Some problems concerning the evaluation of non-isothermal kinetic parameters

The validity of isoconversional methods used to evaluate the activation energy is discussed. The authors have shown that the Flynn-Wall-Ozawa and Friedman methods give results that agree with each other only if the activation energy does not change with the degree of conversion. A criterion for the reaction mechanism as expressed by the differential conversion function is suggested too.     

Influence of octadecylammonium, <Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>-dimethylhexadecylammonium,and 1-hexadecyltrimethylammonium chloride upon the fractionated montmorillonite

The thermal degradation of thermally cured vinyl ester resin systems is studied for different heating rates. The kinetic triplets, the activation energy, pre-exponential factor and the reaction model f(α) for the different reaction extent of conversions (α) are estimated using advanced isoconversional methods. Although the thermal degradation curves show the degradation occurs as a single stage, the kinetic parameters suggest the otherwise. The activation energy remains constant for α?=?0.3–0.575 but varies during the initial and final stages of conversion. Similarly, the pre-exponential factor shows considerable variation between the lower and higher reaction extent (α) values. This shows the complexity in the reaction. The probable reaction mechanism that the degradation follows has been explained. The complexity of the thermal degradation and the changes in reaction model f(α) over different reaction extent has been related. The appropriate working temperature for different thermal lifetime of the cured vinyl ester resin system for the failure of conversion α?=?0.2 has been predicted under the nitrogen atmosphere.     

Pyrolysis of olive residue/low density polyethylene mixture: Part I Thermogravimetric kinetics

This paper demonstrates the thermal pyrolysis of olive residue, low density polyethylene (LDPE) and olive residue/LDPE mixture in an inert atmosphere of N2 using thermogravimetric analysis (TGA). Measurements were carried out in the temperature range 300K~973K at heating rates of 2K/min, 10K/min, 20K/min and 50K/min. Based on the results obtained, three temperature regimes were selected for studying the nonisothermal kinetics of olive residue/LDPE mixture. The first two were dominated by the olive residue pyrolysis, while the third was linked to the LDPE pyrolysis, which occurred at much higher temperatures. Discrepancies between the experimental and calculated TG/DTG profiles were considered as a measurement of the extent of interactions occurring on copyrolysis. The maximum degradation temperatures of each component in the mixture were higher than those the individual components; thus an increase in thermal stability was expected. The kinetic parameters associated with thermal degradation were determined using Friedman isoconversional method.     

Critical Analysis of the Isoconversional Methods for Evaluating the Activation Energy. II. The activation energy obtained from isothermal data corresponding to two successive reactions

An analysis is presented of the consequences of the use of a one term equation containing apparent activation parameters, instead of the true rate equation to describe two successive decomposition reactions undergone by a solid compound. It is demonstrated that the apparent activation energy, obtained by means of isoconversional differential and integral methods, varies with the conversion degree for a relatively narrow temperature range and with temperature at a given value of the conversion degree. The activation energy values obtained with the isoconversional differential method are higher than the corresponding values obtained with the isoconversional integral method. This revised version was published online in August 2006 with corrections to the Cover Date.     

过氧化苯甲酸叔丁酯的热分解动力学研究及SADT推算

研究了过氧化苯甲酸叔丁酯的热分解动力学及不同包装规格下的自加速分解温度(SADT),利用C600微量热仪测试了过氧化苯甲酸叔丁酯的热分解特征,得到升温速率分别为0.1 K/min、0.2 K/min、0.5 K/min、1 K/min下热流随时间的变化曲线,并使用Friedman等转化率法对所得的实验数据进行分析处理,得到了过氧化苯甲酸叔丁酯的分解反应活化能、指前因子等热动力学参数,推算了不同包装规格的过氧化苯甲酸叔丁酯的SADT。结果表明TBPB分解活化能及指前因子随转化率变化而变化,活化能范围为42-135.5 kJ/mol,指前因子范围为0.25-33.5,在25L聚乙烯桶包装下的SADT为59℃,50L下为52℃,200L下为46℃。     

Synthesis and kinetic analysis of isothermal and non-isothermal decomposition of ammonium dinitramide prills

Ammonium dinitramide (ADN) prills were prepared by emulsion crystallization and characterized by optical microscopic, thermogravimetric (TG) and differential scanning calorimetric (DSC) techniques. The isothermal and non-isothermal decomposition kinetics of ADN prills were studied by TG. The differential isoconversional method of Friedman (FR) and integral isoconversional method of Vyazovkin were used to investigate the dependence of activation energy (E _a) with conversion (α) and the results were compared with literature data. The dependence of activation energy was also derived from isothermal data. A strong dependence of E _a with α is observed for the ADN prills. All the methods showed an initial increase in E _a up to α=∼0.2 and later decreases over the rest of conversion. The apparent E _a values of FR method are higher than that of Vyazovkin method up to α=∼0.45. The calculated mean E _a values by FR, Vyazovkin and standard isoconversional method for α between 0.05 and 0.95 were 211.0, 203.9 and 156.9 kJ mol⁻¹, respectively.     

Application of model-free and multivariate non-linear regression methods for evaluation of the thermo-oxidative endurance of a recent manufactured parchment

The thermo-oxidative degradation of a parchment recent manufactured from a goat skin has been investigated by TG/DTG, DSC simultaneous analysis performed in static air atmosphere, at six heating rates in the range 3–15 K min⁻¹. At the progressive heating in air atmosphere, the investigated material exhibits three main successive processes occurring with formation of volatile products, namely the dehydration followed by two thermo-oxidative processes. The processing of the non-isothermal data corresponding to the first process of thermo-oxidation was performed by using Netzsch Thermokinetics—a Software Module for Kinetic Analysis. The dependence of activation energy, evaluated by isoconversional methods suggested by Friedman, and Ozawa, Flynn and Wall, on the conversion degree and the relative high standard deviations of this quantity show that the investigated process is a complex one. The mechanism and the corresponding kinetic parameters were determined by Multivariate Non-linear Regression program. Three mechanisms, one consisting in four successive steps and two others in five successive steps, exhibit the best F-test Fit Quality for TG curves. It was also used the previously suggested criterion, according to which the most probable process mechanism correspond to the best agreement between E _FR  = E _FR (α) (E _FR is the activation energy evaluated by isoconversional method suggested by Friedman; α is the conversion degree) obtained from non-isothermal experimental data and activation energy values, E _iso , obtained by applying the differential method to isothermal data simulated using non-isothermal kinetic parameters. According to this last criterion, the most probable mechanism of parchment oxidation consists in four successive steps. The contribution of the thermo-oxidation process in the parchment damage by natural aging is discussed.     

Thermal degradation of poly(vinyl chloride)/poly(ethylene oxide) blends: Thermogravimetric analysis

Thermal stability of poly(vinyl chloride)/poly(ethylene oxide) (PVC/PEO) blends has been investigated by thermogravimetric analysis (TGA) in dynamic and isothermal heating regime. PVC/PEO blends were prepared by hot-melt extrusion (HME). According to TG analysis, PEO decomposes in one stage, while PVC and PVC/PEO blends in two degradation stages. In order to evaluate the effect of PEO content on the thermal stability of PVC/PEO blends, different criteria were used. It was found that thermal stability of PVC/PEO blends depends on the blend composition. The interactions of blends components with their degradation products were confirmed. By using multiple heating rate kinetics the activation energies of the PVC/PEO blends thermal degradation were calculated by isoconversional integral Flynn–Wall–Ozawa and differential Friedman method. According to dependence of activation energy on degree of conversion the complexity of degradation processes was determined.     

A modified Ortega method to evaluate the activation energies of solid state reactions

The application of the average linear integral isoconversional method developed by Ortega for evaluating the activation energies of solid state reactions may be hindered by experimental noise and the uncertainties associated with selecting appropriate reaction segments. This paper suggests a procedure, called the modified Ortega method, which can avoid or minimize these hindrances. By applying the modified Ortega method to the kinetic analyses of both simulated and experimental data, a more consistent dependence of the activation energy on the extent of reaction conversion was found with those calculated from the modified Vyazovkin method and the Friedman method.     

Cationic crosslinking of solid dgeba resins with ytterbium(III) trifluoromethanesulfonate as initiator

Solid bisphenol-A epoxy resin of medium molecular mass was cured using a Lewis acid initiator (ytterbium(III) trifluoromethanesulfonate) in three different proportions (0.5, 1 and 2 phr). A kinetic study was performed in a differential scanning calorimeter. The complete kinetic triplet was determined (activation energy, pre-exponential factor, and integral function of the degree of conversion) for each system. A kinetic analysis was performed with an integral isoconversional procedure (free model), and the kinetic model was determined both with the Coats-Redfern method (the obtained isoconversional value being accepted as the effective activation energy) and through the compensation effect. All the systems followed the same isothermal curing model simulated from non-isothermal ones. The growth-of-nuclei Avrami kinetic model A_3/2 has been proposed as the polymerization kinetic model. The addition of initiator accelerated the reaction especially when 2 phr was added. 0.5 and 1 phr showed very few kinetic differences between them.     

Critical Analysis of the Isoconversional Methods for Evaluating the Activation Energy. I. Theoretical background

It is demonstrated that, if the activation energy depends on the degree of conversion, its values obtained by isoconversional differential and integral methods are different. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermal behavior of Cd<Superscript>2+</Superscript> and Co<Superscript>2+</Superscript> phenyl-vinyl-phosphonates under non-isothermal condition

The thermal behavior of Cd²⁺ and Co²⁺ phenyl-vinyl-phosphonates was studied using two different experimental strategies: the coupled TG-EGA (FTIR) technique by decomposition in nitrogen respectively air, and the kinetic analysis of TG data obtained in dynamic air atmosphere at four heating rates. In nitrogen two decomposition steps were observed: the loss of crystallization water, respectively the decomposition of the phenyl-vinyl radical. In air, the same dehydration was observed as the first step, but the second one is a thermooxidation of the organic radical with formation of the pyrophosphoric anion. The kinetic analysis of the TG non-isothermal data was performed by the isoconversional methods suggested by Friedman and Flynn, Wall and Ozawa, as well as by the non-parametric (Sempere-Nomen) method. All processes put in evidence in TG curves exhibit strong changes of the activation energy values with the conversion degree, which mean that these processes are complex ones. Assuming that each of these processes consists in two steps, the application of non-parametric method leads to average values of the activation energy close to the average values of this parameter obtained by isoconversional methods.     

A comparison of isoconversional and model-fitting approaches to kinetic parameter estimation and application predictions

A variety of isoconversional and model fitting approaches, all of which use multiple heating schedules, are used to analyze selected data from the ICTAC kinetics and lifetime projects as well as additional simulated data sets created for this work. The objective is to compare the accuracy and suitability of various approaches for various types of chemical reactions. The various simulated data sets show that model fitting and isoconversional methods have comparable reliability for extrapolation outside the range of calibration. First, there is as much variability in prediction for various isoconversional methods as there is between isoconversional methods as a group and different plausible explicit models. Of the three isoconversional models investigated, the Friedman method is usually the most accurate. This is particularly true for energetic materials that have a drop in apparent activation energy in the latter stages of reaction, which leads to a delayed onset of rapid autocatalysis at lower temperatures. It is difficult to determine a priori whether isoconversional or model fitting approaches will give more accurate predictions. The greatest reliability is attained by using both the isoconversional and model fitting approaches on a combination of isothermal and constant heating rate data.     

Non-isothermal kinetic analysis of the thermal denaturation of type I collagen in solution using isoconversional and multivariate non-linear regression methods

To further understand the kinetics of the thermal denaturation of type I collagen, the 16 and 8 mg/mL bovine hide collagen solutions were studied by differential scanning calorimetry at different heating rates. The activation energy of the denaturation process was examined utilizing the differential (Friedman) and the integral (Ozawa-Flynn-Wall) isoconversional methods, and several kinetic models were evaluated using the method of multivariate non-linear regression. Besides, the denaturation behavior was simulated under different temperature conditions. Results showed that the activation energy decreased in a different way at lower and higher degrees of conversion, respectively. A three-state model, in which a reversible step was followed by an irreversible one, was the best of the estimated models to describe the denaturation process, which could be approximated by single-step or two-consecutive-step in terms of temperature 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.     

Crystallization kinetics of Ti20Zr20Cu60 metallic glass by isoconversional methods using modulated differential scanning calorimetry

The study of crystallization kinetics of amorphous alloys has been a matter of great interest for material researchers for past few decades, since it provides information about the kinetic parameters i.e., activation energy of crystallization and the frequency factor. These kinetic parameters can be calculated by model-free isoconversional methods. Isoconversional methods allow calculating the activation energy as a function of degree of conversion, α. Hence, these methods provide accurate results for multistep processes like crystallization. Model-free methods are categorized as linear and non-linear isoconversional methods. Linear methods are further classified as linear differential and linear integral isoconversional methods. In present work, we have used these isoconversional methods to study the effect of non-linear heating rate, employed by modulated differential scanning calorimetry (MDSC), on the non-isothermal crystallization kinetics of Ti₂₀Zr₂₀Cu₆₀ metallic glass. For Ti₂₀Zr₂₀Cu₆₀, MDSC curves clearly indicate a two-step crystallization process. Both crystallization peaks were studied based on the modified expressions for isoconversional methods by non-linear heating rate. The term corresponding to non-linearity comes out to be (A _T ω/2β)². The effect of non-linear heating rate on measurement of kinetic parameters by isoconversional methods is studied. The activation energy of crystallization is calculated for Ti₂₀Zr₂₀Cu₆₀ metallic glass for various degrees of conversion by linear integral isoconversional methods i.e., Ozawa–Flynn–Wall, Kissinger–Akahira–Sunose, and also with Friedman method which is a linear differential isoconversional method.     

New incremental isoconversional method for kinetic analysis of solid thermal decomposition

A simple and precise incremental isoconversional integral method based on Li-Tang (LT) method is proposed for kinetic analysis of solid thermal decomposition, in order to evaluate the activation energy as a function of conversion degree. The new method overcomes the limitation of LT method in which the calculated activation energy is influenced by the lower limit of integration. By applying the new method to kinetic analysis of both the simulated nonisothermal case and experimental case of strontium carbonate thermal decomposition, it is shown that the dependence of activation energy on conversion degree evaluated by the new method is consistent with those obtained by Friedman (FR) method and the modified Vyazovkin method. As the new method is free from approximating the temperature integral and not sensitive to the noise of the kinetic data, it is believed to be more convenient in nonisothermal kinetic analysis of solid decompositions.     

A simulation of the mass‐transfer effects on the kinetics of solid–gas reactions

A theoretical analysis of the influence of mass‐transfer effect on the kinetic of solid–gas reactions has been carried out by assuming that the partial pressures of the gases generated in the reaction are proportional to the reaction rate. The influence of mass‐transfer phenomena on the apparent activation energy, calculated by the isoconversional methods of Friedman, and on the reaction model is discussed. In the present study, simulated nonisotherm, isotherm, and controlled rate thermal analysis (CRTA) data have been used. Master plots based on the differential forms of the kinetic equations describing solid‐state reactions have been employed by using the concept of the generalized time (θ), introduced by Ozawa; this permits the application of these master plots to the kinetic analysis of reactions whatever the type of temperature program used for recording the experimental data. It has been shown that when the simulated mass‐transfer effect is present the variable effective activation energy E remains nearly constant while the reaction model approaches zero order. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 217–222, 2008     

Addition effect of erbium(III) trifluoromethanesulfonate in the homopolymerization kinetics of a DGEBA resin

Solid bisphenol-A epoxy resin of medium molecular weight was cured using a Lewis acid initiator (erbium(III) trifluoromethanesulfonate) in three different proportions (0.5, 1 and 2 phr). A kinetic study was performed in a differential scanning calorimeter. The complete kinetic triplet was determined (activation energy, pre-exponential factor, and integral function of the degree of conversion) for each system. A kinetic analysis was performed with an integral isoconversional procedure (model-free), and the kinetic model was determined both with the Coats-Redfern method (the obtained isoconversional E value being accepted as the effective activation energy) and through the compensation effect. All the systems followed the same isothermal curing model simulated from non-isothermal ones. The “nucleation and growth” Avrami kinetic model A_3/2 has been proposed as the polymerization kinetic model. The addition of initiator accelerated the reaction having higher influence when low temperatures were applied.     

A new iterative linear integral isoconversional method for the determination of the activation energy varying with the conversion degree

The conventional linear integral isoconversional methods may lead to important errors in the determination of the activation energy when the significant variation of the activation energy with the conversion degree occurs. Vyazovkin proposed an advanced nonlinear isoconversional method, which allows the activation energy to be accurately determined [Vyazovkin, J Comput Chem 2001, 22, 178]. However, the use of the Vyazovkin method raises the problem of the time‐consuming minimization without derivatives. A new iterative linear integral isoconversional method for the determination of the activation energy as a function of the conversion degree has been proposed, which is capable of providing valid values of the activation energy even if the latter strongly varies with the conversion degree. Also, the new method leads to the correct values of the activation energy in much less time than the Vyazovkin method. The application of the new method is illustrated by processing of theoretically simulated data of a strongly varying activation energy process. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009