Evaluation of the non-isothermal rate equation proposed by s̆esták and bercgren by computer methods: The dehydration of manganese(II) formate dihydrate

The equation

proposed by S?esták and Berggren was applied to the dehydration of Mn(HCO₂)₂· 2H₂O as studied by differential scanning calorimetry. Systematic variation of the parameters m, n, and p and linear least-squares analysis of the Arrhenius plot resulting from each equation were accomplished with a computer program. The method was found to be successful for preliminary appraisal of reaction mechanism or as a means of checking isothermal results. The problem of finding a suitable fraction of reaction, α, over which any particular rate law is valid, is somewhat circumvented by the ease with which multiple runs may be made with various α ranges. The possible rate expressions found for Mn(HCO₂)₂·2H₂O using the S?esták-Berggren equation include those reported in the literature for 0.15 ? α ? 0.45, and activation energies for interfacial advance agree with those obtained in previous studies.     

DSC and curing kinetics of epoxy resin using cyclohexanediol diglycidyl ether as active diluents

Curing reactions of epoxy resin (diglycidyl ether of bisphenol-A) with curing agent polyamido-amine, using cyclohexanediol diglycidyl ether as active diluents, was investigated by non-isothermal differential scanning calorimetry at different heating rates. Activation energy was calculated based on Kissinger method, and the results showed that E _a changed from 68.01 to 54.84 kJ mol^?1 after the diluents was added, which reduced about 20 %. Málek method was used to deduce the probable mechanism function and the results indicated that ?esták–Berggren model is fairly coincident with the experimental data.     

The applicability of DTA to the study of the crystallisation process of ceramic fibres

?esták's method for the determination of the activation energy of the crystallisation of mullite in ceramic fibres has been applied. The investigations performed proved that the mechanism of the crystallisation of mullite is far from the classical theories describing the devitrification process of glass. The determination of the kinetic parameters by ?esták's method requires the verification of the introduced simplification every single time.     

Synthesis,characterization, and cure kinetics analysis of high refractive index copolysiloxanes

Two kinds of high refractive index of polysiloxane compounds containing both pendent and terminal vinyl groups were successfully synthesized through a cohydrolysis-condensation method based on alkoxy silanes in the presence of acids and anionic ring-opening copolymerization of methylphenycyclosiloxane (D_n) and octamethylcyclotetrasiloxane (D₄), respectively. Their structures were confirmed by Fourier-transformed infrared and nuclear magnetic resonance spectra (¹H NMR and ²⁹Si NMR). The curing kinetics of the silicone resin (MPSR) in the presence of phenylvinyl silicone oil (MPSO) as reactive diluent and T-shaped hydrosiloxane (TPHS) as crosslinking agent was studied by non-isothermal differential scanning calorimeter at different heating rates. The kinetic parameters of the curing process were determined by Friedman and ?esták–Berggren method. A comparison of the results calculated with the experimental data showed that ?esták–Berggren equation was found to be the most adequately selected to describe the cure kinetics of the studied silicone resin, and the experimental data had a great coherence with that theoretically calculated. It would give a valuable guide for the curing process of silicone resin. In addition, TG curves showed that the cured MPSR/MPSO/TPHS system exhibited much higher heat resistance and thermal stability compared to MQ resin/PMVS/PHVS blends.     

Thermal characterization and isothermal kinetic analysis of commercial Creosote decomposition process

Isothermal decomposition process of commercial Creosote was analyzed by thermogravimetric technique in a nitrogen atmosphere, at four different operating temperatures (T = 230, 250, 270, and 290 °C). It was found that the two-parameter autocatalytic ?esták–Berggren kinetic model best describes the investigated process. It was established that the applied logistic function can successfully perform a given kinetic predictions of investigated process, at all operating temperatures. The experimental density distribution function of the apparent activation energy values was evaluated. Based of the characteristic shape of distribution curve, it was concluded that the isothermal pyrolysis of commercial Creosote represent a complex process, which probably includes primary and secondary (autocatalytic) pyrolysis reactions, together with various decomposition reactions and radicals recombination pathways.     

Preparation and characterization of microcapsulated red phosphorus and kinetic analysis of its thermal oxidation

Microcapsulated red phosphorus (MRP) with aluminum hydroxide/phenolic resin coating layer was prepared by a two-step coating process. The results of Fourier-transform infrared spectroscopy and scanning electron microscopy show that red phosphorus (RP) is coated by aluminum hydroxide and phenolic resin. MRP absorbs less water and is more thermally stable than RP. The thermal oxidation kinetics of MRP was investigated by TG/DTG/DTA under air atmosphere using non-isothermal experiments with the heating rates ranging from 10 to 25°C/min. The values of the apparent activation energy E _a were 168 ± 9 kJ/mol as determined by the isoconversional Ozawa–Flynn–Wall method and 164 ± 12 kJ/mol according to the Kissinger?Akahira?Sunose method. Based on Málek’s procedure the kinetic reaction follows the ?esták–Berggren model with f(α) = α0.34(1 ? α)^0.94 (α is RP conversion) and pre-exponential factor A = 3.11 × 10¹² s^–1. The simulated curves were fitted with experimental curves constructed by plotting dα/dt vs temperature at different heating rates.     

Investigation of thermal decomposition kinetics of taurine

The non-isothermal thermal decomposition of taurine was investigated by means of thermogravimetric analysis (TG) and differential thermal analysis (DTA). The experimental data were treated using Flynn–Wall–Ozawa, Doyle, Kissinger, and ?atava–?esták methods, respectively. The results show that the non-isothermal thermal decomposition mechanism of taurine is classified as phase boundary reaction, and the mechanism function is the Mampel Power law with n = 1. The forms of both integral and differential for the mechanism function are $ G(\alpha ) = \alpha $ and $ f(\alpha ) = 1 $ , respectively. The activation energy and the pre-exponential factor are 167.88 kJ mol^?1 and 1.82 × 10¹³min^?1, respectively.     

The influence of reagents solvation on enthalpy change of glycine-ion protonation and silver(I) glycine-ion complexation in aqueous-dimethylsulfoxide solutions

The thermal decomposition process and non-isothermal decomposition kinetic of glyphosate were studied by the Differential thermal analysis (DTA) and Thermogravimetric analysis (TGA). The results showed that the thermal decomposition temperature of glyphosate was above 198?°C. And the decomposition process was divided into three stages: The zero stage is the decomposition of impurities, and the mass loss in the first and second stage may be methylene and carbonyl, respectively. The mechanism function and kinetic parameters of non-isothermal decomposition of glyphosate were obtained from the analysis of DTA?CTG curves by the methods of Kissinger, Flynn?CWall?COzawa, Distributed activation energy model, Doyle and ?atava-?esták, respectively. In the first stage, the kinetic equation of glyphosate decomposition obtained showed that the decomposition reaction is a Valensi equation of which is two-dimensional diffusion, 2D. Its activation energy and pre-exponential factor were obtained to be 201.10?kJ?mol^?1 and 1.15?×?10¹⁹?s^?1, respectively. In the second stage, the kinetic equation of glyphosate decomposition obtained showed that the decomposition reaction is a Avrami?CErofeev equation of which is nucleation and growth, and whose reaction order (n) is 4. Its activation energy and pre-exponential factor were obtained to be 251.11?kJ?mol^?1 and 1.48?×?10²¹?s^?1, respectively. Moreover, the results of thermodynamical analysis showed that enthalpy change of ??H ^??, entropy change of ??S ^?? and the change of Gibbs free energy of ??G ^?? were, respectively, 196.80?kJ?mol^?1,107.03?J?mol^?1?K^?1, and 141.77?kJ?mol^?1 in the first stage of the process of thermal decomposition; and 246.26?kJ?mol^?1,146.43?J?mol^?1?K^?1, and 160.82?kJ?mol^?1 in the second stage.     

Thermal analysis of earlywood and latewood of larch (<Emphasis Type="Italic">Larix gmelinii</Emphasis> (Rupr.) Rupr.) found along the Polar tree line

This work introduces a new method of calculations depending on the essential assumptions of the kinetic methods, with the least amount of approximations to find the apparent kinetic parameters calculated for the crystallization of the Se₉₀Te₁₀ powders with heterogeneous particle sizes and shapes under non-isothermal conditions. The apparent kinetic parameters calculated by the new method are compared with that calculated blindly by applying Málek’s method, ignoring its applicability condition of invariant activation energy. The new method is based on the assumption that the kinetic function \(f\left( \alpha \right)\) parameters are independent of the heating rate \(\beta\) and time \(t\), and the fitting temperature function is assumed to be in the approximated form \(K\left( T \right) = K\left( {t,\beta } \right) = ct^{\text{r}} \beta^{\text{s}}\). The exponents \(r\) and \(s\) are calculated isoconversionally, while the constant \(c\) and the kinetic function \(f\left( \alpha \right)\) parameters are calculated by a curve fitting method using a generalized form of the ?esták and Berggren function, considering the steadily and logarithmic acceleration and deceleration of the curve. According to the data in this work, the fitting temperature function can be roughly approximated to the form \(K\left( T \right) \approx c/t\) which work in with the physical dimensions of the rate constant. Moreover, the Arrhenian and the non-Arrhenian parameters, which describe the fitting temperature function \(K\left( T \right)\), are calculated isoconversionally. The deduced parameters work harmonically together to perfectly fit the experimental and the true data.     

Study on the optimum ratio and non-isothermal curing kinetics of EP2008/EP2008-S system

This paper systematically reports the optimum ratio and non-isothermal curing kinetics of EPOLAM 2008 RESIN (EP2008)/EPOLAM 2008-S HARDENER (EP2008-S) system studied using Differential Scanning Calorimetry (DSC). In view of the gel time, viscosity, and curing reaction heat, the optimum ratio of m (EP2008)/m (EP2008-S) can be confirmed as 100:20. Subsequently, non-isothermal curing kinetics of the composite system with the optimum ratio of m (EP2008)/m (EP2008-S) is investigated by dynamic DSC. The kinetics mechanism function is analyzed with the nth-order model and two-parameter (m and n) autocatalytic model (?esták–Berggren model). Results indicated that the Málek method discloses the autocatalytic behavior, and that the two-parameter autocatalytic model is able to well simulate the curing reaction. Through the analysis of chemical composition of EP2008/EP2008-S and the value of E _a , the possible curing reaction mechanism can be explained.     

Thermal analysis kinetics of thermal decomposition of nickel–viscose composite fiber

In this study, the thermal decompositions of nickel composite fibers (NCF) under different atmospheres of flowing nitrogen and air were investigated by XRD, SEM–EDS, and TG–DTG techniques. Non-isothermal studies indicated that only one mass loss stage occurred over the temperature regions of 298–1,073 K in nitrogen. The mass loss was from the decomposition. But after this decomposition, nickel was oxidized in air, when the temperature was high enough. In nitrogen media, the model-free kinetic analysis method was applied to calculate the apparent activation energy (E _a) and pre-exponential factor (A). The method combining Satava–?esták equation with one TG curve was used to select the suitable mechanism functions from 30 typical kinetic models. Furthermore, the Coats–Redfern method was used to study the NCF decomposition kinetics. The study results showed that the decomposition of NCF in nitrogen media was controlled by three-dimension diffusion; mechanism function was the anti-Jander equation, the apparent activation energy (E _a) and the pre-exponential factor (A) were 172.3 kJ mol^?1 and 2.16 × 10⁹ s^?1, respectively. The kinetic equation could be expressed as following: $$ \frac{{{\text{d}}\alpha }}{{{\text{d}}T}} = \frac{{ 2. 1 6\times 1 0^{ 9} }}{\beta }{ \exp }\left( {\frac{ - 2 0 7 2 4. 1}{T}} \right)\left\{ {\frac{ 3}{ 2}(1 + \alpha )^{2/3} [(1 + \alpha )^{1/3} - 1]^{ - 1} } \right\}. $$      

Comparative curing kinetics of 1,4-bis (4-diaminobenzene-1-oxygen) n-butane and 4,4′-bis-(diaminodiphenyl) methane with tetraglycidyl methylene dianiline systems

Aromatic amine curing agent with flexible unit in backbone, 1,4-bis (4-diaminobenzene-1-oxygen) n-butane (DDBE), was synthesized, and the structure was confirmed by FT-IR and ¹H NMR. The curing kinetics of tetraglycidyl methylene dianiline (TGDDM, or AG80) using DDBE and 4,4′-bis-(diaminodiphenyl) methane (DDM) as curing agents, respectively, were comparatively studied by non-isothermal DSC with a model-fitting Málek approach and a model-free advanced isoconversional method of Vyazovkin. The dynamic mechanical properties and thermal stabilities of the cured materials were investigated by DMTA and TG, respectively. The results showed that the activation energy of AG80/DDBE system was slightly higher than that of AG80/DDM system. ?esták-Berggren model can generally simulate well the reaction rates of these two systems. DMTA measurements showed that the storage modulus of cured AG80/DDBE is similar to that of cured AG80/DDM at the temperature below glass transition temperature (T _g) and lower than that of cured AG80/DDM at the temperature above glass transition temperature, while T _g of cured AG80/DDBE is lower than that of cured AG80/DDM. TG showed that the thermal stabilities of these two cured systems are similar.     

Analysis of isothermal kinetic data from solid-state reactions

In most solid state reactions the reaction velocity can be described as a product of two functionsK(T) andf(1?α) whereT is the temperature and α the degree of conversion of the solid reactant. The physical interpretation of these functions is discussed, and a systematic method is described by whichf(1?α) of a reaction is identified from its kinetic data.K(T) and the reaction mechanism are then determined. This method has been successfully applied to analyse the kinetics of the thermal decomposition of silver azide.     

Kinetics of non-isothermal decomposition of cinnamic acid

The thermal stability and kinetics of decomposition of cinnamic acid were investigated by thermogravimetry and differential scanning calorimetry at four heating rates. The activation energies of this process were calculated from analysis of TG curves by methods of Flynn-Wall-Ozawa, Doyle, Distributed Activation Energy Model, ?atava-?esták and Kissinger, respectively. There are only one stage of thermal decomposition process in TG and two endothermic peaks in DSC. For this decomposition process of cinnamic acid, E and logA[s^?1] were determined to be 81.74 kJ mol^?1 and 8.67, respectively. The mechanism was Mampel Power law (the reaction order, n = 1), with integral form G(α) = α (α = 0.1–0.9). Moreover, thermodynamic properties of ΔH ^≠, ΔS ^≠, ΔG ^≠ were 77.96 kJ mol^?1, ?90.71 J mol^?1 K^?1, 119.41 kJ mol^?1.     

Non-isothermal decomposition kinetics of diosgenin

The thermal stability and kinetics of isothermal decomposition of diosgenin were studied by thermogravimetry (TG) and Differential Scanning Calorimeter (DSC). The activation energy of the thermal decomposition process was determined from the analysis of TG curves by the methods of Flynn-Wall-Ozawa, Doyle, ?atava-?esták and Kissinger, respectively. The mechanism of thermal decomposition was determined to be Avrami-Erofeev equation (n = 1/3, n is the reaction order) with integral form G(α) = [?ln(1 ? α)]^1/3 (α = 0.10–0.80). E _a and logA [s^?1] were determined to be 44.10 kJ mol^?1 and 3.12, respectively. Moreover, the thermodynamics properties of ΔH ^≠, ΔS ^≠, and ΔG ^≠ of this reaction were 38.18 kJ mol^?1, ?199.76 J mol^?1 K^?1, and 164.36 kJ mol^?1 in the stage of thermal decomposition.     

Amorphous-to-crystalline transition in Te-doped Ge2Sb2Se5 glass

Differential scanning calorimetry (DSC) was used to study crystallization in Ge₂Sb₂Se_4.5Te_0.5 glass under non-isothermal conditions. The crystallization kinetics was described in terms of the autocatalytic ?esták–Berggren model. An extensive discussion of all aspects of a full-scale kinetic study for a crystallization process was undertaken. In particular, the effect of Te ? Se substitution on the complexity of the crystallization process was analyzed. The addition of tellurium enhances bulk crystallization originating from volume nuclei at the expense of the surface/defects-based crystallization mechanism. Significantly higher activation energy in the case of the Te-doped material was attributed to the larger mass of the combined Se–Te chains and the larger spatial restrictions for their movement. On the other hand, the slightly lower crystallization temperature of the Te-doped glass corresponds to its higher tendency for crystallization. A supplemental X-ray diffraction study confirmed the findings obtained by DSC.     

Crystallization kinetic of fluoro- zirconate glasses by non-isothermal analysis

Fluoride glasses have been extensively studied due to their high transparency in the infrared wavelength. The crystallization kinetics of these systems has been studied using DTA and DSC techniques. Most of the experimental data is frequently investigated in terms of the Johnson-Mehl-Avrami (JMA) model in order to obtain kinetic parameters. In this work, DSC technique has been used to study the crystallization of fluorozirconate glass under non-isothermal conditions. It was found that JMA model was not fit to be applied directly to these systems, therefore, the method proposed by Málek has been applied and the Šesták-Berggren (SB) model seems to be adequate to describe the crystallization process. This revised version was published online in July 2006 with corrections to the Cover Date.     

Kinetics of the crosslinking reaction of nonionic polyol dispersion from terpene-maleic ester-type epoxy resin

The bulk crosslinking reaction kinetics of a novel two-component waterborne polyurethanes (2K-WPUs) composed of a bio-resin-based polyol dispersion and a hydrophilically modified hexamethylene diisocyanate tripolymer are investigated by freeze–drying and differential scanning calorimetry (DSC) technique at different heating rates. The data fit for the above two components is implemented with the nth-order kinetics equation and Málek’s mechanism function method, respectively. The kinetic parameters of crosslinking reaction are determined by the kinetic analysis of the data obtained from the thermal treatment, and then the kinetic model is built. The results indicate that the nth-order model deduced from Kissinger and Crane equation has great distinction with the experimental data, while the Málek analytic mechanism shows that the crosslinking process of the crosslinking reaction follows an autocatalytic reaction. The two-parameter (m and n) autocatalytic model (S–B model) can well describe the crosslinking reaction process of the studied 2K-WPU. The DSC curves derived from the experimental data show a good agreement with the theoretical calculation under 5–20 °C min^?1 heating rate. The results provide theoretical basis for the choice of the manufacturing process and the optimization of processing window.     

Etude cinetique de la catalyse,due a SnCl4,de l'esterification des olefines

Esterification of cyclopentene, cyclohexene, cycloheptene and trans cyclooctene, with acetic, butyric and propionic acids, has been studied by a kinetic method. SnCl₄ is the catalytic agent. SnCl₄ undergoes a degradation which complicates the mathematical analysis of the reaction process. An appropriate mathematical method has been used. The experimental rate constant is connected with Hammett acidity function, H₀, given by dissolution of SnCl₄ in carboxylic acids: log k?_ex,0 = ?H₀ + δ. The kinetic isotope effects of solvent show that general acid catalysis is implied. A reaction mechanism has been put forward to explain every observed fact. The kinetic equation accounts for every mathematical implication of the mechanism.