Solid—solution interface, surface complexation 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. 

Surface complexation models (SCM s) provide a rational interpretation of the physical and chemical processes of adsorption and are able to simulate adsorption in complex geochemical systems. Chemical reactions at the solid-solution interface are treated as surface complexation reactions analogous to the formation of complexes in solution. Each reaction is defined in terms of a mass action equation and an equilibrium constant. The activities of adsorbing ions are modified by a coulombic term to account for the energy required to penetrate the electrostatic-potential field extending away from the surface. Detailed information on surface complexation theory and the models that have been developed, can be found in (Stumm et al., 1976 ... 

In 1991, Johnson et al. reported one of the first NR studies of phospholipid bilayers at the solid-solution interface [46]. Although these measurements were not the first to employ NR to study molecules adsorbed at the solid-hquid interface, they did constitute the first measurements of a supported bilayer using NR. A bilayer of dimyristoylphosphatidylcholine (DMPC) was spread on a quartz surface by the fusion and rupturing of smaU unilamellar vesicles. The very smooth, singlecomponent substrate aUowed a complex model of the interface to be constructed from layers corresponding to (i) the quartz, (ii) a thin film of water on the quartz... 

Various chemical surface complexation models have been developed to describe potentiometric titration and metal adsorption data at the oxide—mineral solution interface. Surface complexation models provide molecular descriptions of metal adsorption using an equilibrium approach that defines surface species, chemical reactions, mass balances, and charge balances. Thermodynamic properties such as solid-phase activity coefficients and equilibrium constants are calculated mathematically. The major advancement of the chemical surface complexation models is consideration of charge on both the adsorbate metal ion and the adsorbent surface. In addition, these models can provide insight into the stoichiometry and reactivity of adsorbed species. Application of these models to reference oxide minerals has been extensive, but their use in describing ion adsorption by clay minerals, organic materials, and soils has been more limited. 

Surface complexation models of the solid-solution interface share at least six common assumptions (1) surfaces can be described as planes of constant electrical potential with a specific surface site density (2) equations can be written to describe reactions between solution species and the surface sites (3) the reactants and products in these equations are at local equilibrium and their relative concentrations can be described using mass law equations (4) variable charge at the mineral surface is a direct result of chemical reactions at the surface (5) the effect of surface charge on measured equilibrium constants can be calculated and (6) the intrinsic (i.e., charge and potential independent) equilibrium constants can then be extracted from experimental measurements (Dzombak and Morel, 1990 Koretsky, 2000). 

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. 

In surface precipitation cations (or anions) which adsorb to the surface of a mineral may form at high surface coverage a precipitate of the cation (anion) with the constituent ions of the mineral. Fig. 6.9 shows schematically the surface precipitation of a cation M2+ to hydrous ferric oxide. This model, suggested by Farley et al. (1985), allows for a continuum between surface complex formation and bulk solution precipitation of the sorbing ion, i.e., as the cation is complexed at the surface, a new hydroxide surface is formed. In the model cations at the solid (oxide) water interface are treated as surface species, while those not in contact with the solution phase are treated as solid species forming a solid solution (see Appendix 6.2). The formation of a solid solution implies isomorphic substitution. At low sorbate cation concentrations, surface complexation is the dominant mechanism. As the sorbate concentration increases, the surface complex concentration and the mole fraction of the surface precipitate both increase until the surface sites become saturated. Surface precipitation then becomes the dominant "sorption" (= metal ion incorporation) mechanism. As bulk solution precipitation is approached, the mol fraction of the surface precipitate becomes large. 

Physicochemical models of partitioning at the solid-water interface, such as that used here to model ion exchange, require detailed knowledge about the particles. The surface properties of the mineral phases present, as well as equilibrium constants for ion binding to both fixed and variable charge sites associated with each phase, are required. These data requirements and the uncertainty about modeling sorption in mixtures of minerals (e.g., 48-50) make such models difficult to apply to complex natural systems. This is especially the case for modeling solute transport in soil-water systems, which... 

Before leaving the PC method, a comparison with the TMAB method for adsorption at the solution-solid interface will be instractive. Specifically, adsorption occurs by complex formation between solute and surface site molecules in the TMAB model while adsorption occurs by solute partitioning into a surface phase, without forming any specific bond with sohd surface molecules, in the PC model. From a mechanistic point of view one can see that the TMAB and PC methods differ significantly. However, a more quantitative approach can be used to elicit the conditions under which these two models and their respective mass action constants can be compared. 

As mentioned in Sect. I, even the simplest electrosorption systems are extremely complicated. This complexity means that a comprehensive theoretical description that enables predictions for phenomena on macroscopic scales of time and space is still generally impossible with present-day methods and technology. (Note that MD simulations, such as those presented in Sect. II, are only possible up to times of a few himdred nanoseconds.) Therefore, it is necessary to use a variety of analytical and computational methods and to study various simplified models of the solid-hquid interface. One such class of simpHfied models are LG models, in which chemisorbed particles (solutes or solvents) can only be located at specific adsorption sites, commensurate with the substrate s crystal structure. This can often be a very good approximation, for instance, for halides on the (100) surface of Ag, for which it can be shown that the adsorbates spend the vast majority of their time near the fourfold hollow surface sites. A LG approximation to such a continuum model, appropriate for chemisorption of small molecules or ions, ° is defined by the discrete, effective grand-canonical Hamiltonian,... 

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