1、Chapter 12Polymer Glass Transitions,Crystallization is the process by which, upon cooling, an ordered (i.e., crystalline) solid phase is produced from a liquid melt having a highly random molecular structure.,The melting transformation is the reverse process that occurs when a polymer is heated.,The
2、 glass-transition phenomenon occurs with amorphous or noncrystallizable polymers that, when cooled from a liquid melt, become rigid solids yet retain the disordered molecular structure that is characteristic of the liquid state.,Three phenomena that are important with respect to the design and proce
3、ssing of polymeric materials are crystallization, melting, and the glass transition.,12.1、CRYSTALLIZATION,The time dependence of crystallization is the same as for many solid-state transformationsFigure 10.10; that is, a sigmoidal-shaped curve results when fraction transformation (i.e., fraction cry
4、stallized) is plotted versus the logarithm of time (at constant temperature).,Mathematically, fraction crystallized y is a function of time t according to the Avrami equation,where k and n are time-independent constants, whose values depend on the crystallizing system.,Figure 12.1 Plot of normalized
5、 fraction crystallized versus the logarithm of time for polypropylene(聚丙烯) at constant temperatures of 140, 150 and160oC.,Rate of crystallization may be specified in the same manner as for the transformations discussed in Section 10.3; that is, rate is equal to the reciprocal of time required for cr
6、ystallization to proceed to 50% completion.This rate is dependent on crystallization temperature and also on the molecular weight of the polymer; rate decreases with increasing molecular weight.,For polypropylene (as well as any polymer), the attainment of 100% crystallinity is not possible. Therefo
7、re, in Figure 12.1, the vertical axis is scaled as “normalized fraction crystallized.” A value of 1.0 for this parameter corresponds to the highest level of crystallization that is achieved during the tests, which, in reality, is less than complete crystallization.,12.2、MELTING,There are several fea
8、tures distinctive to the melting of polymers that are not normally observed with metals and ceramics;,First of all, melting of polymers takes place over a range of temperatures;,the apparent melting behavior is a function of the rate of heating; increasing this rate results in an elevation of the me
9、lting temperature.,In addition, the melting behavior depends on the history of the specimen, in particular the temperature at which it crystallized.,The thickness of chain-folded lamellae will depend on crystallization temperature; the thicker the lamellae, the higher the melting temperature.,Impuri
10、ties in the polymer and imperfections in the crystals also decrease the melting temperature.,12.3、THE GLASS TRANSITION,Upon cooling, the glass transition corresponds to the gradual transformation from a liquid to a rubbery material, and finally, to a rigid solid.,The temperature at which the polymer
11、 experiences the transition from rubbery to rigid states is termed the glass transition temperature; Tg,Of course, this sequence of events occurs in the reverse order when a rigid glass at a temperature below Tg is heated.,In addition, abrupt changes in other physical properties accompany this glass
12、 transition: for example, stiffness, heat capacity, and coefficient of thermal expansion.,12.4、MELTING AND GLASS TRANSITION TEMPERATURES,The glass transition temperature may also define the upper use temperature for glassy amorphous materials.,Melting and glass transition temperatures define, respec
13、tively, the upper and lower temperature limits for numerous applications, especially for semicrystalline polymers.,The temperatures at which melting and/or the glass transition occur for a polymer are determined from a plot of specific volume (the reciprocal of density) versus temperature.,Figure 12
14、.2 Specific volume versus temperature, upon cooling from the liquid melt, for totally amorphous (curve A), semicrystalline (curve B), and crystalline (curve C) polymers.,12.5、FACTORS THAT INFLUENCE MELTING AND GLASS TRANSITION TEMPERATURES,Melting Temperature,During melting of a polymer there will b
15、e a rearrangement of the molecules in the transformation from ordered to disordered molecular states. Molecular chemistry and structure will influence the ability of the polymer chain molecules to make these rearrangements and, therefore, will also affect the melting temperature.,The presence of dou
16、ble bonds and aromatic groups(芬芳基) in the polymer backbone lowers chain flexibility and causes an increase in Tm.,Furthermore, the size and type of side groups influence chain rotational freedom and flexibility; bulky or large side groups tend to restrict molecular rotation and raise Tm,For example,
17、 polypropylene(聚丙烯) has a higher melting temperature than polyethylene(聚乙烯) (175oC versus 115oC); the CH3 methyl side group for polypropylene is larger than the H atom found on polyethylene.,The presence of polar groups (viz. Cl, OH, and CN), even though not excessively large, leads to significant i
18、ntermolecular bonding forces and relatively high Tms,This may be verified by comparing the melting temperatures of polypropylene (175oC) and poly(vinyl chloride) (212oC).,The melting temperature of a polymer will also depend on molecular weight. At relatively low molecular weights, increasing (or ch
19、ain length) raises Tm (Figure 12.3).,Figure 12.3 Dependence of polymer properties as well as melting and glass transition temperatures on molecular weight.,Degree of branching will also affect the melting temperature of a polymer. The introduction of side branches introduces defects into the crystal
20、line material and lowers the melting temperature.,High-density polyethylene, being a predominately linear polymer, has a higher melting temperature (137oC) than low-density polyethylene (115oC) which has some branching.,Glass Transition Temperature,the value of the glass transition temperature will
21、depend on molecular characteristics that affect chain stiffness; most of these factors and their influences are the same as for the melting temperature, as discussed above. Again, chain flexibility is diminished and is increased by the presence of the following:,1. Bulky side groups; from Table 15.2
22、, the respective values for polypropylene and polystyrene are -18oC and 100oC. 2. Polar groups; for example, the Tg values for poly(vinyl chloride) and polypropylene are 87oC and -18oC, respectively. 3. Double bonds and aromatic groups in the backbone, which tend to stiffen the polymer chain.,Increa
23、sing the molecular weight also tends to raise the glass transition temperature, as noted in Figure 12.3.,A small amount of branching will tend to lower Tg; on the other hand, a high density of branches reduces chain mobility, and elevates the glass transition temperature.,Some amorphous polymers are
24、 crosslinked, which has been observed to elevate Tg; crosslinks restrict molecular motion.,12.6、VISCOELASTIC DEFORMATION,At the highest temperatures, viscous or liquid-like behavior prevails.,For intermediate temperatures the polymer is a rubbery solid that exhibits the combined mechanical character
25、istics of these two extremes; the condition is termed viscoelasticity.,For relatively small deformations, the mechanical behavior of an amorphous polymer at low temperatures may be elastic; that is, in conformity to Hookes law,Figure 12.4 (a) Load versus time, where load is applied instantaneously a
26、t time ta and released at tr. For the loadtime cycle in (a), the strain-versus-time responses are for totally elastic (b), viscoelastic (c), and viscous (d) behaviors.,Viscoelastic Relaxation Modulus,The viscoelastic behavior of polymeric materials is dependent on both time and temperature;,With Str
27、ess relaxation(应力弛豫) measurements, a specimen is initially strained rapidly in tension to a predetermined and relatively low strain level. The stress necessary to maintain this strain is measured as a function of time, while temperature is held constant.,Stress is found to decrease with time due to
28、molecular relaxation processes that take place within the polymer.,We may define a relaxation modulus Er(t), a time-dependent elastic modulus for viscoelastic polymers, as,where is the measured time-dependent stress and is the strain level, which is maintained constant.,Furthermore, the magnitude of
29、 the relaxation modulus is a function of temperature;,Figure 12.5 is a schematic log Er(t)-versus-log time plot for a polymer that exhibits viscoelastic behavior. Curves generated at a variety of temperatures are included.,Key features of this plot are that (1) the magnitude of Er(t) decreases with
30、time, and (2) the curves are displaced to lower Er(t) levels with increasing temperature.,Figure 12.5 Schematic plot of logarithm of relaxation modulus versus logarithm of time for a viscoelastic polymer; isothermal curves are generated at temperatures T1 through T7. The temperature dependence of th
31、e relaxation modulus is represented as log Er(t1) versus temperature.,To represent the influence of temperature, data points are taken at a specific time from the log Er(t) -versus-log time plotfor example, t1 in Figure 12.5and then cross-plotted as log Er(t) versus temperature.(Figure 12.6),Several
32、 distinct regions may be noted on the curve shown in this figure.,At the lowest temperatures, in the glassy region, the material is rigid and brittle, and the value of Er(10) is that of the elastic modulus, which initially is virtually independent of temperature.,As the temperature is increased, Er(
33、10) drops abruptly by about a factor of 103 within a 20oC temperature span; this is sometimes called the leathery(皮革质), or glass transition region, and the glass transition temperature (Tg) lies near the upper temperature extremity.,Within the rubbery plateau temperature region (Figure 12.6), the ma
34、terial deforms in a rubbery manner; here, both elastic and viscous components are present, and deformation is easy to produce because the relaxation modulus is relatively low.,The final two high-temperature regions are rubbery flow and viscous flow. Upon heating through these temperatures, the mater
35、ial experiences a gradual transition to a soft rubbery state, and finally to a viscous liquid.,Figure 12.6 Logarithm of the relaxation modulus versus temperature for amorphous polystyrene, showing the five different regions of viscoelastic behavior,The logEr(10) -versus-temperature behavior for poly
36、styrene materials having several molecular configurations is plotted in Figure 12.7.,The curve for the amorphous material (curve C) is the same as in Figure 12.6.,For a lightly crosslinked atactic polystyrene 无规立构聚苯烯 (curve B), the rubbery region forms a plateau that extends to the temperature at wh
37、ich the polymer decomposes; this material will not experience melting. For increased crosslinking, the magnitude of the plateau Er(10) value will also increase.,For an almost totally crystalline isotactic(全同立构) polystyrene聚苯乙烯 (curve A). the decrease in Er(10) at Tg is much less pronounced than the
38、other polystyrene materials since only a small volume fraction of this material is amorphous and experiences the glass transition.,Furthermore, the relaxation modulus is maintained at a relatively high value with increasing temperature until its melting temperature Tg is approached.,Figure 12.7 Loga
39、rithm of the relaxation modulus versus temperature for crystalline isotactic (curve A), lightly crosslinked atactic (curve B), and amorphous (curve C) polystyrene.,Viscoelastic Creep(黏弹性蠕变),Creep tests on polymers are conducted in the same manner as for metals; that is, a stress (normally tensile) i
40、s applied instantaneously and is maintained at a constant level while strain is measured as a function of time. Furthermore, the tests are performed under isothermal conditions.,Creep results are represented as a time-dependent creep modulus Ec(t) defined by,wherein is the constant applied stress and is the time-dependent strain.,Homework:,15.5, 15.7, 15.28, 15.29, 15.31,
