Dependence of the frequency factor on the temperature: a new integral method of nonisothermal kinetic analysis

A new integral method of nonisothermal kinetic analysis has been developed with the dependence of the frequency factor on the temperature (A = A ₀ T ^m ). The new integral method is obtained from the newly proposed approximation for the general temperature integral, which is more accurate than the other existed approximations. For applications, nonisothermal thermoanalytical data obtained by theoretical simulation have been processed. The results have shown that the newly proposed integral method is an ideal solution for the evaluation of kinetic parameters from nonisothermal thermoanalytical data with the frequency factor dependent the temperature.     

Kinetic analysis of thermogravimetric data obtained under linear temperature programming—a method based on calculations of the temperature integral by interpolation

A new technique, called interpolation method, with general application in the kinetic analysis of processes studied by thermogravimetry (TG) under linear temperature programming is developed. It is based on the linear relationship, with slope 1, between log g() and log I(γ, θ) for the appropriate kinetic function, where I(γ, θ) is the normalized temperature integral, θ the normalized temperature (θ=T/T₀) and γ a dimensionless activation energy (γ=E/RT₀). Values of log I(γ, θ) are calculated by linear interpolations in a pre-built table. This method can easily be programmed and implemented in a personal computer, where the results (kinetic parameters and quality of regressions for the kinetic functions considered) are typically obtained in a very short time. The method is validated by analyzing different simulated thermogravimetric curves and comparing the results with those determined with some classic methods taken from the literature. In addition, the results are compared with the values obtained by a similar method, also developed and explained in this paper, which involves the evaluation of all the values of the temperature integral by numerical integration, therefore, demanding a much larger calculation time. The interpolation method is found to be more accurate than other published methods, particularly in the case of thermogravimetric curves corresponding to processes with low activation energies. The results obtained are always similar to those determined by the integration method, which is taken as reference. Application of the technique to experimental data for various types of reactions shows that the results are in agreement with the published parameters and kinetic laws.     

Thermal degradation behavior of radiation synthesized polydiallyldimethylammonium chloride

Thermogravimetric analysis (TGA) and differential scanning calorimetric (DSC) studies were carried out on gamma radiation synthesized polydiallyldimethylammonium chloride (PDADMAC). The polymer was found to undergo thermal degradation in two stages. The first stage showed a weight loss of 33% and the second stage showed a weight loss of 67%. The DSC thermogram shows two endothermic peaks corresponding to the two stages in the TG thermogram and the experimental enthalpy change associated with the first and second stages were 650 J g⁻¹ and 129.5 J g⁻¹, respectively. The nth-order kinetic parameters (order of the reaction, activation energy and the pre-exponential factor) were determined from a single dynamic DSC or thermogravimetric (TG) thermogram by the method of least square. Theoretical TG/differential thermogravimetric (DTG) and DSC thermograms derived from the calculated kinetic parameters were in good agreement with the experimental ones at the heating rate employed. However, the kinetic parameters determined using TG and DSC were different. This leads to the conclusion that the degradation mechanism could be complicated and may consists of a number of parallel or consecutive reactions. The glass transition temperature (T_g) of the polymer was found to be around 150 °C depending on the test method employed.     

A Computer Program for the Evaluation of Non-isothermal Kinetic Parameters

A program for the evaluation of non-isothermal kinetic parameters is presented. The program allows evaluation of the kinetic parameters under constant heating rate or constant reaction rate conditions. The simulation of temperature vs. conversion curves is also possible. A regression method is included, which allows a discrimination between various conversion functions and also evaluation of the activation parameters. The program was tested with various simulated decomposition curves and the non-isothermal decomposition curves of calcium oxalate. The program is written in Visual BASIC 4.0 and can be run under Windows 95 ©.     

利用模式搜索法求取新的温度积分近似式

利用模式搜索法求取了一个新的温度积分近似式,给出了相应的估算动力学参数的方程。新的温度积分近似式根据数值计算结果得到,可靠性高。讨论了新的近似式计算值与温度积分数值积分结果的偏差。与其它近似式相比,新的温度积分近似式的表达式简单,精确度更高,非常适合非等温过程的动力学参数的计算。     

Analysis of DTA curves and calculation of kinetic data using computer technique

Principles of two computer programs useful for the evaluation of heterogeneous kinetics are described.The first program ALANTA allows to obtain the non-isothermal kinetic curve from the shape of general DTA peak using the DTA-equation derived elsewhere¹.The second program SQUEST determines the kinetic mechanism which is the most appropriate to a given non-isothermal kinetic curve and evaluates the corresponding kinetic parameters. The program decides between 19 kinetic models and uses both integral and differential methods of evaluation.     

Kinetic analysis of derivative curves in thermal analysis

Two methods of obtaining kinetic parameters from derivative thermoanalytical curves are proposed. The methods are based on the general form of kinetic formulae and are applicable to general types of reactions governed by a single activation energy. One method utilizes the linear relation between peak temperature and heating rate in order to estimate the activation energy, and only the information of the rate of conversion versus the temperature is necessary. The other method needs the information of both the conversion and the rate of conversion versus the temperature, and the Arrhenius plot is made for an assumed kinetic mechanism.

     

Assay and Kinetic Studies on the Enzymatic Proteolysis with Ninhydrin Reagent

A method using ninhydrin reagent for proteolytic activity measurement and kinetic studies with protein or modified protein as substrate was explored. As the reagent is specific for amino group, quantitative expression can be made with the number of peptide bonds cleaved. The sensitivity of the method made it possible for the determination of various kinetic parameters such as K_m, V_max and K_cat with the measurement of initial velocity. As an example, these quantities were determined for pancreas protease with casein and N,N-dimethylcasein as substrates. This study made clear the possibility of using a common substrate of proteolytic enzymes for kinetic studies and a general reference for activity expression. By introducing the use of initial velocity in the kinetic studies of proteolysis with protein as the substrate, this study also makes clear that the kinetics of the enzymatic proteolysis very well fits the Michaelis-Menten law instead of the Schütz law.     

The thermal stability of chalcogenide glasses

Crystallization processes of Ge_xS_1-x (0.322≤x≤0.44) glasses have been studied by thermal analysis and a new simple method of kinetic analysis is proposed. This method allows the definition of an appropriate model characterizing the crystallization process of glass, as well as calculation of reliable kinetic parameters. Results of kinetic analysis allow definition of a thermal stability criterion which has a general applicability for any glass-forming system. ICTA Young Scientist Award presentation     

Combined kinetic analysis of solid-state reactions: The integral method (ICKA)

In this work, we propose the first Integral method for the Combined Kinetic Analysis (ICKA) of solid-state reactions typically performed in a thermogravimetric analyzer. The ICKA method prevents the systematic inaccuracies inherent to all the differential methods, including the standard CKA method. Two main achievements have been made for implementing the method: (1) the most accurate approximation for the general temperature integral yet developed, and (2) a general integral form of the kinetic model of the type g (α) = (abcZ)⁻¹ [1 − (1 − α^a)^b]^c, where Z is a parameter evaluated together with the preexponential factor and a, b, and c are fitting parameters. This expression allows any known kinetic model to be exactly or very closely reproduced. Together, the two developments yield an equation for the conversion, α, that has been successfully fitted to simulated conversion values of single-step reaction processes following different kinetic models. The curve fitting resulted in the same values of the kinetic and model parameters as those from which the simulated conversion curves were originally built, proving the validity of the ICKA method.     

Peritektische Zersetzung von YBa2Cu3O7−x

During the heating of YBCO a peritectic reaction takes place at 1020C, which can be described by: 2YBa₂Cu₃O_7–xY₂BaCuO₅+L+(1-2x)/2O₂ (1) whereL = 3BaCuO₂ +2CuO is a fluid with limited amount of yttrium.It has been reported, that many parameters can influence the reaction. From one side not only the starting size of grains but also the heating rate have an influence on the resulting Y₂BaCuO₅-phase. From the other side, there is a change of the peritectical temperature caused by changing of the partial pressure of O₂ and the presence of parasitic phase.From general kinetic consideration one can draw the conclusion, that different mechanisms (nucleation, phase-boundary reaction and diffusion) can control the reaction.Using DTA/TG measurements, the peritectic reaction has been examined. Classical kinetic methods (Kissinger and Friedman) has been used. The Friedman method has given the dependence of the activation energy from reaction degree. This suggests many steps reactions. The dependence of the DTA-peaks from the heat rate suggest a parallel steps of reaction. This assumption can be motivated by evaluation of free O₂, one solid and liquid phase formation. Amount of this phases depends on the heating rate. Additionally X-ray and microscopic methods has been used. In this way was shown, that the perovskit structure is stable up to peritectical temperature and than is dramatically destroyed. From microscopic observations has been got information about shape and size of solid phase and it's creation as a function of temperature, time and starting grain size.

Die Arbeit wurde BMBF gefördert und durch Land NRW unterschtützt.     

Quantum-instanton evaluation of the kinetic isotope effects

A general quantum-mechanical method for computing kinetic isotope effects is presented. The method is based on the quantum-instanton approximation for the rate constant and on the path-integral Metropolis-Monte Carlo evaluation of the Boltzmann operator matrix elements. It computes the kinetic isotope effect directly, using a thermodynamic integration with respect to the mass of the isotope, thus avoiding the more computationally expensive process of computing the individual rate constants. The method should be more accurate than variational transition-state theories or the semiclassical instanton method since it does not assume a single tunneling path and does not use a semiclassical approximation of the Boltzmann operator. While the general Monte Carlo implementation makes the method accessible to systems with a large number of atoms, we present numerical results for the Eckart barrier and for the collinear and full three-dimensional isotope variants of the hydrogen exchange reaction H + H2 --> H2 + H. In all seven test cases, for temperatures between 250 and 600 K, the error of the quantum instanton approximation for the kinetic isotope effects is less than approximately 10%.     

DSC Analysis of the Induction Period in the Vulcanisation of Rubber Compounds

Vulcanisation of rubber compounds was studied by DSC under isothermal and non-isothermal conditions. The parameters of an Arrhenius-like equation describing the temperature dependence of induction period have been obtained both from isothermal and non-isothermal measurements. A new method for obtaining the kinetic parameters from non-isothermal measurements, based on the dependence of onset temperature of vulcanisation peak on heating rate, is presented. Also, a procedure for the evaluation of temperature difference between the furnace and sample is proposed. It has been shown that the treatment of non-isothermal DSC measurements gives the kinetic parameters free of systematic errors. The new method can also be used for studying other reactions exhibiting the induction period. This revised version was published online in August 2006 with corrections to the Cover Date.     

Description of the shape of thermoanalytical curves : Part 3. A Method for estimating kinetic constants from parameters characterizing peak shape

The relationships between empirical parameters characterizing the shape of thermo-analytical curves and the constants of the kinetic equation, dα/dt = A exp (?E/RT)(1 ? α)ⁿ, are studied. A procedure is developed for the estimation of the three constants of this equation from the empirical parameters. The efficiency of this method is compared to that of model fitting. In evaluation of the confidence intervals of estimated constants and in the case of identification, least-squares (or similar) fitting is shown to be inferior because of its low sensitivity to properties other than the position of the peak along the temperature axis. This lack of sensitivity may be a major cause of the apparent kinetic compensation effect often encountered in the field of thermal analysis.     

Application of the Pseudo-Inverse Matrix Method in Non-Isothermal Kinetic Analysis

A method is proposed for evaluation of the activation parameters for reactions which occur under non-isothermal conditions. This method can discriminate between possible differential conversion functions. The proposed method, which was coded into a software package available to the scientific community, is designed to solve an overdetermined systems of equations: da_i/dt=k(T_i)f(a_i) where i equations are to be considered (i can be the number of experimental points). Solution of this overdetermined system with a pseudo-inverse matrix method furnishes the activation parameters and the parameters of the conversion function f(a). Some examples of application of this method in non-isothermal kinetic analysis are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Improved Iterative Version of the Coats-Redfern Method to Evaluate Non-Isothermal Kinetic Parameters

An improved version of the Coats-Redfern method of evaluating non-isothermal kinetic parameters is presented. The Coats-Redfern approximation of the temperature integral is replaced by a third-degree rational approximation, which is much more accurate. The kinetic parameters are evaluated iteratively by linear regression and, besides the correlation coefficient, the F test is suggested as a supplementary statistical criterion for selecting the most probable mechanism function. For applications, both non-isothermal data obtained by theoretical simulation and experimental data taken from the literature for the non-isothermal dehydration of Mg(OH)₂ have been processed.This revised version was published online in November 2005 with corrections to the Cover Date.     

2,4-二硝基甲苯热解自催化特性鉴别及其热解动力学

为研究2,4-二硝基甲苯(2,4-DNT)的热危险性及其分解反应的特征, 利用差示扫描量热仪(DSC)对该物质进行了动态扫描测试, 得到其起始分解温度T₀范围为272.4-303.5℃, 分解热ΔH_d约为2.22 kJ·g^-1. 在此基础上, 采用瑞士安全技术与保障研究所提出的快速鉴别法(瑞士方法)及数值模拟技术, 对其分解反应的特性参数进行了推算, 结果表明其分解具有自催化性. 采用Malek法分析了该物质分解反应的最概然机理函数并得出了相关动力学参数, 表明其分解具有自催化性且符合Sestak-Berggren 双参数自催化模型(SB模型), 这与瑞士方法所得结论一致. 采用等温DSC测试获得了该物质的‘钟形’热解曲线, 从而验证了两种方法的结论.     

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.     

The Use of Modulated Temperature Programs in Thermal Methods

Temperature modulation has long been used in various aspects of thermal methods. Historically, the principle areas of application have been the determination of kinetic parameters using variants of the temperature jump method and the measurement of heat capacity by AC calorimetry. More recently the introduction of temperature modulation in a variety of techniques has been used in combination with deconvolution algorithms to separate sample responses that are dependent on rate of change of temperature from those principally dependent on temperature. Finally, temperature modulation is important in the new field of micro-thermal analysis. This revised version was published online in July 2006 with corrections to the Cover Date.