Single TG Curve Research Articles

Kinetic analysis of nonisothermal solid-state reactions: determination of the kinetic parameters by means of a nonlinear regression method

A nonlinear regression method has been proposed for a simultaneous calculation of the activation energy, frequency factor, and reaction order from a single TG curve. This method was based on the new temperature integral approximation proposed in this paper and the Levenberg–Marquardt method. The newly proposed nonlinear regression method was applied for determining the kinetic parameters from two simulated TG curves. The results of the calculations were compared with values obtained by the traditional method. It can be concluded from this comparison that the new nonlinear regression method is more accurate than the traditional method for the determination of the kinetic parameters of solid-state heterogeneous reactions.

NONISOTHERMAL THERMOGRAVIMETRY OF SPANISH FOSSIL FUELS

Low-rank coals from Mequinenza (type III-S) and Utrillas (type III) basins, characterized by high sulfur content, as well as type I-S oil shales from Ribesalbes were analyzed by thermogravimetry. Process kinetics was studied using the Friedman equation to interpret one point data – temperature of maximum generation of oil and gas (maximum on several experimental and simulated TG curves recorded at heating rates 5, 15 and 25 K ⋅min –1 , Tmax). These results are contrasted with those obtained by a method based on NLS (nonlinear least-squares) algorithms which derives kinetic parameters from a single TG curve recorded within a temperature interval nearby T. The final conclusion is that the reliability of kinetic parameters obtained from one point (Tmax) at several heating rates is low. On the other hand, the Friedman isoconversional method was used to elucidate the kinetic scheme which is derived from dependencies of apparent activation energy (E) on conversion level (α ). Analysis of kinetic data of pyrolysis of Mequinenza coal shows that in this case the dependence of activation energy on conversion level is characteristic of a reversible reaction followed by an irreversible one, whereas in the case of pyrolysis of Utrillas coal and Ribesalbes oil shales such dependence is characteristic of a reversible reaction.

Pitch pyrolysis kinetics from single TG curve

Global pitch pyrolysis kinetic parameters determined by different methods from single thermogravimetric curves are compared. Differential (Freeman–Carroll, Vachuška–Vobořil), integral (Coats–Redfern, Horowitz–Metzger) and the method of direct non-linear regression (NLR) were used. Direct non-linear regression is the most suitable when the whole kinetic triplet (activation energy, frequency factor and reaction order) is searched, but the results are not quite satisfactory. If the global first order kinetic of pitch pyrolysis is accepted, similar values of activation energy and frequency factor were obtained by different methods. Considering the quality of results and applicability Coats and Redfern method is recommended in this case.

Kinetic studies of graphon and coal-char reaction with NO and O 2: direct non-linear regression from TG curves

The reactions of carbonaceous materials (graphon and coal-char) with NO, O 2 and NO+O 2 were investigated by a thermogravimetric analysis (TGA). A method of direct non-linear regression of the kinetic equation was applied for a simultaneous calculation of the apparent activation energy, frequency factor and reaction order from a single TG curve of carbon gasification in various atmospheres. It was proven that the proposed calculation method is applicable for the calculation of kinetic parameters from overlapping processes. Calculations from TG curves of the above reactions demonstrate that NO-carbon and (NO+O 2)-carbon reactions contain two processes, while O 2-carbon is a single process. The reaction order of O 2-carbon is approximate 0.5, while the reaction orders of NO-carbon or (NO+O 2)-carbon reaction are dependent on the process and type of carbon. Graphon shows higher apparent activation energy than coal-char due to the pore structure and uncatalysed effects.

Response to Comments by Hussein M. A. Al-Maydama on ?The effect of UV radiation on the thermal parameters of collagen degradation? by Kaminska A1 and Sionkowska A (Polym Degrad Stab 1996;51:15?18)

This is a response to the comments which critically analysed numerical data and the interpretation for entropy changes from TGA traces for the degradation of collagen. In fact, the method used in this paper can no longer be used, because the evaluation of kinetic parameters of thermal degradation of polymers and polymeric materials by using single TG curve recorded at a certain heating rate does not lead to reliable results.

Response to Comments by Hussein M. A. Al-Maydama on “The effect of UV radiation on the thermal parameters of collagen degradation” by Kaminska A and Sionkowska A (Polym Degrad Stab 1996;51:15–18)

This is a response to the comments which critically analysed numerical data and the interpretation for entropy changes from TGA traces for the degradation of collagen. In fact, the method used in this paper can no longer be used, because the evaluation of kinetic parameters of thermal degradation of polymers and polymeric materials by using single TG curve recorded at a certain heating rate does not lead to reliable results.

Application of direct nonlinear regression from single TG curve to compounds undergoing simple and complex thermal decompositions

Nonlinear regression of the basic kinetic equation was used to determine kinetic parameters of simple and complex decomposition processes related to some pesticides and pharmaceutical substances. The method for this calculation was carried out using a single TG curve. These values were compared with those obtained with model-fitting and model-free methods. Nonlinear regression method is able to define a single mechanism for compounds undergoing one or few steps of decomposition processes. For compounds that undergo many steps of decomposition processes, only the mechanisms of some of them can be hypothesized. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 611–622, 2003

Kinetic Analysis in the Maximum Temperature of Oil Generation by Thermogravimetry in Spanish Fossil Fuels

Low-rank coals characterized by a high content of sulfur from Mequinenza (type III−S), Calaf (type III), and Utrillas (type III) basins, as well as type I−S oil shales from Ribesalbes were analyzed by thermogravimetry for deriving kinetic parameters from many TG curves recorded with different heating rates (5, 15, and 25 K/min) in maximum temperature of oil generation (Tmax) using a equation defined by Zsako. These results are contrasted with those obtained by NLS (nonlinear least squares) algorithms which derive kinetic parameters nearby Tmax from single TG curve. Furthermore, analytical determination of organic sulfur has allowed the comparison of different maximum temperatures of oil generation, as well as apparent activation energies, to establish general trends when different types of kerogen are compared. Finally, a method to compare the kinetic parameters at different heating rates (5, 15, and 25 K/min) is applied nearby the maximum temperature of oil generation (Tmax) obtaining similar kinetic val...

Determination of kinetic parameters by direct non-linear regression from TG curves

A method of direct non-linear regression of the kinetic equation was proposed for a simultaneous calculation of the activation energy, frequency factor, and reaction order from a single TG curve. The method of calculation was utilized for the kinetic parameters calculation from both the simulated and experimental curves (graphite and soot oxidation, Mg(OH) 2 decomposition). The results were compared with the values obtained by traditional methods. A dependence of the calculated parameters on random errors of the experimental data was studied. The method of non-linear regression appears to be the best of the used methods from this point of view. It was proved that the proposed calculation method is as well applicable for the kinetic parameters calculation of more overlapping processes.

Evaluation of kinetic parameters from a single TG curve based on the similarity theory and process symmetry

Abstract The equation for calculation of the activation energy of the diffusion of the evolved products through the matrix (E) from a single TG curve were proposed by solving Fick's laws. The solution is based on the similarly theory by utilizing a Fourier number. The proposed method was examined by using mass loss data for the dehydroxylation of some micas with and without FeO (muscovite and its varieties and lepidolite) as determined from their TG curves. TheE values for the first stage of the dehydroxylation of these micas areE 1,=85±10 kJ mol−1; for the final stageE 2=380±40 kJ mol−1 and for the mass loss connected with fluorineE F=85±10 kJ mol−1.

Some successes and failures of the methods based on several experiments

Abstract The actual kinetics of a solid state reaction cannot be discerned by means of the kinetic analysis of a single TG curve. The cause of this relates to the fact that different kinetic equations appear to fit a set of kinetic data. This paper shows the advantage of a choice of method based on comparing data from several experiments at the same degree of conversion. But this procedure must be carried out with great care. The limitations are discussed.

Thermogravimetric kinetics of polymer degradation: Science or fiction?

AbstractWeight changes in thermogravimetry are dependent on the volatility of the degradation products. Thus, molecular weight determinations (or related studies) must fist be undertaken to prove whether or not nonvolatile chain fragments will be removed only at high temperatures. In this case both thermal stability and kinetic studies by thermogravimetry are senseless. But even if volatile products are formed, the kinetic parameters will depend on the conversion degrees because of the kinetic chain character of the polymer degradation. Changes in reaction mechanism aggravate the situation; it is thus problematic to define in such conditions reliable kinetic parameters. Values calculated from a single TG curve are valid for specific conditions only, but of no sense from the general kinetic view.

Iron compounds in high oxidation states: III. Kinetic analysis of the reaction between BaO 2 and FeSO 4: non-isothermal versus isothermal procedures

The formal kinetic analysis of the reaction between BaO 2 and FeSO 4 yielding BaFeO 3 has been carried out using thermogravimetric data. The comparative study of non-isothermal and isothermal procedures allows one to establish that only a single TG curve would be required to determine the mechanism type and the kinetic parameters for reactions occurring in a unique stage.

On the evaluation of kinetic parameters from thermogravimetric curves

We concluded in a previous work [l] that it is not possible to determine the kinetic law followed by a thermal decomposition reaction of a solid from the kinetic analysis of a single TG curve. It is necessary to carry out at least one isothermal run to determine the actual reaction mechanism without ambiguity. It was shown from a theoretical analysis [l] that TG data of reactions following an Avrami-Erofeev law necessarily fit a first-order kinetic equation. However, it was concluded that very similar activation energies would be obtained whatever the value of the exponent n (1, 2 or 3) in the AvramiErofeev equation. Dharwadkar et al. [2] have studied the mechanism of the thermal decomposition of CdC03 and, from the analysis of both a single TG diagram and a single isothermal curve, they find that the reaction mechanism is described by an Avrami-Erofeev equation with n = 3, concluding that their results support, in part, OUT theoretical conclusions. However, they state [Z] that the apparent activation energies calculated frcm a TG diagram are quite different for different values of n, which is not in agreement with our theoretical deduction [ 11. The aim of the present note is to show that the apparent contradiction between the statement of Dharwadkar et al. and our conclusion is due to the different ways of defining the constant rate. Thus, Dharwadkar et al. [2] seem to express the Avrami-Erofeev isothermal in the form