Model of the electric double layer

Yates, D. E., S. Levine, and T. W. Healy (1974), "Site-binding Model of the Electrical Double Layer at the Oxide/Water Interface", J. Chem. Soc. Faraday Trans. 70,1807. 

Gouy-Chapman, Stern, and triple layer). Methods which have been used for determining thermodynamic constants from experimental data for surface hydrolysis reactions are examined critically. One method of linear extrapolation of the logarithm of the activity quotient to zero surface charge is shown to bias the values which are obtained for the intrinsic acidity constants of the diprotic surface groups. The advantages of a simple model based on monoprotic surface groups and a Stern model of the electric double layer are discussed. The model is physically plausible, and mathematically consistent with adsorption and surface potential data. 

Two models of surface hydrolysis reactions and four models of the electrical double layer have been discussed. In this section two examples will be discussed the diprotic surface group model with constant capacitance electric double layer model and the monoprotic surface group model with a Stern double layer model. More details on the derivation of equations used in this section are found elsewhere (3JL). ... 

Diprotic Surface Groups. Most of the recent research on surface hydrolysis reactions has been interpreted in terms of the diprotic surface hydrolysis model with either the triple layer model or the constant capacitance model of the electric double layer. The example presented here is cast in terms of the constant capacitance model, but the conclusions which are drawn apply for the triple layer model as well. 

The representation of the data for TiC in terms of the monoprotic surface group model of the oxide surface and the basic Stern model of the electric double layer is shown in Figure 5. It is seen that there is good agreement between the model and the adsorption data furthermore, the computed potential Vq (not shown in the figure) is almost Nernstian, as is observed experimentally. 

Figure 7.4. Schematic model of the Electrical Double Layer (EDL) at the metal oxide-aqueous solution interface showing elements of the Gouy-Chapman-Stern-Grahame model, including specifically adsorbed cations and non-specifically adsorbed solvated anions. The zero-plane is defined by the location of surface sites, which may be protonated or deprotonated. The inner Helmholtz plane, or [i-planc, is defined by the centers of specifically adsorbed anions and cations. The outer Helmholtz plane, d-plane, or Stern plane corresponds to the beginning of the diffuse layer of counter-ions and co-ions. Cation size has been exaggerated. Estimates of the dielectric constant of water, e, are indicated for the first and second water layers nearest the interface and for bulk water (modified after [6]).

Figure 4.1 Helmholtz and Gouy-Chapman model of the electric double layer.

Fig. 1.11 Behavior of Cd as a function of the electrolyte concentration for the Stem s model of the electrical double layer, calculated from Eq. (1.81) for a 1 1 electrolyte.

From the discussion so far it can be appreciated that the Stern model of the electric double layer presents only a rough picture of what is undoubtedly a most complex situation. Nevertheless, it provides a good basis for interpretating, at least semiquantitatively, most experimental observations connected with electric double layer phenomena. In particular, it helps to account for the magnitude of... 

Much work on these composite systems has to be done, For example, we have not considered yet the study of phenomena occurring at the surface of an electrified metal the version of PCM for ionic solutions [10] has been available for a longtime, but the modeling of the electric double layer has not been done yet (every new modeling requires considerable intellectual and computational efforts). 

The composition of this chapter is based on a well-known and well-understood model of the electrical double layer and therefore does not pretend to enhance overall understanding. It does, however, aim to answer the question of whether a useful mathematical technique exists that may allow for a numerical, if not analytical, description of the double layer for a surface of arbitrary shape and topography. It is fair to say that the colloid scientist ultimately seeks a quantitative description of the electrical double layer for whatever reason. The task then now faced is to uncover the most appropriate theoretical method of calculating the electrical double layer properties for a given nonideal situation. Here we suggest a few methods that may help in this respect. 

IV. The Site Binding Models of the Electric Double Layer 148... 

IV. THE SITE BINDING MODELS OF THE ELECTRIC DOUBLE LAYER... 

The substantial parameter at the modeling of the electric double layer at metal oxide-electrolyte solution interface is a number of the hydroxyl group per surface unit of the oxide. For the titanium dioxide, although different crystalline faces form the surface [rutile 60% of the surface is formed by the face (110) whereas for anatase by (001)] the same density 12.8 of —OH group/nm2 is assumed [28]. That results from the very similar intersection of the elementary cells of the mentioned face, which have the highest density of the atoms in both oxides. 

The Nonprimitive Model of the Electric Double Layer at a Metal/Aqueous Electrolyte Interface... 

Finally we shall argue that present-day theories of the nonprimitive models of the electric double layer have considerable difficulty in treating properly ion adsorption in the Stern inner region at metal-aqueous electrolyte interfaces and we suggest that this region is a useful concept which should not be dismissed as unphysical. Indeed Stern-like inner region models continue to be used in colloid and electrochemical science, for example in theories of electrokinetics and aqueous-non-metallic (e.g., oxide) interfaces. 

Carnie and Chan (CC) [92,96,97] and Blum and Henderson (BH) [91,94,95] first made important studies of the simplest of nonprimitive models of the electric double layer. They assumed the ions and solvent molecules to be hard spheres with point charges and point dipoles, respectively, and the interface to be a hard smooth charged wall. Image effects were neglected so that the material of the wall was replaced by a vacuum. Also electron overspill from... 

Figure 10. Electrical double layer models. Top right (a) typical type of potential vs. composition plot for a charged surface compared to (b) constant capacitance model. Top left Two double-layer models, (a) diffuse double layer, (b) part parallel plate capacitor and part diffuse layer.. Bottom left Stem layer model. Incorporation of adsorbed ions to surface. From Hiemenz and Rajagopalan (1997) Bottom right Comparison of Gouy-Chapman and Stem-Grahame models of the electrical double layer. From Davis and Kent (1990).

FIGURE 2-1 Helmholtz model of the electrical double layer, (a) Distribution of counterions in the vicinity of the charged surface. (b) Variation of electrical potential with distance from the charged surface. 

We propose a model of the electric double layer for ionized mono-layers at A—W or O-W interfaces, which is a compromise between strong... 

Fig. 12. Cyclic voltammogram and model of the electrical double layer at a silver electrode surface. Arrows indicate the direct-ions of molecular dipoles in the water (smallest circles) and pyridine (largest circles, Py) molecules, the arrow head being the positive end. The cations (solvated) could he Na+ or K+, the anions (unsolvated) Cl or SOJ-. IHP and OHP designate the inner and outer Helmholtz planes, respectively, and PZC is the potential of zero charge (see text for further explanations). (Reproduced with permission from ref. 14.)...

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