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1、1.Size exclusion chromatography (SEC) is used to determine the molar mass distribution of polymers. SEC is not an absolute method. It requires calibration. Narrow molar mass fractions of atactic polystyrene are commonly used for calibration. The time for a given molecular species to flow through the

2、 column is dependent on the hydrodynamic volume of the molecule. It has been shown that the hydrodynamic volume is proportional to the product of the intrinsic viscosity and the molar mass M. The Mark-Houwink equation relates the two quantities according to:where K and are constants unique for a giv

3、en combination of polymer, solvent and temperature. Derive the relationship between the molar masses of the polymer studied and of atactic polystyrene for a given eluation time.解:At equal eluation time conditions the following expression holds: where X and PS are indices for the studied (X) polymer

4、and polystyrene. Insertion of the Mark-Houwink equation yields: which after taking logarithms and simplification gives: 2.It is well known that polyvinylchloride (PVC) is not miscible with its own monomer (VC). This gives the polymer a characteristic particle structure which remains even after melt-

5、processing and leads to poor mechanical properties. The solubility parameters of PVC are: , , , (Barton 1983). The solubility parameter values of VC are: , , . Confirm that PVC is immiscible with VC on the basis of these data.（）解:Calculate first the distance between PVC and VC in three-dimensional s

6、olubility space;keep in mind that the dispersion values should be doubled:It is thus predicted that PVC should be insoluble in VC.3.有一块iPP试样，体积为1.422.960.5cm3, 重为1.94g。计算这块试样的结晶度?(i指isotactic)已知：amorphous polypropylene的比容晶胞参数a=6.66, b=20.37 , c=6.49 ,每一晶胞内有12个单体单元。结晶部分体积分数: ,晶胞密度公式: 解:是试样中结晶部分的体积分数:

7、 有, 晶胞属斜方晶系 晶胞体积 4.The glass transition temperature of polyisobutene is Tg = 202K. The characteristic values C1、C2 are taken as C1 = 16.6, C2 = 104K in its WLF equation. If one modulus measured at 80 0C for1 hour is equal to the other modulus at certain temperature and measured for 10-6 hour. At whi

8、ch temperature is the modulus measured?解:Let T2 be the measuring temperature, and Ts = Tg = 202K be the reference temperature，then C1 = 16.6 K，C2 = 104K. According to the WLF equation, it is known that:, where , and thus Substituting the known data in the above equation,By solving the equations （1）

9、and（2）, T2 = 239.82 K, i.e., 33.3 0C is obtained.5.The rubber in a blown-up balloon is stretched in a biaxial fashion. Derive the force-strain relationship under the assumption that the rubber follows the Gaussian statistical theory of rubber elasticity.解:The general expression for the free energy i

10、s:Biaxial stretching under constant volume yields the following deformation matrix:andThe force (f) is obtained by taking the derivative of :6.Calculate the average end-to-end distance for polyethylene with M=107 g mol-1 at 140 under theta conditions. Compare this value with the contour length of th

11、ese molecules.解：For PE, the equation relating number of carbon atoms (n) and end-to-end distance (r) is given by :The number of carbons is g mol-1; l is 0.127 nm: The contour length of the chain is： The ratio becomes： 7.从大量聚合物的c、a数据归纳得到： c/a1.13。若晶区与非晶区有线性加和性，试证明下列粗略估计聚合物密度与体积结晶度fcV的关系式成立：/a10.13 fcV证：fcV（ -a）/(c-a)=(/a-1)/(c/a-1)=(/a-1)/(1.13-1) /a10.13 fcV