Interface controlled reactions

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. 

To summarize the structure of a moving interface on the atomic scale depends on the atomic mechanism which operates in the structure transformation. The mode selection depends on the driving force and thus on the interface velocity. The interface mobility itself is determined by its structure and depends therefore on the driving force. This means that interface controlled reactions are normally nonlinear functions of the driving force. 

Figure 1. Nucleation-controlled interface reaction (NCI) and interface-controlled reaction (ICI) at various times to-tj.

For interface-controlled reactions, the rate of reaction at the interface, r is proportional to the area of the interface S with a proportionality factor k, which is the rate or velocity of interface movement ... 

Reaction of a solid] with a gas J L Reaction at immobile A surface <"l Interface control or Diffusion control No barrier layer Interface phenomena Geometric control... 

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.

The maintenance of product formation, after loss of direct contact between reactants by the interposition of a layer of product, requires the mobility of at least one component and rates are often controlled by diffusion of one or more reactant across the barrier constituted by the product layer. Reaction rates of such processes are characteristically strongly deceleratory since nucleation is effectively instantaneous and the rate of product formation is determined by bulk diffusion from one interface to another across a product zone of progressively increasing thickness. Rate measurements can be simplified by preparation of the reactant in a controlled geometric shape, such as pressing together flat discs at a common planar surface that then constitutes the initial reaction interface. Control by diffusion in one dimension results in obedience to the... 

Strictly speaking, the validity of the shrinking unreacted core model is limited to those fluid-solid reactions where the reactant solid is nonporous and the reaction occurs at a well-defined, sharp reaction interface. Because of the simplicity of the model it is tempting to attempt to apply it to reactions involving porous solids also, but this can lead to incorrect analyses of experimental data. In a porous solid the chemical reaction occurs over a diffuse zone rather than at a sharp interface, and the model can be made use of only in the case of diffusion-controlled reactions. 

In studying interfacial electrochemical behavior, especially in aqueous electrolytes, a variation of the temperature is not a common means of experimentation. When a temperature dependence is investigated, the temperature range is usually limited to 0-80°C. This corresponds to a temperature variation on the absolute temperature scale of less than 30%, a value that compares poorly with other areas of interfacial studies such as surface science where the temperature can easily be changed by several hundred K. This "deficiency" in electrochemical studies is commonly believed to be compensated by the unique ability of electrochemistry to vary the electrode potential and thus, in case of a charge transfer controlled reaction, to vary the energy barrier at the interface. There exist, however, a number of examples where this situation is obviously not so. 

Penn, L.S., Tesoro, G.C. and Zhou, H.X. (1988). Some effects of surface-controlled reaction of Kevlar 29 on the interface in epoxy composites. Polym. Composites 9, 184-191. 

The previous section discussed the structure at the junction of two phases, the one a solid electron conductor, the other an ionic solution. Why is this important Knowledge of the structure of the interface, the distribution of particles in this region, and the variation of the electric potential in the double layer, permits one to control reactions occurring in this region. Control of these reactions is important because they are the foundation stones of important mechanisms linked to the understanding of industrial processes and problems, such as deposition and dissolution of metals, corrosion, electrocatalysis, film formation, and electro-organic synthesis. 

In heterogeneous solid state reactions, the phase boundaries move under the action of chemical (electrochemical) potential gradients. If the Gibbs energy of reaction is dissipated mainly at the interface, the reaction is named an interface controlled chemical reaction. Sometimes a thermodynamic pressure (AG/AK) is invoked to formalize the movement of the phase boundaries during heterogeneous reactions. This force, however, is a virtual thermodynamic force and must not be confused with mechanical (electrical) forces. 

Figure 6-14. Course of component k chemical potential during a heterogeneous multiphase reaction which is partly interface controlled.

Figure 10-10. Representation of the chemical potential of A during the heterogeneous solid state reaction A+B = AB. a) Diffusion control, b) interface control at b2, c) rate control by rearrangement (relaxation) of A in B in zone A (B), d) simultaneous diffusion and interface control (bj).

Let us finally comment on the morphological stability of the boundaries during metal oxidation (A + -02 = AO) or compound formation (A+B = AB) as discussed in the previous chapters. Here it is characteristic that the reaction product separates the reactants. 1 vo interfaces are formed and move. The reaction resistance increases with increasing product layer thickness (reaction rate 1/A J). The boundaries of these reaction products are inherently stable since the reactive flux and the boundary velocity point in the same direction. The flux which causes the boundary motion pushes the boundary (see case c) in Fig. 11-5). If instabilities are occasionally found, they are not primarily related to diffusional transport. The very fact that the rate of the diffusion controlled reaction is inversely proportional to the product layer thickness immediately stabilizes the moving planar interface in a one-... 

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