Precision of integral methods for the determination of the kinetic parameters

In this paper, a systematic analysis of the errors involved in the determination of the kinetic parameters (including the activation energy and frequency factor) from five integral methods has been carried out. The integral methods analyzed here are Coats-Redfern, Gorbachev, Wanjun-Yuwen-Hen-Zhiyong-Cunxin, Junmeng-Fusheng-Weiming-Fang, Junmeng-Fang and Junmeng-Fang-Weiming-Fusheng method. The results have shown that the precision of the kinetic parameters calculated by the different integral methods is dependent on u (E/RT), that is, on the activation energy and the average temperature of the process.     

Critical considerations on the methods for evaluating kinetic parameters from nonisothermal experiments

By surveying the most used methods for evaluating the kinetic parameters from nonisothermal experiments, a new classification scheme of the methods is proposed. For each method the number of principles and theoretical approximations required to derive the equation which grounds it, is considered as a comparison criterion. The methods are, finally, classified into classes of equivalence. As a result of the analysis it is also suggested that the activation energy, as calculated from nonisothermal data, should be given as a range of values instead of a unique value. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet 30: 313–327, 1998.     

Some problems concerning the evaluation of non-isothermal kinetic parameters

The validity of isoconversional methods used to evaluate the activation energy is discussed. The authors have shown that the Flynn-Wall-Ozawa and Friedman methods give results that agree with each other only if the activation energy does not change with the degree of conversion. A criterion for the reaction mechanism as expressed by the differential conversion function is suggested too.     

Application of isoconversional and multivariate non-linear regression methods for evaluation of the degradation mechanism and kinetic parameters of an epoxy resin

The thermo-oxidative degradation of an epoxy resin obtained by curing of an industrially produced DGEBA mixture with 4,4′-methylene-dianiline (MDA) and used as electric insulator has been investigated by TG + DTG + DSC simultaneous analyses performed in static air atmosphere, at five heating rates. TG, DTG and DSC curves showed that, in the temperature range 25-900 °C, a glass transition followed by three thermo-oxidative processes occur. The processing of the non-isothermal data corresponding to the first process of thermo-oxidation was performed by using Netzsch Thermokinetics - A Software Module for Kinetic Analysis. The dependence of the activation energy, evaluated by isoconversional methods, on the conversion degree and the relative high standard deviations of this quantity show that the investigated process is a complex one. The mechanism and the corresponding kinetic parameters were determined by multivariate non-linear regression program and checked for quasi-isothermal data. It was pointed out that the first process of thermo-oxidation of the investigated resin consists in four steps, each step having a specific kinetic triplet. The obtained results were used for prediction of the thermal lifetime of the material corresponding to some temperatures of use and the end point criterion 5% and 10% mass loss.     

Fast and reliable numerical methods to simulate complex chemical kinetic mechanisms

Models that simulate atmospheric photochemistry require the use of a stiff ordinary differential equations (ODEs) solver. Since the simulation of the chemical transformations taking place in the system takes up to 80 percent of the CPU time, the numerical solver must be computationally fast. Also, the residual error from the solver must be small. Because most accurate solvers are relatively slow, modelers continue to search for timely, yet accurate integration methods. Over the past years an extensive number of articles have been dedicated to this subject. One of the highly debated questions is whether one should construct specialized algorithms or instead use general methods for stiff ODEs. In the present article we use the second alternative. We apply three linearly (semi-)implicit methods from the classical stiff ODE literature which we modified to implement the sparse routines to solve the system of equations describing a complex kinetic mechanism. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet 30: 349–358, 1998     

Errors in evaluation of the kinetic parameters in temperature programmed reduction

The objective of this work was to develop and validate a fast and reproducible method which is able to determine the concentration of ketoconazole in raw materials and tablets. The samples were analyzed by dynamic thermogravimetry at heating rates of 10, 20, 40, 60 and 80°C min⁻¹ in nitrogen and nitrogen-synthetic air mixture. The concentrations of ketoconazole in the raw material and in the tablets were obtained from the vapor pressure curves. The data showed that there is no significant difference between the vapor pressure profiles of ketoconazole itself and in its tablet in both studied environmental conditions confirming that the process is really vaporization. The concentration of ketoconazole was determined in the raw material and tablets of the drug.     

由热重数据计算动力学参数

热重法(TG)是一种动态测量技术,可在程序升温或降温情况下对给定物质或体系提供一个连续的,以温度或时间为函数的重量变化曲线,所以由它跟踪反应能给出反应动力学的有关信息。这种非等温法与早期使用的等温法相比,有快速、连续和需要较少实验数据等优点,近年来在动力学研究方面得到广泛应用,但还只限于研究下列几种类型的简单     

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.     

Thermogravimetry. Generalization of Reich's method

A new method is proposed for the determination of kinetic parameters, where Reich's method is a special case. This method involves a knowledge of the values of the weight loss, the temperature, the rate of weight loss and the derivative of the rate of weight loss, corresponding to a certain point in the TG curve. The findings are in good agreement with those of Reich's method.     

Simulations for evaluation of kinetic methods in differential scanning calorimetry. Part 1. Application to single-peak methods: Freeman-Carroll, Ellerstein, Achar-Brindley-Sharp and multiple linear regression methods

In order to simplify the choice between different kinetic methods used in differential scanning calorimetry, an interesting way for testing kinetic treatments is proposed, using simulated thermoanalytical curves computed from given kinetic parameters. Applied to the study of a polymerization, we tested the Freeman-Carroll, Ellerstein, multiple linear regression (reaction-order model) and Achar-Brindley-Sharp methods. The test of the validity of the methods is performed using the LSM parameter that represents the fit between the mathematical treatment used in the kinetic model and known data. The study reveals the importance of the number of points used, i.e. the resolution, in the thermoanalytical curve recording, especially for the Freeman-Carroll and Ellerstein methods, there being an increase in the relative error on all the kinetic parameters when the number of points is decreased. Maximum relative errors are reported for the pre-exponential factor calculations. Evaluation of the enthalpy error on the determination of the kinetic parameters has been performed. Simulations obtained with various enthalpies indicate the necessity in such cases of computing a relative dimensionless LSM parameter (relative to the amplitude of the phenomena) in order to compare different thermal effects.     

Theoretical evaluation of methods for extracting retention factors and kinetic rate constants in liquid chromatography

A three-dimensional stochastic simulation is used to provide a detailed understanding of mass transfer processes in liquid chromatography. In this simulation, the migration of individual molecules is established through diffusion and laminar convection within the mobile phase. The molecules interact with the stationary phase by a partition (absorption) mechanism. For these studies, the column length, linear velocity, stationary-phase diffusion coefficient, interfacial mass transfer coefficient, and equilibrium constant are varied in a system with a homogeneous surface. Heterogeneous surfaces are also investigated by having multiple types of interaction sites that are equally or unequally distributed. For each simulation, the molecular distribution is examined and characterized at specified times or column lengths. Five individual methods are then applied to extract the thermodynamic and kinetic information for transport between the mobile and stationary phases. In the first method, all of the molecules are initially distributed in the mobile phase and the fraction remaining is monitored as a function of time. These simulation data are fit to a single exponential decay by nonlinear regression to determine the "true" retention factors and rate constants. The other methods rely on evaluating the shape of the zone profiles along the column. The statistical moments of the profiles are used to calculate the mean and the variance, which are related to the retention factors and the rate constants, respectively. The profiles are also fit to the exponentially modified Gaussian equation, the Giddings equation, and the Thomas equation. The fitting parameters from these equations are then used to calculate the retention factors and rate constants. Comparisons of the accuracy relative to the "true" retention factors and "true" rate constants, as well as the advantages and limitations of each method are discussed.     

Checking of mathematical calculation methods for the determination of kinetic parameters from non-isothermal measurements by test functions

The applied computing programs are checked by means of test values from theoretical models. First-order kinetics, the Avrami equation and the 2-dimensional diffusion equation have been calculated as theoretical values. The computer calculation was carried out both for the total reaction and for individual reaction intervals.For the calculation of kinetic parameters and the distinction between the various models, in principle, the integral method should be used. The calculation does not give any answer to the question whether there exists another equation not involved in the models selected, which describes the processes better. If there is no indication of the reaction, it should first be checked by the differential method. The correlation coefficient does not allow the individual model equations to be distinguished with statistical significance.     

Optimization of parameters for semiempirical methods I. Method

A new method for obtaining optimized parameters for semiempirical methods has been developed and applied to the modified neglect of diatomic overlap (MNDO) method. The method uses derivatives of calculated values for properties with respect to adjustable parameters to obtain the optimized values of parameters. The large increase in speed is a result of using a simple series expression for calculated values of properties rather than employing full semiempirical calculations. With this optimization procedure, the rate-determining step for parameterizing elements changes from the mechanics of parameterization to the assembling of experimental reference data.     

Optimization of parameters for semiempirical methods II. Applications

MNDO/AM1-type parameters for twelve elements have been optimized using a newly developed method for optimizing parameters for semiempirical methods. With the new method, MNDO-PM3, the average difference between the predicted heats of formation and experimental values for 657 compounds is 7.8 kcal/mol, and for 106 hypervalent compounds, 13.6 kcal/mol. For MNDO the equivalent differences are 13.9 and 75.8 kcal/mol, while those for AM1, in which MNDO parameters are used for aluminum, phosphorus, and sulfur, are 12.7 and 83.1 kcal/mol, respectively. Average errors for ionization potentials, bond angles, and dipole moments are intermediate between those for MNDO and AM1, while errors in bond lengths are slightly reduced.     

Methods for potentiostatic evaluation of heterogeneous kinetic parameters in the presence of an irreversible following chemical reaction

A theoretical study of Brdi?ka's adsorption waves and of the corresponding i-E curves in cyclic voltammetry and E-t curves in chronopotentiometry is presented under the following conditions: (a) the electrochemical reaction 0+ne?R is reversible; (b) both the oxidized and the reduced forms are strongly adsorbed; (c) the adsorption is rapid; (d) allowance is made in the isotherm for interactions between the molecules (Frumkin type isotherm). One mathematical function and its derivative are sufficient to describe the results in the three cases. The equations derived account in particular for the following experimental characteristics: (1) the linear variation of the half-wave potential of the adsorption wave (or of the chronopotentiogram) and of the voltammetric peak potential with the concentration c; (2) the changes in the slope of the wave when c varies and the discontinuous increase of current which is observed for high concentrations; (3) the changes in peak width and the hysteresis phenomenon observed in cyclic voltammetry; (4) the S-shaped experimental chronopotentiograms; (5) the appearance of prewaves (or postwaves) in cases where both O and R are equally adsorbed; (6) the fact that prewaves or postwaves usually appear for large molecules. The results show that the appearance of a Brdi?ka prewave or postwave is often caused by energy effects arising from the interactions between adsorbed molecules, rather than by energy effects caused by interactions with the electrode surface.     

Calculation of the kinetic parameters

The paper reports the calculation of kinetic parameters (activation energy, pre-exponent and reaction order) of thermodegradation of some phenol stabilizers. For this purpose, a software package for IBM-compatible personal computers is proposed. The first calculation of kinetic parameters (E, Z, n) was carried out for these compounds. The package can be applied for kinetic calculations on the thermodegradation of other substances.