Kinetic analysis of thermogravimetric data

Thermal decomposition of 6 complexes of the type AH[Cr(NCS)₄ (am)₂]· nH₂O is studied with derivatograph. The formation of Cr(NCS)₃ as a labile intermediate is presumed. For some decomposition stages kinetic parameters are derived. The kinetic compensation effect is discussed.     

Kinetic Analysis of Thermogravimetric Data XXXI. Derivation of a non-linear kinetic compensation law

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. This revised version was published online in July 2006 with corrections to the Cover Date.     

Kinetic analysis of thermogravimetric data

The potassium, ammonium and thirteen amine salts of hexabromoplatinic acid were obtained and characterized by chemical analysis. The thermal decompositions of these complex salts were studied by derivatograph and differential scanning calorimetry. The natures of the pyrolysis processes are discussed and compared with those obtained for the analogous chlorocomplexes. From the TG curves, kinetic parameters were derived for different stages of the thermal decomposition.

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Zusammenfassung Es wurden die Kalium-, Ammonium- und dreizehn verschiedene Aminsalze von Hexabromoplatinsäure hergestellt und mittels Elementaranalyse charakterisiert. Mittels Derivatographie und DSC wurde die thermische Zersetzung dieser Komplexsalze untersucht. Das Wesen der Pyrolysevorgänge wird besprochen und mit dem der analogen Chlorokomplexe verglichen. Anhand der TG-Kurven wurden für verschiedene Schritte der thermischen Zersetzung kinetische Parameter ermittelt.

     

Dehydration kinetics of ulexite from thermogravimetric data

In the present study, the kinetic parameters of the thermal decomposition of ulexite were investigated by using TGA data. For the kinetic analysis, the Suzuki and Coats-Redfern methods were applied. It was determined that the process fits a first-order kinetic model, and the value of the activation energies and frequency factors decreased with decreasing particle size, which can be attributed to the increasing particle internal resistance to the escape of water as the grain size increases. The activation energy values were found to be 47.34–60.01 kJ mol^–1 for region I and 0.225–1.796 kJ mol^–1 for region II for the range of particle size fraction used. The frequency factors were calculated to be 9821.8–524.9 s^–1 for region I and 3.05×10^–44–2.807×10^–5 for region II for the same conditions.     

Kinetic analysis of thermogravimetric data

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.     

Kinetic analysis of thermogravimetric data

Journal of Thermal Analysis and Calorimetry - The thermal decomposition rates of seven [CoX 2(amine)2] type complexes (amine=aromatic amines) have been studied by thermogravimetry at 3 different...     

Kinetic analysis of thermogravimetric data

Fifteen thermogravimetric curves of the thermal decomposition of CaCO₃ reported in the literature have been analysed and kinetic parameters have been derived by means of Coats and Redfern's method. The activation energy varies between 26 and 377 kcal/mole, and the pre-exponential factors between 10² and 10⁶⁹, as functions of the working conditions. The kinetic compensation effect has been observed, and the results are well described by the following empirical compensation law: logZ=0.195E? 1.86.     

Kinetic analysis of thermogravimetric data

Nineteen salts of hexachloroplatinic acid with monovalent metals, aromatic and heterocyclic amines and phosphine were obtained and characterized by chemical analysis. The thermal decomposition of these complexes was studied by means of derivatograph and differential scanning calorimetry. The nature of the pyrolysis processes is discussed. From the TG curves, kinetic parameters were derived for different stages of the thermal decompositions.     

Kinetic analysis of thermogravimetric data XVI

The influence of the sample weight and the heating rate upon the thermal deamination of [Co(niox · H)₂(pyridine)₂]I(I), [Co(niox · H)₂(aniline)₂]I (II) and [Co(niox · H)₂ (pyridine)₂] NCS · 1.5 H₂O (III) and upon the dehydration of (III) has been studied (niox · H₂ stands for nioxime: 1,2-cyclohexanedione dioxime). Kinetic parametersn, E andZ have been derived by means of the authors' three computerized integral methods. Analysis of the results shows method 1 to be equivalent to method 2 with respect to the numerical values obtained, but it needs a tenfold computer time. Method 3 gives better results due to the better choice of input data. The influence of the working conditions and of the chemical constitution upon the kinetic parameters, as well as the kinetic compensation effect, are discussed.

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Zusammenfassung Der Einfluss des Probengewichts und der Aufheizgeschwindigkeit auf die thermische Desaminierung von [Co(niox · H)₂(pyridin)₂]I (I), [Co(niox · H)₂(anilin)₂]I (II) und [Co(niox · H)₂(pyridin)₂]NCS · 1.5 H₂O (III) sowie auf die Dehydratisierung von (III) wurde untersucht (niox · H₂ bedeutet Nioxim: 1,2-cyclohexandion-dioxim). Die kinetischen Parametern, E undZ wurden mit Hilfe der drei komputerisierten Integralmethoden der Autoren abgeleitet. Die Analyse der Ergebnisse zeigt, da\ Methode 1 der Methode 2 hinsichtlich der erhaltenen numerischen Werte ebenbürtig ist, doch eine zehnfache Rechenzeit beansprucht. Methode 3 ergibt bessere Resultate dank der besseren Wahl der eingegebenen Daten. Der Einfluss der Arbeutsbedingungen und der chemischen Struktur auf die kinetischen Parameter, sowie der kinetische Kompensationseffekt werden diskutiert.

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Résumé On a étudié l'influence du poids de l'échantillon et de la vitesse de chauffage sur la désamination thermique de [Co(niox · H)₂(pyridine)₂]I (I), [Co(niox · H)₂(aniline)₂]I (II) et [Co(niox · H)₂(pyridine)₂]NCS · 1.5 H₂O (III) ainsi que sur la déshydratation de (III) (niox · · H₂ représente la nioxime: 1,2-cyclohexanedione dioxime). A l'aide des trois méthodes d'intégration sur ordinateur des auteurs, les paramètres cinétiquesn, E et Z ont pu Être déduits. L'analyse des résultats montre que la méthode est équivalente à la méthode 2 quant aux valeurs numériques obtenues; elle exige cependant dix fois plus de temps d'ordinateur. La méthode 3 donne de meilleurs résultats en raison de la meilleure sélection des données d'entrée. On discute l'influence des conditions de travail et de la structure chimique sur les paramètres cinétiques ainsi que l'effet de compensation cinétique.

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[(. )₂ ( I (I), [(. )₂ ()₂] I (II) [Co(.)₂ ( NCS. 1.5 H₂O (III), ( .)₂ — : 1.2-. . , , , , E.Z. , 1 2 , . 3 , . , .

     

Kinetic analysis of DSC and thermogravimetric data on combustion of lignite

Thermal analysis increasingly being used to obtain kinetic data relating to sample decomposition. This work involves a comparative study of several methods used to analyse DSC and TG/DTG data obtained on the oxidation of Beypazari lignite. A general computer program was developed and the methods are compared with regard to their accuracy and the ease of interpretation of the kinetics of thermal decomposition. For this study, the ratio method was regarded as the preferred method, because it permits the estimation of reaction order, activation energy and Arrhenius constant simultaneously from a single experiment.The experimental part of this research was supported in part by NATO-SFS Project TU-Energy II. The authors express their appreciation to the NATO-SFS program for providing financial support for this project.     

Kinetic analysis of thermogravimetric data,III

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.     

Kinetic analysis of TG data XXXVI: Influence of procedural variables upon the apparent kinetic parameters of the thermal deamination

A number of 7 complexes of the [Co(DH)₂(amine)₂)]I type (DH₂ stands for dimethyloxime) have been studied by means of thermogravimetry and differential scanning calorimetry in nitrogen atmosphere, by using heating rates of 2.5, 5 and 10 K min^–1. In all cases an endothermal deamination reaction occurs leading to the relatively stable [Co(DH)₂I(amine)] intermediate. For this reaction apparent kinetic parameters have been derived. The influence of heating rate is discussed. The validity of a linear and a non-linear kinetic compensation law was verified.This revised version was published online in November 2005 with corrections to the Cover Date.     

Kinetic analysis of thermogravimetric data. XII

Shape and position parameters and 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 conditionsn=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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Zusammenfassung Die Gestalts- und Positionsparameter , und werden zur Charakterisierung von TG-Kurven vorgeschlagen, bzw. durch die Gleichungen (6), (7) und (8) definiert. Durch Reduktion dieser Parameter auf die Standardbedingungenn=0 undq=1/6 K sec^–1 mit Hilfe der Gleichungen (9), (11) und (12) kann das Nomogramm in Abb. 1 konstruiert werden. Eine Iterationsmethode wird vorgeschlagen, welche die Ableitung der kinetischen Parameter,n, E undZ einfacher thermischer Zersetzungsreaktionen aus den Parametern and unter Anwendung der empirischen Formeln (9), (10), (11) und (12) sowie des Nomogramms ermöglicht. Tabelle 3 enthält die zur Konstruktion des Nomogramms nötigen Angaben.

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Résumé Pour caractériser les courbes TG, on propose les paramètres de forme et de position , et définis par les équations (6), (7) et (8). En réduisant ces paramètres aux conditions standardsn=0 etq=1/6 K sec^–1, à l'aide des équations (9), (11) et (12), le nomogramme donné dans la figure 1 peut être construit. On propose une méthode d'itération pour déduire les paramètres cinétiquesn, E etZ à partir des paramètres , et dans le cas des réactions simples de décomposition thermique, en utilisant les formules empiriques (9), (10), (11) et (12) ainsi que le nomogramme. Le tableau 3 contient les données nécessaires pour construire ce nomogramme.

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G , , (6), (7) (8). « » =0 q=1/6 ^–1 , . 1, (9), (11) (12). , , E Z , (9), (10), (11) (12) . 3 , .

     

Kinetic analysis of thermogravimetric data,V

The statistical analysis of activation energy and of logZ values derived from thermogravimetric data for 134 decomposition reactions of bisdioximatocobalt(III) complexes shows the validity of a linear compensation law, i.e. both the effects of heating rate and of the nature of the ligand manifest themselves in the kinetic compensation effect. The parametera of the compensation law is sensitive to ligand effects and its value is influenced both by the nature of the coordinated dione-dioxime and by the nature of the outer sphere anion X, which replaces an ammonia molecule in the thermal decomposition reaction.

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Zusammenfassung Die statistische Analyse der aus den thermogravimetrischen Resultaten erhaltenen Aktivierungsenergiewerte und log Z-Werte von 134 Zersetzungsreaktionen der verschiedenen bisdioxamato Kobalt(III) Komplexen zeigte die Gültigkeit eines Gesetzes der linearen Kompensation, d.h. der Effekt der Heizungsgeschwindigkeit und der Natur des Liganden verursachten in erster Näherung den kinetischen Kompensationseffekt. Parametera des Kompensationsgesetzes (1) repräsentiert den Ligandeffekt. Sein Wert wird durch die Natur des koordinierten Dion-dioxims und des Anions X in der äußeren Sphäre beeinflußt, das ein Aminmolekül während der thermischen Zersetzungsreaktion ersetzt.

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Résumé L'analyse statistique des valeurs des énergies d'activation et de celles de logZ obtenues à partir des résultats thermogravimétriques de 134 réactions de décomposition des complexes différent de bisdioximato-cobalt(III) montre la validité d'une loi de compensation linéaire du type (1); ceci signifie que l'effet de la vitesse de chauffage et celui de la nature du ligand sont responsables en première approximation de l'effet de compensation cinétique. Le paramètrea de la loi de compensation est sensible aux effets du ligand et la nature de la bis-dioxime coordonnée ainsi que la nature de l'anion X dans la sphère externe remplaÇant une molécule d'aminé durant la réaction de décomposition thermique influencent sa valeur.

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logZ, 134 - (III), . a - X, .

     

Kinetic analysis of thermogravimetric data. X

A study was made of the thermal decompositions of 22 derivatives of[M(en) ₃]X ₃ type complexes. Partial de-amination leading to the formation of[M(en) ₂ X ₂]X type complexes occurs in the case ofM=Cr(III) ifX=Cl, Br, I orNCS, but in the case ofM=Co(III) it is possible only ifX=Cl. In other cases redox reactions hinder the formation of stable intermediates. Kinetic parameters were derived for the dehydration of 19 compounds.

The validity of a linear kinetic compensation law was observed. The dependence of the kinetic compensation parameters on the nature of the thermal process is discussed.

     

Kinetic analysis of thermogravimetric data. XXVI

Ten metal and ammonium salts of the acid H₂[ReCl₆] were obtained by double decomposition reactions, and their pyrolyses in air atmosphere were studied by means of DSC measurements. The kinetic parameters of these reactions were derived and are discussed.

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Zusammenfassung 10 Metall- und Ammoniumsalze der Säure H₂[ReCl₆] wurden durch Doppelzersetzungsreaktionen erhalten. Die Pyrolyse dieser Salze in Luft wurde mittels DSC untersucht. Die kinetischen Parameter dieser Reaktionen wurden ermittelt und diskutiert.

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H₂[ReCl₆]. . .

     

Kinetic analysis of thermogravimetric data,VI

The basic hypotheses of methods used for deriving kinetic parameters from TG data are discussed. The erroneous character of the methods which use more than a single TG curve is shown by comparing the shapes of ideal and real TG curves. The correctness of three integral methods is tested on ideal TG curves. The physical significance of the kinetic parameters and their correlation are discussed.

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Zusammenfassung Die Grundhypothesen der zur Ableitung kinetischer Parameter aus TG-Daten verwendeten Methoden werden erörtert. Der fehlerhafte Charakter der Methoden, welche mehr als eine einzige TG-Kurve verwenden, wird durch den Vergleich der Formen idealer und realer TG-Kurven veranschaulicht. Die Richtigkeit dreier Integralmethoden wird an idealen TG-Kurven geprüft. Die physikalische Bedeutung kinetischer Parameter und ihre Korrelation werden erläutert.

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Résumé On discute les hypothèses de base des méthodes utilisées pour déduire les paramètres cinétiques des données TG. Le caractère erroné des méthodes utilisant plus d'une courbe TG est mis en évidence en comparant les formes idéales et réelles des courbes TG. Le degré d'exactitude de 3 méthodes intégrales est examiné sur des courbes TG idéales. On discute la signification physique des paramètres cinétiques et leur corrélation.

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, . , , . 3- . .

     

Characterization and kinetic compensation effect of corn biodiesel

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.     

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     

测定高聚物动力学结晶能力的非等温DSC方法

研究了从非等温ＤＳＣ结晶曲线计算高聚物动力学结晶能力的方法．从高聚物非等温结晶动力学微分方程出发导出了计算高聚物动力学结晶能力的新方程．以含有不同催化剂的聚对苯二甲酸乙二酯为例，对其结晶进行了测试与计算．发现合理地选定最快结晶速率温度是计算动力学结晶能力的关键．本方法所得动力学结晶能力能正确反映高聚物的整体结晶信息