The kinetic equation under non-isothermal conditions

Data generated from selected model expressions for solid-state kinetics have been analysed in terms of expressions of closely-related form to test distinguishability of the models on which the expressions are based. Random errors have then been introduced into these data and the data have been re-analyzed in terms of the original and closely-related expressions. As is to be expected, introduction of errors decreases distinguishability further and estimates have been made of the accuracy of measurement of the extent of reaction, α, required, the most suitable ranges of α to use, from plots of residuals, and the acceptable levels of various statistical parameters, for reliable distinction between alternative models.     

Determination of the kinetic parameters from non-isothermal measurements with a general temperature program

This paper deals with a new method for the evaluation of the kinetic parameters from thermogravimetric measurements with a general temperature program. The procedure assumes the use of a computer or calculator. In principle, it is an integral method with two variants. The kinetic parameters can be determined from a single and/or from two general temperature programs. This method is free of the shortcomings that the existing method has, i.e. the self-heating and/or self-cooling, resulting in errors in measurements and the limitation of the weight of sample. The two variants of the submitted method have been tested by evaluation of the experimental data of the thermal decomposition of CaCO₂.     

Computation in kinetics, IV. Regression estimation of Arrhenius equation parameters from non-isothermal kinetic data

Computer method for evaluation of Arrhenius equation parameters from non-isothermal kinetic data is offered in KILET program. Changes of temperature can be linear, hyperbolic or of any smooth function which could be expressed by a polynomial of up to 4th degree. The method is demonstrated on examples of linear and hyperbolic changes for simulated and experimental data. The advantage of non-isothermal experiment over isothermal one for evaluation of kinetic solution data is stressed.

---

KILET. , , 4- . . .

     

A computer program system for kinetic analysis of non-isothermal thermogravimetric data: I. Data acquisition and preparation for kinetic analysis

FORTRAN software is described which enables the generation of rate of weight change data (DTG) from percentage weight change measurements (TG), obtained under non-isothermal conditions. The program also transposes this information into the dimensionless extent and rate of reaction at unit temperature intervals by means of a cubic spline interpolation. A simple search routine identifies all DTG spikes in the thermogravimetric record, and the temperature and extent of reaction at which the rate attains its maximum value. This total information serves as input data for the kinetic analysis software to be discussed in part II of this communication. An example of the application of this program to the pyrolysis of bituminous coal is presented.     

Applicability of one-stage chemical reaction kinetic equation to describe non-isothermal destruction processes

The applicability of the traditional kinetic power equation to describe the thermal destruction of solids, and in particular polymers, is discussed. It is shown that in the majority of cases the use of such an equation is reasonable, even though the true mechanism of the process under study is either obscure or so complex that it cannot be analytically described in detail. In such cases the effective rather than the true kinetic parameters are obtained and provide certain useful information on the process. The fixed conversion temperature dependence on the heating rate is analyzed with examples on the model process and the thermal degradation of an epoxy binder.     

On the kinetic parameters from non-isothermal data: mathematical considerations

The kinetic parameters determination of the crystallization of a disordered solid solution subjected to non-isothermal treatments is often considered using a large variety of physical models. Some authors propose the use of Johnson-Mehl-Avrami's classic expression which corresponds to both isothermal and non-isothermal kinetic parameters, according to experimental results.In this paper we carry out research, starting from the generalized model most widely used by the non-isothermal problem, in which we prove the validity of Johnson-Mehl-Avrami's expression.     

A computer program system for kinetic analysis of non-isothermal thermogravimetric data: II. Generalized kinetic analysis and application to coal pyrolysis

A FORTRAN program is presented which enables the kinetic analysis of extent and rate of reaction data resulting from transposed experimental TG/DTG data obtained under non-isothermal conditions. This software allows one to perform Arrhenius, Friedman and Kissinger analyses for up to nine different solid-state rate-controlling reactions, including nth order, Avrami-Erofeev, phase boundary movement and diffusional models. Data from an investigation of the pyrolysis of a bituminous coal serve as an example of the application of the program.     

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.     

Analysis of kinetic data by Johnson-Mehl equation

Johnson-Mehl equation is written as d/dt=k ⁿ t ^n–1 (1–) where is the degree of reaction,t time andn a constant. Use of this equation in kinetic analysis present problems because of the presence of a t term on the right hand side. The equation is not a true kinetic equation andk is not a true rate constant.This paper presents a brief discussion on the use of this equation as such or in a modified form and also indicates the proper procedure for evaluating kinetic parameters correctly. Some experimental data on the reduction of Fe₂O₃ to Fe₃O₄ have been used to test the mathematical procedure proposed. This reaction is known to follow the typical trend described by Johnson-Mehl equation.

---

Zusammenfassung Die Johnson-Mehl-Beziehung lautet:d/dt=k ⁿ t ^n–1(1–) mit der Reaktionskoordinate, der Zeitt und der Konstanten. Eine Anwendung dieser Gleichung in der kinetischen Analyse verursacht Probleme, da auf der rechten Seite der Gleichung ein t-haltiger Ausdruck steht. Die Gleichung ist keine wirkliche kinetische Gleichung undk ist keine wahre Geschwindigkeitskonstante.Diese Arbeit beschreibt eine kurze Diskussion der Anwendung dieser Gleichung in dieser oder einer modifizierten Form und beschreibt, wie korrekte kinetische Parameter erhalten werden können. Zum Testen des vorgeschlagenen mathematischen Verfahrens wurden einige experimentelle Daten der Reduktion von Fe₂O₃ zu Fe₃O₄ benutz. Diese Reaktion ist bekannt, dem typischen, durch die Johnson-Mehl-Gleichung beschriebenem Trend zu folgen.

---

---

Dr. S. B. Sarkar wishes to acknowledge the financial support of the Commonwealth Commission (U.K.) and the experimental facilities provided by the Imperial College of Science and Technology, London U.K.     

Remarks on the relationship between isothermal and non-isothermal kinetic results. A new method for the kinetic analysis of isothermal data

Addition of 10mg/l of the haevy metal ions Zn⁺⁺, Cu⁺⁺, Pb⁺⁺, Cd⁺⁺ and Cr⁺⁺ to nongrowing E.coli cells shows a decrease in heat production by aerobic and anaerobic glycolysis up to 80 %. The heat production of cells incubated without glucose was decreased drastically too, after addition of 10mg/l of these heavy metal ions.The pattern of heat released during active transport of α MG was influenced by these haevy metal ions in a way, that there was a decrease in maximum heat flow, whereas the total heat production seemed to be constant.After increasing the metal ion concentration up to 100mg/l no endogenous heat production could be detected. The inhibition of heat production after addition of glucose was higher than 90 % in this case and there was a strong inhibition in α MG uptake.The results of these investigations indicate that the basic action of all tested metal ions is the energy metabolism and not the transport as stated earlier.     

Discrimination of the kinetic model of overlapping solid-state reactions from non-isothermal data

A method has been developed that allows the deconvolution of up to 15 overlapping solidstate reactions without previous assumptions. Both the kinetic parameters and the reaction mechanisms fitted by the unit reactions can be determined from a series of non-isothermal experiments carried out at different heating rates.

---

Zusammenfassung Es wurde eine methode zur Dekonvolution von bis zu 15 einander überlappenden Festphasenreaktionen entwickelt, die keinerlei vorherige Annahmen notwendig macht. Mittels einer Reihe nichtisothermer Experimente mit unterschiedlichen Aufheizgeschwindigkeiten können sowohl die kinetischen Parameter als auch der Reaktionsmechanismus der Teilreaktionen bestimmt werden.

---

, 15. .

     

The correctional kinetic equation for the peak temperature in the differential thermal analysis

The peak temperature (T _p) and different temperature (ΔT) are the basic information in the differential thermal analysis (DTA). Considering the kinetic relation and the heat equilibrium in DTA, a correctional differential kinetic equation (containing T _p and ΔT parameter) is proposed. In the dehydration reaction of CaC₂O₄·H₂O, the activation energy calculated from the new equation showed some smaller than that from Kissinger equation, but some bigger than that from Piloyan equation.     

Differential thermometric kinetic analysis. a new general technique of interpreting the data obtained in kinetic analyses

The concentration-time data obtained in kinetic analyses may be easily and conveniently interpreted by multiparametric curve-fitting. A new technique of kinetic analysis, in which the overall extent of reaction is monitored by following the variation with time of the difference between the temperature of a reaction mixture and that of a reference solution, is described. Both these techniques are illustrated with-data obtained in oximations of mixtures of propanal-and cyclohexanone. The results confirm the existence of the synergic effect reported by Siggia and Hanna.     

Exponential temperature change in thermal analysis at non-isothermal kinetics

The applying of exponential temperature programming: dT/dt=T orT=T ₀ e ^t in thermal analysis at non-isothermal kinetics is discussed. An approach for the integration of the temperature integral is presented.     

Devolatilization non-isothermal kinetic analysis of agricultural stalks and application of TG-FT/IR analysis

Devolatilization behavior of several types of agricultural stalks (sunflower, rice, corn, and wheat) was studied using thermogravimetric system (TG) under nitrogen atmosphere at different heating rates (10, 15, and 20 °C min^-1). Coats&Redfern, Horowitz&Metzger, and Arrhenius non-isothermal kinetic models were applied to calculate the devolatilization kinetic parameters and the devolatilization rate equations have been established. In addition, the kinetic compensation effect (KCE) has also been used to correlate pre-exponential factor (k _o) with activation energy (E _a) and an existence of the KCE is accepted. TG-FT/IR analyses were applied of the different stalks and FT/IR stack plot used to analyze the devolatilization gas products (CO₂, CH₄, HCOOH, CH₃OH). Infrared vibrational frequencies, micro structure and crystallinity of stalks were investigated by Fourier transform infrared spectroscopy (FT/IR), scanning electron microscope (SEM), and X-ray diffraction analysis (XRD), respectively.