Enthalpy glass transition temperatures

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.)...

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. 

Eq. (26) is valid for any temperature provided that the enthalpy terms are all known at that temperature and that they all represent the enthalpy per gram referred to the same standard state. In our work we have taken the liquid well above the melting point as the standard state, because this state should be more reproducible and less subject to the previous history of the polymer than a state below the melting point or below T , the glass transition temperature. 

In DSC the measured energy differential corresponds to the heat content (enthalpy) or the specific heat of the sample. DSC is often used in conjunction with TA to determine if a reaction is endothermic, such as melting, vaporization and sublimation, or exothermic, such as oxidative degradation. It is also used to determine the glass transition temperature of polymers. Liquids and solids can be analyzed by both methods of thermal analysis. The sample size is usually limited to 10-20 mg. 

While physicochemical and spectroscopic techniques elucidate valuable physical and structural information, thermal analysis techniques offer an additional approach to characterize NOM with respect to thermal stability, thermal transitions, and even interactions with solvents. Information such as thermal degradation temperature (or peak temperature), glass transition temperature, heat capacity, thermal expansion coefficient, and enthalpy can be readily obtained from thermal analysis these properties, when correlated with structural information, may serve to provide additional insights into NOM s environmental reactivity. 

The glass transition is characterized in part by an observed second-order transition distinguished by a discontinuity of the Gibbs free energy with respect to the aforementioned state variables, but by continuity of entropy, volume, and enthalpy. Hence, heat capacity, Cp, as well as the thermal expansion coefficient, a, as defined below, both exhibit a discontinuity at the glass transition temperature (McKenna, 1989). 

This quantity is related to the effective activation enthalpy at the glass transition temperature... 

It has been recently realized that the activation enthalpy of the Johari-Goldstein beta ((3) relation is cross-correlated with the glass transition temperature of the alpha (a) relaxation of various glass formers [168,169]. This indicates a deep link between the fragility index of the a and the [3 relaxation [170],... 

As appears from Fig. 5.5, the enthalpy curves for crystalline and amorphous polypropylene run parallel up to the glass transition temperature. The distance between these curves is called AH(0) = the enthalpy of the amorphous polymer at 0 K. From the glass transition temperature on the curve for the amorphous polymer gradually approaches the curve for the melt, while the curve for the crystalline polymer shows a discontinuity at the melting point. The distance between the curves for crystal and liquid at the melting point is the latent heat of fusion, AHm. 

Table 12.3. Glass transition temperatures Tg and the activation energies AFreiax of enthalpy relaxation of dry amorphous disaccharidesa...

Haida O, Matsuo T, Suga H, Seki S (1974) Calorimetric study of the glassy state, X. Enthalpy relaxation at the glass transition temperature of hexagonal ice. J Chem Thermodyn 6 815-825... 

Figures 14 and 15 show the relations between the amount of iron arene initiator, the reaction enthalpy (AHj and the glass transition temperature Tg of the polymerized Bisphenol-A diglycidylether (cf. Table 2, structure I, x = 0.15) and the oligomer product based on the former compound (cf. Table 2, structure I, x = 11.8). The maximum polymerization heat per mole of epoxide is observed ivith an initiator concentration of 1.5-2.5% (w/w). At this concentration, Tg of the crosslinked resin is about 115 °C for the polymerized low-molecular-weight expoxide and about 80 "C for the polymerized high-molecular-weight epoxide resin.

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