Comprehensive method based on model free method and IKP method for evaluating kinetic parameters of solid state reactions

This article presents, firstly, a short review of methods for evaluating kinetic parameters of solid state reactions and a critical analysis of the isoconversional principle of model free methods. It shows theoretically that the activation energy for complex reactions is not only a function of the reaction degree but also of heating programs, and points out that any method that attempts to extract the dependences of activation energy on conversion degree without considering the dependences of heating programs is problematic. Then an analysis is given of the invariant kinetic parameters (IKP) method and recommends an incremental version of it. Based on the incremental IKP method and model free method, a comprehensive method is proposed that predicts the degree of the dependences of activation energy on heating programs, selects reliable values of activation energy and extracts the values of variable pre‐exponential factor. This comprehensive method is tested using both simulation data and experimental data, the results of which show it can not only give reliable values of kinetic parameters but also be helpful in explaining inconsistencies of kinetic results in solid state reactions. © 2012 Wiley Periodicals, Inc.     

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     

Computational thermal and kinetic analysis

A software package to determine the non-isothermal kinetic parameters of heterogeneous reactions has been developed. The dynamic handle of conversion degree step and ranges, heating rates and kinetic models makes the evaluation of the activation parameters much faster. The standard procedure: ‘model-free’ kineitc, IKP and Perez-Maqueda et al. methods, is applied for the determination of the kinetic triplet corresponding to thermal induced transformations. The software is designed mainly for thermogravimetric, temperature programmed reduction and dilatometry data processing, but may also import already transformed numeric data.     

Kinetic parameters determination in non-isothermal conditions for the crystallisation of a silica-soda-lead glass

Two integral isoconversional methods (Flynn–Wall–Ozawa and Kissinger–Akahira–Sunose) and the invariant kinetic parameters method (IKP) were used in order to examine the kinetics of the non-isothermal crystallisation of a silica-soda-lead glass. The objective of the paper is to show the usefulness of the IKP method to determine both the activation parameters and the kinetic model of the investigated process. Thismethod associated with the criterion of coincidence of kinetic parameters for all heating rates and some procedures of the evaluation of the parameter from Johnson–Mehl–Avrami–Erofeev–Kolmogorov (JMAEK) equation led us to the following kinetic triplet: activation energy, E=170.5±2.5 kJ mol^–1 , pre-exponential factor, A=1.178±0.350·10 10 min^–1 and JMAEK model (A _m) m=1.5.     

Non-isothermal kinetic study on the decomposition of Zn acetate-based sol-gel precursor

The paper presents a non-isothermal kinetic study of the decomposition of Zn acetate-based gel precursors for ZnO thin films, based on the thermogravimetric (TG) data. The evaluation of the dependence of the activation energy (E) on the mass loss (Δm) using the isoconversional methods (Friedman (FR), Flynn-Wall-Ozawa (FWO) and Kissinger-Akahira-Sunose (KAS)) has been presented in a previous paper. It was obtained that the sample dried at 125°C for 8 h exhibits the activation energy independent on the heating rate for the second decomposition step. In this paper the invariant kinetic parameter (IKP) method is used for evaluating the invariant activation parameters, which were used for numerically evaluation of the function of conversion. The value of the invariant activation energy is in a good agreement with those determined by isoconversional methods. In order to determine the kinetic model, IKP method was associated with the criterion of coincidence of the kinetic parameters for all heating rates. Finally, the following kinetic triplet was obtained: E=91.7 (±0.1) kJ mol⁻¹, lnA(s⁻¹)=16.174 (±0.020) and F1 kinetic model.     

Thermal degradation kinetics of g-HA/PLA composite

Thermal degradation behaviors of a composite constituted by poly(l-lactide) (PLA) and hydroxyapatite nanoparticle that was surface-grafted with l-lactic acid oligomer (g-HA) in a nitrogen atmosphere were studied using thermogravimetric analysis (TGA) and compared with PLA. The kinetic models and parameters of the thermal degradation of PLA and the g-HA/PLA composite were evaluated by the invariant kinetic parameters (IKP) method and Flynn–Wall–Ozawa (FWO) method based on a set of TGA data obtained at different heating rates. It was shown that the conversion functions calculated by means of the IKP method depend on a set of kinetic models. The g-HA particle slowed down the thermal degradation of PLA polymer matrix.     

The Kissinger law and the IKP method for evaluating the non-isothermal kinetic parameters

The following problems concerning the apparent compensation effect (CE) (lnA=a+bE, where A is the pre-exponential factor, E is the activation energy, a and b are CE parameters) due to the change of the conversion function and on which the invariant kinetic parameters method (IKP method) is based, are discussed: (1) the explanation of this kind of CE; (2) the choice of the set of conversion functions that checks CE relationship; (3) the dependencies of CE parameters on the heating rate and the temperature corresponding to the maximum reaction rate. Using the condition of maximum of the reaction rate suggested by Kissinger (Kissinger law), it is pointed out that, for a certain heating rate, the CE relationship is checked only for reaction order (Fn) and Avrami-Erofeev (An) kinetic models, and not for diffusion kinetic models (Dn). Consequently, IKP method, which is based on the supercorrelation relationship between CE parameters, can be applied only for the set Fn+ An of kinetic models. The dependencies of a and b parameters on the heating rate and T _m (temperature corresponding to maximum reaction rate) are derived. The theoretical results are discussed and checked for (a) TG simulated data for a single first order reaction; (b) TG data for PVC degradation; (b) the dehydration of CaC₂O₄·H₂O.     

Evaluation of the kinetics and mechanisms of hybriding reactions

A scheme for a kinetic study of the hydriding reactions of metals is presented. This scheme is based on a combined kinetic and metallographic study of hydride formation in metallic samples with well defined geometrical shapes.Since the directly measured kinetic quantity (which is the overall reaction rate) depends also on parameters which are not related to the intrinsic nature of the reaction (i.e., on the geometrical shape of the sample and on the topochemistry of the product development) an intrinsic kinetic parameter IKP, should be evaluated in order to characterize uniquely a given reacting system. The choices for these intrinsic parameters and the methods for their evaluation are presented.Different theoretical models for the hydriding reactions are summarized and the predicted pressure-temperature dependence of the IKP's are discussed in light of these models. In some cases the comparison between the experimental and theoretical pressure-temperature behavior may elucidate the mechanisms controlling the respective reactions.     

Thermal decomposition kinetics of some aromatic azomonoethers

The non-isothermal kinetic parameters corresponding to the decomposition of 4-[(4-chlorobenzyl)oxy]-4’-nitro-azobenzene were evaluated. The kinetic analysis was performed by means of different multi-heating rates methods: isoconversional (‘model-free’) methods (Flynn–Wall–Ozawa) and invariant kinetic parameters method (IKP) associated with the criterion of the independence of activation parameters on the heating rate. The values of the obtained non-isothermal kinetic parameters are in satisfactory agreement.     

On the evaluation of the nonisothermal kinetic parameters of (GeS2)0.3(Sb2S3)0.7 crystallization using the IKP method

The isoconversional method suggested by Friedman and the invariant kinetic parameters method (IKP) were used in order to examine the kinetics of the nonisothermal crystallization of (GeS₂)_0.3(Sb₂S₃)_0.7. The objective of the paper is to show the usefulness of the IKP method both for determining the activation parameters as well as the model of the investigated process. It was shown that the kinetic triplet [(E, A, f(α), where E is the activation energy, A is the preexponential factor, and f(α) is the differential function of conversion], which results through the application of the IKP method, depends on the set of kinetic models considered. For different sets of kinetic models, proportional values of f(α) are obtained. A criterion for the selection of this set, the use of which lead to the true kinetic triplet corresponding to the analyzed process (E = 163.2 kJ mol^?1; A = 2.47 × 10¹² min^?1 and the Avrami‐Erofeev model, A_m, for m = 2.5–2.6 was suggested. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 309–315, 2004     

Determining the temperature to initiate the explosion of a propellant

Summary Gun propellants are per definition instable substances. During their lifetime a slow decomposition process is going-on. During this decomposition process the heat that is generated accelerates the process, which could result to an unsafe situation, or an unexpected explosion of the material. The temperature to initiate the explosion of a propellant is of importance for the storage conditions of such a substance. The method used so far to evaluate this temperature is based on an extrapolation of the Kissinger equation at zero heating rate. A new proposal is the use of the invariant kinetic parameters (IKP) method to determine the iso-kinetic temperature and extrapolating it to zero heating rate as an alternative method. The results are discussed for some examples.     

较快反应的热动力学天空

根据热导式热量计的工作原理,提出了热导式热量计的界面模型,建立了感温滞后条件下热量计的理论方程,从而提出了一种较快反应的热动力学研究法---失真热谱曲线修正法,并利用该法成功地研究了几个较快的准一级和等浓度二级反应的热动力学。     

Utilization of criterial equations for quantitative processing of thermogravimetric results

A system of criterial equations is proposed for determining the parameters of kinetic equations by thermogravimetric results. The criterial equations take into account the particularities of the effect of each parameter on the shape and position of the TG curve. It is shown that the method ensures uniqueness of the solution obtained, which best fits to the experimental data.     

A simple kinetic method for the determination of the reaction model from non-isothermal experiments

In a recent article, we obtained an approximate solution for the evolution of a transformed fraction under isochronal conditions for a large variety of single-step transformations. We verified that this solution is accurate and can, in many instances, be used instead of the exact numerical solutions of the corresponding differential equations. In this article we want to examine the possibilities offered by an analytical solution in the analysis of thermoanalytical curves. We will show that for single-step transformations, our model predicts that under the proper time scaling the thermograms obtained at different heating rates merge into a single curve. This ‘universal curve’ is exclusively related to the kinetic model. In addition, the universal curve can be obtained from experimental thermograms by means of a simple transformation. In this way, the dependence of the experimental curves on the rate constant and the kinetic model can easily be separated, making it possible to independently determine the kinetic parameters and the kinetic model. In addition, one can easily check the validity of the kinetic analysis as well as calculate a reliable statistical measure of the goodness of the single-step assumption.     

Determination of kinetic parameters from TG curves by non-linear optimization

The results obtained so far by kinetic analysis of non-isothermal experiments indicate that the kinetic parameters found by the conventional methods, in general, do not describe the experimental curve in an optimum manner. This is due to the fact that the initial differential equation is transformed into the logarithmic and, consequently, linear form and that the initial and final weights of the conversion curve cannot be determined exactly, which may falsify the slope of the curve.Investigations have shown that the determination of the kinetic parameters by non-linear optimization (simplex method) results in a better fit of the theoretical conversion curve to the experimental one. But this procedure gives optimum results only when the initial and final weights of the reaction can be determined exactly. If this is impossible, exact parameters can be obtained only by the use of the non-standardized TG curve.Examples are cited to prove that it is possible to evaluate overlapping reactions by the formation of intervals. However, the evaluation of conversion curves merely by the use of mathematical methods can easily result in an erroneous interpretation of the reaction course investigated. Therefore, it is necessary to check the mathematical results as to their physical and chemical meaning.     

Comparative kinetic study of the non-isothermal thermal curing of <Emphasis Type="Italic">bis</Emphasis>-GMA/TEGDMA systems

The thermal polymerization kinetics of dimethacrylate monomers was studied by differential calorimetry using non-isothermal experiments. The kinetic analysis compared the following procedures: isoconversional method (model-free method), reduced master curves, the isokinetic relationship (IKR), the invariant kinetic parameters (IKP) method, the Coats-Redfern method and composite integral method I. Although the study focused on the integral methods, we compared them to differential methods. We saw that even relatively complex processes (in which the variations in the kinetic parameters were only slight) can be described reasonably well using a single kinetic model, so long as the mean value of the activation energy is known (E). It is also shown the usefulness of isoconversional kinetic methods, which provide with reliable kinetic information suitable for adequately choosing the kinetic model which best describes the curing process. For the system studied, we obtained the following kinetic triplet: f(α)=α^0.6(1−α)^2.4, E=120.9 kJ mol⁻¹ and lnA=38.28 min⁻¹.     

Reaction kinetics at linearly increased temperature. IV. Relationships between dta curves,rate curves and adiabatic calorimetry

A general concept is presented for the kinetic interpretation of DTA curves. This is based on the limiting conditions of a DTA measurement: either the kinetic cell constant is zero (adiabatic conditions), or infinite (rate curve). On the other hand, the self-heating effect (thermal feedback), based on the product of the reaction enthalpy with the reactant feed, may be absent (“ideal” kinetic DTA curve) or infinite (impulse reaction). Our recent formulae for the correction of the kinetic classification parameters, shape index and reaction type index, as well as other relationships and their utility, are successfully tested by application to ca. 2000 experimental DTA curves obtained in stirred solutions.The expressions reveal the influence of the activation parameters, heating rate, maximum signal height and cell constant and, therefore, allow a general discussion of the kinetics, independent of the experimental conditions.     

非等温液-固相酯化反应动力学研究

根据稀土盐催化剂催化的乙二醇单乙醚醋酸酯的液相合成反应的特点, 导出了非等温变体积条件下的反应速率方程, 并提出了利用一条实验曲线, 计算动力学参数的动态方法, 以此为基础, 对不同实验条件下的多组实验数据进行了动力学处理。大量计算结果表明, 该反应服从二级动力学模型, 表观反应活化能为213.59kJ·mol^-^1, 指前因子为5.903×10^2^5dm^3·mol^-^1·min^-^1。计算结果的合理性及一致性, 进一步证明了动态原理用于液-固相反应体系的动力学研究是简便可行的。