Polymers specific heat values

Both kinetic and thermodynamic approaches have been used to measure and explain the abrupt change in properties as a polymer changes from a glassy to a leathery state. These involve the coefficient of expansion, the compressibility, the index of refraction, and the specific heat values. In the thermodynamic approach used by Gibbs and DiMarzio, the process is considered to be related to conformational entropy changes with temperature and is related to a second-order transition. There is also an abrupt change from the solid crystalline to the liquid state at the first-order transition or melting point Tm. 

Two different approaches need to be considered. In the first one the thermodynamic parameters are calculated on the basis of spectroscopic and specific heat data of monomer and its polymer. The estimation of entropy from specific heat values is based on the assumption that at 0 °K the entropy of the perfect crystal equals zero. Since polymers are never perfectly crystalline this method is based on a rough approximation. 

Putting in some typical values, the difference between the principal specific heats for polymers at room temperature is of the order of 0.004 J gK. which is usually small enough to be ignored [5]. Typical specific heat values for solids, including polymers, range from 0.4 J gk to 4 J gK. An extensive collection of data is given in the review by Wunderlich and Baur [61]. 

Specific heat values for amorphous polymers are computed directly from Eq. (25). Semicrystalline polymers are handled by a weighting procedure. 

The crystalline melting temperature and glass transition temperature of reinforced PP is not substantially different to those of the unreinforced grades. However, substantial changes in HDT values are observed. Reinforced PP grades have reduced specific heat values since the reinforcing materials have considerably lower values than the base polymer. 

Physical and Chemical Properties - Physical State at 15 V and I atm. Solid Molecular Weight Values for anhydrous salt run from 120 to high polymer values Boiling Point at I atm. Not pertinent (decomposes) Freezing Point Not pertinent Critical Temperature Not pertinent Critical Pressure Not pertinent Specific Gravity 1.8-2.5 at 25 °C (solid) Vtpor (Gas) Specific Gravity Not pertinent Ratio of Specific Heats of Vapor (Gas) Not pertinent Latent Heat of Vaporization Not pertinent Heat of Combustion Not pertinent Heat of Decomposition Not pertinent. 

The amount of heat required to raise the temperature of a material is related to the vibrational and rotational motions thermally excited within the sample. Polymers typically have relatively (compared with metals) large specific heats, with most falling within the range of 1 to 2 kJ kg-1 K . Replacement of hydrogen atoms by heavier atoms such as fluorine or chlorine leads to lower Cp values. The Cp values change as materials undergo phase changes (such as that at the T ) but remain constant between such transitions. 

The coefficient of linear expansion of unfilled polymers is approximately 10 X 10 5 cm/cm K. These values are reduced by the presence of fillers or reinforcements. The thermal conductivity of the polymers is about 5 X 10 4 cal/sec cm K. These values are increased by the incorporation of metal flake fillers. The specific heat is about 0.4 cal/g K, and these values are slightly lower for crystalline polymers than for amorphous polymers. 

Before taking up the subject of phase transitions in solid high polymers, it is of interest to scrutinize the absolute values of the specific heats in order to see what generalizations can be gained from such a... 

Analogous calorimetric results obtained in a bomb calorimeter are shown in Figure 2.36. It is a very laborious process to obtain actual values of the specific heat as a function of temperature. At each temperature a known amount of heat must be added to the polymer sample, in a sealed bomb calorimeter, and the temperature increase must be measured carefully. Because this is so time consuming, simpler techniques have been developed, and some are described in the following sections. 

The thermophysical properties, such as glass transition, specific heat, melting point, and the crystallization temperature of virgin polymers are by-and-large available in the literature. However, the thermal conductivity or diffusivity, especially in the molten state, is not readily available, and values reported may differ due to experimental difficulties. The density of the polymer, or more generally, the pressure-volume-temperature (PVT) diagram, is also not readily available and the data are not easily convertible to simple analytical form. Thus, simplification or approximations have to be made to obtain a solution to the problem at hand. 

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. 

If this method is applied to thermodynamic data of polymers, the same difficulty arises as mentioned in Sect. 5.1 for the determination of the specific heat most polymer samples are partly crystalline, only. The thermodynamic quantities have values somewhere between those for purely crystalline and purely amorphous polymer. A large number of measurements are needed to derive the data for these two idealized states. Only for a limited number of polymers have data of this kind been published. 

The degree of flammability of a polymeric material may be predicted from its chemical structure. One of the most valuable criteria in fire research, the so-called limiting oxygen index (LOI) may be estimated either from the specific heat of combustion or from the amount of char residue on pyrolysis. Since both quantities can be determined if the chemical structure is known, also the LOI can be estimated. An approximate assessment of the LOI value direct from the elementary composition of the polymer is also possible. 

TABLE 26.4 Specific heat of combustion of some polymers comparison of calculation values... 

Many relatively slow or static methods have been used to measure Tg. These include techniques for determining the density or specific volume of the polymer as a function of temperature (cf. Fig. 11-1) as well as measurements of refractive index, elastic modulus, and other properties. Differential thermal analysis and differential scanning calorimetry are widely used for this purpose at present, with simple extrapolative eorrections for the effects of heating or cording rates on the observed values of Tg. These two methods reflect the changes in specific heat of the polymer at the glass-to-rubber transition. Dynamic mechanical measurements, which are described in Section 11.5, are also widely employed for locating Tg. 

Skuratov et al. [39] tried to estimate the polymerization entropy from specific heat measurements of the monomer and polymer. However, the calculated value of AS29 8> -g- foi caprolactam (+1.1 eu), is too positive because the authors disregarded the fact that the polymer was not completely crystalline. Making allowance for the partial crystallinity, the value of ASp becomes more negative and approaches the value —3.2 eu calculated from the monomer-polymer equilibria [45]. 

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