Kinetic analysis of liquid-phase depolymerization of trioxane from programmed temperature data

A sequential kinetic discrimination of potential kinetic models for non-isothermal linear programmed temperature data on the depolymerization of trioxane in a homogeneous liquid phase has been discussed.The influence of the initial concentration on the kinetic curves has been used as an experimental confirmation of the first-order influence of the concentration on the model.Kinetic analysis at constant temperature and conversion permits separation of the effects of concentration and temperature on the kinetic analysis at different levels of the variables.It is provided via non-isothermal kinetic data on the depolymerization of trioxane that nonisothermal experiment's allow a systematic approach to the kinetic behaviour in a wide range of the variables temperature and concentration, leading to maximum knowledge of the reaction model through minimum experimental effort.

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Zusammenfassung Eine sequentielle kinetische Unterscheidung potentieller kinetischer Modelle für die nicht-isotherme, linear temperaturprogrammierte Depolymerisation von Trioxan in homogener flüssiger Phase wird diskutiert. Der Einfluß der Ausgangskonzentration auf die kinetischen Kurven wurde als experimentelle Bestätigung dafür angesehen, daß die Konzentration auf das Modell nach erster Ordnung einwirkt. Die kinetische Analyse bei konstanter Temperatur und Konversion ermöglicht eine Trennung des Einflusses der Konzentration und Temperatur auf die kinetische Analyse bei unterschiedlichen Werten dieser Variablen. In der vorliegenden Arbeit wurde anhand von nichtisothermen kinetischen Daten für die Depolymerisation von Trioxan gezeigt, daß nicht-isotherme Experimente eine systematische Näherung an das kinetische Verhalten in einem weiten Bereich der Variablen Temperatur und Konzentration erlauben und zu einen Maximum an Erkenntnissen über das Reaktionsmodell bei einem Minimum an experimentellen Aufwand führen.

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Kinetic analysis of the liquid-phase depolymerization of trioxane from programmed-temperature data

An experimental method for the determination of kinetic data for liquid-phase reactions under linear rise of temperature is explained for the depolymerization of trioxane. Integral kinetic analysis of the data is performed in order to determine the kinetic model and the kinetic parameters. Experiments have been carried out at different heating rates between 0.5 and 2 deg/min, leading to similar kinetic parameters. The obtained results are in agreement with the kinetic model and parameters obtained from isothermal kinetic analysis. The programmedtemperature method seems to be a useful tool for a quick determination of kinetic models, avoiding experimental work.

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Zusammenfassung Eine experimentelle Methode zur Bestimmung der kinetischen Daten von Reaktionen in flüssiger Phase bei linearer Temperaturerhöhung wird am Beispiel der Depolymerisation von Trioxan erklärt. Eine integrale kinetische Analyse der Daten wird ausgeführt, um das kinetische Modell und die kinetischen Parameter zu ermitteln. Bei unterschiedlicher Aufheizgeschwindigkeit zwischen 0,5 und 2 K/min ausgeführte Experimente ergaben ähnliche kinetische Parameter. Die erhaltenen Ergebnisse stimmen mit dem kinetischen Modell und den kinetischen Parametern, die durch isotherme kinetische Analyse erhalten wurden, überein. Die Temperaturprogrammierung scheint eine brauchbare, experimentelle Arbeit einsparende Methode zur schnellen Bestimmung des kinetischen Modells zu sein.

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. . , (0,5–2° .), . , . , .

     

Analysis of dynamic kinetic data from solid-state reactions

The kinetics of heterogeneous reactions, involving one reactant in the solid phase, usually follow the lawα=K _∞ exp(?E/kT)f(1?α), where α is the degree of conversion of the solid, andK _∞ andE are the kinetic constants. A critical examination is given of the various methods which are currently used to analyse dynamic experimental data. The limitations of these methods and their insensitivity to the form off(1-α) are pointed out. An alternative approach free from these limitations is suggested. In this,f(1?α) is determined from isothermal experiments, and then the dynamic data are accurately analyzed to obtain the values of the kinetic constants. A case study is given to elucidate the applicability of the approach.     

Analysis of isothermal kinetic data from solid-state reactions

In most solid state reactions the reaction velocity can be described as a product of two functionsK(T) andf(1?α) whereT is the temperature and α the degree of conversion of the solid reactant. The physical interpretation of these functions is discussed, and a systematic method is described by whichf(1?α) of a reaction is identified from its kinetic data.K(T) and the reaction mechanism are then determined. This method has been successfully applied to analyse the kinetics of the thermal decomposition of silver azide.     

Evaluation of kinetic parameters and mechanisms of complex reactions from thermal analysis data

A method is for TA data-processing: the method of exponential multipliers (MEM). The application of this method permits determination of the steps of the process, the type of the kinetic function, the type of the reaction and the kinetic parameters of the reaction steps. The method is simple and is easily carried out with the use of a mini-computer. The efficiency of the method is illustrated on the example of the thermal decomposition of ammonia copper chromate. The mechanism of the process and the kinetic constants were determined. They agree with available literature data.

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Zusammenfassung Ein Verfahren zur Verarbeitung von TA-Daten wurde entwickelt: das Verfahren exponentieller Multiplizierglieder (MEM). Die Anwendung dieses Verfahrens erlaubt die Bestimmung der Schritte eines Vorganges, des Typs der kinetischen Function, des Reaktionstypes und der kinetischen Parameter der Reaktionsschritte. Es handelt sich um eine einfache Methode, die auf einem Mini-Computer leicht verwirklicht werden kann. Die Wirksamkeit dieses Verfahrens wird am Beispiel der thermischen Zersetzung von Ammoniumkupferchromat gezeigt. Der Mechanismus und die kinetischen Konstanten des Prozesses wurden bestimmt, sie stimmen mit erreichbaren Literaturdaten überinen.

     

Temperature programmed retention indices: Calculation from isothermal data. Part 1: Theory

Direct conversion of isothermal to temperature programmed indices is not possible. In this work it is shown that linear temperature programmed retention indices can only be calculated from isothermal retention data if the temperature dependence of both the distribution coefficients and the column dead time are taken into account. Procedures are described which allow calculation of retention temperatures and from these, accurate programmed retention indices. Within certain limits the initial oven temperature and programming rate can be chosen freely. The prerequisite for this calculation is the availability of reliable isothermal retention data (retention times, retention factors, relative retention times, or retention indices) at two different temperatures for one column. The use of compiled isothermal retention indices at two different temperatures for the calculation of retention temperatures and thus temperature programmed indices is demonstrated. For the column for which programmed retention indices have to be determined, the isothermal retention times of the n-alkanes and the column dead time as a function of temperature have to be known in addition to the compiled data for a given stationary phase. Once the programmed retention indices have been calculated for a given column the concept allows the calculation of temperature programmed indices for columns with different specifications. The characteristics which can be varied are: column length, column inner diameter, phase-ratio, initial oven temperature, and programming rate.     

Kinetic analysis of sequence of two consecutive reactions from thermogravimetric data under non-isothermal conditions. I. Calculated thermograms

This paper suggests a method of drawing the thermogram of a sequence of two consecutive, partially overlapping processes of a given order, run under non-isothermal conditions.     

Kinetic analysis of solid-state reactions: Evaluation of approximations to temperature integral and their applications

The temperature integral, which has no exact analytical solution, is involved in the analysis of the experiment data obtained under nonisothermal conditions. Some approximations for the temperature integral have been proposed in the literature for the determination of the kinetic parameters, in particular the activation energy. Those approximations are classified into two categories, that is, exponential and rational approximations. The precision of them for estimating the temperature integral was evaluated within a certain continuous range rather than at several discrete points. Some applications of the approximations in the kinetic methods were presented. The relative errors of the activation energy and pre-exponential factor with four rational approximations by employing model-fitting method were calculated. The relative errors of the activation energy for a series of conversion rate with four rational and four exponential approximations by employing linear integral isoconversional methods were evaluated.     

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. 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]. . .

     

Kinetics of reactions in solution: Method for the treatment of data from non-isothermal chemical kinetic experiments

A new method is proposed for the treatment of kinetic data derived from non-isothermal kinetic experiments for the determination of the parameters of the Arrhenius equation. The results obtained from its application show the excellent precision of this method.

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A computer program system for kinetic analysis of non-isothermal thermogravimetric data: I. Data acquisition and preparation for kinetic analysis

FORTRAN software is described which enables the generation of rate of weight change data (DTG) from percentage weight change measurements (TG), obtained under non-isothermal conditions. The program also transposes this information into the dimensionless extent and rate of reaction at unit temperature intervals by means of a cubic spline interpolation. A simple search routine identifies all DTG spikes in the thermogravimetric record, and the temperature and extent of reaction at which the rate attains its maximum value. This total information serves as input data for the kinetic analysis software to be discussed in part II of this communication. An example of the application of this program to the pyrolysis of bituminous coal is presented.     

Discrimination of the kinetic model of overlapping solid-state reactions from non-isothermal data

A method has been developed that allows the deconvolution of up to 15 overlapping solidstate reactions without previous assumptions. Both the kinetic parameters and the reaction mechanisms fitted by the unit reactions can be determined from a series of non-isothermal experiments carried out at different heating rates.

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Zusammenfassung Es wurde eine methode zur Dekonvolution von bis zu 15 einander überlappenden Festphasenreaktionen entwickelt, die keinerlei vorherige Annahmen notwendig macht. Mittels einer Reihe nichtisothermer Experimente mit unterschiedlichen Aufheizgeschwindigkeiten können sowohl die kinetischen Parameter als auch der Reaktionsmechanismus der Teilreaktionen bestimmt werden.

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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.     

Errors of kinetic data obtained from thermogravimetric curves at increasing temperature

Errors of kinetic data obtained from thermogravimetric curves at increasing temperature are discussed.     

Extracting the mechanisms and kinetic models of complex reactions from atomistic simulation data

Determining reaction mechanisms and kinetic models, which can be used for chemical reaction engineering and design, from atomistic simulation is highly challenging. In this study, we develop a novel methodology to solve this problem. Our approach has three components: (1) a procedure for precisely identifying chemical species and elementary reactions and statistically calculating the reaction rate constants; (2) a reduction method to simplify the complex reaction network into a skeletal network which can be used directly for kinetic modeling; and (3) a deterministic method for validating the derived full and skeletal kinetic models. The methodology is demonstrated by analyzing simulation data of hydrogen combustion. The full reaction network comprises 69 species and 256 reactions, which is reduced into a skeletal network of 9 species and 30 reactions. The kinetic models of both the full and skeletal networks represent the simulation data well. In addition, the essential elementary reactions and their rate constants agree favorably with those obtained experimentally. © 2019 Wiley Periodicals, Inc.     

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