all the samples. The nucleation activity and crystallization activation energy of PP/kaolin composites were computed using Dobreva and Kissinger methods, respectively. In this article, the samples were subjected to three different processing
We performed the analysis of the thermokinetic equations taking into account Kissinger law. The formulas obtained were verified
by the use of the so-called isokinetic effect. It was shown that the thermokinetic equation, g(α)=(AT/q)exp(-E/RT), appeared to connect both laws analyzed. Moreover, this approach validates equation km=q/Tm which takes a form of Kissinger law, i.e. ln(q/Tm) vs. 1/Tm.
Authors:P. Sánchez-Jiménez, J. Criado, and L. Pérez-Maqueda
The dynamic heating rate method developed by TA Instruments (Hi-ResTM) is a kind of sample controlled thermal analysis in which a linear relationship between the logarithm of the heating rate
and the rate of mass change is imposed. It is shown in this paper that the reacted fraction at the maximum reaction rate strongly
depends on the parameters selected for the Hi-Res heating algorithm, what invalidates the use of the Kissinger method for
analysing Hi-Res data unless that the reaction fits a first order kinetic law. Only in this latter case, it has been demonstrated
that it is not required that a constant value of the reacted fraction at the maximum reaction rate is fulfilled for determining
the activation energy from the Kissinger method. In such a case the Kissinger plot gives the real activation energy, independently
of both the heating schedule used and the value of the reacted fraction, αm, at the maximum.
On the basis of copper sulphate pentahydrate thermal dissociation, for analyzed reactions I to IV, 6 thermokinetic equations was discussed. Arrhenius law parameters were determined and the isokinetic effect (IE) and Kissinger law appearing was analyzed. It was found that only dependence resulting from isokinetic effect, in the form km=q/Tm, relates to the suitable thermokinetic Eq. (2) and Kissinger law in modified form (14). The confirmation was made that the possibility of determining the averaged activation energy from thermokinetic equations using suitable correction coefficients exists.
For the most common kinetic models used in heterogeneous reactions, the dependencies on xm = E/RTm (E is the activation energy, Tm is the temperature corresponding to maximum process rate, R is the gas constant) on the relative errors (e%) in the determination of the activation energy from the slope of the Kissinger straight line ln(β / Tm2) vs. 1/Tm (β is the heating rate) are evaluated. It is pointed out that, for xm≥10.7 and all kinetic models, ∣e%∣≤5%. Some possible cases exhibiting high values of ∣e%∣, which can be higher than 10%, are put in evidence and discussed.
Authors:Yanchun Li, Yi Cheng, Yinghua Ye, and Ruiqi Shen
The relative errors (e%) in the determination of the activation energy from the slope of the Kissinger straight line ln(β/βTp2) vs. 1/Tp (β is the heating rate) are in-depth discussion. Our work shows that the relative errors is a function containing the factors
of xp and Δxp, not only xp (xp = E/RTp, E is the activation energy, Tp is the temperature corresponding to maximum process rate, R is the gas constant). The relative error between Ek and Ep will be smaller with the increase of the value of x and/or with the decrease of the value of Δx. For a set of different heating rates in thermal analysis experiments, the low and close heating rates are proposed from
the kinetic theory.
A brief derivation of the Kissinger’s equation for analysis of experimental data of non-isothermal glass transition peaks
based on the free volume model is given. This equation was applied successfully to Cu0.3(SSe20)0.7 chalcogenide glass for different heating rates. For granted this model, the obtained glass transition activation energy,
Eg must be constant throughout the whole glass transition temperature range. This required that Tg to be determined for three characteristic temperature points for each DSC curve.
The non-isothermal kinetics of precipitation of an Al-12.6 mass% Mg alloy for different heating rates were studied using thermal
expansion techniques. The structural changes associated with the precipitation of the and b phases were identified. The conversion
degree of each phase was associated with the area under the derivative curve of the thermal expansion with respect to temperature.
Using the Kissinger relation and an iso-conversional method we calculated the apparent activation energies associated with
formation of the precipitated phases. We report an increasing dependence of the activation energy on the conversion degree,
the values obtained being within the range reported in the literature.
Augis and Bennett (J. Thermal Anal. 13 (1978) 283.)  recently proposed a modified Kissinger method for determining the activation energy of a transformation. It is shown that the proposed method was, in fact, based upon a modification to the equation for the rate of reaction under non-isothermal conditions. The apparent discrepancy between the proposed method and the original Kissinger method is therefore resolved. The modified rate equation appears to have, at best, only a limited application. However, if the equation should be appropriate for a particular transformation, it is demonstrated that Augis and Bennett's method would be the correct method for determining the activation energy.
The following problems concerning the apparent compensation effect (CE) (lnA=a+bE, where A is the pre-exponential factor, E is the activation energy, a and b are CE parameters) due to the change of the conversion function and on which the invariant kinetic parameters method (IKP
method) is based, are discussed: (1) the explanation of this kind of CE; (2) the choice of the set of conversion functions
that checks CE relationship; (3) the dependencies of CE parameters on the heating rate and the temperature corresponding to
the maximum reaction rate. Using the condition of maximum of the reaction rate suggested by Kissinger (Kissinger law), it
is pointed out that, for a certain heating rate, the CE relationship is checked only for reaction order (Fn) and Avrami-Erofeev
(An) kinetic models, and not for diffusion kinetic models (Dn). Consequently, IKP method, which is based on the supercorrelation
relationship between CE parameters, can be applied only for the set Fn+ An of kinetic models.
The dependencies of a and b parameters on the heating rate and Tm (temperature corresponding to maximum reaction rate) are derived.
The theoretical results are discussed and checked for (a) TG simulated data for a single first order reaction; (b) TG data
for PVC degradation; (b) the dehydration of CaC2O4·H2O.