Sergey Vyazovkin

Model-free and model-fitting approaches to kinetic analysis of isothermal and nonisothermal data

The model-free and model-fitting kinetic approaches have been applied to data for nonisothermal and isothermal thermal decompositions of HMX and ammonium dinitramide. The popular model-fitting approach gives excellent fits for both isothermal and nonisothermal data but yields highly uncertain values of the Arrhenius parameters when applied to nonisothermal data. These values cannot be meaningfully compared with the values derived from isothermal measurements, nor they can be used to reasonably predict the isothermal kinetics. On the other hand, the model-free approach represented by the isoconversional method yields similar dependencies of the activation energy on the extent of conversion for isothermal and nonisothermal experiments. The dependence derived from nonisothermal data permits reliable predictions of the isothermal kinetics. The use of the model-free approach is recommended as a trustworthy way of obtaining reliable and consistent kinetic information from both nonisothermal and isothermal data.

Computational aspects of kinetic analysis. Part A: The ICTAC kinetics project-data, methods and results

Abstract Part A of this series of papers (Parts B to E follow) presents the data and methods used, as well as the results obtained by participants in the ICTAC Kinetics Project. The isothermal and non-isothermal data sets provided were based on a hypothetical simulated process as well as on some actual experimental results for the thermal decompositions of ammonium perchlorate and calcium carbonate. The participants applied a variety of computational methods. Isoconversional and multi-heating rate methods were particularly successful in correctly describing the multi-step kinetics used in the simulated data. Reasonably consistent kinetic results were obtained for isothermal and non-isothermal data. There is, of course, no ‘true’ answer for the kinetic parameters of the real data, so the findings of the participants are compared. An attempt has been made to forecast the tendencies for the future development of solid state kinetics.

Evaluation of activation energy of thermally stimulated solid‐state reactions under arbitrary variation of temperature

The thermal effect of a reaction makes the temperature inside the reaction system deviate from a prescribed heating program. To take into account the effect of such temperature deviations on kinetic evaluations, a computational method applicable to an arbitrary variation in temperature has been developed. The method combines the isoconversional principle of evaluating the activation energy with numerical integration of the equation, dα/dt = k[T(t)]f(α), over the actual variation of the temperature with the time, T(t). Details of the numerical algorithm are reported. A model example has been used to verify the reliability of this method as compared to an analogous method which does not account for the deviations of the temperature from a prescribed program. The method has been tested for tolerance for noise in the temperature.

Computational aspects of kinetic analysis. Part C. The ICTAC Kinetics Project — the light at the end of the tunnel?

Abstract The paper discusses the kinetic results, which the participants in the ICTAC Kinetics Project have produced from the provided isothermal and nonisothermal data on a hypothetical simulated process, as well as on the thermal decomposition of ammonium perchlorate. The majority of the participants have applied various model-free techniques that employ multiple sets of isothermal or/and nonisothermal data obtained at different temperatures or/and at different heating rates. These ‘multi-set’ methods have been very successful in detecting multi-step kinetics in the data provided. Fitting data to multi-step kinetic models has allowed the ‘true mechanism’ to be guessed for the simulated data. For the real data, the mechanistic guesses happened to be uncertain. Various ‘multi-set’ methods have allowed fairly consistent values of the Arrhenius parameters to be derived from isothermal and nonisothermal data.

A UNIFIED APPROACH TO KINETIC PROCESSING OF NONISOTHERMAL DATA

Basic problems of kinetic processing of nonisothermal data ascertained from thermal analysis measurements can be solved by isoconversional methods. Analysis of the dependence of the activation energy on conversion often permits the identification of the kinetic scheme for the process. This dependence may also be used to solve applied kinetic problems related to predicting the behavior of a substance outside the range of experimental temperatures. Methods for using this dependence for evaluating both the preexponential factor and the reaction model, as well as for detecting isokinetic relationships, have been discussed. Because all of these operations have a common origin in computing the dependence of the activation energy on conversion, isoconversional methods may be considered as a basis of a unified approach to kinetic processing of nonisothermal data.

Kinetics of the Thermal and Thermo-Oxidative Degradation of Polystyrene, Polyethylene and Poly(propylene)

Full Paper: The thermal degradations of polystyrene (PS), polyethylene (PE), and poly(propylene) (PP) have been studied in both inert nitrogen and air atmospheres by using thermogravimetry and differential scanning calorimetry. The model-free isoconversional method has been employed to calculate activation energies as a function of the extent of degradation. The obtained dependencies are interpreted in terms of degradation mechanisms. Under nitrogen, the thermal degradation of polymers follows a random scission pathway that has an activation energy L200 kJ N mol ‐1 for PS and 240 and 250 kJ N mol ‐1 for PE and PP, respectively. Lower values (L150 kJ N mol ‐1 ) are observed for the initial stages of the thermal degradation of PE and PS; this suggests that degradation is initiated at weak links. In air, the thermoxidative degradation occurs via a pathway that involves decomposition of polymer peroxide and exhibits an activation energy of 125 kJ N mol ‐1 for PS and 80 and 90 kJ N mol ‐1 , for PE and PP respectively.

Linear and Nonlinear Procedures in Isoconversional Computations of the Activation Energy of Nonisothermal Reactions in Solids

An integral isoconversional method provides a linear procedure to estimate the activation energy (Eα) at a given conversion (α) but only when an oversimplified approximation of the temperature integral (p(x), where x = E/RT, R is the gas constant and T is the temperature) is used. Although the relative error in Eα is several times less than the relative error in p(x) it happens to be substantial at x < 13. In the present study a nonlinear procedure to estimate Eα has been developed. It shows very low relative errors in Eα which are practically independent of x. The computations have been performed for model reactions as well as for the thermal decomposition of Cu4OCl6(triphenylphosphine oxide)4.

Isothermal and non-isothermal kinetics of thermally stimulated reactions of solids

This review covers both the history and present state of the kinetics of thermally stimulated reactions in solids. The traditional methodology of kinetic analysis, which is based on fitting data to reaction models, dates back to the very first isothermal studies. The model fitting approach suffers from an inability to determine the reaction model uniquely,and this does not allow reliable mechanistic conclusions to be drawn even from isothermal data. In non-isothermal kinetics, the use of the traditional methodology results in highly uncertain values of Arrhenius parameters that cannot be compared meaningfully with isothermal values. An alternative model-free methodology is based on the isoconversional method. The use of this model-free approach in both isothermal and non-isothermal kinetics helps to avoid the problems that originate from the ambiguous evaluation of the reaction model. The model-free methodology allows the dependence of the activation energy on the extent of conversion to be determined. Th...

Kinetic concepts of thermally stimulated reactions in solids: A view from a historical perspective

Historical analysis suggests that the basic kinetic concepts of reactions in solids were inherited from homogeneous kinetics. These concepts rest upon the assumption of a single-step reaction that disagrees with the multiple-step nature of solid-state processes. The inadequate concepts inspire such unjustified anticipations of kinetic analysis as evaluating constant activation energy and/or deriving a single-step reaction mechanism for the overall process. A more adequate concept is that of the effective activation energy, which may vary with temperature and extent of conversion. The adequacy of this concept is illustrated by literature data as well as by experimental data on the thermal dehydration of calcium oxalate monohydrate and thermal decomposition of calcium carbonate, ammonium nitrate and 1,3,5,7- tetranitro-1,3,5,7-tetrazocine.

An approach to the solution of the inverse kinetic problem in the case of complex processes: Part 1. Methods employing a series of thermoanalytical curves

Abstract An approach to the solution of the inverse kinetic problem in the case of complex processes is proposed. This approach is based on the analysis of the dependence of activation energy calculated by the isoconversion method on the transformation degree. The inter-relationship between the shape of this dependence and the type of process has been determined. An algorithm for identifying the type of complex process in the simplest case is proposed. The possibility of assessing the parameters of individual stages has been investigated. All the calculations have been made using the isoconversion method for several model thermoanalytical curves.