Thermoset Cure Kinetics by Isoconversional Methods

The curing kinetics of thermosets based on unsaturated polyester resin crosslinked with styrene was studied by differential scanning calorimetry (DSC). The isoconversional kinetic analysis was applied to non-isothermal data. The results obtained show a dependence of the activation energy (E_α) on conversion (α) that proves the existence of a multistep process and a complex kinetic scheme that must be interpreted in terms of chemical and physical mechanisms. The interrelationship of the Arrhenius parameters obtained from the isoconversional kinetic data has been used as a tool to investigate the production of free radicals by the action of a promoter (cobalt octoate) and the temperature on the initiator (methyl ethyl ketone peroxide). An optimum promoter/initiator ratio has been found. This revised version was published online in August 2006 with corrections to the Cover Date.     

Critical study of the isoconversional methods of kinetic analysis

A critical study of the use of isoconversional methods for the kinetic analysis of non-isothermal data corresponding to processes with either a real or an apparent variation of the activation energy, E, with the reacted fraction, α, has been carried out using for the first time simulated curves. It has been shown that the activation energies obtained from model-free methods are independent of the heating rate. However, the activation energy shows a very strong dependence of the range of heating rates used for simulating the curves if the apparent change of E with α is caused by overlapping processes with different individual activation energies. This criterion perhaps could be used for determining if a real dependence between E and α is really occurring.     

Complementary use of model-free and modelistic methods in the analysis of solid-state kinetics

There are many methods for analyzing solid-state kinetic data. They are generally grouped into two categories, model-fitting and isoconversional (model-free) methods. Historically, model-fitting methods were widely used because of their ability to directly determine the kinetic triplet (i.e., frequency factor [A], activation energy [E(a)], and model). However, these methods suffer from several problems among which is their inability to uniquely determine the reaction model. This has led to the decline of these methods in favor of isoconversional methods that evaluate kinetics without modelistic assumptions. This work proposes an approach that combines the power of isoconversional methods with model-fitting methods. It is based on using isoconversional methods instead of traditional statistical fitting methods to select the reaction model. Once a reaction model has been selected, the activation energy and frequency factor can be determined for that model. This approach was investigated for simulated and real experimental data for desolvation reactions of sulfameter solvates.     

多孔物质气固反应动力学研究

利用自主研制的微型流化床反应分析仪（MFBRA）在等温条件下测试了高比表面活性炭氧化反应,并根据基于固体转化的热分析动力学方法及考虑气体在微孔内扩散与反应的应用化工动力学方法求算了动力学参数．在内外扩散抑制最小化的实验条件下,粒径小于5μm的活性炭在700-1000℃的燃烧反应动力学研究表明,根据微型流化床中实验数据,采用等温热分析动力学方法求算得内扩散控制区活化能约为95kJ／mol;弓l入化工动力学方法中的随机孔模型对低温区等温燃烧数据拟合,可得孔结构参数在0．17m^-3左右,反应活化能为178kJ／mol,约为内扩散反应活化能的两倍,最为接近本征的碳燃烧反应活化能．     

A unified approach to kinetic processing of nonisothermal data

Basic problems of kinetic processing of nonisothermal data ascertained from thermal analysis measurements can be solved by isoconversional methods. Analysis of the dependence of the activation energy on conversion often permits the identification of the kinetic scheme for the process. This dependence may also be used to solve applied kinetic problems related to predicting the behavior of a substance outside the range of experimental temperatures. Methods for using this dependence for evaluating both the preexponential factor and the reaction model, as well as for detecting isokinetic relationships, have been discussed. Because all of these operations have a common origin in computing the dependence of the activation energy on conversion, isoconversional methods may be considered as a basis of a unified approach to kinetic processing of nonisothermal data. © 1996 John Wiley & Sons, Inc.     

Isoconversional methods

In this paper, fundamentals of the isoconversional methods are summarized and the methods are analyzed from the point of view of their correctness, their applications and the physical meaning of the activation parameters obtained. It is concluded that the activation parameters represent apparent quantities without a mechanistic interpretation. The parameters cannot be used for any theoretical considerations; however, they enable modelling the processes for other temperature regimes than those applied in the measurements. The differential and incremental isoconversional methods give the actual values of activation parameters whereas the isothermal and integral isoconversional methods provide the averaged values. For the modelling, the activation parameters obtained from the treatment of non-transformed kinetic data should be used. 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.     

Simulation of isothermal cure of A powder coating

The curing of a thermosetting powder coating was studied by means of differential scanning calorimetry (DSC). The isothermal cure was simulated by non-isothermal experiments. The results of the simulation were compared with experimental isothermal data. From non-isothermal isoconversional procedures (free model), it was concluded that these permit simulation of the isothermal cure but do not enable us to determine the complete kinetic triplet (A preexponential factor, E activation energy, f(a) and/or g(a) function of conversion). Non-isothermal procedures based on a single heating rate or on master curves present difficulties for determination of all the kinetic parameters, due to the compensation effect between preexponential factor and activation energy. The kinetic triplet can be determined by a combination of various non-isothermal methods or by using experimental isothermal data in addition to non-isothermal data. This revised version was published online in July 2006 with corrections to the Cover Date.     

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     

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.     

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.     

Advanced isoconversional method

A nonlinear algorithm has been suggested to increase the accuracy of evaluating the activation energy by the integral isoconversional method. A minor modification of the algorithm has made it possible to adapt the isoconversional method for an arbitrary variation of the temperature. This advanced isoconversional method allows for trustworthy estimates of the activation energy when the thermal effect of a reaction makes the temperature of a sample deviate from a prescribed heating program.     

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.     

Kinetic studies on the thermal polymerization of N‐chloroacetyl‐11‐aminoundecanoate potassium salt

A potassium salt of N‐chloroacetyl‐11‐aminoundecanoate was thermally polymerized to obtain the corresponding poly(glycolic acid‐alt‐11‐aminoundecanoic acid). A kinetic study was then performed that was based on isothermal and nonisothermal polymerizations performed in a differential scanning calorimeter. The complete kinetic triplet was determined (the activation energy, pre‐exponential factor, and integral function of the degree of conversion). 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. The polymerization followed a three‐dimensional growth‐of‐nuclei (Avrami) kinetic mechanism. Isothermal polymerization was simulated with nonisothermal data. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1166–1176, 2005     

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.     

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     

Kinetics of non-isothermal crystallization of some glass-ceramics based on basalt

The crystallization kinetics of some glass-ceramics obtained from Romanian (Şanoviţa) basalt has been studied in non-isothermal conditions using DTA technique. The activation energies of the crystallization processes were calculated using the isoconversional methods Kissinger-Akahira-Sunose and Ozawa-Flynn-Wall. The results obtained show a dependence of the activation energy (E _α) on the crystallized fraction (α) that proves the complex mechanism of the glass-ceramics crystallization process. It has been proved that the Johnson-Mehl-Avrami model cannot be applied for the studied glass-ceramics crystallization process. The effect of 2% TiO₂ as nucleating agent upon the crystallization kinetics and upon the microstructure of the studied glass-ceramics was analyzed.     

Isoconversional Kinetic Analysis of Thermally Stimulated Processes in Polymers

Summary: Isoconversional kinetic analysis involves evaluating a dependence of the effective activation energy on conversion or temperature and using this dependence for making kinetic predictions and for exploring the mechanisms of thermally stimulated processes. The paper discusses major results obtained by the authors in the area of the isoconversional analysis of polymer kinetics over the past decade. It provides a brief introduction to isoconversional methods and surveys the impact made by isoconversional analysis in several application areas that include kinetic predictions, thermal degradation, crosslinking (curing), glass transition, and glass and melt crystallization. It is concluded that isoconversional analysis has been used broadly and fruitfully because it presents a fortunate compromise between the single‐step Arrhenius kinetic treatments and the prevalent occurrence of processes whose kinetics are multi‐step and/or non‐Arrhenius.

An isoconversional method applies the Arrhenius equation to a narrow temperature region, ΔT related to a given extent of conversion.     

Modification of the integral isoconversional method to account for variation in the activation energy

Integral isoconversional methods may give rise to noticeable systematic error in the activation energy when the latter strongly varies with the extent of conversion. This error is eliminated by using an integration technique that properly accounts for the variation in the activation energy. The technique is implemented as a modification of the earlier proposed advanced isoconversional method [Vyazovkin, S. J Comput Chem 1997, 18, 393]. The applications of the modified method are illustrated by simulations as well as by processing of data on the thermal decomposition of calcium oxalate monohydrate and ammonium nitrate. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 178–183, 2001     

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.