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 6 Molecular Motion of Polymer 6.1 Thermal Motion of Polymer
一 、The Major Characteristic of Polymer Molecular Motion 1. Multiplicity of motion units（运动单元的多重性 ) 整链运动 (Whole chain) 链段运动 (Chain segment) 链节运动 (Chain node) 侧基运动 (Side chain)

3 2. Thermal Motion is Relaxation Process (高分子热运动是松弛过程)
在外界条件下，物质从一种平衡态通过分子热运动而过渡到另一种平衡状态需要一定的时间，这个时间称为松弛时间，用  表示。(Relaxation time) 对于具体的松弛过程： 松弛时间 是x(t) 变到等于 x0 的 1/e 倍时所需的时间。 松弛时间与运动单元大小和温度有关。

4 3. Thermal Motion dependent on Temperature (高分子的热运动与温度有关)
温度升高对高分子热运动的影响有两方面： 使运动单元活化 使高聚物发生体积膨胀 高聚物的次级松弛过程，松弛时间与温度的关系为： Eyring Theory 玻璃化转变过程的松弛时间与温度的关系： 符合 WLF 半经验方程

5 二、 Mechanical State and Thermal Transition (高聚物的力学状态和热转变)
1.非晶态高聚物 三种力学状态： 玻璃态 (Glass state) 高弹态 (Rubber state) 粘流态 (Fluid state) 两个转变： 玻璃化转变温度(Tg) (Glass transition temperature) 粘流温度(Tf) (Viscous fluid temperature)

6 2. 晶态高聚物： 结晶高聚物的宏观表现与结晶度有关。 ⑴. 轻度结晶的高聚物 ⑵. 结晶度大于40%的高聚物 ⑶. 当分子量较小时，Tf < Tm ⑷. 当分子量较大时，Tf >Tm 轻度结晶聚合物 结晶聚合物

7 6.2 The Glass Transition The phenomenon and measurement of the glass transition 玻璃化转变现象 玻璃化温度的测量 (Glass transition temperature) 利用体积变化的方法 ( According to volume change)) Dilatometer

8 利用热力学性质变化的方法 (Thermodynamic properties)
差热分析 (DTA)

9 示差扫描量热仪 (DSC)

10 利用力学性质变化的方法 (Mechanical properties)
利用电磁性质变化的方法 (Electromagnetic properties) 静态测量温度-形变曲线 动态力学测量方法：扭摆法、扭辫法、 强迫振动共振法、强迫振动非共振法（动态粘弹谱仪） 介电松弛谱仪

11 One view is that the glass transition marks an isoviscous state
One view is that the glass transition marks an isoviscous state. This means that, as a polymer is cooled from its melt state, viscosity increases rapidly to a common (maximum) value, ca Pa-s (1013 poise) at Tg, for all glassy materials-both low-molecular-weight and polymeric.

12 A second view is that the glass transition represents a state of isofree volume. Free volume, Vf, may be defined as the difference between an actual volume (or specific volume), V, of the polymer at given temperature and its equilibrium volume at absolute zero, V0, The volume at absolute zero can be approximated by the sum of the van der Waals volumes of each chain segment, which can be easily obtained by group-contribution methods.

13 The concept of free volume has significant importance for a number of other related subjects in polymer science, including time-temperature superposition of viscoelastic properties, melt viscosity, and permeability. The glass-transition temperature of amorphous polymers can vary widely with the chemical structure of the polymer chain. In general, polymers with flexible backbones and small substituent groups have low Tg, while those with rigid backbones, such as polymers containing main-chain aromatic groups, have high Tg.

14 The Theories for the Glass Transition
1. Free volume theory When T  Tg ： When T < Tg ：

15 WLF方程定义的自由体积 Doolittle 方程

16 2. Thermodynamical theory
The glass transition approximates an Ehrenfest second-order transition. This means that a discontinuity should be observed in the second derivatives of the Gibbs free energy. Three possible second derivatives can be used to provide a basis for the experimental measurement of Tg.

17 (1) (2) (3) Since entropy is not an experimentally measurable quantity, eq.(1) may be recast into a more useful form in terms of the specific heat at constant pressure, Cp, which is defined as

18 From the first law of thermodynamics, dH=TdS+VdP, a relation between Cp and entropy can be obtained as Substitution of above equation into eq.(1) indicates that a second-order transition should occur as a discontinuity in specific heat. Specific heat is easily measured by calorimetric techniques such as differential scanning calorimetry.

19 The other two second derivatives indicate that second-order transitions should occur as discontinuities in the slope of volume as a function of pressure or volume as a function of temperature. These slopes define two useful parameters-the isothermal compressiblity coefficient, , and the (isobaric) thermal-expansion coefficient, . As defined earlier, these are

20

21 This means that a discontinuity in a plot of  or  versus temperature, or alternately a change in slope of a plot of volume versus temperature (at constant pressure) or a plot of volume versus pressure (at constant temperature), marks the occurrence of a second-order transition. Both coefficients may be obtained by dilatometric measurements, although the constant-pressure experiment is the easier experiment and, therefore, the more commonly used.

22 The magnitudes of the discontinuities in Cp, , and  at the second-order transition may be expressed as Where the subscripts, 1 and 2, represent values at temperatures below and above the transition, respectively. The glass transition is not a true thermodynamic transition but, rather, it is considered to be a pseudo-second-order transition that is influenced by the kinetics of glass formation (i.e., the rate of heating or cooling). Both volume and specific-heat data for polymers closely approximate second-order transition behavior, but the discontinuities or change in slope are more gradual and are affected by the heating rate.

23 3. 动力学理论 (Dynamical theory)
当高聚物冷却时，体积收缩包括： 直接的，链段的热运动降低 间接的，链段的构象重排成能量较低的状态，松弛过程 当构象重排的松弛时间适应不了降温速度，这种运动被冻结出现玻璃化转变

24 思考题： 为什么在较大的压力下观察到Tg提高了？

25 Measurement Techniques
A wide variety of experimental methods can be used to determine the glass-transition and crystalline-melting temperatures in polymers. For example, thermal transitions may be detected by a changes in refractive index, NMR line width, and birefringence as function of temperature; However, the most commonly used techniques are dilatometry and, especially, differential scanning calorimetry (DSC). Another important method of detecting thermal transitions is by recording the response to a cyclical strain (dynamic-mechanical analysis) or electric voltage (dielectric spectroscopy).

26 An additional advantage of dynamic-mechanical and dielectric measurements is the ability to detect low-temperature secondary relaxations. By contrast, dilatometric or calorimetric methods are insensitive to the occurrence of secondary-relaxation processes. The glass and melt transitions can also be detected by measurement of modulus as a function of temperature in tensile, stress relaxation, and other mechanical tests.

27 Dilatometry In this procedure, a small sample of polymer is sealed in a glass bulb to which a precision-bored, calibrated glass capillary is attached. Mercury, whose coefficient of thermal expansion is accurately known, is used to fill the bulb and part of the capillary. The dilatometer is then immersed in a controlled-temperature bath and the height of the mercury in the capillary is recorded at different temperatures. Heating rate is normally kept very small (1 to 2 min-1) to assure thermal equilibrium, especially near Tg. From this information, the specific volume of the polymer sample can be obtained as a function of temperature.

28 The glass-transition temperature is determined as that temperature at which the volume-temperature curve changes slope (i.e., a discontinuity in ), while at the crystalline-melting temperature ( a first-order transition temperature), there is a discontinuity, or step change, in specific volume. As an approximation, the change in thermal-expansion coefficient going from the liquid (i.e., T>Tg) to the glassy state (i.e., T<Tg), =l-g, is sometimes taken to be 4.810-4 K-1.

29 Calorimetry One of the most widely used techniques to measure Tg and Tm is differential scanning-calorimetry (DSC). This method uses individual heaters to maintain identical temperatures for two small platinum holders—one contains a small (10 to 30 mg) polymer sample mechanically sealed in a small aluminum pan and the other contains an empty (reference) pan. Temperatures are measured by use of identical platinum-resistance thermistors. The differential power needed to maintain both the reference and sample pans at equal temperatures during a programmed heating cycle is then recorded as a function of temperature.

30 In place of differential power, values of specific heat, Cp, may be obtained from the recorded heat-flow rate by calibration with a pure compound such as sapphire for which Cp is known precisely at different temperatures from calorimetry measurements. A discontinuity in Cp (i.e., Cp=Cpl-Cpg), characteristic of a second-order transition, is observed at the polymer Tg, which is often identified as the temperature at the midpoint of the step change in Cp (i.e., at Cp/2). During heating of a semicrystalline polymer, additional crystallization may occur at temperatures between Tg and Tm, as illustrated by the crystallization exotherm.

31 At Tm, which may be defined as the extrapolated temperature of the initial slope of the melt endotherm, the crystallites begin to melt over a wide range of temperatures. The breadth of the endotherm is much larger than typically observed for pure low-molecular-weight compounds as a consequence of the lower order of perfection of polymer crystallites. By calibration with a low-molecular-weight standard such as benzoic acid, the heat of fusion (Q) of a semicrystalline polymer can be determined from measurement of the area under the melt endotherm recorded by DSC.

32 The heat of fusion of the same polymer at 100% crystallinity (Hf) can be estimated from a comparison of the heats of fusion of a homologous series of low-molecular-weight crystals, or from measurement of the melting-point depression of the semicrystalline polymer by diluents. With this information, the fractional crystallinity () of the polymer sample can be obtained by the equation

33 Recently, a variation of differential scanning calorimetry, temperature-modulated DSC (TMDSC), has been commercialized. The principle behind TMDSC is the superimposition of a periodic modulation (typically sinusoidal) of temperature upon the constant heating (or cooling) rate of conventional DSC operation. This method has advantages in the separation of thermal events such as the glass transition from enthalpy relaxation and crystallization.

34 Structure-Property Relationships
Both Tg and Tm are strongly influenced by the chemical structure of 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.

35 Flexible chains, as may be obtained by incorporating an oxygen atom into the main chain (e.g., polydimethylsiloxane), are capble of large-scale molecular motions at very low temperature and, therefore, have low Tg. Bulky substituent groups hinder chain rotation and therefore raise Tg. For comparably sized substituent groups, increasing polarity, which may enhance intermolecular interactions, can elevate Tg. Increasing flexibility of the side group can lower Tg. Syndiotacticity increases Tg. Trans geometric isomers have higher Tg than cis-isomers.

36 影响玻璃化温度的因素 化学结构的影响 ⑴. 主链结构 主链由饱和单键构成的高聚物：分子链的柔性越大，Tg 越低。 主链中引入苯基等芳杂环以后：分子链的刚性增大，Tg 升高。 主链中含有孤立双键的高聚物：分子链都较柔顺，Tg 比较低。 共扼二烯烃聚合物：由于几何异构体的存在，分子链较刚性的反式异构体有较高的Tg 。

37 ⑵. 取代基的空间位阻和侧基的柔性 一取代烯类聚合物：取代基的体积增大，Tg 将升高。

38 但也有例外，例如甲基丙烯酸酯类的侧基增大，Tg 反而下降。
Tg=-56 C Tg=-22 C Tg=43 C 如果有旋光异构体存在，通常一取代聚烯烃的不同旋光异构体，不表现出 Tg 的差别，间同聚合物有高得多的Tg。 。

39 1,1-二取代的烯类聚合物： 作不对称取代时，空间位阻增加，Tg将升高。 作对称双取代时，链柔顺性增加， Tg下降。 有旋光异构体存在时，间同聚合物有高得多的Tg。 Tg=3 C Tg=115 C Tg=-10 C Tg=40 C Tg=87 C Tg=-70 C Tg=-40 C Tg=-17 C

40 ⑶. 分子间力的影响 侧基的极性越强，Tg 越高。 分子间氢键可使Tg显著升高。 含离子聚合物的离子键对Tg 的影响很大。一般正离子的半径愈小，或其电荷量愈多，则Tg 愈高。 同一高聚物的两个特征温度Tg 和Tm 存在一定的关系： 结构对称的高聚物： 结构不对称的高聚物： （Tg和 Tm用绝对温标）

41 Effect of Molecular Weight, Composition, and Pressure on Tg
Molecular-Weight Dependence The glass-transition temperature increases with molecular weight at low molecular weight but reaches a point at moderate molecular weight where further increase in molecular weight has very little effect on Tg. This is an example of a limiting-property relationship. The crystalline-melting temperature, Tm, follows a similar dependence on molecular weight. The particular molecular-weight average most relevant to Tg is the number-average, Mn. This dependence can be rationalized on the basis of the free-volume theory of the glass transition. Since larger free volume is associated with the ends of long polymer chains than with other chain segments, free volume increases with an increasing number of chain ends (i.e., decreasing molecular weight).

42 The form of dependence of Tg on molecular weight is approximated by the Fox-Flory equation
Where Tg is the limiting value of Tg at high molecular weight (obtained from the intercept of a plot of Tg versus reciprocal number–average molecular weight) and K is a constant for a given polymer.

43 Composition Dependence
When a second component, either a low-molecular-weight additive or a second polymer, is blended to form a homogeneous mixture, the Tg of the mixture will depend upon the amount of each component and upon the Tg of the second component. The form of the Tg-composition dependence may be approximated by several theoretical or semiempirical models. An approximate relationship between the Tg of a miscible mixture and composition is given by the simple rule of mixtures, which for a binary mixture is given as Where W1 is the weight fraction and Tg,i (in Kelvins) is the glass-transition temperature of the ith component (i.e., component 1 or 2 in a binary mixture).

44 Improved predictive capability is available through a number of other empirical or theoretical relationships. A more recent relation is the inverse rule of mixtures Which is known as the Fox equation when applied to Tg. Fox equation has been considered to be an empirical relation; however, the preceding derivation shows that it may be viewed as representing a limiting case of the more general theoretical relationship. Another commonly used empirical relation is the logarithmic rule of mixtures given as

45 Pressure Dependence Compared to effects of molecular weight and plasticization, Tg is relatively insensitive to pressure. The glass-transition temperature will increase with increasing pressure at a rate of approximately 25 K per kbar pressure. The pressure dependence can be estimated from the compressibility and thermal expansion coefficients as

46 Effect of Heating Rate The Tg has a small dependence on the heating or cooling rates in DSC and other methods of thermal characterization. Samples that are slowly heated through the glass transition exhibit a lower Tg than those that are rapidly heated due to the non-equilibrium state of the glass. The relationship between Tg and the heating rate, q (K min-1), is given in the following form

47 Effect of crosslinks As a result of the restriction of long-range segmental motion, crosslinking elevates Tg. The form of relationship between Tg and crosslink density is often given by the Fox-Loshaek equation Where Kc is a polymer-specific constant and c represents the number of crosslinks per gram.

48 其他结构因素的影响 Gordon-Taylor equation 应用于非晶无规共聚物 ⑴ 共聚 (Copolymerization)： 无规共聚物，Fox 方程： 交替共聚物，可看成均聚物，只有一个Tg。 嵌段共聚和接枝共聚物有两个Tg ，但两种组分结构相似,只有一个Tg 。

49 ⑵ 交联 (Cross-linking)： 交联作用使Tg 升高，交联度越大，Tg 增加越多。 ⑶ 分子量 (Molecular weight)：

50 ⑷ 增塑剂或稀释剂 (Plastization)：
加入增塑剂，可使Tg 明显地下降。 注：共聚作用在降低熔点的效应比增塑作用更为有效，增塑作用在降低玻璃化温度的效应比共聚更为有效。 ⑸ 共混 (Blend)： Tg 由两种均聚物的互溶性决定。如果两组分完全互溶，共混物的性质与相同组分的无规共聚物相同； 如果两组分不互溶，有两相存在，每一相都有自己的Tg。

51 外界条件的影响 ⑴ 升温速度 (Heating rate)： 由于玻璃化转变不是热力学平衡过程，测量Tg时，随着升温速度的减慢，所得数值偏低。在降温测量中，降温速度减慢， Tg向低温方向移动。 ⑵ 外力 (Additional force)： 单向外力促使链段运动，使Tg降低，外力越大， Tg降低越多。 ⑶ 围压力 (Pressure)： 随着高聚物周围流体静压力的增加，许多高聚物的Tg线性地升高。 ⑷ 测量频率 (Frequence)： 由于玻璃化转变是一个松弛过程，外力作用的速度不同将引起转变点的移动。

52 玻璃化转变的多维性 玻璃化转变压力 (Glass transition pressure), Pg 玻璃化转变频率 (Glass transition frequence), Fg 玻璃化转变分子量 (Glass transition molecular weight), Mg

53 思考题： 试从自由体积理论解释增塑作用降低聚合物玻璃化温度。

54 Secondary-Relaxation Processes
Secondary-relaxation processes are small-scale molecular motions that can occur in the amorphous glassy state. These can involve limited motions of the main chain or rotations, vibrations, or flips of substituent groups. An example of a main chain secondary relaxation that has been proposed is the Schatzki crankshaft rotation model. According to this model, five continuous bonds join in rotation around in the main chain consisting of C-C bonds. A simpler crankshaft model proposed by Boyer involves the rotation of three continuous bonds. Such limited, or non-cooperative, motions may occur at very low temperatures (e.g., ca.-120C).

55 Other examples of main chain secondary relaxations include rotations or flips of aromatic rings in the backbone of some high-temperature polymers, such as polycarbonate. In addition to these main-chain secondary-relaxation motions, substituent groups can rotate or wag at extremely low temperatures in the glassy state. For example, the phenyl ring of polystyrene may rotate at temperatures as low as 70 K. All these motions can occur in the glassy state, below Tg, as a precursor to the onset of long-range, main-chain cooperative-motions that mark the glass transition.

56 The magnitude and temperature assignment of secondary-relaxation process can have significant influence on glassy-state properties. For example, the presence of main-chain secondary-relaxation processes has been correlated with impact strength and even the gas permeability of amorphous polymers.

57 6.3 Introduction to Polymer Rheology
高聚物的粘性流动的特点 ⑴ 高分子流动是通过链段的位移运动来完成的 液体的粘度与温度之间的关系: 流动活化能与蒸发热的关系: 流动活化能与碳原子数的关系: 流动模型不需整个分子链大小空穴，只要链段大小的空穴 nc=20-30

58 ⑵ 高分子流动不符合牛顿流体的流动规律 (Non-Newtonian fluid)
低分子液体的流动可以看成是层流: 高分子液体的流动有四种形式： 牛顿流体 (Newton fluid) 假塑性流体 (Pseudoplastic fluid) 膨胀性流体 (dilatable fluid) 宾汉流体 (Bingham fluid) n=1 n<1 n>1

59

60 ⑶ 高分子流动时伴有高弹形变 (elastic strain)

61 The viscous flow of a Newtonian fluid is described by Newton’s law of viscosity given for shear flow as Where  is shear stress,  is the Newtonian viscosity coefficient, and  is the shear strain. The time dependence of shear strain is called the shear strain rate or simply shear rate:

62 In the case of Newtonian fluids such as water and mineral oil, the viscosity, , is a function of temperature and pressure but is independent of ŕ. In contrast, the viscosity of non-Newtonian fluids such as concentrated polymer solutions and polymer melts is a function of temperature, pressure, and ŕ. In addition, the viscosity of polymer solutions and melts exhibits a strong dependence on molecular weight.

63 Shear-Rate Dependence
Non-Newtonian Flow Shear-Rate Dependence A non-Newtonian or apparent viscosity, a, of polymer solutions and melts is defined following Newton’s law of viscosity as The actual analytical relationship between s and  and, therefore, the dependence of  on  are given by the constitutive equation of the materials.

64 At low shear rates,  is nearly independent of  (i. e
At low shear rates,  is nearly independent of  (i.e., Newtonian behavior) and approaches a limiting zero shear rate value of 0. At higher ,  decreases with increasing . Fluids that display this behavior are termed shear thinning. Finally,  once again approaches a limiting Newtonian plateau, , at very high .

65 At low shear rates, the entanglements impede shear flow and, therefore, viscosity is high.
As the shear rate increases, chains begin to orient in the flow direction and disentangle from one another-the viscosity begins to drop. Finally, the molecules become fully oriented in the flow direction at very high shear rates. At this point, stable entanglements are no longer possible and the viscosity reaches a low level that is again independent of shear strain rate.

66 This second Newtonian plateau region is observed in the case of polymer solutions but is rarely observed for polymer melts because the shear rates required for chain orientation in the melt are so high that the chains actually can be broken. In rare cases, viscosity may increase with increasing shear rate. Fluids that exhibit this behavior are called shear thickening (or dilatant). Examples of shear-thickening behavior are generally limited to concentrated suspensions such as PVC pastes and polymer melts that undergo shear-induced crystallization.

67 Molecular-Weight Dependence
The significance of entanglements to shear-thinning flow suggests that molecular weight and the critical molecular weight for entanglements, Mc, should significantly influence the rheological properties of polymers. It has been shown that the zero-shear viscosity, 0, is directly related to the weight-average molecular weight, Mw, when Mw<Mc, but follows a 3.4 power dependence on Mw when MwMc. In addition, the onset of shear-thinning behavior occurs at progressively lower  as molecular weight increases.

68 Temperature Dependence
The temperature dependence of the apparent viscosity of a polymer melt follows a typical Arrhenius relationship at high temperatures, ca. 100C above Tg, as given by Where r is the viscosity at some reference temperature, Tr, E is the activation energy, and R is the ideal gas constant.

69 At lower temperatures, in the vicinity of the glass-transition temperature, approximately Tg<T<Tg+100C, viscosity increases much more rapidly with decreasing temperature than given by the Arrhenius expression. In this case, the temperature dependence of melt viscosity can be obtained by the WLF equation as Where (Tg) is the viscosity at Tg.

70 影响粘流温度的因素 1. 分子结构的影响 分子链柔顺性的好坏,决定分子链移动所需要的孔穴大小,而孔穴的大小直接影响粘流温度的高低。 分子间作用力的大小，决定粘流温度的大小。 2. 分子量的影响 分子量越大，粘流温度越高 3. 粘流温度与外力大小和外力作用的时间有关 外力使分子链沿与外力相反方向的热运动大大减少。 有外力时，在较低的温度下，聚合物即可发生流动。 增加外力作用的时间就相当于降低粘流温度。

71 高聚物的流动性表征 1. 剪切粘度 (Shear viscosity) ⑴ 零切粘度 ⑵ 表观粘度 ⑶ 微分粘度

72 2. 拉伸粘度 (Stretching viscosity)
3. 熔融指数 (Melting index) 在一定温度下，熔融状态的高聚物在一定负荷下，十分钟内从规定直径和长度的标准毛细管中流出的重量（克数）。

73 Rheometry The relationship between stress and shear rate, and therefore the dependence of apparent viscosity upon shear rate, can be determined over a wide temperature range by a variety of techniques. These include capillary and Couette rheometry, which are based upon simple pressure flow through a capillary and simple shear flow through two rotating, concentric cylinders, respectively. Other common methods include cone-and-plate and parallel-plate rheometry, which can also give information concerning normal stresses through measurements by force transducers mounted in the direction normal to the plane of shear. Slit rheometers, which can be used to measure exit pressures in pressure flow through a rectangular channel, can be used to measure normal stress under typical processing conditions.

74 Capillary Rheometer r =R, =0

75 Couette Rheometer r =R2, =  r =R1, =0

76 Cone-and-Plate Rheometer
 锥体面积：

77 Falling-Ball Rheometer
Stocks 定律：粘滞阻力 落球方程： 当达到稳态，圆球下落速度不变，d/dt=0

78 高聚物熔体的流动曲线 (Flow curve)
1. 牛顿流体： 2. 高聚物熔体：有三个区域存在。 第一牛顿区：表现出牛顿流体的行为，可o。 非牛顿区：出现剪切变稀的假塑性行为，可求a。 第二牛顿区：再次表现出牛顿流体的行为，可求。 由图知o > a > 

79 1 醋酸纤维素； 2 聚苯乙烯； 3 有机玻璃； 4 聚碳酸酯； 5 聚乙烯； 6 聚甲醛； 7 尼龙
影响聚合物熔体粘度和流动的因素 1. 温度的影响： 在粘流温度以上,高聚物的粘度与温度的关系为： 1 醋酸纤维素； 2 聚苯乙烯； 3 有机玻璃； 4 聚碳酸酯； 5 聚乙烯； 6 聚甲醛； 7 尼龙 分子链越刚性或分子间作用力大，流动活化能愈高，粘度对温度有较大的敏感性

80 当温度降低到粘流温度以下，高聚物在 Tg ~ Tg + 100℃范围内粘度与温度的关系为：
实现分子位移的链段协同跃迁，决定于链段跃迁的能力和跃迁链段周围是否有可以接纳它跃入的空位两个因素。 在较高温度下，高聚物内部的自由体积较大，后一条充分，取决于跃迁能力（流动活化能） 当温度较低，自由体积随温度降低而减小，后一条件不充分，此时链段跃迁过程不再是一般的活化过程，随温度降低，表观粘度急剧增大。

81 1 聚甲醛； 2 聚碳酸酯； 3 聚乙烯； 4 聚甲基丙烯酸甲酯； 5 醋酸纤维素； 6 尼龙
2.剪切应力和剪切速率的影响： 在第一牛顿区和第二牛顿区，粘度不随剪切速率而改变。 在非牛顿区，柔性链的表观粘度随剪切速率和剪切应力的增加而明显下降；而刚性链则下降不多。 1 聚甲醛； 2 聚碳酸酯； 3 聚乙烯； 4 聚甲基丙烯酸甲酯； 5 醋酸纤维素； 6 尼龙 柔性链分子容易通过链段运动取向，而刚性高分子链段链段较长，内摩擦阻力大，在流动过程中取向作用小，随剪切速率增大粘度变化小。

82 3. 压力的影响 按照自由体积的概念，液体的粘度是自由体积决定的，压力增加，自由体积减小，分子间的相互作用增大，导致粘度升高。

83 4.分子量的影响 高聚物的剪切粘度随分子量的增大而增加。且分子量对流动性的影响也很大，分子量大，流动性差，表观粘度高。 熔融指数与分子量的关系为： 许多高聚物熔体的粘度与分子量有依赖性,每种高聚物有自己的特征临界分子量Mc 。

84 5.分子量分布的影响 分子量分布窄的单分散高聚物，熔体的剪切粘度主要由重均分子量决定；分子量分布较宽的高聚物，熔体的剪切粘度与重均分子量没有严格的关系。 分子量分布较宽的高聚物，其高分子量部分对零切粘度的贡献比低分子量部分要大得多，因此，两重均分子量相同的同种高聚物，分子量分布宽的试样可能比单分散试样具有较高的零切粘度，且非牛顿现象要早一些。 窄分布 宽分布

85 6.链支化的影响 当支链不太长时,支化对熔体粘度的影响不大，短支链高聚物的零切粘度比同分子量的线形高聚物略低一些。 当支链长到足以互相缠结时，支化高聚物的粘度开始急快上升，粘度很快增加到线形高聚物的100倍以上。

86 7.其它结构因素的影响 凡能使玻璃化温度升高的因素，也使粘度升高。 分子量相近的不同高聚物，柔性链的粘度比刚性链低。 分子的极性、氢键和离子键等，对高聚物的熔融粘度有很大的影响，力越强，粘度增加的幅度越大。

87 高聚物流动时的几种特殊现象 韦森堡效应 (Weissenberg effect) 挤出物胀大 (Barus Effect) 不稳定流动和熔体破裂 (Melt Instabilities and Melt Fracture)

88 思考题 粘弹性松弛的表观活化能Ea可由平移因子lnT对1/T作图的曲线斜率乘以气体常数R求得。此图得到的是一根曲线，反映了活化能的温度依赖性。(a) 由WLF方程（采用通用常数c1=-17.44，c2=51.6）求出活化能的函数表达式，(b)分别计算Tg=200K和Tg=400K两种聚合物的表观活化能，(c)证明T>>Tg时，表观活化能变得与温度无关，所有材料都趋近于17.14千卡/摩尔。 作业： P334: (7) (8) (9) P331: (9) (11) (12)