Kinetic method. Kissinger

Originally proposed as a method for calculating kinetic parameters for reactions of the type solid solid + gas from DTA experiments, Kissinger s method [7] also assumes that the reaction rate is described by equation 5.8. The most important additional assumption of this method is that the maximum in the DTA curve occurs at the same temperature as the maximum reaction rate. The reaction is further assumed to proceed at a rate which varies with temperature and therefore the position of the DTA peak is a function of heating rate. From the variation in the peak temperature with heating rate E can be calculated for any value of n. The maximum reaction rate occurs when d/(h(x/(h) = 0. From equation 5.8 it follows that... 

The kinetic parameters can be estimated according to Kissinger s method [27] from the dependence of the exothermal peak temperature of DSC curves on heating rate. Knowing the reaction order, the maximum point of the DSC curve, dHjdt vs T, is used to obtain the ratio E/n from the expression [28] ... 

To evaluate the apparent activation energy, the isoconversional methods are use as suitable analysis procedures. These methods are based on the assumption that at a constant extent of conversion degree (a), the decomposition rate da/dt is a function only of the temperature. In methods developed by Friedman and Flynn-Wall-Ozawa, linear functions are obtained from which slopes the apparent activation energy at constant conversion a is achieved. In the free kinetic method set by Kissinger is calculated from the slope of the linear function takes into consideration the relationship between the heating rate and peak temperature of the first-derivative thermogravimetric curve [97]. 

Apart from this approach which implies the evidence of Tmax, there is another which includes the value of peak width in the analysis. Also, many authors rely on the application of other, even more simplified methods that enable the calculation of kinetic parameters. Particularly popular among surface scientists are the Redhead s and Kissinger s methods. 

For the SDT data, we considered only mass loss for kinetic analysis. Instability of the DTA baseline meant that results were inconclusive as to whether the mass loss corresponds to an endothermic or exothermic reaction or some combination thereof Kissinger s method yielded A = 2.19x1013 s-1 and E = 173.5 kj/ mol, with a standard error of 8.7 kj/mol on the activation energy. The Freidman parameters are shown in Figure 3 and are approximately equal to the Kissinger value. The AKTS code with its baseline optimization feature has less noise at low conversion, but the two programs agree very well overall. 

The two most popular methods of calculation of energy of activation will be presented in this chapter. First, the Kissinger method [165] is based on differential scanning calorimetry (DSC) analysis of decomposition or formation processes and related to these reactions endo- or exothermic peak positions are connected with heating rate. The second method is based on Arrhenius equation and determination of formation or decomposition rate from kinetic curves obtained at various temperatures. The critical point in this method is a selection of correct model to estimate the rate of reaction. 

Nearly all the computer applications to DTA have been concerned with the calculations of reaction kinetics where they find the ideal means of simulating the DTA curve of a chemical reaction of known kinetics. One of the first of these applications was that by Reed et al. (25) in which the quantitative determination of kinetics by the methods of Borchardt and Daniels (26) and Kissinger (27) were evaluated and compared. The DTA curve was generated numerically by use of equations such as... 

Table 4.2 Kinetic parameters obtained from Friedman, Kissinger, and Ozawa methods [12].

Kinetic analysis according to the model-free approach by Kissinger-Akahira-Sunose [25, 26] was performed with the computer program Excel. For kinetic analysis according to the advanced Vyazovkin method [27], the STAR software... 

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