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698 6 Single Component Materials

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Fig. 6.134

6.3.5 Network Effects

Cross-linking of linear macromolecules as described in Sect. 3.4.3 and 3.4.5 hinders the large-amplitude motion similar to the presence of crystals, discussed in Sect. 6.3.4. In addition, the chemically different nature of the cross-link may lead to a solution of the two components, and for more extensive changes in the chemical nature, there may even be a phase separation with the effects described in Chap. 7. Because of the lesser mobility, one expects an increase in the glass transition temperature. A broadening of the transition may occur if the cross-links are nonuniform, or the influence of the cross-link component on the phase-structure becomes significant. At least initially, the liquid and glassy heat capacities are not affected significantly by the cross-links, but the higher glass transition temperature must ultimately lead to a lower increase in heat capacity, Cp, at Tg.

Figure 6.135 illustrates the increase of Tg of polystyrene when copolymerized with divinyl benzene for cross-linking (CH2=CH2 C6H4 CH2=CH2). All samples were gels (see Sect. 3.4.3), practically without extractable polystyrene. The decrease in the change of the heat capacity at Tg on cross-linking is shown in Fig. 6.136. The curve drawn in Fig. 6.136 is calculated from the heat capacities of the liquid and glassy polymers at the measured glass transition temperature of Fig. 6.135. Considerable deviations are observed, but one may still extrapolate the data to a point where Cp becomes zero ( 50% divinyl benzene, Tg 500 550 K). Indeed, highly cross-linked polystyrenes with practically no Cp at Tg have been reported.

Cross-linking during curing of an epoxy resin, as observed with quasi-isothermal TMDSC, is described in Fig. 4.141. As the curing proceeds, the glass transition increases until it reaches the reaction temperature. At this point the reaction changes

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Fig. 6.135

Fig. 6.136

to a diffusion-controlled, slow process. Figure 6.137 represents the change of the glass transition with the degree of curing for two epoxy systems. The glass transition is in this case a measure of the reaction history of the sample. Complete time- temperature-transformation (TTT) plots can be drawn using the quantitative changes in the glass transition temperature and following the heats of reaction by DSC and TMDSC as shown in Fig. 4.142.

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Fig. 6.137

To summarize the observations of Sect. 6.3, one must remember that the history of a metastable sample is stored in its internal variables, i.e., for description, one must use the irreversible thermodynamics of Sect. 2.4, instead of the equilibrium thermodynamics. The internal variables that characterize the metastable state must be uniquely coupled to the history to be discovered. The evaluation of the thermal history of a glass is simple if the initial cooling of the sample is the only contributing factor to the history. In this case, a simple hysteresis determination, matched empirically to a reference, may be sufficient for the task (see Sect. 6.3.1, Fig. 6.6).

The quantitative prediction of the hysteresis can be attempted, as shown in Sect. 6.2 with Figs. 6.10 and 6.11, but is, at best, approximate. Problems in the theory of the glass transition which are not fully resolved are:

(1)The asymmetry of the approach to equilibrium—self-retardation and autocatalysis, see Eq. (1) of Sect. 6.3.1, causing an N-dependent relaxation time in Eq. (2) of Sect. 6.3.2 (see Fig. 4.126).

(2)A cooperative kinetics with a temperature-dependent activation energy (see Fig. 6.117 and Sects. 6.3.1 and 6.3.2).

(3)The need to handle more than one internal variable (see Fig. 6.123, Sect. 6.3.3).

(4)The quasi-isothermal TMDSC analyses result in the reversing Cp, not the actual, apparent, reversible Cp (see Fig. 6.118, Sect. 6.3.2 and Sect. 4.4.3).

(5)The standard TMDSC causes interactions between the rate of change of the underlying temperature and the modulation which result in differences in the reversing heat capacity with underlying temperature change and changes in the frequency of the response (see Figs. 4.133 and 6.7, and Sect. 6.3.2).

(6)The strain, crystallinity, and cross-linking effects lead to additional internal variables that can set the history of a sample.

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References

General References

Sect. 6.1–3. The basis for the phase scheme of equilibrium melting is based on the thermodynamic description developed by Ehrenfest [2] and later expanded to copolymers by Flory PJ (1953) Principles of Polymer Chemistry. Cornell University Press, Ithaca.

The discussion of metastable, semicrystalline phases of polymers and their irreversible melting is based on the two early papers: Wunderlich B (1964) A Thermodynamic Description of the Defect Solid State of Linear High Polymers. Polymer 5: 125–134; and: The Melting of Defect Polymer Crystals. Polymer 5: 611–624. A later review and expansion is given in: Wunderlich B (1997) Metastable Mesophases. Macromol Symp 113: 51–65.

More details about the main first-order phase transition, the melting, can be found in: Ubbelohde AR (1965) Melting and Crystal Structure. Oxford University Press, London. See also the sequel (1978) The Molten State of Matter. Melting and Crystal Structure. Wiley, New York.

The following book deals specifically with crystallization and melting of macromolecules: Wunderlich B (1976,1980) Macromolecular Physics, Vol 2, Crystal Nucleation, Growth, Annealing. Vol 3, Crystal Melting. Academic Press, New York.

A general discussion of the glass transition is given in: Seyler RJ, ed (1994) ASTM Symposium on the Assignment of Glass Transition Temperatures Using Thermomechanical Analysis. Atlanta GA, March 4 5, 1993, ASTM STP 1249, Am Soc Testing and Materials, Philadelphia; and by: Tant MR, Hill AJ, eds (1998) Structure and Properties of Glassy Polymers. ACS Symposium Series, 710, Am Chem Soc, Washington; see also: Matsuoka S (1992) Relaxation Phenomena in Polymers. Hanser, Munich. Finally see also the references to Chap 7.

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CHAPTER 7

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Multiple Component Materials

In this last Chapter of Thermal Analysis of Polymeric Materials, the link between microscopic and macroscopic descriptions of multi-component macromolecules is discussed, based on the thermal analysis techniques which are described in the prior chapters. The key issue in polymeric multi-component systems is the evaluation of the active components in the system. The classical description of the term component was based on small-molecule thermodynamics and refers to the number of different molecules in the different phases of the system (see Sect. 2.2.5). If chemical reactions are possible within the system, the number of components may be less than the different types of molecules. It then represents the species of molecules that can be varied independently. For example, the three independent species CaO, CO2, and CaCO3 represent only two components because of the equation that links their concentrations:

CaO + CO2 = CaCO3 .

More complicated is the mixture of the eight independent species in the four chemical equations:

NaCl + KBr = NaBr + KCl

NaCl + H2O = NaCl H2O

KBr + H2O = KBr H2O

NaBr + H2O = NaBr H2O .

Together with the material-balance equation, this system is described by only three components in the phase rule given in Sect. 2.5.7.

For macromolecules, the meaning of the term component was already relaxed to account for the fact that small changes in their length do not affect their properties, as discussed in Chap. 6. Similarly, decoupled segments of a polymer chain at a phase boundary may change the accounting for components, as is shown in Fig. 6.69. The main issues in Chap. 7 are the additional problems arising from the size of the macromolecule when one treats it as a single component in phase diagrams with components of smaller size (Sect. 7.1). Additionally, the flexibility of the macromolecules after copolymerization allows a decoupling of different repeating-unit sequences, leading to phase separation into domains of micrometer and nanometer dimensions without changing of the molecular structure. This may, for example, allow the treatment of copolymers as a multiple-component system (Sect. 7.2), even if the reactions that lead to the copolymer are fully arrested. Finally, Sect. 7.3 deals with the effect of multiple components in polymers on the glass transition.