Philosophy of non-isothermal kinetics

The most debatable and discrepant viewpoints of non-isothermal kinetics are discussed in the form of twelve questions and answers. The reputation of non-isothermal kinetics when carried out by thermoanalysts; the consequences of simplified concepts transferred from the kinetics of homogeneous reactions; the physical meaning of basic kinetic parameters in solid-state processes; the kinetic compensative effect and interdependence of kinetic parameters using the Arrhenius rate constant; the mutual usefulness of differential and integral methods of kinetic data evaluation; their accuracy and correctness; the reliability of DTA measurements; non-isothermal versus isothermal investigations; equilibrium and kinetic data and their mutual effect; the extended discussion initiated by MacCallum and Tanner; non-isothermal data publication policy; and finally the use of computers.

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Zusammenfassung In der Form von zwölf Fragen und Antworten werden die meist umstrittenen und auseinandergehenden Aspekte der nicht-isothermen Kinetik diskutiert. Insbesondere das Ansehen der nicht-isothermen Kinetik bei Durchführung durch Thermoanalytiker, die Konsequenzen der vereinfachten von der Kinetik homogener Reaktionen übertragenen Konzepte, die physikalische Bedeutung der kinetischen Grundparameter in Festphasenprozessen, der kinetische Kompensationseffekt und die gegenseitige Abhängigkeit der kinetischen Parameter bei Anwendung der Geschwindigkeitskonstante nach Arrhenius, die gegenseitige Nützlichkeit der Differential- und Integralmethoden der Auswertung kinetischer Daten, ihre Genauigkeit und Richtigkeit, die Zuverlässigkeit der DTA-Messungen, nichtisotherme gegenüber von isothermen Untersuchungen, Gleichgewichts- und kinetische Daten und ihre gegenseitige Wirkung, die Ausbreitung der von MacCallum und Tanner initierten Diskussion Politik der Veröffentlichung nicht-isothermer Angaben und, endlich, Einsatz und Hilfeleistung der Computer.

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Résumé Les aspects les plus discutables de la cinétique non-isotherme sont traités sous forme de douze questions et réponses, en particulier: réputation de la cinétique non-isotherme appliquée par les thermoanalystes, conséquences des concepts simplifiés déduits de la cinétique des réactions en phase homogène, signification physique des paramètres cinétiques fondamentaux dans les processus en phase solide, effet de compensation cinétique et interdépendance des paramètres cinétiques lors de l'utilisation de la constante de vitesse d'Arrhenius, utilité mutuelle des méthodes différentielles et intégrales d'évaluation des données cinétiques, leur exactitude et leur degré de justesse, fiabilité des mesures par ATD, études non-isothermes vis-à-vis des méthodes isothermes, données à l'équilibre et en régime dynamique et leurs effets mutuels, extension de la discussion engagée par MacCallum et Tanner, politique de publication des données non-isothermes et finalement utilisation des ordinateurs et aide apportée par ceux-ci.

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Compensation effect in heterogeneous non-isothermal kinetics

A number of 1145 sets of kinetic parameters derived in our earlier papers from TG curves have been worked up. The apparent activation energy and pre-exponential factor values have been found to obey a linear compensation law (isokinetic relation) if the thermal decomposition begins in the same temperature interval, irrespective of the nature of the chemical reaction. The isokinetic temperatureT _i has been found to be very close to the mean value of the temperaturesT _0.1 at which the conversion becomes equal to 0.1 and atT _i the rate constant has been found to be approximately equal to 10^?3s^?1 in allT _0.1 intervals investigated. It is concluded that the kinetic compensation effect observed in heterogeneous non isothermal TG kinetics is not a true one.     

A solution of the exponential integral in the non-isothermal kinetics for linear heating

A simple and satisfactorily accurate solution of the exponential integral in the nonisothermal kinetic equation for linear heating is proposed: $$\mathop \smallint \limits_0^T e^{ - E/RT} dT = \frac{{RT^2 }}{{E + 2RT}}e^{ - E/RT} $$      

非等温液-固相酯化反应动力学研究

根据稀土盐催化剂催化的乙二醇单乙醚醋酸酯的液相合成反应的特点, 导出了非等温变体积条件下的反应速率方程, 并提出了利用一条实验曲线, 计算动力学参数的动态方法, 以此为基础, 对不同实验条件下的多组实验数据进行了动力学处理。大量计算结果表明, 该反应服从二级动力学模型, 表观反应活化能为213.59kJ·mol^-^1, 指前因子为5.903×10^2^5dm^3·mol^-^1·min^-^1。计算结果的合理性及一致性, 进一步证明了动态原理用于液-固相反应体系的动力学研究是简便可行的。     

Criterion of the existence of compensation relationship for non-isothermal kinetics

If, for a series of similar-type chemical transformations in non-isothermal kinetics, identical or closely similar values of T _cr are observed in the equation 1/T _cr =1/T _si + + (R/E _i)·ln (E _i q/RT _si ² the existence of the compensation relationship lnA _i= =E _i/RT _cr may regularly be assumed.     

3,4-二硝基吡唑热分解及非等温动力学

采用TG-DSC综合热分析的方法,对3,4-二硝基吡唑(DNP)的热分解和非等温动力学进行了研究。结果表明DNP的热分解分两阶段进行,并且在升温速率达到15K/min时才能明显区分。分别采用Archar微分法和Coats-Redfen积分法计算了DNP第一阶段热分解反应动力学参数:Ea=91.6kJ.mol-1,lnA=42.7s-1。最可能的DNP热分解机理为随机成核和随后生长机理,符合动力学机理函数Avrami-Erofeev方程,n=3。     

Thermal decomposition and non-isothermal decomposition kinetics of carbamazepine

The thermal stability and kinetics of isothermal decomposition of carbamazepine were studied under isothermal conditions by thermogravimetry (TGA) and differential scanning calorimetry (DSC) at three heating rates. Particularly, transformation of crystal forms occurs at 153.75°C. The activation energy of this thermal decomposition process was calculated from the analysis of TG curves by Flynn-Wall-Ozawa, Doyle, distributed activation energy model, ?atava-?esták and Kissinger methods. There were two different stages of thermal decomposition process. For the first stage, E and logA [s^?1] were determined to be 42.51 kJ mol^?1 and 3.45, respectively. In the second stage, E and logA [s^?1] were 47.75 kJ mol^?1 and 3.80. The mechanism of thermal decomposition was Avrami-Erofeev (the reaction order, n = 1/3), with integral form G(α) = [?ln(1 ? α)]^1/3 (α = ～0.1–0.8) in the first stage and Avrami-Erofeev (the reaction order, n = 1) with integral form G(α) = ?ln(1 ? α) (α = ～0.9–0.99) in the second stage. Moreover, ΔH ^≠, ΔS ^≠, ΔG ^≠ values were 37.84 kJ mol^?1, ?192.41 J mol^?1 K^?1, 146.32 kJ mol^?1 and 42.68 kJ mol^?1, ?186.41 J mol^?1 K^?1, 156.26 kJ mol^?1 for the first and second stage, respectively.     

Isothermal and non-isothermal pyrolysis kinetics of Kapton polyimide

The kinetics involved in the thermal decomposition of Kapton^® polyimide 100HN under nitrogen atmosphere were studied by applying various fitting techniques to the isothermal and non-isothermal gravimetric data. The correlation of the reaction mechanism fitting, the analytical model fitting and the isoconversional method to these data was examined in relation to the kinetic parameters and the kinetic predictions. The mechanisms for solid-state reactions fit the isothermal data very well but result in highly uncertain values for the kinetic parameters when applied to the non-isothermal data. Isoconversional methods show that the apparent activation energy depends on the extent of conversion but do not provide information for the reaction order and the pre-exponential factor. Three single heating-rate analytical models by Coats-Redfern, MacCallum-Tanner and van Krevelen were analysed using the non-isothermal data. A multi-heating rate model is proposed and its validity is compared to the single-heating rate models on the basis of kinetic predictions.     

碱式碳酸锌非等温热分解动力学研究

采用TG-DTA曲线分析研究了碱式碳酸锌在氮气气氛中的热分解反应动力学,利用Doyle-Ozawa法和Kissinger法对碱式碳酸锌非等温热分解动力学数据进行了分析,同时运用Satava-Sestak法研究了碱式碳酸锌的热分解机理.结果表明,碱式碳酸锌的热分解反应服从随机成核和随后生长机理.     

A simple method of evaluating non-isothermal crystallization kinetics in multicomponent polymer systems

A new simple method of evaluating non-isothermal crystallization kinetics is proposed. The procedure based on mathematical treatment of DSC cumulative crystallization curves at their inflection point provides three kinetic parameters: temperature of start of crystallization (T_s), temperature of maximum crystallization rate (T_i) and numerical value of the maximum crystallization rate (s_i), and also final crystallinity after cooling (CR_c). The method is demonstrated on the system poly(ɛ-caprolactone)/poly(lactic acid)/clay C15 and related microfibrillar composite. The method provides the values of T_s and T_i with standard deviation σ = 0.3 and 0.4 °C, respectively. The coefficient of variation v of s_i and CR_c is 5.8 and 1.5%, respectively. The proposed method does not refer to any crystallization model and does not require exact determination of the starting time. It is particularly useful for characterizing a series of samples derived by modification of the neat polymer.     

Derivation of the Kissinger equation for non-isothermal glass transition peaks

A brief derivation of the Kissinger’s equation for analysis of experimental data of non-isothermal glass transition peaks based on the free volume model is given. This equation was applied successfully to Cu_0.3(SSe₂₀)_0.7 chalcogenide glass for different heating rates. For granted this model, the obtained glass transition activation energy, E _g must be constant throughout the whole glass transition temperature range. This required that T _g to be determined for three characteristic temperature points for each DSC curve.     

An approximation to the linear heating rate in non-isothermal kinetics

A near-linear representation of the linear heating rate is presented which converts the exponential integral into an integrable form and allows a simple determination of the activation energy to high accuracy.     

On the dependence of kinetic parameters and functions in non-isothermal kinetics

The approaches to overcoming local ambiguity due to the dependence of the kinetic equation parameters are considered. The application of the mathematical apparatus of the Jacobi matrices enables one to determine the number of both independent kinetic parameters and kinetic functions used to describe a process. No more than five parameters in the Šestak-Berggren equation and only some kinetic functions are found to possess independence.