Thermal decomposition kinetics of magnesite from thermogravimetric data

Thermal decomposition kinetics of magnesite were investigated using non-isothermal TG-DSC technique at heating rate (β) of 15, 20, 25, 35, and 40 K min⁻¹. The method combined Friedman equation and Kissinger equation was applied to calculate the E and lgA values. A new multiple rate iso-temperature method was used to determine the magnesite thermal decomposition mechanism function, based on the assumption of a series of mechanism functions. The mechanism corresponding to this value of F(a), which with high correlation coefficient (r-squared value) of linear regression analysis and the slope was equal to −1.000, was selected. And the Malek method was also used to further study the magnesite decomposition kinetics. The research results showed that the decomposition of magnesite was controlled by three-dimension diffusion; mechanism function was the anti-Jander equation, the apparent activation energy (E), and the pre-exponential term (A) were 156.12 kJ mol⁻¹ and 10^5.61 s⁻¹, respectively. The kinetic equation was

Isothermal kinetic analysis of the thermal decomposition of magnesium hydroxide using thermogravimetric data

In the present study, the kinetics of the thermal decomposition of magnesium hydroxide is investigated, using isothermal methods of kinetic analysis. For this purpose, experiments in thermogravimetric analyser were carried out in standard values of temperature (350°, 400°, 450° and 500°C) which resulted in weight loss percent as a function of time. The data were further modified to give fraction reacted ‘' versus time to be tested in various forms of ‘' functions. In order to determine the mechanism of the magnesium hydroxide decomposition and the form of the conversion function which governs the dehydroxylation of Mg(OH)₂, four different methods of isothermal kinetic analysis were used. Applying each of these methods to the data, it was concluded that the nucleation mechanism predominates the Mg(OH)₂, decomposition for all values of temperature tested; at 350°C the kinetic model which represents the experimental data is that of reaction at phase boundaries (random nucleation), F₁: ln(1−)=kt) while for the higher temperatures 400°, 450° and 500°C the kinetic equation of nucleation and development in two dimensions, A₂: [−ln (1−)]^1/2=kt was found to fit better the experimental results. The activation energy was evaluated applying two alternative methods; the Arrhenius plot, using maximum rates of reaction, from which the activation energy was evaluated to be 20.54 kcal/mol. An alternative method based on plots of ln t versus 1/T corresponding to the same value of ‘' gave values of 10.72, 13.82 and 16.31 kcal/mol for ‘' values of 0.25, 0.50 and 0.75, respectively.     

On the thermal decomposition mechanism for dehydroxylation of alkaline-earth hydroxides

The activation energy for thermal dehydroxylation in vacuum of alkaline-earth hydroxides has been calculated from thermogravimetric data. The experimental results of Mg(OH)₂ Ca(OH)₂ and Sr(OH)₂ are in agreement with an unimolecular decay law and their activation energies are similar to the values of enthalpies of decomposition. In contrast, as the dehydroxylation process of Ba(OH)₂ takes place in liquid phase and the BaO does not dissolve into the molten Ba(OH)₂, a kinetic of zero order describes the reaction rate and the activation energy is lower than the enthalpy of decomposition.

---

Zusammenfassung Die Aktivierungsenergie zur thermischen Dehydroxilierung von Erdalkali-Hydroxiden im Vakuum wurde aus thermogravimetrischen Daten errechnet. Die Versuchsergebnisse bezüglich Mg(OH)₂, Ca(OH)₂ und Sr(OH)₂ sind mit einem unimolekularen Zersetzungsgesetz in Übereinstimmung und die entsprechenden Aktivierungsenergien sind den Werten der Zersetzungsenthalpien ähnlich. Im Gegensatz hierzu wird im Falle von Ba(OH)₂, da der Dehydroxylierungsvorgang in der flüssigen Phase stattfindet und das BaO sich nicht im geschmolzenen Ba(OH)₂ löst, die Reaktionsgeschwindigkeit durch eine Kinetik nullter Ordnung beschrieben und die Aktivierungsenergie liegt hierbei niedriger als die Zersetzungsenthalpie.

---

Résumé L'énergie d'activation de la déshydroxylation sous vide des hydroxydes des métaux alcalins est calculée à partir des données thermogravimétriques. Les résultats expérimentaux obtenus avec Mg(OH)₂, Ca(OH)₂ et Sr(OH)₂ sont en accord avec une loi de décomposition unimoléculaire et les énergies d'activation correspondantes sont du même ordre de grandeur que les enthalpies de décomposition. Par contre, du fait que la déshydroxylation de Ba(OH)₂ a lieu en phase liquide et que BaO ne se dissout pas dans Ba(OH)₂ fondu, la vitesse de la réaction est décrite par une cinétique d'ordre zéro et l'énergie d'activation est plus faible que l'enthalpie de décomposition.

---

. Mg(OH)₂, Ca(OH)₂ Sr(OH)₂ . , Ba(OH)₂ BaO , , .

     

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. XI thermal decomposition of some metal dithionates

A thermal analytical study of Li, Na, K, Rb, Cs, NH₄, Mg, Ca, Sr, Ba and Zn dithionates is reported. The decomposition of the dithionate ion is endothermic in the case of the Na, K, Rb, Cs and NH₄ salts, but exothermic with Li, Mg, Sr, Ba and Zn. Kinetic parameters have been derived from the TG curves by means of the Coats-Redfern method. The validity of a linear kinetic compensation law is reported for the loss of crystal water and separately for the decomposition of the dithionate ion.

---

Zusammenfassung Es wird über eine thermoanalytische Untersuchung der Dithionate von Li, Na, K, Rb, Cs, NH₄, Mg, Ca, Sr, Ba und Zn berichtet. Die Zersetzung des DithionatIons ist im Falle von Na, K, Rb, Cs und NH₄-Salzen endotherm, im Falle von Li, Mg, Sr, Ba und Zn hingegen exotherm. Die kinetischen Parameter wurden aus den TG-Kurven mittels der Coats-Redfern-Methode abgeleitet. Es wird über die Gültigkeit eines linearen kinetischen Kompensationsgesetzes für den Verlust von Kristallwasser berichtet und gesondert für die Zersetzung des Dithionat-Ions.

---

Résumé On présente les résultats d'une étude par analyse thermique des dithionates de Li, Na, K, Rb, Cs, NH₄, Mg, Ca, Sr, Ba et Zn. La décomposition est endothermique dans le cas des sels de Na, K, Rb, Cs et ammonium tandis qu'elle est exothermique dans le cas des sels de Li, Mg, Sr, Ba et Zn. Les paramètres cinétiques sont déduits des courbes TG par la méthode de Coats-Redfern. La validité d'une loi de compensation cinétique linéaire est étudiée pour la perte de l'eau d'hydratation ainsi que pour la décomposition de l'ion dithionate.

---

Li, Na, K, Rb, Cs,. NH₄, Mg, Ca, Sr, Ba Zn. [ Na, K, Rb, Cs NH₄ , Li, Mg, Sr, Ba Zn . - . .

     

Kinetic analysis of thermogravimetric data XIX. Study of the thermal decomposition of some hexathiocyanatochromates

Ammonium and metal salts of the acid H₃[Cr(NCS)₆] have been obtained and characterized. Their thermal decomposition has been studied with a derivatograph. The thermal decomposition of the ammonium salts begins with an endothermic stage, leading to the formation of the intermediate Cr(NCS)₃, which in exothermic processes finally yields Cr₂O₃. The decomposition of the metal salts is exothermal and the polarizing effect of the cation plays an important part in this. Kinetic parameters have been derived by means of the nomogram method.

---

Zusammenfassung Ammonium- und Metallsalze der Säure H₃[Cr(NCS)₆] wurden hergestellt und charakterisiert. Ihre thermische Zersetzung wurde mit einem Derivatographen verfolgt. Sie beginnt beiden Ammoniumsalzen mit einer endothermen Phase, welche zur Bildung des Zwischenprodukts Cr(NCS)₃ führt, das in exothermen Vorgängen als Endprodukt Cr₂O₃ ergibt. Die Zersetzung der Metallsalze ist exotherm und der Polarisationseffekt des Kations spielt hierbei eine wichtige Rolle. Kinetische Parameter wurden nach der Nomogramm-Methode abgeleitet.

---

H₃[Cr(NCS)₆]. . , Cr(NCS)₆, ₂₃. .

     

由热重数据计算动力学参数

热重法(TG)是一种动态测量技术,可在程序升温或降温情况下对给定物质或体系提供一个连续的,以温度或时间为函数的重量变化曲线,所以由它跟踪反应能给出反应动力学的有关信息。这种非等温法与早期使用的等温法相比,有快速、连续和需要较少实验数据等优点,近年来在动力学研究方面得到广泛应用,但还只限于研究下列几种类型的简单     

Thermochemical data of barium peroxide from thermogravimetric measurements

Decomposition temperatures of barium peroxide in equilibrium with the oxygen pressure in the gas phase have been determined by thermogravimetric measurements at temperatures from 670 to 843. Enthalpies and entropies of the reaction BaO₂= =BaO+0.5O₂ and of the formation of BaO₂ have been calculated.

---

Zusammenfassung Zersetzungstemperaturen von mit dem Sauerstoffdruck in der Gasphase in Gleichgewicht stehendem Bariumperoxyd wurden thermogravimetrisch im Temperaturbereich von 670 bis zu 843 ermittelt. Enthalpie- und Entropiewerte der Reaktion BaO₂= =BaO+0.5 O₂ und der Bildung von BaO₂ wurden errechnet.

---

Résumé On a déterminé les températures de décomposition du peroxyde de baryum en équilibre avec la pression d'oxygène de la phase gazeuse, par mesures thermogravimétriques entre 670 et 843. On a calculé les enthalpies et les entropies correspondant à la réaction BaO₂=BaO+0.5 O₂ et à la formation de BaO₂.

---

, , , 670 843. BaO₂= + +0.5 O₂ BaO₂.

     

Kinetic constants of polymeric materials from thermogravimetric data

The thermal decomposition of polytetrafluoroethylene (TFE, Teflon), high and low density polyethylene (HDP and LDP), Delrin Acetal (DA), AVCO Phenolic Fiberglass (APFG), and carbon phenolic (CP), were studied by a thermogravimetric technique which utilized a constant heating rate. Loss in sample weight was recorded as a function of time or temperature from room temperature to approximately 700°. Reaction orders were established from logarithmic rate versus temperature plots. Arrhenius frequency factors and overall activation energies were determined from computerized integrations of the appropriate rate equations in which the results were treated on the basis of first-order reaction mechanisms for specific temperature regions. Zero-order mechanisms were estimated by the usual graphical methods.

---

Zusammenfassung Die thermische Zersetzung von Polytetrafluoräthylen (TFE, Teflon), von Polyäthylen niedriger und hoher Dichte (HDP und LDP), von Delrin Acetal (DA), von AVCO Phenolglaswolle (APFG) und von Phenolkohle (CP) wurde thermogravimetrisch mit konstanter Aufheizgeschwindigkeit untersucht. Der Gewichtsverlust wurde als Funktion der Zeit und der Temperatur von Zimmertemperatur bis zu 700° registriert. Aus der Darstellung der Logarithmen der Reaktionsgeschwindigkeit gegen die Temperatur wurde die Reaktionsordnung ermittelt. Die Arrheniusschen Frequenzfaktoren und die Werte der durchschnittlichen Aktivierungsenergien wurden durch komputerierte Integrierung der geeigneten Geschwindigkeitsgleichungen bestimmt. In den entsprechenden Geschwindigkeitsgleichungen wurden für spezielle Temperaturgebiete die Ergebnisse aufgrund des Reaktionsmechanismus von erster Ordnung behandelt. Reaktionen nullter Ordnung wurden nach den üblichen graphischen Methoden ausgewertet.

---

Résumé Etude de la décomposition thermique du polytétrafluoroéthylène (Teflon), du polyethylene haute et basse densité, de l'acétal Delrin, de la fibre de verre phénolique AVCO et du carbone phénolique par TG à vitesse d'échauffement constante. Enregistrement de la perte de poids en fonction du temps ou de la température, depuis la température ambiante jusqu'à 700°C environ. Détermination de l'ordre des réactions en portant le logarithme de la vitesse en fonction de la température. Détermination des facteurs de fréquence et des énergies d'activation moyennes par intégration numérique des équations de vitesse appropriées en traitant les résultats sur la base de mécanismes réactionnels du 1er ordre dans les domaines de température correspondants. Emploi des méthodes graphiques habituelles dans le cas des réactions d'ordre zéro.

---

(, ), c ( , ), (), () () c . ( , , 700°). . . . .

---

---

The authors wish to acknowledge the many hours of valued assistance accomplished by Leonie Boehmer who performed all computational calculations reported herein and for the programming and compilation of data for the CDC 6061 computer. Acknowledgment is also extended to Mark Middleton who assisted with the technical measurements and calculations presented in this report.     

Remarks on the determination of kinetic constants from thermogravimetric data

The methods for determining kinetic constants may have significant effects on the estimation results. The two-variable linear correlation method leads to values of the kinetic constants for which the difference between the calculated and measured values is comparable to or greater than the measurement precision. The non-linear method for calculating kinetic constants by searching for the minimum of the error function \(S1 = \sum\limits_{i = 1}^N {(m_{it} - m_i )^2 /N}\) , wherem _i andm _i are the measured and calculated values, respectively, andN is the number of experimental data, gives very precise results. A simple calculating technique is necessary for the fitting of the minimum point and the confidence region limit at the significance level. An appropriate calculation was made for metal oxidation according to the parabolic law.     

Thermal decomposition reactions of solids controlled by diffusion and phase-boundary processes: possible misinterpretation of the mechanism from thermogravimetric data

A comparative study of phase -boundary and diffusion-controlled reactions has been carried out using thermogravimetric data. The results reported support the hypothesis that a single TG diagram does not allow the determination of whether a solid decomposition reaction is controlled by a diffusion mechanism or governed by the movement of an interface coming from a nucleation process. However, the analysis of both a single TG diagram and an isothermal curve might be a quick and valid way for discerning between these mechanisms. These statements are confirmed by studying the thermal decomposition kinetics of Ba(OH)₂ and CaCO₃.     

Computer-aided treatment of thermogravimetric data and calculation of effective kinetic parameters of thermal decomposition processes

Separate stages of mathematical processing of thermogravimetric data, the difficulties most often encountered, and typical error sources are considered. A complex procedure of automatic acquisition and editing of experimental data, including calculation of effective kinetic parameters, is described and an appropriate algorithm for the 15 BCM-5 microcomputer is presented. The computer calculation of the kinetic parameters of the multistage thermal decomposition of a polyamide fibre is given as an example.

---

Zusammenfassung Verschiedene Phasen der mathematischen Behandlung von thermogravimetrischen Daten, am häufigsten auftretende Schwierigkeiten und typische Fehlerquellen werden erörtert. Das komplexe Verfahren der automatischen Eingabe und Ausgabe experimenteller Daten wird, einschliessliche der Berechnung von effektiven kinetischen Parametern, beschrieben. Ein entsprechender Algorithmus wird für den Mikrokomputer 15 BCM-5 angegeben. Als Beispiel wird die Berechnung der kinetischen Parameter der mehrstufigen thermischen Zersetzung von Polyamidfasern ausgeführt.

---

, . , , - 15 BCM-5. .

     

The use of the IKP method for evaluating the kinetic parameters and the conversion function of the thermal decomposition of NaHCO3 from nonisothermal thermogravimetric data

Three linear isoconversional methods (Friedman, Flynn–Wall–Ozawa, and Kissinger–Akahira–Sunose) and the invariant kinetic parameters (IKP) method were used in order to examine the kinetics of the nonisothermal decomposition of a sodium bicarbonate (NaHCO₃). The objective of the paper is to show the usefulness of the IKP method to determine both the kinetic parameters and the kinetic model of the investigated process. The activation energy (E_a) value obtained by the IKP method is in good agreement with the values obtained by isoconversional methods. The IKP method associated with the criterion of coincidence of kinetic parameters for all heating rates led us to the following kinetic triplet: E_a = 95.5 kJ mol^?1, A = 2.65 × 10¹⁰ min^?1, and conversion function f(α) = (1 ? α) (first‐order reaction model, F1). © 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39: 462–471, 2007     

Kinetic analysis of thermogravimetric data

Four many curves methods, viz. calculation techniques based on Eqs (30), (31), (34) and (36), respectively, for deriving kinetic parameters from several TG curves recorded with different heating rates are tested on two sets of theoretical TG curves. The maximum reaction rate temperature and conversion, as well as the approximate formulae used for their calculation are discussed. Some aspects of the kinetic compensation effect are analysed. The final conclusion is that the use of the many curves methods is not reasonable.     

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

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

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...