Interface advance reactions

The systematic treatment of interface advance reactions given by Jacobs and Tompkins [28] remains a valuable survey of the kinetics of solid phase decompositions. A later account was given by Young [29]. Greater mathematical emphasis is to be found in the books by Delmon [30] and by Barret [31]. 

KINETIC EXPRESSIONS DERIVED FOR INTERFACE ADVANCE REACTIONS... 

The dissociations described above have mostly been identified as interface advance reactions for which the nucleation step occurs relatively readily. The dominant kinetic feature is the progress of the reaction zone inwards to the particle centres. The Polanyi-Wigner reaction model (Chapter 7) was developed to account for the rates of such processes. Shannon [83] identified 29 different chemical changes of this type and found that only one-third of the reported kinetic parameters were within an order of magnitude of the theoretically expected values. From these, the dissociations of CaCO, and MgCOj were selected for more quantitative application of the absolute reaction rate theory. The known crystal structure and physical properties of the participating bonds were used to represent the transition state as follows ... 

So important are lattice imperfections in the reactions of solids that it is considered appropriate to list here the fundamental types which have been recognized (Table 1). More complex structures are capable of resolution into various combinations of these simpler types. More extensive accounts of crystal defects are to be found elsewhere [1,26,27]. The point which is of greatest significance in the present context is that each and every one of these types of defect (Table 1) has been proposed as an important participant in the mechanism of a reaction of one or more solids. In addition, reactions may involve structures identified as combinations of these simplest types, e.g. colour centres. The mobility of lattice imperfections, which notably includes the advancing reaction interface, provides the means whereby ions or molecules, originally at sites remote from crystal imperfections and surfaces, may eventually react. 

While the topochemistry of interface advance can be observed, the chemistry of reactions proceeding within that interface, localized inside the bulk of reactant particles, is less easily investigated. Intermediates cannot be isolated without destruction of the specialized environment in the strained region at the juxtaposition of two phases where these are generated. Identification of those species which are the necessary participants in a chemical transformation can be difficult since the total quantity... 

From the various possible geometric shapes of reactant crystallites, discussion here will be restricted to a consideration of reaction proceeding in rectangular plates knd in spheres [28]. A complication in the quantitative treatment of such rate processes is that reaction in those crystallites which were nucleated first may be completed before other particles have been nucleated. Due allowance for this termination of interface advance, resulting from the finite size of reactant fragments accompanied by slow nucleation, is incorporated into the geometric analysis below. 

Hulbert [77] discusses the consequences of the relatively large concentrations of lattice imperfections, including, perhaps, metastable phases and structural deformations, which may be present at the commencement of reaction but later diminish in concentration and importance. If it is assumed [475] that the rate of defect removal is inversely proportional to time (the Tammann treatment) and this effect is incorporated in the Valensi [470]—Carter [474] approach it is found that eqn. (12) is modified by replacement of t by In t. This equation is obeyed [77] by many spinel formation reactions. Zuravlev et al. [476] introduced the postulate that the rate of interface advance under diffusion control was also proportional to the amount of unreacted substance present and, assuming a contracting sphere (radius r) model... 

Kinetic expressions for appropriate models of nucleation and diffusion-controlled growth processes can be developed by the methods described in Sect. 3.1, with the necessary modification that, here, interface advance obeys the parabolic law [i.e. is proportional to (Dt),/2]. (This contrasts with the linear rate of interface advance characteristic of decomposition reactions.) Such an analysis has been provided by Hulbert [77], who considers the possibilities that nucleation is (i) instantaneous (0 = 0), (ii) constant (0 = 1) and (iii) deceleratory (0 < 0 < 1), for nuclei which grow in one, two or three dimensions (X = 1, 2 or 3, respectively). All expressions found are of the general form... 

Fig. 3. Reduced time plots, tr = (t/t0.9), for the contracting area and contracting volume equations [eqn. (7), n = 2 and 3], diffusion-controlled reactions proceedings in one [eqn. (10)], two [eqn. (13)] and three [eqn. (14)] dimensions, the Ginstling— Brounshtein equation [eqn. (11)] and first-, second- and third-order reactions [eqns. (15)—(17)]. Diffusion control is shown as a full line, interface advance as a broken line and reaction orders are dotted. Rate processes become more strongly deceleratory as the number of dimensions in which interface advance occurs is increased. The numbers on the curves indicate the equation numbers.

It is appropriate to emphasize again that mechanisms formulated on the basis of kinetic observations should, whenever possible, be supported by independent evidence, including, for example, (where appropriate) X-ray diffraction data (to recognize phases present and any topotactic relationships [1257]), reactivity studies of any possible (or postulated) intermediates, conductivity measurements (to determine the nature and mobilities of surface species and defects which may participate in reaction), influence on reaction rate of gaseous additives including products which may be adsorbed on active surfaces, microscopic examination (directions of interface advance, particle cracking, etc.), surface area determinations and any other relevant measurements. 

It is usually assumed in the derivation of isothermal rate equations based on geometric reaction models, that interface advance proceeds at constant rate (Chap. 3 Sects. 2 and 3). Much of the early experimental support for this important and widely accepted premise derives from measurements for dehydration reactions in which easily recognizable, large and well-defined nuclei permitted accurate measurement. This simple representation of constant rate of interface advance is, however, not universally applicable and may require modifications for use in the formulation of rate equations for quantitative kinetic analyses. Such modifications include due allowance for the following factors, (i) The rate of initial growth of small nuclei is often less than that ultimately achieved, (ii) Rates of interface advance may vary with crystallographic direction and reactant surface, (iii) The impedance to water vapour escape offered by... 

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. 

The (en) compound developed nuclei which advanced rapidly across all surfaces of the reactant crystals and thereafter penetrated the bulk more slowly. Kinetic data fitted the contracting volume equation [eqn. (7), n = 3] and values of E (67—84 kJ mole"1) varied somewhat with the particle size of the reactant and the prevailing atmosphere. Nucleus formation in the (pn) compound was largely confined to the (100) surfaces of reactant crystallites and interface advance proceeded as a contracting area process [eqn. (7), n = 2], It was concluded that layers of packed propene groups within the structure were not penetrated by water molecules and the overall reaction rate was controlled by the diffusion of H20 to (100) surfaces. 

The kinetic principles operating during the initiation and advance of interface-controlled reactions are identical with the behaviour discussed for the decomposition of a single solid (Chaps. 3 and 4). The condition that overall rate control is determined by an interface process is that a chemical step within this zone is slow compared with the rate of arrival of the second reactant. This condition is not usually satisfied during reaction between solids where the product is formed at the contact of a barrier layer with a reactant. Particular systems that satisfy the specialized requirements can, however, be envisaged for example, rate processes in which all products are volatilized or a solid additive catalyzes the decomposition of a solid yielding no solid residue. Even here, however, the kinetic characteristics are likely to be influenced by changing effectiveness of contact as reaction proceeds, or the deactivation of the catalyst surface. 

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