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Kinetic analysis of thermogravimetric data

XIV. Three integral methods and their computer programs

Journal of Thermal Analysis and Calorimetry
Authors: J. Zsakó and J. Zsakó

Computer programs are given in Fortran language for three integral methods of deriving kinetic parameters from TG curves. Method 1 is a computerized variant of Doyle's curve-fitting method and performs the calculation of the exponential integralp(x) by means of author's empirical formula. Methods 2 and 3 are variants of the Coats-Redfern linearization method. Testing of the methods on both theoretical and experimental TG curves shows them to be almost equivalent as far as the results obtained are concerned, but Method 1 needs a ten-fold higher computer time.

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Shape and position parameters △Δ and τ are proposed for the characterization of TG curves and are defined by Eqs (6), (7) and (8), respectively. These parameters being reduced to the standard ”conditions”n=0 andq=1/6 K sec−1, the nomogram given in Fig. 1 can be constructed by means fo Eqs (9), (11) and (12). An iteration method is proposed, allowing derivation of the kinetic parametersn, E andZ of simple thermal decomposition reactions, from the parameters n,E andZ, by using the empirica formulae (9), (10), (11) and (12) and the nomogram. Table 3 contains data necessary to construct this nomogram.

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A new method is proposed for the derivation of kinetic parameters of reactions in homogeneous systems, by carrying out kinetic measurements under conditions of programmed temperature variations, instead of performing them under isothermal conditions at different temperatures. The basic relations are given for simple, paralle and complex reactions, without specifying the analytical shape of the temperature programme function.

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Doyle's isothermal method is analysed by using it for deriving activation energies from theoretical curves. Empirical formulae are given for the time correctiont c, as well as for the factorr in the following equation:E a=−rm cal/mole. An iterative procedure is suggested, which eliminates the inaccuracy of Doyle's method and permits the derivation of activation energies with an accuracy of ±0.1 kcal/mole in ideal cases.

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A hyperbolic heating program enables us to integrate the general kinetic equation.

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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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Abstract  

The kinetic compensation effect observed in heterogeneous non-isothermal kinetics is only an apparent effect. In general, the correlation derived between the kinetic parameters E and log A from TG curves can be described by means of a non-linear compensation law, expressed by Eq. (14). This equation may become approximately linear in certain particular cases, i.e. it may change into an isokinetic relation. The validity of the non-linear compensation law has been tested by using over 1000 sets of kinetic parameters reported earlier.

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Kinetic analysis of thermogravimetric data, VI

Some problems of deriving kinetic parameters from TG curves

Journal of Thermal Analysis and Calorimetry
Author: J. Zsakó
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