On the Apparent Compensation Effect Observed for Two Consecutive Reactions

A critical analysis is presented of the use of an overall single rate reaction equation instead of the true rate equation corresponding to a complex process consisting of two consecutive reactions. In accordance with this approximation, which is often used in the kinetic analysis of systems in which several reactions take place, the overall process is described by apparent activation parameters (the apparent activation energy E_ap and the apparent pre-exponential factor A_ap) and an apparent conversion function. The theoretical isotherms (α=α(t), where α is the conversion degree and t is time) were simulated for a system in which two consecutive reactions occur. In this case, the apparent activation parameters depend on (a) the considered range of temperature; and (b) the temperature for a given conversion degree. It is shown that the apparent activation parameters are correlated by the compensation effect relationship: ln A_ap = α^* + β^*E_ap where α^* and β^* are the linear regression parameters. The possibility of using the apparent kinetic parameters to predict the isotherms α=α(t) for temperatures lower than those for which these parameters were evaluated is discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Non-isothermal Kinetics of Consecutive Reactions

Theoretical consideration has been made of the non-isothermal kinetics of consecutive reactions based on the superposition principle. In the model the first reaction product reacts to form the final product and the two reactions proceed independently. The amount of the first reaction product and the production rate of the final product have been obtained as a function of time for isothermal cases and as a function of the reduced times for non-isothermal cases. This revised version was published online in August 2006 with corrections to the Cover Date.     

Change of the Apparent Reaction Order with Temperature as a Consequence of the Reaction Mechanism Complexity

The theoretical isotherms (α=α(t), where α is the conversion degree and t is the time) and the theoretical thermogravimetric curves(α=α(T), where T is the temperature) were simulated for a system in which two consecutive reactions occur. A critical analysis of the use of an overall single rate reaction equation instead of the use of the true rate equations is presented. Both for isothermal and non-isothermal data and α≤0.50, the apparent reaction order depends on temperature. It is pointed out that the apparent reaction order for a given temperature can be evaluated if the parameters of the compensation effect are known. This revised version was published online in July 2006 with corrections to the Cover Date.     

滴定量热法研究连串一级反应热动力学

本文用滴定量热法分别建立了滴定期和停滴反应期1-1级连串反应热动力学的数学模型。根据这两种模型,由非线性最小二乘法原理直接拟合单次实验结果可同时求得1-1级连串反应的速率常数（ k ₁和 k ₂）和摩尔反应焓。并用滴定量热法研究了丁二酸二乙酯皂化反应的热动力学,实验结果验证了两种数学模型的正确性。     

On the Compensation Effect at the Form of the Differential Conversion Function

From the general form of the rate equation under non-isothermal conditions, some relationships showing the existence of a compensation effect due to the change of the analytical form of the differential conversion function were derived. These relationships were checked for some simulated TG curves, as well as thermogravimetric data corresponding to the degradation of some polymers and to the decomposition of calcium carbonate. This revised version was published online in July 2006 with corrections to the Cover Date.     

两种量热模式下物质热分解的动力学补偿效应

热分析量热仪主要包括动态、等温、恒温及绝热四种操作模式。很多学者基于动态及等温模式的测试结果,采用Arrhenius速率常数进行动力学计算,进而发现了所谓的“动力学补偿效应”。为了解绝热模式下是否也存在动力学补偿效应,分别采用绝热加速量热法(ARC)及动态差示扫描量热法(DSC)研究了过氧化二异丙苯(DCP)、40%(质量分数,下同)DCP溶液、葡萄糖、45%葡萄糖溶液的热分解特性,在此基础上基于Arrhenius公式计算了对应的表观活化能E和指前因子A,并对计算结果进行了分析。结果表明:绝热模式下,不同质量的同种样品及其溶液的最佳动力学参数,或者同一组数据采用不同的反应级数获得的lnA和E之间均存在明显的线性关系。此外,尽管由动态DSC数据计算获得的E和lnA普遍小于绝热模式的结果,但两种模式下获得的lnA和E之间仍然存在动力学补偿效应。由此可以推断,具有相同或类似反应机理的反应,虽然实验模式不同,但其E和lnA之间存在明显的动力学补偿效应。     

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.     

CS2水解催化反应动力学补偿效应

考察了常压下ＣＳ２水解催化剂活性组分含量和温度对ＣＳ２水解的综合影响，并进行了ＣＳ２水解动力学研究，发现在所研究的４个系列催化剂中都存在着补偿效应，在反应温度范围内，Ａ、Ｅ两类催化剂符合“顺Ａｒｒｈｅｎｉｕｓｆｗｔｖ”；而Ｏ、Ｃ两类催化剂符合“反Ａｒｒｔｈｅｎｉｕｓ规律”，另外，针对多相表面催伦反应过程，提出了修正的阿累尼乌斯公式，即：ｋ＝Ａ‘ｅｘｐ（△Ｅ／ＲＴ）ｅｘｐ（－Ｅａ／ＲＴ），且从此角度     

Compensation Effect in the Kinetics of Spatially Hindered Phenols

This paper reports a linear relationship between kinetic characteristics from the Arrhenius equation describing a decomposition process found when studying the kinetics of thermolysis of spatially hindered phenols. This relationship between the coefficients is known in the literature as a 'compensation effect'. The existence of the compensation effect permits some conclusions concerning the decomposition mechanism and thermal characteristics of the compounds under investigation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Isokinetic relationships for nucleophilic substitution reactions at the saturated carbon atom. Reactions in aqueous solutions

An isokinetic relationship (IKR) with the parametersT _iso=6145 K and logk _iso=10.622 is valid for nucleophilic substitution reactions at the saturated carbon atom with the participation of anionic nucleophiles in aqueous solutions. The IKR describes the rate constants of the reactions with different anionic nucleophiles, leaving groups, and substituents at the electrophilic reaction center. Similar reactions with neutral nucleophiles, which follow another mechanism, are described by a separate IKR withT _iso=−1232 K and logk _iso=16.226. The reactions of haloforms with hydroxide ion, which proceed by a specific mechanism involving the haloform ionization equilibrium followed by α-elimination of the halide ion, are described by yet another IKR withT _iso=−1463 K and logk _iso=21.057. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 5, pp. 809–814, May, 2000.     

A Thermoanalytical Study of the Solid State Reactions in the K2CO3-MxOy Systems. Evidence for a kinetic compensation effect

This paper presents the results obtained in the investigation of the reactions of potassium carbonate with some transition metals oxides (TiO₂ , V₂ O₅ , Cr₂ O₃ , MnO₂ , Fe₂ O₃ ). The reactions were carried out under non-isothermal conditions, and thermogravimetric analysis was used to monitor the transformation degree a. Experimental data indicated that the reaction of potassium carbonate and iron(III) oxide occurs in one stage, whereas the reactions of the oxides of titanium, vanadium, chromium and manganese are more complex, involving two-stage processes. Activation energies and pre-exponential factors were determined for all the processes taking place in the investigated systems. For the second stage of the reaction of K₂ CO₃ with Cr₂ O₃ , and V₂ O₅ the obtained values of activation energy were 59.2 and 512 kJ mol⁻¹ respectively. Based on the values of activation energy and pre-exponential factor, the existence of a kinetic compensation effect was postulated for the three homologous series of reactions. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of the solvent on the kinetics of thermal decomposition of acetylcyclohexylsulfonyl peroxide

The kinetics of the decomposition of acetylcyclohexylsulfonyl peroxide (ACSP) in CCl₄, benzene, toluene, ethylbenzene, cumene, acetonitrile, ethanol, and 2-propanol in an atmosphere of O₂ were studied at 40–70 °C. The rate constants (k ₀) and activation parameters of the monomolecular decomposition of ACSP were determined. A linear dependence between logA ₀ and activation energyE ₀ (compensation effect) was established. The dependence ofk ₀ on the nature of a solvent is described by the four-parameter Koppel-Palm equation. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 935–937, May 1997.     

非催化气固反应动力学热分析方法与仪器

准确测量近本征反应速率和计算反应动力学参数是热化学工程和应用化学工程领域的重要研究问题.以热重为代表的传统热分析方法与仪器在非催化气固反应的测试与分析中得到了广泛应用,形成了许多典型的非等温反应分析方法与模型方程.本研究概述了现有热分析的方法原理及在气固反应分析中存在的缺陷,剖析了自主研发的利用微型流化床反应器强化反应...     

Support Effect in the Thermal Decomposition of Some Catalyst Precursors

The thermal decompositions of ammonium metavanadate, molybdic acid and ammonium phosphomolybdate supported on carborundum or silica were subjected to non-isothermal kinetic study. The compensation effect is discussed in connection with the quantitative estimation of the support effect. This revised version was published online in July 2006 with corrections to the Cover Date.     

金属氧化物脱硫/固硫反应动力学中的补偿效应

讨论了氧化锌中温脱硫、氧化钙高温固硫的补偿效应。实验发现,脱除硫化氢 和二氧化硫在反应过程中均先后在动力学控制区和粒子扩散控制区进行。改变非硫 气氛或添加催化组分,所得热重数据均可有效粒子模型处理。lnk_0-E_a及lnD_0- E_D呈线性关系。给出了补偿效应的理论解释。指出晶粒表面及内部缺陷等的随机 指数分布是出现该效应的主要原因。计算了两反应体系的等动力学温度。讨论了高 于和低于该温度时,反应活性与活化能不同的变化规律。并对粒子扩散化学反应性 质进行了探讨。     

Evidence for a compensation effect during the temperature-programmed reduction of copper oxide in hydrogen

The reduction of copper oxide derived from basic Cu-carbonate in hydrogen has been studied under temperature-programmed conditions (TPR) and the TPR patterns were analyzed by means of Arrhenius plots at constant conversion (Friedman plots). These plots indicate that the reduction process cannot be described on the basis of constant kinetic parameters and reveal the presence of isokinetic temperatures. These suggest the presence of a compensation effect requiring a modification of the rate equation.     

Kinetic parameters of decomposition of some selenites

Studying the kinetics of isothermal decomposition of thirteen selenites at isothermal heating, the values of activation energy E of the process, pre-exponential factor A in Arrhenius equation and changes of entropy for the formation of the activated complex of the reagent were calculated. Direct dependence between the thermal stability of the selenites and their cation radii on their 'hardness' or 'softness' was found. The dependence was interpreted in the terms of the generalized perturbation theory of chemical reactivity. Kinetic compensation effect was observed only for the selenites, which thermally decompose by the same mechanism.     

Positronium Conversion Reactions for Testing the Electron Delocalization in 3d Complexes Caused by Ligands

The rate constants of ortho- into para-positronium conversion reactions promoted by paramagnetic 3d complexes were found to be linearly correlated with the delocalization, of unpaired metal electrons caused by ligands. It is shown here that s, usually obtained by UV/Vis absorption spectroscopy, may also be deduced from the correlations mentioned above.     

The Kissinger law and the IKP method for evaluating the non-isothermal kinetic parameters

The following problems concerning the apparent compensation effect (CE) (lnA=a+bE, where A is the pre-exponential factor, E is the activation energy, a and b are CE parameters) due to the change of the conversion function and on which the invariant kinetic parameters method (IKP method) is based, are discussed: (1) the explanation of this kind of CE; (2) the choice of the set of conversion functions that checks CE relationship; (3) the dependencies of CE parameters on the heating rate and the temperature corresponding to the maximum reaction rate. Using the condition of maximum of the reaction rate suggested by Kissinger (Kissinger law), it is pointed out that, for a certain heating rate, the CE relationship is checked only for reaction order (Fn) and Avrami-Erofeev (An) kinetic models, and not for diffusion kinetic models (Dn). Consequently, IKP method, which is based on the supercorrelation relationship between CE parameters, can be applied only for the set Fn+ An of kinetic models. The dependencies of a and b parameters on the heating rate and T _m (temperature corresponding to maximum reaction rate) are derived. The theoretical results are discussed and checked for (a) TG simulated data for a single first order reaction; (b) TG data for PVC degradation; (b) the dehydration of CaC₂O₄·H₂O.