Double layer: counter ions ionic

In the diffuse double-layer model, the ionic atmosphere consists of two regions a so-called Stem (or near-Stem) layer and a diffuse layer after that. In the Stem layer we have approximately one sharp counter-ion plane. The counter-ions dominate close to the interface due to attractions... 

The physical meaning of the g (ion) potential depends on the accepted model of an ionic double layer. The proposed models correspond to the Gouy-Chapman diffuse layer, with or without allowance for the Stem modification and/or the penetration of small counter-ions above the plane of the ionic heads of the adsorbed large ions. " The experimental data obtained for the adsorption of dodecyl trimethylammonium bromide and sodium dodecyl sulfate strongly support the Haydon and Taylor mode According to this model, there is a considerable space between the ionic heads and the surface boundary between, for instance, water and heptane. The presence in this space of small inorganic ions forms an additional diffuse layer that partly compensates for the diffuse layer potential between the ionic heads and the bulk solution. Thus, the Eq. (31) may be considered as a linear combination of two linear functions, one of which [A% - g (dip)] crosses the zero point of the coordinates (A% and 1/A are equal to zero), and the other has an intercept on the potential axis. This, of course, implies that the orientation of the apparent dipole moments of the long-chain ions is independent of A. 

Ionic compounds such as halides, carboxylates or polyoxoanions, dissolved in (generally aqueous) solution can generate electrostatic stabilization. The adsorption of these compounds and their related counter ions on the metallic surface will generate an electrical double-layer around the particles (Fig. 1). The result is a coulombic repulsion between the particles. If the electric potential associated with the double layer is high enough, then the electrostatic repulsion will prevent particle aggregation [27,30]. 

As mentioned above, a substantial part of the electrical charge of the micelle surface has been shown to be neutralized by the association of the counter ions with the micelle. In the calculation based on Equation 12, however, the loss in entropy arising from this counter ion association is not taken into account. This is by no means insignificant in comparison to of Equation 12 (4). A major part of the counter ions are condensed on the ionic micelle surface and counteract the electrical energy assigned to the amphiphilic ions on the micellar surface. The minor part of the counter ions,in the diffuse double layer, are also restricted to the vicinity of the micellar surface. 

An important aspect of analyzing the double layer data in the presence of specific adsorption is the determination of the dielectric properties of the irmer layer. In the Grahame model for ionic adsorption [Gl], the adsorbed ions are assumed to have their charge centers located on the inner Helmholtz plane (iHp). Furthermore, the iHp is closer to the electrode surface than the oHp. This is due to the fact that the adsorbed ions replace solvent molecules on the electrode surface, whereas the counter ions on the oHp do not. Another feature of the following treatment is that the charge on the adsorbed ions is assumed to be located on the iHp. Accordingly, the potential drop across the inner layer is given by... 

Any portion of a dynamic ionic adsorption layer leads to an electrical double layer out of electroneutrality. The adsorbed layer acquires the charge of the fast diffusing ion, while the diffusion layer takes the charge of the slow diffusing ion. It is possible to describe qualitatively the adsorption layer interactions and their kinetics without rigorous mathematical analysis. The initial adsorption of siuface active ions is followed by the adsorption of the counter ions which reside in the diffuse double layer. Macroscopically equivalent numbers of oppositely charged ions are involved to preserve overall electric neutrality, each ion is transported by diffusion. 

In colloid science we are particularly interested in the ionic atmosphere which is developed around a charged colloid particle, rather than around a single ion. In this context it is usual to call this ionic atmosphere an electrical double layer. The charge on the particle is distributed over its surface and is just balanced by the total charge in the double layer in which there is an excess of oppositely charged ions (counter-ions) (Figure 3.4). 

In the above argument we have ignored the efl eet of the ionic atmosphere, or electrical double layer, around the charged particle. Its presence has two consequences (Figure G.7). First, the counter-ions in the double layer tend to move in a direction opposite to that of the particle, which in effect has to drag its double layer with it. Secondly, it does not entirely succeed in taking all of its double layer, but fresh ions become attached to it as some an- left behind this reconstruction of the double layer does not take plaee instantaneously. Both effects lead to a retardation of the movement of the particle. More complete theories lead to the introduction of an additional term J(Ka) into equation (6.45) ... 

Finedly, it should also be pointed out that the alkali and alkali earth metal ions also participate in important non-specific interactions. These include (1) acting as counter ions in the electrical double layer stabilisation of ma-cromolecular and colloidal organo-metallic complexes (Shapiro, 1964 Parks, 1975 Eckert and Sholkovitz, 1976) and (2) in regulating the electrolyte properties and ionic strength (I) of natural waters (Whitfield, 1975) which, in turn, will affect the activity coefficients and conditional stability constants (K ) of organo-metallic complexes. For example, log values for Cu -, Pb - and Cd -humate complexes were found to decrease linearly with -v/l (Stevenson, 1976) or simply with I (Schnitzer and Khan, 1972). 

The last effect to be described here is film elasticity In case of ionic surfactants the aqueous phase in the double layers contain dissolved counter ions of the surfactants. When the ionic density increases, the repulsive forces of equally charged ions become substantial, see Fig. 11. The repulsive forces are also responsible for a certain elasticity of double layers. The thickness of double layers in the well-known coloured air bubbles lies between 1,000 and 10,000 A. It can be determined by the order of interferential colours The process is very dynamic and fluctuates over the surface area. Under certain conditions the drainage reaches an end at a metastable state (so called black films ) giving the lamella or bubble a limited time of existence ... 

It is obvious that such calculations, which prove to be rather laborious, may be carried out for a great variety of parameters, as apart from the double layer potential the capacity of the Stern layer, too, (which is determined for instance by the dimensions and the polarizability of the counter ions) and the adsorption potential of the ions (see 5 of Qiapter II) may be different for different systems. Furthermore, a new calculation has to be set up for each ionic concentration and for each value of the valency of the ions. A further difficulty is that especially the adsorption potentials of the ions, which depend on the properties of the ions and of the wall material, are entirely unknown quantities. 

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