Glass transition enthalpy

For polymer liquids, the partition funetion, Q, normalized per unit volume is given 

Vf the free volume per molar structural unit for a polymer 

From equation [5.2.5], the enthalpy and the entropy per molar ehain for polymer liquids, H] and Sj, are derived  

The first terms on the right hand side of equations [5.2.6] and [5.2.7] are the eonformational enthalpy and entropy per molar ehain, xh and xs , respeetively. Assuming that ehains at Tg are in quasi-equilibrium state, the eriterions on Tg are obtained  

From equations [5.2.8] and [5.2.9], whieh show the eonditions of thermodynamie quasi-equilibrium and freezing for polymer liquids, the eonformational enthalpy and entropy per molar stmetural unit at T h and s are derived, respeetively  

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Rewriting equation [5.2.10], the glass transition enthalpy per molar stmetural unit,... 

Precise analysis of enthalpy relaxation is not possible owing to the nonequilibrium nature of glassy polymers above and below the glass transition. Enthalpy relaxation can be characterized under certain limiting assumptions. If the viscous or rubbery state of the polymer above is assumed to be an... 

Figure 4.3b is a schematic representation of the behavior of S and V in the vicinity of T . Although both the crystal and liquid phases have the same value of G at T , this is not the case for S and V (or for the enthalpy H). Since these latter variables can be written as first derivatives of G and show discontinuities at the transition point, the fusion process is called a first-order transition. Vaporization and other familiar phase transitions are also first-order transitions. The behavior of V at Tg in Fig. 4.1 shows that the glass transition is not a first-order transition. One of the objectives of this chapter is to gain a better understanding of what else it might be. We shall return to this in Sec. 4.8. 

These techniques help in providing the following information specific heat, enthalpy changes, heat of transformation, crystallinity, melting behavior, evaporation, sublimation, glass transition, thermal decomposition, depolymerization, thermal stability, content analysis, chemical reactions/polymerization linear expansion, coefficient, and Young s modulus, etc. 

Figure 5 Changes in volume, V, energy, E, and enthalpy, H, during cooling or heating of the liquid, crystalline, and glassy (vitreous) forms of a substance. Tm is the melting point, and Ts is the glass transition temperature. (Adapted with permission from Ref. 14.)...

The members of Class II in Table 1 present very small enthalpies of the mesophase-liquid transition [ AHml < 0.5 kJ/(mol of chain bonds)], suggesting that their mesophase is hardly stabilized by specific interatomic interactions. By contrast, we point out that in all cases the crystal-mesophase transition has a significant enthalpy value, mostly AHqm > 1 kJ/(mol of chain bonds). Consistent with their relatively flexible character, the polymers listed in the Tables have their glass transition below ambient temperature. 

Chung, H.-J., Lee, E.-J., and Lim, S.-T. (2002). Comparison in glass transition and enthalpy relaxation between native and gelatinized rice starches. Carbohydr. Polym. 48, 287-298. 

A sample of the polymer to be studied and an inert reference material are heated and cooled in an inert environment (nitrogen) according to a defined schedule of temperatures (scanning or isothermal). The heat-flow measurements allow the determination of the temperature profile of the polymer, including melting, crystallization and glass transition temperatures, heat (enthalpy) of fusion and crystallization. DSC can also evaluate thermal stability, heat capacity, specific heat, crosslinking and reaction kinetics. 

A second-order phase transition is one in which the enthalpy and first derivatives are continuous, but the second derivatives are discontinuous. The Cp versus T curve is often shaped like the Greek letter X. Hence, these transitions are also called -transitions (Figure 2-15b Thompson and Perkins, 1981). The structure change is minor in second-order phase transitions, such as the rotation of bonds and order-disorder of some ions. Examples include melt to glass transition, X-transition in fayalite, and magnetic transitions. Second-order phase transitions often do not require nucleation and are rapid. On some characteristics, these transitions may be viewed as a homogeneous reaction or many simultaneous homogeneous reactions. 

Chung, H. -J., Woo, K. -S., Lim, S. -T. (2004). Glass transition and enthalpy relaxation of eross-linked corn starches. Carbohydr. Polym., 55, 9-15. 

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