Crystallinity specific heat capacity

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. 

First, second and 5th order polynomial interpolation for the specific heat capacity of a semi-crystalline thermoplastic (PA6). When performing a heat transfer simulation (heating or cooling) for a thermoplastic, the complete course of the specific heat capacity as a function of temperature is needed. A common way to do this... 

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. 

Gruneisen parameter (y) - Defined by y = u /k Cy p, where is the cubic thermal expansion coefficient, k is the isothermal compressibility, c, is the specific heat capacity at constant volume, and p is the mass density, y is independent of temperature for most crystalline solids. [1]... 

Figure 10-3. Specific heat capacity Cp at constant pressure of partially crystalline (— — —) and amorphous (—0 — 0—) poly[oxy-(2,6-dimethyl)-l,4-phenylene]. Tcryst denotes the beginning of recrystallization, Tg is the glass transition temperature, and Tm is the melting temperature (after F. R. Karasz, H. E. Bair, and J. M. O. Reilly).

The reversing heat capacity and the total heat-flow rate of an initially amorphous poly(3-hydroxybutyrate), PHB, are illustrated in Fig. 6.18 [21]. The quasi-isothermal study of the development of the crystallinity was made at 296 K, within the cold-crystallization range. The reversing specific heat capacity gives a measure of the crystallization kinetics by showing the drop of the heat capacity from the supercooled melt to the value of the solid as a function of time, while the total heat-Uow rate is a direct measure of the evolution of the latent heat of crystallization. From the heat of fusion, one expects a crystallinity of 64%, the total amount of solid material, however, when estimated from the specific heat capacity of PHB using the ATHAS Data Bank of Appendix 1, is 88%, an indication of a rigid-amorphous fraction of 24%. 

Figure 10-4. Specific heat capacity r, at constant pressure of partially crystalline (— — —) and amorphous (—O—O—) poly[oxy-(2.6-dimethyl)-l,4-phenylene]. denotes the...

In SMPs with a liquid crystalline transition the specific heat capacity increases significantly up to the transition point due to long range fluctuations of the order parameter near the transition [49]. At the transition temperature, a first-order phase transition occurs. The recorded DSC peak of the liquid crystalline transition will be the mixture of these two contributions. A schematic example for a liquid crystalline polymer is shown in Fig. 2 (diagram e), showing transitions in the form of sharp endothermic peaks, Tc-n for the crystal-nematic transition and for the nematic-isotropic transition. 

This work involved the use of photothermal techniques for determining the diffusion coefficients of O2 and CO2 of commercial LDPE. The methodology involved the monitoring of diffused gas hy a photoacoustic analysen Diffusion coefficients measured for CO2 and O2 were 2.77 x 10 cm Vs and 16.8 x 10 cm Vs, respectively. To support the gas diffusion results, thermal properties were studied using photoacoustic spectroscopy and crystallinity was determined using X-ray diffraction. Values obtained for the thermal diffusivity and specific heat capacity were 0.00165 cm and 2.33 J/cm /K, respectively, which were in good agreement with the values found in the literature for pure LDPE and thus, assured the reliability of the diffusion coefficient values. 

To determine the degree of crystallinity om the enthalpy fitncHon via the specific heat capacity, the following measurement cycle was programmed ... 

Semi-crystalline plastics have higher specific heat capacity than the amorphous plastics. Hence, the energy required for melting of the resin will be more leading to costly melt processing. 

Figure 7 shows the variations in the volume per unit mass, the thermal expansion coefficient, and the specific heat capacity for the same substance [6] in both the amorphous and the crystalline forms (melting point at 7 = 415 K). 

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. 

In Fig. 1 there are three example applications from a Mettler DSC Application Description (DSC of the type illustrated in Fig. 4.4, left center). Calculate the crystallinity of the polyethylene sample (for the heat of fusion, look in the Appendbc) and the calibration constant for heat capacity measurement in J/(s V) [the aluminum oxide specific heat capacity is 1.005 J/(K g)j. Furthermore, estimate the heat of fusion of phenacetin [use Eq. (1), of Fig. 5.28 the equilibrium melting temperature of pure phenacetin is 407.6 K]. 

Molar specific heat capacities of crystalline solids... 

Conclusion as to the specific heat capacity of a crystalline solid... 

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