Nobuyoshi Koga

A review of the mutual dependence of Arrhenius parameters evaluated by the thermoanalytical study of solid-state reactions: the kinetic compensation effect

Abstract The kinetic compensation effect (KCE) has been observed in numerous kinetic studies of solid-state reactions using thermoanalytical methods. An attempt has been made to separate phenomenologically the KCE into the variation and the mutual dependence of the resultant Arrhenius parameters. The probability of the mutual dependence of the Arrhenius parameters caused by the properties of the general kinetic equation was discussed in relation to: (1) the reaction temperature interval, (2) the fractional reaction α, (3) the kinetic model function f (αf), and (4) the isokinetic hypothesis. The mutual dependence of the Arrhenius parameters due to the properties of the general kinetic equation was first checked before discussing the KCE in relation to a physico-chemical factor for a series of reactions under investigation. The necessity of establishing a check system for the kinetic calculation is discussed briefly on the basis of the prerequisities of the methods of kinetic calculation and the properties of the general kinetic equation.

Kinetic analysis of thermoanalytical data by extrapolating to infinite temperature

Abstract The extrapolation of a set of thermoanalytical (TA) curves to infinite temperature is proposed as a possible method to calculate the kinetic parameters of solid-state reactions from the TA curves without assuming a constant heating rate. It is shown theoretically that the method is applicable for the TA curves under any temperature program if the kinetic model function does not change among the temperature conditions applied. The practical applicability of the method is investigated through the kinetic analysis of TA curves for the thermal decomposition of synthetic malachite CuCO 3 · Cu(OH) 2 . The present method of kinetic analysis is widely useful for nonlinear nonisothermal TA curves in which the sample temperature does not change linearly.

Kinetic compensation effect as a mathematical consequence of the exponential rate constant

Abstract It is shown that the kinetic compensation effect mathematically results from the exponential form of the rate constant. A change of activation energy is thus compensated by the same change in temperature or in the logarithm of the pre-exponential factor.

A physico-geometric approach to the kinetics of solid-state reactions as exemplified by the thermal dehydration and decomposition of inorganic solids

By reviewing various microscopic studies on the mechanisms of the thermal dehydration and/or decomposition reactions of inorganic solids, the physico-geometric and chemical features of the solid-state reactions were investigated. A model of reaction interface and a classification of interfacial chemical behavior for the thermal dehydration of solids, which have extensively been studied by professors Galwey and Brown, were introduced in order to evaluate the significance of such mechanistic understandings on the solid-state reactions. The meanings of the kinetic models and kinetic equations, which have been employed conventionally for analyzing the overall kinetics of solid-state reactions, were discussed in relation to the complicated physico-geometric and chemical behaviors of the solid-state reactions revealed by the mechanistic investigations. Possible extensions of the conventional kinetic theory by incorporating various physico-geometric and chemical features were examined for an advanced kinetic understanding of the solid-state reactions. The kinetic data required for the advanced kinetic analysis of the solid-state reactions were discussed by emphasizing the usefulness of the controlled rate thermal analysis (CRTA). The present status and future subjects of the kinetic and mechanistic studies on the solid-state reactions were summarized briefly through the present review.

A unified theory for the kinetic analysis of solid state reactions under any thermal pathway

The Ozawa concept of generalized time has been used for developing master plots for the different kinetic models describing solid state reactions. These plots can be indistinctly used for analysing isothermal or non-isothermal experimental data. It is demonstrated that it is not possible to discriminate the kinetic model from a single non-isothermal curve without a previous knowledge of the activation energy. However, it has been shown that the ln [(da/dt)/f(a)] data taken from a set of DTG curves obtained at different heating rates lie on a single straight line when represented as a function of 1/T only if the kinetic model really obeyed by the reaction is considered. Moreover, the true values of E and A are obtained from the slope and the intercept of this straight line.

The influence of mass transfer phenomena on the kinetic analysis for the thermal decomposition of calcium carbonate by constant rate thermal analysis (CRTA) under vacuum

The influence of the mass transfer phenomena on the thermal decomposition of calcium carbonate powders under vacuum was investigated through a detailed kinetic analysis by the constant transformation rate thermal analysis (CRTA). Reliable kinetic curves, free from the mass transfer problems, can be obtained by CRTA under vacuum, but within a restricted range of small sample sizes, <10 mg. The influence of mass transfer phenomena on the apparent kinetic parameters is discussed in relation to the distribution of fractional reaction α of the individual particles in a sample assemblage. Only when the distribution of α is maintained constant among a series of experimental kinetic curves, can a reliable activation energy, E, be obtained by one of the isoconversion methods. In this respect, a single cyclic CRTA permits the α distribution to be maintained constant between the two adjacent data points with different decomposition rates. In the present study, an apparent E value of about 223 kJ mol−1 was obtained by the Friedman method from a series of CRTA curves with sample sizes less than 10 mg and by the rate jump method from a single cyclic CRTA curve with sample size of about 40 mg. The first-order (F1) law was determined to be the most appropriate kinetic model function, from a series of CRTA curves, instead of the ideal contracting geometry (R3) law formalized for the three-dimensional shrinkage of the reaction interface in the respective particles. The particle size distribution of the sample particles is suggested to be one possible reason for the apparent agreement with the F1 law. A kinetic exponent n of the nth-order law that deviated from unity was obtained from the CRTA curves with sample sizes larger than 10 mg, due to an additional distribution of α produced by mass transfer phenomena. Because the α distribution due to the mass and heat transfer phenomena cannot be expressed practically in an analytical function, a meaningful kinetic model and preexponential factor are difficult to estimate from kinetic data that are influenced by the transfer phenomena.

Ozawa’s kinetic method for analyzing thermoanalytical curves

By reviewing the history of thermal analysis and its application to the kinetic analysis of the solid-state processes, we investigate the theoretical basis and historical perspective of Ozawa’s kinetic method for analyzing thermoanalytical curves. Ozawa’s nonisothermal kinetic method is demonstrated using thermoanalytical data for the thermal decomposition of sodium hydrogencarbonate and the crystallization of anhydrous magnesium acetate glass as examples. Through investigating recent theoretical advancements in nonisothermal kinetic analysis in view of the theoretical fundamentals of Ozawa’s kinetic method, it is indicated that they are in line with Ozawa’s kinetic theory. On the basis of the above investigations, we discuss the role of Ozawa’s kinetic theory in advancing the analysis of complex reaction kinetics.

Kinetic approach to partially overlapped thermal decomposition processes

Practical usefulness of the kinetic deconvolution for partially overlapped thermal decomposition processes of solids was examined by applying to the co-precipitated basic zinc carbonate and zinc carbonate. Comparing with the experimental deconvolutions by thermoanalytical techniques and mathematical deconvolutions using different statistical fitting functions, performance of the kinetic deconvolution based on an accumulative kinetic equation for the independent processes overlapped partially was evaluated in views of the peak deconvolution and kinetic evaluation. Two-independent kinetic processes of thermal decompositions of basic zinc carbonate and zinc carbonate were successfully deconvoluted by means of the thermoanalytical measurements in flowing CO2 and by applying sample controlled thermal analysis (SCTA). The deconvolutions by the mathematical curve fittings using different fitting functions and subsequent formal kinetic analysis provide acceptable values of the mass-loss fractions and apparent activation energies of the respective reaction processes, but the estimated kinetic model function changes depending on the fitting functions employed for the peak deconvolution. The mass-loss fractions and apparent kinetic parameters of the respective reaction processes can be optimized simultaneously by the kinetic deconvolution based on the kinetic equation through nonlinear least square analysis, where all the parameters indicated acceptable correspondences to those estimated through the experimental and mathematical deconvolutions. As long as the reaction processes overlapped are independent kinetically, the simple and rapid procedure of kinetic deconvolution is useful as a tool for characterizing the partially overlapped kinetic processes of the thermal decomposition of solids.

A kinetic compensation effect established for the thermal decomposition of a solid

Two causes for the kinetic compensation effect (KCE) were recognized for a given solidstate reaction at various heating rates. One is due to any change in the range of reaction. This KCE is quantitative and meaningful, provided thatF(α) remains constant under the given conditions. The other is due to misestimation of the appropriate rate law, which in turn leads to a superficial KCE. It was also shown that the existence of an isokinetic point does not necessarily imply the occurrence of a meaningful KCE.ZusammenfassungFür den kinetischen Kompensationseffekt (KCE) für eine gegebene Feststoffreaktion bei verschiedenen Aufheizgeschwindigkeiten wurden zwei Gründe angegeben. Der eine Grund steht in Beziehung zur Änderung der Reaktionstemperatur. Dieser KCE ist quantitativ und von Bedeutung, vorausgesetzt, daßF(α) unter den gegebenen Bedingungen konstant bleibt. Der andere liegt in der falschen Aufstellung des entsprechenden Geschwindigkeitsgesetzes. Es wurde weiterhin gezeigt, daß die Existenz eines isokinetischen Punktes nicht zwangsweise das Auftreten eines bedeutenden KCE beinhaltet.

Thermal Dehydration of Magnesium Acetate Tetrahydrate: Formation and in Situ Crystallization of Anhydrous Glass

The kinetics and mechanism of the thermal dehydration of magnesium acetate tetrahydrate were investigated as a typical example of the glass formation process via the thermal decomposition of solids. Formation of an intermediate fluid phase was identified as the characteristic phenomenon responsible for the formation of anhydrous glass. Thermal dehydration from the surface fluid layer regulates the zero-order-like rate behavior of the mass-loss process with an apparent activation energy E(a) ≈ 70-80 kJ mol(-1). Because of variations in the mechanism of release of the water vapor with changes in the reaction temperature range, the mass-loss behavior is largely dependent on the particle size of the sample and heating conditions. The formation of hollow anhydrous glass is the novel finding of the present study. The mechanism of formation is discussed in terms of complementary interpretations of the morphological changes and kinetic behavior of the thermal dehydration. On further heating, the as-produced anhydrous glass exhibits a glass transition phenomenon at approximately 470 K with an E(a) ≈ 550-560 kJ mol(-1), and subsequently crystallizes via the three-dimensional growth of nuclei controlled by diffusion. The crystallization process is characterized by an E(a) ≈ 280 kJ mol(-1) and an enthalpy change ΔH = -13.3 kJ mol(-1), resulting in the formation of smaller, rounded particles of crystalline anhydrate.