Solid polymers heat capacity

Details for the ATHAS calculations are given in Pyda M, Bartkowiak M, Wunderlich B (1998) Computation of Heat Capacities of Solids Using a General Tarasov Equation. J. Thermal Anal Calorimetry 52 631-656. Zhang G, Wunderlich B (1996) A New Method to Eit Approximate Vibrational Spectra to the Heat Capacity of Solids with Tarasov Eunctions. J Thermal Anal 47 899-911. Noid DW, Varma-Nair M, Wunderlich B, Darsey JA (1991) Neural Network Inversion of the T arasov Eunction Used for the Computation of Polymer Heat Capacities. J Thermal Anal 37 2295-2300. Pan R, Varma-Nair M, Wunderlich B (1990) A Computation Scheme to Evaluate Debye and Tarasov Equations for Heat Capacity Computation without Numerical Integration. J Thermal Anal 36 145-169. Lau S-F, Wunderlich B (1983) Calculation of the Heat Capacity of Linear Macromolecules from -Temperatures and Group Vibrations. J Thermal Anal 28 59-85. Cheban YuV, Lau SF, Wunderlich B (1982) Analysis of the Contribution of Skeletal Vibrations to the Heat Capacity of Linear Macromolecules. Colloid Polymer Sd 260 9-19. 

Figure 11.7 Experimental and calculated heat capacities of solid and liquid PTT [49], From Heat capacity of poly(trimethylene terephthalate), Pyda, M., Boiler, J., Grebowicz, J., Chuah, H., Lebedev, B. V. and Wunderlich, B., J. Polym. Sci., Polym. Phys. Ed., 36, 2499-2511 (1998), Copyright (1998 John Wiley Sons, Inc.). Reprinted by permission of John Wiley Sons, Inc...

The state of polarization, and hence the electrical properties, responds to changes in temperature in several ways. Within the Bom-Oppenheimer approximation, the motion of electrons and atoms can be decoupled, and the atomic motions in the crystalline solid treated as thermally activated vibrations. These atomic vibrations give rise to the thermal expansion of the lattice itself, which can be measured independendy. The electronic motions are assumed to be rapidly equilibrated in the state defined by the temperature and electric field. At lower temperatures, the quantization of vibrational states can be significant, as manifested in such properties as thermal expansion and heat capacity. In polymer crystals quantum mechanical effects can be important even at room temperature. For example, the magnitude of the negative axial thermal expansion coefficient in polyethylene is a direct result of the quantum mechanical nature of the heat capacity at room temperature." At still higher temperatures, near a phase transition, e.g., the assumption of stricdy vibrational dynamics of atoms is no... 

For common thermally thick combustible materials (greater than a few millimeters) the time to ignition is proportional to the product k p c (where k is the thermal conductivity, p is the density, and c is the heat capacity), which represents the thermal inertia of the sample. Thermal inertia characterizes the rate of surface temperature rise of the material when exposed to heat. Low values of thermal inertia lead to a rapid temperature rise for a given applied heat flux and hence, to a rapid ignition.4 Polymeric foams have much lower thermal conductivity and density than the corresponding solid materials, thus the surface temperature of the first heats up more rapidly than that of the latter. Foam surface may reach the ignition temperature 10 times faster than the solid polymer.5... 

Molar heat capacity of solid and liquid polymers at 25°C ... 

Reliable values for the molar heat capacity in the solid and the liquid state are available for a limited number of polymers only. This emphasizes the importance of correlations between Cp(298) and Cp(298) and the structure of polymers. 

According to this figure a crystalline polymer follows the curve for the solid state to the melting point. At Tm, the value of Cp increases to that of the liquid polymer. The molar heat capacity of an amorphous polymer follows the same curve for the solid up to the glass transition temperature, where the value increases to that of the liquid (rubbery) material. 

In general a polymer sample is neither completely crystalline nor completely amorphous. Therefore, in the temperature region between Tg and Tm the molar heat capacity follows some course between the curves for solid and liquid (as shown in Fig. 5.1 for 65% crystalline polypropylene). This means that published single data for the specific heat capacity of polymers should be regarded with some suspicion. Reliable values can only be derived from the course of the specific heat capacity as a function of temperature for a number of samples. Outstanding work in this field was done by Wunderlich and his co-workers. Especially his reviews of 1970 and 1989 have to be mentioned here. 

Examination of the available literature data showed that, for all the polymers investigated, the curves for the molar heat capacity of solid and liquid might be approximated by straight lines, except for the solid below 150 K. So if the slopes of these lines are known, the heat capacity at an arbitrary temperature may be calculated approximately from its value at 298 K. For a number of polymers the slopes of the heat capacity curves, related to the heat capacity at 298 K, are mentioned in Table 5.3. 

The slopes of the heat capacity lines for solid polymers show an average value... 

Bicerano (2002) calculated the heat capacity at 298 K for solid as well as soft polymers on the basis of the so-called connectivity indices % and of rotational degrees of freedom in the backbone (Nbb rot) as well as in the side groups (Nsg rot). He found a close relationship between many calculated and experimental values of both Cp(298) and Cp(298). 

D. Correlation for the heat capacity of "solid" polymers at room temperature... 

Cps Molar heat capacity of "solid" (glassy or crystalline) polymers at constant pressure. 

The heat capacities of polymers can be classified into two types, namely, the heat capacities of "solid" polymers, which will be denoted by Cps, and the heat capacities of "liquid" polymers, which will be denoted by Cp. ... 

Similarly, the heat capacities of both "rubbery" and "molten" polymers can be considered under the category of "liquid" heat capacities. The heat capacity increases discontinuously from its "solid" value to its "liquid" value when an amorphous phase undergoes the glass transition, or when a crystalline phase melts. The jump ACp(Tg) in the heat capacity at the glass transition, which is defined by Equation 4.9, is of considerable interest ... 

D. Correlation for the Heat Capacity of "Solid" Polymers at Room Temperature... 

Table 4.1. Experimental heat capacities Cps of solid polymers at room temperature (298K) in J/(mole K), the geometrical parameter Nrot and the atomic correction index NSi used in the correlation, and the fitted values of Cps, for 95 polymers. The connectivity indices and 1xv. 

Figure 4.3. Correlation using topological and geometrical parameters, for the experimental heat capacities Cps of 95 "solid" (i.e., glassy or crystalline) polymers, at room temperature (298K). Cps(298K) is in J/(mole-K).

---