Applications of the Triple-Layer Model

Both types of adsorption should not necessarily be considered in the TLM. In a study of As-organic compounds (Mitchell, Goldberg, and Al-Abadleh 2011), the triple-layer surface complexation model was applied to adsorption isotherm and pH envelope data for dimethylarsinic acid (DMA) and p-arsanilic acid (p-AsA) on 

FIGURE 12.3 Chromate adsorption on two B horizons of North American soils. 

Experimental data (symbols) and the triple-layer model predicted results (lines) for ( ,-) 

FIGURE 12.4 2,4-Dichlorophenol isotherms in allophanic soil, at pH 4.5, in 0.1 mol L i KCl background electrolyte at temperatures of 25°C, 35°C, and 45°C. (Reprinted from Chemosphere, 78, cea, M. et al.. Kinetic and thermodynamic study of chlorophenol sorption in an allophanic soil, 86-91. Copyright 2010, with permission from Elsevier.) 

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The discussion above pertains to the diprotic acid chemical model and the constant capacitance electrostatic model. It is interesting to note that in some applications of the triple layer model with site binding of electrolyte ions at the IHP, the... 

Sonnefeld, J., Lobbus, M., and Vogelsberger, W.. Determination of electric double layer parameters for spherical silica particles under application of the triple layer model using surface charge density data and results of electrokinetic sonic amplitude measurements, Colloids Surf. A, 195, 215, 2001. 

With respect to the mechanisms of ion binding, model e places all charges of adsorbed ions in the fi plane, except the protons, which are placed in the surface plane. This corresponds to the original application of the triple-layer model by Davis et al. [4], In the more recent interpretation this practice would mean that all ions are considered as outer-sphere complexes. The consequence is that competition between electrolyte ions (A , C ) and the other ions placed in the fi plane can be made substantial (this is also at least partially the case for charge distribution, which has actually been mentioned in these early papers). 

Figure 7.12 illustrates tliesc considerations. It shows the components of the surface charge as determined by application of the triple-layer model on a feal system for... 

M. C. Kavanaugh and J. O. Leckie, Particulates in Water Characterization, Fate, Effect, and Removal. Advances in Chemistry Series 189. American Chemical Society, Washington, D.C. 1980. Chapters 1 and 2 give excellent accounts of the constant capacitance model in theory and application. Chapter 2 also contains a discussion of the computational aspects of the triple layer model. 

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. 

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. 

CCM) (Stumm et al., 1970, 1976, 1980 Schindler et al., 1976), the triple-layer model (TLM) (Davis and Leckie, 1978, 1980 Davis et al., 1978 Hayes and Leckie, 1987 Hayes et al., 1988), and the 1 pK basic Stem model (Bolt and van Riemsdijk, 1982 Van Riemsdijk et al., 1986, 1987). The application of many of the commonly used computer models in the determination of the speciation in solution phase has been dealt with exhaustively by Lumsdon and Evans (1995). 

Various types of SCM have been assessed namely, the diffuse-layer model (DLM) [27], the constant-capacitance model [28], the Stern model [29], and the triple-layer model (TLM) [30]. They differ in complexity from the simplest, DLM, which has four adjustable parameters, to the most complex, TLM, which includes seven adjustable parameters. The number of parameters is dependent on the hypothesis relative to the model. In various researches, the DLM is selected because of its simplicity and its applicability to various solution conditions [31]. It takes into account ionic strength effects on protolysis equilibria through the Gouy-Chapman-Stern-Grahame charge-potential relationship ... 

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. 

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). 

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. 

Another major disadvantage of the commonly used surface complexation models, and of most equilibrium-based sorption models, is that three-dimensional surface products are not included as possible complexes. However, there are several exceptions. Farley et al. (5) and James and Healy (6) considered surface precipitation in successfully modeling sorption of hydrolyzable metal ions. Dzombak and Morel (7) modified the diffuse layer surface complexation model to include surface precipitation. However, these applications relied solely on macroscopic data without molecular-level identification of the sorption complex structure. Recently, Katz and Hayes (8,9) employed triple layer models, that included a surface solution model, a surface polymer model, and a surface continuum model to describe molecular level data for Co sorption on y-AljOj over a wide range of surface coverages (0.1 to 100%). 

The sphalerite-ferrous surface binding constants in NaCl solutions were determined. Applications of the hybrid triple-layer model in predicting electrokinetics, surface charge density, metal ion adsorption, and surface solution speciation were described and illustrated with examples. 

The original Smit model separates the surface plane into two sections one fiuction [i.e., 1 — /], of the overall surface (respectively the fraction of the surface sites) where only uncomplexed surface groups are present, and another fraction /, where only ion pairs formed with the electrolyte. For both sections, a different electrostatic model concept is introduced a Stem model (obviously without electrolyte binding) for the fraction 1 —/ and a triple-layer model for the fraction /. This separation is, of course, artificial. A mean value of the zeta potential is calculated from the equation given in Fig. 17i. Application of the model to experimental surface-charge data requires very low values for C2 One advantage of this model can be seen in the closer agreement of the model with the experimental observations quoted by Smit. 

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