vaporiza

8、tion and fusion.nvbcMHRTcT1lim20DDrnffcMHRTcT1lim20DDrncMRTcP0lim Vapor-phase osmometry (VPO, 气相渗透法气相渗透法) Small temperature difference resulting from different rates of solvent evaporation from and condensation onto droplets of pure solvent and polymer solution maintained in an atmosphere of solvent

9、 vapor. Measure Mn that is too lower for membrane osmometry method. Calibrated with low-molecular weight standards: a relative method. Quasi-steady-state phenomena. care must be taken to standarize such variables as time of measurement and drop size between calibration and sample measurement.1122122

10、12/MwMwAnnAnnnATDMeasurement chamber of VPO (Pasternak, 1962). Droplets of solvent and polymer solution are placed, with the aid of hypodemic syringer, on the “beads” of two theristors used as temperature-sensing elements and maintained in equilibrium with an atmosphere of solvent vapor. Membrane os

11、mometry (膜渗透压法膜渗透压法)00icciPPiiicRTMiiiiicMRTcc2221112RTVx P 21MxVr122121211122VRTccRTcVMMVrrP0cRTcMP221212AVr22cr12cxVMiiiiinRTcn M1nRTcM Membrane osmometry (膜渗透压法膜渗透压法)Diagram of the Zimm-myerson osmometer (Zimm 1946). A typical diameter for the measuring and reference (solvent cell) capillary is 0

12、.5 - 1 mm. The closure of the filling tube is a 2-mm metal rod. A mercury seal is used at the top to ensure tightness.Two membrane are held against a glass solution cell by means of perforated metal platesThe assembled instrument is suspended in a large tube partly filled with solvent The success of

13、 the osmotic experiment depends on the availability of a membrane through which solvent but not solute molecules can pass freely. Existing membranes only approximately ideal semipermeability. Measurable molecular weight: 2 104 Mn 106. Static light scattering (静态光散射静态光散射)General set-up of a scatterin

14、g (散射散射) experimentIncident beamIntensity I0Scattered beamIntensity I(q)DetectorSampleifkkq2ifkk4sin2qScattering vector (散射矢量散射矢量):where : wavelength of the radiation Theory of Light Scattering 121212ddiISeqrrqqrrrr 1AABB112,ABSgNgNqqqRandom Phase Approximation by de GennesFor polymer/polymer mixtur

15、eFor Polymer SoultionBB1 and ,1BNgNq 1AAA112,1ASgNqqg: Structure factor of a single chainA: Polymer B: Solvent(1) small particles dl/20rI0II S SAi)2 1122221exp 1/ 133NNimnnmgd egiNSSNNq rqrrqRRqq 1112,1SgNqq4sin2q 12211 213ISSNq qq22111 23SccRN qq00111xxx 222222111212318SKchYA cA cRMMqq4sin2q2222218

16、1sin.292AYhcMMw, z, z具体方法：配置一系列已知浓度的溶液，测量不同散射 角的Y，分别作浓度和散射角度外推0212MAYc0,01cYM22022181sin.92chYM0,01cMY0212MAYc0,01cYMcY1Msin2/2c1c2c3Y10,cY20,cY30,cY22022181sin.92chYM0,01cMYc123Y10,cY20,cY30,cYY1Msin2/222289h The Zimm-Plot22289h2A21/MwSmall angle laser light scattering22222181sin.292AYhcM 00212MAYc

17、用光陷阱扣除中心光的干扰用光陷阱扣除中心光的干扰Solution viscosity as a measure of polymer molecular weightddFvAy/dv dyd dx dtdyd dx dydtddtaKM Mark-Houwink equation: Flory-Fox equation： 3/23/22201/23hhMMM For Newtonian fluidsNomenclature (术语术语) of solution viscosity r: 粘度比粘度比(相对粘度相对粘度); sp: 粘度相对增量粘度相对增量(增比粘度增比粘度); red: 粘数

18、粘数(比浓粘度比浓粘度); inh: 对数粘数对数粘数(比浓对数粘度比浓对数粘度); : 极限粘数极限粘数(特性粘度特性粘度) : viscosity of polymer solution at temperature T 0: viscosity of pure solvent at T.Viscosity measurement The small molecular liquids and dilute polymer solutions are Newtonian flow: the viscosity does not change with the shear stress an

19、d shear rate。 Measurements of solution viscosity are usually made by comparing the effux time t (流出时间流出时间) required for a specified volume of polymer solution to flow through a capillary (毛细管毛细管) tube with the corresponding effux time t0 of the pure solvent.tBAtltVmlVtghRrrr884000/tBAttBAtrrr0ttr001

20、tttrsp If B/t is much small than At and r r r r0 Treatment of viscosity dataaaiiiMWM/1aKM ckcsp2.321lnln32spspspspr 2323121lnckckcr ckcr2ln Huggins equation:If sp 1000 nm.PE chains are perpendicular to the lamellar surface. Polyoxymethylene (聚甲醛聚甲醛) PEO(聚氧乙烯聚氧乙烯)-b-PS(聚苯乙烯聚苯乙烯) diblock copolymerLame

21、llae Crystallized from Melt Spherulites (球晶球晶) of polymersUnder Polarized optical microscopy Lamellae in a spherulite Lamellae Tie Molecules AmorphousThe mechanism of Maltese cross extinction patternQE OP: PolarizerOA: AnalyzerQE: Vector of polarized lightI0QRQT projectingon OAOP QM QN2QNQMI Theoret

22、ical analysis of Maltese cross extinction pattern0QEi tE e 02222sin 2 sQNMin2QIE 0QRsinitEe0QTcosi tEe projectingon OA0QMsincositEe 0QNcos sini tEe00200sin2sincos2sin22sin2sincossin2sinsincos2QNQMcossi2222212n1ii ti ti ti tEeEeEeeeiiEi / positive spherulite negative spherulitennnnnnRelations of POM

23、and SALS (small angle light scattering)M/nEnEE n nn nM 2IM OA POMSALS22222/2coscos2sin 2E nn OAnE nnE nn OAnn OAnnnnn diSM OA e q rqr *I qS q SqSALS patterns of spherulitesVvHvqmax1/R5.2.3 Polymer Crystallization How do the polymer chains pack in the lamellar crystals?Random coil with the chain cont

24、our length (轮廓长度轮廓长度) longer than 1 m mmLamella with the thickness of 5-50 nm and lateral size of microns. Crystallization Macroconformations (巨构象巨构象):Extended chains(伸展链伸展链)Folded chains(折叠链折叠链)Random coils(无规线团无规线团)Fringed micelle(缨状微束缨状微束)Chain-Folded Lamellae of PolymersRandom coilCrystallizatio

25、nTC or D DT Chain folding (链折叠链折叠) conceptChain-folded Lamellae eFolded chain (折叠链折叠链)Fold surface(折叠表面折叠表面) Lateral surface(侧表面侧表面)TC: crystallization temperature (结晶温度结晶温度)D DT: supercooling (过冷度过冷度), D DT = Tm0 - TC e: fold surface free energy (折叠表面自由能折叠表面自由能) : lateral surface free energy (侧表面自由

26、能侧表面自由能), e 10 lLamellar thickness or fold length (片晶片晶厚度厚度) Process of Polymer CrystallizationTwo steps: 1. Nucleation (成核成核) processSizeD DG0embryosuper critic. sizestablecritical nucleusD DG = Gcrystal Gmelt , D DG = D DH TD DSGcrystal = Gbulk + S SA D DG = Gbulk - Gmelt + S SA =D DGf + S SA A is

27、 the suface area and D DGf is the bulk free energy change.abcSchematic representation of the change in free energy as a function of size illustrating the nucleation processTypes of crystal nuclei. (a) primary (初次初次), (b) secondary (二次二次), (c) tertiary (三次三次) nucleus. Homogeneous (均相均相) and heterogen

28、eous (异相异相) nucleationEstimate the critical nucleus size*44eemffTlghTDDDefaalglaG2224DD0fmfmfgThTsDDD For primary nucleus For secondary nucleus*22eemffTlghTDDDefalgalaG442DDagalGf42DDfgaD4*feglD4*mffThsDD22feGabl gblabD D2*mfTahTDD4*mfTahTDD0GaD0GlD ffmfcfcffmhsTTgThTshTDDDD DD D2. Linear Growth of

29、Polymer Crystallization Temperature dependence of linear growth rate (线生长速度线生长速度)Temperature dependence of the radial growth rate u of spherulites in isotactic polystyrene (left), polyamid 6 (center) and poly(tetramethl-p-silpheylene siloxane) (right). Tf : equilibrium melting temperature. Surface n

30、ucleation on substrate with length L with a rate i Linear growth rate G: the growth rate of crystal perpendicular to the substratel: fold length; a: width of stem; b: thickness of the stem; g: substrate completion rateOverall Polymer Crystallization Rate Overall crystallization rate (总结晶速度总结晶速度)Tm0T

31、gTMAXOverall rateBell curve of overall crystallization rateTotal volume or density: or Crystallinity: or 1(1) or 1 oracaaccacccccccccacacccaaacaacWWWVVVWVwvWVwwvvvvwvvrrrrrrrrrrrrrrrr rr usually 0.70.2cacacvwrrrrwc: weight fraction; vc: volume fractionW: weightsr r: density (g/cm3) : specific volume

32、 (cm3/g)1/ r r Definition of crystallinity (结晶度结晶度)wc Wc/Wtotal; vc Vc/VtotalTimeCrystallinityIsothermal crystallizationT1T2T3t1/2IIIIIIIVOverall Crystallization KineticsnAvrami equation0nkttvvevv0lnlnlnln 1lnlnctvvvvvntkh0h 00011tcathhvvhhhhhh 1/2tt1/21/2ln2nktlnt0lnlntvvvvhtht1/tttvhrDilatometric

33、(膨胀计法膨胀计法)Kinetics models of overall crystallizationn1. Free growth modelRvt3crystaltotal43icVVvNvtVVb. new nucleus produced - homogeneousa. constant numbers of nucleus- heterogeneoust tDDt tt tD Dt t3*3 403*043334d/tctvIv tIIvvtttttttDt3* 3 4IttvtttDI* nucleation rate*33*340430 +4.3.3iIv tItv ttIvt

34、ttttDDDtPoissons raindrop problemIf raindrops fall randomly on a pond creating expanding circular waves, what is the chance that the number of waves created by different raindrops which pass over a representative point P up to time t is exactly n?Kinetics models of overall crystallization-Avramin2.I

35、mpingement modelP solution: / !EnnP teEnPoisson distributionWhat is the chance that no wave reaches a given point P in space ?1cv 01EcPev iV tE tVheterogeneoushomogeneous 34/31Nvtcve*3 4/31cIv tveThe Avrami equation for 3DE(t): wave spreading area during tWhile t or v is very small cvE t1xex *3 4/3I

36、v t343NvtorThermodynamics of Crystallization: 1. Melting point of Lamellar CrystalsThermodynamics of Crystallization: 1. Melting point of Lamellar Crystals000fmfmfgThTsDDD0mT0ffmhsTDD021emmTTl hDMelting data for lamellar polyethylene grown from the melt and from solutionTm = 414.2(1-0.627/l)Lauritze

37、n-Hoffman equation002emmmTlh TTDSimilar to critical nucleus size Gibbs-Thomson extrapolation2224feGa l gaalD D0 GDmTla00fmfmfmmfmgThTsTThTD DD DThermodynamics of Crystallization: 2. Melting point of Polymer mixtureChemical Potential of Polymer in amorphous phase2022212ln11RTxxmmConsider a system of

38、Polymer/Impurity mixture:Chemical Potential of one monomer unit of polymer in amorphous phasePolymer is compatible with impurity but cant co-crystallize with impurity00uCuuuImmmm20212ln111uuRTxxmmEffects of “Impurities” on TmCondition of Phase Equilibrium00uICuuummmmSuperscript of C: Crystalline Pha

39、se0uCuuuumGHTSmm DDD00ummmmuHSTHTSDDDD02212ln111IuuRTxxmm22120ln1111mumRTTHxxTD02212ln11111mmuTTHRxxDSuperscript of I: Amorphous Phase01mumTHT DEffects of “Impurities” on Tm22120ln11111mmuRTTHxx DFor x2, x1=1211011mmuRTTH DFor end-group effects: 1=2/N, =00112mmuRTTHNDFor copolymer011lnmmuRPTTH Dalte

40、rnating copolymer: PXA 1P: Probability of crystalline unit with sequential connection 2221111211ln22uuRRHH DD211121ln 1ln2Note:For polymer blends220111mmuRTTH D22120212ln11111mmuRTTHxxx Dpolymer/small moleculepolymer/polymer3. Effects of Chain Structure on TmmmmHTSDD1) Symmetry and Asymmetry2) Flexi

41、ble and Rigid3) Molecular Interaction5.3 Oriented States of PolymersnDefinitionn nApplicationsn Fiber, BOPP, BOPET, BOPE, nOrientation function213 cos12F fully orientedfully disorder10perpendicular011/30F10-1/2 : 0180one or two dimensional order5.4 Liquid Crystalline Polymers “Liquid crystals stand

42、between the isotropic liquid phase and the strongly organized solid state. Life stands between complete disorder, which is death, and complete rigidity, which is death again.” Dervichian D. G. Mol. Cryst. Liq. Cryst. 1977, 40, 19. States of matter: Solids, liquids, and gases “Liquid crystals” (LCs)

43、represent a number of different states of matter in which the degree of molecular order lies intermediate between the perfect long-range positional and orientational order found in crystalline solid and the statistical long-range disorder found in an isotropic liquid. Phenomenologically, LCs exhibit

44、 both solid-like anisotropic features and liquid-like fluidity. On the basis of these characteristics, the term “mesomorphic phases” or “mesophases”, may be a more appropriate name than liquid crystals.What are Liquid Crystals Anisotropic molecular shape of liquid crystals Rod-like or ellipsoid-like

45、Space filling model of molecule 7S5 Plate-like or disk-like Lyotropic liquid crystals (溶致型液晶溶致型液晶):The liquid crystal phase is dependent on the concentration of one component in another. Thermotropic liquid crystals (热致型液晶热致型液晶):The liquid crystal phases of pure substance are caused by temperature c

46、hange.Nematic Phase (向列相向列相) Director NLong-range orientational order of moleculesMoleculesNnnnnnnn Molecular arrangement in a nematic phasePolydomain structure in a nematic phase. Local directors are represented by n, and the global director is represented by N.Smectic Phases (近晶相近晶相)Director NLaye

47、rsMolecules Layer structure in smectic phasesSmectic ASmectic CTilt AngleDirector N LayersMoleculesLiquid Crystal Phase of Chiral MoleculesStructure of chiral smectic or smectic C* phase. The planes represent the smectic layers. The director always makes the same angle with the smectic planes, but the orientation of the director rotates about the line perpendicular to the planes in going from one layer to the next. Cholesteric phase (胆甾相胆甾相) (chiral (手性手性) nematic phase)