Thermal Analysis of Polymeric Materials

___________________________________________________________________

Rigid-amorphous fraction, R AF, in semicrystalline polymers. The influence of interfaces with crystals on the glass transition of the amorphous phase may not only cause the commonly observed broadening and shifting of the glass-transition range to higher temperature, as shown in Figs. 4.136 and 6.132 for the reversing heat capacity from TMDSC of poly(ethylene terephthalate), it may also give rise to a rigidamorphous fraction, RAF, that is metastable to much higher temperatures. In Fig. 4.136, Tg has shifted on crystallization by 10 K from 347 K to 357 K and the end of the glass transition reaches up to about 375 K. Between 380 and 420 K a second Tg seems to exist, attributed to a RAF (for Te, see also Fig. 4.137).

The first quantitative analysis of RAF was carried out by analysis of the heat capacity of semicrystalline poly(oxymethylene), POM, as shown in Fig. 6.16 [20]. Clearly, the 67% of crystallinity computed from the heat of fusion, which would require a 33% amorphous fraction as indicated by the dotted line in the left trace, does

Fig. 6.16

not agree with the experimental data given by the solid line. The right trace identifies the rigid fraction, wr, as 0.80 of the total sample, leading to a rigid-amorphous fraction, (wr wc) = 0.13 which does not contribute to the glass transition, but is also not crystalline. The glass transition is completed at about 210 K. In Fig. 6.17 the analysis of several POM samples is given, allowing an overview of the polymer behavior. The RAF is a significant part of the material and does not permit a description of the properties of the polymer with a two-phase model, as is often done. For every semicrystalline sample, the RAF should be analyzed as a function of temperature since it may be as important for the determination of the thermal and mechanical properties of the material as the crystallinity. The data of the right trace Fig. 6.16 show that there is no indication that for POM the RAF changes up to the melting region. In Sect. 6.3 it is shown that for other polymers, the RAF may have a glass transition below, above,

608 6 Single Component Materials

___________________________________________________________________

Fig. 6.17

or at the melting transition. Some polymers, such as polyethylene, show no separate glass transition, but have only a broadened glass transition. On drawing, the RAF of semicrystalline polymers can be oriented and then be the supporting structure which determines the overall modulus and even the ultimate strength (tensile strength) of the fibers and films which are discussed in Sect. 6.2.6. Proof of such structures is given in Figs. 5.68–72 and 5.113–115 for fibers of poly(ethylene terephthalate) and Figs. 5.157, 5.158, and 6.4 for gel-spun, ultra-high-molar-mass polyethylene.

The reversing heat capacity and the total heat-flow rate of an initially amorphous poly(3-hydroxybutyrate), PHB, are illustrated in Fig. 6.18 [21]. The quasi-isothermal study of the development of the crystallinity was made at 296 K, within the coldcrystallization range. The reversing specific heat capacity gives a measure of the crystallization kinetics by showing the drop of the heat capacity from the supercooled melt to the value of the solid as a function of time, while the total heat-flow rate is a direct measure of the evolution of the latent heat of crystallization. From the heat of fusion, one expects a crystallinity of 64%, the total amount of solid material, however, when estimated from the specific heat capacity of PHB using the ATHAS Data Bank of Appendix 1, is 88%, an indication of a rigid-amorphous fraction of 24%.

There are two possibilities for the production of the RAF. Either it forms at the same time as the crystallinity, or it forms later, when the crystals impinge or when secondary crystallization occurs. Figure 6.18 shows clearly that the formation of RAF goes parallel with the crystallization as long as the temperature is below the Tg of RAF. Furthermore, the analysis of PHB indicates no significant defect contribution to Cp, in contrast to polyethylene (see Fig. 2.51). The reason is that there must be at least three consecutive CH2-groups to form gauche-trans-gauche defects (2g1 kinks) as in polyethylene (see Sect. 5.3), and in addition, the melting temperature of PHB is lower than for polyethylene, also keeping the Cp closer to its vibrational limit.

610 6 Single Component Materials

___________________________________________________________________

is a schematic of the mechanical properties of an amorphous polymer as a function of temperature (at constant frequency) or frequency (at constant temperature). Note that the in-phase storage modulus is plotted logarithmically, and tan represents the linear, out-of-phase modulus, normalized to the storage modulus (see, for example Fig. 4.169), i.e., it represents the maximum energy dissipated per unit storage modulus (see Fig. 4. 160). A comparison of the glass transition of polystyrene measured at equal frequencies by TMDSC and DMA is depicted in Fig. 6.20. Despite the identical

Fig. 6.20

frequency, the Tg by DMA is more than 10 K higher than by DSC. If one would have picked Tg where the modulus approaches 50% of its glassy value, the two values would have been much closer. Much of the difference in glass transition temperatures that may arise when not measuring with the same thermal analysis technique, thus, is caused by differences in definition of the glass transition.

6.2 Size, Extension, and Time Effects During Fusion

In this section the broad spectrum of melting of one-component macromolecular systems is described by means of several specific polymers. The description starts with polyethylene, the most analyzed polymer. It continues with two sections that present several special effects seen in the thermal analysis of polymers including some examples of detailed analyses by TMDSC, documenting the locally reversible melting and crystallization equilibrium within a globally metastable structure. Then illustrations of poly(oxymethylene) and PEEK are given as typical common polymeric materials. This is followed in the last section with the discussion of special effects seen in drawn polymers, as are commonly found in fibers and films.

___________________________________________________________________

6.2.1. Melting of Polyethylene

Polyethylene has experimentally been produced in many of the crystal morphologies of Fig. 5.41, including macroscopic, isometric-to-platy equilibrium crystals (Fig. 5.76 and 5.77), lamellar crystals (Fig. 5.51–53), and fibrillar structures (Fig. 5.66 and 5.67). The macroconformations of polyethylene include all areas of the diagram of Fig. 5.42. The crystal sizes (phase sizes) could be found to cover the full range from macroscopic phases to nanophases (see Sect. 2.5.2). Finally, the phases could not only be the classical glassy, crystalline, and melted phases, but also a mesophase (condis crystal, see Fig. 2.103) and a mesophase glass have been observed in addition to a less stable, monoclinic crystal (see Sect. 5.1.7). This enormous breadth of different, mostly metastable, phase structures (see Fig. 6.1) are naturally also influencing the mechanical properties. For a specific sample, thermal analysis has, thus, the goal to identify the combination of phases and establish the link of structure to property.

Figure 4.18 represents the slow dilatometry of a strictly linear poly(methylene) with 1.4×107 Da molar mass without molecules of molar mass less than 106 Da. By crystallization at elevated pressure, the sample had reached a crystallinity of 98% and an extended-chain macroconformation, i.e., it was close to equilibrium. In the melting region, one point was taken every 24 h to avoid superheating and to establish the equilibrium melting temperature of 414.6 K. Within the estimated experimental error of ±0.3 K, the same value was found by an extrapolation of the zero-entropy- production melting temperatures of lamellar crystals as a function of the lamellar thickness, given in Fig. 2.90, and resulted also from the extrapolation of the melting temperatures of many paraffins to infinite chain length, shown in Fig. 3.4.

The kinetics of melting of a similar high-molar-mass poly(methylene) is illustrated in Fig. 6.21 for different temperatures [22]. It was measured by isothermal DSC, as illustrated in Fig. 3.98. Measurements of this type, when coupled with data for the crystallization kinetics, allow to establish the temperature region of metastability that is caused by the need of crystal and molecular nucleation, discussed in Sect. 3.6 (see Fig. 3.76). The change in the melting-peak temperature of a series of different polyethylene crystals is shown in Fig. 6.22 [23]. These data were measured with a DSC as in Fig. A.9.2D. Curve E illustrates the slow-melting of the extended-chain crystals of Fig 6.21. Characteristic for the superheating of the crystals is the constant Tb with rate of heating, while Tp and Te increase (the temperatures Tb, Tp, and Te are defined in Fig. 4.62). An example of DSC curves of crystals which superheat on melting is shown in Fig. 6.92 for extended-chain crystals of poly(oxymethylene). Curve F displays data for an extended-chain polyethylene of broad molar-mass distribution as illustrated in Fig. 5.76. The crystals of Curve F have a chain extension of up to 2 m. Curve E, in contrast, was generated from crystals with an extension of up to 10 m. The superheating of the crystals of F is less than the crystals of E, and in addition, the melting range on slow dilatometry is broader because of the presence of molecules of lower molar mass which melt at a lower temperature, as is indicated in Fig. 3.76, and is documented in more detail in Sect. 7.1.

These experiments prove that crystals of the type E and F are at low temperatures, at least in part, close to equilibrium and allow the direct assessment of the equilibrium melting parameters: heat of fusion, volume change on fusion, and equilibrium melting

612 6 Single Component Materials

___________________________________________________________________

Fig. 6.21

Fig. 6.22

temperature. Adding the heat capacity to these equilibrium data, as described in Sect. 2.3 (Figs. 2.46, 2.51, 2.59, and 2.65), conversion to the integral functions of Fig. 2.23, and the phase diagram of Fig. 5.156, gives a full quantitative description of the equilibrium thermodynamics of polyethylene. This is possible even though equilibrium melting cannot be reversed, and must be done slowly to avoid superheating of the crystals.

___________________________________________________________________

The equilibrium crystals just discussed had to be grown in the hexagonal condis phase area of the phase diagram (Fig. 5.156) to achieve the chain extension by subsequent annealing of the initially grown chain-folded crystals. On crystallization from the melt in the orthorhombic phase area, the initially produced lamellar crystals also do not correspond to the crystals that one melts in a later experiment, although the crystal perfection is less than in the condis phase area. Figure 6.23 illustrates the

Fig. 6.23

change of the melting characteristics as a function of time of a polyethylene sample of the same molar mass as the extended-chain crystals F of Fig. 6.22, but crystallized at 398.7 K at atmospheric pressure [24]. As the crystallinity increases, melting peak and melting end shifts to higher temperature. At later times, crystals grow which are poorer and have lower melting temperatures. Even isothermally grown crystals, thus, are far from uniform and, as the melting temperatures indicate, they are also far from equilibrium (Tmo = 414.6 K). Only at the highest crystallization temperatures is the equilibrium melting temperature approached, but at these temperatures crystallization is exceedingly slow, as illustrated by curve 9 of Fig. 3.67. Crystallizing a melt during cooling, as is often the case in industrial applications, leads to an even broader distribution of crystals of different degrees of perfection, as can be surmised from the curves on the right of Fig. 6.23 and seen from fast calorimetry of Fig. A.10.6.

Once produced, the metastable crystal distributions must be analyzed under conditions of zero-entropy-production melting (see Sect. 2.4.2 and 2.4.3). If annealing occurs during heating, the measurements do not correspond to the starting material and cannot be linked to the properties of the sample, as shown schematically in Fig. 2.86. Crystals with lamellar thicknesses 1 and 2 melt above the zero-entropy-production melting temperature of the initial thickness . Figure 6.22 also shows a comparison of melt-crystallized polyethylene with a morphology as indicated in Fig. 5.64 [22,23].

614 6 Single Component Materials

___________________________________________________________________

Sample C was cooled at 0.65 K min 1, and sample D at 450 K min 1 C. Both had the same molar mass distribution as sample F. The melting peaks of sample C are close to zero-entropy-production melting with some reorganization or superheating. Samples of this type can be used to create a free-enthalpy map, as shown in Fig. 6.3. On faster cooling, crystallization occurs at lower temperature, as shown in Fig. A.10.6, leading to less crystal perfection and lower melting temperatures. In addition, there is a decrease in peak temperature with the rate of heating, indicating that on slow heating, the crystals improve and yield a higher melting temperature by going fromto 1 or 2 in the free enthalpy diagram of Fig. 2.86.

Crystallizing the same polyethylene used for generating the curves C, D, and F in Fig. 6.22 from dilute solution yields at higher temperatures rather well-defined lamellar crystals, as illustrated in Fig. 5.57. Their morphology is seen in Figs. 5.51 and 5.52. The fold lengths are 10 and 15 nm, as shown in Fig. 5.43. On faster cooling, crystallization begins at lower temperature and the lamellae change to dendrites as seen in Fig. 5.57. Melting of the well-formed lamellae and growth spirals is illustrated in Fig. 6.22 by curve B. A zero-entropy-production melting temperature could be established with the fast-heating microscopy, discussed in Fig. 3.95 for heating rates of 100–1000 K min 1. The dendritic morphology is illustrated in Figs. 5.56, 5.58, and 5.59. The melting of these less perfect crystals is mirrored in curve A of Fig. 6.22. It is assumed that reorganization is even faster than for the more perfect lamellae [22,23] so that no thermodynamic evaluation of the sample is possible at the rates of Fig. 3.95. The melting characteristic of dendrites can only be assessed with very fast calorimetry as described in Appendix 10.

Comparing all observed melting-peak temperatures of Fig. 6.22, one covers values from 393 to 427 K [23]. Thermodynamic equilibrium is only reached at the temperature Tmo = 414.6 K. This range of 34 K is characterizing the various metastable and unstable crystal distributions. Since the experiments assess only the melting-peak temperatures, the actual melting range is even broader. Considering the apparent heat capacities of samples of different crystallinity in the left graph of Fig. 2.45, one can deduce that the poorest crystals may melt in the glass-transition region and melting may extend up to the nonequilibrium melting caused by superheating. Overall, this may cover temperatures from 190 to 500 K.

Before the low-temperature region of melting can be explored in more detail, it is necessary to separate the contribution of the changing equilibrium-defect concentration on the heat capacity, Cp. In polyethylene, this contribution is based on the transgauche equilibrium which also influences the mechanical properties, as discussed in Sect. 5.6.6 (see Fig. 5.171). This effect on Cp is illustrated in Fig. 2.65, and the defects are analyzed with Figs. 5.98–103. Further endothermic contributions to Cp can then be assigned to irreversible latent heats of fusion. In addition, with temperature modulation, locally reversible melting was discovered within the globally metastable structure. This adds additionally to the apparent Cp [25] (see Fig. 3.92).

For polyethylene a full homologous series of oligomers exists in form of the normal paraffins. The low-molar-mass paraffins grow at atmospheric pressure into the extended-chain macroconformation. Figure 6.24 represents standard DSC and quasiisothermal TMDSC of pentacontane, C50H102. The standard DSC trace and the quasiisothermal TMDSC with small modulation amplitude are almost identical until

___________________________________________________________________

Fig. 6.24

reaching about 0.5 K from the melting end at 365.30 ±0.05 K. The broader melting peak of the standard DSC is due to instrument lag, and the lower area for the heat of fusion by TMDSC is due to incomplete melting during the modulation cycles [26], discussed in more detail with Figs. A.13.11–15. At the last point in the melting peak, over 60% of the heat of fusion should have been absorbed, making the major part of the reversible melting less than 0.1 K wide. The calorimeter, however, could not deliver that much heat of fusion at the 0.05 K amplitude, resulting in incomplete melting and crystallization. The first 13 quasi-isothermal cycles at the next temperature produced the final melting before reaching the response due to the liquid heat capacity. The first deviation of the measured Cp from the vibrational value occurs at about 250 K, as seen in Fig. 4.50. This is due to equilibrium defects in the crystal as found in polyethylene (Fig. 2.65). It gradually changes into a small amount of reversible melting of either short-chain impurities on the crystal surfaces, or a small fraction of poorly crystallized pentacontane. A small amount of irreversible melting of impurities is also seen in the standard DSC trace. The TMDSC completes 62% of the fusion within the last 0.1 K of the melting peak. The information about the reversibility of paraffins and narrow molar mass fractions of polyethylene (PE) is collected in Fig. 3.75. Up to 75 carbon atoms the crystallization can be reversible, above, a need of molecular nucleation introduces supercooling (see Sect. 3.5.6).

Changing from pure paraffins to narrow fractions of similarly low-molar-mass fractions of PE, the reversibility is largely retained, as seen from Fig. 6.25 which illustrates the melting of fraction PE560 of a weight average molar mass of 560 Da and polydispersity of 1.06. The melting temperature of 354.5 K for C40H82 with a similar molar mass as PE560 approximates the melting end of the quasi-isothermal data, as well as the beginning of crystallization on quasi-isothermal TMDSC on cooling. The low-temperature melting peak at 332.6 K is most likely the eutectic

616 6 Single Component Materials

___________________________________________________________________

Fig. 6.25

temperature of the distribution of molecular lengths discussed in detail in Chap. 7 and may contain some of the transitions to a high-temperature mesophase which are observed in paraffins with a lower mass than that of C40H82. The apparent reversing heat capacity shows a sizeable contribution to the melting, but not as much as seen for the pure C50H102 in Fig. 6.24 where all fusion is complete within 1.0 K, i.e., with a modulation amplitude of 0.5 K, the melting of C50H102 would be fully reversing. The width of the melting region of PE560 is about 30 K. The broadening of the melting of PE560 in the quasi-isothermal measurements is due to the chain-length distribution and much of the irreversibility is due to slow diffusion and recrystallization needed to set up the eutectic crystal distributions. On quasi-isothermal TMDSC during cooling, the change in reversing crystallization due to perfection of the crystal distribution can be followed. It is similar to the slow changes observed in Fig. 6.36 for the reversing melting of a POE of similar molar mass.

Figure 6.26 illustrates the standard DSC and quasi-isothermal TMDSC of average molar mass 2,150 Da (PE2150) with a polydispersity of 1.15. This molar mass still yields largely extended-chain crystals on slow crystallization. The melting region is narrower and the reversing heat capacity is much less than for PE560 since at higher molar masses the spread of the melting temperatures of the components is less, and it exceeds the critical length of Fig. 3.75 for most of its components. The supercooling can be seen from the difference between the marked end of melting and beginning of crystallization in Fig. 6.27. Almost identical reversibility on cooling after the irreversible crystallization and on second heating characterize PE2150 and is seen in the quasi-isothermal TMDSC traces. The first heating indicates the presence of poorer crystals which result in larger and more time-dependent reversing contributions. Most likely, the slow TMDSC with modulation on cooling has led to a better separation of the various lengths of the molecules.