Equation Kissinger

The activation energy for the reaction calculated using Kissinger equation was 52.9kJmol and the order of reaction (n) was 0.92. The peculiarity of this system is that two reactions, namely, the reaction between epoxy resin and polypropylene carbonate or epoxy resin and MTHPA shown in Scheme 21.1a and b, respectively, could occur. 

Fig. 5.5 Example data set used for calculation of reaction activation energies (BCYlOSp, per-ovskite formation on heating) change in DTA peak temperature with changing heating rate (a) and the same data plotted in the form of the Kissinger equation (b) (the slope of the tine is -E/R, where E is the activation energy and R is the universal gas constant...

Calculated by the Kissinger equation using results from up to four heating rates. (R > 0.95) Initial, but smaller peak used. 

The DTA measurements reveal a further - somewhat smeared - exothermic peak in the temperature range from 1390 to 1510 °C. Obviously, this peak arises from processes of re-crystallization. By XRD a drastic increase of the crystallite sizes is observable in the same temperature region. Thus, when the ACC is consumed by the crystallization process, a new mechanism starts to be responsible for the development of the microstructure of the final SiC ceramics. A further increase of the crystallite size becomes possible only by recrystallization, i.e. Ostwald ripening. The activation energy for such processes determined by the Kissinger equation in the way mentioned above was found to be significantly lower Ea, recr = 581 20 KJ moP. ... 

Figure 12.7 An example of the application of the Kissinger equation to the crystallization...

Rearranging the logarithmic form of (6), one has the generalized Kissinger equation, (9)... 

As can be seen, with the exception of the R3, D3 and D4 models, the exclusion of the In (j)m (o max term in the generalized Kissinger equation (9) has less than a 3% effect, and for the simple n order and Avrami-Erofeev models, A2, A3, less than a 1% effect. Similar figures result if one sets m - h or m = 1 in the rate equation (1). As the Arrhenius exponent E/RTjjjqx increases, there is a gradual small increase in Umax models. For all n order and diffusion controlled... 

The Kissinger equation, when expressed in its modified form (9) is a general thermoanalytical expression, applicable to a wide range of kinetic models. In the absence of other criteria, the value of ot ax assist in indentifying the... 

The modified Kissinger equation (Matusita Sakka, 1980) given below can be utilized to derive the activation energy ( ). 

The activation energy can be evaluated by the modified Kissinger equation by Matusita et al. (Araujo Idalgo, 2009 Qelikbilek et al., 2011 Kissinger, 1956 Matusita Sakka, 1981 Prasad Varma, 2005) ... 

The value of activation energy can also be calculated also by using the variation of Tp with the heating rate jS for both ciystallization phases (Afify, 1990 Afify et al., 1991). By using similar relations to Kissinger equation, the relations can be written in the form ... 

The activation energy for crystallization was determined to be 411 and 315 kj/mol by Kissinger (Equation 58) and Augis Bennett (Equation 60) method, respectively (Fig. 28a-b) (Liu Duh, 2007). Comparing with this study, previous works on near equiatomic NiTi films showed that the activation energy was 370-419 kJ/mol (Chen Wu 1999 Seeger Ryder, 1994). 

To further understand the effect of the interaction between the nanoparticles and the epoxy resin, the curing reaction kinetics of the composites have been studied. Based on non-isothermal DSC measurements and the Kissinger equation, the activation energy E, the pre-exponential factor A, and the reaction order , of the curing kinetics are obtained (Table 4). Comparison of the kinetic data suggests that the presence of the nanoparticles in epoxy does not change the overall reaction... 

Fig-3 Kissinger plot with the use of the modified Kissinger equation for PP blends with various talc contents... 

---