Crystallinity specific heat

Polymer compounds vary considerably in the amount of heat required to bring them up to processing temperatures. These differences arise not so much as a result of differing processing temperatures but because of different specific heats. Crystalline polymers additionally have a latent heat of fusion of the crystalline structure which has to be taken into account. 

In principle the heat required to bring the material up to its processing temperature may be calculated in the case of amorphous polymers by multiplying the mass of the material (IP) by the specific heat s) and the difference between the required melt temperature and ambient temperature (AT). In the case of crystalline polymers it is also necessary to add the product of mass times latent heat of melting of crystalline structures (L). Thus if the density of the material is D then the enthalpy or heat required ( ) to raise volume V to its processing temperature will be given by ... 

These techniques help in providing the following information specific heat, enthalpy changes, heat of transformation, crystallinity, melting behavior, evaporation, sublimation, glass transition, thermal decomposition, depolymerization, thermal stability, content analysis, chemical reactions/polymerization linear expansion, coefficient, and Young s modulus, etc. 

The specific heat of amorphous plastics increases with temperature in an approximately linear fashion below and above Tg, but a steplike change occurs near the Tg. No such stepping occurs with crystalline types. 

Dependence on Density.—If the density of a metal is increased by hammering, its specific heat is slightly decreased. The same change is observed if the change of density is due to a change of crystalline form, or to change from an amorphous state to a crystalline state, and with different allotropic forms (Wigand, loc. cit,). 

The transition between crystalline and amorphous polymers is characterized by the so-called glass transition temperature, Tg. This important quantity is defined as the temperature above which the polymer chains have acquired sufficient thermal energy for rotational or torsional oscillations to occur about the majority of bonds in the chain. Below 7"g, the polymer chain has a more or less fixed conformation. On heating through the temperature Tg, there is an abrupt change of the coefficient of thermal expansion (or), compressibility, specific heat, diffusion coefficient, solubility of gases, refractive index, and many other properties including the chemical reactivity. 

The cubic dependence of cph on temperature accounts for the small specific heat at low temperature of crystalline insulators. Specific heat of rare gas crystals is shown in Fig. 3.2. 

Figure 3.10 shows the typical dependence on temperature of the specific heat of an amorphous and a crystalline polymer. For both materials, the specific heat has a steep dependence on temperature, but the behaviour is more complex in the case of the amorphous material. 

As an example, in Fig. 3.11, a schematic two-dimension representation of the structure of cristobalite (a crystalline form of Si02) and of vitreous Si02 is shown. A, B and C represent three cases of double possible equilibrium positions for the atoms of the material in the amorphous state [41]. Atoms can tunnel from one position to another. The thermal excitation of TLS is responsible for the linear contribution to the specific heat of amorphous solids. 

In the literature [55], typical energies involved in the nuclear quadrupole moments -crystalline electric field gradient interactions range up to A E 2x 10-25 J. The measured AE seems to confirm the hypothesis that the excess specific heat of the metallized wafer is due to boron doping of the Ge lattice. 

However the carbon specific heat was not as low as the crystalline materials employed later. Also important, the resistor material exhibits an excess low-frequency noise. Nowadays, two types of resistance sensors are used to realize LTD NTD Ge sensors and TES. 

A solution of 500 kg of Na2S04 in 2500 kg water is cooled from 333 K to 283 K in an agitated mild steel vessel of mass 750 kg. At 283 K, the solubility of the anhydrous salt is 8.9 kg/100 kg water and the stable crystalline phase is Na2SO4.10H2O. At 291 K, the heat of solution is —78.5 MJ/kmol and the specific heat capacities of the solution and mild steel are 3.6 and 0.5 kJ/kg deg K respectively. If, during cooling, 2 per cent of the water initially present is lost by evaporation, estimate the heat which must be removed. 

It is most important to know in this connection the compressibility of the substances concerned, at various temperatures, and in both the liquid and the crystalline state, with its dependent constants such as change of. melting-point with pressure, and effect of pressure upon solubility. Other important data are the existence of new pol3miorphic forms of substances the effect of pressure upon rigidity and its related elastic moduli the effect of pressure upon diathermancy, thermal conductivity, specific heat capacity, and magnetic susceptibility and the effect of pressure in modif dng equilibrium in homogeneous as well as heterogeneous systems. 

H is the heat given off by that part of the polymer sample which was already in the crystalline state before the polymer was heated above T. With this number H it is possible to figure out the percent crystallinity it is divided by the specific heat of melting, H, which is the amount of heat given off by a certain amount of the polymer. So the mass of crystalline material, m, follows as ... 

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. 

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. 

It resembles the crystalline variety in behaviour except in such properties as are influenced by its fineness of division. The electrometric properties of the two forms are identical.2 The density of the amorphous form ranges from 5-85 to 5-87 3 the specific heat is 0-052.4... 

The specific heat of nitroglycerine was determined by Nauckhoff [18] as 0.356 cal/g and that of the crystalline substance (stable form) as 0.315 cal/g. For liquid nitroglycerine Belayev [45] published the value 0.4 cal/g. 

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