Kinetics of thermal decomposition of the solid state II. Delimiting the homogeneous-reaction model

Present evidence shows that many thermal processes can be described by the generalized rate equation

−dx/dt = Z exp(E*/RT)f(x) but many others cannot. Still others may be adequately describable by a modified equation. A small set of tests will enable the experimenter to determine whether or not the equation applies. These include change of sample size, change of sample geometry, and extended time of reaction.     

Artificial neural network applied to solid state thermal decomposition

A multi-layer neural network is constructed to describe the thermal decomposition of rhodium acetate. Critical analysis of the residual, trained, interpolated and extrapolated errors, with the number of neurons, indicates the efficiency of the present approach. It was possible, within this framework, to improve the A _n model, with a better correlation between the results. A new value of the activation energy, E _a, and frequency factor, Z, are calculated for the decomposition process. Since the neural network is more precise than a particular model, the calculated values for these quantities are believed to be more precise. The computed values are E _a=194.0 kJ mol^-1 and Z=5.23·1016 s^-1. The neural network eliminates the step to decide, among the available models, the one that best fit the data. An agreement up to four significant figures can be achieved even for data not used in the training process, both in the interpolated and extrapolated regions. This method suggests, therefore, an important alternative tool for the experimentalists. The present approach can also be adapted to other systems and to data in two dimensions. This revised version was published online in July 2006 with corrections to the Cover Date.     

The measurement of meaningful kinetic parameters for solid state decomposition reactions

Following previous work on the measurement of meaningful activation energies and the application of Constant Rate Thermal Analysis (CRTA) to the determination of kinetic parameters [1, 2], here we further examine sources of error in determining activation energies and go on to consider the form of the alpha function and the value ofA. Using theoretical arguments based on transition state theory, we conclude that allowing significant pressures of product gas to appear in the reaction environment will lead to very high values for apparent activation energies. We note that, although this is observed in practice for calcium carbonate, it in no way invalidates the application of the Arrhenius equation to solid state decomposition reactions, provided care is taken to avoid this type of distortion of experimental results. We attempt to determine the alpha function for the decomposition of calcium carbonate using data gathered from a variety of different types of temperature programme and reaction conditions. We find that the apparent alpha function depends on the method adopted and the experimental conditions used. We propose an explanation of why this occurs and tentatively introduce a new way of looking at the development of a reaction interface for this type of reaction. We review the literature and conclude that, while significant variations for the activation energy for the decomposition of calcium carbonate exist, a critical appraisal leads to good agreement amongst values that follow good experimental practice and reliable methods of data reduction. The apparent divergence of results can be explained in the light of the theoretical arguments advanced and the easily understood sources of experimental error.

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Zusammenfassung Im Anschlu\ an vorangehende Arbeiten zur Messung sinnvoller Aktivierungsenergien und zur Anwendung von CRTA bei der Bestimmung kinetischer Parameter untersuchen wir hier weitere Fehlerquellen bei der Bestimmung der Aktivierungsenergien und stellen überlegungen zur Form der Alpha-Funktion bzw. zum Wert von A an. Ausgehend von theoretischen Argumenten, die auf der Theorie des übergangszustandes basieren, schlossen wir darauf, da\ es unter Berücksichtigung bedeutender Drücke der in der Reaktionsumgebung auftretenden gasförmigen Produkte zu sehr hohen Werten für die scheinbaren Aktivierungsenergien kommt. Es sei bemerkt, da\, obwohl dies in der Praxis für Calciumkarbonat beobachtet werden kann, es in keiner Weise die Anwendung der Arrheniusschen Gleichung bei Feststoff-Zersetzungsreaktionen in Frage stellt, vorausgesetzt, man vermeidet diese Art von Beeinflussung der Versuchsergebnisse. Für die Zersetzung von Calciumkarbonat versuchten wir, die Alpha-Funktion unter Anwendung von Daten zu bestimmen, die einer Reihe verschiedener Temperaturprogramme und Reaktionsbedingungen entstammen. Man fand, da\ die scheinbare Alpha-Funktion von der angewendeten Methode und den Versuchsbedingungen abhÄngt. Es wird eine ErklÄrung dafür vorgeschlagen und vorlÄufig eine neue Betrachtungsweise für derartige Reaktionen eingeführt. Bei einer Durchsicht der Literatur konnte darauf geschlossen werden, da\ zwar sehr viele Varianten für die Aktivierungsenergie von Calciumkarbonat existieren, da\ aber eine kritische EinschÄtzung zu einer guten übereinstimmung derjenigen Werte führt, denen gute Versuchspraktiken und eine zuverlÄssige Datenverdichtung zugrunde liegen. Die scheinbaren Unterschiede der Ergebnisse können unter Berücksichtigung der vorgebrachten theoretischen Argumente und leicht verstÄndlicher experimenteller Fehlerquellen erklÄrt werden.

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One of the authors (M. Reading) would like to thank the French goverment for a scholarship that enabled him to carry out part of the work in France and J. Rouquerol and F. Rouquerol for allowing him to use their specialised thermobalance.     

Kinetics of thermal decomposition of dinitramide

Kinetic regularities of thermal decomposition of dinitramide in aqueous and sulfuric acid solutions were studied in a wide temperature range. The rate of the thermal decomposition of dinitramide was established to be determined by the rates of decomposition of different forms of dinitramide as the acidity of the medium increases: first, N(NO₂)⁻ anions, then HN(NO₂)₂ molecules, and finally, protonated H₂N(NO₂)₂ ⁺ cations. The temperature dependences of the rate constants of the decomposition of N(NO₂)⁻ (k _an) and HN(NO₂)₂ (k′_ac) and the equilibrium constant of dissociation of HN(NO₂)₂ (K _a) were determined:k _an=1.7·10¹⁷ exp(−20.5·10³/T), s⁻¹,k′_ac=7.9·10¹⁶ exp(−16.1·10³/T), s⁻¹, andK _a=1.4·10 exp(−2.6·10³/T). The temperature dependences of the decomposition rate constant of H₂N(NO₂)₂ ⁺ (k _d) and the equilibrium constant of the dissociation of H₂N(NO₂)₂ ⁺ (K _d) were estimated:k _d=10¹² exp(−7.9·10³/T), s⁻¹ andK _d=1.1 exp(6.4·10³/T). The kinetic and thermodynamic constants obtained make it possible to calculate the decomposition rate of dinitramide solutions in a wide range of temperatures and acidities of the medium. In this series of articles, we report the results of studies of the thermal decomposition of dinitramide performed in 1974–1978 and not published previously. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2129–2133, December, 1997.     

Kinetics of thermal decomposition of hexanitrohexaazaisowurtzitane

Thermal decomposition of hexanitrohexaazaisowurtzitane (HNIW) in the solid state and in solution was studied by thermogravimetry, manometry, optical microscopy, and IR spectroscopy. The kinetics of the reaction in the solid state is described by the first-order equation of autocatalysis. The rate constants and activation parameters of HNIW thermal decomposition in the solid state and solution were determined. The content of N₂ amounts to approximately half of the gaseous products of HNIW thermolysis. The thermolysis of HNIW and its burning are accompanied by the formation of a condensed residue. During these processes, five of six nitro groups of the HNIW molecule are removed, and one NO₂ group remains in the residue, which contains amino groups and no C−H bonds. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 5, pp. 815–821, May, 2000.     

Retarded solid state reactions

Reconstructive phase transitions and formation or decomposition reactions in the solid state exhibit in DTA-measurements a more or less great hysteresis between the temperatures from heating and cooling curves; at worst the reaction can be suppressed completely. By e.m.f.vs. T-measurements in appropriate galvanic cells for solid electrolytes equilibrium temperatures in the case of such kinetic hindrance can be determined and additionally the existence of metastable states can be proved.

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Zusammenfassung Rekonstruktive Phasenumwandlungen sowie Bildungs- und Zersetzungsreaktionen im festen Zustand zeigen bei DTA-Messungen eine mehr oder minder große Hysteresis zwischen den aus Aufheiz- bzw. Abkühlkurven ermittelten Temperaturen; schlimmstenfalls kann die Festkörperreaktion völlig unterdrückt sein. Mißt man in geeigneten galvanischen Zellen für Festelektrolyte EMK-gegen-T-Kurven, so erhält man auch im Falle kinetischer Hemmungen Gleichgewichtstemperaturen und kann darüber hinaus das Vorliegen metastabiler Zustände nachweisen.

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We have to thank the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industry for supporting our work from the outset.     

Theory of solid-state thermal decomposition reactions

A case is presented to recommend strongly that scientists interested in thermal chemistry should make comprehensive, conscientious, clinical and critical analyses of the strengths and weaknesses of The L??vov Thermochemical Theory (L??vov, Thermal decomposition of solids and melts??new thermochemical approach to the mechanism, kinetics and methodology, Springer, Berlin, 2007), used to interpret the kinetics and mechanisms of reactions that occur on heating. The shortcomings underlying the theory (some originally developed for solid decompositions) currently uncritically accepted in this field are reviewed, and these deficiencies are contrasted with the successes of L??vov??s approach. To promote the use of this alternative theory, features that may have discouraged researchers unfamiliar with its assumptions, methodology and applications are discussed here. A new scientific theory cannot be ignored or discounted without adequate consideration and testing, particularly in a stagnant area of chemistry that lacks guiding principles and unifying concepts. Novel ideas in the literature (L??vov 2007) deserve recognition, critical appraisal and, if possible, exploitation to maintain the progress of scientific research.     

Kinetic analysis of thermal decomposition reactions

The effect of⁶⁰C0-gamma radiation on the kinetic parameters of the thermal decomposition of potassium bromate crystals has been investigated. Radiation did not modify the mechanism of thermal decomposition reaction, but resulted in a decrease in activation energy and frequency factor with a rate which is large at small doses and decreases at higher doses. The results showed that the increase in the concentration of decomposition nuclei tends to be more important than the increase in the porous character of the solid.     

Kinetics of thermal decomposition of metal acetates

The acetates of magnesium, nickel, copper, manganese, sodium and barium were subjected to thermal decomposition by means of thermogravimetric techniques (TG) under a constant flow of nitrogen. The decompositions occurred in steps and the kinetics of every set of reactions was determined by the Coats and Redfern method. These results were analysed to establish the decomposition kinetics and hence to calculate activation energies. The activation energies were also determined by applying the Horowitz-Hugh method, which yielded similar results.

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Zusammenfassung Mittels TG in konstantem Stickstoffstrom wurde die thermische Zersetzung von Magnesium-, Nickel-, Kupfer-, Mangan-, Natrium- und Bariumazetat untersucht. Es erfolgte eine schrittweise Zersetzung, die Kinetik für jede der Reaktionen wurde mit Hilfe der Methode von Coats und Redfern bestimmt. Diese Ergebnisse wurden genutzt, um die Kinetik der Zersetzung und anschlie\end die Aktivierungsenergien festzustellen. Ähnliche Werte für die Aktivierungsenergien erhielt man auch mit Hilfe der Methode von Horowitz Hugh.

     

Kinetics of thermal decomposition of ammonium persulfate

Kinetics of thermal decomposition of ammonium persulfate was studied by calorimetry and Raman spectroscopy. The values of activation energies of the overall reaction and its individual stages were estimated.     

Kinetics of the thermal decomposition of dinitramide

The kinetic regularities of the heat release during the thermal decomposition of liquid NH₄N(NO₂)₂ at 102.4–138.9 °C were studied. Kinetic data for decomposition of different forms of dinitramide and the influence of water on the rate of decomposition of NH₄N(NO₂)₂ show that the contributions of the decomposition of N(NO₂)₂ ⁻ and HN(NO₂)₂ to the initial decomposition rate of the reaction at temperatures about 100 °C are approximately equal. The decomposition has an autocatalytic character. The analysis of the effect of additives of HNO₃ solutions and the dependence of the autocatalytic reaction rate constant on the gas volume in the system shows that the self-acceleration is due to an increase in the acidity of the NH₄N(NO₂)₂ melt owing to the accumulation of HNO₃ and the corresponding increase in the contribution of the HN(NO₂)₂ decomposition to the overall rate. The self-acceleration ceases due to the accumulation of NO₃ ⁻ ions decreasing the equilibrium concentration of HN(NO₂)₂ in the melt. For Part 2, see Ref. 1. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 3, pp. 395–401 March 1998.     

Kinetics of the thermal decomposition of dinitramide

The kinetic regularities of the thermal decomposition of dinitramide in aqueous solutions of HNO₃, in anhydrous acetic acid, and in several other organic solvents were studied. The rate of the decomposition of dinitramide in aqueous HNO₃ is determined by the decomposition of mixed anhydride of dinitramide and nitric acid (N₄O₆) formed in the solution in the reversible reaction. The decomposition of the anhydride is a reason for an increase in the decomposition rates of dinitramide in solutions of HNO₃ as compared to those in solutions in H₂SO₄ and the self-acceleration of the process in concentrated aqueous solutions of dinitramide. The increase in the decomposition rate of nondissociated dinitramide compared to the decomposition rate of the N(NO₂)₂ ⁻ anion is explained by a decrease in the order of the N−NO₂ bond. The increase in the rate constant of the decomposition of the protonated form of dinitramide compared to the corresponding value for neutral molecules is due to the dehydration mechanism of the reaction. For Part 1, see Ref. 1. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 41–47, January, 1998.     

Kinetics of thermal decomposition of alkaline phosphates

Summary The thermal behavior of KH₂PO₄, NaH₂PO₄ and Na₂HPO₄ under non-isothermal conditions using TG method with different heating rates was studied. The values of the reaction rate were processed by means of Friedmans differential-isoconversional method. A dependence of the activation energy vs. conversion was observed. Therefore a procedure based on the compensation effect (suggested by Budrugeac and Segal) was applied. A less speculative data processing protocol was offered by the non-parametric kinetics method suggested by Serra, Nomen and Sempere. Three steps were observed by non-isothermal heating: a dehydration, a dimerization and a polycondensation. The differences in the intimate reaction mechanism are determined by the initial number of water molecules.     

硫化氢热分解制氢过程的化学动力学研究

采用化学热平衡分析方法研究了硫化氢热分解制氢过程,研究了硫化氢在不同温度和体积分数下的分解过程,并与试验数据进行了比较。结果表明,基元反应机理能较好地模拟硫化氢热分解制氢过程。硫化氢的热分解率依赖于反应温度,高温下能获得较好的分解制氢效果;温度较低时,时间是硫化氢趋于平衡的主要影响因素,随着温度的提高,温度成为影响硫化氢趋于平衡的主要影响因素。硫化氢初始体积分数对热分解制氢反应具有较大的影响,采用较低体积分数的硫化氢混合气有利于获得高的硫化氢热分解制氢率。     

Kinetics of the thermal decomposition of kyanite

The kinetics of the solid state high-temperature transformation of kyanite (Al₂SiO₅Al₂O₃·SiO₂) powders (≤40 μm) to 3:2-mullite (3Al₂O₃·2SiO₂) and silica (SiO₂ were investigated by means of quantitative X-ray diffraction techniques. The transformation interval was found to lie between about 1150 and 1350°C. The reaction law best fitting the kinetic data is: 1-α = kt^a. The transformation is believed to be reconstructive, with decomposition of the kyanite structure, solid-state atom diffusion, and (epitactic) rearrangement of mullite and cristobalite. Cristobalite represents part of the ⪡free⪢ silica, the rest being present as a glassy phase. Addition of Fe₂O₃ and TiO₂ to the starting material exerts a marked decrease of the transformation temperature, with TiO₂ having a somewhat stronger influence than Fe₂O₃. The reason may be an oxide-catalyzed reaction; the decomposition begins at nuclei formed at the surfaces of the kyanite particles, which are coated with thin layers of hematite and rutile respectively.     

Kinetics of thermal decomposition of aseptic packages

Kinetics of thermal decomposition of aseptic packages (e.g. Tetrapak cartons) and pyrolysis of this waste in a laboratory flow reactor was studied. Three different models for the calculation of the reaction rate and the determination of apparent kinetic parameters of thermal decomposition were used. The first method assumes a two stage thermal decomposition and the kinetic parameters were determined by fitting a derivative thermogravimetric (DTG) curve to experimentally determined thermogravimetric data of whole aseptic cartons. The second method uses kinetic parameters determined by fitting DTG curves to thermogravimetric data of individual components of aseptic packages. The last method was a multi-curve isoconversion method assuming a change of kinetic parameters with the increasing conversion. All types of the determined kinetic parameters were used in a mathematical model for thermal decomposition of mini briquettes made from aseptic packages at the temperature of 650°C. The model calculated also the heat conduction in the particles and it was verified by an independent set of experiments conducted in a laboratory screw type flow reactor.     

A Study of solid state thermal decomposition characteristics of some metallo-organic compounds. IV

Solid state dehydration of the hydrated Ca(II), Co(II), Ni(II) and Cu(II) salts of furan-2-carboxylic acid (furoic acid) and subsequent decarboxylation of the corresponding anhydrous salts have been studied by simultaneous TG, DTA and DTG techniques. The order of thermal stability of the hydrated and the anhydrous compounds have been determined from the analysis of the TG, DTA and DTG traces for the dehydration of the hydrated salts and for the decarboxylation of the anhydrous compounds. Thermal parameters such as activation energy, enthalpy change and order of reaction for the different stages of each process have been computed by standard methods. An attempt has been made to account for the observed trend in the thermal stability of the anhydrous salts towards decarboxylation. A mechanism of thermal decarboxylation of calcium furoate has also been proposed.

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Zusammenfassung Die Dehydratisierung in fester Phase der hydratisierten Salze von Ca(II), Co(II), Ni(II) und Cu(H) mit Furan-2-carboxylsäure und die darauffolgende Decarboxylierung der entsprechenden wasserfreien Salze wurde mittels simultan ausgeführter TG, DTA and DTG untersucht. Die Reihenfolge der thermischen Stabilität der hydratisierten und wasserfreien Verbindungen wurde aus dem Verlauf der TG-, DTA- und DTG-Kurven ermittelt. Die thermischen Parameter (Aktivierungsenergie, Enthalpieveränderung, Reaktionsordnung) wurden für die verschiedenen Schritte eines jeden Prozesses nach Standardmethoden berechnet. Es wurde ein Versuch zur Erklärung des beobachteten Trends in der Thermostabilität der wasserfreien Salze gegenüber Decarboxylierung unternommen und ein Mechanismus für die themische Decarboxylierung von Calciumfuorat in Vorschlag gebracht.

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