Analysis of isothermal kinetic data from solid-state reactions

In most solid state reactions the reaction velocity can be described as a product of two functionsK(T) andf(1?α) whereT is the temperature and α the degree of conversion of the solid reactant. The physical interpretation of these functions is discussed, and a systematic method is described by whichf(1?α) of a reaction is identified from its kinetic data.K(T) and the reaction mechanism are then determined. This method has been successfully applied to analyse the kinetics of the thermal decomposition of silver azide.     

Analysis of dynamic kinetic data from solid-state reactions

The kinetics of heterogeneous reactions, involving one reactant in the solid phase, usually follow the lawα=K _∞ exp(?E/kT)f(1?α), where α is the degree of conversion of the solid, andK _∞ andE are the kinetic constants. A critical examination is given of the various methods which are currently used to analyse dynamic experimental data. The limitations of these methods and their insensitivity to the form off(1-α) are pointed out. An alternative approach free from these limitations is suggested. In this,f(1?α) is determined from isothermal experiments, and then the dynamic data are accurately analyzed to obtain the values of the kinetic constants. A case study is given to elucidate the applicability of the approach.     

Expanding spherical shell kinetic model for diffusion-controlled solid-state reactions

A reaction kinetic model has been derived for a solid-state diffusion-controlled reaction in a system of spherical particles of A isolated in a matrix of B. This model is analogous to the Ginstling-Brounsthein model except that the diffusion of A is the rate-controlling step. The model, therefore, resulting in an expanding spherical shell of product AB, is

where t = time, x = fraction reaction, K = reaction rate constant.     

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.

---

. , , .

     

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.     

A simple kinetic method for the determination of the reaction model from non-isothermal experiments

In a recent article, we obtained an approximate solution for the evolution of a transformed fraction under isochronal conditions for a large variety of single-step transformations. We verified that this solution is accurate and can, in many instances, be used instead of the exact numerical solutions of the corresponding differential equations. In this article we want to examine the possibilities offered by an analytical solution in the analysis of thermoanalytical curves. We will show that for single-step transformations, our model predicts that under the proper time scaling the thermograms obtained at different heating rates merge into a single curve. This ‘universal curve’ is exclusively related to the kinetic model. In addition, the universal curve can be obtained from experimental thermograms by means of a simple transformation. In this way, the dependence of the experimental curves on the rate constant and the kinetic model can easily be separated, making it possible to independently determine the kinetic parameters and the kinetic model. In addition, one can easily check the validity of the kinetic analysis as well as calculate a reliable statistical measure of the goodness of the single-step assumption.     

A computer method to determine the kinetic law of solid-state reactions from DSC curves

A computer program has been worked out to evaluate the activation energy, the Arrhenius pre-exponential factor and the mechanism of solid-state reactions from non-isothermal measurements. A univocal determination of the reaction mechanism is obtained by the simultaneous application of two selection criteria: (a) activation energy value by the Ozawa method; (b) degree of linearity in the <Satava method.A modification of the Rogers and Smith method was then used to obtain empirically complete agreement between kinetic expression and experimental results when the kinetic law has to be improved to account for a whole experimental curve.The accuracy of the computer method has been checked through a calibration of the program by means of 16 theoretical functions proposed by <Sesták.     

Weibull mixture model for modeling nonisothermal kinetics of thermally stimulated solid-state reactions: application to simulated and real kinetic conversion data

The possibility of applying Weibull mixture model for the fitting of the nonisothermal kinetic conversion data has been investigated. It has been found that the kinetic conversion data at different heating rates can be successfully described by one or the linear combination of few Weibull distribution functions. Several simulated and real kinetic conversion traces have been analyzed. An optimal fitting of the kinetic conversion data has been obtained by a mixture of Weibull distribution functions. The results obtained have shown that the obtained conversion curves calculated by the model proposed in this paper are in agreement with the raw kinetic conversion data.     

Comprehensive kinetic studies on isothermal and non-isothermal reactions of some aluminium compounds

Residual differences after model fitting were investigated in both isothermal and non-isothermal kinetics in order to make numerical comparisons between several models and various parameter-estimating methods. Data from two independent experimental series were evaluated. A large data set, collected earlier under isothermal conditions from decompositions and hydrothermal reactions of aluminium hydroxides and oxides, was processed first. It showed that mechanical activation of the starting gibbsite affected reactivity of samples in several subsequent reactions for all model equations tried. The relative residual deviation concept is introduced, and statistics were applied to find a model that fits a certain reaction in most of the cases. In the second study, the sulphate decomposition step of aluminium sulphate octadecahydrate was investigated. TG curves were measured using a constant heating rate. Dynamic models were fitted by three mathematical methods, including a new general purpose one. Fitting ability of the methods with various complexity were compared on the basis of residual deviations obtained after integration of the model equations. As well as evaluating the best fit, this new parameter-estimating method provides a statistical analysis of the reliability of the whole model fitting process.     

A generalized computer program for determining the kinetic mechanism of solid-state reactions

A consideration of the various types of reactions controlling kinetic processes in general appears to suggest that it is possible to express all such reactions by a differential equation of the form $\text{dα}\text{d}\text{t}$ = A exp(?E/RT)(1?α)ⁿαⁿ[?1n(1?α1]^pwhere α = fraction of the substance reacted, t = time of reaction, A = pre-exponential factor, E = energy of activation, R = universal gas content, and m, n, p are constants The presence (or absence) of the indices m, n, p, cr any combination of these, in this equation when it is fitted to a set of thermogravimetric data relating to the fraction of the substance decomposed and the absolute temperature can reasonably be expected to throw light on the mechanism of the process.This paper presents the features of a numerical algorithm for studying kinetic data on the above lines and suggests a possible scheme for predicting the most probable kinetic mechanism by a consideration of the differences of the predicted from the experimental values. A computer program was developed on an IBM 360 computer for implementing this scheme and evaluating the kinetic parameters from experimental thermogravimetric data. The values obtained from the program for a pyrolysis reaction which typifies the system and the inferences drawn therefrom regarding the relevant reaction mechanism are included.     

Determination of activation energy in enzymatic reactions by a single non-isothermal kinetic experiment

A non-isothermal kinetic method with linear heating was applied to enzymatic catalysis and rapidly provided the activation energy. The results obtained showed the excellent precision of the 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.     

Pyrolysis and combustion model of oil sands from non-isothermal thermogravimetric analysis data

Thermogravimetric (TG) data of oil sand obtained at Engineering Research Center of Oil Shale Comprehensive Utilization were studied to evaluate the kinetic parameters for Indonesian oil sand samples. Experiments were carried out at heating rates of 5, 15, and 25 °C min^?1 in nitrogen, 10, 20, and 50 °C min^?1 in oxygen atmosphere, respectively. The extent of char combustion was found out by relating TG data for pyrolysis and combustion with the ultimate analysis. Due to distinct behavior of oil shale during pyrolysis, TG curves were divided into three separate events: moisture release, devolatilization, and evolution of fixed carbon/char, where for each event, kinetic parameters, based on Arrhenius theory, were calculated. Coats–Redfern method, Flynn–Wall–Ozawa method, and distributed activation energy model method have been used to determine the activation energies of degradation. The methods are compared with regard to their characteristics and the ease of interpretation of the thermal kinetics. Activation energies of the samples were determined by three different methods and the results are discussed.     

Computation in kinetics, IV. Regression estimation of Arrhenius equation parameters from non-isothermal kinetic data

Computer method for evaluation of Arrhenius equation parameters from non-isothermal kinetic data is offered in KILET program. Changes of temperature can be linear, hyperbolic or of any smooth function which could be expressed by a polynomial of up to 4th degree. The method is demonstrated on examples of linear and hyperbolic changes for simulated and experimental data. The advantage of non-isothermal experiment over isothermal one for evaluation of kinetic solution data is stressed.

---

KILET. , , 4- . . .

     

Accommodation of the actual solid-state process in the kinetic model function

The degree of coordination between the kinetic information from the thermonalytical measurements and the kinetic theory of the solid-state reactions was investigated through the microscopic study of the thermal dehydration of several inorganic salt hydrates. An accommodation function was applied to the conventional kinetic model functionsf(α), in an attempt to reduce the disagreement between the actual process and the idealized one assumed in formulatingf(α). The significance of the non-integral kinetic exponent in the kinetic model function was discussed with its physico-chemical meanings. In celebration of the 60^th birthday of Dr. Andrew K. Galwey     

Extracting the mechanisms and kinetic models of complex reactions from atomistic simulation data

Determining reaction mechanisms and kinetic models, which can be used for chemical reaction engineering and design, from atomistic simulation is highly challenging. In this study, we develop a novel methodology to solve this problem. Our approach has three components: (1) a procedure for precisely identifying chemical species and elementary reactions and statistically calculating the reaction rate constants; (2) a reduction method to simplify the complex reaction network into a skeletal network which can be used directly for kinetic modeling; and (3) a deterministic method for validating the derived full and skeletal kinetic models. The methodology is demonstrated by analyzing simulation data of hydrogen combustion. The full reaction network comprises 69 species and 256 reactions, which is reduced into a skeletal network of 9 species and 30 reactions. The kinetic models of both the full and skeletal networks represent the simulation data well. In addition, the essential elementary reactions and their rate constants agree favorably with those obtained experimentally. © 2019 Wiley Periodicals, Inc.