On the calculation of the activation energy for solid state reactions

A novel and convenient method for the determination of the activation energy from isothermal kinetic runs has been proposed recently. A significant limitation of this method is discussed and is illustrated with an experimental example. A modification of the proposed method is suggested to circumvent this limitation.     

On the calculation of activation energies using a modified Kissinger method

Augis and Bennett (J. Thermal Anal. 13 (1978) 283.) [6] recently proposed a modified Kissinger method for determining the activation energy of a transformation. It is shown that the proposed method was, in fact, based upon a modification to the equation for the rate of reaction under non-isothermal conditions. The apparent discrepancy between the proposed method and the original Kissinger method is therefore resolved. The modified rate equation appears to have, at best, only a limited application. However, if the equation should be appropriate for a particular transformation, it is demonstrated that Augis and Bennett's method would be the correct method for determining the activation energy.

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Zusammenfassung Von Augis und Bennett (J. Thermal Anal.13, (1978) 283) wurde eine modifizierte Kissinger-Methode zur Bestimmung der Aktivierungsenergie einer Umwandlung vorgeschlagen. Es wird gezeigt, dass die vorgeschlagene Methode tatsächlich in einer Modifizierung der Gleichung für die Reaktionsgeschwindigkeit unter nicht-isothermen Bedingungen ihren Ursprung hat. Die scheinbare Diskrepanz zwischen der vorgeschlagenen Methode und der ursprünglichen Kissinger-Methode wird dadurch behoben. Die modifizierte Geschwindigkeitsgleichung hat bestenfalls nur eine begrenzte Anwendung. Jedoch, bei Eignung dieser Gleichung für eine bestimmte Umwandlung zeigt sich, dass die Methode von Augis und Bennett die richtige Methode zur Bestimmung der Aktivierungsenergie sein kann.

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The author is indebted to the Senate of the University of Queensland for the award of a University Research Fellowship; and to Professor R. R. Stephens for providing laboratory facilities.     

A simple method for determining activation energies of organic reactions from DSC curves

An approximate formula for a rapid and simple estimation of activation energies from DSC curves is given and applied to various homogeneous reactions. The results obtained are compared with the approximate values of the Duswalt method and with the results by the mathematically more demanding method of Borchardt and Daniels (additional application of multiple linear regression). In this connection the efficiency of the new approximation method is demonstrated.     

A simple empirical method for the estimation of activation energies in radical molecule metathesis reactions

Several new empirical methods are presented for the prediction of activation energies E of the metathetical transfer reaction of single bonded atoms in radical-molecule reactions of the type A· + BC → AB + C· The methods assign additive contributions to E for the endgroups A· and C·, neglecting the effect of the transferred atom B. Most of the predicted values agree to within l kcal mol^?1 with the experimental activation energies (average error = 0.82 and standard deviation = 1.02 kcal mol^?1). This is comparable to the best of the more complex schemes available for such estimation.     

Retarded solid state reactions

Reconstructive phase transitions and formation or decomposition reactions in the solid state exhibit in DTA-measurements a more or less great hysteresis between the temperatures from heating and cooling curves; at worst the reaction can be suppressed completely. By e.m.f.vs. T-measurements in appropriate galvanic cells for solid electrolytes equilibrium temperatures in the case of such kinetic hindrance can be determined and additionally the existence of metastable states can be proved.

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Zusammenfassung Rekonstruktive Phasenumwandlungen sowie Bildungs- und Zersetzungsreaktionen im festen Zustand zeigen bei DTA-Messungen eine mehr oder minder große Hysteresis zwischen den aus Aufheiz- bzw. Abkühlkurven ermittelten Temperaturen; schlimmstenfalls kann die Festkörperreaktion völlig unterdrückt sein. Mißt man in geeigneten galvanischen Zellen für Festelektrolyte EMK-gegen-T-Kurven, so erhält man auch im Falle kinetischer Hemmungen Gleichgewichtstemperaturen und kann darüber hinaus das Vorliegen metastabiler Zustände nachweisen.

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We have to thank the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industry for supporting our work from the outset.     

Solvent free reactions in the solid state: solid state metathesis

Transition Metal Chemistry -     

Ab initio group contribution method for activation energies of hydrogen abstraction reactions.

The group contribution method for activation energies is applied to hydrogen abstraction reactions. To this end an ab initio database was constructed, which consisted of activation energies calculated with the ab initio CBS-QB3 method for a limited set of well-chosen homologous reactions. CBS-QB3 is shown to predict reaction rate coefficients within a factor of 2-4 and Arrhenius activation energies within 3-5 kJ mol(-1) of experimental data. Activation energies in the set of homologous reactions vary over 156 kJ mol(-1) with the structure of the abstracting radical and over 94 kJ mol(-1) with the structure of the abstracted hydrocarbon. The parameters required for the group contribution method, the so-called standard activation group additivity values, were determined from this database. To test the accuracy of the group contribution method, a large set of 88 additional activation energies were calculated from first principles and compared with the predictions from the group contribution method. It was found that the group contribution method yields accurate activation energies for hydrogen-transfer reactions between hydrogen molecules, alkylic hydrocarbons, and vinylic hydrocarbons, with the largest deviations being less than 6 kJ mol(-1). For reactions between allylic and propargylic hydrocarbons, the transition state is believed to be stabilized by resonance effects, thus requiring the introduction of an appropriate correction term to obtain a reliable prediction of the activation energy for this subclass of hydrogen abstraction reactions.     

A Hartree-Fock SCF calculation of the activation energies for two SN2 reactions

Roothaan Hartree-Fock SCF calculations for points on the F⁻ + CH₃F and CN⁻ + CH₃F minimum potential energy surfaces are reported. Considerable care has been taken in the choice of basis sets used to describe these systems.     

Relationship between bond dissociation energies and activation energies for bond scission reactions

Bond dissociation energies are frequently derived from values of the high pressure activation energy for bond scission reactions. The value derived depends on the transition state structure chosen for the reaction. We consider several models of the transition state and show that the variation in derived BDE values can be quite substantial, 3 to 6 kcal/mol at the high temperatures of pyrolysis kinetics. Application of the restricted Gorin model of the transition state results in BDE values in good agreement with current thermochemistry, while the other models tested result in lower to much lower values. © 1994 John Wiley & Sons, Inc.     

Calculation of the relative activation energies for reactions forming metal sulfides

Theoretical and Experimental Chemistry -     

固态有机反应新进展

总结了一些典型的固态有机反应。由于固态反应的特性，多数固态有机反应表现出较溶液中更高的反应效率和更好的选择性，在某些情况下，利用光活性主体与反应物形成包结物，可实现对映选择性的不对称固态合成。     

Kinetics of solid state thermal decomposition reactions

The author wishes to thank Prof. C. G. R. Nair, Dr. V. R. Gowarikar, Mr. M. R. Kurup and Dr. K. V. C. Rao for their encouragements. Thanks are due to Prof. P. M. Madhusudanan and Dr. K. Krishnan for helpful discussions and to Director, VSSC for the kind permission to publish this work.     

On the nonlinear isoconversional procedures to evaluate the activation energy of nonisothermal reactions in solids

A general procedure for deriving the equations that underlie various isoconversional nonlinear methods for evaluating the activation energy is presented. A new integral isoconversional nonlinear method with integration over a given range of conversion is suggested. This method was applied to simulated nonisothermal data as well as to data for the nonisothermal decomposition of ammonium perchlorate. The obtained dependencies of the activation energy on the degree of conversion were compared with those resulting from other nonlinear and linear methods of analysis. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 87–93 2004     

A new method for the measurement of vibrational-state-selected ion-molecule reactions at thermal energies

A photoelectron-secondary-ion-coincidence method is described that allows us to determine the relative vibrational-energy-dependent cross sections for reactions of molecular ions with neutral atoms or molecules at thermal energies. Results for reactions of H₂⁺(ν) in vibrational states ν = 0–8 with H₂(H₃⁺), Ne(NeH⁺) and He(He⁺) are reported.     

A method to evaluate the Sachs formula

A rule-based method for evaluating the Sachs formula is introduced. For simple molecules, such as linear chains and monocycles, the Sachs formula can be evaluated by directly using the rules. For complex molecular systems, the Sachs formula can be evaluated by first breaking up the molecule into constituent pieces of sufficient simplicity so that data for them are available in the data base and then constructing the molecule from the known data by adding all pieces together, one at a time, via a series of binary rules. The method changes the way of evaluating the Sachs formula from a trial-and-error-type numerical search to a purely algebraic manipulation and thus tremendously reduces the computing times. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 19–36, 1997     

Comparative method to evaluate reliable kinetic triplets of thermal decomposition reactions

Reliable kinetic information for thermal analysis kinetic triplets can be determined by the comparative method: (1) An iterative procedure or the KAS method had been established to obtain the reliable value of activation energy E _a of a reaction. (2) A combined method including Coats-Redfern integral equation and Achar differential equation was put forward to confirm the most probable mechanism of the reaction and calculate the pre-exponential factor A. By applying the comparative method above, the thermal analysis kinetic triplets of the dehydration of CaC₂O₄·H₂O were determined, which apparent activation energy: 81±3 kJ mol^-1, pre-exponential factor: 4.51·106-1.78·10⁸ s^-1, the most probable mechanism function: f(α)=1 or g(α)=α, which the kinetic equation of dehydration is dα/dt=Ae^-E _a ^/RT. This revised version was published online in August 2006 with corrections to the Cover Date.     

A new differential method for determining orders and rates of reactions and its application to solid state reactions. Part I. Some simple decompositions

The thermal dehydroxylation of natural Al-bearing geothite was investigated by IR spectroscopy. Venezuelan lateritic bauxites (which in addition to goethite contain kaolinite, gibbsite, ilmenite and quartz), as well as chemically isolated samples of Al-goethites, were heated to 300, 600 and 1000°C. The spectral features of the iron oxides formed during the thermal treatment depend on the heating temperature, showing that the first dehydroxylation product is Al-bearing protohematite which at temperatures above 600°C is recrystallized to Al-bearing hematite. Part of the aluminum which is occuled in this hematite originates from the gibbsite and to a smaller extent from the kaolinite.