Surface double layer

The surface sites and complexes lie in a layer on the mineral surface which, because of the charged complexes, has a net electrical charge that can be either positive or negative. A second layer, the diffuse layer, separates the surface layer from the bulk fluid. The role of the diffuse layer is to achieve local charge balance with the surface hence, its net charge is opposite that of the sorbing surface. Double layer theory, applied to a mixed ionic solution, does not specify which ions make up the diffuse layer. 

Figure 15. Schematic drawings of various models (a, left) mosaic SEI model by Peled et al. (Reproduced with permission from ref 270 (Figure 1). Copyright 1997 The Electrochemical Society.) (b, right) Surface double layer capacitor model by Ein-Eli (Reproduced with permission from ref 272 (Figure 1). Copyright 1999 The Electrochemical Society.)...

The total interaction between the two metal spheres can therefore be classified into two parts (1) the surface, or double-layer, interaction determined by the Gouy-Chapman potential t f0e"Krand (2) the volume, or bulk, interaction —Ar-6 + Br 12. The interaction between double layers ranges from indifference at large distances to increasing repulsion as the particles approach. The bulk interaction leads to an attraction unless the spheres get too close, when there is a sharp repulsion (Fig. 6.131). The total interaction energy depends on the interplay of the surface (double layer) and volume (bulk) effects and may be represented thus... 

The influence of the presence of an organic monolayer on the surface potential measured at the water surface can also provide interesting information. However, this information can be difficult to interpret as it depends on the dipole moments associated with both the upper and the lower ends of the molecules and also the surface double layer in the water immediately below the film. There are two different ways of measuring this quantity. Both, of course, involve a counter electrode below the water surface. 

Keywords Hairy surface Double-layer interaction Hydration energy, Specific ion effect... 

The surface double layer is important for the electrochemical potential. In Section 4.2, it was discussed that the (electro)chemical potential of the electrons depends on the potential of the metal phase. If we take the potential energy of an electron at rest outside the metal (hence Fyac) as a reference, the electrochemical potential can be rewritten as follows (see Eq. 56) ... 

The results can be understood, at least qualitatively, if the surface double layer of the metal itself is taken into account [2]. A simple picture is presented in Figure 16 a water layer with specific orientation contacts the jellium double layer. Conceptually, the potential drop over the electrochemical double layer, A9>, sol) be separated into two contributions a drop over the metal double layer and a drop over the first layer of solvent molecules [see Figure 16(b)] ... 

Coordinate along the x axis normalized reaction coordinate distance between the centers of reacting molecules distance from the electrode surface Double layer thickness... 

Thus, in the approximation of a uniform dipole layer, the resulting electrostatic potential has the form of a sharp step of hight AV = Aixpn. This effect is well-known and is used in the surface double layer model for the work function of metals (see (45), (46)). In our case the height of the step AV = Airpn 0.1 V at the interface. Thus, the electric field in the region of a step with an effective thickness a is equal Ez = Airpn/a, opposite to the direction of the CTE dipole... 

Generally, the disjoining pressure consists of the electrostatic repulsion forces between the two overlapping surface double layers, the attractive van der Waals forces among all the molecules of the film, the steric forces due to steric hindrance in closely packed monolayers and, in the presence of micelles, the structural forces. 

Both Eqs. (8.1.11) and (8.1.12) show that the repulsive potential is inversely proportional to the Debye length and to exp(h/ [ ), which characterizes the interaction of the tails of each plate s surface double layer. A principal difference is that at low surface potential the repulsion is proportional to Y while at high surface potential the repulsion is independent of the surface potential (tanh 1) and is inversely proportional to... 

The image potential is a specific surface contribution to W, and a second surface contribution is the existence of a surface double layer or dipole layer. Surface atoms are in an unbalanced environment, they have other atoms on one side of them but not on the other thus, the electron distribution around them will be unsymmetrical with respect to the positive ion cores. This leads to the formation of a double layer. Two important effects emanate from this the work function is sensitive to both the crystallographic plane exposed and to the presence of adsorbates. 

RALEIGH I wish to make the point that if you want to use a solid-electrolyte cell to measure diffusion coefficients in this way, you don t necessarily have to measure the double layer capacitance and electron redistribution characteristics in the electrolyte. When you apply a d.c. bias that fixes a significant activity of the diffusant at the substrate surface, double-layer charging should be completed fairly soon. If you plot the cell current versus and get a significant linear... 

In many problems it is necessary to know either the number of particles (flocculation phenomena) or their total surface (double layer problems) or their size and shape (optical properties) ... 

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