Potential electric double layer, equation defining

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. 

The advantage is that the electrode potential, E, can be varied continuously and that the intrinsic barrier is defined only by the acceptor. A drawback, however, is related to the effect of the electric double layer. If this effect is neglected, the electrochemical equivalents of equations (7) and (53) are equations (56) and (57). Now, E = E° when a = 0.5... 

Next, let us consider the application of Equation (21) to a particle migrating in an electric field. We recall from Chapter 4 that the layer of liquid immediately adjacent to a particle moves with the same velocity as the surface that is, whatever the relative velocity between the particle and the fluid may be some distance from the surface, it is zero at the surface. What is not clear is the actual distance from the surface at which the relative motion sets in between the immobilized layer and the mobile fluid. This boundary is known as the surface of shear. Although the precise location of the surface of shear is not known, it is presumably within a couple of molecular diameters of the actual particle surface for smooth particles. Ideas about adsorption from solution (e.g., Section 7.7) in general and about the Stern layer (Section 11.8) in particular give a molecular interpretation to the stationary layer and lend plausibility to the statement about its thickness. What is most important here is the realization that the surface of shear occurs well within the double layer, probably at a location roughly equivalent to the Stern surface. Rather than identify the Stern surface as the surface of shear, we define the potential at the surface of shear to be the zeta potential f. It is probably fairly close to the... 

It has been shown in Section 9.4.2, that the distance over which the electric potential / decays across the double layer depends on the ionic strength. This dependency is quantitatively given by Equations 9.27 or 9.28. Thus, / drops off to //e over a distance of (approximately) the Debye length K", defined by Equations 9.29 or 9.30. For intermediate ionic strengths, say, between 10 and 10" M, the Debye length is in the nanometer range. 

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