Gouy-Chapman diffuse double layer

Some emphasis is given in the first two chapters to show that complex formation equilibria permit to predict quantitatively the extent of adsorption of H+, OH , of metal ions and ligands as a function of pH, solution variables and of surface characteristics. Although the surface chemistry of hydrous oxides is somewhat similar to that of reversible electrodes the charge development and sorption mechanism for oxides and other mineral surfaces are different. Charge development on hydrous oxides often results from coordinative interactions at the oxide surface. The surface coordinative model describes quantitatively how surface charge develops, and permits to incorporate the central features of the Electric Double Layer theory, above all the Gouy-Chapman diffuse double layer model. 

Compute the equilibrium composition, and the extent of Pb(II) sorption to a-Fe203, as a function of pH, using the Gouy-Chapman diffuse double-layer model. 

A commonly used model for describing counterion distribution at a charged surface is based on the Gouy-Chapman diffuse double-layer (DDL) theory. This model assumes that the surface can be visualized as a structurally featureless plane with evenly distributed charge, while the counterions are considered point charges in a uniform liquid continuum. In this simplified picture, the equilibrium distribution of counterions is described by the Boltzmann equation ... 

The Gouy-Chapman theory provides a better approximation of reality than does the Helmholtz theory, but it still has limited quantitative application. It assumes that ions behave as point charges, which they cannot, and it assumes that there is no physical limit for the ions in their approach to the TPB, which is not true. Stem, therefore, modified the Gouy-Chapman diffuse double layer. His theory states that ions do have finite size, so they cannot approach the TPB closer than a few nm [54, 60], The first ions of the Gouy-Chapman diffuse double layer are in the gas phase but not at the TPB. They are at some distance 8 away from the zirconia-metal-gas interface. This distance will usually be taken as the radius of the ion. As a result, the potential and concentration of the diffuse part of the layer are low enough to justify treating the ions as point charges. Stem also assumed that it is possible that some of the ions are specifically adsorbed by the TPB in the plane 8, and this layer has become known as the Stem layer. Therefore, the potential will drop by T o - Pg over the molecular condenser (i.e., the Helmholtz plane) and by T g over the diffuse layer. Pg has become known as the zeta (Q potential. 

Figure 21. A schematic diagram of the Stern adsorption layer (top) and the average potential profile of the Stern layer and Gouy-Chapman diffuse double layer.

In AOT microemulsions, where the aqueous core of the droplets also contains counterions, a considerable part of the dielectric response to the applied fields originates from the redistribution of the counterions. As mentioned in Sec. II, the counterions near th charged surface can be distributed between the Stem layer and the Gouy-Chapman diffuse double layer (28-31). The distribution of counterions is essentially determined by their concentration and the geometry of the water core. Thus, for very large droplets the diffuse double layer peters out and the polarization can be described by the Schwarz model (32). However, as already mentioned, this approach is more relevant to the dielectric behavior of emulsions than to that of micro emulsions. 

The Gouy-Chapman diffuse double-layer differential capacitance Cr which is associated with the charge-transfer reaction resistance Rr appearing in Fignre 2.2.6 is given by... 

Figure 2. Three models of the electrochemical interface (a) the Helmholtz fixed (rigid) double layer, 1879 (b) the Gouy-Chapman diffuse double layer 1910-1913 (c)the Stern double layer, 1924, being a combination of the Helmholtz and the Gouy-Chapman concepts.

Extending out into solution from the electrical double layer (or the compact double layer, as it is sometimes known) is a continuous repetition of the layering effect, but with diminishing magnitude. This extension of the compact double layer toward the bulk solution is known as the Gouy-Chapman diffuse double layer. Its effect on electrode kinetics and the concentration of electroactive species at the electrode surface is manifest when supporting electrolyte concentrations are low or zero. 

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