Amorphous polymers specific heat capacity

Figure 4.1. Schematic illustration of temperature dependences of specific heat capacities of amorphous polymers. The heat capacity jumps to a much higher value over a narrow temperature range as the polymer goes through the glass transition. It increases more slowly with increasing temperature above Tg than it did below Tg.

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. 

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. 

The reversing specific heat capacity in the glass transition region is illustrated in Fig. 6.52 [21 ]. The analysis in terms of the ATHAS Data Bank heat capacities shows that there is no low-temperature contribution due to conformational motion below the glass transition. The glass transition of the semicrystalline sample is broadened to higher temperature relative to the amorphous sample, as found in all polymers. Of... 

Figure 7 Scheme of the dynamics taking place at the glass transition for amorphous polymers, (a) Imaginary part e" of the complex dielectric function vs. frequency for two temperatures Ti and T2- The different processes are indicated, (b) Relaxation map (relaxation rate vs. inverse temperature) for the different processes, (c) Thermal glass transition where the specific heat capacity is plotted vs. inverse temperature. 

Specific heat capacity of any material is defined as the amount of energy required to change the temperature of a unit mass of the material by one degree Celsius (or Kelvin). Heat capacity of plastic materials is temperature dependent, and is different for different phases. For example, in the case of semi-crystalline polymers, the heat capacity of the crystalline phase is typically lower than that of the amorphous phase. The most widespread technique used to measure heat capacity of polymers is differential scanning calorimetry (DSC). Alternatively, differential thermal analysis (DTA) can also be used to determine heat capacity. 

Specific Heat Capacity. Representative values of specific heat capacity are shown in Tables 3 and 6. The range of values is only about 850 to 2400 J/(kgK) or barely a factor of three. As a general rule, differences are usually associated with the molecular composition of the polymer and less with molecular architecture, although crystallinity may be important. For example, a comparison of three forms of polyethylene (Table 6) reveals little difference in heat capacity the high density, and hence more crystalline, form has a somewhat lower value. Similarly, no differences are observed between two grades of phenol-formaldehyde resin, or between them and phenol-furfural resin. However, in comparing isotactic and atactic (amorphous) polypropylene shown in Table 3 with values of 1790 and 2350 J/(kg K), respectively, a fairly substantial difference is observed the more ordered, denser isotactic form has the lower heat capacity, as is to be expected. However, comparable values of isotactic and atactic polystyrene have been reported to be 1264 and 1227 J/(kg-K), respectively (65) here the difference is small. 

They include physical methods such as the determination of electrical resistivity, enthalpy or specific heat capacity of the semi-crystalline polymer which require knowledge of the values of these different parameters for both the crystalline and amorphous phases. Spectroscopic methods such as n.m.r. and infrared spectroscopy which have been outlined in Section 3.6 have also been employed. In general there is found to be an approximate correlation between the different methods of measurement employed although the results often differ in detail. 

The heat capacity, or specific heat, is the amount of energy required to raise the temperature of a unit mass of a material one degree. In metric units it is expressed in cal/g°C. It can be measured at constant pressure or constant volume at constant pressure, it is larger than at constant volume because additional energy is required to bring about the volume change against external pressure. The specific heat of amorphous polymers increases with... 

Rehable data regarding the heat capacity of amorphous and crystalline phases are available for only a limited number of polymers. The usual techniques for measuring specific heat are differential thermal analysis (DTA) and differential scanning calorimetry (DSC). 

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