Calculation method based on DTG curve for evaluation of activation energy

Authors have pointed out three calculation methods based on the weight loss rate of the sample to discuss and to compare them by means of describing kinetically the thermal decomposition of malonic acid. Values ofE _A calculated by different methods are well comparable. The method based on the calibrated DTG curve measured by the Derivatograph leads to reliable results and it seems to be convenient for the calculation ofE _A of transformations involving weight changes.     

A simple model of entropy relaxation for explaining effective activation energy behavior below the glass transition temperature

Strong changes in relaxation rates observed at the glass transition region are frequently explained in terms of a physical singularity of the molecular motions. We show that the unexpected trends and values for activation energy and preexponential factor of the relaxation time tau, obtained at the glass transition from the analysis of the thermally stimulated current signal, result from the use of the Arrhenius law for treating the experimental data obtained in nonstationary experimental conditions. We then demonstrate that a simple model of structural relaxation based on a time dependent configurational entropy and Adam-Gibbs relaxation time is sufficient to explain the experimental behavior, without invoking a kinetic singularity at the glass transition region. The pronounced variation of the effective activation energy appears as a dynamic signature of entropy relaxation that governs the change of relaxation time in nonstationary conditions. A connection is demonstrated between the peak of apparent activation energy measured in nonequilibrium dielectric techniques, with the overshoot of the dynamic specific heat that is obtained in calorimetry techniques.     

A novel method for analyzing energy relaxation in condensed phases using nonequilibrium molecular dynamics simulations: application to the energy relaxation of intermolecular motions in liquid water

We present a novel method to investigate energy relaxation processes in condensed phases using nonequilibrium molecular dynamics simulations. This method can reveal details of the time evolution of energy relaxation like two-color third-order IR spectroscopy. Nonetheless, the computational cost of this method is significantly lower than that of third-order response functions. We apply this method to the energy relaxation of intermolecular motions in liquid water. We show that the intermolecular energy relaxation in water is characterized by four energy transfer processes. The structural changes of the liquid associated with the energy relaxation are also analyzed by the nonequilibrium molecular dynamics technique.     

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.     

Solvent-dependent activation of intermediate excited states in the energy relaxation pathways of spheroidene

In carotenoids internal conversion between the allowed (S(2)) and forbidden (S(1)) excited states occurs on a sub-picosecond timescale; the involvement of an intermediate excited state(s) (S(x)) mediating the process is controversial. Here we use high time resolution (sub-20 fs) broadband (1.2-2.5 eV) pump-probe spectroscopy to study the solvent dependence of excited state dynamics of spheroidene, a naturally-occurring carotenoid with ten conjugated double bonds. In the high polarizability solvent, CS(2), we find no evidence of an intermediate state, and the traditional three-level (S(0), S(1), S(2)) model fully accounts for the S(2)→ S(1) process. On the other hand, in the low polarizability solvent, cyclohexane, we find that rapid (~30 fs) relaxation to an intermediate state, S(x), lying between S(1) and S(2) is required to account for the data. We interpret these results as due to a shift of the S(2) energy, which positions the state above or below the energy of S(x) in response to changes in solvent polarizability.     

Clean energy from sugarcane bagasse: quality evaluation by neutron activation analysis

The energy from sugarcane is one of the most important in Brazil’s energy matrix and the efficiency of extraction and processing is fully dependent on the quality of the raw material. The soil present in sugarcane was investigate here as a factor that can affect the production of energy. Chemical elements (Fe, Hf, Sc and Th) determined by instrumental neutron activation analysis were used for tracing soil in sugarcane and its derived bagasse. The lower calorific value (LCV) of bagasse demonstrated a good negative correlation (r = ?0.9727) with the ash content of the bagasse, which in turn was positively correlated to the amount of soil in the sugarcane. Therefore, the presence of soil reduces the production of energy from burning bagasse. The proportion of loss in the LCV was just slightly higher than the soil content, i.e. for an soil content of 10 % a reduction of 12.7 % was observed in the LCV.     

A simple method for estimating activation energy from derivative thermoanalytical curves and its application to thermal shrinkage of polycarbonate

Activation energy can be estimated by a new simple method, in which logarithm of maximum rate of conversion observed at different heating rates is plotted against reciprocal absolute temperature, because the conversion at the maximum rate is approximately independent of the heating rate. The method is applied to thermal shrinkage of polycarbonate, and the estimated activation energy is in good agreement with those obtained by conventional methods.

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Zusammenfassung Die Schätzung der Aktivierungsenergie kann mittels einer neuen Methode erfolgen, bei welcher der Logarithmus der für verschiedene Aufheizgeschwindigkeiten gemessenen maximalen Konversionsgeschwindigkeit als Funktion der reziproken Temperatur aufgetragen wird, da die Konversion bei der maximalen Geschwindigkeit inetwa unabhängig von der Aufheizgeschwindigkeit ist. Das Verfahren wurde beim thermischen Schrumpfen von Polycarbonat angewendet und die geschätzte Aktivierungsenergie liegt in guter Übereinstimmung mit den in herkömmlichen Verfahren ermittelten Werten.

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Dedicated to Professor Dr. H. J. Seifert on the occasion of his 60^th birthday     

A simple method of determining the activation energy of an isothermal solid-state decomposition reaction

A simple approach to determine the activation energy (E) of solid-state decomposition reactions is described. The activation energy is calculated from the slope of the logarithm of the maximum peak height of the isothermal DTA trace versus the reciprocal of the absolute temperature. The proposed method is applied in the study of the kinetics of thermal decomposition of cadmium carbonate. The activation energy calculated from this method (90.8±2.2 kJ mole^–1) is in very good agreement with the value (87.5±2.5 kJ mole^–1) obtained by the conventional method.

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Zusammenfassung Eine einfache Annäherung zur Bestimmung der Aktivierungsenergie (E) von Festphasenzersetzungsreaktionen wird beschrieben. Die Aktivierungsenergie wird aus dem Anstieg des Logarithmus der maximalen Peakhöhe der isothermen DTA-Kurve als Funktion der reziproken absoluten Temperatur errechnet. Die vorgeschlagene Methode wird zur Untersuchung der Zersetzungskinetik von Cadmiumcarbonat eingesetzt. Die hiernach berechnete Aktivierungsenergie (90.8±2.2 kJ mol^–1) ist in guter Übereinstimmung mit dem durch die konventionelle Methode erhaltenen Wert (87.5±2.5 kJ mol^–1).

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Résumé On décrit une méthode simple d'approximation pour déterminer l'énergie d'activation (E) des réactions de décomposition en phase solide. Le calcul de l'énergie d'activation s'effectue à partir de la pente du logarithme de la hauteur maximale du pic de la courbe d'ATD isotherme en fonction de l'inverse de la température absolue. On a appliqué la méthode proposée lors de l'étude de la cinétique de la décomposition thermique du carbonate de cadmium. L'énergie d'activation calculée à partir de cette méthode (90.8±2.2 kJ mole^–1) est en bon accord avec la valeur (87.5±2.5 kJ mole^–1) obtenue par la méthode conventionnelle.

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. . . (90.8+2.2 .^–1) 87.5± 2.5 .^–1, .

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The authors express their thanks to Dr. V. V. Deshpande and to Shri M. S. Kumbhar for their help in the DTA studies.     

A suite of 2H NMR spin relaxation experiments for the measurement of RNA dynamics

A suite of (2)H-based spin relaxation NMR experiments is presented for the measurement of molecular dynamics in a site-specific manner in uniformly (13)C, randomly fractionally deuterated ( approximately 50%) RNA molecules. The experiments quantify (2)H R(1) and R(2) relaxation rates that can subsequently be analyzed to obtain information about dynamics on a pico- to nanosecond time scale. Sensitivity permitting, the consistency of the data can be evaluated by measuring all five rates that are accessible for a spin 1 particle and establishing that the rates obey relations that are predicted from theory. The utility of the methodology is demonstrated with studies of the dynamics of a 14-mer RNA containing the UUCG tetraloop at temperatures of 25 and 5 degrees C. The high quality of the data, even at 5 degrees C, suggests that the experiments will be of use for the study of RNA molecules that are as large as 30 nucleotides.     

A new method to explain the model dependence of apparent activation energy derived from a single nonisothermal dynamic curve

A single nonisothermal dynamic curve can be relatively correctly described by several reaction models in model-fitting approach, which yields model-dependent kinetic parameters. The model dependence of the apparent activation energy is explained mathematically by a new method which is developed from the peak property method in this paper. It has been found that the apparent activation energy rises linearly with the increase of the order of nth-order and Avrami-Erofeev reaction models, which can be verified by data from the literature and can explain some phenomena appeared in some articles. Moreover, the apparent activation energies derived from fitting a single nonisothermal dynamic curve to nth-order and Avrami-Erofeev reaction models can be correlated through the activation energy of 1st-order model.     

Modification of the integral isoconversional method to account for variation in the activation energy

Integral isoconversional methods may give rise to noticeable systematic error in the activation energy when the latter strongly varies with the extent of conversion. This error is eliminated by using an integration technique that properly accounts for the variation in the activation energy. The technique is implemented as a modification of the earlier proposed advanced isoconversional method [Vyazovkin, S. J Comput Chem 1997, 18, 393]. The applications of the modified method are illustrated by simulations as well as by processing of data on the thermal decomposition of calcium oxalate monohydrate and ammonium nitrate. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 178–183, 2001     

Model-independent extraction of adhesion energy from indentation experiments

We present a model-independent method for extraction of adhesion energy from indentation experiments in which force, deflection, and contact area are measured. It is based on calculating the difference between external work supplied and stored strain energy, the deficit, which is assigned as work expended in opening (or closing) an interface. The critical step in the method is determination of the elastic indentation response without adhesion, using measured compliance. We show that this model-independent method accurately reproduces results obtained using the Johnson-Kendall-Roberts theory when it is applicable, and is particularly useful when an analytical contact mechanics solution is unavailable.     

A method for determining the relaxation spectrum from the decay curve of electric birefringence of macromolecular solutions

Summary A numerical method for determining the distribution function of relaxation times from the decay curve of electric birefringence in macromolecular solutions has been described. The distribution function is expanded in a series of appropriate functions, and the best values of the coefficients are determined by the method of least squares. An application of this method to poly-Lglutamic acid in methanol is presented. It is shown that the distribution of molecular lengths can be obtained from the relaxation spectrum in the case of helical polypeptides in solution.

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Zusammenfassung Es wird eine numerische Methode beschrieben, die die Relaxationszeit-Verteilungsfunktion aus der Abklingkurve der elektrischen Doppelbrechung bei makromolekularen Lösungen zu bestimmen erlaubt. Die Verteilungsfunktion wird in eine Reihe geeigneter Funktionen entwickelt und die besten Werte der Koeffizienten werden nach der Methode der kleinsten Quadrate bestimmt. Eine Anwendung dieser Methode zur Poly-L-glutaminsäure in Methanol-Lösung wird exemplifiziert. Es zeigt sich, daß die Verteilung von Moleküllängen im Falle helicaler Polypeptide aus dem Relaxationsspektrum gewonnen wird.

     

A new iterative linear integral isoconversional method for the determination of the activation energy varying with the conversion degree

The conventional linear integral isoconversional methods may lead to important errors in the determination of the activation energy when the significant variation of the activation energy with the conversion degree occurs. Vyazovkin proposed an advanced nonlinear isoconversional method, which allows the activation energy to be accurately determined [Vyazovkin, J Comput Chem 2001, 22, 178]. However, the use of the Vyazovkin method raises the problem of the time‐consuming minimization without derivatives. A new iterative linear integral isoconversional method for the determination of the activation energy as a function of the conversion degree has been proposed, which is capable of providing valid values of the activation energy even if the latter strongly varies with the conversion degree. Also, the new method leads to the correct values of the activation energy in much less time than the Vyazovkin method. The application of the new method is illustrated by processing of theoretically simulated data of a strongly varying activation energy process. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

A quotient method of evaluation for the catalytic-kinetic difference method

A new variant of the catalytic-kinetic difference method is presented.The course of a catalyzed reaction, which proceeds simultaneously in two mixtures containing different catalyst concentrations, is followed by photometry. The maximum of the difference in transmittance being measured is a function of the quotient of the catalyst concentrations in the two mixtures and is independent of the rate constant. With this method of evaluation, a single calibration graph suffices for the determination of two different catalysts activating the same reaction. The maximum of the difference in transmittance is independent of temperature. The reaction between cerium(IV) and arsenic(III) catalyzed by iodide or osmium serves as an example. Two further examples are mentioned.     

A method for determining the mean translational energy of particles desorbed from solid surfaces

A method for determinig the mean molecular translational energy in gas flows of low intensity (10¹²–10¹⁴ molec. s^–1) has been proposed. The method was verified using various gases (H₂, N₂, O₂, and CO₂ flowing into a vacuum out of a heated capillary. The translational energies were determined for CO and N₂ molecules desorbing from the surface of polycrystalline Ir. The translational temperature (T _tr) measured for CO equals 650±90 K and almost coincides with the surface temperature (T _s = 600 K). In the case of nitrogen molecules,T _tr = 4600±500 K atT _s = 500 K. The method proposed is applicable to the determination of the spatial distribution of molecular beam particles.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 30–34, January, 1995.The authors express their gratitude to A. V. Sklyarov for fruitful discussions during the elaboration of the theoretical basis and technical realization of the method.The reseach was carried out with the partial financial support of the International Science Foundation (Grant MBN 000).