Surface complex 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). 

The triple layer model has been described in detail elsewhere (11, 16, 17) however, the model as reported here has been slightly modified from the original versions (11, 15) in two ways (i) metal ions are allowed to form surface complexes at either the o- or 8-plane insted of at the 8-plane only, and (ii) the thermodynamic basis of the TLM has been modified leading to a different relationship between activity coefficients and interfacial potentials. The implementation and basis for these modifications are described below. 

The elegance of the surface complexation approch lies in the fact that it can be incorporated into the thermodynamic speciation models used for soluble complexes. Consequently many of the computer models, e.g. SOILCHEM, HYDRAQL, MINTEQA2 and ECOSAT, include several different SCMs. Some commonly used SCMs are the diffuse-double-layer model, DDLM (Huang and Stumm, 1973 Dzombak and Morel, 1990), the constant capacitance model, CCM (Stumm et al., 1970 1976 1980 Schindler et al., 1976), the triple-layer model, TLM (Davis etal., 1978 Davis and Leckie, 1978,1980 Hayes and Leckie, 1987 Hayes et al., 1988) and the 1 pK basic Stern model (Bolt and Van Riemsdijk, 1982 Van Riemsdijk et al., 1986 1987). 

There is a range of equations used describing the experimental data for the interactions of a substance as liquid and solid phases. They extend from simple empirical equations (sorption isotherms) to complicated mechanistic models based on surface complexation for the determination of electric potentials, e.g. constant-capacitance, diffuse-double layer and triple-layer model. 

Figure 3. Schematic representation of coordinative surface complexes and ion pairs formed between inorganic ions and hydroxyl groups of an oxide surface in the triple layer model. Reprinted from Hayes (1987) with permission.

Current surface complexation models were developed with a focus on minor and trace ions and hence do not consider sorption in the diffuse layer. Even the triple-layer model (34), which can include electrolyte sorption as outer-sphere complexes, does not consider sorption in the diffuse layer. To... 

As detailed above, the adsorption behavior of most actinides varies widely with solution pH, Eh, complexation, competitive adsorption and ionic strength, and the surface properties of sorbent phases. For this reason, many researchers have modeled actinide adsorption using surface complex-ation (SC) models that can quantitatively account for such variables. These models include the constant capacitance (CC), diffuse-layer (DL), and triple-layer (TL) models (Chap. 10). Much of the ra-... 

The models describing hydrolysis and adsorption on oxide surfaces are called surface complexation models in literature. They differ in the assumptions concerning the structure of the double electrical layer, i.e. in the definition of planes situation, where adsorbed ions are located and equations asociating the surface potential with surface charge (t/> = f(5)). The most important models are presented in the papers by Westall and Hohl [102]. Tbe most commonly used is the triple layer model proposed by Davis et al. [103-105] from conceptualization of the electrical double layer discussed by Yates et al. [106] and by Chan et al. [107]. Reviews and representative applications of this model have been given by Davis and Leckie [108] and by Morel et al. [109]. We will base our consideration on this model. 

If a strongly adsorbing bivalent metal ion is added to the system described by Eqs. (39) and (40), in which competitive adsorption of protons and ions of basic electrolyte occurs, then according to the triple layer model [103-105] its addition can cause the formation of two kinds of surface complexes inner-sphere complexes SOM formed at the 0-plain of the triple layer and outer-sphere complexes SO M + formed at the, 3-plain. Some recent studies by Hayes and Leckie [142-145] suggest that the formation of the inner-sphere complexes is more probable for divalent cations like Cu, Pb, Cd" ", etc. than the formation of outer-sphere surface complexes. So, in general [142,143] ... 

In the triple layer model one of the o-plane metal surface complexes is represented as bidentate, Eq. (6.9), while one of the P-plane metal surface complexes is represented as a hydroxy-metal surface species, Eq. (6.30). Davis and Leckie (1978) considered the hydroxy-metal complexation reaction to be more consistent with their experimental data. Often, an additional metal surface complex containing the background electrolyte anion is postulated to form in the P-plane ... 

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... 

Some triple layer model intrinsic equilibrium constants for surface complexation in the o-plane are Eqs. (6.10) to (6.13) as in the constant capacitance model, where h is replaced by 1, . Possible intrinsic equilibrium constants for surface complexation in the (3-plane are... 

In the triple layer model, values for the intrinsic protonation and dissociation constants, as well as values for tlie intrinsic surface complexation constants for the background electrolyte, can be obtained from hnear, double, or electrokmetic extrapolations to zero surface charge and zero and infinite electrolyte concentration. Values of intrinsic protonation-dissociation constants and intrinsic surface complexation constants for background electrolytes obtamed for the triple layer model using the various extrapolations are compiled in Goldberg (1992). Use of graphical extrapolation methods has been criticized because the triple layer parameter values obtained are not unique (Koopal et al., 1987). 

Criscenti and Sverjensky (1999, 2002) continued to build the internally consistent set of triple layer model equilibrium constants developed by Sverjensky and Saliai (1996) and Sahai and Sverjensky (1997a,b) by reexamining sets of adsorption edge and isotherm data for divalent metal cation adsorption onto oxide surfaces. In contrast to previous investigations, they found tliat the adsorption of transition and heavy metals on solids such as goethite, y-ALOs, corundum, and anatase, which have dielectric constants between 10 and 22, was best described by surface complexes of the metal with the electrolyte anion. Metal (M +j adsorption from NaNOs solutions is described by... 

VIBRATIONAL SPECTROSCOPY Infrared and Raman spectroscopies have proven to be useful techniques for studying the interactions of ions with surfaces. Direct evidence for inner-sphere surface complex formation of metal and metalloid anions has come from vibrational spectroscopic characterization. Both Raman and Fourier transform infrared (FTIR) spectroscopies are capable of examining ion adsorption in wet systems. Chromate (Hsia et al., 1993) and arsenate (Hsia et al., 1994) were found to adsorb specifically on hydrous iron oxide using FTIR spectroscopy. Raman and FTIR spectroscopic studies of arsenic adsorption indicated inner-sphere surface complexes for arsenate and arsenite on amorphous iron oxide, inner-sphere and outer-sphere surface complexes for arsenite on amorphous iron oxide, and outer-sphere surface complexes for arsenite on amorphous aluminum oxide (Goldberg and Johnston, 2001). These surface configurations were used to constrain the surface complexes in application of the constant capacitance and triple layer models (Goldberg and Johnston, 2001). 

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... 

Kosmulski, M., Adsorption of cadmium on alumina and silica Analysis of the values of stability constants of surface complexes calculated for different parameters of triple layer model. Colloids Surf. A, 117, 201, 1996. 

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... 

For modeling surface adsorption using the surface complexation theory, we need properties of the surfaces as well as complexation constants for the sorbant. Surface properties include site density, surface areas, and molecular formula weight. If we use the triple layer model, capacitance data are also needed see Chapter 7 for more details. 

The triple layer model is, on the other hand, a slightly more complex version of the double layer theory, in which the surface layer is considered to be made up of two different layers - one closely bound to the surface, and one less closely bound. Several variations on this theme are to be found in the literature (Davis el al., 1978). 

HYDRAQL (10) treats adsorption as surface complexation with bound hydroxide functional groups, SOH, and their ionization products, SO and SOH2. The calculations in this paper use HYDRAQL in its triple layer mode. Surface charge and countercharge accumulate in three layers (1) at the surface itself, i.e., in the plane of the SOH groups where the surface potential is T o (2) in the outer Helmholtz plane (OHP), where adsorbed ions retain their inner hydration sheaths (26) and the potential is and (3) in the diffuse layer. The triple layer model is ideal for our purposes because of its ability to compute an estimate of Pp. The computed T p can be compared with experimental measurements of the zeta potential, providing an additional means of constraining models. 

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. 

The specifics of surface complexation is associated with the participation of the surface and minerals electrostatic field whose potential depends on the structure of the dual electric layer. Due to this, there are several different models of surface complexation. Most commonly used are the constant capacitance model, dual diffuse-layer model and triple layer model. 

---