Charge potential relationship

Although a family of OgS - Jig8 values are allowed under Equation 7 the actual equilibrium state of the oxide/solution interface will be determined by the dissociation of the surface groups and the properties of the electrolyte or the diffuse double layer near the surface. For surfaces that develop surface charges by different mechanisms such as for semiconductor, there will be an equation of state or charge-potential relationship that is analogous to Equation 7 which characterizes the electrical response of the surface. 

The determination of the ( -potential from the directly measured disjoining pressure isotherms will be treated in Section 3.4. Thus, the (po(h) dependence can be followed along with understanding the charge-potential relationship of interacting diffuse electric layers in foam films. 

It appears that the data obtained in the above manner prove to be reliable for inferring the charge-potential relationship. Therefore, Fig 3.45 provides convincing evidence that in the case considered double layer repulsive interaction under the conditions of constant charge of the diffuse electric layer is operative. If so, the first integration of Eq. (3.90) predicts that... 

There is no doubt that the FE(/i) isotherms of foam films from non-ionic surfactants plotted at various pH provide reliable information. The quantitative analysis in this case requires account of the role of the Stem-layer and of the charge-potential relationship of interacting diffuse electric layers. This is an object of further research. 

The charge potential relationship is given by the Stem-Gouy-Chapmann model. In this model it is assumed that the Stem layer is a region of constant capacitance, Cj, separating the surface plane from the plane where the diffuse layer starts. The charge-potential relationship in the Stem layer is... 

The modeling approaches used to describe the surface reactions of metal ions differ in their definition of surface structure and the charge/potential relationships within the compact layer of the EDL ( 2, 5,. In our previous calculations ( 2) we... 

The origin and history of the constant capacitance (CC) and diffuse-layer (DL) models have been well documented by Davis and Kent (1990). Depicted schematically for the two models in Fig. 10.18 are the locations of adsorbed ions and assumed charge-potential relationships within the double layer. The DL model assumes that potentials measured at the zero plane and diffuse-layer plane are equal, or In both models, overall solution charge balance dictates that the charge due to the... 

Various types of SCM have been assessed namely, the diffuse-layer model (DLM) [27], the constant-capacitance model [28], the Stern model [29], and the triple-layer model (TLM) [30]. They differ in complexity from the simplest, DLM, which has four adjustable parameters, to the most complex, TLM, which includes seven adjustable parameters. The number of parameters is dependent on the hypothesis relative to the model. In various researches, the DLM is selected because of its simplicity and its applicability to various solution conditions [31]. It takes into account ionic strength effects on protolysis equilibria through the Gouy-Chapman-Stern-Grahame charge-potential relationship ... 

The goal in applying any SCM is to develop a self-consistent methodology for parameter estimation such that a set of standard parameters to describe surface acidity, site density, and the charge/potential relationships for different minerals can be developed and can be used in conjunction with spectroscopic data to guide the selection of appropriate adsorption reactions for the formation of metal ion surface complexes (i.e., inner vs. outer sphere, mono vs. hidentate, mononuclear vs. 

In this chapter we present a general method for solving surface/ solution equilibrium problems described by a surface complexation model, applicable for arbitrary surface layer charge/potential relationships and arbitrary surface/solution interface structures. 

The next question that arises is, having included the electrostatic potential in the set of components, how do we write a total concentration for this component For the other components, hydrogen ion and surface hydroxyl groups, the total concentration is determined simply by how much acid or base, or how much surface we have added to the system. In the case of the electrostatic component, we can use the independent electrostatic charge-potential relationship to define a total concentration or charge for the surface—in the case of the constant-capacitance model... 

Between the planes, fixed surface capacitances are assumed thus, the following charge-potential relationships are included ... 

The charge-potential relationship for the spherical geometry assumed is given approximately for a 1 1 electrolyte of concentration c by (Ohshima, Healy, and White 1982)... 

For a formally correct treatment of data at temperatures substantially different from 298.15 K, the constant-capacitance model has often been used. With the constant-capacitance model, a very simple charge potential relationship is used ... 

Figures 21 and 22 show the influence of using the HNC approximation instead of the Gouy-Chapman equation for a purely difiuse-layer model. Figure 21 shows the charge potential relationship, which in the purely difiuse-double-layer model has a direct bearing on the ealeulation of surfaee-charge density (Fig. 22). Thus, it is apparent that even at low ionic strength, the influenee is quite strong, indicating that for this kind of model, the HNC approximation is preferable.

In the Gouy-Chapmann model based on only electrostatics (i.e., point charges are supposed and the medium is considered as a dielectric continuum), the charge potential relationship for the diffuse part of the EDL can be derived from the Poisson-Boltzmann equation. 

The charge potential relationship in the diffuse part of the EDL can be deduced. The total charge, per unit area of surface, in the diffuse layer, cr, is given by... 

Substituting for p fi om the Poisson equation and taking into consideration the solution of the Poisson-Boltzmann equation leads to the charge potential relationship well known as the Gouy-Chapmann equation for the diffuse EDL ... 

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