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.     

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.     

THEORETICAL ANALYSIS OF KINETICS OF NONISOTHERMAL CRYSTALLIZATION OF POLYMERS

The classical crystallization theories proposed by Avrami, Evans, and Mandelkern wereextended to the nonisothermal situation. The expressions derived from the classical equations canbe expressed in either the differential form or the integral form. A method was provided so as toobtain the parameters characterizing the crystallization rate and mechanism from DSC curves withseveral constant heating or cooling rates. The rate constants of crystallization obtained from bothisothermal and nonisothermal curves of poly(ethylene terephthalate)were compared.     

差示扫描量热法测定咔唑-9-乙基氯甲酸酯的热动力学参数

利用差动热分析仪测得新合成的咔唑 9 乙基氯甲酸酯(CEOC)的差示扫描量热曲线,利用普适积分法和微分方程法逻辑选择确定了CEOC的相变和热分解过程的最可几机理函数,并计算出相应的指前因子和活化能.     

Kinetic analysis of nonisothermal solid-state reactions: determination of the kinetic parameters by means of a nonlinear regression method

A nonlinear regression method has been proposed for a simultaneous calculation of the activation energy, frequency factor, and reaction order from a single TG curve. This method was based on the new temperature integral approximation proposed in this paper and the Levenberg–Marquardt method. The newly proposed nonlinear regression method was applied for determining the kinetic parameters from two simulated TG curves. The results of the calculations were compared with values obtained by the traditional method. It can be concluded from this comparison that the new nonlinear regression method is more accurate than the traditional method for the determination of the kinetic parameters of solid-state heterogeneous reactions.     

差示扫描量热法确定L-脯氨酸的热动力学参数

利用差动热分析仪测得L 脯氨酸的差示扫描量热分析(DSC)曲线,采用普适积分法和微分方程法通过逻辑选择确定了L 脯氨酸相变和热解过程的最可几机理函数,并计算出相应的指前因子和活化能.     

Application of non-linear regression methods for the estimation of common kinetic parameters from several thermoanalytical curves

Novel methods of unified evaluation of two (or more) thermogravimetric curves have been worked out on the basis of known non-linear parameter estimating procedures (Gauss-Newton-Marquardt-type regression and the direct integral method of Valkó and Vajda were adapted). Their ability to provide estimate for common kinetic parameters of several TG (m?T) or DTG (dm/dt-T) curves were tested for pairs of curves of different heating rates, and for repeated curves of the same heating rate, obtained for the decomposition of CaCO₃ in open crucible. In these cases the Arrhenius terms and then-th order model functions were assumed. The fitting ability of estimations made for single curves and for pairs of curves sharing different number of parameters, was judged on the base of residual deviations (S _res ) and compared to the standard deviation of the measurements. In the case of different heating rates, the two curves could not be described with the assumption of three common parameters, because of the minimum residual deviation was very high. However, sharing of activation energy and preexponential term only, and applying different exponents for the two curves, provided a satisfactory fit by our methods. Whilst in the case of repeated curves, we could find such a common three-parameter set, which has a residual deviation comparable with the standard deviation of the measurements. Because of their flexibility (taking into account the variable number of common parameters and the versatile forms of model equations), these methods seem to be promising means for unified evaluation of several related thermoanalytical curves.     

Non-isothermal Kinetics of the Thermal Decomposition of 3-Nitro-1,2,4-triazol-5-one Magnesium Complex

Introduction3 Nitro 1,2 ,4 triazol 5 one (NTO)metalcomplexeshavemanyspecialstructuresandsomepotentialusesinammunition .1 4 Wepreviouslypreparedanddeterminedthecrystalstructureofitsmagnesiumcomplex ,5andinthispaper ,wediscusseditsthermalbehaviorbyDSCandTG/DTGtechniquesandstudieditsnon isothermalkineticsbythemeansoftheKissingermethod ,theOzawamethod ,thedifferentialmethodandtheintegralmethod .ExperimentalSample[Mg(H2 O) 6 ](NTO) 2 ·2H2 Owaspreparedasfollows :AcalculatedamountofMg(OH…     

过渡金属与邻香兰素氨基酸类Schiff碱配合物合成及其性质的研究

本文合成了邻香兰素白氨酸合Cu(Ⅱ) 1, Ni(Ⅱ) 2, 邻香兰素苯丙氨酸合Ni(Ⅱ) 3及邻香兰素丙氨酸合Zn(Ⅱ) 4四种配合物。对其组成、结构进行了分析表征, 研究了它们的热稳定性及非等温热分解动力学, 用微分和积分法进行分析, 推断了第一步热分解反应机理, 得到了热分解反应动力学方程此外, 还得到了配合物的热分解反应动力学补偿效应数学表达式。     

Gamma irradiation effects on the kinetics of the non-isothermal decomposition of potassium nickel oxalate

The kinetics of the non-isothermal decomposition of potassium nickel(II) oxalate in air were studied for non-irradiated and irradiated crystals using thermogravimetric techniques. Analysis of kinetic data were performed using the direct differential method, the integral methods due to Coats-Redfern, Ozawa and a composite integral method. The results of the kinetic analysis of dynamic data and the effects of radiation were discussed and compared with those obtained under isothermal conditions.     

The Thermal Decomposition of Calcium Carbonate

The thermal decomposition reaction of calcium carbonate is a typical thermal decompo- sition reaction of the solid state. A great deal of studies on this reaction have been performed by previous investigators. This paper reports a procedure for estimating the non-isothermal kinetic parameters and the reaction mechanism of calcium carbonate.TG-DTG experiments were carried out on a LCT-1 model thermobalance and a WF-1 model differentiator with a TG-DTA-DTG simultaneous device. The size of…     

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 decomposition kinetics of M (mnt) (5-NO2-phen) (M=Co, Cu, Zn) complexes

Studies of the non-isothermal decomposition of M (mnt) (5-NO₂-phen) (M=Co^II, Cu^II, Zn^II) were carried out by thermogravimetry. The thermal decomposition mechanisms and associated kinetics have been investigated. The kinetic parameters were obtained from an analysis of the TG–DTG curves by integral and differential methods. The most probable kinetic model functions were suggested by comparison of the kinetic parameters. Mathematical expressions for the kinetic compensation effect were derived.     

TG Study of the Kinetic Parameters of Regeneration of Coked HZSM-5 Zeolite

A thermogravimetric method is proposed for study of the kinetic parameters of coked HZSM-5 zeolite regeneration. The technique, which makes use of integral thermogravimetric curves, was optimized by microprocessed integrated mathematical methods. The kinetic parameters obtained from the TG curves are the activation energy, the rate constants, the half-life times, and in particular the coke removal time as a function of temperature. The activation energy calculated by using the Flynn and Wall kinetic method was 81.4 kJ mol⁻¹. It was observed that, to remove 99% of the coke from the zeolite in a period of 1 h, it would be necessary to carry out thermo-oxidation at 748 K, with a dry air purge flow of 120 cm³ min⁻¹. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermal Decomposition Kinetics of Lead 2,4,6-Trinitroresorcinate Monohydrate

IntroductionLead 2 ,4,6- trinitroresorcinate monohydrate,Pb( TNR)· H2 O,has good detonating propertiesand is sensitive to flame.It can be used as initiat-ing agent,igniter powder or delay powder.Itspreparation,properties,crystal structure[1] andthermal behavior[2 ] have been reported.In the pre-sent paper,we will report its kinetic parametersand mechanism of thermal decomposition reactionstudied with TG- DTA,IR and DSC.This is quiteuseful in the evaluation of its thermal stability un-d…     

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.     

The Non‐Isothermal Decomposition Kinetics of NaNTO·H2O and the Relationship between its Structure and Properties

NaNTO·H₂O was prepared by mixing 3‐nitro‐1,2,4‐triazol‐5‐one (NTO) aqueous solution and sodium hydroxide aqueous solution. Its thermal decomposition and kinetics were studied under non‐isothermal conditions by DSC and TG/DTG methods. The kinetic parameters were obtained from analysis of the DSC and TG/DTG curves by the Kissinger method, the Ozawa method, the differential method and the integral method. The most probable mechanism function for the thermal decomposition of the first stage was suggested by comparing the kinetic parameters. The critical temperature of thermal explosion (T_b) was 240.93 °C. The theoretical investigation on the structure unit of the title compound was carried out by DFT‐B3LYP/CEP‐31G methods; atomic net charges and the population analysis were discussed.     

地开石热分解过程及非等温动力学研究

Fourier-transform infrared emission spectroscopy was used to study the dehydroxylation behavior of the thermal decomposition of dickite from Chenxi, Hunan Province, China. Dehydroxylation of dickite was followed by a loss of intensity of the 3620.73, 3695.34 cm-1 OH-stretching bands and 916.06, 1009.33 cm-1 OH bending bands. The thermal decomposition was investigated by thermogravimetric analysis (TGA). A good agreement is found with TG curves of dickite and the mass loss is 13.7% (close to the theoretical value). The non-isothermal kinetics of the thermal decomposition of dickite was studied in TG-DTG curves over the temperature range from 298 K to 1123 K by thermogravimetry and differential thermal analysis in air. Mathematical analysis of TG-DTG data using the integral methods (Coats-Redfern equation, HM equation, MKN equation) and differential method (Achar equation) shows that the thermal decomposition of dickite accords F2 mechanism. The kinetic parameters such as the activation energy (E=131.62 kJ/mol), pre-exponential factor (A=108.30 s-1) and reaction order (n=2.1) are reported. The Ozawa method was used to analyse the activation energy of the same sample at different heating rate and gave 133.07 kJ/mol. The kinetic parameters calculated from different equation are rather close to each other.     

Thermal decomposition of barium(II) tetraphenylborate

Barium(II) tetraphenylborate, Ba(Bph₄))₂·4H₂O was prepared, and its decomposition mechanism was studied by means of TG and DTA. The products of thermal decomposition were examined by means of gas chromatography and chemical methods. A kinetic analysis of the first stage of thermal decomposition was made on the basis of TG and DTG curves and kinetic parameters were obtained from an analysis of the TG and DTG curves using integral and differential methods. The most probable kinetic function was suggested by comparison of kinetic parameters. A mathematical expression was derived for the kinetic compensation effect.     

邻香兰素L-甲硫氨酸Schiff碱二吡啶合锌(Ⅱ)配合物的合成、晶体结构和热分解动力学

X射线单晶结构分析结果表明: 标题化合物晶体-ZnVAL C~2~8H~3~0N~4O~4SZn属正交晶系, 空间群P2~12~12~1, a=0.9259(2), b=1.4409(4), c=2.1046(8)nm, Z=4,最终因子Rw=0.080。利用热重分析对配合物第一步热分解过程进行了非等温动力学研究, 探讨了反应的可能机理。得到了其相应的动力学参数以及非等温动力学方程。