On the nonlinear isoconversional procedures to evaluate the activation energy of nonisothermal reactions in solids

A general procedure for deriving the equations that underlie various isoconversional nonlinear methods for evaluating the activation energy is presented. A new integral isoconversional nonlinear method with integration over a given range of conversion is suggested. This method was applied to simulated nonisothermal data as well as to data for the nonisothermal decomposition of ammonium perchlorate. The obtained dependencies of the activation energy on the degree of conversion were compared with those resulting from other nonlinear and linear methods of analysis. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 87–93 2004     

A new iterative linear integral isoconversional method for the determination of the activation energy varying with the conversion degree

The conventional linear integral isoconversional methods may lead to important errors in the determination of the activation energy when the significant variation of the activation energy with the conversion degree occurs. Vyazovkin proposed an advanced nonlinear isoconversional method, which allows the activation energy to be accurately determined [Vyazovkin, J Comput Chem 2001, 22, 178]. However, the use of the Vyazovkin method raises the problem of the time‐consuming minimization without derivatives. A new iterative linear integral isoconversional method for the determination of the activation energy as a function of the conversion degree has been proposed, which is capable of providing valid values of the activation energy even if the latter strongly varies with the conversion degree. Also, the new method leads to the correct values of the activation energy in much less time than the Vyazovkin method. The application of the new method is illustrated by processing of theoretically simulated data of a strongly varying activation energy process. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

Critical Analysis of the Isoconversional Methods for Evaluating the Activation Energy. II. The activation energy obtained from isothermal data corresponding to two successive reactions

An analysis is presented of the consequences of the use of a one term equation containing apparent activation parameters, instead of the true rate equation to describe two successive decomposition reactions undergone by a solid compound. It is demonstrated that the apparent activation energy, obtained by means of isoconversional differential and integral methods, varies with the conversion degree for a relatively narrow temperature range and with temperature at a given value of the conversion degree. The activation energy values obtained with the isoconversional differential method are higher than the corresponding values obtained with the isoconversional integral method. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.

     

Kinetic analysis of wheat straw pyrolysis using isoconversional methods

The pyrolysis of wheat straw has been carried out by means of thermogravimetric analysis in inert atmosphere. The samples were heated over a range of temperatures that includes the entire range of pyrolysis with three different heating rates of 5, 10 and 20 K min⁻¹. The activation energy values as a function of the extent of conversion for the pyrolysis process of wheat straw have been calculated by means of the Flynn–Wall–Ozawa isoconversional method, the Vyazovkin–Sbirrazzuoli isoconversional method and an iterative isoconversional method presented in this article. The results have showed that there are small differences between the activation energy values obtained from the three methods, and the pyrolysis process reveals a dependence of the activation energy on conversion and have indicated the validity of the iterative integral isoconversional method. The effective activation energy for the pyrolysis of wheat straw is 130–175 kJ mol⁻¹ in the conversion range of 0.15–0.85. Furthermore, the prediction of the pyrolysis process under isothermal conditions from the dependence of the activation energy on the extent of conversion has been presented.     

The mathematical incorrectness of the integral isoconversional methods in case of variable activation energy and the consequences

Kinetic parameters resulting from the application of isoconversional methods mostly depend on the degree of conversion. This paper shows that the integral isoconversional methods are mathematically incorrect if the activation energy depends on conversion. In this case, the incorrectness resides in improper separation of variables in the general rate equation. As a consequence, non-sensical snake-like shape of the conversion versus time curves is observed when the kinetic results are extrapolated to lower temperatures.     

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.     

The Study of Nonisothermal Kinetics of Dehydration of Gibbsite in a Mixture with Zinc Oxide

Nonisothermal kinetics of dehydration of gibbsite in a mixture with zinc oxide has been studied by Friedman analysis (differential method) and Flynn‐Wall‐Ozawa analysis (integral method). The values of the activation energy and preexponential factor depending on the decomposition extent of gibbsite to boehmite have been determined. It has been shown that both methods give similar results. It has been established that the activation energy has a maximum value of 150–170 kJ/mol in the start stages of thermolysis (for conversion extent of less than 0.3). During further dehydration, the activation energy is reduced to 100–110 kJ/mol. It has been found that comilling of the mixture results in decreasing activation energy to 40–50 kJ/mol for a conversion extent more than 0.8. This testifies to the transition of the dehydration process out of the kinetic mode to the diffusion mode. It was explained by the accumulation of mechanical energy in the form defects of crystal lattice of gibbsite at the comilling stage.     

Critical Analysis of the Isoconversional Methods for Evaluating the Activation Energy. I. Theoretical background

It is demonstrated that, if the activation energy depends on the degree of conversion, its values obtained by isoconversional differential and integral methods are different. This revised version was published online in August 2006 with corrections to the Cover Date.     

Critical Considerations on the Isoconversional Methods. III. On the evaluation of the activation energy from non-isothermal data

The differential and integral isoconversional methods for evaluation the activation energy, described in the first note of this series, were applied for: a) simulated data for two successive reactions; b) dehydration of calcium oxalate monohydrate. It was shown that for these systems the activation energy depends on the conversion degree as well as on the method of evaluation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Kinetics of Gypsum Dehydration

The kinetics of gypsum dehydration in non-isothermal conditions with constant heating rate as well in quasi-isotherm, quasi-isobar regime, was investigated. The latter ones of these methods allowed putting in evidence the autocatalytic character of the dehydration, as well as the change of the activation energy with the conversion.The activation energy change was explained by the crystal growth and sample compaction observed by optical microscopy.Microscopic observations show that at higher conversions a compaction occur. This process is probably favoured by the accumulation of the water vapour from the dehydration (autogenerate atmosphere). These are the reason for step III characterised by higher activation.This revised version was published online in November 2005 with corrections to the Cover Date.     

Modification of the integral isoconversional method to account for variation in the activation energy

Integral isoconversional methods may give rise to noticeable systematic error in the activation energy when the latter strongly varies with the extent of conversion. This error is eliminated by using an integration technique that properly accounts for the variation in the activation energy. The technique is implemented as a modification of the earlier proposed advanced isoconversional method [Vyazovkin, S. J Comput Chem 1997, 18, 393]. The applications of the modified method are illustrated by simulations as well as by processing of data on the thermal decomposition of calcium oxalate monohydrate and ammonium nitrate. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 178–183, 2001     

Comprehensive method based on model free method and IKP method for evaluating kinetic parameters of solid state reactions

This article presents, firstly, a short review of methods for evaluating kinetic parameters of solid state reactions and a critical analysis of the isoconversional principle of model free methods. It shows theoretically that the activation energy for complex reactions is not only a function of the reaction degree but also of heating programs, and points out that any method that attempts to extract the dependences of activation energy on conversion degree without considering the dependences of heating programs is problematic. Then an analysis is given of the invariant kinetic parameters (IKP) method and recommends an incremental version of it. Based on the incremental IKP method and model free method, a comprehensive method is proposed that predicts the degree of the dependences of activation energy on heating programs, selects reliable values of activation energy and extracts the values of variable pre‐exponential factor. This comprehensive method is tested using both simulation data and experimental data, the results of which show it can not only give reliable values of kinetic parameters but also be helpful in explaining inconsistencies of kinetic results in solid state reactions. © 2012 Wiley Periodicals, Inc.     

氧离子导体La2Mo2O9中α→β相变非等温动力学的研究

以差热分析(differential thermal analysis,DTA)为手段研究了La2Mo2O9中α→β相变的非等温动力学。采用Flynn-Wall-Ozawa法计算了不同转化分数下的相变活化能E,并用Ozawa迭代法对E值进行了修正。应用Criado-Ortega法获得了α-La2Mo2O9→β-La2Mo2O9相变各温度区间的动力学机理函数,并用譒atava-譒esták法进行了验证。结果表明:La2Mo2O9中α→β相变的表观活化能与转化分数有关,说明该相变不属于一步简单反应。不同温度区间α→β相变的动力学机理函数不同,836～840K、842～848 K和850～853 K的动力学机理函数G(x)可依次表示为:-ln(1-x)、[-ln(1-x)]2/3、[-ln(1-x)]3/4。     

Photon energy limits for food irradiation: a feasibility study

The penetrating nature of the photons produced by the X-ray (bremsstrahlung) process makes them attractive for the treatment of dense materials in industrial radiation processing. The inefficiency of the conversion process can be balanced by the exposure of high Z materials to electrons with high energy. However, activation of the product being irradiated and the equipment imposes energy limits. Results of a theoretical and experimental study to investigate the key parameters have resulted in recommendations for the design of X-ray converters in the electron energy range 7 to 11 MeV. Results of the Monte Carlo calculations and the methods used in conversion experiments with the 50 kW IMPELA accelerator are reported.     

Recent application of biochar on the catalytic biorefinery and environmental processes

Biochar, produced and activated from thermochemical methods, was applied as catalyst for catalytic biorefinery and environmental pollutant removal. In this review, recent advanced studies of biochar catalyst were discussed.     

Recent application of biochar on the catalytic biorefinery and environmental processes

Lignocellulosic biomass is an abundant and environment-friendly source for renewable energy production. The value and application of biochar, which is obtained from the thermochemical conversion of biomass, is increasing rapidly because of its high carbon content and porosity. The property of biochar, such as surface area, porosity, and number of functional groups, can be improved by controlling the conditions of biomass conversion, biochar activation, and functionalization methods. The production and activation of biochar as well as its potential use for soil remediation, pollutant adsorption, and biorefinery have been reviewed extensively over recent decades. This paper provides a conceptual approach for biochar production and activation together with its application as a catalyst for biorefineries and the removal of environmental contaminants.     

碱及碱土金属对准东煤热解特性及动力学影响分析

利用程序升温热重(TG)技术对准东原煤(R-form)和酸洗煤(H-form)样品的热解过程进行了研究,同时,采用分布活化能模型(DAEM)法对两者的热解动力学参数进行了计算。结果表明,准东煤在热解过程中保持了丰富的孔隙结构;碱及碱土金属(AAEM)的存在不会对准东煤大分子网络结构造成显著影响,但会提高准东煤的平衡水分含量及二次脱气阶段挥发分释放速率,降低其主热解阶段挥发分释放速率及热解最终失重率;DAEM法可以在较宽的温度范围内对准东煤的热解过程进行准确的描述,R-form和H-form煤样品的热解活化能均随转化率的增大而升高;相同转化率下R-form煤样品的活化能高于H-form,前者活化能分布函数的最大值出现在261.85kJ/mol处,而后者出现在264.51kJ/mol处;AAEM的存在使准东煤的热解活化能升高且分布更加集中,使其热解反应活性降低;准东煤热解的频率因子与活化能之间呈现明显的动力学补偿效应。     

Study of Kinetics of Dispersion Polymerization of Styrene in Organic Media

The kinetics of dispersion polymerization of styrene in alcohol/methyl or butyl cellosolve was investigated with dried-weigh methods. The reaction parameters, such as concentration of initiator, polymerization temperature, and solvent, play an important role in determine polymerization rate. It was found that polymerization rate increases with the reaction temperature. The apparent activation energy is of 42.2kJ/mole and 52.6kJ/mole for the initial polymerization stage and the stationary polymerization interval. The polymerization rate increases with the concentration of the initiator with approximately 0.67 order dependence at conversion about 5%. It was described that the relation of conversion with the Hansen Parameters of media in detail by analysis of solvent dispersion, polarity and hydrogen bonding contributions. More significant was the result that polymerization rate versus conversion curve consisted of 3 intervals (2 non-stationary and 1 stationary one). The plateau of polymerization rate was observed in the curve of polymerization rate vs. monomer conversion.