Theory of solid state reaction kinetics

Two alternative methods have been used in kinetic investigations of thermal decomposition and, indeed, other reactions of solids in one, yield—time measurements are made while the reactant is maintained at a constant (known) temperature [28] while, in the second, the sample is subjected to a controlled rising temperature [76]. Measurements using both techniques have been widely and variously exploited in the determination of kinetic characteristics and parameters. In the more traditional approach, isothermal studies, the maintenance of a precisely constant temperature throughout the reaction period represents an ideal which cannot be achieved in practice, since a finite time is required to heat the material to reaction temperature. Consequently, the initial segment of the a (fractional decomposition)—time plot cannot refer to isothermal conditions, though the effect of such deviation can be minimized by careful design of equipment. 

Characteristic features of a—time curves for reactions of solids are discussed with reference to Fig. 1, a generalized reduced-time plot in which time values have been scaled to t0.s = 1.00 when a = 0.5. A is an initial reaction, sometimes associated with the decomposition of impurities or unstable superficial material. B is the induction period, usually regarded as being terminated by the development of stable nuclei (often completed at a low value of a). C is the acceleratory period of growth of such nuclei, perhaps accompanied by further nucleation, and which extends to the 

Increases in reaction rate with temperature are often found to obey the Arrhenius equation, from which the apparent values of the reaction frequency factor, A, and the activation energy, E, are calculated. The possibility that the kinetic obedience changes with temperature must also be considered. 

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It is not accidental that the consideration bears a polemic character. It was not my intention merely to give a number of ready mathematical formulae for the experimentalists to treat their data and to obtain some constants, although such a work is clearly also necessary and useful and must therefore be welcomed. However, it seemed to be far more important to show that, firstly, not all has yet been done in the field of theory of solid-state reaction kinetics and, secondly, some of wide-spread views should be modified or even rejected as contradicting not only the available experimental data but the common sense as well. 

The theory of solid state reaction kinetics includes no consideration of surface properties other than the recognition that crystal faces are the most probable location for nucleation in many reactions. Dehydration studies have provided evidence that, in many such processes, all surfaces are modified soon after the onset of chemical change [20,21], This is ascribed to a surface reaction that is limited in extent and can continue only at local sites of special reactivity where the recrystallization required for nucleation is possible. In other decompositions there is evidence that the modified reactivity associated with surfaces may influence the overall reaction [11] and may also preserve the identity of crystals. This, incidentally, masks the occurrence of melting during decomposition [22],... 

Introduction to the Theory of Solid-State Reaction Kinetics.179... 

INTRODUCTION TO THE THEORY OF SOLID-STATE REACTION KINETICS... 

In 1937, dost presented in his book on diffusion and chemical reactions in solids [W. lost (1937)] the first overview and quantitative discussion of solid state reaction kinetics based on the Frenkel-Wagner-Sehottky point defect thermodynamics and linear transport theory. Although metallic systems were included in the discussion, the main body of this monograph was concerned with ionic crystals. There was good reason for this preferential elaboration on kinetic concepts with ionic crystals. Firstly, one can exert, forces on the structure elements of ionic crystals by the application of an electrical field. Secondly, a current of 1 mA over a duration of 1 s (= 1 mC, easy to measure, at that time) corresponds to only 1(K8 moles of transported matter in the form of ions. Seen in retrospect, it is amazing how fast the understanding of diffusion and of chemical reactions in the solid state took place after the fundamental and appropriate concepts were established at about 1930, especially in metallurgy, ceramics, and related areas. 

The unjustified neglect of a chemical interaction step in analysing the process of compound-layer formation appears to be the main source of discrepancies between the diffusional theory and the experimental data. The primary aim of this book is, on the basis of physicochemical views regarding solid state reaction kinetics, to attempt... 

The summary of the theory of kinetics of solid-state reactions given here is applicable to TG investigations and also equally to rate measurements by other methods of thermal analyses. For more extensive treatments and further background information see References 4,5,10,29,71,76,103. 

The correctness of new ideas and theories in scientific research is commonly evaluated by their fruitfulness in interpretation of problems accumulated in one or another field and by their capability to predict unknown trends and effects. The other general criteria that are applied to new theories are simplicity, internal consistency, experimental reliability (verifiability), and compliance with previous theories. The thermochemical approach to the kinetics of solid-state reactions used in this study meets these criteria. 

It follows from this discussion that all of the transport properties can be derived in principle from the simple kinetic theory of gases, and their interrelationship through A, and c leads one to expect that they are all characterized by a relatively small temperature coefficient. The simple theory suggests that this should be a dependence on T1/2, but because of intermolecular forces, the experimental results usually indicate a larger temperature dependence even up to r3/2 for the case of molecular inter-diffusion. The Arrhenius equation which would involve an enthalpy of activation does not apply because no activated state is involved in the transport processes. If, however, the temperature dependence of these processes is fitted to such an expression as an algebraic approximation, then an activation enthalpy of a few kilojoules is observed. It will thus be found that when the kinetics of a gas-solid or liquid reaction depends upon the transport properties of the gas phase, the apparent activation enthalpy will be a few kilojoules only (less than 50 kJ). 

Consequently, while I jump into continuous reactors in Chapter 3, I have tried to cover essentially aU of conventional chemical kinetics in this book. I have tried to include aU the kinetics material in any of the chemical kinetics texts designed for undergraduates, but these are placed within and at the end of chapters throughout the book. The descriptions of reactions and kinetics in Chapter 2 do not assume any previous exposure to chemical kinetics. The simplification of complex reactions (pseudosteady-state and equilibrium step approximations) are covered in Chapter 4, as are theories of unimolecular and bimolecular reactions. I mention the need for statistical mechanics and quantum mechanics in interpreting reaction rates but do not go into state-to-state dynamics of reactions. The kinetics with catalysts (Chapter 7), solids (Chapter 9), combustion (Chapter 10), polymerization (Chapter 11), and reactions between phases (Chapter 12) are all given sufficient treatment that their rate expressions can be justified and used in the appropriate reactor mass balances. 

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