Thermal Analysis of Polymeric Materials

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The three polyesters in Fig. 5.126 show that the reason for the low melting of the aliphatic poly(ethylene suberate) is the larger number of beads. The two aromatic polyesters contain one and two phenylene groups of six carbons linked into rigid rings, losing considerable entropy relative to the all flexible aliphatic chain. The aliphatic nylons, finally, have higher melting temperatures than the corresponding esters because of the higher CED.

Once these empirical rules have been established, it is possible to link the melting temperatures of polymers to chain flexibility, interactions (cohesive energy densities), internal heats of fusion, and the possible presence of mesophases (see Fig. 2.103). Such analyses are of importance for the design of new polymers and of changes in existing polymers when there is a need to alter thermal stability.

5.5 Mesophases and Their Transitions

Mesophases are intermediate phases between rigid, fully ordered crystals and the mobile melt, as explained in the introductory discussion of phases in Sect. 2.5, and summarized in Figs. 2.103 and 2.107. The quantitative analysis of melting in Sect. 5.4 shows that with a suitable molecular structure, three types of disorder and motion can be introduced on fusion: (1) positional disorder and translational motion, (2) orientational disorder and motion, and (3) conformational disorder and motion [43]. In case not all the possible disorders and motions for a given molecule are achieved, an intermediate phase, a mesophase results. These mesophases are the topic of this section. Both structure and motion must be characterized for a full description of mesophases.

5.5.1 Multiple Transitions

First experimental evidence for mesophases is often the presence of more than one first-order transitions in DSC curves on heating from the crystal to the melt. The disordering of a crystal to its mesophase causes a substantial endotherm. Much smaller endotherms may indicate solid-solid transitions which only involve changes in crystal structure without introduction of large-amplitude motion. Figure 5.127 illustrates the behavior of poly(oxy-2,2'-dimethylazoxybenzene-4,4'-dioxydo- decanoyl), DDA-12, a mesophase-forming macromolecule. Before analysis, the sample was quenched to a LC glass, i.e., a solid with liquid-crystalline order, but without large-amplitude motion (see Fig. 2.103). On cold crystallization above the glass transition temperature at about 345 K, metastable condis crystals grow with an exotherm to a partial crystallinity. At about 395 K, the CD crystals again disorder with an endotherm to the liquid crystal. The second endotherm in Fig. 5.127 is the isotropization to the melt. The isotropization is reversible, the disordering is not, as can be tested with TMDSC. Low-molar-mass analogs behave similarly. For example, p-butyl-p'-methoxyazoxybenzenes can be quenched to a semicrystalline LC glass and shows then a DSC-trace, as displayed in Fig. 5.128, which can be compared to Fig. 5.127. The difference is that the cold crystallization of the small molecules yields close to equilibrium crystallinity instead of the polymeric semicrystalline sample.

548 5 Structure and Properties of Materials

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Fig. 5.127

Fig. 5.128

Another example of mesophase calorimetry is shown in Fig. 5.129. On the left, DSC traces are given for poly(dimethyl siloxane), PDMS, which does not exhibit a mesophase, on the right, for poly(diethyl siloxane), PDES, with a stable mesophase. The samples A were quenched with liquid N2 to the amorphous state, samples B, cooled at 10 K min 1, and samples C, slowly cooled or annealed. The quickly cooled

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Fig. 5.129

samples, A, show cold crystallization at Tc (see Sect. 3.5.5). The samples C show only weak glass transitions, and PDMS displays one, PDES two relatively sharp endotherms. On cold crystallization, A, PDES forms only the condis phase with partial crystallinity. The semicrystalline PDES of samples B and C disorder to the condis phase at about 200 K. The condis phase was shown to be able to be annealed to extended-chain crystals.

In Sect. 2.5 a similar two-step melting was discussed for the condis state of trans- 1,4-polybutadiene. The cis-isomer shows in Fig. 2.113 complete gain of the entropy of fusion at a single melting temperature, while the trans isomer loses about 2/3 of its entropy of transition at the disordering transition. The structure of the trans isomer is close to linear, so that conformational motion about its backbone bonds can support a condis crystal structure with little increase in volume of the unit cell.

The existence-range of the condis crystal of poly(tetrafluoroethylene), PTFE, can be seen from the phase diagram of Fig. 5.130. The calorimetric heat capacity analysis of PTFE is described as an example of the ATHAS applications in Fig. 2.63, and the entropies of transition, which lead to the high isotropization temperature, are discussed in Sect. 5.4.3.

A TMDSC analysis at different frequencies and amplitudes reveals in Fig. 5.131 that the solid-solid transition which changes the 1*13/6 helix to the 1*15/7 helix is irreversible, while the transition to the condis state is reversible [44]. The conformational disorder consists mainly of a mobility of the 1*15/7 helix from leftto right-handed, averaging the structure of the backbone chain so that it fits into the trigonal symmetry. The low-temperature crystals are triclinic with a fixed leftor right-handed 1*13/6 helix (see Sects. 5.1 and 5.2). Crystal form III is a high-pressure phase with a close-to-planar chain conformation, and form IV, located between the two endotherms of Fig. 5.131, is made up of rigid 1*15/7 helices.

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Fig. 5.130

Fig. 5.131

Figure 5.132 illustrates that mesophases can also be identified by rheological properties. The crystals of PTFE show a highly anisotropic flow parallel to the molecular axes, a property often found in smectic liquid crystals. As soon as the molecules start to melt, however, the shear-stress increases abruptly because of the chain-entanglement that occurs during melting. On a microscopic basis, PTFE

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Fig. 5.132

crystallizing in the condis state can, given enough time, extend their initially chainfolded crystals, and yield extended-chain, equilibrium crystals (see Sect. 5.2).

On a molecular scale, mesophases are most easily detected by direct determination of the mobility of their molecules. An example is shown for trans-1,4-polybutadiene in Fig. 2.112 by measurement of the second moment of the line-width of the proton NMR signal [45]. At the glass transition, the usual gradual narrowing of the linewidth is observed, while disordering to the condis-phase shows a further decrease. On isotropization, the NMR signal becomes a very narrow line.

A listing of the typical properties that distinguish the different mesophases is also given in Sect. 2.5 with Fig. 2.107. Furthermore, Sect. 2.5 contains examples for low- molar-mass liquid crystals and plastic crystals in Figs. 2.108–111, important model compounds for polymers.

5.5.2 Classes of Mesophases

The three different classes of mesophases are characterized in Fig. 2.107. Their disorder, and large-amplitude motion are at the root of their characteristic properties [43]. The change from an ideal crystal to a defect crystal, and finally to a plastic crystal can be understood as follows: The defects in the ideal crystal do not disturb the long-range order and concentrate at the surface. The motion of the defects is largely localized, as described in Sect. 5.3. The plastic crystal, in contrast, has all motifs rotating, averaging the shape of the close-to-spherical mesogen in time and over locations. A concerted rotation of nearest neighbors permits closer approach of the motifs than needed for free rotation.

The condis crystal motion results in a similar rotation as in the plastic crystal, but the molecules do not rotate as a whole, rather they undergo segmental motion and

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Fig. 5.138

energy-level diagram on the upper right. The character of the increasing excitation depends on the parameter w, which is a measure of the cooperativity. If w is zero, the beginning of the motion is spread over a wide temperature range, as shown in the heat-capacity curve derived in Fig. 2.33. The figure illustrates the change in sharpness as w increases. A true first-order transition is reached with a critical value for w of 1.89 when the condition of Fig. 2.119 is reached.

5.5.3 Jump-motion in Crystals

The main molecular motion in crystals is vibrational, as described in detail in Sect. 2.3. Heat capacity is the macroscopic tool of choice for its evaluation. Comparing, however, the heat capacity of polymer crystals and glasses with the contributions expected from vibrations, one finds deviations at elevated temperatures, as already noted in Figs. 2.51 and 2.65 for polyethylene. The deviations are linked in Sect. 5.3 to isolated, large-amplitude defect motion. Similarly, the large-amplitude motion accessible in mesophases causes entropy changes which are not always collected in the well-defined transitions, as is discussed in Sect. 5.5.4, below. In the present section, the often overlooked large-amplitude jump-motion is added to the better-known vibrations and large-amplitude motion as a cause of molecular mobility. A jump-motion usually does not register a measurable entropy of disordering if it represents an exchange between states of equal symmetry. In this case disorder exists only during the short time of the actual jump which is usually negligible. If the states before and after jumps are distinguishable and of different degree of overall order, entropies of disordering are measurable.

A jump-motion about an axis of symmetry is a common example of initial largeamplitude motion on the path from a rigid crystal to the melt. It could be identified

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only after the development of solid-state NMR as a quantitative tool to probe molecular motion [45]. Since after the jump, the molecule is indistinguishable from its initial state, and the molecule spends only a very short time in transition, there is hardly any increase in disorder (entropy) or change in X-ray structure expected at the onset of this motion. As an example, Fig. 5.139 displays the heat capacity of a cyclopropane. For the crystals, there is little indication of any heat capacity

Fig. 5.139

contributions besides vibrational. Also, all the expected heat of fusion of the rigid molecule is absorbed at 145.5 K. The second moment of the proton NMR linewidth, however, proves the existence of motion about the threefold axis of rotation, as illustrated in the figure. Good agreement between calculated and measured second moment is achieved with the assumption that at low temperature the crystal shows vibrations only, i.e., it is rigid. The second moment between 120 and 140 K is, in turn, that of C3H6, averaged about the threefold axis. In order to be observed, this jumpmotion must reach the NMR frequency of 10 100 kHz. This happens at 150 K, 30 K below the melting temperature. This is a much different picture of the motion in the crystal above 125 K from that of a vibrations-only solid.

Figure 5.140 shows a similar analysis for crystals of benzene. Again, rapid jumps about the sixfold axis are possible much below the melting temperature. Closer to the melting point even jumps about the twofold axes are possible. It is of interest that furan, C4H4O, also a planar, rigid, cyclic molecule, but without the symmetry of benzene, shows a transition with entropy 13.6 J K 1 mol 1 at 150 K where rotational jumping becomes possible. In this case the jumping occurs to positions with different symmetry, so that an entropy of transition is observed on losing long-range order.

More complicated motions are found in the flexible cycloalkanes of larger size [46]. The molecules possess two endotherms between crystal and melt. Figure 5.141