Temperature 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. 

The Kissinger method can also be used to determine the activation energy for viscous flow, by replacing the exothermic peak maximum temperature with the glass transformation temperature in equation 12.8. This method is particularly useful for glasses where it is difficult to form the sample needed for application of the beam-bending or fiber elongation methods discussed in Chapter 6. 

A = quantity of heat (meal) corresponding to the area under DSC curve ((mcal/s) s). By the Kissinger method (Boudart), one can determine the activation energy (E) via DSC curves obtained under three different heating rates (P) at least. Once the rates (P) are known, as well as temperatures corresponding to the maximum on each peak (Tc), it is possible to establish the following linear relationship ... 

The non-isothermal crystallization activation energy can be derived by the combination of cooling rate and exothermic peak temperature (Tp), shown as the Kissinger method [22] in Equation (6). 

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]. 

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... 

Nonisothermal crystallization is frequently analyzed via calculation of the so-called energy of activation of crystallization according to the Kissinger method [69, 70]. The method is based on the simplifying assumption that a transformation rate during a reaction (crystallization in the present case) is a product of two functions, one depending solely on the transformed fraction,/( ), and the other depending solely on temperature, with an Arrhenius-type dependence ... 

The dependence of the crystallization temperature (T ) on the heating rate (j) can be used to obtain experimental values for the activation energy of crystallization (Luborsky and Liebermann, 1978 Scott, 1978). The method of analysis is based on the results of Kissinger (1957). For a first-order rate process one may write... 

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] ... 

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