Melting-transition temperature polymer thermodynamics, first-order

The most common applications of DSC are to the melting process which, in principle, contains information on both the quality (temperature) and the quantity (peak area) of crystallinity in a polymer [3]. The property changes at Tm are often far more dramatic than those at Tg, particularly if the polymer is highly crystalline. These changes are characteristic of a thermodynamic first-order transition and include a heat of fusion and discontinuous changes in heat capacity, volume or density, refractive index, birefringence, and transparency [3,8], All of these may be used to determine Tm [8],... 

Both kinetic and thermodynamic approaches have been used to measure and explain the abrupt change in properties as a polymer changes from a glassy to a leathery state. These involve the coefficient of expansion, the compressibility, the index of refraction, and the specific heat values. In the thermodynamic approach used by Gibbs and DiMarzio, the process is considered to be related to conformational entropy changes with temperature and is related to a second-order transition. There is also an abrupt change from the solid crystalline to the liquid state at the first-order transition or melting point Tm. 

The glass transition and other transitions in polymers can be observed experimentally by measuring any one of several basic thermodynamic, physical, mechanical, or electrical properties as a function of temperature. Recall that in first-order transitions such as melting and boiling, there is a discontinuity in the volume-temperature plot. For second-order transitions such as the glass transition, a change in slope occurs, as illustrated in Figure 8.5 (9). 

Polymer crystallization and melting are typically first-order phase transitions between the amorphous phase and the crystalline phase. When these two phases are in thermodynamic equilibrium, two phase transitions are thermodynamically reversible under a certain temperature. This temperature is referred to the equilibrium melting point of polymer crystallization. The free energy changes of amorphous phase and crystalline phase under various temperatures are depicted in Fig. 4.1, illustrating the definition of the equilibrium melting point 7. ... 

In contrast to a change in slope at the glass transition, a thermodynamic property such as specific volume exhibits a discontinuity with temperature at the crystalline melting point in polymers as in other materials (Figure 6.2). The glass transition is therefore known as a second-order thermodynamic transition (where v versus Tis continuous and dv/dT versus T is discontinuous) in contrast to a first-order transition such as the melting point (where v versus T is discontinuous). 

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