Electric double layer model

The electrostatic potential between a solid and an aqueous solution can be esplained in terms of a parallel plate condenser with a jiositiye excess charge on one phase and a negative excess charge on the other. The interfacial charge on the solid (electronic conductor) is usually carried by mobile excess electrons and holes, while it is carried by mobile excess hydrated ions on the side of aqueous solution (ionic conductor). 

An adsorbed layer of water molecules at the interface separates hydrated ions from the solid surface. The interfacial electric double layer can be represented by a condenser model comprising three distinct layers a diffuse charge layer in the ionic solution, a compact layer of adsorbed water molecules, and a diffuse charge layer in the solid as shown in Fig. 5-8. The interfacial excess charge on the 

The diffuse layer of excess electrons and holes in solids is called the space charge layer and the diffuse layer of excess hydrated ions in aqueous solution is simply called the diffuse layer and occasionally called the Gouy layer [Gouy, 1917]. The middle layer of adsorbed water moleciiles, between the diffuse layer on the aqueous solution side and the space charge layer on the soUd side, is called the compact or the inner layer. This compact or inner layer is also called the Helmholtz layer [Helmholtz, 1879] or the Stem layer [Stem, 1924] the plane of the closest approach of hydrated ions to the solid surface is called the outer Helmholtz plane (OHP) [Graham, 1947]. 

Usually, there is an electrostatic potential of the order of 1 V across the electric double layer at tbe interface between a metal and an aqueous solution this potential produces an intense electric field of the order of 10 V cm in the compact layer 0.3 to 0.5 mn thick. Such an intense electric field can not be realized in any dielectrics of macroscopic size, because of diele tec breakdown by the electron avalanche, but the intense electric field can be sustained in a layer of several atomic thidmess where no electron avalanche can occur. 

In the three layer model shown in Fig. 5-8, the electric capacity C of an interfacial electric double layer is represented by a series connection of three 

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Various pc electrode models have been tested.827 Using the independent diffuse layer electrode model74,262 the value of E n = -0.88 V (SCE) can be simulated for Cd + Pb alloys with 63% Pb if bulk and surface compositions coincide. However, large deviations of calculated and experimental C,E curves are observed at a 0. Better correspondence between experimental and calculated C,E curves was obtained with the common diffuse-layer electrode model,262 if the Pb percentage in the solid phase is taken as 20%. However, the calculated C, at a Ois noticeably lower than the experimental one. It has been concluded that Pb is the surface-active component in Cd + Pb alloys, but there are noticeable deviations from electrical double-layer models for composite electrodes.827... 

The description of the sorption of charged molecules at a charged interface includes an electrostatic term, which is dependent upon the interfacial potential difference, Ai//(V). This term is in turn related to the surface charge density, surface charge density is calculated from the concentrations of charged molecules at the interface under the assumption that the membrane itself has a net zero charge, as is the case, for example, for membranes constructed from the zwitterionic lecithin. Moreover,... 

Equations 9-14 provide the framework for combining either of the two surface hydrolysis models that were presented with any of the four electric double layer models to define the interface model completely and to solve for all unknown potentials, charges, and surface concentrations. In the following section some specific limiting cases are considered. 

Two models of surface hydrolysis reactions and four models of the electrical double layer have been discussed. In this section two examples will be discussed the diprotic surface group model with constant capacitance electric double layer model and the monoprotic surface group model with a Stern double layer model. More details on the derivation of equations used in this section are found elsewhere (3JL). ... 

The simplest, self-consistent model of the diffuse-ion swarm near a planar, charged surface like that of a smectite is modified Gouy-Chapman (MGQ theory [23,24]. The basic tenets of this and other electrical double layer models have been reviewed exhaustively by Carnie and Torrie [25] and Attard [26], who also have made detailed comparisons of model results with those of direct Monte Carlo simulations based in statistical mechanics. The postulates of MGC theory will only be summarized in the present chapter [23] ... 

An alternative to integral equation theories of the nonprimitive inhomogeneous electric double layer is a mean electrostatic field analysis of an ion-solvent dipole mixture against a charged wall [83-90]. Although this approach has been successful with the primitive model and avoids the difficult problem with the bridge function, it is still in the early stages of development with the nonprimitive electric double layer model. 

To determine the spatial variation of a static electric field, one has to solve the Poisson equation for the appropriate charge distribution, subject to such boundary conditions as may pertain. The Poisson equation plays a central role in the Gouy-Chapman (- Gouy, - Chapman) electrical - double layer model and in the - Debye-Huckel theory of electrolyte solutions. In the first case the one-dimensional form of Eq. (2)... 

Figure 17.1 An electrical double-layer model (a) and a double-layer capacitor (b).

Chen, J.G. et al. Electrical double layer models of ion-modified (ion -pair) reversed-phase liquid chromatography. J. Chromatogr A. 1993, 656, 549-576. 

Liu, H. and Cantwell, F.F. Electrical double-layer model for sorption of ions on octade-cylsilyl bonded phases including the role of residual silanol groups. Anal. Chem. 1991, 63, 993-1000. 

H.-J. Liu and F. F. Cantwell, Electrical double-layer model for ion-pair chromatographic retention on octadecylsilyl bonded phases. Anal. Chem. 63 (1991), 2032-2039. 

Figure 10. Electrical double layer models. Top right (a) typical type of potential vs. composition plot for a charged surface compared to (b) constant capacitance model. Top left Two double-layer models, (a) diffuse double layer, (b) part parallel plate capacitor and part diffuse layer.. Bottom left Stem layer model. Incorporation of adsorbed ions to surface. From Hiemenz and Rajagopalan (1997) Bottom right Comparison of Gouy-Chapman and Stem-Grahame models of the electrical double layer. From Davis and Kent (1990).

Kitamura, A. et al., Analysis of adsorption behavior of cesium onto quartz using electrical double layer model, J. Nucl. Sci. Technol., 33, 840, 1996. 

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