Surface 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 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 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 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... 

Fig. 10.1. Relationship (Eqn. 10.6) between surface charge density cr and surface potential T for a sorbing surface in contact with solutions of differing ionic strengths I (molal).

The iteration step, however, is complicated by the need to account for the electrostatic state of the sorbing surface when setting values for mq. The surface potential T affects the sorption reactions, according to the mass action equation (Eqn. 10.13). In turn, according to Equation 10.5, the concentrations mq of the sorbed species control the surface charge and hence (by Eqn. 10.6) potential. Since the relationships are nonlinear, we must solve numerically (e.g., Westall, 1980) for a consistent set of values for the potential and species concentrations. 

The pH shift model of Park and Regalbuto combined (1) a proton balance between the surface and bulk liquid with (2) the protonation-deprotonation chemistry of the oxide surface (single amphoteric site), and (3) a surface charge-surface potential relationship assumed for an... 

Because of the different potential distributions for different sets of conditions the apparent value of Tafel slope, about 60 mV, may have contributions from the various processes. The exact value may vary due to several factors which have different effects on the current-potential relationship 1) relative potential drops in the space charge layer and the Helmholtz layer 2) increase in surface area during the course of anodization due to formation of PS 3) change of the dissolution valence with potential 4) electron injection into the conduction band and 5) potential drops in the bulk semiconductor and electrolyte. 

Relationship between pH, surface potential, xp or Coulombic term, log P, or Coulombic free energy, AGcoui), and surface charge density, a (or surface protonation) for various ionic strengths of a 1 1 electrolyte for a hydrous ferric oxide surface (P = exp(-Fi //RT). 

For simplicity, we will consider the case in which surface charge and potential are positive, and that only anions adsorb. Furthermore, the potential drop in the Gouy-Chapman layer will be assumed to be small enough that its charge/potential relation can be linearized. The V o/oo/pH relationship can then be derived parametrically, with the charge in the Gouy-Chapman layer cr4 as the parameter. The potential at the plane of anion adsorption can then be calculated and substituted in Equation 28 to give ... 

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