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]. This model (Kissinger) is also employed to study the thermal stability of current CdS/PMMA system in terms of activation energy which is given by the following relation: 2 where α is the heating rate, C is constant, and E t is the glass

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to calculate thermodynamic parameters such as change in activation energy for dipole orientation Δ G* , enthalpy Δ H* , entropy of activation Δ S* , and the other temperature dependent parameters such as relaxation time τ , the distribution parameter

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Abstract  

A new approach for determining the activation energy of amorphous alloys is developed. Setting the second order differential coefficient of heterogeneous reaction rate equation of non-isothermal heating as zero at extreme points of DSC curve, we obtain the new correlation taking form:

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\gamma_{1} = Lambertw\left( {\gamma_{3} e^{{ - \gamma_{2} }} } \right) + \gamma_{2}$$ \end{document}
where γ 1, γ 2 and γ 3 are symbols comprising parameters, and Lambertw(…) is the Lambert W function symbol. Through this function, the activation energy can be calculated with DSC test at single heating rate without the isoconversion assumption. To evaluate the feasibility of calculating the activation energy with the new method, the glass transition activation energy of as-cast Pd40Ni40P20 amorphous alloy is measured. The value is 1.6 eV, which agrees well with the result of viscosity measurements. Thus, it is a good possibility that the new approach can be used to determine the activation energy of amorphous phase.

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mass%Ag; ( c ) Cu–11 mass%Al– X mass%Ag The methods of Kissinger and Ozawa were used to study the influence of additions of 4, 6, 8, and 10 mass%Ag on the activation energy of the (α + γ 1 ) → β reverse eutectoid

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Meaningful activation energies for complex systems II

Evaluation of the Friedman method when applied to multiple reactions, and comparison with the Ozawa-Flynn-Wall method

Journal of Thermal Analysis and Calorimetry
Author: D. R. Dowdy

The validity of the Friedman method is assessed for systems of overlapping reactions. By means of mathematical analysis and numerical examples it is shown that, in the case of competitive reactions, the method gives the true value of the instantaneous mean activation energy. However, some error may be incurred if this method is applied to systems of independent reactions. The relative accuracy of the Friedman and Ozawa-Flynn-Wall methods is discussed in respect of complex systems of reactions.

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The measurement of meaningful activation energies

Using thermoanalytical methods. A tentative proposal

Journal of Thermal Analysis and Calorimetry
Authors: M. Reading, D. Dollimore, J. Rouquerol, and F. Rouquerol

The uncertainty surrounding the significance of the measured kinetic parameters of solid state decomposition reactions is discussed briefly. Some suggestions are made about what precautions should be taken in order to favour the measurement of undistorted results. Some criteria are proposed for deciding whether a measuredE value can be considered to have its usual meaning. The results of a series of experiments aimed at measuring the activation energy of the decomposition of calcium carbonate using a variety of methods, sample sizes and experimental conditions are presented. These results are compared with results found in the literature and it is concluded that it is possible to measure a reproducible value forE and it is tentatively proposed that this value is meaningful in terms of the energy barrier model of chemical reaction kinetics.

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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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Summary  

Activation energy was experimentally determined using the curve-fitting, initial-rise and the peak-shape methods involving pulse annealing experiments in NaCl samples irradiated at 10, 20, 30 and 40 Gy beta-doses and infrared stimulated luminescence (IRSL) signal at a temperature range of 100-300 °C. It was observed that the activation energy for NaCl decreases as the dose increased. The results were compared to other studies and discussed.

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Abstract  

In order to identify the kinetic process of self-heating in DSC experiment for Ti+3Al→TiAl3 reaction, two approaches, linear-fitting approach developed from Semenov"s theory of spontaneous ignition and variation of Friedman method, were carried out with cylindrical Ti-75 at% Al samples. Following these approaches, two identical activation energies are obtained as 16915 kJ mol-1 and 1705 kJ mol-1, respectively. Compared with the activation energies of reactions and interdiffusions between Ti and Al, the possible rate-controlling process of self-heating in DSC experiment for Ti+3Al→TiAl3 reaction is the interdiffusion between Ti and Al through TiAl3-layer.

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Abstract  

Activation energy is calculated from a single curve of a derivative of mass loss perturbed by a sinusoidal modulation of a temperature-time relationship. The method is based on a prediction of a hypothetical derivative of mass loss that corresponds to the absence of this modulation (perturbation). Simple considerations show that the unperturbed derivative coincides with the modulated derivative at inflection points of the modulated temperature-time relationship. The ratio of the perturbed and unperturbed derivatives at the points of time corresponding to maxima and minima of the sinusoidal component of the modulated temperature immediately leads to activation energy. Accuracy of the method grows with decreasing in the amplitude of the modulation. All illustrations are prepared numerically. It makes possible to objectively test the method and to investigate its errors. Two-stage decomposition kinetics with two independent (parallel) reactions is considered as an example. The kinetic parameters are chosen so that the derivative of mass loss would represent two overlapping peaks. The errors are introduced into the modulated derivative by the random-number generator with the normal distribution. Standard deviation for the random allocation of errors is selected with respect to maximum of the derivative. If the maximum of the derivative is observed within the region from 200 to 600C and the amplitude of the temperature modulation is equal to 5C, the error in the derivative 0.5% leads to the error in activation energy being equal to 2-6 kJ mol-1. As the derivative vanishes, the error grows and tends to infinity in the regions of the start and end of decomposition. With the absolute error 0.5% evaluations of activation energy are impossible beyond the region from 5 to 95% of mass loss.

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