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.     

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     

Influence of the addition of erbium and ytterbium triflates in the curing kinetics of a DGEBA/<Emphasis Type="Italic">o</Emphasis>-tolybiguanide powder mixture

Solid bisphenol-A epoxy resin (DGEBA) of medium molecular mass was cured using o-tolylbiguanide (TBG) as cross-linking agent. In order to improve the kinetics of the reactive system, two Lewis acid catalysts (erbium(III) and ytterbium(III) trifluoromethanesulfonates) were added in proportions of 1 phr. The kinetic study was performed by dynamic scanning calorimetry (DSC) and the complete kinetic triplet (E, A and g(α)) determined. The kinetic analysis was performed with an integral isoconversional procedure (model-free), and the kinetic model was determined by the Coats-Redfern method and through the compensation effect (IKR). All the systems followed the m=1.5/n=0.5 isothermal curing model simulated from non-isothermal experiments. The addition of a little proportion of ytterbium or erbium triflates accelerated the curing process. In order to extract further information about the role of the lanthanide triflates added to epoxy/TBG systems, the kinetic results were compared with our previous kinetic studies made on DGEBA/lanthanide triflates initiated systems.     

非等温反应过程中新的动力学方程

对于非等温过程中的动力学方程，正确的Arrhenius方程的温度积分应该是从T₂到T₁，但是许多动力学方程中的温度积分是从T到0 K，例如Ozawa等方程。我们的研究指出对于某些反应，这些方程中的活化能存在较大的误差，因此我们提出了一个新的动力学方程。凭借等转化率法，应用新的方程可以精确求解线性或非线性加热过程中化学反应的活化能。用新方程对2个经典反应（聚酰胺的热裂解和一水草酸钙的热分解）的研究表明：Ozawa方程的活化能有时是精确的，有时偏差太大。     

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.     

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.     

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.     

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.     

Comparative results of kinetic data obtained with different methods for complex decomposition steps

A comparative kinetic analysis on the thermal decomposition of tartaric acid and potassium tartrate under non-isothermal conditions was performed. The non-isothermal kinetic parameters were determined by the following four methods: integral isoconversional method suggested by Flynn-Wall-Ozawa (FWO method); differential isoconversional method suggested by Friedman; Budrugeac-Segal method and Non-Parametric-Kinetic (NKP) method suggested by Sempere and Nomen and modified by Vlase and Doca. The comparison of the results obtaining by these methods leads to interesting conclusions. The experimental data were obtained in dynamic nitrogen atmosphere at heating rates of 5, 7, 10, 12 and 15 K min⁻¹. The less speculative kinetic analysis was possible by the NPK method.     

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 decomposition of basic zinc carbonate in nitrogen atmosphere

Dynamic kinetic analyses were performed on basic zinc carbonate using TG and DTA measurements in N₂. The thermal behavior and the kinetics of decomposition were studied. The effect of procedural variables on the kinetics was investigated. In this work, the procedural variables included heating rate and sample size. To estimate the activation energy of decomposition, the Friedman isoconversional method was applied. The activation energy (E_a) was calculated as a function of conversion (a).     

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     

Influence of the proportion of ytterbium triflate as initiator on the mechanism of copolymerization of DGEBA epoxy resin and γ-butyrolactone

Non-isothermal differential scanning calorimetry (DSC) experiments were performed to study the kinetics of the curing process of mixtures of diglycidylether of bisphenol A (DGEBA) and γ-butyrolactone (γ-BL) with ytterbium triflate as an initiator. It can be deduced that the cured material consists of epoxide homopolymers with incorporated poly(ether-ester) unities, which come from the lactone incorporated into the network. The kinetic parameters, obtained using the non-isothermal isoconversional procedure, show not only the importance of the proportion of initiator but also the influence of γ-butyrolactone on the polymerization of DGEBA. The homopolymerization of DGEBA catalyzed by ytterbium triflate has an activation energy of 85.3 kJ mol⁻¹, which decreases to 68.2 kJ mol⁻¹ in the presence of γ-butyrolactone forming copolymers. Analysis from DSC and FTIR data showed that, when the proportion of ytterbium triflate was increased, the reaction process accelerated and the mechanism of the cationic non-linear polymerization named activated monomer (AM) became more evident than the activated chain-end mechanism (ACE). Finally, the activation energies and the pre-exponential factors were determined for both mechanisms.     

Kinetic analysis for non-isothermal decomposition of un-irradiated and gamma-irradiated potassium bromate

The thermal decomposition of un-irradiated and gamma-irradiated potassium bromate (KBrO₃) was performed under non-isothermal conditions at different heating rates (5, 10, 15 and 20 K min^?1). The data was analysed using isoconversional and non-isoconversional methods. The kinetic parameters of thermal decomposition process were obtained by three model-free isoconversional methods: Flynn–Wall–Ozawa, Kissinger–Akahira–Sunose and Friedman. Irradiation enhances the decomposition and the effect increases with the irradiation dose. The activation energy decreases on irradiation. Kinetic analysis of data in view of various solid-state reaction models showed that the decomposition of un-irradiated and irradiated anhydrous KBrO₃ is best described by the Avrami–Erofeev model equation, [?ln(l?α)]^1/2 = kt.     

Preparation,Characterization and Non‐isothermal Kinetics of the Dehydration Process of [Sm(p‐MOBA)3bath]2·4H2O

The new complex of [Sm(p‐MOBA)₃bath]₂·4H₂O (p‐MOBA, p‐methoxybenzoate; bath, 4,7‐diphenyl‐1,10‐phenanthroline) was synthesized and characterized by elemental analysis, molar conductance, IR, UV and XRD patterns. The thermal decomposition of the complex was studied under the non‐isothermal condition by TG‐DTG and IR techniques. The most probable mechanism function of the dehydration process was obtained from the analysis of DSC curves of the complex employing the double extrapolated method on the basis of integral isoconversional non‐linear (NL‐INT) and Tang‐Wanjun integral equations. The integral function of the mechanism was [1? (1?α)^1/2]^1/2 and the corresponding kinetic parameters (activation energy E and the pre‐exponential factor A) were obtained.     

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.     

二水草酸锌脱水的热分解动力学研究

提出一种多升温速率-等温法确定机理函数g(α)的新方法;并用迭代的等转化率法求出较为可靠的活化能Ea;在Ea和g(α)的基础上计算出指前因子A.用该法对二水草酸锌（ZnC2O4•2H2O）脱水反应的热分解动力学三因子进行了求算,得出Ea为87.22 kJ•mol－1, A为4.2120×108～7.2328×108 s－1;以及随机成核和随后生长型机理函数Am（Avrami-Erofeer）,其积分形式g(α)=[－ln(1－α)] 1/m和微分形式f(α)=m(1－α)•[－ln(1－α)](1－1/m),调节因子m=1.85～2.00.     

Estimation of the curing rate of acrylamide used as a consolidant in heritage sandstone conservation

An investigation of the curing (polymerisation) rate of acrylamide was carried out using isothermal and non-isothermal DSC in order to estimate the time for complete conversion of monomer at ambient temperatures. The non-isothermal data were used to model the rate using integral isoconversional and incremental isoconversional kinetic methods. Applying the equations for integral isoconversional methods and extrapolating to ambient temperatures resulted in non-sensical conversion–time curves, where the time estimated decreased for increasing degree of conversion to be reached. This odd behaviour was attributed to the incorrectness of the integration where the kinetic parameters (e.g. the activation energy) are a function of conversion. The problem was addressed by applying incremental methods which provided more reasonable results as the integration is carried out over small conversion increments where the kinetic parameters are assumed to be constant. Estimates of the conversion were compared to isothermal measurements and, although isothermal DSC produced significant variability in the data, extrapolated estimates from non-isothermal kinetic analysis produced, at best, an upper boundary for the estimation of the time to reach a fixed degree of conversion.     

Crystallization kinetics of metallic glasses

In this study, the temperature-heating rate diagram of the main crystallization process of two metallic glasses, Fe₇₄Ni_3.5Mo₃B₁₆Si_3.5 and Fe₄₁Ni₃₈Mo₃B_18, was obtained from one experimental differential scanning calorimetry (DSC) scan and the knowledge of their activation energy as determined by an isoconversional method. A good concordance was observed between the diagram curves obtained by calculation (isoconversional approach) and the experimental data, which verifies the reliability of the method and the validity of the kinetic approach in these alloys.     

Application of non-isothermal cure kinetics on the interaction of poly(ethylene terephthalate) — Alkyd resin paints

Samples of paint (P), reused PET (PET-R) and paint/PET-R mixtures (PPET-R) were evaluated using DSC to verify their physical-chemical properties and thermal behavior. Films from paints and PPET-R are visually similar. It was possible to establish that the maximum amount of PET-R that can be added to paint without significantly altering its filming properties is 2%. The cure process (80–203°C) was identified through DSC curves. The kinetic parameters, activation energy (E _a) and Arrhenius parameters (A) for the samples containing 0.5 to 1% of PET-R, were calculated using the Flynn-Wall-Ozawa isoconversional method. It was observed that for greater amounts of PET-R added, there is a decrease in the E _a values for the cure process. A Kinetic compensation effect (KCE), represented by the equation InA=−2.70+0.31E _a was observed for all the samples. The most suitable kinetic model to describe this cure process is the autocatalytic Šesták-Berggreen, model applied to heterogeneous systems.