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Abstract  

In this paper, a systematic analysis of the errors involved in the determination of the kinetic parameters (including the activation energy and frequency factor) from five integral methods has been carried out. The integral methods analyzed here are Coats-Redfern, Gorbachev, Wanjun-Yuwen-Hen-Zhiyong-Cunxin, Junmeng-Fusheng-Weiming-Fang, Junmeng-Fang and Junmeng-Fang-Weiming-Fusheng method. The results have shown that the precision of the kinetic parameters calculated by the different integral methods is dependent on u (E/RT), that is, on the activation energy and the average temperature of the process.

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Abstract  

The dependence of the frequency factor on the temperature (A=A 0 T m) has been examined and the errors involved in the activation energy calculated from some integral methods without considering such dependence have been estimated. Investigated integral methods are the Coats-Redfern method, the Gorbachev-Lee-Beck method, the Wanjun-Yuwen method and the Junmeng-Fusheng method. The results have shown that the error in the determination of the activation energy calculated ignoring the dependence of the frequency factor on the temperature can be rather large and it is dependent on x=E/RT and the exponent m.

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The integral methods proposed to compute the kinetic parameters of heterogeneous reactions under non-isothermal conditions are usually worked by the help of the least squares method and the obtained correlation coefficient is taken as a criterion to choose the best integral method.

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Abstract  

Recently, Órfão obtained two simple equations for the estimation of the relative error in the activation energy calculated by the integral methods [2]. In this short communication, the validity of the equations has been evaluated by comparing the results calculated by the equations with the results calculated by the equation from theoretical derivation without introducing any assumption.

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Summary  

The paper contains an analysis of the used of Diefallah's composite integral method of kinetic parameters evaluation. It is shown that the application of this method should be preceded by the application of an isoconversional method through which the dependence of the activation energy, E, on the conversion degree,a, should be established. If Edepends ona, Diefallah's composite integral method leads to erroneous results. If Edoes not depend ona, the true kinetic model should be comprised in the pre-established set of kinetic models. These observations were checked for two sets of non-isothermal data, namely: (a) the TG curves corresponding to the dehydration of CaC2O4H2O; (b) the TG curves corresponding to the thermal decomposition of polyvinyl chloride (PVC).

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Non-isothermal kinetics in solids

The precision of some integral methods for the determination of the activation energy without neglecting the temperature integral at the starting temperature

Journal of Thermal Analysis and Calorimetry
Authors: J. Cai and R. Liu

Abstract  

The integral methods, which are obtained from the various approximations for the temperature integral, have been extensively used in the non-isothermal kinetic analysis. In order to obtain the precision of the integral methods for the determination of the activation energy, several authors have calculated the relative errors of the activation energy obtained from the integral methods. However, in their calculations, the temperature integral at the starting temperature was neglected. In this work, we have performed a systematic analysis of the precision of the activation energy calculated by the integral methods without doing any simplifications. The results have shown that the relative error involved in the activation energy determined from the integral methods depends on two dimensionless quantities: the normalized temperature θ=T/T 0, and the dimensionless activation energy x 0=E/RT 0 (where E is the activation energy, T is the temperature, T 0 is the starting temperature, R is the gas constant).

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Abstract  

The problem of computing the properties of a low mass quantum particle in equilibrium in a disordered medium is considered. With the advancement of computational speed, statistical methods for sampling a complex phase space are now viable. The Feynman-Kac path integral establishes a connection between a quantum particle and classical polymer consisting of p atoms. This allows the computation of quantum mechanical equilibrium values using well known methods devised for classical systems. Here we review the application of the path integral to the computation the properties of thermalized positron and positronium and introduce some new directions of investigation.

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