Triple-layer model expressions

The triple-layer model calls for capacitances C and C2, corresponding to zones between the zero and beta planes and beta and d planes, respectively. The capacitances are related to the net charge and potentials of those planes through the expressions... 

The triple layer model has been used with different standard and reference states for both aqueous and surface species (e.g., Davis et al., 1978 Hayes and Leckie, 1987). These differences can result in different best-fit surface complexes for the same experimental adsorption data. For example, Hayes and Leckie (1987) expressed both the chemical potentials for aqueous and surface species by the expression... 

Various empirical and chemical models of metal adsorption were presented and discussed. Empirical model parameters are only valid for the experimental conditions under which they were determined. Surface complexation models are chemical models that provide a molecular description of metal and metalloid adsorption reactions using an equilibrium approach. Four such models, the constant capacitance model, the diffuse layer model, the triple layer model, and the CD-MUSIC model, were described. Characteristics common to all the models are equilibrium constant expressions, mass and charge balances, and surface activity coefficient electrostatic potential terms. Various conventions for defining the standard state activity coefficients for the surface species have been... 

For this purpose it is possible to extend to a multiple oxide the one-site model of Johnson (1984), which provides a thermodynamic description of the double layer surrounding simple hydrous oxides. Briefly, in this model the double layer charge is divided into the charge inside the slip plane, slip plane a[d]. While occupied sites, a[tl] is obtained from the Poisson-Boltzmann equation. Note that unlike the triple-layer model (Davis et al., 1978) which allows ions to form surface complexes at two different planes (0 or / ) instead of al the slip plane only, this model does not distinguish between inner- and outer-sphere complexes. Expression of the... 

A number of different surface complexation models have been applied to describe and predict divalent metal ion sorption data over the past 20 to 30 yr. All of Ihe models incorporate surface acidity and the formation of metal ion complexes with surface hydroxyl groups via equilibrium mass law expressions such at those presented in Tabic 7-2. In addition, each model employs a description of the elec-Irical double layer lo correcl for electrostatic effects at the mineral/water interface (as shown in Fig. 7 4 lor (he triple layer model and described in Table 7-3). These... 

---