The Reaction Layer

All the above methods, when hers are present, have one very serious drawback many hers give rise to a compact reaction layer, as described in Chap. 2. The above Reinert-Berg reaction does not, but the EC reaction, 

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Quasi-equilibrium exposure regime. After tire 7 x 7 stmcture has been removed, quasi-equilibrium between etching and growtli of tire reaction layer is established. The reaction layer is about one monolayer tliick, and contains primarily SiF. Defects fonn near tire surface, partly from tire large reaction exotliennicity. 

Though using a much lower total amount of catalyst than in the homogeneous case, a considerably higher catalyst concentration in the reaction layer can be supplied. 

A general theory based on the quantitative treatment of the reaction layer profile exists for pure redox catalysis where the crucial function of the redox mediator is solely electron transfer and where the catalytic activity largely depends only on the redox potential and not on the structure of the catalyst This theory is consistent... 

Enantioselective electron transfer reactions are not possible in principle because the electron cannot possess chirality. Whenever the choice of enantiodifferentiation becomes apparent, it will occur in chemical steps subsequent (or prior) to electron transfer. Thus, enantioselectivities require a chiral environment in the reaction layer of electrochemical intermediates although asymmetric induction was report-... 

Each of the particles of Red produced in the chemical reaction will, after some (mean) time t, have been reconverted to A. Hence, when the current is anodic, only those particles of Red will be involved in the electrochemical reaction which within their own lifetime can reach the electrode surface by diffusion. This is possible only for particles produced close to the surface, within a thin layer of electrolyte called the reaction layer. Let this layer have a thickness 5,.. As a result of the electrochemical reaction, the concentration of substance Red in the reaction layer will vary from a value Cg at the outer boundary to the value Cg right next to the electrode within the layer a concentration gradient and a diffusion flux toward the surface are set up. 

It can be seen here that the larger the valne of k, the thinner will be the reaction layer and the more readily will the particles avoid getting involved in the electrochemical reaction and instead, participate in the reverse chemical reaction. However, becanse of the increase in concentration gradient, the flnx to the surface and the current density will still increase. 

Figure 5.37 depicts the stationary distribution of the electroactive substance (the reaction layer) for kc—> oo. The thickness of the reaction layer is defined in an analogous way as the effective diffusion layer thickness (Fig. 2.12). It equals the distance [i of the intersection of the tangent drawn to the concentration curve in the point x = 0 with the line c = cA/K,...

Orui et al. [169] studied the stability of La(Ni, Fe)03 with 10 mol% Sc203-l mol% Al203-stabilized Zr02 (SASZ) and found that LNF was more reactive with SASZ electrolyte than LSM. For the cell sintered at 1100 and 1200°C, a reaction layer was clearly visible at the LNF/SASZ interface. The thickness of the reaction layer increased with the sintering temperature and the layer was identihed as the oxide-containing La and Zr by the TEM/EDS analysis. 

Several approaches have been undertaken to construct redox active polymermodified electrodes containing such rhodium complexes as mediators. Beley [70] and Cosnier [71] used the electropolymerization of pyrrole-linked rhodium complexes for their fixation at the electrode surface. An effective system for the formation of 1,4-NADH from NAD+ applied a poly-Rh(terpy-py)2 + (terpy = terpyridine py = pyrrole) modified reticulated vitreous carbon electrode [70]. In the presence of liver alcohol dehydrogenase as production enzyme, cyclohexanone was transformed to cyclohexanol with a turnover number of 113 in 31 h. However, the current efficiency was rather small. The films which are obtained by electropolymerization of the pyrrole-linked rhodium complexes do not swell. Therefore, the reaction between the substrate, for example NAD+, and the reduced redox catalyst mostly takes place at the film/solution interface. To obtain a water-swellable film, which allows the easy penetration of the substrate into the film and thus renders the reaction layer larger, we used a different approach. Water-soluble copolymers of substituted vinylbipyridine rhodium complexes with N-vinylpyrrolidone, like 11 and 12, were synthesized chemically and then fixed to the surface of a graphite electrode by /-irradiation. The polymer films obtained swell very well in aqueous... 

The relative importance of reaction with respect to diffusion can be described in terms of the nondimensional (second) Damkohler number [30-36] (also called Thiele modulus), in terms of the reaction layer thickness [37,38] or in terms of lability criteria [39,40]. 

A quantitative discrimination between labile and nonlabile complexes is made by comparing the diffusion timescale with those of the association/dissociation reactions (or alternatively, the reaction layer, /i (equation (58)) and the diffusion layer, <5, thicknesses (e.g. equations (15), (18) and (19)). 

We note incidentally that the reaction layer thickness is on the same order as that of the double layer for k+ 1010 s-1 (typical values of the diffusion coefficient are of the order of 10 5 cm2 s 1). It is only for such fast reactions that their kinetics may be perturbed by the strong electric field present in the close vicinity of the electrode.3... 

We now start examining how competing follow-up reactions control product distribution. The way in which these reactions interfere depends on their rate relative to the diffusion process, or alternatively, on the relative size of the corresponding reaction and diffusion layers (Figure 2.31). For a follow-up reaction with a first (or pseudo-first-order) rate constant, k, occurring in the framework of an EC reaction scheme (see Section 2.2.1), the reaction layer thickness is y/D/k. 

The opposite situation (y/D/k -C <5), where the reaction layer is much thinner than the diffusion layer (as represented in the lower diagram of Figure 2.31) is more specific of electrochemistry, in the sense that the homogeneous follow-up reactions are more intimately connected with the electrode electron transfer step. The same pure kinetic conditions discussed earlier for cyclic voltammetry (Section 2.2.1) apply. In the case of a simple EC reaction scheme, as shown in the figure, the production of C in the bulk solution obeys exactly the same equations (2.32) to (2.34) as for B in the preceding case, as established in Section 6.2.8. 

This is no longer the case when competition involves reactions with different orders, as in Scheme 2.17. Unlike the preceding case, the C and D concentration profiles do not have the same shape. Appropriate dimensionless analysis (see Section 6.2.8), where the space variable is normalized toward the reaction layer thickness, leads to the dimensionless parameter... 

Dealing now with Scheme 2.16, which involves two competing first-order reactions, the A concentration profile and gradients are not modified. The following differential equations govern the concentration profiles of the intermediate B and the two products C and D within the reaction layer ... 

The concentration profile of B is squeezed within the reaction layer. It may be analyzed in dimensionless term so as to obtain the expression of the yields with introduction of a minimal number of parameters. This is arrived at by normalizing the space variable versus the reaction layer thickness as y = xy/k /D(y = 1 corresponds to x = fi) and the concentrations as... 

Because the ratio of the reaction layer over the diffusion layer thickness tends toward zero, (CA) — (Ca)jc=0, and thus... 

Assuming that pure kinetic conditions are fulfilled, the Q profile is confined within a thin layer adjacent to the electrode surface. It therefore follows from the condition (0[S]/0x) c=o = 0 that [S] may be regarded as constant throughout the reaction layer and equal to its value, [S], at the electrode surface. Within this framework, we consider the case where the catalytic response is controlled by the enzymatic reaction. Equations (6.233) may be simplified upon consideration that [S] = C( and also from the fact that pure kinetic conditions implies that 0[Q]/0t = 0. It follows that... 

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