Surface complexation models Stem layer model

Position of the outer Helmholtz (Stem) plane start of diffuse layer in surface complexation models Equivalent fraction in exchanger phase Numeric charge of ion i (in units of q )... 

The data in Figure 3.32 show the theoretical estimated concentration of Na+, Li+, and K+ or Rb+ between the Stem layer and the diffuse layer based on the Stem model. The distribution appears to be consistent, as expected, with the hydration energy of the cation. The greater the heat of hydration (see Chapter 4, Table 4.1) is, the greater the concentration of the cation in the diffuse layer in relationship to the Stern layer. The Stern model has been the basis for many variations of the model recently also known as the surface complexation model (Goldberg, 1992). 

Another very important issue in this respect is the way to account for the surface conductivity. The formula of Bikerman (Equation 5.359), the correction factor to the electrophoretic mobility of Henry 3 (Equation 5.368), and the formula of O Brien and Hunter (Equation 5.371), quoted above are derived under the assumption that only the ions in the movable part (x > x Figure 5.67) of the EDL contribute to the surface conductivity, Xs- Moreover, the ions in the EDL are taken to have the same mobility as that in the bulk electrolyte solution. A variety of experimental data ° suggest, however, that the ions behind the shear plane (x < x ) and even those adsorbed in the Stem layer may contribute to Xs- Th term anomalous surface conductance was coined for this phenomenon. Such an effect can be taken into account theoretically, but new parameters (such as the ion mobility in the Stem layer) must be included in the consideration. Hence, the interpretation of data by these more complex models usually requires the application of two or more electrokinetic techniques which provide complementary information. Dukhin and van de Ven specify three major (and relatively simple) types of models as being most suitable for data interpretation. These models differ in the way they consider the surface conductivity and the connection between i and "Q. 

The triple layer model attempts to take into account inner sphere complex formation and electrostatic adsorption simultaneously by considering "specifically adsorbed" ions which are supposed to be maintained very close to the surface, whether it be through the formation of covalent bonds with some surface groups, or of some outer sphere complex. No specific interpretation of the bonding is required, provided one can define a plane of specific adsorption, located a few A from the surface and containing those ions this is called the Stem layer. The theory distinguishes then between three successive parallel layers the surface plane proper, the Stem layer, and the diffuse layer. 

Note that numerical solutions or approximate analytical expressions have to be applied in other cases. It must also be pointed out that if the complex stmcture of the double layer is simplified to a model considering that the diffuse layer starts right on the solid surface (no Stem layer is present), Aq can be used instead of Pj in Equations (3.4), (3.7), and (3.8). 

Figure 3. Highly schematic view of the electrical double layer (EDL) at a metal oxide/aqueous solution interface showing (1) hydrated cations specifically adsorbed as inner-sphere complexes on the negatively charged mineral surface (pH > pHpzc of the metal oxide) (2) hydrated anions specifically and non-specifically adsorbed as outer-sphere complexes (3) the various planes associated with the Gouy-Chapman-Grahame-Stem model of the EDL and (4) the variation in water structure and dielectric constant (s) of water as a function of distance from the interface, (from Brown and Parks 2001, with permission)...

The variation of potential out into solution is actually more complex. For example, a layer of specifically adsorbed ions bounded by a plane, the Stem plane, can be added to the model represented by Equation (4.1), in which case the potential changes from at the surface, to i/<5) at the Stern plane, to = 0 in bulk solution. Additional details are provided elsewhere [65-67]. 

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