Kinetic Analysis Of Solid-state Reactions Research Articles

Relevance of Particle Size Distribution to Kinetic Analysis: The Case of Thermal Dehydroxylation of Kaolinite

Kinetic models used for the kinetic analysis of solid-state reactions assume ideal conditions that are very rarely fulfilled by real processes. One of the assumptions of these ideal models is that all sample particles have an identical size, while most real samples have an inherent particle size distribution (PSD). In this study, the influence of particle size distribution, including bimodal PSD, in kinetic analysis is investigated. Thus, it is observed that PSD can mislead the identification of the kinetic model followed by the reaction and even induce complex thermoanalytical curves that could be misinterpreted in terms of complex kinetics or intermediate species. For instance, in the case of a bimodal PSD, kinetics is affected up to the point that the process resembles a reaction driven by a multi-step mechanism. A procedure for considering the PSD in the kinetic analysis is presented and evaluated experimentally by studying the thermal dehydroxylation of kaolinite. This process, which does not fit any of the common ideal kinetic models proposed in the literature, was analyzed considering PSD influence. However, when PSD is taken into account, the process can be successfully described by a 3-D diffusion model (Jander’s equation). Therefore, it is concluded that the deviations from ideal models for this dehydroxylation process could be explained in terms of PSD.

Insight into master plots method for kinetic analysis of lignocellulosic biomass pyrolysis

The determination of the kinetic triplet including the activation energy, frequency factor, and kinetic mechanism function is a key objective in kinetic analysis of solid-state reactions like lignocellulosic biomass pyrolysis. The master plots method is usually used to determine the kinetic mechanism function once the activation energies as a function of conversion are estimated from an isoconversional method. A critical study of the master plots method has been performed by analyzing theoretically simulated processes with varying activation energies and frequency factors. The accuracy of the resulting kinetic mechanism function calculated by the master plots method is strongly dependent on the variation degree of the frequency factor with conversion and the conversion dependency of activation energy from isoconversional methods. The utilization of the master plots method without considering the variation degree of the frequency factor with conversion may result in misestimating kinetic mechanism function.

Applications of sample-controlled thermal analysis (SCTA) to kinetic analysis and synthesis of materials

The advantages of the sample-controlled thermal analysis (SCTA) for both the kinetic analysis of solid-state reactions and the synthesis of materials are reviewed. This method implies an intelligent control of the temperature by the solid-state reaction under study in such a way that the reaction rate as a function of the time fits a profile previously defined by the user. It has been shown that SCTA has important advantages for discriminating the kinetic model of solid-state reactions as compared with conventional rising temperature methods. Moreover, the advantages of SCTA methods for synthesising materials with controlled texture and structure are analysed.

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.

Kinetic Analysis of Solid-State Reactions: A General Empirical Kinetic Model

In this research note, we presented a general empirical kinetic model that can fit any ideal kinetic model and even deviations produced by heterogeneities in particle shapes. The algebraic expression of the general empirical kinetic model is f(α) = αm(1 − qα)n. The kinetic model can be used for performing the kinetic analysis of experimental data without previous assumptions about the form of the reaction kinetic model. The empirical kinetic model has been evaluated from the theoretical and experimental data.

Experimental tests to validate the rate-limiting step assumption used in the kinetic analysis of solid-state reactions

The kinetic analysis of experimental data obtained in the case of solid-state reactions (thermal decompositions, reactions of gases with solids) relies on various assumptions among which two are of very high importance: the steady-state approximation and the rate-limiting step. Both assumptions may be verified using simple experimental tests. The first one needs the coupling of measurements of the kinetic rate by two methods (in general thermogravimetry and calorimetry). The second one is based on sudden changes (jumps), during an experiment, of the temperature, or of the partial pressure of gases which have an influence on the kinetic rate. The basic principles of these tests are first explained, then various examples are given in order to illustrate their application to solid-state reactions.

Kinetic analysis of solid-state reactions: Precision of the activation energy obtained from one type of integral methods without neglecting the low temperature end of the temperature integral

Many approximated equations have been proposed to approximate the temperature integral, which frequently occurs in the nonisothermal kinetic analysis of solid-state reactions and has no exact analytical solution. The main application of those equations is the determination of the activation energy, not the estimation of the temperature integral. Several authors have analyzed the precision of the activation energy obtained from some integral methods. In their calculations, the low temperature end of the temperature integral was neglected. In this paper, a systematic analysis of the precision of one type of integral methods for the determination of the activation energy has been carried out without doing any simplification. Our results have indicated that for all integral methods analyzed in this work, there is a significant influence of two dimensionless quantities ( γ, the dimensionless activation energy, and ξ, the normalized temperature) in the precision of the calculated activation energy values.

Kinetic analysis of solid-state reactions: errors involved in the determination of the kinetic parameters calculated by one type of integral methods

The integral methods are extensively used for performing the kinetic analysis of solid-state reactions. As the Arrhenius integral function p(u) does not have an exact analytical solution, many approximations have been proposed. One popular type of approximations is called the exponent approximation which can be put in the form $$p(u) = e^{a+b\,ln\,u+cu}$$ . In this study, a systematic analysis of the errors involved in the determination of the kinetic parameters calculated by the integral methods based on the exponent approximations for p(u) has been carried out. The results have shown that the precision of the kinetic parameters computed from the integral methods analyzed in this paper depends on u and the errors of the kinetic parameters determined from Doyle approach are the largest.

Kinetic analysis of solid-state reactions: A new integral method for nonisothermal kinetics with the dependence of the preexponential factor on the temperature ( A = A0T n)

In this study, we have proposed a new approximation for the general temperature integral, which frequently occurs in the nonisothermal kinetics with the dependence of the preexponential factor on the temperature and has no exact analytical solution. The validity of the new approximation has been tested by some numerical analyses. As the solution of the general temperature integral, the new approximation is more accurate than other approximations. Based on the newly proposed approximation, the corresponding integral method has been given. The precision of the integral methods for the determination of the activation energy has been calculated, and the results have shown that the relative error involved in the activation energy obtained from the new integral method is smaller than that from other integral methods. For applications, nonisothermal data obtained by theoretical simulation have been successfully processed using the new integral method.

Combined Kinetic Analysis of Solid-State Reactions: A Powerful Tool for the Simultaneous Determination of Kinetic Parameters and the Kinetic Model without Previous Assumptions on the Reaction Mechanism

The combined kinetic analysis implies a simultaneous analysis of experimental data representative of the forward solid-state reaction obtained under any experimental conditions. The analysis is based on the fact that when a solid-state reaction is described by a single activation energy, preexponetial factor and kinetic model, every experimental T-alpha-dalpha/dt triplet should fit the general differential equation independently of the experimental conditions used for recording such a triplet. Thus, only the correct kinetic model would fit all of the experimental data yielding a unique activation energy and preexponential factor. Nevertheless, a limitation of the method should be considered; thus, the proposed solid-state kinetic models have been derived by supposing ideal conditions, such as unique particle size and morphology. In real systems, deviations from such ideal conditions are expected, and therefore, experimental data might deviate from ideal equations. In this paper, we propose a modification in the combined kinetic analysis by using an empirical equation that fits every f(alpha) of the ideal kinetic models most extensively used in the literature and even their deviations produced by particle size distributions or heterogeneities in particle morphologies. The procedure here proposed allows the combined kinetic analysis of data obtained under any experimental conditions without any previous assumption about the kinetic model followed by the reaction. The procedure has been verified with simulated and experimental data.

Experimental test to validate the rate equation “d α/d t = kf( α)” used in the kinetic analysis of solid state reactions

In order to improve the soundness of the kinetic analysis of solid-state reactions, we present an experimental test based on a sudden change (jump), during an experiment, of the temperature, or of the partial pressure of gases, which have an influence on the kinetic rate. This test, denoted “ f( α) test” allows to discriminate if the kinetic modelling may or may not involve the rate equation d α/d t = kf( α) for any kind of reaction: thermal decomposition, solids reacting with gases, … Numerous examples are given and discussed according to the answer of the test, mainly based on the consideration of nucleation and growth processes.

Stocktaking in the kinetics cupboard

Some of the continuing problems of kinetic analysis of solid-state reactions are reviewed and some recent advances towards their solution are discussed. Attention is drawn to the important findings of an ICTAC Kinetics Project that need consideration by authors and editors of kinetics papers.

Sample Controlled Thermal Analysis and Kinetics

AbstractFor Abstract see ChemInform Abstract in Full Text.

Sample controlled thermal analysis and kinetics

The SCTA methods for the kinetic analysis of solid-state reactions have been reviewed. It has been shown that these methods present two important advantages with regards to the more conventional rising temperature experiments. Firstly, they have a higher resolution power for discriminating among the reaction kinetic models and, secondly, SCTA is a powerful tool for minimizing the influence of the experimental conditions on the forward reaction.

On the Li and Tang's isoconversional method for kinetic analysis of solid-state reactions from thermoanalytical data

A criterion for the reaction mechanism as expressed by differential conversion function based on the Li and Tang's isoconversional method is suggested. The suitability of the use of Li and Tang's method for the estimation of a conversion dependent activation energy is discussed.

Kinetic Analysis of Solid-State Reactions: The Universality of Master Plots for Analyzing Isothermal and Nonisothermal Experiments

Master plot methods based on the integral and/or the differential forms of the kinetic equation describing solid-state reactions have been redefined by using the concept of the generalized time, θ, introduced by Ozawa. This redefinition permits the application of these master plots to the kinetic analysis of solid-state reactions, whatever the type of temperature program used for recording the experimental data. In isothermal conditions, a single curve is enough to construct the experimental master plots. In nonisothermal conditions, the knowledge of both α as a function of temperature and activation energy is required for calculating the master plot curves from the experimental data. Practical usefulness of the present master plot methods is examined, and exemplified by being applied to the thermal decomposition of ZnCO3 under isothermal, linear nonisothermal, and nonlinear nonisothermal conditions.

Formal kinetic analysis of processes in the solid state

The applicability of an unconventional approach in the formal kinetic analysis of solid-state reactions is discussed. This approach is based on the joint use of so-called isoconversional methods and of the non-linear regression analysis. By means of this approach reliable kinetic parameters for the phase transitions between three polymorphic modifications of calcium carbonate were obtained. The influence of the conditions of sample preparation on the transition kinetics has been studied. Two different transition mechanisms are compared using the calculated kinetic data. The isoconversional method, proposed by Friedman, delivers activation energy values, which deviates from data, obtained by means of the Flynn–Wall–Ozawa method. Additionally, the calculated apparent activation energy is dependent on the degree of conversion. The influence of some model deviations on the accuracy of the isoconversional methods is discussed. It is shown that the robustness of these methods towards model deviations may be tested by an analysis of theoretical plots.

Isoconversion method for kinetic analysis of solid-state reactions from dynamic thermoanalytical data

The activation energy for a heterogeneous reaction involving a solid may be obtained from a plot of ∫α0 ln(dα/dt) dα against ∫α0(1/T) dα, where α represents the fractional conversion of the solid reactant, and T(t) is the (time-dependent) reactant temperature. This new approach to the analysis of dynamic thermoanalytical kinetic data has distinct advantages over existing methods, as it needs to make no assumption about the kinetic model, involves no approximation to the temperature integral, and is easy to implement on the computer.

The Prout-Tompkins rate equation in solid-state kinetics

Abstract In more than 50 years since its publication, a paper in the Transactions of the Faraday Society by Prout and Tompkins has been extensively cited in the literature. The paper dealt with the kinetics of the thermal decomposition of crystals of potassium permanganate, and suggested a rate equation, which has become known within the field as the Prout-Tompkins equation, for use in the kinetic analysis of solid-state reactions. This equation and its applications in a variety of different fields, including general kinetics of solid-state reactions; continuing work on KMnO 4 ; irradiation effects; pharmaceutical stability studies, and colloid and interfacial chemistry, are discussed.

Isothermal kinetic analysis of solid-state reactions using plots of rate against derivative function of the rate equation

Since the advent of digital data capture and the development of quick and accurate numerical methods for data processing, the use of rate measurements ( dα dt ) for kinetic analysis of solid-state reactions has gained in popularity. Rate measurements may readily be obtained through use of isothermal derivative thermogravimetry (DTG), or from isothermal differential scanning calorimetry (DSC) (on the assumption that the evolution or absorption of heat may be used to measure the extent of reaction, α). In this paper, the feasibility and desirability of using plots of experimental dα dt values against the derivative functions for the various models for solid-state reactions is considered critically and discussed quantitatively.