Charge balances, triple-layer model

To be useful in modeling electrolyte sorption, a theory needs to describe hydrolysis and the mineral surface, account for electrical charge there, and provide for mass balance on the sorbing sites. In addition, an internally consistent and sufficiently broad database of sorption reactions should accompany the theory. Of the approaches available, a class known as surface complexation models (e.g., Adamson, 1976 Stumm, 1992) reflect such an ideal most closely. This class includes the double layer model (also known as the diffuse layer model) and the triple layer model (e.g., Westall and Hohl, 1980 Sverjensky, 1993). 

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... 

When represents a metal cation not in the background electrolyte, the intrinsic constants are determined by fitting the triple layer model to adsorption edge data. This fitting entails a surface speciation calculation with previously measured values of the intrinsic constants in Eq. 5.61, the capacitance parameters Ci and C2, and the parameter Af. The computation includes Eqs. 5.58, 5.59, and 5.69, as well as surface charge and mole balance equations imposed as constraints. " ... 

The adsorption of protons and hydroxyls necessarily leads to charges on the surface, which are balanced by counterions of opposite charge in the solution. Assumptions about the structure of the charged layers, which also contain other adsorbed species, lead to different models (i.e., double- or triple-layer models). 

The TLM (Davis and Leckie, 1978) is the most complex model described in Figure 4. It is an example of an SCM. These models describe sorption within a framework similar to that used to describe reactions between metals and ligands in solutions (Kentef fll., 1988 Davis and Kent, 1990 Stumm, 1992). Reactions involving surface sites and solution species are postulated based on experimental data and theoretical principles. Mass balance, charge balance, and mass action laws are used to predict sorption as a function of solution chemistry. Different SCMs incorporate different assumptions about the nature of the solid - solution interface. These include the number of distinct surface planes where cations and anions can attach (double layer versus triple layer) and the relations between surface charge, electrical capacitance, and activity coefficients of surface species. 

---