Thermal Analysis of Polymeric Materials

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sequential values for To for the same quasi-isothermal TMDSC of the melting of indium as shown in Figs. 4.109 and 4.134. Without melting and crystallization, the almost horizontal Lissajous ellipses are so flat that they are only slightly thicker horizontals on the left and right of the center figure. The continuity of melting and crystallization with a slope determined by the heat conductivity of the calorimeter is obvious in the center modulation. It is evident that steady state is lost as soon as melting starts. The melting of the remaining 75% of indium on increasing the base temperature shows also clearly. The heat capacities of solid and liquid indium are almost identical, so that the heat-flow rate before and after melting is the same. It is apparent from this discussion indium that, although the analysis of the heat of fusion is best and more precisely done by standard DSC, the check with TMDSC teaches much about the quality and limitations of the calorimeter on hand. No TMDSC should be used for quantitative measurements without testing its limits on the melting and crystallization of a reversibly melting substance like indium.

It remains to introduce the thermal characterization of semicrystalline polymers with incompletely irreversible melting. While separation of cold crystallization from heat capacity was from the beginning one of the premier applications of TMDSC, as illustrated in Fig. 4.122, and the inability to improve on the quantitative analysis of sharp melting substances one of its biggest detractions, polymer melting, being intermediate in reversibility, caused most confusion. A schematic plot of melting and crystallization rates based on a large volume of kinetic data on large, intermediate, and small molecules (polymers, oligomers, and monomers, respectively) is given in Fig. 3.76, together with details of the kinetics in Sects. 3.5 and 3.6. Melting is usually rather fast. In calorimetry, it is often sufficient to assume melting is limited only by heat conduction. Also, many small molecules show continuity of melting through the equilibrium melting temperature, Tm. Flexible, longer molecules, however, lose on melting their shape and become conformationally disordered. It was suggested that each flexible molecule must undergo a molecular nucleation step before it can crystallize, leading to the 5 15 K region of metastability in which neither melting nor crystallization is possible, even in the presence of crystal nuclei.

From the analysis of the melting and crystallization kinetics of polymers, one would expect no contribution of melting to the reversing heat capacity. Indeed, this could be documented on well-crystallized poly(oxyethylene) with Figs. 3.89 and 4.123. With help of Fig. 3.76 it can be seen that whenever the sample sensor reached or exceeded the melting temperature, some melting occurred, but during the cooling cycle no recrystallization reverses the melting. Using the quasi-isothermal mode, the remaining small effect of the melting spike due to loss of stationarity, as modeled in Fig. 4.100, appears only in the first cycle and is not included in the analysis when using only the last 10 min of a 20-min experiment. Again, as in the indium melting, the actual melting is best analyzed by standard DSC or in the time domain of TMDSC under conditions of regaining steady state within each modulation cycle.

A similar analysis of a melt-crystallized poly(ethylene terephthalate), PET, of the typical molecular mass of a polyester showed a surprising reversing melting peak, as seen in Fig. 3.92. On comparison with an amorphous PET, one finds that the reversing peak depends on crystallization history, as is shown in Fig. 4.136. The change of the glass transition with crystallization is typical for polymers. It shows a

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but ultimately a reversible portion remains at very long time. These experiments were interpreted as showing that the melting of polymers is basically irreversible, but specific details of crystal melting had been uncovered that were never before seen by calorimetry. To show reversible melting and crystallization, some polymer molecules must melt only partially. On cooling, these partially melted molecules do not need to undergo any molecular nucleation and can recrystallize close to reversibly (see Sects. 3.5 and 3.6). Some reversibility of melting and crystallization is thus maintained on a sub-molecular level. Once a molecule melts completely, it cannot recrystallize without supercooling beyond the region of metastability of Fig. 3.76. A new tool for the assessment of the morphology of semicrystalline polymers has thus been found in TMDSC. It is likely that the partially meltable molecules can be linked to decoupling of parts of molecules on the crystal surfaces, as is discussed in Sect. 6.2.

The melting range of polymers, in addition, is much broader than the sharp melting standards, such as indium. Most of this broadening is due to two causes, a wide distribution of crystal sizes, and the possible presence of lower melting oligomers or the existence of a distribution of lengths of crystallizable sequences in copolymers. Indications of small amounts of oligomers that may have a sufficiently small gap of metastability in polymer samples were found in low-molar-mass poly(oxyethylene). Figure 4.114 shows the Lissajous figures of a long-time quasi-isothermal experiment of such a sample in the melting range. In this case the amount of melting and crystallizing crystals increases with time. The analysis can be carried out with varying modulation amplitude, so that the metastable melting/crystallization gap can be assessed quantitatively. Since the low-molar-mass crystals melt at the low-tempera- ture side of the melting peak, they can be easily distinguished from the partially melted crystals of high molar mass.

A final topic in polymer melting concerns reorganization, recrystallization, or annealing of crystals during melting, a process very difficult to study with standard DSC. In the past, measurements with different heating rates or on chemically altered crystals were necessary for the study of reorganization as described in Chaps. 5 and 6. Figure 4.138 shows a qualitative proof of such reorganization on PET. Despite loss of steady state in the melting range, it is possible by using a modulation that never permits cooling described in Fig. 4.86, to show a substantial exothermic heat flow in the melting region. The loss of steady state in the experiment of Fig. 4.138 is indicated by the variation of heating rate, but the reorganization exotherm is also seen at temperatures where the heating rate is zero. Any heat evolved, thus, must come from crystallization or from crystal perfection, recrystallization, or annealing. In Fig. 4.139 one can see that the reversing melting endotherm is larger than the total melting endotherm, indicating that the exotherm is not additional, new crystallization. Again, a quantitative analysis must rely on time-domain data because of the loss of steady state.

Converting the data of Fig. 4.138 to the reversing and total contributions without considering the time-domain analysis, reasonable data are obtained only up to the beginning of melting, as seen in Fig. 4.139 (see also Fig. 4.122). Following the endotherms and exotherms of Fig. 4.138 gives for the chosen time scale a picture of the two processes. Figure 4.116 shows the change in reversing melting with modulation period for the example of nylon 6 and its possible analysis through the

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Fig. 4.138

Fig. 4.139

model in Fig. 4.117. In this example, as for the TMDSC of poly(ethylene terephthalate) in Fig. 4.138, only irreversible melting with a temperature-dependent rate was analyzed by avoiding cooling of the sample. The quasi-isothermal analyses in Figs. 4.136 and 4.137, in contrast, test the reversibility by applying fully symmetric heating and cooling cycles and give proof that true reversibility exists, but is only a small fraction of the reversing melting peak of Fig. 4.139.

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4.4.8 Chemical Reactions

In the description of applications of TMDSC, heat capacity is the most subtle effect, followed by the glass transition which manifests itself in a time-dependent step in the heat capacity with a possible additional small enthalpy-relaxation. The next larger step is the first-order transitions with heat flows up to 100 times those experienced in heat capacity measurements. The topic of this section can bring even larger heat flows. The main point is, as before, to distinguish between reactions that are close enough to equilibrium to be influenced by the modulation amplitudes and fully irreversible reactions. The fully irreversible reactions are naturally best studied by standard DSC. By TMDSC it is, however, possible to study simultaneously reversing effects, not possible with a DSC. Figure 4.140 shows the apparent heat capacity of a fullerene, C70, measured while the sample underwent considerable oxidation. The first two small endotherms in the vicinity of 300 K are rather broad, reversible mesophase transitions of the type crystal to plastic crystal and can be seen in both, the heat capacity and the total heat-flow rate. The huge exotherm starting at about 575 K does not seriously affect the reversing heat capacity measurement. One can conclude safely, that up to almost 700 K, no further phase transitions exist.

Fig. 4.140

A second example of a chemical reaction during TMDSC is the analysis of the cure of an epoxide. In this case both the exotherm and the change in heat capacity could be used to analyze the cure kinetics as shown in Fig. 4.141. The exothermic, nonreversing heat-flow rate is a measure of the progress of the cross-linking, and the reversing Cp indicates the development of the glass with time. A full TTT (time- temperature-transition) diagram of the liquid-gel-glass transitions is thus established by TMDSC to the control the curing of such materials [42], as shown in Fig. 4.142.

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Fig. 4.141

Fig. 4.142

In summary, the applications of TMDSC look quite different from those of DSC. Many important applications can only be solved by TMDSC. A good number of others are, however, still better, and sometimes only, solvable by DSC. Fortunately any TMDSC can also be run without modulation under DSC conditions. The development of TMDSC has also led to long-awaited progress in the hardware and software improvements of DSC as illustrated with Fig. 4.54 and Appendix 11.

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Hooke’s law, which holds for the ideal, reversible, linear, elastic response of a system to an applied stress. All elastic materials follow Hooke’s law when the stress is sufficiently small.

Figure 4.144 shows a list of some typical bulk moduli, illustrating the large range possible for different materials. The elastic spring shown, is the symbol of an elastic response of a material. The sketch in the center illustrates the extension of a rigid macromolecule on an atomic scale. Each atom of the network polymer undergoes a reversible, affine deformation, i.e., it is strained by the same amount as the macroscopic sample. At larger stresses, the deformation becomes plastic, meaning the sample deforms beyond the elastic limit and does not regain its original shape on removal of the stress.

Fig. 4.144

The bulk modulus 1/ and Young’s modulus E are related through the equation at the bottom of Fig. 4.144. The symbol represents Poisson’s ratio, the linear, lateral contraction divided by the linear extension in a tensile experiment. One can compute that a value of 0.5 for Poisson’s ratio leads to a constant volume on extension, a situation often achieved in rubbery materials. Most crystals and glasses have a Poisson’s ratio between 0.2 and 0.35. Note that a value of close to 0.5 makes Young’s modulus much smaller than the bulk modulus, a case realized by rubbery macromolecules which can change their shape on extension at constant volume (see Sect. 4.6.5). The bulk modulus of small-molecule liquids and solids decreases normally with increasing temperature, while increasing pressure causes an increase.

The graph in Fig. 4.145 illustrates Young’s modulus, E, for atactic polystyrene. This graph shows that for linear macromolecules, the modulus changes in a complicated manner with temperature. In addition, one finds that the modulus depends on time, a topic which is taken up in Section 4.5.5 when discussing DMA.

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Fig. 4.145

The present graph refers to a time scale of about 10 s for any one measurement and is to be compared, for example, to a DSC scan at 6 K min 1. On the left-hand side of the graph, the high moduli of the glassy and semicrystalline solid are seen and can be compared to the table of bulk moduli in Fig. 4.144. At the glass transition, Young’s modulus for amorphous polystyrene starts dropping towards zero, as is expected for a liquid. The applied stress causes the molecules to flow, so that the strain increases without a limit when given enough time. Before very low values of E are reached, however, the untangling of the macromolecular chains requires more time than the 10 s the experiment permits. For a given time scale, the modulus reaches the so-called rubber-elastic plateau. Only at higher temperature (>450 K) is the molecular motion fast enough for the viscous flow to reduce the modulus to zero. Introducing permanent cross-links between the macromolecules by chemical bonds, the rubberelastic plateau is followed with a gradual increase in E.

The data for a semicrystalline sample of polystyrene are also shown in the graph of Fig. 4.145. They show a much higher E than the rubbery plateau. Here the crystals form a dense network between the parts of the molecules that become liquid at the glass transition temperature. This network prohibits flow beyond the rubber elastic extension of the liquid parts of the molecules. Unimpeded flow is possible only after the crystals melt in the vicinity of 500 K.

4.5.2 Instrumentation of TMA

A schematic diagram illustrating a typical thermomechanical analyzer is shown in Fig. 4.146. This instrument was produced by the Perkin–Elmer Co. Temperature is controlled through a heater and the coolant at the bottom. Atmosphere control is possible through the sample tube. The heavy black probe measures the position of the