Kinetic analysis Kissinger method

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. 

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... 

The simplest methods of kinetic analysis used in Kinetics05 is Kissingers method [12], in which the shift of temperature of maximum reaction rate (Tmax) with heating rate (P) is given by... 

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 kinetics of non-isothermal crystallization using differential scanning calorimeUy (DSC) has been a known approach to study the crystallization behavior of polymers. The analysis was commonly performed through the use of modified Avrami [1 ], Ozawa [5] and other methods [6-7]. Kissinger method [8] was often used to obtain the activation energy of crystallization. These methods have been helpful to differentiate the crystallization behavior between materials. 

Budrugeac, P. (2007). The Kissinger law and the IKP method for evaluating the non-isothermal kinetic parameters. Journal of Thermal Analysis and Calorimetry, Vol. 89, pp. 143-151 ISSN 1388-6150 (Print), 1572-894 (electronic version)... 

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]. 

Another, rather popular method of kinetic data analysis is based on expressing the maximum value (index max) on the dependence of a vs. T, for which it holds, a = 0 = a, ax [E/RT /ZJ exp(-E/RTmux) df(a)/da]. The result provides simple but rather useful dependence, often called Kissinger plot and known since 1959 [505], which in various modifications and reproves shows the basic proportionality In (( )/Tn,) = (E/R) (1/Tm). 

Kissinger relationship, the most extensively used method in kinetic studies since 1957 [13], was in use to determine the energy of activation and the order of reaction, from plots of the logarithms of the heating rate against the temperature inverse at the maximum reaction rate in isothermal conditions. This method is usually based on the Differential Scanning Calorimetry (DSC) analysis of formation or decomposition processes and in relation to these processes the endothermic and exothermic peak positions are related to the heating rate. 

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. 

Reaction kinetics from DSC, DTA or TGA, have been used to examine the stability of a limited number of pharmaceutical materials. Various models have been used including the Power Law, Avarami-Erofeev and Prout-Tomkins models [72]. These methods are also based on the Kissinger [73], ASTME 698 [74] or Ozawa [75] methods [8]. Most frequently, they have been applied to the dehydration of various materials such as theophylline monohydrate [76], phenobarbitone monohydrate or hemihydrate [77], phenylbutazone [78], oxazepam [23] and trazodone tetrahydrate [79]. The uses are limited for pharmaceutical systems, not least because dehydration is particle size dependent. Thermal analysis, especially DSC, DTA and TG, has been used outside the pharmaceutical area in the prediction of reaction kinetics as described elsewhere in this handbook. Methods used include those by Borchart and Daniels [80], Kissinger [73], Freeman and Carroll [81] and Flynn and Wall [82]. Although these techniques are well established and, if used properly, can give pertinent information, their use in pharmaceutical arenas is restricted to dehydration and decomposition. 

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