Triple-layer model, defined

In fig. 3.20b specific adsorption Is also accounted for. The notion of specific adsorption has been defined In sec. 3.3. In disperse systems, its occurrence is de facto Inferred from the dependence of certain double layer properties on the natures of counter- and co-lons Generally, ions interacting specifically (non-electrostatlcally) with the surface approach it to shorter distance p < d). The plane where these specifically adsorbed ions reside is called the inner Helmholtz plane (iHp) In colloid science, the model of fig. 3.20b Is also known as the triple layer model. In this model three charges and three capacitances can be distinguished. For the two inner layer differential capacitances... 

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... 

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. 

Several models have been developed to describe reactions between aqueous ions and solid surfaces. These models tend to fall into two categories (1) empirical partitioning models, such as distribution coefficients and isotherms (e.g., Langmuir and Freundlich isotherms), and (2) surface-complexation models (e.g., constant-capacitance, diffuse-layer, or triple-layer model) that are analogous to solution complexation with corrections for the electrostatic effects at the solid-solution interface (Davis and Kent, 1990). These models have been described in numerous articles (Westall and Hohl, 1980 Morel, Yeasted, and Westall, 1981 James and Parks, 1982 Barrow, 1983 Westall, 1986 Davis and Kent, 1990 Dzombak and Morel, 1990). Travis and Etnier (1981) provided a comprehensive review of the partitioning and kinetic models typically used to define sorption of ions by soils. The reader is referred to the cited articles for details of the models. 

Since the solvation force is defined as the difference between the observed net force and the net van der Waals plus electrostatic force, as calculated with Eqs. 6.9, 6.11, and 6.20, it follows from the foregoing discussion that Eq. 6.12 should be integrated in the context of an appropriate surface complexation model (e.g., the triple layer model) to provide the most accurate theoretical estimate of the electrostatic force. ... 

Surface complexation reactions are assumed on surface sites, S—OH. The total site density (Ns, mol/m ), has to be defined for the given system. In the constant-capacitance and diffuse-layer models, all surface species are supposed to be inner-sphere complexes, whereas in the triple-layer model, both inner- and outer-sphere complexes are assumed. 

In all situations discussed so far only one Stern layer capacitance is required. In literature it is however often assumed [7, 8, 22] that diffuse ions can approach the surface up to the Stern plane and that s.a. ions are located at a newly defined adsorption plane, the inner Helmholtz plane. The inner Helmholtz plane is located in between the surface plane and the Stern or outer Helmholtz plane. The double layer model composed of an inner and outer Helmholtz layer plus a diffuse layer is generally called the triple layer (TL) model. 

---