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 ©.     

A computer method to determine the kinetic law of solid-state reactions from DSC curves

A computer program has been worked out to evaluate the activation energy, the Arrhenius pre-exponential factor and the mechanism of solid-state reactions from non-isothermal measurements. A univocal determination of the reaction mechanism is obtained by the simultaneous application of two selection criteria: (a) activation energy value by the Ozawa method; (b) degree of linearity in the <Satava method.A modification of the Rogers and Smith method was then used to obtain empirically complete agreement between kinetic expression and experimental results when the kinetic law has to be improved to account for a whole experimental curve.The accuracy of the computer method has been checked through a calibration of the program by means of 16 theoretical functions proposed by <Sesták.     

Non-isothermal depolymerisation kinetics of poly(ethylene oxide)

The depolymerisation of low molecular weight poly(ethylene oxide) (PEO) under mild conditions was studied using a linear temperature ramped non-isothermal technique and the results compared with those obtained from a conventional isothermal technique. The analysis of the non-isothermal kinetic (NIK) data was performed using an original computer program incorporating an algorithm that systematically minimizes the sum of the squares of the residuals between the experimental data and the calculated theoretical kinetic profile in order to extract the kinetic parameters. The results revealed that the depolymerisation of PEO proceeds in accordance with the Ekenstam model and follows the Arrhenius equation over the temperature range of ca. 40-130 °C. The NIK analysis resulted in a two-dimensional convergence to produce a unique solution set for the kinetic parameters of E_a = 89.4 kJ mol⁻¹ and A = 9.6 × 10⁶ h⁻¹. These data are consistent with the results obtained from the isothermal experiments. It is proposed that NIK analysis is a quick and reliable means of obtaining kinetic parameters relevant to lifetime predictions in polymers whose degradation behaviour can be considered to be close to ideal.     

Kinetics of Direct Reduction of Chrome Iron Ore

The kinetics of direct reduction of artificial chrome iron ore was studied by isothermal and non-isothermal methods. In the initial, middle and final periods, the reaction is controlled by nucleation and growth, a phase boundary reaction, and diffusion, respectively. In the main reaction region, the kinetic equation is 1–(1–)^1/3=kt and the apparent activation energy is 270 kJ mol^–1. The kinetic mechanisms found with the isothermal and non-isothermal methods do not differ, and the activation energy values are approximately the same. However, the non-isothermal method can demonstrate the kinetic process completely.This revised version was published online in November 2005 with corrections to the Cover Date.     

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.     

Thermal stability of pentoxifylline: active substance and tablets

Thermal analysis is a routine method in the solution of pharmaceuticals problems such as the control of raw materials, to the determination of purity, to the qualitative and quantitative analysis of drug formulation, tests of thermal stability and compatibility, the determination of kinetic parameters, etc. The evaluation of thermal stability in the solid state is mostly made by analyzing their decomposition under isothermal and non-isothermal conditions. The present work reports the study on the thermal behavior of pentoxifylline—active substance and tablets, respectively, the determination of the kinetic parameters for the decomposition process under non-isothermal conditions and in a nitrogen atmosphere at five heating rates: 2.5, 5, 7.5, 10 and 15 °C min^?1. For the determination of kinetic parameters from the TG/DTG curves, the following differential methods were utilized: Friedman isoconversional and Chang, respectively, integral methods: Flynn–Wall–Ozawa, Kissinger–Akahira–Sunose, Li–Tang, and Starink. Thermoanalytical curves showed that the active substance is thermally more stable than the tablets. The decrease in stability was attributed to the presence of excipients.     

Thermal behaviour of erythromycin-active substance and tablets

The application of thermal methods is of great importance in the solution of pharmaceutical problems, such as the control of raw materials, the determination of purity, the qualitative and quantitative analysis of drug formulation, tests of thermal stability and compatibility, the determination of kinetic parameters etc. The evaluation of thermal stability in the solid state is mostly made by analyzing their decomposition under isothermal and non-isothermal conditions. This study reports the study on the thermal behaviour of erythromycin-active substance and tablets, respectively, the determination of the kinetic parameters for the decomposition process under non-isothermal conditions. For the determination of kinetic parameters from the TG/DTG curves, were utilized the following methods: Friedman isoconversional, Flynn–Wall–Ozawa, Kissinger–Akahira–Sunose, Li–Tang, and Kissinger, respectively, a dynamic nitrogen atmosphere and different heating rates: 2.5, 5, 7.5, 10, and 15 °C min^?1. Thermoanalytical curves showed that the active substance is thermally more stable than the tablets and the values of activation energy indicate a considerable thermal stability of active substance. The decrease in stability was attributed to the presence of excipients.     

Synthesis,characterization and kinetics of the non-isothermal degradation of copper and cobalt adducts with ethyleneurea,ethylenethiourea and propyleneurea

Six adducts of general formula MCl₂·4L (M = Cu and Co; L = ethyleneurea, eu; ethylenethiourea, etu; and propyleneurea, pu) were prepared and characterized by elemental analysis, i.r. spectroscopy and by thermogravimetry (t.g.). Using the non-isothermal Coats–Redfern method, the kinetic parameters for the non-isothermal degradation of the adducts were calculated using thermogravimetric data. The i.r. results show that, for eu and pu adducts, coordination occurs through oxygen, whereas for etu nitrogen is the donor atom. All the adducts exhibited a single mass loss step in the t.g. curve, related to the release of ligand molecules. For eu, etu and pu adducts, the associated activation energies for the degradation process are: 36.4; 68.07 and 103.07 kJ mol^–1; 67.15; 80.86 and 121.06 kJ mol^–1 for copper and cobalt adducts, respectively.     

Isoconversional analysis of solid-state transformations

A key issue in kinetic analysis is the "prediction" of the evolution of a solid state transformation for a particular temperature program. Many methods have been proposed to calculate this evolution from kinetic parameters determined from non-isothermal isoconversional methods. In this study, we will review and compare the most accurate methods. We will then introduce a new method that provides an accurate prediction for an arbitrary temperature program.     

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.     

Die bestimmung kinetischer parameter endothermer zersetzungsreaktionen unter nicht-isothermen bedingungen

By using the kinetic parameters calculated from non-isothermal measurements according to Freeman and Carroll a computer programm is given, which permits the determination of the more probable reaction mechanism by use of 17 different kinetic equations. The computer programm includes the kinetic equation for chemical reaction, nucleation, phase boundary reaction and diffusion and can easily be extended to other equations. The evaluation of the experimental values by a distinct kinetic equation is quantitatively characterized by means of the correlation coefficient.The kinetic parameters are calculated on the basis of a regression analysis. By dividing the thermogravimetric curve in different reaction intervals a differential calculation is possible.Decomposition of CaCO₃, MgCO₃ and CaSO₄·2H₂O is discussed from the results of the computer calculation. It is seen that the kinetic parameters and the reaction mechanism are not constant during the reaction. Further experiments for a physical interpretation are being carried out.     

非等温TG- DTG法确定2,2'- 联吡啶- 对甲氧基苯甲酸铕(Ⅲ)热分解反应的机理函数和动力学参数

采用TG-DTG和DTA技术研究了2,2'-联吡啶-对甲氧基苯甲酸铕(Ⅲ)在静态空气中的非等温热分解过程及动力学,根据TG曲线确定了热分解过程中的中间产物及最终产物,运用微分法与积分法对非等温动力学数据进行分析,推断出第一步的动力学方程为dα/dt=Aexp(-E/RT)2(1-α)1/2.     

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.     

Study of oxidation properties and decomposition kinetics of three-dimensional (3-D) braided carbon fiber

The XRD, SEM, isothermal oxidation-weight loss and non-isothermal thermogravimetry (TG)-differential thermogravimetry (DTG) were used to study the oxidation properties and oxidation decomposition kinetics of three-dimensional (3-D) braided carbon fiber (abbreviated as fiber). The results showed that the non-isothermal oxidation process of fiber exhibited self-catalytic characteristic. The kinetic parameters and oxidation mechanism of fiber were studied through analyzing the TG and DTG data by differential and integral methods. The oxidation mechanism was random nucleation, the kinetic parameters were: lg A=10.299 min⁻¹; E_a=156.29 kJ mol⁻¹.     

Non-isothermal thermogravimetric pyrolysis kinetics of waste petroleum refinery sludge by isoconversional approach

Pyrolysis of petroleum refinery sludge has received global acclamation as a clean conversion technique for providing solution of sludge disposal as well as efficient resource utilization. This communication reports the kinetics study of pyrolysis of petroleum refinery sludge. Experiments were carried out by means of thermogravimetric analysis at different heating rates of 5, 10 and 20°C min⁻¹. The pyrolytic reaction is significant in the temperature range of 200–350°C and analysis and evaluation of kinetic parameters is done in the 100–500°C region of non-isothermal TG curves obtained in nitrogen atmosphere. The activation energy is calculated by iso-conversional method, then other kinetic parameters are determined by considering single reaction and two reaction global kinetic model. Two-reaction model is found to fit satisfactorily the experimental results.     

A kinetic study on the thermal behaviour of chitosan

The thermal behaviour of chitosan was studied by means of thermogravimetry, mass spectrometry and infrared spectrometry. Kinetic parameters were obtained by advanced kinetic evaluation (differential isoconversional analysis) from DSC curves, in non-isothermal conditions, at several heating rates, between 5 and 30°C min⁻¹. The results showed that the decomposition of chitosan does not follow a single mechanism because both the activation energy and the pre-exponential factor are not constant during the course of the reaction. A comparison with the results obtained by applying different conventional calculating methods is also shown.     

Determination of kinetic parameters from TG curves by non-linear optimization

The results obtained so far by kinetic analysis of non-isothermal experiments indicate that the kinetic parameters found by the conventional methods, in general, do not describe the experimental curve in an optimum manner. This is due to the fact that the initial differential equation is transformed into the logarithmic and, consequently, linear form and that the initial and final weights of the conversion curve cannot be determined exactly, which may falsify the slope of the curve.Investigations have shown that the determination of the kinetic parameters by non-linear optimization (simplex method) results in a better fit of the theoretical conversion curve to the experimental one. But this procedure gives optimum results only when the initial and final weights of the reaction can be determined exactly. If this is impossible, exact parameters can be obtained only by the use of the non-standardized TG curve.Examples are cited to prove that it is possible to evaluate overlapping reactions by the formation of intervals. However, the evaluation of conversion curves merely by the use of mathematical methods can easily result in an erroneous interpretation of the reaction course investigated. Therefore, it is necessary to check the mathematical results as to their physical and chemical meaning.     

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.     

Desorption kinetic parameters as deduced from temperature programmed desorption curves

Temperature programmed desorption is a typical non-isothermal method and therefore it needs a careful experimentation and a careful evaluation of the experimental data, in order to obtain meaningful kinetic parameters. A simple treatment of the data and some criteria, concerning the experimental methodology are therefore indicated, having in mind not only the advantages but also the difficulties and the limitations of a non-isothermal approach to kinetic studies.