The ‘Temperature Integral’ — Its use and abuse

This paper first reviews the history of the temperature dependence of reaction rate in reaction kinetics. The various equations which are in use today for expressing this dependence were delineated by van't Hoff almost one hundred years ago. Since an exponential form best describes this dependence for most thermal analysis reactions and, due to the fact that the simple Arrhenius equation (with a temperature-independent preexponential factor) has traditionally been used for this purpose, the mathematically intractable temperature integral often has become a necessary evil in the analysis of thermal analysis kinetics. Methods which avoid the temperature integral in kinetics analysis are discussed. The merits of various evaluations and approximations for the temperature integral are described and assessed in this paper.     

Kinetic analysis of thermogravimetric data

Four many curves methods, viz. calculation techniques based on Eqs (30), (31), (34) and (36), respectively, for deriving kinetic parameters from several TG curves recorded with different heating rates are tested on two sets of theoretical TG curves. The maximum reaction rate temperature and conversion, as well as the approximate formulae used for their calculation are discussed. Some aspects of the kinetic compensation effect are analysed. The final conclusion is that the use of the many curves methods is not reasonable.     

反映工艺条件对管式反应器催化反应影响的转化率方程

根据幂指函数g(u))=ua+bu的特点,借用虚拟反应组分和变动级数的概念,提出了管式反应器系统中反应转化率与工艺条件的关系式XM=1-exp[-exp(A+B/Tr+CTr)Prnp0+np1Prτnrr0+nr1τrm∏i=1yniy0+ny1y1].为了验证该转化率方程的普适性,考察了二乙苯催化脱氢、乙苯...     

Hydrolysis kinetics of the sulfonylurea herbicide Sulfosulfuron

The kinetics of hydrolytic degradation of Sulfosulfuron was investigated to predict the fate of the herbicide in an aqueous environment. The study revealed that the hydrolytic degradation of Sulfosulfuron followed first-order kinetics. The degradation of the herbicide was dependent on pH and temperature. Hydrolysis rate was faster in acidic condition (t _1/2 = 9.24 d at pH 4.0) than alkaline environment (t _1/2 = 14.14 d at pH 9.2). Several fold increase in the degradation rate was found when temperature was increased from 10 ± 1°C (t _1/2 = 518 h) to 50 ± 1°C (t _1/2 = 10 h). Activation energy (E _a) was also calculated as 63.87 KJ mol^?1, which is required for the hydrolytic degradation of the molecule. Both media pH and temperature effects were coupled together and derived a complex equation to estimate the overall effect of these two abiotic factors. The major degradation mechanism of the compound was the breaking of the sulfonylurea bridge yielding corresponding sulfonamide and aminopyrimidine. The possible significance of the results to persistence of the herbicide in the field condition is discussed.     

Solid-state Decompositions — Stagnation or Progress?

An appraisal of the trends discerned in the recent literature concerned with solid-state decompositions suggests that this research area lacks a general theoretical framework and, hence, order in the subject is difficult to recognize. There have been surprisingly few reviews of the field. Many of the continuing flow of research publications may be of individual value, but most do not contribute to the overall development of the topic. For example, in many studies of reversible dissociations the sensitivity of rate characteristics to prevailing conditions is not discussed so that the fit of data to rate equations and the magnitudes of calculated Arrhenius parameters may be of empirical value only. Some studies report kinetic results without mechanistic discussions supported by complementary observations. Progress forward from an apparent state of stagnation depends upon more critical examination of the existing literature, coupled with better designed experiments to establish the reproducibility and reliability of kinetic conclusions. Techniques capable of providing insights into the bond redistribution steps that occur during reactions in crystals are also urgently needed. This revised version was published online in August 2006 with corrections to the Cover Date.     

An incremental isoconversional method for kinetic analysis based on the orthogonal distance regression

The parameters obtained from a kinetic analysis of thermoanalytical data often exhibit a conversion‐dependent behavior. A novel incremental isoconversional method able to deal with this phenomenon is proposed. The kinetic model is directly fitted to the experimental data using nonlinear orthogonal least squares procedure. The data are processed without transformations, so their error distribution is preserved. As the objective function is based on a maximum likelihood approach, reliable uncertainties of the parameters can be estimated. In contrast to other methods, the activation energy and the pre‐exponential factor are treated as equally important kinetic parameters and are estimated simultaneously. Validity of the method is verified on simulated data, including a dataset with local nonlinearity in the temperature variation. A practical application on the nonisothermal cold crystallization of polyethylene terephthalate is presented. © 2014 Wiley Periodicals, Inc.     

A Thermal Analysis Study of Hydroxy Benzoic Acid Derivatives Using Rising Temperature Thermogravimetry

Hydroxy benzoic acids were subjected to rising temperature thermogravimetric analysis. After optimizing the procedural variables, the kinetics of decomposition was determined and methyl paraben was taken as the calibration compound to characterize the evaporation patterns for the ortho and meta derivatives. The E _act values for ortho, meta and para derivatives were 64.8, 78.2, and 119.1 kJ mol^–1, respectively. The Antoine and Langmuir equations were utilized to determine the coefficient of evaporation k, which was 124525±0.8, units being in the SI system. The vapor pressure plots were generated for the ortho and meta derivatives; ΔH _vap for these two compounds were obtained as 66.7 and 80.4 kJ mol^–1, respectively. This revised version was published online in August 2006 with corrections to the Cover Date.     

Role of isoconversional methods in varying activation energies of solid-state kinetics: I. isothermal kinetic studies

Solid-state kinetics was developed from kinetic concepts for reactions in homogeneous phase systems, which has created considerable debate over issues such as variable activation energy. This behavior has been viewed by some as a violation of basic chemical kinetic principles. Variation in activation energy has been detected by isoconversional or ‘model-free’ calculation methods. The relationship between different calculation methods and the occurrence of variable activation energy was investigated in this work by employing model-fitting and isoconversional methods to analyze simulated isothermal data. In addition, these approaches were applied for sulfameter-dioxolane solvate desolvation data. We showed that variable activation energy is of two types—a true variation that results from the complex nature of the solid-state process and an artifactual one resulting from the use of some isoconversional methods.     

Elementary Steps in Heterogeneous Catalysis

Despite the great importance of heterogeneous catalysis, research in this field has long been characterized by its empiricism. Now, however, thanks to the rapid development of methods in surface physics, the elementary steps can be identified at the atomic level and the underlying principles understood. Defined single crystal surfaces are employed as models, based on the analysis of the surfaces of ‘real’ catalysts. Direct images, with atomic resolution, can be obtained using scanning tunneling microscopy, while electron spectroscopic methods yield detailed information on the bonding state of adsorbed species and the influence of catalyst additives (promotors) upon them. The successful application of this approach is illustrated with reference to the elucidation of the mechanism of ammonia synthesis. The catalyst surface is usually transformed under reaction conditions, and, as the processes involved are far-removed from equilibrium, such transformations can lead to intrinsic spatial and temporal self-organization phenomena. In this case, the reaction rate may not remain constant under otherwise invariant conditions but will change periodically or exhibit chaotic behavior, with the formation of spatial patterns on the catalyst surface.     

热分析动力学研究方法的新进展

"非等温动力学"作为热分析动力学研究的核心,已经被广泛应用于化学、化工、冶金、地质、药物和环保等重要领域。热分析动力学研究的主要任务是确定机理函数、活化能和指前因子等动力学参数。在众多的热分析动力学研究方法中,"等转化率法"由于其可以在不涉及动力学模式函数的前提下,获得较为可靠的活化能值,因此被国际热分析与量热学协会(ICTAC)推荐使用。本文简要介绍了近十年来提出的热分析动力学研究方法,特别是等转化率方法的研究进展情况,评述了各种方法的特点与局限。同时,展望了热分析动力学研究方法未来的发展趋势。     

Analysis of crystallization kinetics of poly(ether ether ketone) by a nonisothermal method

During cooling at a rate of 10°C/min from the melt state of PEEK we have followed the growth of spherulites using an optical microscope equipped with a camera. The isothermal growth rates of crystallization in the temperature range of 266–308°C could be estimated by means of a differential equation. These continuous growth rate data were used further for kinetic analysis, which indicated that PEEK exhibited an unmistakable regime II → III transition at 296°C. The results compared favorably with those obtained by the traditional isothermal method, which is time consuming. Due to chain folding, the Thomas–Staveley constant should be closer to 0.25 instead of 0.1 or 0.3. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2393–2399, 1998     

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.     

ThermoSlope: A Software for Determining Thermodynamic Parameters from Single Steady-State Experiments

The determination of the temperature dependence of enzyme catalysis has traditionally been a labourious undertaking. We have developed a new approach to the classical Arrhenius parameter estimation by fitting the change in velocity under a gradual change in temperature. The evaluation with a simulated dataset shows that the approach is valid. The approach is demonstrated as a useful tool by characterizing the Bacillus pumilus LipA enzyme. Our results for the lipase show that the enzyme is psychrotolerant, with an activation energy of 15.3 kcal/mol for the chromogenic substrate para-nitrophenyl butyrate. Our results demonstrate that this can produce equivalent curves to the traditional approach while requiring significantly less sample, labour and time. Our method is further validated by characterizing three α-amylases from different species and habitats. The experiments with the α-amylases show that the approach works over a wide range of temperatures and clearly differentiates between psychrophilic, mesophilic and thermophilic enzymes. The methodology is released as an open-source implementation in Python, available online or used locally. This method of determining the activation parameters can make studies of the temperature dependence of enzyme catalysis more widely adapted to understand how enzymes have evolved to function in extreme environments. Moreover, the thermodynamic parameters that are estimated serve as functional validations of the empirical valence bond calculations of enzyme catalysis.     

What theoretical and/or chemical significance is to be attached to the magnitude of an activation energy determined for a solid-state decomposition?

This critical survey argues that the theory, conventionally used to interpret kinetic data measured for thermal reactions of initially solid reactants, is not always suitable for elucidating reaction chemistry and mechanisms or for identifying reactivity controls. Studies of solid-state decompositions published before the 1960s usually portrayed the reaction rate as determined by Arrhenius type models closely related to those formulated for homogeneous rate processes, though scientific justifications for these parallels remained incompletely established. Since the 1960s, when thermal analysis techniques were developed, studies of solid-state decompositions contributed to establishment of the new experimental techniques, but research interest became redirected towards increasing the capabilities of automated equipment to collect, to store and later to analyze rate changes for selected reactions. Subsequently, much less attention has been directed towards chemical features of the rate processes studied, which have included a range of reactants that is much more diverse than the simple solid-state reactions with which early thermokinetic studies were principally concerned. Moreover, the theory applied to these various reactants does not recognize the possible complexities of behaviour that may include mechanisms involving melting and/or concurrent/consecutive reactions, etc. The situation that has arisen following, and attributable to, the eclipse of solid-state decomposition studies by thermal analysis, is presented here and the consequences critically discussed in a historical context. It is concluded that methods currently used for kinetic and mechanistic investigations of all types of thermal reactions indiscriminately considered by the same, but inadequate theory, are unsatisfactory. Urgent and fundamental reappraisal of the theoretical foundations of thermokinetic chemical studies is now necessary and overdue. While there are important, but hitherto unrecognized, delusions in thermokinetic methods and theories, an alternative theoretical explanation that accounts for many physical and chemical features of crystolysis reactions has been proposed. However, this novel but general model for the thermal behaviour and properties of solids has similarly remained ignored by the thermoanalytical community. The objective of this article is to emphasize the now pressing necessity for an open debate between these unreconciled opinions of different groups of researchers. The ethos of science is that disagreement between rival theories can be resolved by experiment and/or discussion, which may also strengthen the foundations of the subject in the process. As pointed out below, during recent years there has been no movement towards attempting to resolve some fundamental differences of opinion in a field that lacks an adequate theory. This should be unacceptable to all concerned. Here some criticisms are made of specific features of the alternative reaction models available with the stated intention of provoking a debate that might lead to identification of the significant differences between the currently irreconciled views. This could, of course, attract the displeasure of both sides, who will probably criticise me severely. Because I intend to retire completely from this field soon, it does not matter to me if I am considered to be ‘wrong’, if it contributes to us all eventually agreeing to get the science ‘right’.     

Comments on the interpretation of temperature dependence of processes in polymers

The interpretation of the results of thermal measurements followed over decades the Arrhenius law. In recent years an apparently different interpretation (Eyring's equation) has been emerging in the literature on polymers. As the main reason for this, a direct connection to material properties has been claimed.The paper shows some weak points in the Eyring theory and in its application as well. Firstly, the parameters of the two equations are mathematically convertible to each other. Thus Eyring's conceptual quantities (entropy and enthalpy of activation) give no new physical information. Secondly, the Eyring theory postulates an equilibrium for the activated state. In the case of processes, however, in which change is an inherent characteristic, this assumption seems to be unjustified.The authors acknowledge the support of this work by the Hungarian Research Foundation. Contract No. 2772.     

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     

Significance of Non-isothermal Kinetic Data. A statistical study

Arrhenius parameters values, in non-isothermal kinetic vaporisation processes for a series of compounds with related structures, have been calculated. This was made using a method of calculation that allows to find the most probable vaporisation mechanisms. According to this method DTG curves were compared with some theoretical ones reported in literature, whose shape results to be only a function of the mechanisms. In this way the choice of the mathematical functions which can be inserted in the kinetic equations, was influenced by the shape of the DTG plots and other thermal analysis signals thus allowing to choose the most probable mechanisms. The kinetic parameters derived from these mechanisms were compared, using statistical analysis, with those obtained from another method of calculation based on ‘a priori’ vaporisation mechanism chosen for the investigated liquid–gas transition. The standard deviations of the slope and of the intercept, together with the standard deviation and the square correlation coefficient (r ²) of the linear regression equations related to the mechanisms of the two methods were calculated. Student t-test, Fisher F-test, confidence intervals (c.i.) and residuals valueswere also given. Statistical analysis shows that the mechanisms obtained with the former method (diffusive and geometrical models) and the related Arrhenius parameters result to be more significant (in terms of probability) than the corresponding quantities of the latter for which a first-order model was chosen. This revised version was published online in August 2006 with corrections to the Cover Date.     

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     

Novel theoretical and computer-assisted modeling of isothermal and non-isothermal depolymerization kinetics

A novel kinetic model accounting for the observed asymptotic approach of the degree of polymerization (DP) to a limiting value significantly greater than unity on prolonged degradation is derived and applied to the solid-state degradation of cellulose (Kraft paper) and poly(acrylic acid) (PAA) under isothermal and non-isothermal conditions. Experimental data were fitted using two iterative computer algorithms: one for isothermal DP data and the other for non-isothermal DP data obtained under a linear temperature ramp. The apparent activation energy for the solid-state recombination of chain radicals was found to be low in each case and was attributed to the proximity of free radicals being facilitated by restrictions imposed by the polymer matrix. The application of the model to non-isothermal DP yielded rate parameters that could be reconciled with those obtained from isothermal analyses, suggesting the novel approach has much merit for the future study of polymer degradation.     

聚丙烯/聚(丙烯-g-马来酸酐)/蒙脱土纳米复合材料结晶动力学研究

非等温结晶动力学;聚丙烯/聚(丙烯-g-马来酸酐)/蒙脱土纳米复合材料结晶动力学研究