Guoy-Chapman layer

Figure 4-34. Wall effects in capillary electrophoresis. The capillary walls, which are usually made of fused silica contain a small proportion of dissociated silanyl groups which bind positively charged counterions. In the region close to the wall, defining the Stern layer, these ions are relatively immobile mobility increases beyond this layer in a region which defines the Guoy-Chapman layer. The distribution of positively charged ions is termed the Zeta-potential it is fairly constant in the Stern layer, but falls off sharply with distance from the wall in the Guoy-Chapman layer.

The above definition of the symmetric surface excess and the classical Guoy-Chapman model of the diffuse double layer are combined to show that the surface excess cannot be considered a surface concentration in the presence of an ionized monolayer on an impenetrable solid/liquid interface. 

The double layer model of Helmholtz assumes fixed layer of charges on the electrode and the outer Helmholtz plane. This model has been modified by Guoy-Chapman analysis, which assumes that the ions of charge opposite of the charge on the electrode distribute themselves in a diffuse manner as shown in Figure 1.15. 

Ions are considered to be held at the charged surface in a dijfuse double layer (the Guoy-Chapman model) in which the concentration of cations falls, and that of anions increases, with distance from the surface. In a reflnement of this, the Stern model introduces a layer of cations held directly on the surface of the soil component (Figure 13). Small cations, or dehydrated ions having lost their water of hydration, can sit at the surface and form a strong coulombic bond. This allows for the specificity described above. 

The micellar charge was also corroborated by the Guoy—Chapman diffused, double-layer model. At equilibrium, the surface charge of the micelle alters the ionic composition of the interface with respect to the bulk concentration. The difference between the actual proton concentration on the interface and the one measured at the bulk by pH electrode is observed as a pK shift of the indicator and is related with the Gouy-Chapman potential (Goldstein, 1972). 

Explain in your own words the differences between the Helmholtz, Guoy-Chapman, and Stem models of (he double layer. 

In between the Stem layer and the bulk water, there is another diffuse layer which is sometimes termed the Guoy-Chapman (GC) layer [1]. The GC layer contains free counterions and water molecules. 

The calculations were based on the Guoy-Chapman model for an electric double layer at the interface, a modified Stem model for the inner layer, and experimental input data for predicting the most likely cation-anion arrangement at the surface as shown below in Figure 7.15. The surface potential values 0 were measured and derived for the three ionic liquids mentioned above that had prositive values in the order of [BMIM][Bp4] > [BMIM][DCA] > [BMIM][MS] with potentials of 0.42, 0.37, and 0.14 V respectively. These surface potential values confirm that ionic liquids have a high charge density and different behavior at the interface versus the isotropically distributed molecules in the bulk. The surface potential at the interface includes ions in the Stern layer as well as the dipole contributions. The ion composition of the outer diffuse layer is assumed to give electroneutrality. 

Figure 13.15 The Distribution of Charge in the Diffuse Double Layer According to the Guoy-Chapman Theory.

Guoy and Chapman developed a theory of the charge distribution in the double layer about 10 years before Debye and Hiickel developed their theory of ionic solutions, which is quite similar to it. If one neglects nonelectrostatic contributions to the potential energy of an ion of type i with valence Zi, the concentration of ions of type i in a region of electric potential cp is given by the Boltzmann probability formula, Eq. (9.3-41) ... 

Guoy and Chapman combined Eq. (13.4-1) with the Poisson equation of electrostatics and found that if the potential is taken equal to zero at large distances, the electric potential in the diffuse double layer is given as a function of x, the distance from the electrode, by... 

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