CHAPTER
4.4 The Glass Transition
4.4.1 Modulus Temperature Relations
At sufficiently low temperatures a polymer will be a hard, brittle material with a modulus greater than 109N m22 (1010dyn/cm2). This is the glassy region. The tensile modulus is a function of the polymer temperature and is a useful guide to mechanical behavior. Figure 4.8 shows a typical modulustemperature curve for an amorphous polymer.
In the glassy region the available thermal energy (RT energy units/mol) is insufficient to allow rotation about single bonds in the polymer backbone, and movements of large-scale (about 50 consecutive chain atoms) segments of macro- molecules cannot take place. When a material is stressed, it can respond by deforming in a nonrecoverable or in an elastic manner. In the former case there must be rearrangements of the positions of whole molecules or segments of mole- cules that result in the dissipation of the applied work as internal heat. The mech- anism whereby the imposed work is absorbed irreversibly involves the flow of
Temperature (°C) Transition Glassy
Rubbery Rubbery liquid
Increasing polymer molecular weight Log modulus (dyn/cm2)
4 6 8 10
FIGURE 4.8
Modulustemperature relations for an amorphous polymer.
166 CHAPTER 4 Mechanical Properties of Polymer Solids and Liquids
sections of macromolecules in the solid specimen. The alternative, elastic response is characteristic of glasses, in which the components cannot flow past each other. Such materials usually fracture in a brittle manner at small deforma- tions, because the creation of new surfaces is the only means available for release of the strain energy stored in the solid (window glass is an example). The glass transition region is a temperature range in which the onset of motion on the scale of molecular displacements can be detected in a polymer specimen. An experi- ment will detect evidence of such motion (Section 4.4.4) when the rate of molecu- lar movement is appropriate to the time scale of the experiment. Since the rate of flow always increases with temperature, it is not surprising that techniques that stress the specimen more quickly will register higher transition temperatures. For a typical polymer, changing the time scale of loading by a factor of 10 shifts the apparentTgby about 7C. In terms of more common experience, a plastic speci- men that can be deformed in a ductile manner in a slow bend test may be glassy and brittle if it is struck rapidly at the same temperature.
As the temperature is raised the thermal agitation becomes sufficient for seg- mental movement and the brittle glass begins to behave in a leathery fashion. The modulus decreases by a factor of about 103 over a temperature range of about 1020C in the glass-to-rubber transition region.
Let us imagine that measurement of the modulus involves application of a ten- sile load to the specimen and measurement of the resulting deformation a few sec- onds after the sample is stressed. In such an experiment a second plateau region will be observed at temperatures greater thanTg. This is the rubbery plateau. In the temperature interval of the rubbery plateau, the segmental displacements that give rise to the glass transition are much faster than the time scale of the modulus mea- surement, but the flow of whole macromolecules is still greatly restricted. Such restrictions can arise from primary chemical bonds as in cross-linked elastomers (Section 4.5.1) or by entanglements with other polymer chains in uncross-linked polymers. Since the number of such entanglements will be greater the higher the molecular weight of the polymer, it can be expected that the temperature range cor- responding to the rubbery plateau in uncross-linked polymers will be extended to higher values ofT with increasingM. This is shown schematically inFig. 4.8. A cross-plot of the molecular weighttemperature relation is given inFig. 4.3a.
The rubbery region is characterized by a short-term elastic response to the application and removal of a stress. This is an entropy-driven elasticity phenome- non of the type described inSection 4.5. Polymer molecules respond to the gross deformation of the specimen by changing to more extended conformations. They do not flow past each other to a significant extent, because their rate of translation is restricted by mutual entanglements. A single entangled molecule has to drag along its attached neighbors or slip out of its entanglement if it is to flow. The amount of slippage will increase with the duration of the applied stress, and it is observed that the temperature interval of the rubbery plateau is shortened as time between the load application and strain measurement is lengthened. Also, molecu- lar flexibility and mobility increase with temperature, and continued warming of
the sample causes the scale of molecular motions to increase in the time scale of the experiment. Whole molecules will begin to slip their entanglements and flow during the several seconds required for this modulus experiment. The sample will flow in a rubbery manner. When the stress is released, the specimen will not con- tract completely back to its initial dimensions. With higher testing temperatures, the flow rate and the amount of permanent deformation observed will continue to increase.
If the macromolecules in a sample are cross-linked, rather than just entangled, the intermolecular linkages do not slip and the rubbery plateau region persists until the temperature is warm enough to cause chemical degradation of the macromolecules. The effects of cross-linking are illustrated in Fig. 4.9. A lightly cross-linked specimen would correspond to the vulcanized rubber in an automo- bile tire. The modulus of the material in the rubbery region is shown as increasing with temperature because the rubber is an entropy spring (cf. Fig. 1.3a and Section 4.5.2). The modulus also rises with increased density of cross-linking in accordance with Eq. (4-31). At high cross-link densities, the intermolecular link- ages will be spaced so closely as to eliminate the mobility of segments of the size (B50 main chain bonds) involved in motions that are unlocked in the glassrubber transition region. Then the material remains glassy at all usage tem- peratures. Such behavior is typical of tight network structures such as in cured phenolics (Fig. 8.1).
Tightly cross-linked
Lightly cross-linked
Not cross-linked 10
8
6
4 Log modulus (dyn/cm2)
Temperature (°C) FIGURE 4.9
Effect of cross-linking on modulustemperature relation for an amorphous polymer.
168 CHAPTER 4 Mechanical Properties of Polymer Solids and Liquids
In a solid semicrystalline polymer, large-scale segmental motion occurs only at temperatures between Tg and Tm and only in amorphous regions. At low degrees of crystallinity the crystallites act as virtual cross-links, and the amor- phous regions exhibit rubbery or glassy behavior, depending on the temperature and time scale of the experiment. Increasing levels of crystallinity have similar effects to those shown inFig. 4.9 for variations in cross-link density. Schematic modulustemperature relations for a semicrystalline polymer are shown in Fig. 4.10. As with moderate cross-linking, the glass transition is essentially unaf- fected by the presence of crystallites. At very high crystallinity levels, however, the polymer is very rigid and little segmental motion is possible. In this case the glass transition has little practical significance. It is almost a philosophical ques- tion whether a Tg exists in materials like the superdrawn thermoplastic fibers noted in Section 4.3.2.3 or the rodlike structures mentioned inSection 4.6.
The modulustemperature behavior of amorphous polymers is also affected by admixture with plasticizers. These are the soluble diluents described briefly in Section 6.3.2. As shown inFig. 4.11, the incorporation of a plasticizer reducesTg and makes the polymer more flexible at any temperature aboveTg. In poly(vinyl chloride), for example, Tg can be lowered from about 85C for unplasticized material to 230C for blends of the polymer with 50 wt% of dioctyl phthalate plasticizer. A very wide range of mechanical properties can be achieved with this one polymer by variations in the types and concentrations of plasticizers.
Temperature (°C) Amorphous
Partially crystalline
Increasing crystallinity 10
8
6
4 Log modulus (dyn/cm2)
FIGURE 4.10
Modulustemperature relations for amorphous and partially crystalline versions of the same polymer.