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Abstract  

The activation energies of the same process are often reported to have different values, which are usually explained by the differences in experimental conditions and sample characteristics. In addition to this type of uncertainty, which is associated with the process (ΔE process) there is an uncertainty related to the method of computation of the activation energy (ΔE method). For a method that uses fitting single heating rate data to various reaction models, the value of ΔE method) method is large enough to explain significant differences in the reported values of the activation energy. This uncertainty is significantly reduced by using multiple heating rate isoconversional methods, which may be recommended for obtaining reference values for the activation energy.

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Model-free kinetics

Staying free of multiplying entities without necessity

Journal of Thermal Analysis and Calorimetry
Author: S Vyazovkin

Abstract  

The paper presents the model-free kinetic approach in the context of the traditional kinetic description based on the kinetic triplet, A, E, and f(α) or g(α). A physical meaning and interpretability of the triplet are considered. It is argued that the experimental values of f(α) or g(α) and A are unlikely to be interpretable in the respective terms of the reaction mechanism and of the vibrational frequency of the activated complex. The traditional kinetic description needs these values for making kinetic predictions. Interpretations are most readily accomplished for the experimental value of E that generally is a function of the activation energies of the individual steps of a condensed phase process. Model-free kinetic analysis produces a dependence of E on α that is sufficient for accomplishing theoretical interpretations and kinetic predictions. Although model-free description does not need the values of A and f(α) or g(α), the methods of their estimating are discussed.

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Abstract

A nonlinear algorithm has been suggested to increase the accuracy of evaluating the activation energy by the integral isoconversional method. A minor modification of the algorithm has made it possible to adapt the isoconversional method for an arbitrary variation of the temperature. This advanced isoconversional method allows for trustworthy estimates of the activation energy when the thermal effect of a reaction makes the temperature of a sample deviate from a prescribed heating program.

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Some aspects of mathematical statistics as applied to nonisothermal kinetics

Part III. Unified approach to the analysis of kinetic functions

Journal of Thermal Analysis and Calorimetry
Authors: S. Vyazovkin and A. Lesnikovich
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Some aspects of mathematical statistics as applied to nonisothermal kinetics V

Comparison of the amount of information obtained in traditional and nontraditional approaches

Journal of Thermal Analysis and Calorimetry
Authors: S. V. Vyazovkin and A. I. Lesnikovich

The paper gives a quantitative comparison of two methodological approaches to the solution of the inverse kinetic problem: the traditional approach and the nontraditional approach suggested by the authors. It is shown that the amount of information (in the sense of Shannon) obtained within the scope of the nontraditional approach is always greater than that obtained with the use of the traditional approach.

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This review deals with the choice of a method of solving the inverse kinetic problem (IKP) which would provide the most definite description of the process under conditions of ambiguity. Two fundamentally different methodologies are possible for the IKP solution: one is based on the principle of unambiguous description (discrimination), while the other relies upon the complementarity principle (generalized descriptions). Specific IKP solution methods have been classified, the methodological differences being taken into account. In the first part of this review, general and special limitations in discrimination of formal models have been analysed.

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