Differential thermal analysis calculations

Crystallization kinetics have been studied by differential thermal analysis (92,94,95). The heat of fusion of the crystalline phase is approximately 96 kj/kg (23 kcal/mol), and the activation energy for crystallization is 104 kj/mol (25 kcal/mol). The extent of crystallinity may be calculated from the density of amorphous polymer (d = 1.23), and the crystalline density (d = 1.35). Using this method, polymer prepared at —40° C melts at 73°C and is 38% crystalline. Polymer made at +40° C melts at 45°C and is about 12% crystalline. 

Fig. 12. Calculated liquidus and solidus in the InSb-GaSb pseudobinary section and experimental points. Squares from differential thermal analysis, circles from thermal analysis, and triangles from x-ray diffraction, all from Wooley and Lees (1959). Diamonds are from Blom and Plaskett (1971).

FIGURE 1 shows the equilibrium pN2 - T curves for AIN, GaN and InN. The curve for AIN was calculated by Slack and McNelly [6], The one for GaN was determined by Karpinski and Porowski [5] based on gas pressure and Bridgman anvil experiments performed by Karpinski et al [4], The curve for InN was obtained by Grzegory et al [7] and follows from differential thermal analysis (DTA) and annealing of InN at high N2 pressure. The curves for GaN and InN deviate from linear dependence at... 

The heat of pyrolysis (in an inert atmosphere) can be calculated by integrating the area under the differential thermal analysis curve and comparing it with the value obtained for a reference substance according to the following equation... 

Besides the isothermal kinetic methods mentioned above, by which activation parameters are determined by measuring the rate of dioxetane disappearance at several constant temperatures, a number of nonisothermal techniques have been developed. These include the temperature jump method, in which the kinetic run is initiated at a particular constant initial temperature (r,-), the temperature is suddenly raised or dropped by about 15°C, and is then held constant at the final temperature (7y), under conditions at which dioxetane consumption is negligible. Of course, for such nonisothermal kinetics only the chemiluminescence techniques are sufficiently sensitive to determine the rates. Since the intensities /, at 7 ,- and If at Tf correspond to the instantaneous rates at constant dioxetane concentration, the rate constants A ,- and kf are known directly. From the temperature dependence (Eq. 32), the activation energies are readily calculated. This convenient method has been modified to allow a step-function analysis at various temperatures and a continuous temperature variation.Finally, differential thermal analysis has been employed to assess the activation parameters in contrast to the above nonisothermal kinetic methods, in the latter the dioxetane is completely consumed and, thus, instead of initial rates, one measures total rates. 

Hara, Kamei and Osada 86] obtained similar results.. Among the gases from the decomposition of tetryl they also found methane. They carried out the experiments at temperatures from 150 to 175 0. By differential thermal analysis they found the endothermic (negative) peak at I31 C due to the melting of the substance and exothermic decomposition occurred at 160 C. They calculated the activation energy as being 35 kcal/mol. This is in agreement with formerly obtained results (Vol. HI, p. 53). 

Frey s variant of the silvered vessel test has been in use in the Germany. In its variant, different amounts of heat are supplied to the electric heating elements mounted inside the Dewar flask, and the temperature differences between the interior of the Dewar vessel and the furnace are measured by thermocouples. A calibration curve is plotted from the values thus obtained, and the heat of decomposition of the propellant is read off the curve. In this way, the decomposition temperature at a constant storage temperature can be determined as a function of the storage time, and the heat of decomposition of the propellants can thus be compared with each other. If the measurements are performed at different storage temperatures, the temperature coefficient of the decomposition rate can be calculated. (-< also Differential Thermal Analysis.)... 

In many of the methods of quantitative differential thermal analysis, the calibration coefficient can be mathematically deiermined and no experimental procedures are necessary. For example, Kronig and Snoodjik ((04) calculated K for a cylindrical sample holder as... 

There are two main applications for such real-time analysis. The first is the determination of the chemical reaction kinetics. When the sample temperature is ramped linearly with time, the data of thickness of formed phase together with ramped temperature allows calculation of the complete reaction kinetics (that is, both the activation energy and the pre-exponential factor) from a single sample [6], instead of having to perform many different temperature ramps as is the usual case in differential thermal analysis [7, 8, 9,10 and 11]. The second application is in determining the... 

The phase diagram in the CaO-Ca(OH)2 system was determined by thermodynamic calculations from equilibria determined in Reactions 13 and 14. The phase diagram for the Ca(0H)2-CaC03 system was determined by differential thermal analysis using the equipment shown in Figure 4. Two thermocouples were used, one in the melt and one positioned at the wall of the inner vessel. A temperature differential corresponding to the appearance of the first solid phase developed on... 

The force constant of the Si—Si bond has been calculated as 1.3 x 10 dynes cm however, it is believed that this value is probably in error (f04). The dipole moments of several aromatic disilanes have been reported (2) which allowed one to calculate an aryl—Si—aryl valence angle of 115°. The dipole moment of 1,2-dichlorotetramethyldisilane was found (105) to be 1.75 debye in carbon tetrachloride and 1.35 debye in benzene. On the basis of the dipole moments, the infrared and the Raman spectra (in the gas, liquid, and solid state), information on the rotation about the Si—Si axis in 1,2-dichlorotetramethyldisilane was obtained. In the solid state, the chlorine atoms assume the tram position, whereas in the liquid and gas state the molecule exerts torsional oscillations about the Si—Si axis to a certain extent. The phase transformations of hexamethyldisilane were studied by NMR (80) and thermodynamically by means of differential thermal analysis (25). From such studies it appears that at higher temperatures rotations about both the Si—Si and Si—CH3 axes occur in combination with the overall molecular rotation about the molecular axis, whereas at lower temperatures all movements are hindered except for the Si—CH3 axial rotation. 

Schwartz and co-workers [97] used isothermal differential thermal analysis to study the diffusion of Irganox 1330 (1,3,5 tris (3,5 di-tor -butyl-4-hydroxyl benzyl) mesitylene) in extruded sheets of isotactic polypropylene (iPP). Studies were conducted over the temperature range 80-120 °C. The measurements showed a clear relation between oxidation induction time and oxidation maximum time [both determined by isothermal dynamic thermal analysis (DTA)] and the concentration of stabiliser. It was possible to calculate the diffusion coefficients and the activation energy of diffusion of Irganox 1330 in iPP by measuring the oxidation maximum times across stacks of iPP sheets. 

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