Reaction 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). 

Diprotic Surface Groups. Most of the recent research on surface hydrolysis reactions has been interpreted in terms of the diprotic surface hydrolysis model with either the triple layer model or the constant capacitance model of the electric double layer. The example presented here is cast in terms of the constant capacitance model, but the conclusions which are drawn apply for the triple layer model as well. 

Figure 14. Triple-layer model (1) results for Cd(II) adsorption onto a-alumina at different site/adsorbate ratios. Top, Cd(II) surface reaction best fit constants middle, Cd(II) surface species mole fractions and bottom, slopes of fractional adsorption edges used as the criteria of fit.

A more sophisticated model is the triple-layer model, allowing the surface reaction of the background electrolyte (Hayes et al. 1991). The potential-determining ions (hydrogen and hydroxide) are directly on the surface (inner Helmholtz layer), the other ions are at a certain distance from the surface (outer Helmholtz layer), and there is a diffuse layer, also. 

A more mechanistic and robust depiction of reversible metal adsorption is provided by SCMs that account explicitly for competitive speciation reactions using an equilibrium thermodynamic framework. Examples of SCMs in current use include the constant capacitance model (CCM), the diffuse double-layer model (DDLM), and the triple-layer model (TLM) (Stumm Morgan, 1996 Koretsky, 2000). Each of these models envisages... 

Because the various SCM s have different formulations for treating adsorption reactions and the electrostatic terms, parameters fit to one model may not he applicable to other models (Morel et al, 1981). For example, Gao and Mucci (2001) determined different Log K s for As(V) adsorption by goethite when the data were fit to the Constant Capacitance Model, the Basic Stem Model, and the Triple Layer Model. 

The following adsorption reactions and intrinsic constants are available for the triple-layer model, where FeO", FeOH, and FeOHJ are surface sites. 

Triple layer model TLM is very popular and it is build into many commercial speciation programs. It combines the 2-pK model, i.e. reactions (5.32) and (5.33) with binding of inert electrolyte ... 

In the triple layer model the surface reactions for protonation and dissociation of the surface functional group are Eqs. (6.6) and (6.7) as written for the constant capacitance model, where h is replaced by I, . The reactions for adsorption of the background electrolyte in the P-plane are... 

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 ... 

Generalized composite approaches have also been used in application of the constant capacitance model to describe molybdenum (Goldberg et al., 1998) and arsenate adsorption by soil (Goldberg and Glaubig, 1988) and sediments (Gao et al., 2006) and the triple layer model to describe calcium and magnesium adsorption by soil (Charlet and Sposito, 1989). In these applications the electrostatic terms and protonation-dissociation reactions were retained. 

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 triple-layer model (TLM) [753] considers surface protonation and deprotonation according to Reactions 2.21 and 2.22 (2-pA model) and two additional types of surface species ... 

Wu. Ch.H. et al.. Modeling competitive adsorption of molybdate, sulfate, and selenate on y-ALO, hy the triple-layer model, J. Colloid Interf. Sci., 233, 259, 2001. Hachiya. K. et al.. Static and kinetic studies of adsorption-desorption of metal ions on y-ALO, siuface. 1. Static study of adsorption-desoiption, J. Pltys. Chem., 88, 23, 1984. Tamiu a, H.. Katayama. N., and Furuichi, R.. Modeling of ion-exchange reactions on metal oxides with the Frumkin isotherm. 1. Acid-base and charge characteristics of MnO,. TiO,. Fe,O4. and ALO, surfaces and adsorption affinity of alkali metal ions. Environ. Sci. Technol.. 30. 1198. 1996. 

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 triple layer model is applicable for solutions with a wide range of ionic strength. To use it, it is necessary to know the concentrations of active centres acidity constants and and electric capacitances and of the mineral surface, and also equilibrium constants of all specific and nonspecific complexation reactions. 

The triple layer modeP offers a molecular description of surface complexation reactions that differs from the constant capacitance model in several fundamental respects. These differences can be brought into clear relief through a comparative listing of the principal chemical assumptions that underlie the triple layer model ... 

THE NET PROTON CHARGE. In the triple layer model, the protonation and proton dissociation reactions in Eq. 5.41 are described by the conditional equilibrium constants... 

METAL CATION ADSORPTION. The formation of outer-sphere surface complexes involving metal cations has been described typically in the triple layer model by the reactions ... 

The charge reversal behavior shown in Fig. 4.7 also can be described by the triple layer model.The mechanism relies on the competition between the reactions in Eq. 5.41 and that in Eq. 5.67b. When an adsorptive, bivalent metal cation is present, an increase in pH value causes the... 

Recent developments in spectroscopic techniques offer the opportunity to increase our understanding of oxyanion surface speciation and binding. This understanding is essential to properly use mechanistic sorption models, such as the constant capacitance model and the triple layer model. A recent criticisms of these models is that selection of the surface species and reaction from the sorption data alone results in an empirical model which could be replaced with the traditional Langmuir model (7). However determination of the surface species and reactions will constrain the parameterization and allow for mechanistic evaluation of the sorption models. Knowledge of the actual species and reaction should also enable more generalized prediction of sorption behavior outside the range of the actual experiment, which is not possible at present. 

Kinetics of Selenium Adsorption. Zhang and Sparks 4G) examined selenate and selenite adsorption and desorption on goethite using pressure jump relaxation techniques. Selenate produced a single relaxation, that was interpreted as outer-sphere complexation with surface protonation based on fitting to the triple layer model. The forward rate constant was 10 L mol s Selenite adsorption was proposed to occur via two steps, an initial outer-sphere complex and subsequent replacement of a water molecule by formation of inner-sphere complexes of both HSeOj and SeOj, based on optimized fits using the triple layer model. The model optimized fit for the pK, of the surface species was approximately 8.7. Forward rate constants for the first step were on the order of 10 L -mor -s for HSeOj and 10 L -mor -s for SeOj. Forward rate constants for the formation of the inner-sphere complexes were 100 and 13 s respectively for HSeOj and SeOj. Agreement between the equilibrium constant obtained from batch and kinetic studies was taken as confirmation of the proposed reactions. 

Kinetics of Molybdenum Adsoiption. Zhang and Sparks 41) examined molybdate adsorption on goethite using pressure jump relaxation experiments. Molybdate adsorption was proposed to occur via two steps, an initial outer-sphere complex and subsequent replacement of a water molecule by formation of an inner-sphere complex of Mo04, based on optimized fits using the triple layer model. Forward rate constants were on the order of 4x10 L mol s and 40 s for the first and second reaction steps. 

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. 

The surface charge density was not required as input rather it was calculated from the fitted equilibrium constants of surface complexing reactions. An improved fit was clearly demonstrated with the hybrid triple-layer model compared to the conventional one. 

Three frequently used SCMs can be found based on the EDL structure used constant capacitance model (CCM), double layer model (DLM) and triple layer model (TLM). For aU three models the electrostatic variables are fitting parameters and the available complexation reaction constants are model dependent. 

Recently, the extended triple layer model (ETLM) was introduced by Sveijensky and coworkers (Sverjensky 2005 Sveijensky and Fukushi 2006), incorporating prediction of intrinsic equilibrium constants based on crystal chemical, electrostatic, and thermodynamic theory, allowing the reduction of adjustable parameters. In the ETLM, proton sorption Reactions 12.2 and 12.3 are written as associations ... 

Surface complexation reactions are assumed on surface sites, S—OH. The total site density (Ns, mol/m ), has to be defined for the given system. In the constant-capacitance and diffuse-layer models, all surface species are supposed to be inner-sphere complexes, whereas in the triple-layer model, both inner- and outer-sphere complexes are assumed. 

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