Compact-diffuse layer model

Combustion, 27 189, 190 reaction, sites for, 33 161-166 reaction scheme, 27 190, 196 Commercial isomerization, 6 197 CoMo catalysts, 40 181 See also Cobalt (nickel)-molybdenum-sulfide catalysts Compact-diffuse layer model, 30 224 Compensation behavior, 26 247-315 active surface, 26 253, 254 Arrhenius parameters, see Arrhenius parameters... 

The potential distribution of Fig. 1 is typical of the compact-diffuse layer models (42-44). The potential varies almost linearly within the compact double layer, decaying exponentially within the diffuse layer. The thickness of the latter depends on the electrolyte ionic strength and becomes negligible in strong electrolytic solutions (42). This feature becomes important in electrocatalytic studies, since it is the potential difference (0 — < e) that can be measured or fixed experimentally versus a reference electrode, while reacting ions and molecules experience a potential difference ((j) —... 

At present it is impossible to formulate an exact theory of the structure of the electrical double layer, even in the simple case where no specific adsorption occurs. This is partly because of the lack of experimental data (e.g. on the permittivity in electric fields of up to 109 V m"1) and partly because even the largest computers are incapable of carrying out such a task. The analysis of a system where an electrically charged metal in which the positions of the ions in the lattice are known (the situation is more complicated with liquid metals) is in contact with an electrolyte solution should include the effect of the electrical field on the permittivity of the solvent, its structure and electrolyte ion concentrations in the vicinity of the interface, and, at the same time, the effect of varying ion concentrations on the structure and the permittivity of the solvent. Because of the unsolved difficulties in the solution of this problem, simplifying models must be employed the electrical double layer is divided into three regions that interact only electrostatically, i.e. the electrode itself, the compact layer and the diffuse layer. 

On the basis of this model, the overall differential capacity C for a system without specific adsorption, i.e. if the compact layer does not contain ions, is divided into two capacities in series, one corresponding to the compact layer Cc and the other to the diffuse layer Cd ... 

At the beginning of this century Gouy13 and Chapman13 independently developed a double layer model in which they considered that the applied potential and electrolyte concentration both influenced the value of the double layer capacity. Thus, the double layer would not be compact as in Helmholtz s description but of variable thickness, the ions being free to move (Fig. 3.6a). This is called the diffuse double layer. 

Fig. 3.7 The Stern model of the double layer, (a) Arrangement of the ions in a compact and a diffuse layer (b) Variation of the electrostatic potential, cf>, with distance, x, from the electrode (c) Variation of Cd with potential.

As in the Gouy-Chapman model, the more concentrated the electrolyte the less the importance of the thickness of the diffuse layer and the more rapid the potential drop. At distance xH there is the transition from the compact to the diffuse layer. The separation plane between the two zones is called the outer Helmholtz plane (OHP) the origin of the inner Helmholtz plane will be discussed below. 

Using this model, one cannot forecast the adsorption of the background electrolyte ions because this model do not consider the reactions responsible for such a process. Zeta potential values, calculated on the basis of this model, are usually too high, nevertheless, because of its simplicity the model is applied very often. In a more complicated model of edl, the three plate model (see Fig. 3), besides the mentioned surface plate and the diffusion layer, in Stern layer there are some specifically adsorbed ions. The surface charge is formed by = SOHJ and = SO- groups, also by other groups formed by complexation or pair formation with background electrolyte ions = SOHj An- and = SO Ct+. It is assumed that both, cation (Ct+) and anion (A-), are located in the same distance from the surface of the oxide and form the inner Helmholtz plane (IHP). In this case, beside mentioned parameters for two layer model, the additional parameters should be added, i.e., surface complex formation constants (with cation pKct or anion pKAn) and compact and diffuse layer capacities. 

Figure 14. Schematic representation of the electrode-solution interfacial region, (a) Helmholtz model (b) structured layer model (c) thermally disorganized layers and (d) resulting potential variations with distance of the electrode electrode potential Ojoi, solution potential OHP, outer Helmholtz plane (few A) Xq, extremity of the diffuse layer (few tens of A) x < xohP compact layer xqhp < x < x, diffuse layer.

Girault (lb) pointed out that the apparent potential dependence of the ET rate may be attributed to the change in concentration of the reactants near the interface rather than to activation control. This model, further developed by Schmickler (9), postulates that the rate constant is essentially potential-independent because the potential drop across the compact part of the double-layer at the ITIES is small. In this model, the ET rate dependence on the interfacial potential drop is only due to the diffuse layer effect similar to Frumkin effect at metal electrodes. 

As a result, for sufficiently concentrated solutions, about 1 M or higher, the diffuse-layer contribution in Eq. (20) represents in most cases only a minor correction to the compact-layer term. Then, one can even use the simple Helmholtz model for qualitative interpretation of the data. In particular, far from the p.z.c., this approximation is acceptable for aU concentrations. On the contrary, the diffuse... 

If one relies on the validity of the GC model for the diffuse-layer properties, one can use Eq. (20) to calculate the values of the compact-layer capacitance, Ch, from experimental data for C and theoretical formula (21a) for Cqc- This operation performed for all available values of the charge and the electrolyte concentration results in Fig. 3, in which the effect of the experimental dispersion is shown again for two dilute solutions. 

One has to keep in mind this impossibility to separate the compact-layer term and the concentration independent part of the diffuse-layer contribution in Eq. (20) at significant electrode charges. It results in an uncertainty in the values of the compact-layer capacitance, which is of primary importance in the modeling of the metal-solvent interfacial structure. 

In accordance with the Stern-Grahame model of the EDL structure the values of C are determined by both the diffuse and compact-layer properties, the latter being dependent on the metal properties. However, in very dilute solutions of a surface-inactive electrolyte the dominant contribution to C near the p.z.c. (at the capacitance minimum) is given by the diffuse layer, C = Cgc(0, c). Therefore the ratio of capacitances in these conditions should be close to the RF for the surface of the solid metal M ... 

The aforementioned diffuse-layer and discreteness-of-charge effects have been taken into consideration in the model proposed by Grahame and Parsons [26,250-252]. First, it was assumed (unlike in the Stern model) that the specifically adsorbed ions were located at the distance from the metal surface (in the inner Helmholtz plane ) ensuring their maximum bond strength, owing to the combination of forces of electrostatic and quantum-mechanical origins. It shows the need for the partial or even complete desolvation of the adsorbed species and its deep penetration into the compact layer. The position of this adsorption plane depends on all components of the system, metal, solvent, and adsorbed ion. 

In the MVN model, the EDL consists of two diffuse ion layers back-to-back, which produce a compact inner layer between the two phases (Fig. 3). Dielectric permittivity of the medium at any point in the diffuse layer is assumed to be constant and equal to the bulk phase value s. The compact layer or inner Helmholtz layer is located between —5 and +S. In a more detailed analysis, the dielectric permittivities in both parts of the compact layer are and... 

One of the major drawbacks of MPB theory is that it does not take into account the discreteness of a solvent. In the diffuse layer, the discreteness of solvent molecules strongly influences ion-ion interactions at small distances. Furthermore, an understanding of the structure and properties of the compact layer is impossible without an adequate model of solvent molecules and their interactions with the electrode and between themselves. 

Two planes are usually associated with the double layer. The first one, the inner Helmholtz plane (IHP), passes through the centers of specifically adsorbed ions (compact layer in the Helmholtz model), or is simply located just behind the layer of adsorbed water. The second plane is called the outer Helmholtz plane (OHP) and passes through the centers of the hydrated ions that are in contact with the metal surface. The electric potentials linked to the IHP and OHP are usually written as 4 2 and 4f, respectively The diffuse layer develops outside the OHP. The concentration of cations in the diffuse layer decreases exponentially vs. the distance from the electrode surface. The hydrated ions in the solution are most often octahedral complexes however, in Fig. 1.1.2. they are shown as tetrahedral structures for simplification. 

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