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1、Chapt 4 Molecular Weight and Molecular Weight Distribution of Polymers,4.1 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,4.3 分子量分布的测定方法,4.2.1 数均分子量的测定方法,4.2.2 重均分子量的测定方法,4.2.3 粘均分子量的测定方法,Molecular weight and molecular weight distribution,Distribution of molecular weights in a typical polymer,4.1 Definitions of Ave
2、rage MWs and MW Distribution,n: 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 fraction of ith molecule.,(1) Number-average molecular weight (数均分子量):,(2) Weight-aver
3、age molecular weight (重均分子量):,Schulz Tung Logarithm normal distribution,用简化的函数拟合,MW Distribution,Width of molecular weight distribution (分子量分布宽度):,Polydispersity (多分散系数):,MW Distribution Function,实验测量,平均分子量 分布宽度,4.2 Measurement of Molecular Weight,End group analysis (端基分析) molecular weight determina
4、tion 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) measurement: measure the number-average molecular weight Mn vapor-pressure lowing boiling-point elevati
5、on (ebulliometry) freezing-point depression (cryoscopy) osmotic pressure (osmometry),DTb, DTf, and P are the boiling-point elevation, freezing-point depression, and osmotic pressure. r is the density of the solvent. DHv and DHf are the enthalpies of vaporization and fusion.,Vapor-phase osmometry (VP
6、O, 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 vapor. Measure Mn that is too lower for membrane osmometry method. Calibrated with low-molecula
7、r 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.,Measurement chamber of VPO (Pasternak, 1962). Droplets of solvent and polymer solution are placed, wit
8、h 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 osmometry (膜渗透压法),Membrane osmometry (膜渗透压法),Diagram of the Zimm-myerson osmometer (Zimm 1946). A typical diameter for th
9、e measuring and reference (solvent cell) capillary is 0.5 - 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 plates,The assembled instrument is suspended
10、in a large tube partly filled with solvent,The success of 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 l
11、ight scattering (静态光散射),General set-up of a scattering (散射) experiment,Incident beam Intensity I0,Scattered beam Intensity I(q),Detector,Sample,Scattering vector (散射矢量):,where,: wavelength of the radiation,q,Theory of Light Scattering,Random Phase Approximation by de Gennes,For polymer/polymer mixtu
12、re,For Polymer Soultion,g: Structure factor of a single chain,A: Polymer B: Solvent,(1) small particles dl/20,I (SAi)2 SAi2,q,r,I0,I,(Rayleigh ratio)瑞利比,(2) large particles dl/20,I (SAi)2,q0,同时可测量出w, 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,(1),(2),c,Y,斜率2A2,sin2q/2,c1,c2,c3,Y,c,q1,q2,q3,Y,Y,斜
13、率,sin2q/2,The Zimm-Plot,2A2,1/Mw,Small angle laser light scattering,q 0,用光陷阱扣除中心光的干扰,Solution viscosity as a measure of polymer molecular weight,Mark-Houwink equation:,Flory-Fox equation：,For Newtonian fluids,Nomenclature (术语) of solution viscosity,hr: 粘度比(相对粘度); hsp: 粘度相对增量(增比粘度); hred: 粘数(比浓粘度); h
14、inh: 对数粘数(比浓对数粘度); h: 极限粘数(特性粘度),h: viscosity of polymer solution at temperature T h0: 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 shear rate。 Measurements o
15、f solution viscosity are usually made by comparing the effux time t (流出时间) required for a specified volume of polymer solution to flow through a capillary (毛细管) tube with the corresponding effux time t0 of the pure solvent.,If B/t is much small than At and r r0,Treatment of viscosity data,Huggins eq
16、uation:,If hsp 1, hr can be expressed by Taylor series expansion,Mark-Houwink equation:,Viscosity-average molecular weight (粘均分子量):,4.3 Measurement of MWD,Molecular weight dependence of phase diagram (相图),Polymer-solvent-nonsolvent system,Ternary phase diagram for a polymer-solvent-nonsolvent system, showing phase separation boundaries for the indicated values of x. The high molecular weight fractions will precipitat
