Thermal Analysis of Polymeric Materials

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Fig. 5.101

Fig. 5.102

twist, the whole chain has been rotated by about 90o. It remains with minor fluctuations in this position until 7 ps when the rotation reverses. The twist is so gradual that no gauche conformations are necessary for its occurrence.

The sequence of Figs. 5.103 105 illustrates the details of the diffusion of a chain through the crystal. The figures refer to a chain that was driven into the direction of

528 5 Structure and Properties of Materials

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Fig. 5.103

Fig. 5.104

the indicated gradient by application of an external force. Figure 5.103 illustrates the gauche conformations that appear during the diffusion (compare to Fig. 5.98). There is no direct involvement of the gauche defects in the motion. At later time, the increase in gauche bonds is connected with the chain having moved out of the crystal in the positions above 85.

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Fig. 5.105

Figure 5.104 shows more details how the chain moves. The almost horizontal, dotted lines represent the non-moving chains which surround the chain being moved out of the crystal by the force gradient. One should note the initial pulling of the lower chain-end into the crystal at 0 2 ps. This is followed by an expulsion of the upper chain-end out of the crystal between 2 and 4 ps.

The mechanism of the diffusion of the chain is shown even better in the enlarged plot of the end-to-end distance of the moving chain in Fig. 5.105. The longitudinal acoustic mode of vibration (LAM) is clearly visible. From the LAM frequency one can extract a sound velocity in the chain direction which agrees with experiments. On this LAM vibration a series of spikes is superimposed which occur on motion of the chain into or out-of the crystal as seen in Fig. 5.104. The sliding diffusion of the chain through the crystal is, thus, coupled strongly with the skeletal vibrations and does not involve diffusion of the point defects themselves, but rather seems to be connected with the twisting motion of the chain which is illustrated in the movie of the chain dynamics of a single chain in Fig. 5.102.

The change of the rate of diffusion with temperature is illustrated in Fig. 5.106. Although point defects are not directly involved in the motion, they help in the motion of the chain. The motion decreases towards zero in the temperature range where the concentration of gauche bonds reaches zero in Fig. 5.100, i.e., with gauche defects present, the diffusion is more facile.

Instantaneous projections of segments of C50H100 within a crystal at different temperatures are shown in Fig. 5.107. The MD simulation represents the hexagonal polymorph. One can see that the crystal is divided in nanometer-size domains and has increasingly averaged chain cross-sections at higher temperatures. Both yield on macroscopic X-ray analysis hexagonal, average symmetry. At higher temperature, chains start to leave the surface of the crystal, indicating the first stages of fusion.

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Fig. 5.106

Fig. 5.107

5.3.5 Deformation of Polymers

Turning to the macroscopic deformation of polyethylene, as experienced on drawing of fibers, one observes frequently the formation of a neck at the yield point, as illustrated in Fig. 5.108. The stress-strain curve in Fig. 5.108 illustrates a typical

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Fig. 5.110

from the actual cross-section at the moment of stress measurement for experiments on drawing at different temperatures. Figure 5.110 shows three regions of different behaviors. Region (1) is the Hookean region. It indicates elastic deformation with a constant Young’s modulus as defined in Fig. 4.143. In the scale of the stress in the figure the slope appears almost vertical, i.e., Young’s modulus is rather large. This region of elastic deformation decreases with increasing temperature parallel to the increase of gauche defects seen in Fig. 5.100. In the region of the neck of Fig. 5.108, a catastrophic change occurs, the polymer yields as marked by (2). Rather than breaking, the modulus increases in parallel with the production of a stronger fiber morphology in a process called strain hardening (3). At the ultimate break, most molecules are arranged along the fiber axis in fibrillar crystals and inter-fibrillar, oriented intermediate-phase material. The oriented, noncrystalline material can often be described as a mesophase. Its structure was derived in Sect. 5.2 on the example of poly(ethylene terephthalate) in Figs. 5.68–72. A more detailed deformation mechanism is schematically given in Fig. 5.111. It was suggested already in 1967 by Peterlin and coworkers (see also [34]).

The simulations discussed in the previous Section begin to explain some of the details of the drawing process. In particular, they show the enormous speed that is possible on a molecular scale for the sliding of the chain within the crystal. The ratio between macroscopic time scales of about 1.0 s and the molecular time scale of 1.0 ps is 1012! The simulations indicated that the initiation of the diffusion seems to come from a sessile gauche defect or kink. On application of an external force, this can lead to a moving of the chains, catastrophically deforming the crystal morphology with the possible creation of a metastable mesophase as an intermediate, as indicated schematically in Fig. 5.111 and shown sometimes to be able to remain as a third phase in Fig. 5.69–72. On annealing, part or all of the initial structure may be regained.

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Fig. 5.111

5.3.6 Ultimate Strength of Polymers

To use flexible linear macromolecules as high-strength materials, the molecular chains should be arranged parallel to the applied stress and be as much extended as possible. The resulting modulus is then dependent on the properties of the isolated chain and the packing of the chains into the macroscopic cross-section. The properties of the chain can be derived from the same force constants as are used for the molecular dynamics calculation in Sect. 5.3.4 with Figs. 1.43 and 1.44. The ultimate strength, also called tenacity or tensile strength, in turn, depends on the defects in form of chain ends and other defects that produce the slipping mechanism and reduce the ultimate number of chains available at break to carry the load. The moduli, thus, are close-to structure insensitive, while the ultimate strengths are structure sensitive as was suggested in the summary discussion of Fig. 5.80 of Sect. 5.3.1.

Figure 5.112 compares the specific tensile strengths and moduli of a number of strong materials. The specific quantities are defined as shown in the figure as the modulus divided by the density. This quantity is chosen to emphasize the materials of high strength at low weight. For these properties most desirable are the materials found in the upper right corner of the plot. Many rigid macromolecules as defined in Fig. 1.6 collect along the drawn diagonal with a rather small ratio of strength-to- modulus because of the above-mentioned deformation mechanism followed ultimately by a crack development that breaks the crystals by separating a few crystal layers at a time needing much less stress. In flexible polymers, the covalent backbone bonds are stronger than metallic or ionic bonds (see Sect. 1.1). High-strength fibers result when chains of a proper mesophase gradually orient parallel to the stress and the molecules become fully extended in large numbers over a small deformation limit.

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Fig. 5.114

Fig. 5.115

of Figs. 4.114 and 4.116. The right curves are computed assuming the fibers consist only of two phases and, using the total orientation, were summed over all chains. Only the left curves extrapolate within a factor of two to the known ultimate modulus of the crystal of poly(ethylene terephthalate). The extrapolated tenacity is, as expected, smaller than the extrapolated modulus.

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5.4 Transitions and Prediction of Melting

The discussion in this chapter has dealt in Sects. 5.1 to 5.3 with the description of structure and properties of crystals, perhaps the best-known branch of material science of polymers. Complications arise, however, since most crystallizing polymers do not reach equilibrium. The metastable, multiphase structures will be discussed in Chaps. 6 and 7. They represent the most complex structure and need for their description all tools of thermal analysis of polymeric materials.

In this section, the upper temperature limit of the crystalline state is explored on the basis of experimental data on the thermodynamics of melting, extrapolated to equilibrium. The more common nonequilibrium melting will see its final discussion in Sects. 6.2 and 7.2. The other condensed states of macromolecules, the mesophases, glasses, and melts are treated in Sects. 5.5 and 5.6. Much less is known about them than about the crystals.

5.4.1 Transitions of Macromolecules

The transitions in flexible linear macromolecules are distinguished by their nonequilibrium nature. Figure 5.116 gives a schematic overview of the possible transitions, modeled on the thermal analysis of a quenched, amorphous poly(ethylene terephthalate) presented as a fingerprint DSC in Fig. 4.74. Examples of more quantitative TMDSC analyses of PET are given in Figs. 3.92, 4.122, and 4.136–139. A special review of TMDSC of the glass transition of PET is seen in Figs. 4.129–133. In Fig. 5.116, the glass transition temperature is labeled Tg and characterized by an increase in heat capacity (see Sects. 2.3 and 2.5) and marks the change of the brittle, glassy solid to a supercooled, viscous melt. More details on glass transitions are discussed in Sects. 5.6, 6.1, and 6.3.

Next is the exothermic crystallization transition at Tc. Such crystallization on heating above the glass transition temperature is called cold crystallization [37]. It contrasts to crystallization on cooling from the melt, see also Figs. 4.122, 4.136, and 4.138. After cold crystallization, the sample is semicrystalline with about 40% crystallinity, as indicated in Fig. 4.136.

The following melting range is rather broad and indicated by the endotherm, centered about Tm. Most of the breadth is produced by the wide range in lamellar crystal perfection and thickness (see Sects. 5.2 and 5.3), and additional reorganization occurs during the melting experiment which will be addressed in Sect. 6.2. The resulting melt is stable up to over 600 K, and finally shows an exothermic peak that signals decomposition. The appearance of decompositions of other polymers in thermogravimetry is illustrated in Fig. 3.49.

The main object in the present section is to gain a quantitative understanding of the equilibrium melting temperature and the changes in enthalpy and entropy during the transition. The melting transition assigns the upper temperature limit of the solid state of the crystalline polymers, as pointed out in Fig. 1.6, just as the glass transition alone limits the solid state of amorphous and mesophase polymers (see Sects. 5.5 and 5.6). Beyond these temperatures, polymers cannot be used as bulk structural materials, fibers, or films.