On the kinetic parameters from non-isothermal data: mathematical considerations

The kinetic parameters determination of the crystallization of a disordered solid solution subjected to non-isothermal treatments is often considered using a large variety of physical models. Some authors propose the use of Johnson-Mehl-Avrami's classic expression which corresponds to both isothermal and non-isothermal kinetic parameters, according to experimental results.In this paper we carry out research, starting from the generalized model most widely used by the non-isothermal problem, in which we prove the validity of Johnson-Mehl-Avrami's expression.     

Some considerations on the treatment of the kinetic data of heterogeneous isotope exchange

A direct curve simulation treatment has been worked out for the evaluation of the kinetic curves of heterogeneous isotope exchange. Based on the data obtained by a personal computer some considerations have been made on the transport processes in the fully and half exchanged sodium forms of crystalline zirconium phosphate.     

On the evaluation of dynamic X-ray diffractometric data for kinetic and structural purposes

Possible errors made due to incorrect evaluation of time- or temperature-resolved X-ray data (TXRD) are described. The extraction of compositional information, e.g., for kinetic purposes, can be highly erroneous when neglecting the influence of the changing mass absorption coefficient and a proper conversion of mass fractions to molar fractions. When structural data are computed, care should be given to a possible volume change of the sample. The correct way of evaluation and the extent of these errors is demonstrated for the thermal decarboxylation of calcium carbonate.     

Regularities in the consumption of the initial reactants in various kinetic regimes

Using hydrogen oxidation as an example, it is demonstrated that, when gas ignition is prevented by means of inhibition, there is practically no consumption of the initial reactants because reaction chains do not form for lack of time and the rates of intermolecular reactions are insignificant. When the propagating flame and detonation wave are partially suppressed, the inhibitor is consumed only in chain termination reactions involving reactive intermediate species. Oxygen is additionally consumed in its reactions with products of incomplete inhibitor conversion.     

Importance of proper baseline identification for the subsequent kinetic analysis of derivative kinetic data

Theoretically, simulated kinetic data were used to evaluate the performance of the linear, cubic spline and Bezier mathematic interpolations (in comparison with the physically meaningful tangential area-proportional interpolation) in case of the complex kinetics involving two independent processes with different degrees of overlapping. The Bezier interpolation exhibited best performance; the linear interpolation performed significantly worse than the two other ones. In general, the data distortions caused by application of the mathematic interpolations do not significantly influence the model-free kinetic parameters—apparent activation energy and pre-exponential factor; errors below 2% occurred even for the most extremely distorted data. On the other hand, the integrated peak area and the model-based parameters such as kinetic exponents and the complexity ratio can be significantly influenced by the interpolations-caused data distortions, with the associated errors being in the order of tenths of percent. Nevertheless, the distortions associated with the choice of the thermokinetic interpolation were found to not affect the thermal stability predictions for the complex kinetic processes; only the precise predictions based on the mid-range degrees of conversion (e.g., controlled preparation of glass–ceramics) can be significantly affected by the incorrect interpolation of the thermokinetic background.

     

Obtaining thermochemical data by the extended kinetic method

A microcanonical analysis of the extended kinetic method is performed using statistical rate calculations based on orbiting transition state theory. The model systems simulate polydentate bases M which exhibit losses of entropy upon protonation of up to 35 kJ mol(-1) K(-1). It is shown that the correlations using the natural logarithm of the ratio of rate constants vs the proton affinity of the reference bases, at several effective temperatures, lead to correct proton affinity and protonation entropy of the base M of interest. A systematic underestimate of the latter quantity (by 5-15%), mainly due to the use of a linear rather than a polynomial curve fitting procedure, is noted, however. When considering experimental data, more severe underestimates are observed for the protonation entropies of polydentate bases (by 50-90%). The origins of these considerable discrepancies are beyond the limits of the present modeling and remain to be determined.     

Kinetics of reactions in solution: Method for the treatment of data from non-isothermal chemical kinetic experiments

A new method is proposed for the treatment of kinetic data derived from non-isothermal kinetic experiments for the determination of the parameters of the Arrhenius equation. The results obtained from its application show the excellent precision of this method.

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Computer-aided treatment of thermogravimetric data and calculation of effective kinetic parameters of thermal decomposition processes

Separate stages of mathematical processing of thermogravimetric data, the difficulties most often encountered, and typical error sources are considered. A complex procedure of automatic acquisition and editing of experimental data, including calculation of effective kinetic parameters, is described and an appropriate algorithm for the 15 BCM-5 microcomputer is presented. The computer calculation of the kinetic parameters of the multistage thermal decomposition of a polyamide fibre is given as an example.

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Zusammenfassung Verschiedene Phasen der mathematischen Behandlung von thermogravimetrischen Daten, am häufigsten auftretende Schwierigkeiten und typische Fehlerquellen werden erörtert. Das komplexe Verfahren der automatischen Eingabe und Ausgabe experimenteller Daten wird, einschliessliche der Berechnung von effektiven kinetischen Parametern, beschrieben. Ein entsprechender Algorithmus wird für den Mikrokomputer 15 BCM-5 angegeben. Als Beispiel wird die Berechnung der kinetischen Parameter der mehrstufigen thermischen Zersetzung von Polyamidfasern ausgeführt.

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On the single-electron local kinetic energy

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Estimation of kinetic parameters from thermochemical data

A method is described by which kinetic parameters may be calculated from the measured temperature changes caused by the heat produced during a chemical reaction. An isoperibol titration calorimeter with an ampoule-breaking facility is used to obtain the temperature data. The temperature changes resulting from the reaction between tri-isopropyl phosphite and sulphur (S(8)) are used as an example to demonstrate the effectiveness of the method. The temperature changes are used to calculate an enthalpy of reaction. From the enthalpy of reaction and intermediate heats, instantaneous concentrations of the reactants may be calculated.     

Analysis of kinetic data by Johnson-Mehl equation

Johnson-Mehl equation is written as d/dt=k ⁿ t ^n–1 (1–) where is the degree of reaction,t time andn a constant. Use of this equation in kinetic analysis present problems because of the presence of a t term on the right hand side. The equation is not a true kinetic equation andk is not a true rate constant.This paper presents a brief discussion on the use of this equation as such or in a modified form and also indicates the proper procedure for evaluating kinetic parameters correctly. Some experimental data on the reduction of Fe₂O₃ to Fe₃O₄ have been used to test the mathematical procedure proposed. This reaction is known to follow the typical trend described by Johnson-Mehl equation.

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Zusammenfassung Die Johnson-Mehl-Beziehung lautet:d/dt=k ⁿ t ^n–1(1–) mit der Reaktionskoordinate, der Zeitt und der Konstanten. Eine Anwendung dieser Gleichung in der kinetischen Analyse verursacht Probleme, da auf der rechten Seite der Gleichung ein t-haltiger Ausdruck steht. Die Gleichung ist keine wirkliche kinetische Gleichung undk ist keine wahre Geschwindigkeitskonstante.Diese Arbeit beschreibt eine kurze Diskussion der Anwendung dieser Gleichung in dieser oder einer modifizierten Form und beschreibt, wie korrekte kinetische Parameter erhalten werden können. Zum Testen des vorgeschlagenen mathematischen Verfahrens wurden einige experimentelle Daten der Reduktion von Fe₂O₃ zu Fe₃O₄ benutz. Diese Reaktion ist bekannt, dem typischen, durch die Johnson-Mehl-Gleichung beschriebenem Trend zu folgen.

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Dr. S. B. Sarkar wishes to acknowledge the financial support of the Commonwealth Commission (U.K.) and the experimental facilities provided by the Imperial College of Science and Technology, London U.K.     

Determination of kinetic parameters of the FeCl3/FeCl2 systemvia a novel treatment of chronoamperometric data

Summary Computer based methods for the processing of chronoamperometric datavia convolutions are discussed. On the example of the quasi-reversible Fe³⁺/Fe²⁺ couple, their application for data acquisition and determination of the heterogeneous electrochemical parameters is demonstrated. The plot of Q/i vs. t/i is superior to that employingi/I ₁, being less sensitive to distortions by charging currents once these have died away and by the effects of damping on the initially rapidly varying currents. Cyclic voltammetry is often combined with convolution or deconvolution, and digital simulation studies are also frequently performed to confirm the results.

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Bestimmung kinetischer Parameter des Systems FeCl₃/FeCl₂ mittels einer neuen Verarbeitung chronoamperometrischer Daten

Zusammenfassung Computerunterstützte Verfahren zur Verarbeitung chronoamperometrischer Daten mittels Faltungsintegralen werden diskutiert. Am Beispiel des quasireversiblen Systems Fe³⁺/Fe²⁺ wird die Anwendung der neuen Methoden zur Datenerfassung und zur Bestimmung der heterogenen elektrochemischen Parameter gezeigt. Der Plot von Q/i gegen t/i ist dem voni/I ₁ überlegen, da er durch Ladeströme und Dämpfung der ursprünglich stark variierenden Ströme weniger stark beeinflußt wird. Cyclische Voltammetrie wird häufig im Zusammenhang mit Konvolutions- und Dekonvolutionsmethoden angewandt; digitale Simulation zur Überprüfung der Ergebnisse wird ebenfalls oft eingesetzt.

     

On the kinetic interpretation of metal-support interaction

Metal-support interaction (MSI) in catalysis is discussed in terms of the surface electron gas model (SEGM), which accounts for the case of inhomogenous surface. In the case of MSI the initial heat of adsorption as well as the effective charge of adsorbed particles can differ from that in the absence of metal-support interaction. Conditions at which either negligible small adsorption coefficients (reaction rate) or their enhancement compared to non-MSI conditions are presented.     

On the application of exponential kinetic equations

An exponential kinetic equation for complex chemical reactions in solid-liquid heterogeneous systems is discussed. The integral form of the equation is analyzed and the conditions specified for the application of an approximate form. The meaning of constant t₀ is explained.

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