1、Introduction to Polymer Physics,Prof. Dr. Yiwang Chen School of Materials Science and Engineering, Nanchang University, Nanchang 330047,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
2、 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 constan
3、t and T is temperatureStatic force usually ranges from 13 to 21 kJ/mol,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 o
4、f 1 和 2, their interactional potential is:Induced force usually ranges from 6 to13 kJ/mole,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,以上三种力统称范德华力，永久存在
5、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12个数量级。,氢键是极性很强的XH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（XH-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。,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
6、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。,2.2 The Amorphous state,Completely amorphous polymers like atactic polystyrene exist as long, randomly coiled, int
7、erpenetrating 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 re
8、ached 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 substitu
9、ent groups. These processes are called secondary relaxations.,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 visco
10、elastic properties, melt viscosity, and mechanical properties such as stress relaxation, creep, and craze formation.,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
11、motion (i.e., reptation) of the chain within a virtual tube.,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
12、 low-molecular-weight compounds or low-molecular-weight polymers crystallized from the solution.,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
13、 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 eac
14、h fold.,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 (gro
15、wth) 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.,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0.5至100微米，大的可以达到厘米数量级。球晶中分子链总是垂直于分子链球晶的半径方向。这说明球晶的基本结构单元仍然是具有折叠
16、链结构的片晶。以一定的方式扭曲，同时从一个中心向四面八方生长，发展成为一个球状的多晶聚集体。,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。,The anisotropic morphology of a spherulite results in the appearance of a characteristic extinction cross, or Maltese cross, when viewed under polarized light.,Conformations of Polymer Crystallite Hi
17、gh 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. Suc
18、h polymers include polyethylene, syndiotactic vinyl polymers, and polymers capable of hydrogen bonding between chains, such as poly(vinyl alcohol) and nylons.,In cases of polymers with large substituent groups, such as the methyl group in polypropylene, for most isotactic polymers, and for polymers
19、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
20、 two terms (i.e., 72 or 7/2 helix).,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 CC 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。,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
21、扭转构象。 当T 19时，旋转角为12，变成H157 的螺旋构象。,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。,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
22、构象。,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。,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
23、向是无规的。,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。,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。,2.5 Crystallization of Polymers,The chemical struct
24、ure 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
25、 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
26、 against favored.,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
27、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.,For example, cis-polyisoprene is amorphous, while more easily packed trans-poly
28、isoprene 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 (2C) compared to trans-1,4-poly(1,3-butadiene) (145C). In general, tactic polymers with their more stereo-regu
29、lar chain structure are more likely to be crystalline than their atactic counterparts.,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
30、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。,Crystallization Kinetics For a given polymer, the extent of crystallization attained during melt processing depends upon the rate of crystallization
31、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 c
32、rystallization, such as polyethylene, cannot be quenched quickly enough to prevent crystallization. For a given polymer, the rate of crystallization depends upon the crystallization temperature.,At Tm, the crystalline lamellae are destroyed as fast as they are formed from the melt and, the net rate
33、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 crystal
34、lization rate reaches a maximum is independent of molecular weight; however, the maximum crystallization rate decreases as the molecular weight increases.,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：,高聚物结晶速度温度的关系： 区 熔点以
35、下1030范围内，是熔体由高温冷却时的过冷区。 区 从区下限开始，向下3060范围内，该区内成核速度控制结晶速度。 区 熔体结晶生成的主要区域，Tmax 在该区。 区 结晶速度随温度迅速下降。,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
36、总速度。,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,Avrami Equation for
37、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
38、nature of nucleation and growth process.,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, includin
39、g infrared spectroscopy, density, X-ray diffraction measurements, and calorimetric methods, which will be described in next section.,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
40、核：n = 3 + 1 = 4 ； 异相成核：n = 3 + 0 = 3,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。,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
41、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。,影响结晶速度的其他因素 分子结构 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。 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。 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。,2.6 Techniques to Det
42、ermine Crystallinity,Density Measurement Density can be easily measured at some standard temperature (e.g., 23C) 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 densitie
43、s of a totally amorphous (a) and totally crystalline sample (c) are known or can be estimated.,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 crystalli
44、ne 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.,X-Ray Diffraction X-ray diffraction is widely used technique of polymer characterization that can prov
45、ide 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
46、 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
47、atoms in a polymer.,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 con
48、stant given as:where e (1.602210-19C) and m (9.109510-35 kg) are the charge and mass of an electron, respectively, and c is the speed of light (3.00108 m s-1).,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 in
49、vestigation 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
50、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.,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.,
