Triple-layer model interfaces

The structure of the interface according to the Stern model and several limiting-case approximations is presented in Figure 4. The electrostatic models of the interface will be introduced in terms of the most complete one, the triple layer model (Figure 4a). Then the relationship of the triple layer model to the simplified models in Figures 4b-d will be discussed. 

S. Goldberg, Inconsistency in the triple layer model description of ionic strength dependent boron adsorption, J. Colloid Interface Sci. 285, 509-517 (2005). 

Leroy, P. and A. J. Revil. 2003. A triple-layer model of the surface electrochemical properties of clay minerals. J. Coll. Interface Sci. 270, 371-380. 

Several SCM s have been described in the literature. The more commonly used models include the Constant Capacitance Model (Schindler and Stumm, 1987), the Diffuse Double Layer Model (Stumm et al., 1970) and the Triple Layer Model (Davis et al., 1978 Yates et al, 1974). All are based on electric double layer theory but differ in their geometric description of the oxide-water interface and the treatment of the electrostatic interactions. 

Figure 10.19 Schematic plot of surface species, charge (cr), and potential tfr) relationships versus distance from the surface, used in the triple-layer model. Integral capacitances C and C2 are assigned to regions between the 0 and /3 and the fi and d planes, respectively. Electrolyte ions are adsorbed at the plane. Reprinted from Adv. Colloid Interface ScL 12,...

Figure 14. (A) Diagram of the charge distribution in the triple layer model. (B) Flat capacitors connected in series as equivalent of a triple layer model at the aqueous solution/metal oxide interface. Charge distribution on capacitor plates is obtained from the electroneutrality condition written in the form 6g = (— o) + ( d).

Triple Layer Model The triple layer model of tire oxide-solution interface (Yates et al., 1974 Davis and Leckie, 1978 Davis et al., 1978 Hayes and Leckie, 1987) contains the following assumptions ... 

Sverjensky, D. A. (2001). Interpretation and prediction of triple-layer model capacitances and the structure of the oxide-electrolyte-water interface. Geochim. Cosmochim. Acta 65, 3643-3655. 

Kulik, D.A., Thermodynamic properties of surface species at the mineral-water interface under hydrothermal conditions A Gibbs energy minimization single-site 2pK3 triple-layer model of rutile in NaCl electtolyte to 250 °C, Geochim. Cosmochim. Acta, 64, 3161, 2000. 

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... 

Fiq. 1. The triple layer model of the electrode-electrolyte interface (10). 

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. 

Comprehensive recent surveys of the triple layer model are to be found in J. A. Davis and J. O. Leckie, Speciation of adsorbed ions at the oxide/water interface, in Chemical Modeling in Aqueous Systems (E. A. Jenne, ed. American Chemical Society, Washington, D.C., 1979) and in R, O, James and... 

Equations (l)-(4) are the foundations of electrical double layer theory and are often used in modeling the adsorption of metal ions at interfaces of charged solid and electrolyte solutions. In a typieal TLM, the outer layer capacitance is often fixed at a lower value (i.e., C2 = 0.2 F/m ), whereas iimer layer capacitance (Ci) can be adjusted to between 1.0 and 1.4 F/m [25]. It should be noted that the three-plane model (TPM) is a variation of the classical triple-layer model, in which the outer layer eapaeitanee is not fixed. Although the physical presentations of the TLM and TPM are identical as shown in Fig. 2, i.e., both involve a surface layer (0), an inner Helmholtz plane (p), and an outer Helmholtz plane d) where the diffuse double layer starts, a one-step protonation process (i.e., 1 piC approach) is, in general, assumed in the TPM, in eontrast to a two-step protonation process (i.e., 2 p/C approach) in the TLM. Another distinct difference is that pair-forming ions are assumed to be on the outer Helmholtz plane in the TPM but on the inner Helmholtz plane in the TLM. In our study, the outer layer capacitance is allowed to vary while the pair-forming ions are placed on the iimer Helmholtz plane with a complete set of surface eomplexation reactions being considered. Therefore, our approach represents a hybrid of the TPM and TLM. 

Let s now examine the second important mechanistic point. As the surface of the oxidic supports is charged in electrolytic solutions, an electrical double layer is formed between the support surface and the solution. Various models have been developed to describe the oxide/solution interface [43, 56-63]. It has been widely accepted that the triple layer model describes better this interface in the most of cases [33-39, 41]. A simplified picture of this model is illustrated in fig. 9. It should be noted that the SOH2+. SOH and SO groups are considered to be localized on the surface of the support (zero plane). On the other hand the centers of the water molecules surrounding the surface of the support particles constitute the so called Inner Helmholtz Plane (IHP). Moreover, the counter ions (of the indifferent electrolyte) are located on the Outer Helmholtz Plane (OHP). Very near to this plane is the shear plane and then the diffuse part of the double layer and the bulk... 

The AustraUan [3]/American [4] approach, which led to the widespread use of the 2-pK triple-layer model much of the traditional knowledge on solid electrolyte interfaces was incorporated into this model. Nowadays, it is still the favorite model in American circles, which deal with surface complexation and which were not influenced by the Swiss approach. 

Various models have been proposed for the electric double layer at an electrode-electrolyte interface. Briefly explain the structure of the electric double layer starting from the Helmholtz model to the triple-layer model and then identify the key features of each model. 

The siuface complexes formed between surface sites and protons or hydroxide ions formed at the IHP are referred to as inner surface complexes. Surface complexes formed between surface sites and solutes other than protons and hydroxide ions at the SP are referred to as outer surface complexes. While these adsorption layers might at first suggest that adsorbed layer stracture might be determined from adsorption experiments, upon careful reflection, the assumption that proton and hydroxide ions complex with the same surface sites as do other solutes, but at different locations relative to the interface, seems curious at best. As a result of the arbitrary assignment of two adsorption planes it would seem that any information from the triple layer model about adsorbed layer stracture must be equally arbitrary. 

Fig. 3. Structure of the solid-solution interface according to the "triple layer model", o., o j and o refer to the total charge from the surface of the support to the IHP, to the OHP, and to the shear plane,respectively.

Chemical relaxation methods can be used to determine mechanisms of reactions of ions at the mineral/water interface. In this paper, a review of chemical relaxation studies of adsorption/desorption kinetics of inorganic ions at the metal oxide/aqueous interface is presented. Plausible mechanisms based on the triple layer surface complexation model are discussed. Relaxation kinetic studies of the intercalation/ deintercalation of organic and inorganic ions in layered, cage-structured, and channel-structured minerals are also reviewed. In the intercalation studies, plausible mechanisms based on ion-exchange and adsorption/desorption reactions are presented steric and chemical properties of the solute and interlayered compounds are shown to influence the reaction rates. We also discuss the elementary reaction steps which are important in the stereoselective and reactive properties of interlayered compounds. 

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. 

FIG. 3 Schematic representation of the ionic distribution and potential characteristic of the double layer model of electrical triple layer at metal oxide-electrolyte 1 1 interface. 

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. 

Dove and Elston, this interfadal layer can be described by a triple layer snrface com-plexation model (TLM) as shown in Fig. 4.31. The interface consists of three electrostatically charged regions, each with an associated electric potential and snrface charge these are termed the o, p, and d planes. Hydrogen ions are permitted to coordinate with the nnsatnrated sites of the interface at the innermost o layer. Sodinm is positioned at the P layer or the d layer. The surface silicon-oxygen complex may have a different chemical character depending on the adsorbed species, hi a sodium chloride solution the surface complexes can be represented as sSiOHaCl, sSiOHj, =SiOH, =SiO-Na, and SiO". The concentration of each species depends on pH and salt concentration, and the sum of the fractions of these surface species equals 1 ... 

Molecular dynamics simulations of the EDL at the TiCVaqueous solution interface have been carried out by Chialvo et al. (2002) and Predota et al. (2002). These simulations indicate that water is structured at the interface, that Sr2+ ions form dominantly inner-sphere complexes at the 2 (110) surface, and that Rb+ ions form dominantly outer-sphere complexes at the interface. These results agree with those from a small-period X-ray standing wave study of Sr2+ and Rb+ ions at the TiCbQ 10)/solution interface (Fenter et al. 2000c) as well as with predictions from the triple layer capacitance model of Sverjensky (2001). 

The method is based on the chemical equilibrium program MINEQL (2), modified to include the coulombic energy of adsorption caused by the charged surface. First the principles of MINEQL are presented through a short example from solution chemistry and then the extension of the method to the constant-capacitance double-layer model of the surface/solution interface used by Stumm, Schindler, and co-workers (3,4) is demonstrated. Finally, the use of the method in the triple-layer site-binding model introduced by Yates, Levine, and Healy (5), and used by Davis, James, and Leckie (6), is shown. In each case the mathematics are described in suflBcient detail to be reproducible. 

Finally, we demonstrate the application of our general formulation of surface/solution equilibria to a more involved model of the surface/ solution interface, the triple-layer site-binding model of Yates, Levine, and Healy. Again we discuss the principles of the method using simple hydrolysis equilibria, but the extension to more complicated equilibria is straightforward. 

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