On the Validity of the Steady-State Approximation in Non-Isothermal Kinetics: Part IV. The case of constant rate thermal analysis

The paper investigates the validity of steady-state approximation for the case of constant rate thermal analysis experiments. It is shown that the approximation holds for the experiments run with a controlled rate of either the decomposition of the compound, or the production of gas.This revised version was published online in November 2005 with corrections to the Cover Date.     

On the Validity of the Steady-state Approximation in Non-isothermal Kinetics. Part III

The authors continue their considerations concerning the validity of the steady-state approximation in non-isothermal kinetics. A sequence of two first-order consecutive reactions with an active intermediate was subjected to kinetic analysis by numerical solution of the corresponding differential kinetic equations for a number of particular cases. The results demonstrated that the rate of change of concentration of the active intermediate is negligibly small if the assumption made in the isothermal case is also accepted for the non-isothermal case, i.e. k ₂(T(t))>> k ₁(T(t)). This revised version was published online in July 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.     

Determination of the Kinetic Parameters of Chemical Reactions on the Basis of Non-Isothermal Measurements A critical review

A detailed analysis is presented of the applicability of several dependences commonly used for the determination of activation energies from non-isothermal measurements. Reactions proceeding according to different kinetic equations are simulated and the validity of the activation energy values obtained is discussed. The general conclusion is drawn that none of the examined dependences should be used to determine the activation energy. For a rough estimation of activation energy, the Kissinger equation can be applied according to Ockham's razor. This revised version was published online in August 2006 with corrections to the Cover Date.     

On evaluate of the integral methods for the determination of the activation energy

Recently, Órfão obtained two simple equations for the estimation of the relative error in the activation energy calculated by the integral methods [2]. In this short communication, the validity of the equations has been evaluated by comparing the results calculated by the equations with the results calculated by the equation from theoretical derivation without introducing any assumption.     

Differential Non-Linear Isoconversional Procedure for Evaluating the Activation Energy of Non-Isothermal Reactions

A differential isoconversional non-linear procedure for evaluating activation energy from non-isothermal data is suggested. This procedure was applied to model reactions (simulations) and to the dehydration of CaC₂O₄⋅H₂O. The results were compared with those obtained by other isoconversional methods. This revised version was published online in August 2006 with corrections to the Cover Date.     

Estimation of Activation Energies for Thermooxidative Degradations of LDPE and NBR from Non-Isothermal and Isothermal DTA Data

Results obtained on the thermooxidative degradations of LDPE (low-density polyethylene) and NBR (nitrile-butadiene rubber) are presented. The activation energies for the thermooxidations leading to solid products were estimated. For LDPE, the activation energies obtained from non-isothermal data are in satisfactory agreement with those obtained from isothermal data. For NBR, the isothermal activation energy is ≉16% higher than the non-isothermal one. This difference is due to the morphological changes undergone by NBR during its heating at the rather high temperatures at which isothermal measurements were performed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cu-ZSM-5的NH3选择性催化还原NO性能及其稳态动力学

采用浸渍法制备了一系列不同Cu载量的Cu-ZSM-5整体式催化剂.考察了该系列催化剂的NH3选择性催化还原(SCR)NO的反应特性.结果表明,当Cu质量分数为5%时,Cu-ZSM-5催化剂的SCR活性最高,此时催化剂上NO最高转化率高达96.5%,并且催化剂的活性窗口较宽,催化剂在198-470℃之间NO转化率大于80%.H2O和SO2的添加仅轻微影响Cu-ZSM-5催化剂的SCR活性.当Cu载量大于5%时,Cu-ZSM-5催化剂中出现明显的CuO物相.稳态动力学结果表明,在5%Cu载量的Cu-ZSM-5上的SCR反应中,NO的反应级数接近一级,NH3的反应级数接近零级,O2的反应级数接近1/2级.该反应的表观活化能为47.7kJ·mol-1.     

聚对苯二甲酰十碳二胺的制备和非等温结晶动力学研究

以对苯二甲酸和癸二胺为原料,经成盐,预聚合和固相聚合三个步骤合成了新型长碳链和较高相对分子质量的半芳香尼龙聚对苯二甲酰十碳二胺,由红外光谱和核磁共振对其结构进行了确认。用DSC方法研究了聚对苯二甲酰十碳二胺的非等温结晶动力学,用莫志深提出的R～f法对非等温结晶动力学进行了分析,由R～t法得到α值在0.70～0．81之间。利用Kissinger方法求得了半芳香尼龙的非等温结晶活化能,△E=-297．08kJ／mol。     

Advanced isoconversional method

A nonlinear algorithm has been suggested to increase the accuracy of evaluating the activation energy by the integral isoconversional method. A minor modification of the algorithm has made it possible to adapt the isoconversional method for an arbitrary variation of the temperature. This advanced isoconversional method allows for trustworthy estimates of the activation energy when the thermal effect of a reaction makes the temperature of a sample deviate from a prescribed heating program.     

Non-isothermal kinetics in solids

The integral methods, which are obtained from the various approximations for the temperature integral, have been extensively used in the non-isothermal kinetic analysis. In order to obtain the precision of the integral methods for the determination of the activation energy, several authors have calculated the relative errors of the activation energy obtained from the integral methods. However, in their calculations, the temperature integral at the starting temperature was neglected. In this work, we have performed a systematic analysis of the precision of the activation energy calculated by the integral methods without doing any simplifications. The results have shown that the relative error involved in the activation energy determined from the integral methods depends on two dimensionless quantities: the normalized temperature θ=T/T ₀, and the dimensionless activation energy x ₀=E/RT ₀ (where E is the activation energy, T is the temperature, T ₀ is the starting temperature, R is the gas constant).     

Simulation of isothermal cure of A powder coating

The curing of a thermosetting powder coating was studied by means of differential scanning calorimetry (DSC). The isothermal cure was simulated by non-isothermal experiments. The results of the simulation were compared with experimental isothermal data. From non-isothermal isoconversional procedures (free model), it was concluded that these permit simulation of the isothermal cure but do not enable us to determine the complete kinetic triplet (A preexponential factor, E activation energy, f(a) and/or g(a) function of conversion). Non-isothermal procedures based on a single heating rate or on master curves present difficulties for determination of all the kinetic parameters, due to the compensation effect between preexponential factor and activation energy. The kinetic triplet can be determined by a combination of various non-isothermal methods or by using experimental isothermal data in addition to non-isothermal data. This revised version was published online in July 2006 with corrections to the Cover Date.     

Non-isothermal kinetics of dehydration of equilibrium swollen poly(acrylic acid) hydrogel</o:p>

Summary Kinetics of dehydration of equilibrium swollen poly(acrylic acid) hydrogel was investigated using methods of non-isothermal thermal analysis. Methods of Kissinger, Coats-Redfern, Van Krevelen and Horowitz-Metzger were applied for determination the kinetics parameters: activation energy (E), pre-exponent (lnA) as well as the kinetics model ƒ(69) for the process of hydrogel dehydration under different heating rates. An existence of good agreement between determined values of kinetic parameters (Eand A), which were obtained applying different methods under the same heating rate. Functional relationship between changes of kinetic parameters of dehydration and changes of heating rate was established. An existence of compensation effect is accepted and explanation of compensation effect appearance during the hydrogel dehydration is suggested.     

New rational fraction approximating formulas for the temperature integral

Three rational fraction approximations for the temperature integral have been proposed using the pattern search method. The validity of the new approximations has been tested by some numerical analyses. Compared with several published approximating formulas, the new approximations is more accurate than all approximations except the approximations proposed by Senum and Yang in the range of 5≤E/RT≤100. For low values of E/RT, the new approximations are superior to Senum-Yang approximations as solutions of the temperature integral.     

Non-isothermal kinetic analysis and feasibilty study of medium grade crude oil field

In this research, non-isothermal kinetics and feasibility study of medium grade crude oil is studied in the presence of a limestone matrix. Experiments were performed at a heating rate of 10°C min⁻¹, whereas the air flow rate was kept constant at 50 mL min⁻¹ in the temperature range of 20 to 600°C (DSC) and 20 to 900°C (TG). In combustion with air, three distinct reaction regions were identified in all crude oil/limestone mixtures, known as low temperature oxidation (LTO), fuel deposition (FD) and high temperature oxidation (HTO). The activation energy values were in the order of 5–9 kJ mol⁻¹ in LTO region and 189–229 kJ mol⁻¹ in HTO region. It was concluded that the medium grade crude oil field was not feasible for a self-sustained combustion process.     

Dehydration Kinetics of Lithium Sulfate Monohydrate Single Crystals

Some peculiar properties of lithium sulfate monohydrate dehydration kinetics are investigated. Experiments were carried out under both isothermal and non-isothermal conditions on the bulk single crystals (1 cm). Under both heating modes some new data were obtained. Uncommon high dehydration process rate under isothermal conditions and linear dependence of this rate under non-isothermal ones were discovered. Experiments over the water saturated porous ceramics drying and over the water vapors transmitting through the layer of preliminary dehydrated lithium sulfate were carried out. It is attempted to explain observed phenomena considering heat- and mass-transfer conditions.This revised version was published online in November 2005 with corrections to the Cover Date.     

Using ordinary differential equations system to solve isoconversional problems in non-isothermal kinetic analysis

The mathematical evaluation of the activation energy, E, of non-isothermal degradation reactions is usually made using the Ozawa/Flynn–Wall isoconversion principle and involves the numerical resolution of a set of integrals without closed form solution, which are solved by polynomial approximation or by numeric integration. In the present work, the isoconversion principle, originally described and maintained until now as an algebraic problem, was written as a set of ordinary differential equations (ODEs). The individual ODEs obtained are integrated by numeric methods and are used to estimate the activation energy of simulated examples. A least square error (LSE) objective function using the introduced ODEs was written to deal with multiple heating rate CaCO₃ thermal decomposition TG experiments.     

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.     

生物质热反应机理与活化能确定方法Ⅰ.干燥段研究

干燥段是生物质热解的第一个过程.采用热分析仪研究了杉木木屑干燥段质量和热量的变化,推导了非等温干燥动力学模型,探讨了热质传输机理.结果表明,随着温度的升高,木屑含湿量迅速下降,80℃左右出现一个明显的失重峰;非等温干燥动力学Page模型能很好地模拟木屑干燥过程,木屑干燥活化能为12.6 kJ/mol;水分传输与热量传递...     

Non-isothermal kinetics-current problems

The author presents some experimental and theoretical contributions in non-isothermal kinetics developed in the last years. Special emphasis is given on heterogeneous kinetics with the help of Q-derivatograph, kinetic indexes of thermal stability and on the classical non-isothermal change (CNC).

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Zusammenfassung Es werden einige, in den vergangenen Jahren entwickelte experimentelle und theoretische Beiträge zur nichtisothermen Kinetik dargestellt. Besonders betont werden heterogene Kinetik mittels Q-Derivatografie, kinetischer Index der thermischen Stabilität sowie klassische nichtisotherme Umwandlungen (CNC).