Specific heat crystalline materials

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 ... 

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. 

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. 

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 ... 

Just above the melting point the polymer is visually quite viscous and numerous observations have been made that the polymer exhibits a memory effect, that is to say, on recooling the melt crystallites will appear in the same sites where they had been before melting the polymer. Hartley, Lord and Morgan (1954) state It is reasonable to suppose that there will be a few localities in the crystalline polymer which have a very high degree of crystalline order, and therefore the melt can contain, even at considerable temperatures above the observed melting or collapse point, thermodynamically stable minute crystals of the polymer . Especially if the polymer has been irradiated so as to contain a few crosslinks as in irradiated polyethylene, then flow is inhibited and spherulites can be made to appear on recrystallization in the same sites that they had before the polymer was melted, Hammer, Brandt and Peticolas (1957). However, as mentioned above, the specific heat of irradiated polyethylene in the liquid state is identical with that of the unirradiated material, within the limits of experimental error. Dole and Howard (1957). 

In a DSC analysis of a semi-crystalline polymer, a jump in the specific heat curve, as shown in Fig. 2.22, becomes visible. The glass transition temperature, Tg, is determined at the inflection point of the specific heat curve. The release of residual stresses as a material s temperature is raised above the glass transition temperature is often observed in a DSC analysis. 

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. 

Diatomaceous earth is composed of the siliceous skeletons of microorganisms. It is pozzolanic, but its use in concrete is much restricted by its very high specific surface area, which greatly increases the water demand. Some clays react significantly with lime at ordinary temperatures, but while this property can be of value for soil stabilization, their physical properties preclude their use in concrete. Many clay minerals yield poorly crystalline or anrorphous decomposition products at 600-900 C (Section. 3.3.2), and if the conditions of heat treatment are properly chosen, these have enhanced pozzolanic properties. Heat-treated clays, including crushed bricks or tiles, can thus be used as pozzolanas in India, they are called surkhi. Other examples of natural rocks that have been used as pozzolanas, usually after heat treatment, include gaize (a siliceous rock containing clay minerals found in France) and moler (an impure diatomaceous earth from Denmark). The heat-treated materials are called artificial pozzolanas, and this term is sometimes used more widely, to include pfa. 

A variation of the technique is to measure the internal surface energies from the heat of solution. When the solid interface is destroyed, as by dissolving, the internal surface energy appears as an extra heat of solution. With accurate calorimetric experiments it is possible to measure the small difference between the heat of solution of coarse and of finely crystalline material (Table 6). The calorimetric measurements need to be done with high precision, since there is only a few joules per mole difference between the heats of solution of coarse and those of finely divided material. A typical example is NaCI. For large crystals the heat of solution in water is 4046 J/mol. Lipsett et al. [951 measured with finely divided NaCI (specific surface area of 125 nr/mol) a heat of solution that was 51 J/mol smaller. 

Nanocrystalline materials comprising sub-100 / metal particles, when compressed to 50% of their bulk density, show properties (specific heat, thermal conductivity, saturation magnetization and critical temperature for superconductivity) provocatively different from those of their crystalline or glassy counterparts.(48) It is well known that the interfaces of mechanically reduced composites are effective in interacting with dislocations and with flux lines in superconducting composites. Precursor materials for the preparation of ultrafine filamentary composites can also be imagined. Here the combinations of interphasial boundaries and dislocations can... 

The crystallinity or the fraction of crystalline material x(c) can be derived from specific volume data, from specific heat data, from infrared extinction coefficient data, from X-ray scattering data, from NMR data or from heat of fusion data. 

The degree of crystallinity may be derived this way by measurement of a material property such as specific volume, specific heat, enthalpy, and electrical resistivity ... 

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