Surfaces Gouy-Chapman model

A theoretical model for the adsorption of metals on to clay particles (<0.5 pm) of sodium montmorillonite, has been proposed, and experimental data on the adsorption of nickel and zinc have been discussed in terms of fitting the model and comparison with the Gouy-Chapman theory [10]. In clays, two processes occur. The first is a pH-independent process involving cation exchange in the interlayers and electrostatic interactions. The second is a pH-dependent process involving the formation of surface complexes. The data generally fitted the clay model and were seen as an extension to the Gouy-Chapman model from the surface reactivity to the interior of the hydrated clay particle. 

We shall use the familiar Gouy-Chapman model (3 ) to describe the behaviour of the diffuse double lpyer. According to this model the application of a potential iji at a planar solid/electrolyte interface will cause an accumulation of counter-ions and a depletion of co-ions in the electrolyte near the interface. The disposition of diffuse double layer implies that if the surface potential of the planar interface at a 1 1 electrolyte is t ) then its surface charge density will be given by ( 3)... 

Fig. 10.7 Gouy-Chapman model of the interface between a metal and an electrolyte. The metal is shown with a negative charge on its surface.

A polyelectrolyte solution contains the salt of a polyion, a polymer comprised of repeating ionized units. In dilute solutions, a substantial fraction of sodium ions are bound to polyacrylate at concentrations where sodium acetate exhibits only dissoci-atedions. Thus counterion binding plays a central role in polyelectrolyte solutions [1], Close approach of counterions to polyions results in mutual perturbation of the hydration layers and the description of the electrical potential around polyions is different to both the Debye-Huckel treatment for soluble ions and the Gouy-Chapman model for a surface charge distribution, with Manning condensation of ions around the polyelectrolyte. 

The Gouy-Chapman model assumes (1) the exchangeable cations exist as point charges, (2) colloid surfaces are planar and infinite in extent, and (3) surface charge is distributed uniformly over the entire colloid surface. Even though this assumption... 

Fig. 5.5 Distribution of electrical charges and potentials in a double layer according to (a) Gouy-Chapman model and (b) Stern model, where /q and are surface and Stern potentials, respectively, and d is the thickness of the Stern layer...

The Gouy-Chapman model describes the properties of the diffuse region of the double-layer. This intuitive model assumes that counterions are point charges that obey a Boltzmann distribution, with highest concentration nearest the oppositely charged fiat surface. The polar solvent is assumed to have the same dielectric constant within the diffuse region. The effective surface... 

It is noted that the finite size of ions may be taken into account using a modified Gouy-Chapman model of the diffuse double-layer. The finite size of ions limits the maximum concentrations of ions close to the particle surface. 

Noh and Schwarz proposed a modified Huang s and Stumm method for the calculation of surface hydroxyl group ionization constants, based on Gouy-Chapman model [118]. In this method the reactions of the surface complex formations are neglected ... 

In variable charge or pH-dependent charge minerals, the surface potential, /0, remains constant and is not affected by the concentration of ions in solution. In the case of permanent charge minerals, however, y0, varies with the concentration of salt in solution (Fig. 3.26). The relationship between t0 and surface charge is given by the Gouy-Chapman model, as previously demonstrated. 

The Stern model modifies the Gouy-Chapman model and divides ions present in the solution into two groups a part of the ions is placed near the solid surface, forming the so-called Stern layer (similar to the Helmholtz layer), and the other part having a diffuse distribution (Gouy-Chapman layer). It implies that the surface potential is linear in the Stern layer, and the exponential in the Gouy-Chapman layer. 

The jigsaw puzzle was put together by Stem in 1926. Agreement between theory and experiment can be achieved once it is realized that both the Helmholtz and the Gouy-Chapman models are valid and exist simultaneously. Thus, there is a layer of ions on the surface that... 

In the Gouy-Chapman model the countercharge consists of an excess of counterions and a deficit of co-ions. For a positive surface the corresponding ionic components of charge = zFT and a = -zFF are both negative and defined by equations like (3.4.8a and 8b for silver iodide, or (1.5.6.3c and 3d( for oxides. Let us consider the latter systems and let. as usual,. ... 

Figure 9.25. Adsorption of Pb(II) on hematite (a-Fc203) =FeOHr = 2.7 x 10 M Pbr = 10 M / = 5 X 10 M. Electrostatic effects are corrected with the Gouy-Chapman model. (Surface characteristics of a-Fe203 are given in Example 9.7.)...

FIGURE 2-2 Gouy-Chapman 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. 

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