Interface Reaction Mechanism

The rate of coarsening is controlled by two mechanisms, i.e., interface reaction mechanism and diffusion-controlled mechanism, as shown in Fig. 8.4. For interface reaction mechanism, coarsening rate is controlled either by the solubility of the particles into the medium or the deposition of the solute onto the particle surfaces. For diffusion-controlled mechanism, the diffusion of atoms through the medium to combine with larger particles is the controlling step. 

The summation means that all the precipitates in the system are included. Equation (8.5) can be rewritten as follows  

Equation (8.11) indicates that the rate of change in the radius of the precipitate is proportional to the dilference between the critical precipitate curvature and the actual precipitate curvature. 

The evolution of the system of precipitates can be described by using a distribution function /(a, r), with which /(a, r) da represents the fractional number of precipitates in the radium range of (a, a + Aa). The distribution function must satisfy the continuity equation  

Erom the solution of the coupled differential Eqs. (8.11) and (8.12), it is found that the rate of the coarsening reaches a steady state, so that the precipitate size distribution remains stationary against time, after a prolonged duration of coarsening process. When a reduced size, = ala, is used to represent the radius of the precipitate, the distribution function will have the following forms [4]  

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Figure 4-8 Various interface reaction mechanisms, (a) Continuous growth mechanism, (b) Screw disiocation mechanism, (c) Surface nucieation mechanism.

Therefore, all the theories indicate that the NGG in polycrystaUine solids can be treated as the Ostwald ripening governed by the interface reaction mechanism. However, in practice, the grain growth data cannot be always described by the parabolic law, so that a general grain growth equation is used ... 

Kinetic investigations cover a wide range from various viewpoints. Chemical reactions occur in various phases such as the gas phase, in solution using various solvents, at gas-solid, and other interfaces in the liquid and solid states. Many techniques have been employed for studying the rates of these reaction types, and even for following fast reactions. Generally, chemical kinetics relates to tlie studies of the rates at which chemical processes occur, the factors on which these rates depend, and the molecular acts involved in reaction mechanisms. Table 1 shows the wide scope of chemical kinetics, and its relevance to many branches of sciences. 

Another reaction mechanism, which is conveniently mentioned under this heading, is due to Hill [479] who suggested that ions (atoms or molecules) frorh the product may move through the dislocation network of the reactant and activate potential nuclei, particularly in the vicinity of the reaction interface. Thus a reaction zone, within which potential nucleusforming sites are activated, is developed in front of an advancing interface. With appropriate assumptions, this reaction model provides an alternative explanation of the exponential rate law, eqn. (8), which in Sect. 3.2 was discussed with reference to chain reactions. 

A reaction interface is the zone immediately adjoining the surface of contact between reactant and product and within which bond redistributions occur. Prevailing conditions are different from those characteristic of the reactant bulk as demonstrated by the enhanced reactivity, usually attributed to local strain, catalysis by products, etc. Considerable difficulties attend investigation of the mechanisms of interface reactions because this thin zone is interposed between two relatively much larger particles. Accordingly, many proposed reaction models are necessarily based on indirect evidence. Without wishing to appear unnecessarily pessimistic, we consider it appropriate to mention here some of the problems inherent in the provision of detailed mechanisms for solid phase rate processes. These difficulties are not always apparent in interpretations and proposals appearing in the literature. 

While there is agreement that the rates of clay dehydroxylations are predominantly deceleratory and sensitive to PH2G, there is uncertainty as to whether these reactions are better represented by the first-order or by the diffusion-control kinetic expressions. In the absence of direct observational evidence of interface advance phenomena, it must be concluded that the presently available kinetic analyses do not provide an unambiguous identification of the reaction mechanisms. The factors which control the rates of dehydroxylation of these structurally related minerals have not been identified. 

There have been few satisfactory demonstrations that decompositions of hydrides, carbides and nitrides proceed by interface reactions, i.e. either nucleation and growth or contracting volume mechanisms. Kinetic studies have not usually been supplemented by microscopic observations and this approach is not easily applied to carbides, where the product is not volatile. The existence of a sigmoid a—time relation is not, by itself, a proof of the occurrence of a nucleation and growth process since an initial slow, or very slow, process may represent the generation of an active surface, e.g. poison removal, or the production of an equilibrium concentration of adsorbed intermediate. The reactions included below are, therefore, tentative classifications based on kinetic indications of interface-type processes, though in most instances this mechanistic interpretation would benefit from more direct experimental support. 

Another possibility is that one of the reactants is particularly mobile, this is apparent in certain solid—gas reactions, such as the reduction of NiO with hydrogen, which is a well-characterized nucleation and growth process [30,1166]. Attempts have been made to use the kinetic equations developed for interface reactions to elucidate the mechanisms of reactions between the crystalline components of rocks under conditions of natural metamorphism [1167,1168]. 

Two product barrier layers are formed and the continuation of reaction requires that A is transported across CB and C across AD, assuming that the (usually smaller) cations are the mobile species. The interface reactions involved and the mechanisms of ion migration are similar to those already described for other systems. (It is also possible that solid solutions will be formed.) As Welch [111] has pointed out, reaction between solids, however complex they may be, can (usually) be resolved into a series of interactions between two phases. In complicated processes an increased number of phases, interfaces, and migrant entities must be characterized and this requires an appropriate increase in the number of variables measured, with all the attendant difficulties and limitations. However, the careful selection of components of the reactant mixture (e.g. the use of a common ion) or the imaginative design of reactant disposition can sometimes result in a significant simplification of the problems of interpretation, as is seen in some of the examples cited below. 

It is sometimes said that this electrode is reversible with respect to the anion. This claim must be examined in more detail. An electrode potential that depends on anion activity still constitutes no evidence that the anions are direct reactants. Two reaction mechanisms are possible at this electrode, a direct transfer of chloride ions across the interface in accordance with Eq. (3.34) or the combination of the electrode reaction... 

In this chapter, novel oscillations observed with liquid membrane systems by the present authors [22-25] will be introduced, and the mechanisms for the oscillation are clarified by using VITIES, taking into consideration ion transfer reactions and adsorptions at two aqueous-membrane interfaces. The mechanism of the spontaneous potential oscillation in a liquid membrane system proposed by Yoshikawa et al. is also discussed briefly. 

This chapter reviewed some of our group s contributions to the development and application of QM/MM methods specifically as applied to enzymatic reactions, including the use of sequential MD/QM methods, the use of effective fragment potentials for reaction mechanisms, the development of the new QM/MM interface in Amber, as well as the implementation and optimization of the SCC-DFTB method in the Amber program. This last implementation allows the application of advanced MD and sampling techniques available in Amber to QM/MM problems, as exemplified by the potential and free energy surface surfaces for the reaction catalyzed by the Tripanosoma cruzi enzyme /ram-sialidasc shown here. 

While characterization of the electrode prior to use is a prerequisite for a reliable correlation between electrochemical behaviour and material properties, the understanding of electrochemical reaction mechanisms requires the analysis of the electrode surface during or after a controlled electrochemical experiment. Due to the ex situ character of photoelectron spectroscopy, this technique can only be applied to the emersed electrode, after the electrochemical experiment. The fact that ex situ measurements after emersion of the electrode are meaningful and still reflect the situation at the solid liquid interface has been discussed in Section 2.7. 

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