Thermal Analysis of Polymeric Materials

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Fig. 6.26

Fig. 6.27

To summarize, the analysis of the melting of oligomers illustrates cases from practically fully reversible, sharp melting (Fig. 6.24), to broad reversing melting due to the presence of multiple components and possibly incomplete phase separation. At higher mass, the extended-chain crystals decrease rapidly in reversibility, as shown in Fig. 6.26. A comparing of these data to an extended-chain fraction of lower mass and

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an unfractionated polyethylene crystallized to an extended-chain sample of 98% crystallinity and an average molar mass of 130,000 Da is given in Fig. 6.28. The last shows even less reversible melting. The very small remaining amount of reversibility in PE130000 can be linked quantitatively to an equilibrium phase separation of the low-molar-mass fractions and is discussed in Chap. 7. One concludes that the extended-chain crystals of paraffins and polyethylene melt irreversibly if they have a

Fig. 6.28

higher molar mass than the critical length of Fig. 3.75. The data of the extended-chain crystals of poly(oxyethylene) of molar mass 5,000 Da of Figs. 3.97 and 3.98 suggest a similar absence of reversible melting in the aliphatic polyethers.

Turning to folded-chain crystals, the amount of reversing melting increases. Figures 6.29 and 6.30 illustrate TMDSC results of a rather low molar mass PE15520 of a low polydispersity of 1.08. The apparent, reversing heat capacities on cooling after irreversible crystallization and on second heating are almost identical to PE2150 in Fig. 6.27, despite the rather small crystallinity when going to the folded-chain crystals. Below 340 K the PE15520 is also characterized by a higher apparent reversing heat capacity than PE2150. The apparent reversing heat capacity of PE15520 in the melting range is less on cooling than on first and second heating. The increased reversing melting in the heating experiment seems to originate from secondary crystals grown at lower temperature during the cooling experiment within in the matrix of the primary crystals. In part, these secondary crystals have perfected by the time they were analyzed at higher temperature, and in part they crystallized reversibly in the wide temperature range 335±40 K. The reversing melting may involve short molecules or sections of longer molecules of lengths less than 10 nm that remain partially crystallized as expected from Fig. 3.75. On quasi-isothermal experiments of long duration, the reversing melting during the first heating reaches

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Fig. 6.29

Fig. 6.30

ultimate levels of reversibility which are still above the level seen on cooling. As for all other polymers of high molar mass, discussed below, two processes are involved in the kinetics of the apparent reversing heat capacity. Their relaxation times are longer than the response of the calorimeter, and the short-time change is usually based on an exotherm. One expects, thus, that an annealing process is involved in the

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decrease of the reversing heat capacity which starts with an exothermic crystal perfection or further crystallization. Each sufficiently perfected crystal has a higher melting temperature and is removed from the next melting cycle. Similarly, a fully melted molecule or molecular segment above the critical length would ultimately be removed from reversing melting since it would need a renewed molecular nucleation to recrystallize (see Sect. 3.5.6). Because of the slow perfection it takes several hundred minutes to reach steady state within the DSC, which then may be a true local equilibrium within the matrix of the metastable, higher-melting crystals. The supercooling of the sample can be seen from the difference between the marked end of melting and beginning of crystallization in Fig. 6.30 (see also Fig. 3.75).

Other TMDSC analyses differ only little from the data presented in Figs. 6.29 and 6.30. Small changes being expected by the variation in molar mass and sample history [1]. Figure 6.31 shows the results of high-frequency modulation of polyethylene in the melting region (MW = 52,000 Da, polydispersity 2.9, modulation 0.2 K) [28]. Above 0.1 Hz, the reversing Cp becomes almost independent of frequency with a maximum between 38 and 41 J K 1 mol 1 at 402 K. This value compares to about 30 J K 1 mol 1 for the vibrational contribution in the crystal (see Fig. 2.51), 34 J K 1 mol 1

Fig. 6.31

for the experimental Cp of a sample of 99% extended-chain crystallinity, and 35 J K 1 mol 1 for Cp of the liquid. Accidentally the liquid and experimental crystalline Cp are similar, so that the crystallinity is irrelevant at this temperature. Note that the maximum reversing heat capacity at low frequency is also similar to the quasi-isothermal values of Fig. 6.28. The relaxation time for the frequency-dependent part of the excess heat capacity was 14 s. Within error limits, Fig. 6.31 separates the apparent heat capacity from the frequency-dependent, slow reversible latent heat, and the faster contribution from the vibrations and trans-gauche equilibrium.

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A combined study of TMDSC, WAXD, SAXS, and AFM of the crystallization of polyethylene with a weight-average mass of 52,300 Da and a polydispersity of 3.2 was made to study the structural changes of the reversing melting [29]. Figure 6.32 illustrates the change of the apparent reversing Cp with time. An excess Cp is generated beyond the values calculated for the proper proportion of the experimental Cp of amorphous and crystalline polyethylene (dotted line). During the primary

Fig. 6.32

crystallization, the excess Cp follows qualitatively the increase in crystallinity, deduced from the area under the total heat-flow-rate curve (dashed line). During the secondary crystallization phase, after about 75 min, the excess heat capacity decreases slightly, while the crystallinity still increases. The apparent, excess reversing heat capacities are close to the low frequency values of Fig. 6.31 for similar polyethylene. At higher modulation frequencies, the apparent, reversing heat capacity should drop to the reversible level of 38 J K 1 mol 1, as marked by the dotted line. The Cp calculated from the vibrational contribution from the crystal added to the 39% amorphous PE is marked by the thin line and arrow at 32 J K 1 mol 1.

The structural changes of the sample in Fig. 6.32 were followed by similar quasiisothermal temperature modulations during WAXD and SAXS. An excerpt from the data is illustrated in Fig. 6.33. The temperature modulation is indicated by the thin lines. It consists of a cooling ramp from 400.2 to 398.2 K at 3 K min 1, followed by an isotherm of 19.6 s and heating to the starting temperature and another isotherm. The curve (a) shows the change of the crystallinity index, calculated from the area of the 110 and 200 diffraction peaks above an estimated, amorphous scattering background, normalized to the 90 min value. Quite clearly, there exists a modulation out-of-phase with the temperature and the underlying increase in crystallinity due to the secondary crystallization is also noticeable. The fitted curve corresponds to a

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Fig. 6.33

crystallinity-index change of 2.1±0.4% from maximum to minimum, about double that calculated from the calorimetrical data. From the diffraction-peak positions, the change in the density of the crystals could be assessed, as shown in curve (b). The oscillation matched the known density change with temperature of polyethylene. The noticeable decrease in average density with time cannot be due to the perfection of the crystals, which would call for a density increase, but must be assigned to the later growing, less-perfect crystals. The lateral crystal dimensions from the WAXD peak widths remained constant during the modulation at a value of 35 to 40 nm, much smaller than the overall lamellar dimensions seen by AFM to be in the micrometer range, but similar in size to a mosaic substructure, also detectable by AFM. Curve (c) depicts the total SAXS power which also increases parallel to the total heat-flow rate in Fig. 6.32, i.e., with overall crystallinity. The modulation, however, is in-phase with the temperature and should be a measure of an increase in the local amorphouscrystalline volume fraction between the lamellae on increasing the temperature. This interpretation is based on a perfect lamellar structure-model of stacked crystals and amorphous material with a constant (electron-) density difference between the two phases. With further assumptions, the most probable thickness of the amorphous and crystalline layers and the total long period were computed. Figure 6.34 combines these WAXD and SAXS results, suggesting that during the modulation on increasing the temperature, the amorphous layer increases by as much as the crystalline layer decreases. Overall, the crystalline thickness increases slightly with time, as expected

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Fig. 6.34

from the annealing during secondary crystallization, and the modulation amplitude of both, the crystalline and amorphous layers is 0.28 ±0.05 nm and was proposed to coincide with model calculation of “fold-surface melting” [29].

This “fold-surface melting” was observed already some 40 years ago [30]. A comparison to annealing and lateral melting is given in Ref. [31]. The main conclusions from the study of surface melting were that the thermodynamically reversible process occurs over a wide temperature range, does not fully destroy the crystal core, and develops at a lower temperature than the lateral, irreversible melting [32]. It was proposed that this discrepancy can be accounted for by a half-as-large heat of fusion in the surface layer. Such lower heat of fusion was proven to exist for the mobile-oriented phase discovered in gel-spun fibers of polyethylene which is discussed in Sect. 6.2.6.

Although this picture placing the reversible melting exclusively at the fold surface seems possible, it would be unique for polyethylene. The “fold-surface melting” is more likely connected to the gauche-trans equilibrium defects which have a tendency to diffuse to the fold surface (see Sect. 5.3.4). In this case they would need little or no additional latent heat. New experiments on high-density, linear polyethylene led to information about the specific reversible melting, a quantity defined as the ratio of reversible to irreversible melting [33]. Up to 350 K, this specific reversible melting is about 0.5 and decreases toward zero at higher temperatures, within the main melting peak. This measurement is more in accord with reversible growth-face melting since it links the irreversible with reversible melting. Such reversible melting on the growth faces also can be proven for several polymers which cannot change their lamellar surface reversibly, as described in the next section. More details about the melting of polyethylene segments with similar specific reversible melting are discussed in Chap. 7 for copolymers [1]. In this case, growth-face reversibility could be proven.

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6.2.2 Reversible Melting and Poor Crystals

The discussion of the melting of polyethylene in the previous section revealed that it is possible to establish equilibrium and metastable phase diagrams, but only from zero-entropy-production heating experiments, not on cooling. There is no reversible melting of the type that could be accomplished for nucleated indium (see Figs. 4.106 and 4.107, and 4.109 and 4.134), or studied for the isotropization of smalland largemolecule liquid crystals (see Figs. 5.144 and 5.154). The reason of this missing reversibility is the need to molecular nucleation, as seen from the plot of melting and crystallization rates in Fig. 3.76 and discussed in Sects. 3.5 and 3.6.

Poly(oxyethylene). The reversing melting of a poorly crystallized oligomer of poly(oxyethylene) with mass 1500 Da is analyzed in Fig. 6.35 with quasi-isothermal TMDSC. A comparison of this sample with a standard DSC trace is shown in

Fig. 6.35

Fig. 4.123. The reversing melting is observed in the low-temperature range, where one expects the lower-molar-mass crystals to melt. The quasi-isothermal TMDSC experiments with decreasing temperature allow more perfect crystals to grow, and only a gradually changing reversing heat capacity is observed on cooling and second heating, similar to the behavior of extended-chain crystals of paraffins and polyethylene (see Sect. 6.2.1). Only at perhaps 200 K is the vibrational Cp reached.

The following reasoning may explain the reversing melting in Fig. 6.35. Due to the position of the reversing melting on the low-temperature side of the irreversible melting peak in Fig. 4.123, one expects the reversing melting to involve molecules of lower than the average length. Well crystallized, extended-chain poly(oxyethylene) with a molar mass above 1,000 Da, the limit for reversible melting from Fig. 3.91, should melt irreversibly. Comparing the apparent, reversing Cp of POE1500 with a

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higher molar mass sample POE5000, analyzed in Figs. 3.88 and 3.89, one observes that they are equal up to 300 K. This means that the increase in Cp beyond the vibrational limit is due to conformational motion (as also in polyethylene in Fig. 2.65). Above 300 K, the Cp of POE1500 increases faster than the Cp of POE5000. Thus, one expects that for the well-crystallized samples, only the additional increase of the reversing Cp is due to reversible melting of short-chain molecules within the samples. This reversible melting is limited, according to Fig. 3.91, to a length of 75 backboneatoms. These melt at 316 K and should limit reversing melting in Fig. 6.35.

The next problem concerns the reversing melting peak in Fig. 6.35 which is observed for poorly crystallized PO1500. An interesting observation is a strong increase of the reversing melting peak with long time periods on extending the modulation, illustrated in Fig. 6.36. This is in contrast to a decrease, seen in most polymers such as the poly(ethylene terephthalate) shown in Fig. 4.137. Along the curve, a slow decrease in total crystallinity with time after raising the temperature to 315.7 K is marked. These values were obtained by standard DSC performed on

Fig. 6.36

parallel runs, stopped at the indicated times. The heat-flow rates at an early time (13 min) and at a late time (600 min) are shown separately in Fig. 6.37; in addition, Lissajous figures are depicted in Fig. 4.114 for the same run. The curve after 600 min is distinctly of larger amplitude, and the difference between the two curves reveals more melting than crystallization. While the melting which follows the crystallization is practically continuous, there is a small supercooling between melting and crystallization. Overall, then, there is a decrease in crystallinity in time, as demonstrated by Fig. 6.36. Due to the different latent-heat effects on cooling and heating, the heat-flow rate curves in the melting region are not strictly sinusoidal anymore. The calculated apparent heat capacities in Figs. 6.35 and 6.36, thus, can only be an