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Abstract  

This paper reports a linear relationship between kinetic characteristics from the Arrhenius equation describing a decomposition process found when studying the kinetics of thermolysis of spatially hindered phenols. This relationship between the coefficients is known in the literature as a 'compensation effect'. The existence of the compensation effect permits some conclusions concerning the decomposition mechanism and thermal characteristics of the compounds under investigation.

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Abstract  

By kinetics of decomposition of solids in both isothermal and non-isothermal conditions, the compensation effect (CE) is rather a rule. The topic of this work is to suggest an activation mechanism which leads to the dependences similar with CE. The solid is assimilated to a system of the harmonic oscillator with a Bose-Einstein energy distribution. Considering an activation process due to a vibrational energy transfer from a homogeneous and isotropic field of thermic oscillators to the solid-state oscillator, the thermodynamic functions are in the relationship

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\Delta S^ * = \Delta H^ * /T_{is}$$ \end{document}
where ΔH* and ΔS* are the activation functions and T is is the isokinetic temperature. Taking into account the definitions of H and S by means of the partition function, the isokinetic temperature is assimilated with the characteristic temperature
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$T = \hbar \theta /k_B$$ \end{document}
An important consequence, a correlation between the isokinetic temperature and the spectroscopic wavenumber of the activated bond, is illustrated by a number of decomposition reactions under non-isothermal conditions.

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The compensation effect

A reply to Zsakó and Somasekharan's remarks

Journal of Thermal Analysis and Calorimetry
Author: Ravindra K. Agrawal

This paper is a rebuttal to the paper of Zsakó and Somasekharan. It has been shown that the criticisms of Zsakó and Somasekharan are baseless. The procedure proposed earlier by Agrawal to distinguish between true and false compensation effect is reasonable and gives good results. To establish true c.e., it has been reaffirmed that bothT iso and Ink iso are prerequisite.

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Abstract  

It is generally accepted that the compensation effect arises when a linear relation between InA andE is detected for a simple reaction taking place over different catalysts or for different reactions over one catalyst. For a perfect linear relation between InA andE representation of the reaction rate constant in an Arrhenius plot results in a series of straight lines which intersect in a single point. The importance is stressed of defining unambiguously what is meant by the compensation effect, and it is shown how the scatter in the values of InA is translated into Arrhenius plots.

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On the basis of theoretical TG curves it has been shown that the kinetic compensation effect observed in thermal decomposition reactions is not due to the special form of the Arrhenius equation. Formally, the validity of a linear kinetic compensation law implies the existence of a characteristic temperature at which the rate constants of all reactions have the same value, but this temperature can be higher or lower than the temperatures at which the decomposition takes place.

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A critical assessment of a published paper (by Agrawal) is presented. The procedure proposed and used by Agrawal to distinguish a false compensation effect from a true one is shown not to be correct.

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A number of 1145 sets of kinetic parameters derived in our earlier papers from TG curves have been worked up. The apparent activation energy and pre-exponential factor values have been found to obey a linear compensation law (isokinetic relation) if the thermal decomposition begins in the same temperature interval, irrespective of the nature of the chemical reaction. The isokinetic temperatureT i has been found to be very close to the mean value of the temperaturesT 0.1 at which the conversion becomes equal to 0.1 and atT i the rate constant has been found to be approximately equal to 10−3s−1 in allT 0.1 intervals investigated. It is concluded that the kinetic compensation effect observed in heterogeneous non isothermal TG kinetics is not a true one.

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Journal of Thermal Analysis and Calorimetry
Authors: M. Dantas, A. Almeida, Marta Conceição, V. Fernandes Jr, Iêda Santos, F. Silva, L. Soledade, and A. Souza

Abstract  

This work presents the characterization and the kinetic compensation effect of corn biodiesel obtained by the methanol and ethanol routes. The biodiesel was characterized by physico-chemical analyses, gas chromatography, nuclear magnetic resonance and thermal analysis. The physico-chemical properties indicated that the biodiesel samples meet the specifications of the Brazilian National Agency of Petroleum, Natural Gas and Biofuels (ANP) standards. The analyses by IR and 1H NMR spectroscopy indicated the ester formation. Gas chromatography indicated that biodiesel was obtained with an ester content above 97%. The kinetic parameters were determined with three different heating rates, and it was observed that both the methanol and ethanol biodiesel obeyed the kinetic compensation effect.

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The kinetic study of thermal degradation takes into account the validity of the Arrhenius equation. From TG data, the activation energy,E a and pre-exponential factor,A, are evaluated. These results are interpreted by using the ‘kinetic compensation effect’ as basis. A linear correlation between In(A) andE a is obtained in all cases studied. However, in a plot of the logarithm of the rate constant as a function of reciprocal temperature for the same series of reactions, the thermal oxidative degradations of Nylon-6 and PVC display a point of concurrence and one isokinetic temperature, whereas those of HIPS and PC do not. Therefore, in the thermal oxidative degradations of Nylon-6 and PVC a ‘true’ compensation effect occurs, which could be related to the bulk properties of metal oxides, such as different valence states, whereas for other polymers it displays only an ‘apparent’ compensation effect. This means that degradation is largely independent of the bulk properties of oxides, but may be related to the distribution of different kinds of active links in the polymer surface having different activation energies.

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