On One Method of Parameter Estimation in Chemical Kinetics Using Spectra with Unknown Spectral Components

The method of successive estimation of regression parameters, which is widely used in nonlinear regression analysis, is applied to obtain kinetic information from spectral data for the case when the spectra of individual components are unknown. Using a model example with a two-step successive reaction, the reliability of the algorithm is demonstrated. To compare the proposed method with other known methods for estimating kinetic parameters literature data are used. All simulations were done using a new software for nonlinear regression analysis: FITTER. The proposed approach is especially useful when the spectra of reaction components are unknown and when formal calibration methods do not provide desirable accuracy.     

New Temperature Integral Approximate Formula for Non-isothermal Kinetic Analysis

A new approximate formula for temperature integral is proposed. The linear dependence of the new fomula on x has been established. Combining this linear dependence and integration-by-parts, new equation for the evaluation of kinetic parameters has been obtained from the above dependence. The validity of this equation has been tested with data from numerical calculating. And its deviation from the values calculated by Simpson's numerical integrating was discussed. Compared with several published approximate formulae, this new one is much superior to all other approximations and is the most suitable solution for the evaluation of kinetic parameters from TG experiments. This revised version was published online in August 2006 with corrections to the Cover Date.     

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     

A new integral method for the kinetic analysis of thermogravimetric data

Methods for the calculation of activation energies, pre-exponential factors and reaction orders from thermogravimetric data are briefly reviewed. A new integral method is proposed for the determination of these kinetic parameters, using data from pairs of TG curves produced at different heating rates. Employing accurate values of the temperature integral of the Arrhenius equation, tabulated over a range ofE andT, and a simple graphical procedure, the method offers advantages of speed and accuracy over those previously reported. It is suggested that at least one of the kinetic parameters should be allowed to move freely in order to achieve the best possible fit between calculated and experimental traces.     

Thermogravimetry. Generalization of Reich's method

A new method is proposed for the determination of kinetic parameters, where Reich's method is a special case. This method involves a knowledge of the values of the weight loss, the temperature, the rate of weight loss and the derivative of the rate of weight loss, corresponding to a certain point in the TG curve. The findings are in good agreement with those of Reich's method.     

TG Study of the Kinetic Parameters of Regeneration of Coked HZSM-5 Zeolite

A thermogravimetric method is proposed for study of the kinetic parameters of coked HZSM-5 zeolite regeneration. The technique, which makes use of integral thermogravimetric curves, was optimized by microprocessed integrated mathematical methods. The kinetic parameters obtained from the TG curves are the activation energy, the rate constants, the half-life times, and in particular the coke removal time as a function of temperature. The activation energy calculated by using the Flynn and Wall kinetic method was 81.4 kJ mol⁻¹. It was observed that, to remove 99% of the coke from the zeolite in a period of 1 h, it would be necessary to carry out thermo-oxidation at 748 K, with a dry air purge flow of 120 cm³ min⁻¹. This revised version was published online in August 2006 with corrections to the Cover Date.     

Calculation of kinetic parameters from TG curve on the base of dehydration process of hydrous titanium dioxide

A direct method of evaluating of kinetic equation parameters based on TG curve is proposed. The method was applied to calculate kinetic parameters of the process of dehydration of hydrous titanium dioxide.

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Zusammenfassung Es wird ein direktes Verfahren zur Bestimmung der Parameter der kinetischen Gleichung auf der Basis von TG-Kurven gegeben. Das Verfahren wurde zur Berechnung der kinetischen Parameter des Dehydratationsprozesses von wasserhaltigem Titandioxid benutzt.

     

Kinetic analysis of thermal decomposition in liquid and solid state of 3-nitro and 4-nitro-benzaldehyde-2,4-dinitrophenylhydrazones

A kinetic study on the thermal decomposition of 3-nitro and 4-nitro-benzaldehyde-2,4-dinitrophenylhydrazones was carried out. The isothermal and dynamic differential scanning calorimetric curves were recorded for solids and melts, respectively. The standard isoconversional analysis of the obtained curves from both isothermal and nonisothermal analysis suggests an autocatalytic decomposition mechanism. This mechanism is also supported by the temperature dependence of the observed induction periods. Based on the results of the model-free method from nonisothermal regime, the kinetic model was derived and the kinetic parameters were obtained by means of a multivariate nonlinear regression.     

Study on thermal decomposition of calix[6]arene and calix[8]arene

Thermal decomposition kinetics of calix[6]arene (C6) and calix[8]arene (C8) were studied by Thermogravimetry analysis (TG) and Differential thermal analysis (DTA). TG was done under static air atmosphere with dynamic heating rates of 1.0, 2.5, 5.0, and 10.0 K min⁻¹. Model-free methods such as Friedman and Ozawa–Flynn–Wall were used to evaluate the kinetic parameters such as activation energy (E _a) and pre-exponential factors (ln A). Model-fitting method such as linear regression was used for the evaluation of optimum kinetic triplets. The kinetic parameters obtained are comparable with both the model-free and model-fitting methods. Within the tested models, the thermal decomposition of C6 and C8 are best described by a three dimensional Jander’s type diffusion. The antioxidant efficiency of C6 and C8 was tested for the decomposition of polypropylene (PP).     

Dissolution properties of ammonium dinitramide in N-methyl pyrrolidone

The decomposition process of gadolinium hydroxide was studied by means of thermogravimetry in a temperature range from 300 to 900 K. The kinetics of low-temperature dehydroxylation (≈430–600 K) was studied under non-isothermal conditions. A model-free method was used to calculate the activation energy; a nonlinear regression method was applied to calculate the kinetic parameters of multi-stage decomposition reactions. The features of the dehydroxylation kinetics of the multi-stage process can be explained by the formation of GdOOH phase.     

Kinetic Aspect of Thermal Decomposition of Natural Phosphate and its Kerogen. Influence of heating rate and mineral matter

The natural phosphate and its demineralization products from Moroccan deposit were pyrolysed in a thermogravimetric analyser (TG) to examine the influence of the heating rate and mineral matter on their thermal decomposition. The heating rates investigated in the TG were 5–100°C min⁻¹ to final temperature of 1200°C. The integral method was used in the analysis of the TG to determine the kinetic parameters. It has been found that for the natural phosphate and corresponding kerogen analysed in the TG, the increase of the heating rate shifts the maximum rate loss to higher temperature. A first order reaction was found to be adequate for pyrolysis in the range 150–600°C which was attributed to kerogen decomposition. In addition, the results indicate that the removal of mineral matter affected the kinetic parameters found for kerogen in the natural phosphate. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermal decomposition of barium(II) tetraphenylborate

Barium(II) tetraphenylborate, Ba(Bph₄))₂·4H₂O was prepared, and its decomposition mechanism was studied by means of TG and DTA. The products of thermal decomposition were examined by means of gas chromatography and chemical methods. A kinetic analysis of the first stage of thermal decomposition was made on the basis of TG and DTG curves and kinetic parameters were obtained from an analysis of the TG and DTG curves using integral and differential methods. The most probable kinetic function was suggested by comparison of kinetic parameters. A mathematical expression was derived for the kinetic compensation effect.     

Nonisothermal decomposition kinetics of [CoC<Subscript>2</Subscript>O<Subscript>4</Subscript>·2.5H<Subscript>2</Subscript>O]<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

The authors present their results concerning the decomposition in air of the homopolynuclear coordination compound [CoC₂O₄·2.5H₂O] _n . In the temperature range 20–300 °C, the heating curves TG, DTG and DTA allowed to evidence three decomposition steps. The kinetic analysis was performed on the second step which proved to be the only workable one. The application of nonlinear regression procedure shows that this is a complex process consisting in three successive steps. The checking of the mechanism and corresponding kinetic parameters for quasi-isothermal data (T = 150 °C) shows that the obtained results could be used for prediction of the thermal behaviour of the investigated compound in both isothermal and non-isothermal conditions.     

A simplified method to estimate kinetic and thermodynamic parameters on the solid-liquid separation of pollutants

The aim of the present study was to propose a simplified experimental-theoretical method for estimating the kinetic and thermodynamic parameters for the solid-liquid separation of pollutants by using kinetic studies with batch reactors, i.e., the removed quantity of dissolved ion as a function of time at different initial concentration. This method was applied to the removal of uranyl ion (UO(2+)(2)) from aqueous solutions onto synthetic manganese oxide (birnessite). The pseudo-second-order kinetics and one-site saturation models were proposed to fit the experimental and calculated data, the fitting parameters being estimated by nonlinear regression, using the least-squares method. For initial concentration range 0.2-11.8 microM, the results showed that the uranyl removal process in dispersed batch reactors can be efficiently modeled by the proposed models. Then, several kinetic and thermodynamic parameters were calculated, such as maximal removed quantity of uranyl, q(r,max), half-removal time, t(1/2), initial rate of uranyl-ion removal, v(0), initial uranyl-removal coefficient, K, maximal rate of uranyl removal, v(0,max), mass transfer coefficient, D(transfer), equilibrium Langmuir constant, K(L), and constant separation factor, K(s). These parameters make it possible to demonstrate that the removal of U onto birnessite is favorable, and that the maximum surface coverage of the uranyl ions represents about 3% of vacant sites in the Mn layer.     

Thermal behaviour and kinetic study of some triazoles as potential anti-inflammatory agents

Thermogravimetric (TG), differential thermogravimetric analysis and differential scanning calorimetry had been used to characterize the thermal stability of four new heterocyclic compounds with triazolic structure. The four analysed compounds have similar thermal behaviours, namely the thermal mal curves of these new compounds show three thermal events. These compounds were thermally stable up to 110 °C. Above this temperature, the evolution of hydrochloric acid took place as observed by EGA. Identification and the monitoring of gaseous species released during thermal decomposition of pure triazoles in air atmosphere have been carried out by coupled TG–FTIR. Between 110 and 220 °C the main gaseous product is HCl which was identified on the basis of these FTIR spectra. Arguments for a rapid thermooxidation of the four molecules were brought by EGA by identifying the substances which arise from both the destruction of side chains and of triazolic ring. The kinetic analysis of the destruction process of triazolic structure was investigated using the TG data in air for the substance’s decomposition in non-isothermal conditions. The isoconversional methods, Kissinger–Akahira–Sunose, Flynn–Wall–Ozawa and Friedman, were applied to determine the activation energy from the analysis of four curves measured at different heating rates. In order to obtain realistic kinetic parameters, even if the decomposition process is a complex one, the non-parametric kinetics method was also used. A good agreement between the data obtained from the four applied methods was found.     

利用模式搜索法求取新的温度积分近似式

利用模式搜索法求取了一个新的温度积分近似式,给出了相应的估算动力学参数的方程。新的温度积分近似式根据数值计算结果得到,可靠性高。讨论了新的近似式计算值与温度积分数值积分结果的偏差。与其它近似式相比,新的温度积分近似式的表达式简单,精确度更高,非常适合非等温过程的动力学参数的计算。     

Kinetics of exothermal decomposition of some ketone-2,4-dinitrophenylhydrazones

In this study, the thermal stability and exothermal decomposition of some ketone-2,4-dinitrophenylhydrazones have investigated using the DSC technique. The synthesized and purified crystalline solids are thermally stable and start to decompose after melting. Non-isothermal DSC curves, recorded at several heating rates, were used to evaluate the melting properties and the kinetics of thermal decomposition. The isoconversional and model-fitting methods were applied to determine the activation parameters from the common analysis of multiple curves measured at different heating rates. Based on the results of the model??free method, a kinetic model was derived, and the kinetic parameters were obtained by means of a multivariate nonlinear regression. The results are discussed in relation to the effect of the ketone structure.     

Decomposition of Cyclohexyl-t-butyl-Dimethylammonium Tetraphenylborate: Synthesis and kinetics

A new compound cyclohexyl-t-butyldimethylammonium tetraphenylborate, [C₆H₁₁N(CH₃)₂(C(CH₃)₃)]BPh₄ has been prepared, and its decomposition mechanism was studied by TG. The IR spectra of the products of thermal decomposition were examined at every stage. Kinetic analysis for the first stage of thermal decomposition process was obtained by TG and DTG curves, and kinetic parameters were obtained from the analysis of the TG-DTG curves with integral and differential equations. The most probable kinetic function was suggested by comparison of kinetic parameters.This revised version was published online in November 2005 with corrections to the Cover Date.     

Thermal characterization and kinetic analysis of nesquehonite,hydromagnesite, and brucite,using TG–DTG and DSC techniques

Nesquehonite, hydromagnesite, and brucite are important precursors for the preparation of high-purity magnesia (MgO) using magnesium resources from salt lake as raw materials. In this paper, TG–DTG and DSC were used to investigate the thermal decomposition behaviors of the three precursors. Decomposition kinetic parameters at each stage were evaluated based on the TG data using the iso-conversional method. Decomposition mechanisms were determined using the master-plots method. The decomposition temperature range, heat absorption, and kinetic parameters of the three phases were then compared. The most probable mechanism of each stage from the perspective of crystal structure was found to be consistent with the calculation results from the master-plots method. Results led to the conclusion that nesquehonite is the most appropriate precursor for the preparation of high-purity MgO. Further studies on precursor selection and calcining condition selection for the preparation of MgO using bischofite will benefit from this research.     

The Non‐Isothermal Decomposition Kinetics of NaNTO·H2O and the Relationship between its Structure and Properties

NaNTO·H₂O was prepared by mixing 3‐nitro‐1,2,4‐triazol‐5‐one (NTO) aqueous solution and sodium hydroxide aqueous solution. Its thermal decomposition and kinetics were studied under non‐isothermal conditions by DSC and TG/DTG methods. The kinetic parameters were obtained from analysis of the DSC and TG/DTG curves by the Kissinger method, the Ozawa method, the differential method and the integral method. The most probable mechanism function for the thermal decomposition of the first stage was suggested by comparing the kinetic parameters. The critical temperature of thermal explosion (T_b) was 240.93 °C. The theoretical investigation on the structure unit of the title compound was carried out by DFT‐B3LYP/CEP‐31G methods; atomic net charges and the population analysis were discussed.