复旦_高物课件chapter4

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 MnMnMN 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 MMN

5、 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) m

6、olecular 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 l

7、owing 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 vaporizati

8、on 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 v

9、apor. 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.112212212

10、/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 osmo

11、metry (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 0.5

12、 - 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 t

13、he 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 scattering

14、(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 mixtureF

15、or 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 cRMMqq4sin2q22222181s

16、in.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用光

17、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: 粘数粘数

18、(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 and

19、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/tBAttBAtrrr0ttr001tt

20、trsp 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 1, r can be expressed by Taylor series expansion Mark-Houwink equation:Viscosity-average molecular weight(粘均分子量粘均分子量):aaiiiKc MKcM4.3 Measu

21、rement of MWDMolecular weight dependence of phase diagram (相图相图) Polymer-solvent-nonsolvent systemTernary phase diagram for a polymer-solvent-nonsolvent system, showing phase separation boundaries for the indicated values of x. The high molecular weight fractions will precipitate out first when the

22、amount of nonsolvent is increased.Adding nonsolvent into polymer solution may effectively change the value of 1.1/212CxMolecular Weight Fractionations (分子分子量分级量分级) of Polymers Column elution (柱淋洗柱淋洗)Solvent-gradient elution (溶剂梯度淋洗溶剂梯度淋洗) Thermal-gradient elution (温度梯度淋洗温度梯度淋洗)High Temp. Low Temp. Good SolventPoor Solvent Gel permeation chromatography (凝胶渗透色谱凝胶渗透色谱)Size exclusion (体积排除体积