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1、Polymer Physics高分子物理,2 Aggregate Structure of Polymers高分子聚集态的结构,2.1 Introduction,引言,2.1.1 Concept of aggregate state 聚集态结构的内涵,Aggregaste state Arrangement and stacking of different polymer chains. Aggregaste state includes 晶态 Crystalline state 液晶态 Liquid crystalline state 非晶态 Amorphous state 取向态 Ori
2、entation state,2.1.2 Interactions between polymer molecules 高分子的分子间作用力,covalent bond interaction non-covalent bond van de Walls force H bond,高分子由于分子间的相互作用而堆砌在一起,Electrostatic force(静电力): 1.21042.1104 J/mol Induction force(诱导力)： 0.61041.2104 J/mol Dispersion force(色散力)： 0.081040.84104 J/mol,偶极矩,极化率,电
3、离能,分子间距离,van de Walls force,Total van de Walls force: 28 kJ/mol CC bond energy: 347 kJ/mol,Assuming：PEs DP=104 ， Intermolecular interaction force: Ef 2*104 kJ/mol CC bond energy: EJ=347 kJ/mol EfEJ When a single PE chain is pull out, 2*104kJ/mol energy (van de Walls force) must be overcome，which can
4、 lead to breakage of C-C single bond. So, no vapor state for polymer.,Interaction force between the H atom in XH bond and another Y atom with large electronegavity. Electronegativity： H:2.1 O:3.5 N:3.0 F:4.0 Strength：1535 kJ/mol Features：directivity and saturability XHY,Hydrogen bond 氢键,2.1.3 Cohesi
5、ve energy density高分子的内聚能密度,Cohesive energy ：The energy to remove 1 mol liquid or solid molecules out of the range of intermolecular interaction force.,HV: 摩尔蒸发热,Cohesive energy density： Cohesive energy in unit volume.,HS:摩尔升华热,( : 摩尔体积),Cohesive energy density of linear polymers,Rubber,Plastics,Fibe
6、r,2.2 The Crystalline State,高分子的晶态结构,Difference bewteen crystallization of polymers and small molecules: Polymer is not 100% crystalline! crystallinity (结晶度)： faction of crystalline phase weight percentage crystallinity volume percentage crystallinity,1a,2a,2b,3a,3c,A,B,C,AB + BC = 2dsinq,2dsinq = n
7、l,2.2.1 Methods of determining crystallinity,wide angle X-ray diffraction (WAXD) X衍射,Bragg equation,Distance between successive identical planes of atoms in the crystal,X-ray wavelength,Angle between the x-ray beam and these atomic planes,Any whole number,样品,差式扫描量热法 (DSC) Differential scanning calor
8、imetry,(Xcw%),(i) Xcv,Measured by density,(ii) Xcw,Determination of Density,Ni: number of ith atom in unit cell Ai: atom mass of ith atom in unit cell Ve : volume of unit cell NA: Avgadrov constant,c is calculated from the density of unit cell of polymer crystal：,Notice： The values of crystallinity
9、measured by different methods may have a large difference. Usually： XcWAXD () Xcdensity XcDSC,2.2.2 Unit cell and conformation of polymer chain in crystals,spherulite fibrillar branching helical lamellae within fibrils 1 mm(POM) 1 m(AFM) 500 (AFM, TEM),crystal latticeindividual lamellar stacks 1 (WA
10、XD) 100 (SAXS),Unit cell (晶胞)：The smallest repeating unit of crystal structure with parallelepiped shape,a,b,c,高分子无此晶系,c axis:polymer chain direction,Miller indices (h k l),(1) intercept of crystalline plane in axes,(2) removal of unit，getting reciprocal and reduction to common denominator,(3) remov
11、al of denominator,a=2d200,Selected crystallographic data,For polymer chains with no side group (PE) or with side group of small size (polyester，polyamide，POM，PVA). Polymer chains adopt all-trans conformation. The lowest energy of polymer chains. Advantageous to dense packing in crystals.,plane zigza
12、g(平面锯齿结构),PE Orthorhombic 正交晶系,Unit cell of PE: Orthorhombic, a=7.417, b=4.945, c=2.547 Number of C and H atoms in unit cell？ Ve 9210-24 cm3; NA = 6.0231023 mol-1 c 1.01 g/cm3,The hydrogen-bonded structure of nylon 66. The unit cell face is shown dotted,Helix(螺旋形结构),For polymer chains with side grou
13、p of large size, gauche conformation sometimes is adopted to reduce steric hinderance and free energy. For example： isotactic PP(H31), poly(o-methyl styrene)(H41), isotactic PMMA(H52)， isotactic poly(4-methyl pentene-1) (H72), poly(m-methyl styrene)( H11 8).,Isotactic PP The polymer chains are not i
14、n the same plane, but exhibit a helix conformation in the three-dimensioal space. Every three repeating units forms a helix with a periodic length l6.50. H31: H：Helix 3：number of repeating units 1：number of turns within a period,iPP(等规聚丙烯)：Monoclinic 单斜,2.2.3 Models of crystalline polymers高分子晶态结构模型,
15、The Fringed Micelle Model 缨状微束,Crystalline phase,Amorphous phase,100,Contour length = 2000,Bryant 1940,Atactic PP,Isotactic PP,Al,Observation：Both diffraction pattren and diffused circle are observed. The measured size of crystalline domain is about hundred astrongs (much smaller than the length of
16、polymer chain) Model： cocurrence of crystalline and amorphous domains small size of crystalline domain (one polymer chain can traverse several crystalline domains) random orientation of crystalline domains Reasonable： The apparent density density of unit cell melting range due to different sizes of crystalline domains Arc diffr
