Andrew K. Galwey

Application of the Arrhenius equation to solid state kinetics: can this be justified?

Abstract Application of the Arrhenius equation to the kinetics of solid state reactions has been criticised on several grounds. One of the main theoretical objections has been that the energy distribution amongst the immobilised constituents of a crystalline reactant is not represented by the Maxwell–Boltzmann equation. The detailed band structure of a solid may, however, include interface energy levels (analogous to impurity levels in semiconductors) that participate in the crucial bond redistribution step. Occupancy of such levels would be determined by energy distribution functions based on Fermi–Dirac statistics for electrons, and Bose–Einstein statistics for phonons. For the highest energies, necessary for reaction, both distributions approximate to an exponential energy term, thereby countering the above objection to the application of the Arrhenius equation to reactions of solids. The existence of such interface levels, with a limited range of energies, would also allow for the variation of apparent activation energy with extent of reaction, and also with temperature, reported for many complex solid state reactions.

The significance of “compensation effects” appearing in data published in “computational aspects of kinetic analysis”: ICTAC project, 2000

Examination of the results reported for the recent International Congress on Thermal Analysis and Calorimetry (ICTAC) kinetics project [Thermochim. Acta 355 (2000) 125] shows that, from kinetic analyses of identical sets of numerical data measurements, different workers, using different computational procedures, obtained significantly different kinetic parameters. The reported Arrhenius parameters, A (frequency or pre-exponential factor) and E (activation energy), calculated from the data sets supplied, showed apparent (approximate) compensation trends. Thus, when reviewing or applying the values of Arrhenius parameters reported for innumerable and diverse rate processes in the literature, the uncertainties in the magnitudes of A and E (often not even estimated or discussed) cannot be regarded as arising only from differences in the sample or experimental conditions, but must also include consideration of the mathematical and computational methods used. Variations of either type can lead to compensation effects and the recognition of compensation can be a valuable indication of a need to explore the source of this behavior. An observed kinetic compensation effect (KCE) can, thus, be a result of differences in the sample or experimental conditions, be an indication of complex reaction controls, or, as shown in this survey, may be a computational artifact.

Arrhenius parameters and compensation behaviour in solid-state decompositions

Abstract Many instances of compensation behaviour (i.e. conformity of the Arrhenius parameters to a relationship of the form: ln A = bE a + c , where b and c are constants) reported for solid-state decompositions, refer to reactions that are at least partially reversible under reaction conditions used in the kinetic studies. Arrhenius parameters calculated for such processes are sensitive to the prevailing pressure of volatile product and heat transfer controls that may vary appreciably between successive experiments. Thus, compensation effects have been reported for various single reactions (e.g. the decomposition of CaCO 3 , the dehydroxylation of Ca(OH) 2 and the dehydration of Li 2 SO 4 ·H 2 O) where, for each solid, the reactivity of the starting material can be regarded as constant. Compensation has also been reported for sets of chemically comparable reactants that (are expected to) decompose in the same temperature interval. Compensation may then arise either from the aforementioned variation of reaction conditions, or from differences in the reactants, such as particle sizes, packing, etc. Because of the variety of compensation effects reported, the phenomenon is often regarded as an experimental artefact. It is of interest to examine the reasons for the concurrent changes of Arrhenius frequency factors and activation energies. The significance of activation energies in solid-state decompositions is discussed briefly and three classes can be distinguished. The accuracy of measurement of activation energies needs to be increased so that their sensitivity to prevailing reaction conditions can be established, investigated and understood.

Solid-state Decompositions — Stagnation or Progress?

An appraisal of the trends discerned in the recent literature concerned with solid-state decompositions suggests that this research area lacks a general theoretical framework and, hence, order in the subject is difficult to recognize. There have been surprisingly few reviews of the field. Many of the continuing flow of research publications may be of individual value, but most do not contribute to the overall development of the topic. For example, in many studies of reversible dissociations the sensitivity of rate characteristics to prevailing conditions is not discussed so that the fit of data to rate equations and the magnitudes of calculated Arrhenius parameters may be of empirical value only. Some studies report kinetic results without mechanistic discussions supported by complementary observations. Progress forward from an apparent state of stagnation depends upon more critical examination of the existing literature, coupled with better designed experiments to establish the reproducibility and reliability of kinetic conclusions. Techniques capable of providing insights into the bond redistribution steps that occur during reactions in crystals are also urgently needed.

Interpretation of the kinetic compensation effect in heterogeneous reactions: thermochemical approach

The kinetic compensation effect (KCE), unexplained by the Arrhenius activation model, is interpreted in the framework of the novel thermochemical approach to kinetics of heterogeneous reactions. Unlike the activation model, this theory includes the process of congruent dissociative vaporisation of solids described by the Langmuir quasi-equilibrium equations and consideration of the two different reaction regimes: equimolar and isobaric (with the external pressure of gaseous product, respectively, below and above its equilibrium pressure). Change of regimes is shown to be the reason for the mutual variations of the Arrhenius parameters in the equation: ln Au2009=u2009au2009+u2009bE. This theoretical interpretation of the KCE is quantitatively supported by experimental observations for the following different types of heterogeneous reactions: high temperature atomisation of metal oxides, low-temperature solid-state decompositions, NiO reduction by H2 and catalytic oxidations of CO and of H2 on PtO2. Fundamental reasons for the shortcomings of the activation model in the interpretation of mechanisms and kinetics of heterogeneous reactions are identified.

The mechanism and kinetics of NiO reduction by hydrogen

The thermochemical approach to analysis of thermal decomposition of solids, developed earlier by L’vov, is extended here, for the first time, to interpret the kinetics and mechanism of the reduction of an oxide (NiO) by a gas (H2). This approach is based on the mechanism of congruent dissociative vaporization of the reactant, Langmuir kinetics and determination of the Arrhenius E parameter by the third-law method. The calculated enthalpy of the reaction is in good agreement with the experimentally measured E value. Many other mechanistic and kinetic features of the reaction are explained within the framework of the given theoretical approach. These include: the formation of metal nuclei; the initial autocatalytic behavior; the formation of nanocrystalline structure of the reduced metal product; the equimolar and isobaric modes of reduction; the dependence of reduction rate on hydrogen pressure; the more than twofold decrease of the E parameter with the extent of reaction α, and the systematic increase of E with temperature.

Theory of solid-state thermal decomposition reactions

A case is presented to recommend strongly that scientists interested in thermal chemistry should make comprehensive, conscientious, clinical and critical analyses of the strengths and weaknesses of The L’vov Thermochemical Theory (L’vov, Thermal decomposition of solids and melts—new thermochemical approach to the mechanism, kinetics and methodology, Springer, Berlin, 2007), used to interpret the kinetics and mechanisms of reactions that occur on heating. The shortcomings underlying the theory (some originally developed for solid decompositions) currently uncritically accepted in this field are reviewed, and these deficiencies are contrasted with the successes of L’vov’s approach. To promote the use of this alternative theory, features that may have discouraged researchers unfamiliar with its assumptions, methodology and applications are discussed here. A new scientific theory cannot be ignored or discounted without adequate consideration and testing, particularly in a stagnant area of chemistry that lacks guiding principles and unifying concepts. Novel ideas in the literature (L’vov 2007) deserve recognition, critical appraisal and, if possible, exploitation to maintain the progress of scientific research.

Catalytic oxidation of CO on platinum

Using concepts recently developed in thermal decompositions of solids and reduction of bulk oxides by gases and (re)analysis of experimental literature data, a novel mechanism for the catalytic oxidation of CO by PtO2 is proposed. Instead of the conventional Mars–van Krevelen scheme, the reactions proposed are: PtO2(s)xa0+xa02COxa0⟷xa0Pt(g)xa0+xa02CO2 and Pt(g)xa0+xa0O2xa0⟷xa0PtO2(g)xa0→xa0PtO2(s). The first reaction determines the kinetics of CO oxidation and the second determines the kinetics of restoration of the PtO2 layer. Thermochemical consideration of the kinetic features of this model, based on Langmuir’s quasi-equilibrium equations for evaporation of simple substances, allowed calculation of the reaction enthalpy and the absolute rate of CO oxidation. These results are in good agreement with experimental data. The proposed mechanism explains the origin of the surface-retexturing effect, the limited loss of Pt metal from the catalyst, the mechanism of PtO2 regeneration by oxygen, the strong effect of CO2 in reducing the CO oxidation rate and the three-fold variation of the Arrhenius E parameter with temperature.

Solid state reaction kinetics, mechanisms and catalysis: a retrospective rational review

Kinetic studies are widely used to characterize the factors that control the reactivity and the mechanisms of chemical changes that occur on heating solid reactants. This survey appraises the origins, assumptions and scientific foundations that underlie the theoretical methods that are conventionally, and unquestioningly, used to analyze and to interpret thermal analysis (TA) rate measurements. The extensive TA literature is reviewed in the context of the unusual history of this branch of science, in which TA has effectively superseded the formerly thriving subject of Thermal Decomposition of Solids (TDoS) (also reviewed). Such complete replacement of one scientific discipline by another is unusual, so that reasons for, and consequences of, this eclipse merit detailed consideration. The rapid rise of TA, after about 1970, resulted from the unprecedented advances in instrumental and computational methods which massively accelerated the collection and analysis of accurate rate data for thermal reactions (including solids). Consequently, TA theory initially tended to focus on developing experimental equipment together with facilitation of data interpretation by computer programs. These achievements have enabled each TA study to be completed very rapidly and with relatively much less effort than was usual in the former TDoS methodology. However, much less effort was also invested in developing coherent and soundly-based theory for the interpretation of TA kinetic data, with consequences that are critically appraised here in their historical context.

Catalytic oxidation of hydrogen on platinum

Using the thermochemical approach to interpret the kinetics of heterogeneous reactions and the mechanism of congruent dissociative decomposition of solids developed in the 1980s and (re)analyzing the experimental data available in the literature over the last 90xa0years, a novel mechanism for the catalytic oxidation of H2 by PtO2 is proposed. In place of the conventional Langmuir–Hinshelwood and Eley–Rideal adsorption reaction mechanisms, our model is based on the reactions: PtO2(s)xa0+xa02H2xa0↔xa0Pt(g)xa0+xa02H2O and Pt(g)xa0+xa0O2xa0↔xa0PtO2(g)xa0→xa0PtO2(s). The first reaction determines the kinetics of H2 oxidation and the second determines the kinetics of restoration of the PtO2 layer. Thermochemical consideration of kinetic features of this model enables (for first time in the history of this reaction) the enthalpy and equilibrium constants for H2 oxidation on platinum to be calculated. The results are in good agreement with experimental data. In addition, the proposed mechanism explains the origin of the surface-retexturing effect, the impact of autocatalysis, the influence of H2O vapor on oxidation rate, and the three-fold variation of the Arrhenius E parameter with temperature. This all convincingly demonstrates the value of the thermochemical approach in interpreting heterogeneous reactions.