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The new procedure for identification of the effective distribution function for determination of the distributed activation energy models, which is based on the Bayesian statistics, has been established. The five different continuous probability functions (exponential, logistic, normal, gamma and Weibull probability functions (the extended set of distributions)) were used for searching the most appropriate reactivity model for two heterogeneous processes: (a) the isothermal reduction process of nickel oxide under hydrogen atmosphere and (b) the isothermal degradation process of bisphenol-A polycarbonate (Lexan) under nitrogen atmosphere. Using the Bayes weights, it was shown that for both processes, the most suitable distributed reactivity model is the Weibull distribution model. The kinetic parameters (ln A, Ea) attached with the Weibull distribution model were calculated for both investigated processes, using three different computational methods (the maximum likelihood method (MLM), the nonlinear regression analysis (NRA), and the posterior mean (the expected value of scale parameter η, E(η)). It was shown that there is an excellent agreement between the values of kinetic parameters calculated by the MLM, NRA, and E(η) approaches. Using Bayes weights, it is possible to discriminate between different probability models and to quantify how well a distribution fits the experimental data. For the formal reactivity model comparison, the use of the (nonnormalized) Jeffreys prior is recommended. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 641-658, 2010 [ABSTRACT FROM AUTHOR]

The new procedure for identification of the effective distribution function for determination of the distributed activation energy models, which is based on use the maximum likelihood method (MLM), was established. The five different continuous probability functions (exponential, logistic, normal, gamma, and Weibull probability functions (the extended set of distributions)) were used for searching the best reactivity model for two heterogeneous processes: (a) the isothermal reduction process of nickel oxide under hydrogen atmosphere and (b) the isothermal degradation process of bisphenol-A polycarbonate (Lexan) under nitrogen atmosphere. The MLM showed that for both processes, the most suitable reactivity model represents the Weibull distribution model. It was concluded that the values of Arrhenius parameters (ln A and Ea), evaluated from the Weibull distribution model, represent the effective kinetic values for both considered processes. This procedure enables identification the suitable distribution model for considered process only from the experimental data (based on the shapes of obtained integral kinetic curves), and this fact represents the advantage of established analysis. The established mathematical procedure, which is based on the MLM, can be applied as the preliminary analysis for evaluating the distribution of activation energies for complex heterogeneous processes. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 41: 27–44, 2009 [ABSTRACT FROM AUTHOR]

Three linear isoconversional methods (Friedman, Flynn–Wall–Ozawa, and Kissinger–Akahira–Sunose) and the invariant kinetic parameters (IKP) method were used in order to examine the kinetics of the nonisothermal decomposition of a sodium bicarbonate (NaHCO3). The objective of the paper is to show the usefulness of the IKP method to determine both the kinetic parameters and the kinetic model of the investigated process. The activation energy (Ea) value obtained by the IKP method is in good agreement with the values obtained by isoconversional methods. The IKP method associated with the criterion of coincidence of kinetic parameters for all heating rates led us to the following kinetic triplet: Ea = 95.5 kJ mol-1, A = 2.65 × 1010 min-1, and conversion function f(α) = (1 - α) (first-order reaction model, F1). © 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39: 462–471, 2007 [ABSTRACT FROM AUTHOR]