Introduction to Polymer Physics

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1 Introduction to Polymer Physics
Prof. Dr. Yiwang Chen School of Materials Science and Engineering, Nanchang University, Nanchang

2 Chapter 2 Solid-state properties
2.1 Interaction of Molecules in Polymer van der Waals forces and Hydrogen bonding Static force is the force between polar molecules All polar molecules have permanent dipolar moment. The strength of static force between permanent dipoles depends on strength of dipolar moment and orientation degree. The interactional potential between two polar molecules with dipolar moment 1 and 2, and R of distance is: k is the Boltzman constant and T is temperature Static force usually ranges from 13 to 21 kJ/mol

3 Induced force is the interactional force between the permanent dipole of polar molecule and induced dipolar moment of another molecule induced by polar molecule. For two molecules with dipolar moment 1 and 2, and polarizability of 1 和 2, their interactional potential is: Induced force usually ranges from 6 to13 kJ/mole

4 Chromoscatter force is the interaction of instant dipolar moments of molecules.
It depends on ionization energy I, polarizability , and inter-distance R: It usually ranges from 0.8 to 8 kJ/mole

5 以上三种力统称范德华力，永久存在于一切分子之间的一种吸引力。这种吸引力没有方向性和饱和性。作用范围小于1纳米，作用能约比化学键小1－2个数量级。
氢键是极性很强的X－H键上的氢原子，与另一个键上电负性很大的原子Y上的孤对电子相互吸引而形成的一种键（X－H---Y）。 氢键有饱和性和方向性，氢键与化学键相似，键能比化学键小得多，不超过40千焦/摩尔。

6 Cohesive Energy Density
在高聚物中，由于分子量很大，分子链很长，分子间的作用力很大，高分子的聚集态只有固态（晶态和非晶态）和液态，没有气态。 高聚物分子间作用力的大小通常采用内聚能或内聚能密度来表示。内聚能定义为克服分子间的作用力，把一摩尔液体或固体分子移到其分子间的引力范围之处所需要的能量： E是内聚能，Hv是摩尔蒸发热（或摩尔升华热Hs），RT是转化为气体时所做的膨胀功。 内聚能密度（Cohesive Energy Density）是单位体积的内聚能： 为摩尔体积 对于低分子化合物，其内聚能近似等于恒容蒸发热或升华热，可直接由热力学数据估计其内聚能密度，而高聚物不能气化，不能直接测定它的内聚能，只能用低分子溶剂相比较的办法进行估计。

7 2.2 The Amorphous state Completely amorphous polymers like atactic polystyrene exist as long, randomly coiled, interpenetrating chains that are capable of forming stable, flow-restricting entanglements at sufficiently high-molecular-weight. In the melt, thermal energy is sufficiently high for long segments of each polymer chain to move in random micro-Brownian motions. As the melt is cooled, a temperature is reached at which all long-range segmental motions ceases. The characteristic temperature is called the glass-transition temperature, Tg. In the glassy state, at temp below Tg, the only molecular motions that can occur are short-range motions of several contiguous chain segments and motions of substituent groups. These processes are called secondary relaxations.

8 Chain Entanglements and Reptation
Polymer chains that are sufficiently long can form stable, flow-restricting entanglements. A good analogy can be made to a bowl of spaghetti. Entanglements have significant importance in relation to viscoelastic properties, melt viscosity, and mechanical properties such as stress relaxation, creep, and craze formation.

9 In the melt state, individual polymer chains can move by local Brownian motion restricted by the topological constraint of neighboring chains. Movement can be visualized as snakelike motion (i.e., reptation) of the chain within a virtual tube.

10 2.3 The Crystalline state Ordering of Polymer Chains
Under favorable conditions, some polymers cooled from the melt can organize into regular crystalline structures. Such crystalline polymers have less perfect organization than crystals of low-molecular-weight compounds or low-molecular-weight polymers crystallized from the solution.

11 The basic units of crystalline polymer morphology include crystalline lamellae consisting of arrays of folded chains. Reentry of each chain in the folded structure can be adjacent or nonadjacent. A chain participating in adjacent reentry can form a tight (or regular) loop or form a loose (irregular) loop. The thickness of typical crystallite may be only 0.1 to 0.2 nm, indicating that only a portion of the complete chain (e.g., 40 to 80 repeating units in the case of polyethylene) is involved in each fold.

12 For some polymers crystallized from the melt for from concentrated solution, crystallites can organize into large spherical structures called spherulites. Each spherulite contains arrays of lamellar crystallites that are typically oriented with the chain axis perpendicular to the radial (growth) direction of the spherulite. In a few cases, such as occurs in the crystallization of polypropylene, chain folding will occur with the chain oriented along the radial direction.

13 球晶 (Spherulites)：球晶是由无数微小晶片按结晶生长规律长在一起的多晶聚集体。球晶的直径可以达到0

14 球晶是由径向发射的微纤（fibrils）组成的，这些微纤就是长条状的晶片，其厚度在 10 ―20 纳米之间。

15 The anisotropic morphology of a spherulite results in the appearance of a characteristic extinction cross, or Maltese cross, when viewed under polarized light.

16 Conformations of Polymer Crystallite
High thermal energy favors a large number of conformations in the melt. As the melt is cooled, the lower-energy conformations are favored, and chains are free to organize into lamellar structure. For many polymers, the lowest-energy conformation is the extended chain or planar zigzag conformation. Such polymers include polyethylene, syndiotactic vinyl polymers, and polymers capable of hydrogen bonding between chains, such as poly(vinyl alcohol) and nylons.

17 In cases of polymers with large substituent groups, such as the methyl group in polypropylene, for most isotactic polymers, and for polymers of some 1,1-disubstituted ethylenes like polyisobutylene, the lowest-energy conformation is a helix of some preferred geometry. For the examples of polypropylene, three repeat units form a single turn in the helix (i.e., a 31 or 3/1 helix) In the case of polyoxyethylene, there are 7 repeat units per two terms (i.e., 72 or 7/2 helix).

18 全反式聚乙烯的构象 全反式聚乙烯呈平面锯齿状，这种构象能量低。以 C—C 键长为0.154nm，键角为109.5°计算，一个单体单元在键轴方向上的投影为0.252nm， 其应为两个靠得最近的H原子的距离，它大 于H原子范德华半径(0.12nm) 的两倍，因此，这种结构在能量上是合理的。

19 聚四氟乙烯的构象 　 H 被F取代，而F的范德华半径为0.14nm，其两倍0.28nm已大于0.252nm，如果聚四氟乙烯同样采取全反式构象，F原子就会出现拥挤，电子云互相排斥，这种排斥作用使得聚四氟乙烯被迫采取一种稍稍偏离全反式平面构象，呈现一种扭转构象。 　 当T < 19℃时，旋转角为14°，使整个分子呈H136 的螺旋构象。 　 当T > 19℃时，旋转角为12°，变成H157 的螺旋构象。

20 聚甲醛和聚氧化乙烯的构象 　 由于聚甲醛分子主链上有氧原子存在，其对应位置的空间位阻小，与全碳链不同，旁式构象的能量反而比反式构象的能量低, 其中COC 键角为112°，OCO 键角为111°，形成等同周期为1.73nm 的...gg...系列的H95螺旋构象。 聚氧化乙烯则形成等同周期为1.93nm 的...ttg ttg...系列的H72螺旋构象。 90-  (180-)/2

21 等规a – 烯烃分子链的构象 等规a – 烯烃的分子链，由于取代基的空间位阻，全反式构象的能量一般比反式旁式交替出现构象的能量高，所以，这类聚合物的分子链在晶体中通常采取交替出现的反式旁式交替构象序列的螺旋形构象。

22 聚丁二烯在结晶中的构象 聚丁二烯有四种异构体，其中反式 1, 4 – 聚丁二烯、顺式 1, 4 – 聚丁二烯和间规 1, 2 – 聚丁二烯都取主链接近平面锯齿形的全反式构象，而等规 1, 2 – 聚丁二烯取 H31 螺旋形构象。

23 2.4 Solid-State Model of Polymers
Crystalline Model of Polymer The fringed-micelle model 模型要点 高聚物只能部分结晶，具有晶区和非晶区两相同时并存的特殊结构； 每一个高分子链可以贯穿几个晶区和非晶区； 在非晶区，分子链是卷曲且互相缠结的，在晶区，分子链互相平行排列形成规整结构； 晶区的取向是无规的。

24 The loose fold-chain folded model
在结晶高聚物的片晶中，仍以折叠的分子链为基本结构单元，折叠处松散而不规则， 但在晶片中分子链仍是相邻排列的。 在多层片晶中，分子链可以跨层折叠，在一层晶片中折叠几个来回之后，再到另一层中去折叠，使层片之间存在联结链。

25 The power panel model 折叠链部分是由多条链组成的，而且它们的排列是任意的，相邻链属于不同的分子链。
形成多层片晶时，一条分子链可以从一个晶片，通过非晶区进入到另一个晶片中去。

26 2.5 Crystallization of Polymers
The chemical structure and Crystallization In general, symmetrical chain structures, which allow close packing of polymer molecules into crystalline lamellae and specific interactions between chains that favor molecular orientation, favor crystallinity. For example, linear polyethylene and polytetrafluoethylene, which have symmetrical substituted repeating units, are highly crystalline. Atactic poly(vinyl chloride) (PVC) with its asymmetrically placed chlorine is highly amorphous. When two chlorine atoms are symmetrically located on the same carbon atom, as they are in poly(vinylidene chloride), crystallinity is against favored.

27 Although atactic-PVC is amorphous, atactic-poly(vinyl alcohol) is partly crystalline because of the occurrence of specific interchain interactions (i.e., hydrogen bonding). Specific interactions are particularly important in enhancing crystallinity in the case of nylons, for which hydrogen bonds can form between an amide carbonyl group on one chain and the hydrogen atom of an amide group on an adjacent chain. Both tacticity and geometric isomerism (i.e., a trans configuration) favor crystallinity.

28 For example, cis-polyisoprene is amorphous, while more easily packed trans-polyisoprene is crystalline. Although cis-1,4-poly(1,3-butadiene) is partly crystalline, its crystalline form is less stable than the preferred trans configuration, as indicated by its lower Tm (2C) compared to trans-1,4-poly(1,3-butadiene) (145C). In general, tactic polymers with their more stereo-regular chain structure are more likely to be crystalline than their atactic counterparts.

29 高分子结构与结晶能力 结构对结晶能力的影响： 1. 链的对称性：高分子链结构的对称性越高，越容易结晶。 主链全部是碳原子：聚乙烯和聚四氟乙烯，聚偏二氯乙烯和聚异丁烯。 主链含杂原子：聚甲醛、聚醚、聚酯等。 2. 链的规整性：高分子链的规整性越高，越容易结晶。 主链含不对称中心的高聚物：等规度高，结晶能力大。 存在顺反异构的二烯类聚合物：反式构象聚合物大于顺式构象聚合物。 3. 共聚物的结晶能力：共聚会破坏链的规整性，使结晶能力下降。 4. 其他结构因素： 链的柔顺性：柔顺性不好，会降低聚合物的结晶能力。 链的支化：支化使链的对称性和规整性受到破坏，导致结晶能力下降。 交联度：随着交联度的增加，高聚物会迅速失去结晶能力。 分子间力：分子间力使链的柔顺性降低，会影响结晶能力。但分子间如形成。氢键，将有利于结晶结构的稳定。

30 Crystallization Kinetics
For a given polymer, the extent of crystallization attained during melt processing depends upon the rate of crystallization and the time during which melt temperatures are maintained. Above Tm, some polymers that have low rates of crystallization, such as poly(ethylene terephthalate), polycaprolactone, and nylon-6,6 can be quenched rapidly enough to achieve an amorphous state. Other polymers having much higher rates of crystallization, such as polyethylene, cannot be quenched quickly enough to prevent crystallization. For a given polymer, the rate of crystallization depends upon the crystallization temperature.

31 At Tm, the crystalline lamellae are destroyed as fast as they are formed from the melt and, the net rate of crystallization is zero. Since the large-scale segmental mobility required for chain folding ceases at Tg, the crystallization rate is again zero. At some intermediate temperature, Tmax, an optimum balance is reached between chain mobility and lamellae growth. The temperature at which the crystallization rate reaches a maximum is independent of molecular weight; however, the maximum crystallization rate decreases as the molecular weight increases.

32 Crystallization Rate and Temperature Relationship
高聚物的结晶范围在 Tg 与Tm 之间，在适当温度下，结晶速度会出现极大值。 Tmax 可以用 Tg 和 Tm 来估算： 也可以仅从 Tm 进行估算：

33 高聚物结晶速度—温度的关系： Ⅰ区 熔点以下10–30℃范围内，是熔体由高温冷却时的过冷区。 Ⅱ区 从Ⅰ区下限开始，向下30–60℃范围内，该区内成核速度控制结晶速度。 Ⅲ区 熔体结晶生成的主要区域，Tmax 在该区。 Ⅳ区 结晶速度随温度迅速下降。

34 结晶速度及其测定方法 高聚物的结晶过程与小分子相似，包括晶核的形成和晶粒的生长两个步骤，结晶速度包括成核速度、结晶速度和由它们共同决定的结晶总速度。 成核速度：用偏光显微镜、电镜直接观察单位时间内形成晶核的数目。 结晶生长速度：用偏光显微镜、小角激光散射法测定球晶半径随时间的增大速度，即球晶的径向生长速度。 结晶总速度：用膨胀计法、光学解偏振法等测定结晶过程进行到一半所需的时间 t1/2 的倒数作为结晶总速度。

35 Techniques to Determine the Rate of Crystallization
The rate of crystallization can be followed by a variety of techniques, such as: Dilatometric measurement of volume changes; Infrared spectroscopy Optical-microscopic measurement of the growth of spherulite radii with time

36 Avrami Equation for Crystallization
During the crystallization process, the fractional crystallinity, , at time t may be approximated by the Avrami equation: Where k is a temperature-dependent growth-rate parameter and n is a temperature-independent nucleation index. Typically, n varies between 1 and 4 depending on the nature of nucleation and growth process.

37 For example: In the case of sporadically nucleating spherulites, as may result during quiescent melt crystallization near Tm, the nucleation index is approximately 4. The fractional crystallinity of polymer can be determined by variety of techniques, including infrared spectroscopy, density, X-ray diffraction measurements, and calorimetric methods, which will be described in next section.

38 Avrami 方程用于高聚物的结晶过程 高聚物的等温结晶过程，常用Avrami 方程来描述： 当收缩率 半结晶期 结晶的成核机理： 均相成核：由熔体中的高分子链段靠热运动形成有序的链束作为晶核。 异相成核：是以外来的杂质、未完全熔融的残余结晶聚合物、分散的小颗粒固体或容器的壁为中心，吸附熔体中的高分子链作有序排列而形成晶核。 均相成核：n = = 4 ； 异相成核：n = = 3

39

40 Techniques to determine rate of crystallization
Dilatometric measurement: 利用高聚物结晶时分子链作规整紧密堆砌时发生的体积变化，跟踪测量结果中的体积收缩，来研究结晶过程。 规定体积收缩进行到一半所需时间的倒数 1/t1/2 作为实验温度下的结晶速度。

41 Optical depolarization: 利用光学双折射性质来测定结晶速度的方法。解偏振光强度与结晶度成正比。
Polarized optical microscope: 可在等温条件下观察高聚物球晶的生长过程，测量球晶的半径随时间的变化。等温结晶时，球晶的半径与时间成线性关系。

42 影响结晶速度的其他因素 分子结构 ⑴ 结构简单的分子：例如，聚乙烯、聚四氟乙烯 链的对称性、立体规整度越高，取代基的空间位阻越小，链越柔顺，结晶速度越大。 ⑵ 含极性基团，特别是能形成氢键的高聚物：例如，聚酰胺 结晶速度稍慢于聚乙烯。 ⑶ 分子链带有庞大侧基或主链含有苯环、共扼双键的高聚物： 空间阻碍或链段刚性越大，结晶速度越慢。 分子量：分子量越大，其结晶速度越慢。 杂 质：杂质对结晶过程的影响有双重性。 溶 剂：有些溶剂能促进结晶过程。 应 力：应力有加速结晶过程的作用。

43 2.6 Techniques to Determine Crystallinity
Density Measurement Density can be easily measured at some standard temperature (e.g., 23C) by means of a calibrated density-gradient column. Once the density () of the semicrystalline sample has been measured, the fractional crystallinity, , can be determined as: If the densities of a totally amorphous (a) and totally crystalline sample (c) are known or can be estimated.

44 Generally, values of amorphous densities are available only for semicrystalline polymers with low crystallization rates that enable rapid quenching from the melt to a totally amorphous state. The crystalline densities of polymers can be obtained from density measurements of single crystals or crystalline low-molecular-weight analogs or may be determined from X-ray determination of crystal densities.

45 X-Ray Diffraction X-ray diffraction is widely used technique of polymer characterization that can provide information concerning both the crystalline and amorphous states. X-rays are high-energy photons having short wavelengths (0.05 to 0.25 nm) that interact with electrons. When a X-ray beam is focused on a material, some electrons will be absorbed, some will be transmitted unmodified, while others will be scattered due to interaction with electrons. This interaction results in scattering pattern that is a function of the scattering angle, usually designated as 2 for convenience. The scattering pattern provides information on the electron-density distribution and, therefore, the positions of atoms in a polymer.

46 The relationship between the intensity of an (unpolarized) X-ray beam, I0, the scattered intensity, I, and the scattering angle is given by the Thomson formula: r is the distance between the electron and the detector at which the scattered-beam intensity is measured and K is a constant given as: where e (1.602210-19C) and m (9.109510-35 kg) are the charge and mass of an electron, respectively, and c is the speed of light (3.00108 m s-1).

47 Terms often used in X-ray scattering are wide-angle X-ray scattering (WAXS) and small-angle X-ray scattering (SAXS). WAXS is used for the investigation of small-scale structures (<1 nm) while SAXS is used to study large-scale morphological features (1 to 1000 nm). WAXS is used for the determination of fractional crystallinity as well as crystalline dimensions. In WAXS diffraction pattern of crystalline polymer, the background pattern is due to scattering from amorphous regions (the amorphous halo), while the peaks, called Bragg peaks, represent scattering from well-defined crystalline regions having regular spacing.

48 Where fcw is the weight fraction of the crystalline phase.
In many cases, the fractional crystallinity can be estimated by comparing the intensity or height of the amorphous halo (Iam) of the crystalline sample with the intensity (Iam0) of a totally amorphous polymer as sometimes can be obtained by rapid quenching from the melt as: Where fcw is the weight fraction of the crystalline phase. Ac衍射曲线下晶区衍射峰面积 Aa衍射曲线下非晶区衍射峰面积 K校正因子，为了比较可以设定为1，对于绝对测量需要测定

49 量热法 H和H0分别为聚合物试样的熔融热和100%结晶试样的熔融热。
晶粒尺寸 利用X射线衍射曲线可以测定晶粒尺寸，根据Scherrer公式 D(hkl) －(hkl)法线方向的平均尺寸，nm; k －Scherrer 形状因子(0.89)  －(hkl)晶面衍射峰的半高宽（弧度）

50 Fractional Crystallinity
The weight fraction of the crystalline phase: The volume fraction of the crystalline phase: 如果采用两相球棒模型，并假定比容有加和性，则部分结晶的高聚物试样的比容等于晶区的比容与非晶区的比容的线性加和： 从密度的线性加和假定出发：

51 2.7 The Fractional Crystallinity and Physical Properties
Mechanical properties 聚合物的非晶区有玻璃态和橡胶态之分。 ⑴ 弹性模量和硬度：Tg 以下，结晶度的影响不大； Tg 以上，高聚物的模量和硬度随结晶度的增加而升高。 ⑵ 脆性： Tg 以下，高聚物随结晶度的增加而变得很脆。 ⑶ 抗张强度： Tg 以下，随结晶度的增加抗张强度下降； Tg 以上，结晶度增加抗张强度提高，断裂伸长缩小。 ⑷ 蠕变和应力松弛：结晶度增加使蠕变和应力松弛降低。

52 2. Density and Optical Properties
⑵ 光学性质：两相并存时，通常呈乳白色。结晶度减小透明度增加。 3. Thermal properties 塑料不结晶或结晶度低，最高使用温度是玻璃化温度 当结晶度达到40%，Tg以上不软化，最高使用温度是熔点

53 4. Process-Structure-Crystalline Properties
结晶高聚物的物理和化学性质与结晶度、结晶形态及结晶在材料中的织态结构有关，而这些结构的变化又与加工成型的条件密不可分。例如：聚三氟氯乙烯的熔点为210℃ 。如果缓慢冷却，结晶度可达85—90% ，如果淬火，结晶度只有35—40% 左右。

54 5. Molecular weight and Fractional Crystallinity
分子量大于某一数值以上的样品，结晶度随分子量增加而单调下降，直到分子量很高，最后趋于某一极限值。

55 2.8 Thermodynamics of Crystallization
Since no polymer is completely crystalline, even the most crystalline polymers like high-density polyethylene have lattice defect regions that contain unordered, amorphous material. Crystalline polymers may exhibit, therefore, both a Tg corresponding to long-range segmental motions in the amorphous regions and a crystalline-melting temperature, or Tm, at which crystallites are destroyed and an amorphous, disordered melt is formed.

56 Fundamental Thermodynamic Relationships
Many of the commonly used techniques to determine Tg and Tm can be understood on the basis of the thermodynamic definition of a phase transition originally proposed by Paul Ehrenfest in 1933. A first-order transition is defined as one for which a discontinuity occurs in the first derivative of the Gibbs free energy (G). According to the first law of thermodynamics for a reversible, closed system, the Gibbs free energy can be expressed in differential form as a function of temperature and pressure, G(T, p), as: dG=-SdT+Vdp, where S is entropy and V is the system volume.

57 The free energy may be differential with respect to temperature (at constant pressure) as
and with respect to pressure (at constant temperature) as In terms of describing transitions in polymer systems, the most useful of the preceding relationships is the first derivative with respect to p, which indicates that a first-order transition should occur as a discontinuity in volume. Volume is easily measured as function of temperature by technique called dilatometry. The dependence of volume on temperature in the region about the crystalline-melting temperature approximates such a transition.

58 Melting and Melting Temperature
熔限：结晶高聚物的熔融过程，有一个较宽的熔融温度范围，这个温度范围称为熔限。 1. 高聚物的熔融过程是不是热力学的一级相转变过程？ 2. 结晶高聚物的熔点如何确定？ 3. 如何解释结晶高聚物特有的熔融过程？

59

60 Techniques to Determine Melting Temp
膨胀法：基于熔融过程中比容随温度的变化。(Dilatometry) 差热分析法：基于熔融过程中热效应的变化。(DTA) 差动扫描量热法：定量测定熔融过程中热效应。(DSC) 偏光显微镜法：结晶熔融时双折射消失。(Optical polarized microscopy) 其它方法：x-射线衍射，红外光谱，核磁共振等。(XRD, IR, NMR) Will be discussed together with glass transition later…

61 Crystallization Temp and Melting Temp
结晶高聚物的熔点和熔限与结晶形成的温度有关。一般结晶温度愈低，熔点愈低且熔限愈宽；相反，在较高的温度下结晶，则熔点愈高，熔限愈窄。

62 Thickness of lamellae and Melting Temp
结晶的熔点随晶片厚度的增加而增加。一般，晶片厚度对熔点的影响与结晶的表面能有关。晶片厚度越小，单位体积内的结晶物质与完善单晶相比，将具有较高的表面能。因此，晶片厚度较小的和较不完善的晶体，比晶片厚度较大的和较完善的晶体的熔点要低些。

63 Stretching and Melting Temp
对于结晶高聚物，拉伸能帮助高聚物结晶，结果提高了结晶度，也提高了熔点。 结晶过程的自由能： 过程的 T>0，S<0 要使 G<0，必须使  H<0，而且要使  H>T  S。 所以要使过程自发进行，只有两种可能性：1. 降低 T； 2. 降低   S 。 在熔点温度时，晶相与非晶相达到热力学平衡，  G=0， 则：Tm=  H/  S 拉伸使熵减小，熔点提高。

64 Structure-Property Relationships
Both Tg and Tm are strongly influenced by the chemical structure of the repeating unit. In general, both Tg and Tm increase with decreasing flexibility of the polymer chain. Flexibility decreases with increasing aromatic composition of the main chain or by incorporation of bulky substituent groups or nonrotational (e.g., unsaturated) groups in the main chain.

65 1. 聚－－烯烃：随取代基的空间位阻增大，主链内旋转位阻增加，分子链的柔顺性降低，熔点升高。

66 当正烷基侧链的长度增加时，体积增大，影响了链间的紧密堆砌，使熔点下降。
当侧链长度继续增加时，会使熔点回升。

67 当取代基为体积庞大基团时，由于内旋转的空间位阻，使分子链刚性增加，熔点升高。这类取代基的空间位阻越大，熔点升高越多。

68 2. 脂肪族聚酯、聚酰胺、聚氨酯和聚脲：这类聚合物随重复单元的增加，逐渐趋于聚乙烯的熔点。
熔融热不能笼统与分子相互作用相联系，因为熔融热不同于内聚能，熔融过程是固液转变，熔融热是熔融前后分子间相互作用量度。 聚酰胺熔融前后氢键依然存在，熔点升高是由于分子间相互作用导致构象减少导致。 这类熔点变化随重复单元中碳原子个数奇偶变化。

69 3. 主链含苯环或其它刚性结构的高聚物：主链含有环状结构或共扼结构的聚合物，都使链的刚性增加，具有比对应的饱和脂肪链聚合物高得多的熔点。

70 对位芳族高聚物的熔点比相应的间位芳族高聚物的熔点要高。
4. 其它聚合物： 聚四氟乙烯，熔点为327℃ 。 二烯类的1,4 – 聚合物都具有较低的熔点。

71 Melting Temp of Copolymers
当两种单体形成共聚物时，有两种可能情况： 形成的共聚物本身不结晶 形成的共聚物能结晶，但不能进入原聚合物的晶格形成共晶。 对于无规共聚物： 嵌段共聚，P>>XA ，当其趋于1 时，熔点降低很小。 交替共聚物，P<<XA ，熔点将发生急剧降低。

72

73 Influence of Impurity melting Temp
杂质使低分子晶体熔点降低， 对于结晶高聚物，各种低分子的稀释剂（包括增塑剂、未聚合物单体、填充剂）造成熔点降低： 可见良溶剂比不良溶剂使聚合物熔点降低的效应更大 如果把链端当作杂质处理，高分子的分子量对熔点的影响可以表示为： Pn 是高聚物的数均聚合度。 当分子量较大时，链端的数目很小，对熔点影响有限； 当分子量较小时，这种影响不可忽略。

74 2.9 Orientalization of Polymers
取向：由于高分子链的几何不对称性，在外电场的作用下，分子链将沿着外电场的方向排列，这一过程就是取向。分子链的取向现象包括分子链、链段及结晶高聚物晶粒的定向排列。 取向有两种方式，即单轴取向和双轴取向。 (Uniaxial orientation and diaxial orientation)

75 Orientalization Mechanism of Polymers
链段取向 非晶态高聚物的取向{                                         分子取向                                     非晶区的取向（链段、分子的取向） 结晶高聚物的取向{                                     晶区的取向（晶粒的取向)

76 Orientation Index and Techniques to Determine it
取向度一般用取向函数表示： 实际取向试样的平均取向角为： Techniques to determine orientation index 1. Sonic transmission

77 2. Optical Birefringence
3. Wide angle X-ray diffraction 随取向度增加，环形衍射变成圆弧并逐渐缩短，最后成为衍射点，以圆弧的长度的倒数表示微晶取向度的量度。

78 2.10 Liquid-Crystallinity of Polymers
液晶态：具备液态物质的流动性，同时也部分地保存着晶态物质分子的有序排列，在物理性质上表现出各向异性，形成一种兼有晶体和液体的部分性质的过渡状态，该中间态为液晶态。 形成液晶的物质所应具备的条件： 具有刚性的分子结构，具有在液态下维持分子的某种有序排列所需的凝聚力，分子结构上必须含有一定的柔性基团。 Clear point: The transition from anisotropic to isotropic state, it belongs to first-order thermal transition. Liquid-crystalline polymers are classified by formation condition: Thermotropic liquid-crystalline Polymers and Lyotropic liquid-crystalline polymers)

79 Liquid-Crystalline Polymers are classified into Sematic, Nematic, and Cholesteric liquid-crystalline polymers in terms of liquid-crystalline structure.

80 Electric and Magnetic Field Effects
Liquid Crystal Phases Smectic Phase Nematic Phase Cholesteric Phase Discal Phase Banana Phase Properties of LC Electric and Magnetic Field Effects Polarization Birefringence Electric Forces Orientation Light Polarization

81 Polymeric Liquid Crystals
Main-chain liquid crystal polymers Side-chain liquid crystal polymers Terminally attached Laterally attached Combined liquid crystal polymers

82 作业： P330: (8); (11); (13) （1）实验测量含有不同量-氯代萘的一组线型聚乙烯试样的熔点，得到的数据如下：
如果非晶聚乙烯和-氯代萘的密度分别为0.8 gcm-3和1.1 gcm-3，估算聚乙烯的熔融热和聚乙烯与-氯代萘的相互作用参数。 0.00 0.06 0.16 0.32 0.52 0.75 0.95 (C) 137.5 134.5 131 125 120 115 110 -氯代萘的体积分数 聚乙烯的熔点 (2) 聚对苯二甲酸乙二酯的平衡熔点 =280℃ ，熔融热ΔHu=26.9千焦/摩尔重复单元，试预计分子量从10000增大到20000时，熔点将升高多少度？ 作业： P330: (8); (11); (13)