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     

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 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.     

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.     

DSC kinetics of the thermal decomposition of copper(II) oxalate by isoconversional and maximum rate (peak) methods

The copper(II) oxalate was synthesized, characterized using FT-IR and scanning electron microscopy and its non-isothermal decomposition was studied by differential scanning calorimetric at different heating rates. The kinetics of the thermal decomposition was investigated using different isoconversional and maximum rate (peak) methods viz. Kissinger–Akahira–Sunose (KAS), Tang, Starink^1.95, Starink^1.92, Flynn–Wall–Ozawa (FWO) and Bosewell. The activation energy values obtained from isoconversional methods of FWO and Bosewell are 0.9 and 3.0 %, respectively, higher than that obtained from other methods. The variation of activation energy, E _α with conversion function, α, established using these different methods were found to be similar. Compared to the FWO method, the KAS method offers a significant improvement in the accuracy of the E _a values. All but the Bosewell maximum rate (peak) methods yielded consistent values of E _α (~137 kJ mol^?1); however, the complexity of the thermal decomposition reaction can be identified only through isoconversional methods.     

Application of isoconversional calculation procedure to non-isothermal kinetics study

The kinetics of thermal decomposition of NH₄CuPO₄·H₂O was studied using isoconversional calculation procedure. The iterative isoconversional procedure was applied to estimate the apparent activation energy E _a; the values of apparent activation energies associated with the first stage (dehydration), the second stage (deamination), and the third stage(condensation) for the thermal decomposition of NH₄CuPO₄·H₂O were determined to be 117.7 ± 7.7, 167.9 ± 8.4, and 217.6 ± 45.5 kJ mol^?1, respectively, which demonstrate that the third stage is a kinetically complex process, and the first and second stages are single-step kinetic processes and can be described by a unique kinetic triplet [E _a, A, g(α)]. A new modified method of the multiple rate iso-temperature was used to define the most probable mechanism g(α) of the two stages; and reliability of the used method for the determination of the kinetic mechanism were tested by the comparison between experimental plot and model results for every heating rate. The results show that the mechanism functions of the two stages are reliable. The pre-exponential factor A of the two stages was obtained on the basis of E _a and g(α). Besides, the thermodynamic parameters (ΔS ^≠, ΔH ^≠, and ΔG ^≠) of the two stages were also calculated.     

Kinetic and thermodynamic analysis of degradation of doripenem in the solid state

The kinetic and thermodynamic parameters of degradation of doripenem were studied using a high‐performance liquid chromatography method. In dry air, the degradation of doripenem was a first‐order reaction depending on the substrate concentration. At increased relative air humidity, doripenem was degraded according to the autocatalysis kinetic model. The dependence ln k = f1/T) was described by the equations ln k = 5.10 ± 13.06 ? (7576 ± 4939)(1/T) in dry air and ln k = 46.70 ± 22.44 ? (19,959 ± 8031)(1/T) at 76.4% relative humidity (RH). The thermodynamic parameters E_a, ΔH^≠a, and ΔS^≠a of the degradation of doripenem were calculated. The dependence ln k = f (RH%) was described by the equation ln k = (0.155 ± 0.077) × 10^?1 (RH%) ? (3.45 ± 21.8) × 10^?10. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 44: 722–728, 2012     

Estimation of kinetic parameters for the phase change memory materials by DSC measurements

The non-isothermal method for estimating the kinetic parameters of crystallization for the phase change memory (PCM) materials was discussed. This method was applied to the perspective PCM material of Ge₂Sb₂Te₅ with different Bi contents (0, 0.5, 1, 3 mass%) for defining the kinetic triplet. Rutherford backscattering spectroscopy and X-ray diffraction were used to carry out elemental and phase analysis of the deposited films. Differential scanning calorimetry at eight different heating rates was used to investigate kinetics of thermally induced transformations in materials. Dependences of activation energies of crystallization (E _a) on the degree of conversion were estimated by model-free Ozawa–Flynn–Wall, Kissinger–Akahira–Sunose, Tang and Starink methods. The obtained values of E _a were quite close for all of these methods. The reaction models of the phase transitions were derived with using of the model-fitting Coats–Redfern method. In order to find pre-exponential factor A at progressive conversion values, we used values of E _a already estimated by the model-free isoconversional method. It was established that the crystallization processes in thin films investigated are most likely describes by the second and third-order reactions models. Obtained kinetic triplet allowed predicting transition and storage times of the PCM cells. It was found that thin films of Ge₂Sb₂Te₅ + 0.5 mass% Bi composition can provide the switching time of the phase change memory cell less than 1 ns. At the same time, at room temperature this material has a maximum storage time among the studied compositions.     

Advanced isoconversional and master plot analyses on solid-state degradation kinetics of a novel nanocomposite

The decomposition kinetics of glycerol diglycidyl ether (GDE)/3,3-dimethylglutaric anhydride/nanoalumina composite have been investigated by thermogravimetry analysis under nonisothermal mode. The activation energy, E _a, of the solid-state decomposition process was evaluated using the advanced isoconversional method. From the experimental data, the dependence of conversion on temperature and activation energy was constructed allowing calculating the master plots. Our results showed that the decomposition mechanism at temperatures below 400 °C could be fitted by R2 kinetic model with E _a = 143 kJ mol^?1. The information about the kinetic parameters based only on thermal degradation data has been used for quick lifetime estimation at different temperatures. The Vyazovkin method was also employed to predict the times to reach α = 0.5 at isothermal mode using the activation energy calculated by the advanced isoconversional approaches. Scanning electron microscopy (SEM) analysis was carried out to investigate the fracture surface morphology. It was revealed from the SEM images that the presence of nanoalumina results in reinforcement of GDE matrix.     

Thermokinetics simulation for multi-walled carbon nanotubes with sodium alginate by advanced kinetics and technology solutions

To accomplish an effective analysis of adsorption, the strong acid dye from aqueous solution of sodium alginate (SA) and multi-walled carbon nanotubes (MWCNTs) composite gel beads were used as important parameters. Differential scanning calorimetry (DSC) was used to measure the heat of breakdown reaction. The experimental conditions were set at 0.5, 1, 2, 4, and 8 °C min^?1, and the temperature range was 30–300 °C. The heating rates and the temperature range were set as follows: Four kinds of proportion in this experiment contained 2 SA % w/v (SA), 0.03, 0.09, 0.18, 0.36 % w/v (MWCNTs), and 10 % w/v calcium chloride, respectively. Four samples, 5, 6, 7, 8, and 9 mg, were used to detect the experimental data. It contributed to understanding the reaction for the distinctive MWCNTs. With the thermokinetic data by isoconversional approach obtained from advanced kinetics and technology solutions (AKTS), the related thermal safety information can be obtained from the thermal reaction of MWCNTs. Valuable parameters, such as activation energy (E _a) and heat of decomposition, can be applied in operation, including adsorption and desorption processes. After DSC tests, and under the four compositions of SA/MWCNTs, at different heating rates of 0.5, 1, 2, 4, and 8 °C min^?1, primarily we found that when the heating rate was increased, exothermic onset temperature would increase gradually. After analyzing E _a value by isoconversional kinetics, we learned that in four different adsorption compositions, SA/MWCNTs_0.03 (161.20 kJ mol^?1) was the minimum. Among them, the highest value was SA/MWCNTs_0.18 (220.48 kJ mol^?1). However, in this study, for SA/MWCNTs compositions we found that E _a value will drop in the final material SA/MWCNTs_0.36. Accordingly, if the ratio of SA and calcium chloride was fixed, then different compositions of the MWCNTs would affect adsorption efficiency of SA/MWCNTs and E _a variation.     

Non-isothermal oxidation kinetics of single- and multi-walled carbon nanotubes up to 1273 K in ambient

Non-isothermal oxidation kinetics of single- and multi-walled carbon nanotubes (CNTs) have been studied using thermogravimetry up to 1273 K in ambient using multiple heating rates. One single heating rate based model-fitting technique and four multiple heating rates based model-free isoconversional methods were used for this purpose. Depending on nanotube structure and impurity content, average activation energy (E _a), pre-exponential factor (A), reaction order (n), and degradation mechanism changed considerably. For multi-walled CNTs, E _a and A evaluated using model-fitting technique were ranged from 142.31 to 178.19 kJ mol⁻¹, respectively, and from 1.71 × 10⁵ to 5.81 × 10⁷ s⁻¹, respectively, whereas, E _a for single-walled CNTs ranged from 83.84 to 148.68 kJ mol⁻¹ and A from 2.55 × 10² to 1.18 × 10⁷ s⁻¹. Although, irrespective of CNT type, the model-fitting method resulted in a single kinetic triplet i.e., E _a, A, and reaction mechanism, model-free isoconversional methods suggested that thermal oxidation of these nanotubes could be either a simple single-step mechanism with almost constant activation energy throughout the reaction span or a complex process involving multiple mechanisms that offered varying E _a with extent of conversion. Criado method was employed to predict degradation mechanism(s) of these CNTs.     

Calculation of the kinetic parameters of dehydration of lithium peroxide monohydrate in nonisothermic regime by derivatographic method

The dehydration of lithium peroxide monohydrate was studied by derivatography under nonisothermic conditions for the calculation of main kinetic parameters in the temperature range 90–146°C. Experimental conditions (sample size and the linear heating rate) caused by thermoconductivity of the object under investigation were determined. It is shown that the process under study proceeds according to the kinetic law close to the first order one (n = 0.85±0.03). Values of the activation energy and the pre-exponential factor [E _a = 86.0±0.8 kJ mol^?1, k ₀ = (2.19±0.16)×10¹¹ min^?1] were obtained. A suggestion was formulated that the dehydration mechanism of lithium peroxide monohydrate was analogous to that of the hydrates of the alkaline earth metal (calcium, barium, and strontium) peroxides.     

Kinetics of the thermal isomerization of 1,1,2,2‐tetramethylcyclopropane

Reaction rates for the structural isomerization of 1,1,2,2‐tetramethylcyclopropane to 2,4‐dimethyl‐2‐pentene have been measured over a wide temperature range, 672–750 K in a static reactor and 1000–1120 K in a single‐pulse shock tube. The combined data from the two temperature regions give Arrhenius parameters E_a=64.7 (±0.5) kcal/mol and log₁₀(A, s^?1) = 15.47 (±0.13). These values lie at the upper end of the ranges of E_a and log A values (62.2–64.7 kcal/mol and 14.82–15.55, respectively) obtained from three previous experimental studies, each of which covered a narrower temperature range. The previously noted trend toward lower E_a values for structural isomerization of methylcyclopropanes as methyl substitution increases extends only through the dimethylcyclopropanes (1,1‐ and 1,2‐); E_a then appears to increase with further methyl substitution. In contrast, the pre‐exponential factors for isomerization of cyclopropane and all of the methylcyclopropanes through tetramethylcyclopropane lie within ±0.3 of log₁₀(A, s^?1) = 15.2 and show no particular trend with increasing substitution. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 38: 483–488, 2006     

Kinetics of thermal degradation of wood biomass

Pyrolysis kinetics of a hardwood representative, beech (Fagus sylvatica), was investigated by two different kinetic approaches: model-free isoconversional method and model-fitting method. The model-free isoconversional method was used for the determination of apparent kinetic parameters, i.e. the activation energy and pre-exponential factor. The model fitting method was used for the optimization of kinetic parameters of the reaction pathways of three selected reaction mechanisms: one-step, two-step, and three-step one. In both approaches, thermo-gravimetric data were used at five heating rates: 2°C min^?1, 5°C min^?1, 10°C min^?1, 15°C min^?1 and 20°C min^?1. As the most suitable mechanism, the three-step mechanism containing the intermediate degradation step was chosen. This selection was supported by experimental results from the ¹³C NMR analysis of solid residues prepared at the key temperatures within the range of 230–500°C. The progress of mass fraction values of each component in this mechanism was simulated. Conclusions from the simulation were confronted with experimental results from the ¹³C NMR.     

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.     

Non-isothermal reduction of silica-supported nickel catalyst precursors in hydrogen atmosphere: a kinetic study and statistical interpretation

A series of silica-supported nickel catalyst precursors was synthesized with different SiO₂/Ni mole ratios (0.20, 0.80 and 1.15). Non-isothermal reduction of Ni catalyst precursors was investigated by temperature-programmed reduction at four different heating rates (2, 5, 10 and 20 °C min^?1), in a hydrogen atmosphere. Kinetic parameters (E _a, A) were determined using Friedman isoconversional method. It was found that for all mole ratios, apparent activation energy is practically constant in conversion range of α = 30–70 %. In considered conversion range, the following values of apparent activation energy were found: E _a = 129.5 kJ mol^?1 (SiO₂/Ni = 0.20), E _a = 133.8 kJ mol^?1 (SiO₂/Ni = 0.80) and E _a = 125.0 kJ mol^?1 (SiO₂/Ni = 1.15). Using two special functions (y(α) and z(α)), the kinetic model was determined. It was established that reduction of Ni catalyst precursors with different SiO₂/Ni mole ratios is a complex process and can be described by two-parameter ?esták–Berggren (SB) autocatalytic model. Based on established values of SB parameters for each mole ratio, the possible mechanism was discussed. It was found that for all investigated ratios, the Weibull distribution function fits very well the experimental data, in the wide range of conversions (α = 5–95 %). Based on obtained values of Weibull shape parameter (θ), it was found that experimentally evaluated density distribution functions of the apparent activation energies can be approximated by the unbalanced peaked normal distribution.     

Thermogravimetric analysis of lignocellulosic and microalgae biomasses and their blends during combustion

Thermogravimetric analysis was used to study and compare the combustion of different blends of corn bioresidues with sunflower, rape and algae bioresidues. Non-isothermal thermogravimetric data were used to obtain the combustion kinetics of these bioresidues. This paper reports on the application of the Vyazovkin and Ozawa–Flynn–Wall isoconversional methods for the evaluation of kinetic parameters (energy activation, pre-exponential factor and order of reaction) for the combustion of the biomasses studied. Differences were found in the TG curves in accordance with the proximate analysis results for the cellulose, hemicellulose and lignin content of biomasses. The activation energy obtained from combustion (E ~ 151.6 kJ mol^?1) was lower than that from the blends (similar values were obtained for corn–sunflower, E ~ 160.5 kJ mol^?1 and corn–rape, E ~ 156.9 kJ mol^?1) whereas the activation energy obtained from the microalgae was higher (E ~ 171.5 kJ mol^?1). Both the Vyazovkin and Ozawa–Flynn–Wall methods yielded similar results.     

Thermal decomposition of formaldehyde diperoxide in aqueous solution

Thermal decomposition of formaldehyde diperoxide (1,2,4,5-tetraoxane) in aqueous solution with an initial concentration of 6.22 × 10^?3 M was studied in the temperatures range from 403 to 439 K. The reaction was found to follow first-order kinetic law, and formaldehyde was the major decomposition product. The activation parameters of the initial step of the reaction (ΔH ^≠ = 15.25 ± 0.5 kcal mol^?1, ΔS ^≠ = ?47.78 ± 0.4 cal mol^?1K^?1, E _a = 16.09 ± 0.5 kcal mol^?1) support a mechanism involving homolytic rupture of one peroxide bond in the 1,2,4,5-tetraoxane molecule with participation of the solvent and formation of a diradical intermediate.     

A DSC study on the kinetics of disproportionation reaction of (hfac)Cu(COD)

The kinetics of disproportionation reaction of hexafluoroacetylacetonate-copper(I)-cycloocta-1,5-diene [(hfac)Cu^I(COD)] was investigated by the use of differential scanning calorimetry (DSC) with different heating rates in dynamic nitrogen atmosphere. First, the activation energies (E_as) of the disproportionation reaction were estimated with model-free isoconversional methods, respectively. The E_as were found to fall within the range between 17.6 and 18.7 kJ mol⁻¹, with no temperature and heating rate effects observed. Then, when the E_a was ascertained, the model-fitting methods with least square fitting procedure were adopted to determine the kinetic model for the disproportionation reaction. As a result, the disproportionation reaction follows second-order reaction kinetics.