Capacitance complexation model

The main, currently used, surface complexation models (SCMs) are the constant capacitance, the diffuse double layer (DDL) or two layer, the triple layer, the four layer and the CD-MUSIC models. These models differ mainly in their descriptions of the electrical double layer at the oxide/solution interface and, in particular, in the locations of the various adsorbing species. As a result, the electrostatic equations which are used to relate surface potential to surface charge, i. e. the way the free energy of adsorption is divided into its chemical and electrostatic components, are different for each model. A further difference is the method by which the weakly bound (non specifically adsorbing see below) ions are treated. The CD-MUSIC model differs from all the others in that it attempts to take into account the nature and arrangement of the surface functional groups of the adsorbent. These models, which are fully described in a number of reviews (Westall and Hohl, 1980 Westall, 1986, 1987 James and Parks, 1982 Sparks, 1986 Schindler and Stumm, 1987 Davis and Kent, 1990 Hiemstra and Van Riemsdijk, 1996 Venema et al., 1996) are summarised here. 

The above surface complexation models enable adsorption to be related to such parameters as the number of reactive sites available on the oxide surface, the intrinsic, ionization constants for each type of surface site (see Chap. 10), the capacitance and the binding constants for the adsorbed species. They, therefore, produce adsorption isotherms with a sounder physical basis than do empirical equations such as the Freundlich equation. However, owing to differences in the choice of adjustable... 

Although each SCM shares certain common features the formulation of the adsorption planes is different for each SCM. In the DDLM the relationship between surface charge, diffuse-layer potential, d, is calculated via the Gouy-Chapman equation (Table 5.1), while in the CCM a linear relationship between surface potential, s, is assumed by assigning a constant value for the inner-layer capacitance, kBoth models assume that the adsorbed species form inner-sphere complexes with surface hydroxyls. The TLM in its original... 

The site binding model based on reactions (1), (2), (14) and (15), often called surface complexation model (SCM), was, beside the simple site binding models (for example two layer model or constant capacitance model) readily applied to a description of the edl on the metal oxide-electrolyte solution interface. Reactions (14) and (15) describe the adsorption of so-called back-... 

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. 

The evaluation of qAB is a formidable task if done exactly, but the constant capacitance model (as well as other surface complexation models) is the special case that results from equation 12 by a simple approximation (22) ... 

Anderson, P, R., and M. M. Benjamin. 1990a. Constant-capacitance surface complexation model. In Chemical modeling of aqueous systems //, ed D. C. Melchior and R. L. Bassett. Am. Chem. Soc. Symp. Ser. 416, pp. 272-81. Washington DC Am. Chem. Soc. 

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 model used to evaluate surface chemistry in these systems is the constant capacitance surface complexation model. This model has been used to describe the adsorption of cations (41) and anions (4,8) onto oxides similar to those used in our experiments. A significant difference between those studies and the present study is that we have adapted the model to simulate some of the interactions that might occur between particles in a binary suspension. 

Details on the adsorbent preparation and experimental and analytical techniques are presented elsewhere (9). This paper briefly reviews the experimental results for the Fe(OH)3 and Si02 suspensions and describes a conceptual and mechanistic model for particle interactions which is qualitatively consistent with the experimental observations. Similar results were obtained for binary Al(OH)3 and Si02 suspensions (9). The constant capacitance surface complexation model is then used to test the mechanistic model and estimate the quantitative influence of the particle-particle interactions on adsorbate distribution. 

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. 

Surface complexation models, on the other hand, account explicitly for the electrical state of the sorbing surface (e.g., Adamson, 1976 Stumm, 1992). This class of models includes the constant capacitance, double layer, and triple layer theories (e.g., Westall and Hohl, 1980 Sverjensky, 1993). Of these, double layer theory (also known as diffuse layer theory) is most fully developed in the literature and probably the most useful in geochemical modeling (e.g., Dzombak and Morel, 1987). 

Figure 2.18 Used models of surface complexation. A - model of constant capacitance B model of dual or diffusion layer B - model of triple layer.

Most of the research on metal sorption at the mineral/water interface has dealt with equilibrium aspects. Numerous studies have used macroscopic approaches such as adsorption isotherms, empirical and semi-empirical equations (e.g., Freundlich, Langmuir), and surface complexation models (e.g., constant capacitance, triple layer) to describe adsorption, usually based on a 24 hour reaction time. 

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