Amorphous polymers heat capacity

Fig. III. 13. Heat capacity of amorphous and crystalline polyethylene as a function of crystallinity. Open circles show the amorphous, filled circles the crystalline polymer heat capacity. Below 220° K difierences are too small to show on the graph. See Big. 111.9 and TaMe 111.8...

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... 

Pyda and co-workers [49, 60] measured the reversible and irreversible PTT heat capacity, Cp, using adiabatic calorimetry, DSC and temperature-modulated DSC (TMDSC), and compared the experimental Cp values to those calculated from the Tarasov equation by using polymer chain skeletal vibration contributions (Figure 11.7). The measured and calculated heat capacities agreed with each other to within < 3 % standard deviation. The A Cp values for fully crystalline and amorphous PTT are 88.8 and 94J/Kmol, respectively. 

It is assumed that the semi-crystalline polymer consists of an amorphous fraction with heat capacity Cp and a crystalline fraction with heat capacity of Cp. For a polymer with 30% crystallinity the estimated molar heat capacity is Cp(298) = 0.3 x 71.9 + 0.7 x 88.3 = 83.4 J moF1 K-1. The specific heat capacity is Cp/M= 1985 J kg-1 K 1... 

The complete course of the specific heat capacity as a function of temperature has been published for a limited number of polymers only. As an example, Fig. 5.1 shows some experimental data for polypropylene, according to Dainton et al. (1962) and Passaglia and Kevorkian (1963). Later measurements by Gee and Melia (1970) allowed extrapolation to purely amorphous and purely crystalline material, leading to the schematic course of molar heat capacity as a function of temperature shown in Fig. 5.2. 

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. 

In this chapter it is demonstrated that the heat conductivity of amorphous polymers (and polymer melts) can be calculated by means of additive quantities (Rao function, molar heat capacity and molar volume). Empirical rules then also permit the calculation of the heat conductivity of crystalline and semi-crystalline polymers. 

As an amorphous polymer, lignin undergoes chain segment motion upon heating. This motion, a glass transition, is characteristic of all amorphous polymers, and is indicated by an endothermic shift in the DTA or DSC curves. This glass transition is accompanied by abrupt changes in free volume, heat capacity, and thermal expansion coefficient. 

The kinetic treatment of the adiabatic polymerization is very complicated with respect to the variation with increasing temperature of rate coefficients and equilibrium constants. Equations derived with a series of simplifying assumptions (e.g. heat capacity of the monomer (Cp m ) = heat capacity of the amorphous polymer (Cp p) = constant = Cp) lead to [2]... 

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