Gouy-Chapman charge layer

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 ... 

Figure 2. The charge-potential curves for a Gouy-Chapman diffuse layer and an amphoteric surface 10 1 1 electrolyte, ApK = 2, N = 1 X 1018 nf2.

Figure 4. The charge-potential curves for overlapping Gouy-Chapman diffuse layers as a function of separation.

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). 

FIGURE 5.15 Dimensionless surface potential (y-axis, F< >S/RT) vs. pH U-axis) for three types of carbon electrode materials Cl, acidic carbon (pHIEP = pHPZC = 3.0) C2, typical as-received ( amphoteric ) carbon (pHIEP = pHPZC = 6.5) C3, basic carbon (pi In,. = pHPZC = 10.0). Based on Gouy-Chapman double-layer theory, for a maximum surface charge of 0.03 C/m2 and ionic strength of 10 3 M. 

Equations (28.24) and (28.25) are the Gouy-Chapman double-layer potential of the membrane surface with a surface charge density a = —eNds. 

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 layer model, Figure 9.19). A balance between electrostatic and thermal forces is attained. 

Tn recent years, the influence of counterions on the properties of A ionized monolayers has received much attention. Even though Davies (I) application of the Gouy-Chapman double layer theory to ionized monolayers represented a major advance in the understanding of the properties of these systems, it has been increasingly recognized that we must account for the different effects (i.e., specific counterion effects) that counterions of the same net charge may have on the charged mono-layer. Because of counterion sequence inversions which have been ob-... 

Gouy and Chapman later suggested that the thermal energy of the ions would result in a diffuse layer on the solution side of the interface with the concentration of excess charges at a maximum close to the electrode surface and gradually decreasing with distance into the electrolyte (on the order of nanometers). However, the Gouy-Chapman diffuse layer model also does not match well with aU experimental data. 

This scattered layer plus the electrode positive charge array is called the diffuse double-layer or diffuse layer. In the literature, this diffuse layer is also called the Gouy point charge layer or model or the Gouy-Chapman model. We will use the diffuse layer term in this chapter. The thickness of the diffuse layer is dependent on the temperature, the concentration of the electrolyte, the charge number carried by the ion, and the dielectric constant of the electrolyte solution. 

Derive the general equation for the differential capacity of the diffuse double layer from the Gouy-Chapman equations. Make a plot of surface charge density tr versus this capacity. Show under what conditions your expressions reduce to the simple Helmholtz formula of Eq. V-17. 

Fig. 2. Schematic diagram of a suspended colloidal particle, showing relative locations of the Stem layer (thickness, 5) that consists of adsorbed ions and the Gouy-Chapman layer (1 /k) which dissipates the excess charge, not screened by the Stem layer, to 2ero ia the bulk solution (108). In the absence of a...

Stem layer, the Gouy-Chapman layer dissipates the surface charge. 

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... 

The simplest model for the ionic distribution at liquid-liquid interfaces is the Verwey-Niessen model [10], which consists of two Gouy-Chapman space-charge layers back to... 

The non-steady-state optical analysis introduced by Ding et al. also featured deviations from the Butler-Volmer behavior under identical conditions [43]. In this case, the large potential range accessible with these techniques allows measurements of the rate constant in the vicinity of the potential of zero charge (k j). The potential dependence of the ET rate constant normalized by as obtained from the optical analysis of the TCNQ reduction by ferrocyanide is displayed in Fig. 10(a) [43]. This dependence was analyzed in terms of the preencounter equilibrium model associated with a mixed-solvent layer type of interfacial structure [see Eqs. (14) and (16)]. The experimental results were compared to the theoretical curve obtained from Eq. (14) assuming that the potential drop between the reaction planes (A 0) is zero. The potential drop in the aqueous side was estimated by the Gouy-Chapman model. The theoretical curve underestimates the experimental trend, and the difference can be associated with the third term in Eq. (14). 

To evaluate the contribution of the SHG active oriented cation complexes to the ISE potential, the SHG responses were analyzed on the basis of a space-charge model [30,31]. This model, which was proposed to explain the permselectivity behavior of electrically neutral ionophore-based liquid membranes, assumes that a space charge region exists at the membrane boundary the primary function of lipophilic ionophores is to solubilize cations in the boundary region of the membrane, whereas hydrophilic counteranions are excluded from the membrane phase. Theoretical treatments of this model reported so far were essentially based on the assumption of a double-diffuse layer at the organic-aqueous solution interface and used a description of the diffuse double layer based on the classical Gouy-Chapman theory [31,34]. 

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