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.     

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.     

生物质秸秆热重分析及几种动力学模型结果比较

利用热重分析在不同升温速率和氮气气氛下对两种生物质（玉米秸秆和稻秆）的热失重行为进行了研究。根据热重实验数据，采用四种利用热分析获取动力学参数的方法（Coats-Redfern法，Doyle法，最大速率法和分布活化能模型(DAEM)），计算生物质秸秆热分解反应活化能E、反应级数n及频率因子A，并进行比较。结果表明，采用不同的处理方法，得出的热分解动力学参数不同。利用Coats-Redfern法，玉米秸秆和稻秆在热解主要阶段（失重约5 w%～80 w%时）可由一段一级反应过程描述，升温速率10 K/min时活化能值分别为68.8 kJ/mol和70.0 kJ/mol。Doyle法和DAEM模型得到的结果较为接近，可以得到生物质热解过程中的活化能随失重率的变化曲线。生物质秸秆热解包含分子键能断裂的一系列复杂、连续反应过程。     

Kinetic analysis of solid-state reactions: Evaluation of approximations to temperature integral and their applications

The temperature integral, which has no exact analytical solution, is involved in the analysis of the experiment data obtained under nonisothermal conditions. Some approximations for the temperature integral have been proposed in the literature for the determination of the kinetic parameters, in particular the activation energy. Those approximations are classified into two categories, that is, exponential and rational approximations. The precision of them for estimating the temperature integral was evaluated within a certain continuous range rather than at several discrete points. Some applications of the approximations in the kinetic methods were presented. The relative errors of the activation energy and pre-exponential factor with four rational approximations by employing model-fitting method were calculated. The relative errors of the activation energy for a series of conversion rate with four rational and four exponential approximations by employing linear integral isoconversional methods were evaluated.     

An improved version of Junmeng–Fang–Weiming–Fusheng approximation for the temperature integral

An improved version of Junmeng–Fang–Weiming–Fusheng approximation for the temperature integral has been developed. The accuracy of the improved approximation for the temperature integral has been tested by some numerical analyses. The systematic analysis of the relative errors involved in the kinetic parameters obtained from Junmeng–Fang–Weiming–Fusheng integral method and its improved version has been also carried out. The results have shown that the improved approximation is more accurate than Junmeng–Fang–Weiming–Fusheng approximation as the solution of the temperature integral, and that more accurate kinetic parameters can be determined from the integral method based on the improved temperature integral approximation.     

Error evaluation of integral methods by consideration on the approximation of temperature integral

Summary In this paper, the integral methods in general use are divided into two types in terms of their different ways to in order to deal with the temperature integral p(x): for Type A the function h(x)=p(x)x²e^x is regarded as constant vs. x, while for Type B h(x) varies vs. x and ln[p(x)] is assumed to have the approximation form of ln[p(x)]=alnx+bx+c (the coefficients a, b, and c are constant). The errors of kinetic parameters calculated by these two types of methods are derived as functions of x and analyzed theoretically. It is found that Type A methods have the common errors of activation energy, while the Coats-Redfern method can lead to more accurate value of frequency factor than others. The accuracy of frequency factor can be further enhanced by adjusting the expression of the Coats-Redfern approximation. Although using quite simple approximation of the temperature integral, the Coats-Redfern method has the best performance among Type A methods, implying that usage of a sophisticated approximation may be unnecessary in kinetic analysis. For Type B, the revised MKN method has a lower error in activation energy and an acceptable error in frequency factor, and thus it can be reliably used. Comparatively, the Doyle method has higher error of activation energy and great error of the frequency factor, and thus it is not recommended to be adopted in kinetic analysis.     

Kinetic analysis of solid-state reactions: errors involved in the determination of the kinetic parameters calculated by one type of integral methods

The integral methods are extensively used for performing the kinetic analysis of solid-state reactions. As the Arrhenius integral function p(u) does not have an exact analytical solution, many approximations have been proposed. One popular type of approximations is called the exponent approximation which can be put in the form . In this study, a systematic analysis of the errors involved in the determination of the kinetic parameters calculated by the integral methods based on the exponent approximations for p(u) has been carried out. The results have shown that the precision of the kinetic parameters computed from the integral methods analyzed in this paper depends on u and the errors of the kinetic parameters determined from Doyle approach are the largest.     

Kinetic analysis of solid‐state reactions: Precision of the activation energy calculated by integral methods

The integral methods are extensively used for the kinetic analysis of solid‐state reactions. As the Arrhenius integral function [p(x)] does not have an exact analytical solution, different approximated equations have been proposed in the literature for performing the kinetic analysis of experimental integral data. Since the first approximation of Van Krevelen, a large number of equations have been proposed with the objective of increasing the precision in the determination of the Arrhenius integral, as checked from the standard deviation of the approximated function with regard to the real exact value of the integral. However, the main application of these equations is the determination of the kinetic parameters, in particular activation energies, and not the computation of the Arrhenius integral. A systematic analysis of the errors involved in the determination of the activation energy from these integral methods is still missing. A comparative study of the precision of the activation energy as a function of x and T computed from the different integral methods has been carried out. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 658–666, 2005     

Errors involved in the activation energy calculated by integral methods when the frequency factor depends on the temperature ( A = A 0 T m)

The dependence of the frequency factor on the temperature (A=A ₀ T ^m) has been examined and the errors involved in the activation energy calculated from some integral methods without considering such dependence have been estimated. Investigated integral methods are the Coats-Redfern method, the Gorbachev-Lee-Beck method, the Wanjun-Yuwen method and the Junmeng-Fusheng method. The results have shown that the error in the determination of the activation energy calculated ignoring the dependence of the frequency factor on the temperature can be rather large and it is dependent on x=E/RT and the exponent m.     

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.     

聚氯乙烯燃烧特性及HCl的生成机理

采用热重法对聚氯乙烯（ＰＶＣ）的燃烧过程进行了研究,探讨阳聚氯乙烯燃烧科技司,并由它们的微分热重曲线计算出的反应动力学参数及影响反应常数的因素进行了研究。同时,考察了恒速升温和快速升温过程ＨＣＩ的生成特性。结果表明,ＰＶＣ的燃烧机理是由三个过程决定的,可用三个一级反应表示。ＰＶＣ的燃烧过程的第一阶段为脱氯阶段。第二阶段的活化能和指前因子明显低于第一和一阶段。此阶段为挥发分释放阶段。升温速率的增加导     

Thermogravimetric investigation of the pyrolysis of pitch materials. A compensation effect and variation in kinetic parameters with heating rate

Thermogravimetric measurements of weight loss accompanying the pyrolysis of four pitches have been made over a range of linear heating rates. For three of the samples, the data at each heating rate could be described by an integral and a differential method of analysis, assuming a simple order function for f(α), with the result that the apparent activation energy increased with heating rate. The data for all four samples could also be satisfactorily described by the Ozawa or Friedman multiple heating rate methods, and these resulted in apparent activation energies (E_a) which increased with the value of β at which they were determined. It is suggested that this tendency for the apparent activation energy to increase, as the temperature is raised, is due to a change in the relative importance of the different reactions which lead to weight loss in this system. The apparent kinetic parameters all fall on a common compensation plot which is used to explain the relative magnitude of E_a values from Ozawa and Doyle methods of analysis. The higher values of E_a from Friedman than from Ozawa analyses are also explained.     

Aluminum sulphate hydrates

Three different calculation methods of deriving kinetic parameters (activation energy and preexponential factor) from dynamic TG data have been applied for the sulphate decomposition stage of the aluminum sulphate octadecahydrate. The constant rate experiments were carried out by Derivatograph and DuPont thermobalances. The three parameters estimation methods included a simple differential method, the classical Coats-Redfern and a new direct integral method. The fits of the curves obtained by these procedures were compared both graphically and numerically. It was found that the direct integral method gave the most satisfactory results. With the order type reaction models this method in each case produced the smallest residual deviation values and the best fitting curves compared to those obtained by the other two methods. The activation parameters calculated by the differential method were not acceptable at all, for the estimated curves were very far from the measured ones.     

Dependence of the preexponential factor on temperature

Summary The dependence of the preexponential factor on the temperature has been examined and the errors involved in the activation energy calculated from isothermal and non-isothermal methods without considering such dependence have been estimated. It has been shown that the error in the determination of the activation energy calculated ignoring the dependence of Aon Tcan be rather large and it is dependent on x=E/RT, but independent of the experimental method used. It has been also shown that the error introduced by omitting the dependence of the preexponential factor on the temperature is considerably larger than the error due to the Arrhenius integral approach used for carrying out the kinetic analysis of TG data.     

Kinetic analysis of solid-state reactions: A new integral method for nonisothermal kinetics with the dependence of the preexponential factor on the temperature (A = A0Tn)

In this study, we have proposed a new approximation for the general temperature integral, which frequently occurs in the nonisothermal kinetics with the dependence of the preexponential factor on the temperature and has no exact analytical solution. The validity of the new approximation has been tested by some numerical analyses. As the solution of the general temperature integral, the new approximation is more accurate than other approximations. Based on the newly proposed approximation, the corresponding integral method has been given. The precision of the integral methods for the determination of the activation energy has been calculated, and the results have shown that the relative error involved in the activation energy obtained from the new integral method is smaller than that from other integral methods. For applications, nonisothermal data obtained by theoretical simulation have been successfully processed using the new integral method.     

Low-temperature heat capacities and thermodynamic properties of crystalline isoproturon

An incremental integral isoconversional method for the determination of activation energy as a function of the extent of conversion is presented. The method is based on the treatment of experimental data without their transformation so that the resulting values of activation parameters should not be biased. The method was tested for recovering the activation energies from simulated data and employed for the treatment of experimental data of the NiS recrystallisation. This revised version was published online in July 2006 with corrections to the Cover Date.     

垃圾中可燃物的燃烧动力学研究

采用热重法对六种垃圾中的可燃物的燃烧过程进行了研究,探讨了垃圾中可燃物燃烧过程的燃烧特性,并由它们的微分热重曲线计算出它们的一级反应动力学参数。各可燃物的燃烧特性可归纳为纤维类与聚合类,可燃物的活化能与着火点温度相对应,活化能与指前因子直接存在补偿效应。     

Parametric study of the nonisothermal <Emphasis Type="Italic">n</Emphasis><Superscript>th</Superscript>-order distributed activation energy model involved the Weibull distribution for biomass pyrolysis

This paper describes the influences of some parameters relevant to biomass pyrolysis on the numerical solutions of the nonisothermal n ^th-order distributed activation energy model (DAEM) involved the Weibull distribution. Investigated parameters are the integral upper limit, the frequency factor, heating rate, the reaction order and the shape, scale and location parameters of the Weibull distribution. Those influences can be used for the determination of the kinetic parameters of the nonisothermal n ^th-order Weibull DAEM from thermoanalytical data of biomass pyrolysis.     

Determination of Activation Energies by Using Different Factors Φ in Adiabatic Calorimetry

Traditionally, the kinetic treatment of adiabatic calorimetry data has been based on the results of one or more experiments, but always with the assumption of the kinetic model that the reaction follows to calculate the kinetic parameters. In this paper a method for the determination of the activation energy that uses a set of adiabatic calorimetry data is developed. To check the method, the thermal decompositions of two peroxides were studied.This revised version was published online in November 2005 with corrections to the Cover Date.     

Pattern Search Method for Determination of DAEM Kinetic Parameters from Nonisothermal TGA Data of Biomass

The most accurate and up-to-date approach to modeling biomass pyrolysis is to adopt the distributed activation energy model (DAEM). In this study, a pattern search method to be used for the determination of DAEM kinetic parameters from the nonisothermal thermogravimetric analysis (TGA) data of biomass has been introduced. The method has been applied to the nonisothermal TGA data of peanut shell sample, and DAEM kinetic parameters of biomass samples have been determined. Calculated model results from determined kinetic parameters have been compared with nonisothermal TGA data of biomass.