Potential variation through electrical double layer

The variation of the electric potential in the electric double layer with the distance from the charged surface is depicted in Figure 6.2. The potential at the surface ( /o) linearly decreases in the Stem layer to the value of the zeta potential (0- This is the electric potential at the plane of shear between the Stern layer (and that part of the double layer occupied by the molecules of solvent associated with the adsorbed ions) and the diffuse part of the double layer. The zeta potential decays exponentially from to zero with the distance from the plane of shear between the Stern layer and the diffuse part of the double layer. The location of the plane of shear a small distance further out from the surface than the Stem plane renders the zeta potential marginally smaller in magnitude than the potential at the Stem plane ( /5). However, in order to simplify the mathematical models describing the electric double layer, it is customary to assume the identity of (ti/j) and The bulk experimental evidence indicates that errors introduced through this approximation are usually small. 

Figure 1. Potential variation through the electrical double layer for a higher concentration of potential-determining ion (a), a lower concentration of potential-determining ion (b), and in the presence of a specifically adsorbed counter ion with a potential-determining ion below the point-of-zero charge (c). Note that the potential in all three instances could be identical. (Reproduced, with permission, from Ref. 1. Copyright 1970, International Union of Pure and Applied Chemists.)...

For the scale up of a chemical reactor, inadequate mixing may result in spatial variations in, for example, reactant composition or temperature. An electrochemical reactor (cell) is a chemical reactor where the reduction and oxidation reactions are spatially separated on cathodes and anodes. The flow of ionic current through the electrolyte results in an electric field through the electrolyte. Since charged species move in response to an electrical field [1-3] and since the potential difference across the double layer impacts reaction rate, electrical field effects can significantly impact current distribution. Thus, in contrast to a chemical reactor, perfect mixing to eliminate all concentration fields does not necessarily result in uniform reaction rates. 

The electrical properties of an isolated double layer can be described in terms of the variation of the electrical charge or the electrical potential (Fig. 4.10). The two are related through the capacitance so that if one is known, the other can be found. We shall consider the potential mainly. We shall also consider the analysis in one dimension (the x direction) and make a number of simplifying assumptions ... 

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