Thermal Analysis of Polymeric Materials
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7.2 Melting Transitions of Copolymers |
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Fig. 7.37
Fig. 7.38
DSC, as given in Fig. 7.39. It is noted, that reversing melting occurs always along with irreversible melting and is absent far from irreversible melting, suggesting the same basic process for both, different from the reversible changes in fold-length seen in polyethylene in Fig. 6.34. At low temperature, the specific reversibility of LLDPE reaches 70%, at higher temperature, this fraction decreases. Only close to the glass transition does the cooling and heating yields similar specific reversibility.
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Fig. 7.39
Since Fig. 7.39 shows an increase on the reversing melting, just as illustrated in Fig. 6.30, the annealing of LLDPE was followed for different lengths of time after cooling to a given crystallinity and temperature. The results are shown in Fig. 7.40. The time-development of this annealing for one example is reproduced in 7.41. Finally, the annealed samples for the different times shown in Fig. 7.41 are reheated for analysis of the crystallinity distribution. The results are displayed Fig. 7.42.
Fig. 7.40
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Fig. 7.41
Fig. 7.42
This large volume of data shows that the apparent reversing specific heat capacity increases with comonomer content. This is seen best immediately above the glass transition temperature, as displayed in the insert in Fig. 7.37. The amount of irreversible crystals, which are identified as the normally grown folded-chain crystals, decreases with increasing comonomer composition, as expected (see Figs. 7.37 and 7.38 and compare to Fig. 7.35).
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The nature of the crystals, identified by the reversing heat capacity, yields for all analyzed samples similar specific reversibility, as seen in Fig. 7.39. Even normal linear polyethylene has a similar specific reversible melting [18]. One expects that both, the orthorhombic as well as the hexagonal phase contribute to the reversible melting, as can be discerned from the annealing experiments. Figure 7.40 indicates that after long-time annealing much, but not all of the excess heat capacity has disappeared by crystal perfection, as revealed by the higher-temperature endotherm in Fig. 7.41. It is also obvious that only local improvement is possible by annealing at anyone temperature. Figure 7.40 indicates that further cooling reaches again, the same high value of the total and reversing heat capacity.
Using quasi-isothermal TMDSC, the kinetic changes on annealing can be followed even more quantitatively. Figure 7.43 illustrates the first 100 min of annealing with
Fig. 7.43
the heat-flow-rate output, and Fig. 7.44, with the heat capacity. The final time plot includes the frequency correction and a comparison to data in the melt region which show no time dependence. The results are given in Fig. 7.45. From Figs. 43–45 one can see two changes with annealing time. First, there is a residual crystallization or crystal perfection, marked by the excess exotherm in the first few modulation cycles of Fig. 7.43. Its relaxation time is about 5 min as seen in Fig. 7.44. It causes a decrease in the reversing signal due to either the growth of higher melting crystals, or an improvement of crystals still unmelted in the crystallization cycle. Next, there is a slowly decreasing excess endotherm of the heat-flow rate stretching over the whole time shown in Fig. 7.43. Its relaxation time is derived from Fig. 7.44 to be about 100 min. In this case, it seems that some of the crystallizing polymer segments improve sufficiently on crystallization, so that on the next heating cycle they do not melt again. Despite of this slow decrease in reversing melting, considerable reversibility remains
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Fig. 7.44
Fig. 7.45
when the kinetic data are extrapolated to infinite time. The corrected heat capacity in Fig. 7.45 at 500 min is still above that of the liquid polymer and the crystal, as can be seen from Fig. 7.40. The proof of full reversibility after long time annealing is further documented by the perfect Lissajous figures of the sawtooth modulation in Fig. 7.46. The response of the calorimeter is linear, stationary, and reaches steady state for all amplitudes (see Sect. 4.4).
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Fig. 7.46
This analysis of the crystallization, melting, and annealing of LLDPE, has a rather wide application to crystallization of polymers. Its advantage is the rather large concentration of the specific reversing contribution to melting, crystallization, and annealing. This reversing contribution in the melting range varies from polymer to polymer and changes also depending on thermal, mechanical, and chemical history. Quite similar observations were made for a number of homopolymers discussed in Chap. 6. Clearly, there are at least six different contributions to the apparent heat capacity of the copolymers, and under proper circumstances also in homopolymers. The first three contributions are truly reversible:
1.Vibrational heat capacity, as described in Sect. 2.3 for solids and liquids.
2.Gauche-trans equilibrium or other conformational changes which produce an increase beyond the vibrational heat capacity of the solid polymers, as documented with Fig. 2.65 and described in Sect. 5.3 for polyethylene.
3.Fully reversible melting, as just shown for LLDPE and many other polymers. This reversible melting is either caused by short, decoupled segments of the molecules (see Figs. 3.75 and 3.91) or indicates remaining molecular nuclei.
The second three contributions are increasingly more irreversible:
4.Crystal perfection with the relaxation time of ca. 100 min in Fig. 7.44 is often observed on reheating a sample for annealing or recrystallization (see Sect. 6.2.3).
5.Secondary crystallization, which has a time constant of approximately 5 min for the LLDPE. The contributions 4 and 5 contribute to the annealing peak, usually characterized by an endotherm at 5–15 K higher temperature (see Fig. 7.42).
6.The primary crystallization and melting which commonly is the biggest effect and shows temperature differences between crystal growth and melting of usually 10 to 30 K due to crystal and molecular nucleation (see Sect. 3.5).
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PETcoOB and POBcoON. A second example of thermal analysis of copolymers involves the two systems, poly(ethylene terephthalate-co-oxybenzoate), PETcoOB, and poly(oxybenzoate-co-oxynaphthoate), POBcoON. The structural formulas of the CRUs are as follows:
oxyethyleneterephthaloyl: oxy-1,4-benzoyl: oxy-2,6-naphthaloyl:
Of special importance is in this case that the backbone of the copolymer can change chemically by trans-esterification (see Fig. 3.47). In fact, heating poly(ethylene terephthalate) and acetoxybenzoic acid in the melt is a common synthetic route to PETcoOB. The inclusion of oxybenzoate groups makes poly(ethylene terephthalate) increasingly stiffer (see Fig. 1.50). In POBcoON, oxynaphthoate adds an additional off-set of the large zig-zag of the benzoate. As a result of this chain stiffening, the PETcoOB with more than 30 mol-% oxybenzoate shows an anisotropic melt, as for a nematic main-chain liquid crystal (see Fig. 5.136) and the system POBcoON has a mesophase character over the whole concentration range.
Figure 7.47 illustrates the change of the glass transition of PETcoOB with concentration. Surprisingly, the glass transition temperatures stay rather constant. In addition, there is a wide concentration region where two glass transitions can be seen (see also Sect. 7.3 for the normal copolymer behavior). The only simple explanation for such behavior is that locally two different aggregations of stiffer and more flexible segments are possible, each with a practically constant glass transition temperature, almost 100 K apart. The sketch in Fig. 5.136 suggests how such separation, perhaps of nanophase-size, may be possible in a basically liquid-crystal-like structure.
Fig. 7.47
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The melting or disordering transition shown on the right of Fig. 7.47 changes with concentration without noticeable effect from the change in the melt from isotropic to the anisotropic melt (liquid crystal?). Although the diagram looks like a eutectic diagram, it may be showing a partial solid solution (isodimorphism). When comparing to the normal copolymers of poly(ethylene terephthalate) of Figs. 7.26 and 7.28, the changes of the transition temperatures are much smaller than expected for full demixing and remixing of the components and the heats of transition do not decrease below 30% of that of the corresponding homopolymers, which also supports the existence of a nanophase-separation in the melt. In the benzoate-rich region of the phase diagram, macroscopic phase separation becomes noticeable by optical microscopy, particularly for polymers that are not fully randomized. A full characterization has not yet been completed for this interesting copolymer.
The POBcoON is even more intriguing. These copolymers are commercially available under the trade name Vectra™. In contrast to PETcoOB, the melt of POBcoON is over a wide temperature range an anisotropic, but homogeneous solution. On cooling, the copolymer becomes semicrystalline with rather low crystallinity in the mid-range of concentrations. Figure 7.48 illustrates the thermal analysis of the 58/24 copolymer, crystallized at two temperatures for different lengths of time [19]. A very small amount of hexagonal condis crystals forms first (peak B), to be followed by an orthorhombic phase (peak A) which perfects with crystallization temperature and time and ultimately may exceed the stability of the hexagonal phase. On crystallizing above 490 K, the endotherm of the orthorhombic phase disorders directly into the anisotropic melt, as is illustrated in Fig. 7.49. The heat capacity of this copolymer is discussed in Sect. 2.3.10 and reveals a very broad glass transition region, typical for semicrystalline polymers with small crystals (see also Sects. 7.3 and 6.3, for the glass transition, see Figs. 2.64 and 7.50).
Fig. 7.48
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Fig. 7.49
Figure 7.50 displays heat capacities for a high concentration of oxybenzoate, and Fig. 7.51 presents the corresponding X-ray-diffraction results. Two models have been developed for the description of the small crystals. One is called the nonperiodic layer model. In it, one assumes that the ordered domains are formed by the lateral register of similar, but nonperiodic repeating units [20,21] in a fashion similar to the cold crystallization model (see Fig. 7.29). In this case, at least a nanophase separation is
Fig. 7.50
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Fig. 7.51
required. The second model is called the paracrystalline lattice model. In this model, ordered domains are formed without sequence matching by the presence of conformational correlations between the different repeating units [22]. In the common scheme of phase diagrams this corresponds to a solid solution. Detailed X-ray patterns have been computed for the latter model and agree well with the observed patterns [23]. Most likely, the actual crystallization requires elements of both models, a certain amount of phase separation, and some solid solution formation.
The results of thermal analysis and X-ray structure analysis are next combined in Fig. 7.52 to a nonequilibrium phase diagram for samples that were crystallized quickly [24]. Large areas of the diagram are still not fully explored and change considerably for different thermal histories, as outlined above. At least in the orthorhombic areas, one expects a normal semicrystalline structure with nanophase separation, causing the broad glass transition. In the hexagonal and anisotropic melt, however, there seems to be, in contrast to PETcoOB, only a single phase structure. The limit of existence of this copolymer system is set by decomposition, marked in Fig. 7.52 by the symbolsat about 750 K from data based on thermogravimetry.
The observations on the examples of the close-to-random copolymers in the last two sections show that a number of arrested equilibria can be superimposed and give rise to different local nanophases. The chemical equilibrium may be totally arrested, as in most vinyl polymers, or actively drifting towards an equilibrium distribution, as in the described polyesters. The transesterification starts below the melting temperature. Furthermore, there may be equilibria of the different sequences of repeating units which are driven by crystallization or liquid-liquid phase separation. In addition, these phase separations are coupled to the physical diffusion to minimize the free enthalpy. The diffusion of the segments, in turn, is hindered by the chemical connectivity of the macromolecules and the high viscosity which at the glass transition temperature stops