Heat capacity of melt

It may be noted that the entropy of the melt is considered as entirely configurational in AG theory. At Tm, it is equal to = dJiJT . The manner of decrease of this quantity is considered as determined by the difference between the heat capacities of melt and the crystalline phases in the supercooled region. At Tg, the frozen entropy, 5 is calculated as... 

Figure 2.46 illustrates the completed analysis. A number of other polymers are described in the ATHAS Data Bank, described in the next section. Most data are available for polyethylene. The heat capacity of the crystalline polyethylene is characterized by a T dependence to 10 K. This is followed by a change to a linear temperature dependence up to about 200 K. This second temperature dependence of the heat capacity fits a one-dimensional Debye function. Then, one notices a slowing of the increase of the crystalline heat capacity with temperature at about 200 to 250 K, to show a renewed increase above 300 K, to reach values equal to and higher than the heat capacity of melted polyethylene (close to the melting temperature). The heat capacity of the glassy polyethylene shows large deviations from the heat capacity of the crystal below 50 K (see Fig. 2.45). At these temperatures the absolute value of the heat capacity is, however, so small that it does not show up in Fig. 2.46. After...

Figure 4.50. Apparent heat capacity of melt-crystallised PET as measured by standard DSC and quasi-isothermal MTDSC, compared to the baselines of the heat capacity of the melt, solid (vibrational contributions only) and semicrystalline pol)mier [63].

Variations in the vibrational frequencies of (RXe) octahedra should be similar in character to variations in the lattice contribution Ciat(liq) to the heat capacity of melts of compounds of the same type. The only difference is that Ciat(liq) decreases while the frequencies increase. Such... 

The heat capacity can be computed by examining the vibrational motion of the atoms and rotational degrees of freedom. There is a discontinuous change in heat capacity upon melting. Thus, different algorithms are used for solid-and liquid-phase heat capacities. These algorithms assume different amounts of freedom of motion. 

The heat capacity of thiazole was determined by adiabatic calorimetry from 5 to 340 K by Goursot and Westrum (295,296). A glass-type transition occurs between 145 and 175°K. Melting occurs at 239.53°K (-33-62°C) with an enthalpy increment of 2292 cal mole and an entropy increment of 9-57 cal mole °K . Table 1-44 summarizes the variations as a function of temperature of the most important thermodynamic properties of thiazole molar heat capacity Cp, standard entropy S°, and Gibbs function - G°-H" )IT. 

Figure 10.1 Thermal conductivities and heat capacities of the low-melting elements Na, Zn, Sn and Pb...

Magnetic heat capacity of nickel, 133 Magnetic susceptibility, 25 Maleic anhydride, 168 Many electron system, correlations in, 304, 305, 318, 319, 323 Melting temperature and critical temperature for disordering correlation, 129... 

Specific Heats of Solid Mixtures.—The specific heat of a homogeneous solid mixture of solid components is not usually additively composed of the specific heats of the latter. W. Spring (1886) found that the total heat capacity of alloys of lead and tin was always greater than the sum of those of the components, but above the melting-point the two were equal. A. Bogojawlensky and N. Winogradoff (1908) find, however, that the heat capacities of the isomorphous mixtures ... 

Figure 4.4 Heat capacity of N as a function of temperature. A solid phase transition occurs at 35.62 K, the melting temperature is 63.15 K, and the normal boiling temperature is 77.33 K.

Figure 4.8 Heat capacity of glycerol as a function of temperature. The solid line indicates Cp,m for the liquid and glassy phase. The dashed line represents Cp m for the solid. The dotted line at the melting temperature of 291.05 K. indicates the change in heat capacity upon melting. A glass transition occurs in the supercooled liquid at approximately 185 K. The heat capacities of the solid and the glass approach one another as the temperature is lowered they are almost identical below 140 K.

Although Equation (4) is conceptually correct, the application to experimental data should be undertaken cautiously, especially when an arbitrary baseline is drawn to extract the area under the DSC melting peak. The problems and inaccuracy of the calculated crystallinities associated with arbitrary baselines have been pointed out by Gray [36] and more recently by Mathot et al. [37,64—67]. The most accurate value requires one to obtain experimentally the variation of the heat capacity during melting (Cp(T)) [37]. However, heat flow (d(/) values can yield accurate crystallinities if the primary heat flow data are devoid of instrumental curvature. In addition, the temperature dependence of the heat of fusion of the pure crystalline phase (AHc) and pure amorphous phase (AHa) are required. For many polymers these data can be found via their heat capacity functions (ATHAS data bank [68]). The melt is then linearly extrapolated and its temperature dependence identified with that of AHa. The general expression of the variation of Cp with temperature is... 

Heat capacity measurements at the glass transition temperature, Tg, are based on the same differential concept. The weight fraction of amorphous phase is calculated as the ratio of changes of heat capacity of the semi-crystalline sample ACp(S) over the change in heat capacity of the melt (ACp(m)) at the glass transition. For a two-phase system, the degree of crystallinity is given as ... 

At the melting temperature we have AfusG° =0, which implies that A fus S " = AfusH°/rfus i. If the heat capacity of the solid and the liquid are assumed to be equal, the enthalpy of fusion is independent of temperature and eq. (4.17) becomes... 

The melting transition of ultra-pure metals is usually used for calibration of DSC instruments. Metals such as indium, lead, and zinc are useful and cover the usual temperature range of interest. Calibration of DSC instruments can be extended to temperatures other than the melting points of the standard materials applied through the recording of specific heat capacity of a standard material (e.g., sapphire) over the temperature range of interest. Several procedures for the performance of a DSC experiment and the calibration of the equipment are available [84-86]. A typical sensitivity of DSC apparatus is approximately 1 to 20 W/kg [15, 87]. 

If a solid is heated at a constant rate and its temperature monitored during the process, the melting curve as illustrated in Fig. 4.1 is obtained. Below the melting point, the added heat merely increases the temperature of the material in a manner defined by the heat capacity of the solid. At the melting point, all heat introduced into the system is used to convert the solid phase into the liquid phase, and therefore no increase in system temperature can take place as long as solid and liquid remain in equilibrium with each other. At the equilibrium condition, the system effectively exhibits an infinite heat capacity. Once all solid is converted to liquid, the temperature of the system again increases, but now in a manner determined by the heat capacity of the liquid phase. 

Figure 2.3 The heat capacity of glycerol around its melting point (redrawn from reference 5)...

Table 6.9 Parameters for calculation of heat capacity of silicate melts (1) after Carmichael et al. (1977) and Stebbins et al. (1984) (2) model of Richet and Bottinga (1985)...

---