The heating rate as a variable in non-isothermal kinetics. A new method to evaluate the nonisothermal kinetic parameters

The heat exchange calorimetry, hitherto developed for ordinary size samples, was modified for diminishing the sample size to one tenth or less of that commonly used in previous reports. Improvements were made with respect to the vessels for sample and reference, the stirrer of the sample solution, the thermistor and the calibration heater. The value of α, a constant relating to the heat transfer and critically affecting the sensitivity to smaller heat effects, was given an appropriately small value. The improved version of the calorimeter employed a sample vessel of a capacity of 6 cm³ and was suited to accomodate about 3 cm³ of a solution. The calorimeter proved to give sufficiently precise results when total heats ranging from 0.05 to 0.4 J were evolved.     

Checking of mathematical calculation methods for the determination of kinetic parameters from non-isothermal measurements by test functions

The applied computing programs are checked by means of test values from theoretical models. First-order kinetics, the Avrami equation and the 2-dimensional diffusion equation have been calculated as theoretical values. The computer calculation was carried out both for the total reaction and for individual reaction intervals.For the calculation of kinetic parameters and the distinction between the various models, in principle, the integral method should be used. The calculation does not give any answer to the question whether there exists another equation not involved in the models selected, which describes the processes better. If there is no indication of the reaction, it should first be checked by the differential method. The correlation coefficient does not allow the individual model equations to be distinguished with statistical significance.     

Some problems concerning the evaluation of non-isothermal kinetic parameters

The validity of isoconversional methods used to evaluate the activation energy is discussed. The authors have shown that the Flynn-Wall-Ozawa and Friedman methods give results that agree with each other only if the activation energy does not change with the degree of conversion. A criterion for the reaction mechanism as expressed by the differential conversion function is suggested too.     

Determination of the kinetic parameters from non-isothermal measurements with a general temperature program

This paper deals with a new method for the evaluation of the kinetic parameters from thermogravimetric measurements with a general temperature program. The procedure assumes the use of a computer or calculator. In principle, it is an integral method with two variants. The kinetic parameters can be determined from a single and/or from two general temperature programs. This method is free of the shortcomings that the existing method has, i.e. the self-heating and/or self-cooling, resulting in errors in measurements and the limitation of the weight of sample. The two variants of the submitted method have been tested by evaluation of the experimental data of the thermal decomposition of CaCO₂.     

On the kinetic parameters from non-isothermal data: mathematical considerations

The kinetic parameters determination of the crystallization of a disordered solid solution subjected to non-isothermal treatments is often considered using a large variety of physical models. Some authors propose the use of Johnson-Mehl-Avrami's classic expression which corresponds to both isothermal and non-isothermal kinetic parameters, according to experimental results.In this paper we carry out research, starting from the generalized model most widely used by the non-isothermal problem, in which we prove the validity of Johnson-Mehl-Avrami's expression.     

The Kissinger law and the IKP method for evaluating the non-isothermal kinetic parameters

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 T _m (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.     

A statistical comparison of non-isothermal methods of kinetic investigation

A statistical analysis of some non-isothermal kinetic techniques is given. Comparison of the kinetic parameter values obtained by different techniques has shown them to be statistically non-equivalent. Hypotheses of significance or non-significance of discrepancies in the kinetic parameter values should therefore be tested using two-dimensional normal distributions. Comparisons of the results obtained by various techniques using activation energy values only lead to erroneous conclusions.     

On the dependence of kinetic parameters and functions in non-isothermal kinetics

The approaches to overcoming local ambiguity due to the dependence of the kinetic equation parameters are considered. The application of the mathematical apparatus of the Jacobi matrices enables one to determine the number of both independent kinetic parameters and kinetic functions used to describe a process. No more than five parameters in the Šestak-Berggren equation and only some kinetic functions are found to possess independence.     

An attempt to evaluate the vibrational intensity changes due to long-range interactions

The effects of intermolecular interactions within the framework of long-range interactions on IR and Raman intensities are investigated.     

Are kinetic parameters of non-isothermal thermogravimetric degradation of polymers unequivocal?

Due to the complex character of the thermal degradation of polymers as a solid-gas chain reaction, an unequivocal kinetic characteirzation is possible only for stationary states of both radical concentration and reaction mechanism. These conditions are hardly realizable in non-isothermal thermogravimetry. Additional the weight losses are depedent on the volatility of the reaction products. That is not always certain in polymer degradation. As a consequence the deduced ‘kinetic parameters’ are not unequivocal. They are conversion and heating rate dependent and may be influenced by sample shape and size. Thus the ‘kinetic parameters’ are in fact from the point of view of mathematics the fitting parameters of a ‘rate equation’ like relation, specific for the used reaction conditions only. From the point of view of chemical kinetics they are neither attributable to a determined reaction mechanism nor can they be used for predictions. Dedicated to the 70^th Anniversary of Dr. Jo Flynn     

An outline of new calculation methods for the determination of both thermodynamic and kinetic parameters from isothermal heat conduction microcalorimetry

An outline of equations allowing calculation, from calorimetric data, of both thermodynamic and kinetic parameters for reactions which proceed to completion is given. In addition equilibrium constants are calculable for reactions which proceed to an equilibrium position. Advantages of the methods for solid state kinetic and stability studies are briefly discussed.     

An attempt to evaluate dry deposition velocity of airborne210Pb in a forest ecosystem

Atmospheric concentration and total (wet plus dry) and dry deposition of²¹⁰Pb and⁷Be have been measured at our laboratory in Ishikawa Prefecture in Japan which faced the Sea of Japan during 1993–1994. At the same time inventories of excess²¹⁰Pb in soil samples were measured from a mixed pine forest. On the basis of the data obtained, an attempt was made to evaluate the dry deposition velocity as a result of the interception by the canopies of airborne²¹⁰Pb in a pine stand The dry deposition velocity of²¹⁰Pb in the pine stand was roughly estimated to be 0.9–0.8 cm/s, higher by a factor of about 10 than the value (mean: 0.12±0.09 cm/s; range: 0.06–0.28 cm/s) in the open area measured on the roof of our laboratory.     

Precision of integral methods for the determination of the kinetic parameters

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.     

Thermogravimetry. Fast methods for evaluation of kinetic parameters

The paper discusses three fast methods for determination of the reaction order, as follows: the single-point method proposed by Kissinger, Horowitz and Metzger, an original two-point method, and the three-point method suggested by a Gorbachev's paper. These methods cannot elucidate the reaction mechanism, but they can help in the rapid derivation of the apparent kinetic parametersn andE.

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Zusammenfassung Es wurden drei Methoden zur Schnellbestimmung von Reaktionsordnungen ausgewertet: eine Einpunktmethode von Kissinger, Horowitz und Metzger, eine Zweipunktmethode und eine Dreipunktmethode nach einer Anregung von Gorbachev. Mittels dieser Methoden kann man zwar nicht den Reaktionsmechanismus bestimmen, wohl aber eine schnelle Bestimmung der kinetischen Scheinparametern undE durchführen.

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: , , , , . , n .

     

An alternative Avrami equation to evaluate kinetic parameters of the interaction of Hg(II) with thin chitosan membranes

In this work, thin chitosan membranes were utilized as an adsorbent for the removal of Hg(II) from aqueous solutions. A rise of temperature accelerates the mass transfer of Hg(II) to the membranes, surfaces. The kinetic data did not present a good fitting to the traditional Lagergren adsorption kinetic equations. An alternative Avrami kinetic equation was employed and successfully fitted to the kinetic adsorption quantities. From this new equation, two regions presenting distinct kinectic parameters were found, and the use of the parameter n was also relationed to the determination of the kinetic order. Variations of the adsorption kinetic rate in relation to the time, the initial Hg(II) concentration, and the temperature were also calculated and are discussed.