Specific heat capacity, of polymers

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. 

Our discussion of the specific heat capacity of polymers on the preceding pages has been quite empirical. There are, in fact, few fundamental rules that can be used for the prediction of specific heat capacity. At very low temperatures, the equations of Debye and Einstein may be used. 

Table II. Mean Specific Heat Capacity of Polymers at Extrusion ...

To measure the heat of fusion and the specific heat capacity of polymers as a function of temperature, the DSC is the appropriate choice because it enables the user to get reliable results in a rather short time. For the heat capacity... 

There is a lot of misunderstanding over the effect of fillers on specific heat capacity. In fact, some of the notable books in the field give erroneous advice in this regard. The confusion comes from a failure to take into account the units of specific heat capacity. The units for mass-specific heat capacity are J kg K and values for mineral fillers are approximately three times greater than those for polymers. Therefore it is often stated that minerals reduce the specific heat capacity of polymers thus aiding polymer processing. However, like all other properties, one must consider the property on a volume basis and not a weight or mass basis. 

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.

According to the law of equal distribution of energy, the maximum heat capacity is 3/ per mole atom per monomeric unit. In actual fact, however, some degrees of freedom are always frozen in, and the molar heat capacity is consequently lower than the maximum. A value of about 1/ = 8.314 J K" mol" has been empirically found for solid polymers at room temperature per mole atom. A specific heat capacity of 1.22 J K g is obtained for the example in Figure 10-3 at 25° C. Thus, with a monomeric unit chemical formula of CgHgO, a heat capacity of 146.4 J K" moF for one mole of monomeric unit is obtained. With 17 atoms per monomeric unit, a heat capacity of 8.61 J K" mol" per mole atom is obtained. 

For the polymer matrix, it should be noted that the Debye temperature, Tp, for polyester is lower than 27 °C [9]. Consequently, in the range of elevated and high temperature, the specific heat capacity of polyester (Cp ) can be assumed as almost a constant (see Figure 4.12, the portion of curve above Tp). As a result, Cp [, can be... 

Cp is the specific heat capacity of the decomposed material. As the polymer matrix almost decomposed into gases, most mass of the material after decomposition is composed of fibers. As a result, Cp, is approximately equal to the specific heat capacity of the fibers (as the mass fraction of the remaining gases in the composition is negligible compared to that of the fibers) ... 

Polymer applications of DSC are numerous and concern the determination of Tm (ASTM E 794), Tg (ASTM E 1326-03, ISO/FDIS 11357-2), specific heat capacity of a material (ASTM E 1269, ASTM D 4816), crystallisation temperature upon cooling (ASTM E 794), transition temperatures (ASTM D 3418, ASTM D 4419, ASTM D 4591), purity of a material [79,80], contamination outgassing (ASTM E 1559), reaction rates, sample composition, reaction kinetic constants (ASTM E 698), reaction mechanisms, thermal stability (ASTM E 537), minimum processing temperatures, heat of fusion and crystallisation (ASTM D 3417), heat of crystallisation (ASTM E 793), additive effects on a material, quality control of raw materials [25], discrimination between materials, detection of polymorphism [81], characterisation of thermally and UV cured materials (cure state, degree of cure) (ASTM D 2471, ASTM D 5028), oxidative stability testing, QIT (ASTM D 3895, ASTM D 3012, ASTM E 1858-03), etc. 

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. 

Values of specific heat capacity of some pol5miers are given in Table 3 for comparison, values of several ceramics and metals are included. Polymers have relatively large values, t3q)ically on the order of 750-2500 J/(kg-K), which at first glance might seem confusing. However, heat capacity is expressed on a per unit... 

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 value of the heat capacity of a polymer varies as a function of temperature. The heat capacity of polyethylene rises rapidly from a minimal value at absolute zero, leveling off somewhat as the temperature increases further. The value of the specific heat capacity of a polymer can be calculated quite accurately as a function of temperature based upon a knowledge of the atomic vibrations... 

Stockmayer and Hecht (1953) have developed an additional mathematical theory of the heat capacity of chain polymeric crystals. Their theory is based on the concept of strong valence forces between atoms in the polymeric chain and of weak (non-zero) coupling between chains. This model corresponds to that also proposed by Tarassov (1952). There are not many low temperature specific heat data on polymers, but the Stockmayer-Hecht theory can be tested by calculating the Tm constant... 

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