Gouy-Chapman diffuse model

The Stern model (1924) may be regarded as a synthesis of the Helmholz model of a layer of ions in contact with the electrode (Fig. 20.2) and the Gouy-Chapman diffuse model (Fig. 20.10), and it follows that the net charge density on the solution side of the interphase is now given by... 

As we have seen, the electric state of a surface depends on the spatial distribution of free (electronic or ionic) charges in its neighborhood. The distribution is usually idealized as an electric double layer one layer is envisaged as a fixed charge or surface charge attached to the particle or solid surface while the other is distributed more or less diffusively in the liquid in contact (Gouy-Chapman diffuse model, Fig. 3.2). A balance between electrostatic and thermal forces is attained. 

Fig. 20.8 Gouy-Chapman diffuse layer model of the double layer...

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. 

The physical meaning of the g" (ion) potential depends on the accepted model of ionic double layer. The proposed models correspond to the Gouy Chapman diffuse layer, with or without allowance for the Stern modification and/or the penetration of small counterions above the plane of the ionic heads of the adsorbed large ions [17,18]. The presence of adsorbed Langmuir monolayers may induce very high changes of the surface potential of water. For example. A/" shifts attaining ca. —0.9 (hexadecylamine hydrochloride), and ca. -bl.OV (perfluorodecanoic acid) have been observed [68]. 

The Gouy Chapman diffuse layer model has been shown to describe adequately the electrostatic potential produced by charges at the surface of the membrane [137]. For a symmetrical background electrolyte, a and i// are related by ... 

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. 

The earliest models used to describe the distribution of charges in the edl are, besides the Helmholz model, the Gouy-Chapman diffuse layer model and the Stem-Graham model. Details of these models are given in Westall and Hohl (1980), Schindler (1981, 1984) and Schindler and Stumm (1987). 

The Ionic Cloud The Gouy-Chapman Diffuse-Charge Model of the Double Layer... 

Gouy—Chapman Diffuse-Charge Model Jec0kT % ze y 2n Smh 2kT 2 nkT J kT V, = e" Pol 0 er s tial x-> It predicts that differential capacities have the shape of inverted parabolas. Ions are considered as pointcharges. Ion-ion interactions are not considered. The dielectric constant is taken as a constant. 

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. 

Electrostatic correction was made with the diffuse (Gouy-Chapman) doublelayer model. The figure shows the effect of pH on the relative extent of surface... 

Substantial efforts have been made to develop physicochemical models for ion exchange based on the Gouy-Chapman diffuse-layer theory (e.g., 9, 10). This work not only has provided insight into the role of diffuse-layer sorption in the ion-exchange process but also has pointed to the need to consider other factors, especially specific sorption at the surface. Consideration of specific sorption enables description of the different tendencies of ions to... 

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 ... 

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