Gouy-Chapman diffuse layer, adsorption

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. 

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. 

Consider a concentrated electrolytic solution. For all intents and purposes, the entire Gouy-Chapman diffuse charge will be located on the OHP (Section 6.6.4). Further, let there be no contact adsorption, so that the IHP is unpopulated. What is being considered, therefore, is a single layer of charge on the solution side of the interface. 

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.

The electrode roughness factor can be determined by using the capacitance measurements and one of the models of the double layer. In the absence of specific adsorption of ions, the inner layer capacitance is independent of the electrolyte concentration, in contrast to the capacitance of the diffuse layer Q, which is concentration dependent. The real surface area can be obtained by measuring the total capacitance C and plotting C against Cj, calculated at pzc from the Gouy-Chapman theory for different electrolyte concentrations. Such plots, called Parsons-Zobel plots, were found to be linear at several charges of the mercury electrode. ... 

While the linear adsorption isotherms of Figure 4 are illustrative only, they are not inconsistent with reality. The simplest theory of the electrical double layer, the Gouy-Chapman approximation, predicts that if the pH is not far from the isoelectric point, the charge represented by counter ions in the diffuse double layer is related to the surface potential as follows (4, 52, 86) ... 

Although each SCM shares certain common features the formulation of the adsorption planes is different for each SCM. In the DDLM the relationship between surface charge, diffuse-layer potential, d, is calculated via the Gouy-Chapman equation (Table 5.1), while in the CCM a linear relationship between surface potential, s, is assumed by assigning a constant value for the inner-layer capacitance, kBoth models assume that the adsorbed species form inner-sphere complexes with surface hydroxyls. The TLM in its original... 

Complementary is the method of complexation constant calculations based on the adsorption measurements of the 1 1 background electrolyte. The density of this adsorption consists of = SOH An+ or = SO Ct+ complex adsorption and a part, connected with the compensation of the surface charge in the diffuse layer of edl. To estimate the densities, the ions adsorbed in IHP layer, Sprycha assumed the background electrolyte ion density located in the diffuse layer of edl equals to the diffuse layer charge that may be calculated from Gouy-Chapman equation, when potential value is known. Then, the density of the ions that form surface complexes will be equal to ... 

Many more-sophisticated models have been put forth to describe electrokinetic phenomena at surfaces. Considerations have included distance of closest approach of counterions, conduction behind the shear plane, specific adsorption of electrolyte ions, variability of permittivity and viscosity in the electrical double layer, discreteness of charge on the surface, surface roughness, surface porosity, and surface-bound water [7], Perhaps the most commonly used model has been the Gouy-Chapman-Stem-Grahame model 8]. This model separates the counterion region into a compact, surface-bound Stern" layer, wherein potential decays linearly, and a diffuse region that obeys the Poisson-Boltzmann relation. 

At the interface between O and W, the presence of the electrical double layers on both sides of the interface also causes the variation of y with Aq<. In the absence of the specific adsorption of ions at the interface, the Gouy-Chapman theory satisfactorily describes the double-layer structure at the interface between two immiscible electrolyte soultions [20,21]. For the diffuse part of the double layer for a z z electrolyte of concentration c in the phase W whose permittivity is e, the Gouy-Chapman theory [22,23] gives an expression... 

Cantwell and co-workers submitted the second genuine electrostatic model the theory is reviewed in Reference 29 and described as a surface adsorption, diffuse layer ion exchange double layer model. The description of the electrical double layer adopted the Stem-Gouy-Chapman (SGC) version of the theory [30]. The role of the diffuse part of the double layer in enhancing retention was emphasized by assigning a stoichiometric constant for the exchange of the solute ion between the bulk of the mobile phase and the diffuse layer. However, the impact of the diffuse layer on organic ion retention was danonstrated to be residual [19],... 

In the Stern-Gouy-Chapman (SGC) theory the double layer is divided into a Stern layer, adjacent to the surface with a thickness dj and a diffuse (GC) layer of point charges. The diffuse layer starts at the Stern plane at distance d] from the surface. In the most simple case the Stern layer is free of, charges. The presence of a Stern layer has considerable consequences for the potential distribution across the Stern layer the potential drops linearly from the surface potential V s to the potential at the Stern plane, V>d- Often is considerably lower than especially in the case of specific adsorption (s.a.). 

The determination of the real surface area of the electrocatalysts is an important factor for the calculation of the important parameters in the electrochemical reactors. It has been noticed that the real surface area determined by the electrochemical methods depends on the method used and on the experimental conditions. The STM and similar techniques are quite expensive for this single purpose. It is possible to determine the real surface area by means of different electrochemical methods in the aqueous and non-aqueous solutions in the presence of a non-adsorbing electrolyte. The values of the roughness factor using the methods based on the Gouy-Chapman theory are dependent on the diffuse layer thickness via the electrolyte concentration or the solvent dielectric constant. In general, the methods for the determination of the real area are based on either the mass transfer processes under diffusion control, or the adsorption processes at the surface or the measurements of the differential capacitance in the double layer region [56],... 

Due to the short range of the adsorption interactions, it is possible for one to subdivide the EDL into two main parts (Fig. Ill-12) a dense part, that is closer to the surface (the Stem-Helmholtz layer), within which the adsorption forces are of importance, and a diffuse part (the Gouy - Chapman layer), which is further away from the surface, and within which the adsorption forces are negligible. The major task in EDL theory can be defined as the problem of finding the quantitative distribution of the concentrations of all ions, n present in the system and that of the potential at any point in the solution, cp, as a function of the distance from the surface, x (if confined to a single dimension). 

From the theoretical point of view a similarity exists between electrostatic retardation of ion transport and coagulation retardation, known as slow coagulation (Fuchs, 1934). Both phenomena arise from electrostatic repulsion caused by the existence of the diffuse part of the DL. In the slow coagulation theory, the electric field if the DL is derived from the Gouy-Chapman model (cf. Chapter 2). This model does not consider a deviation of the diffuse layer from equilibrium. Initially, the same simplification was used by Dukhin et al. (1973) in describing the DL effect on the electrostatic retardation of adsorption. 

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