Models triple layer

3 Triple-layer model. The TLM was developed to allow for species adsorbed as inner- 

Mass balance - For surface species in the TLM the mass balance is given by 

Once the constants K / Na, K 1, Kb k2 are known the relative proportions of any surface species can be calculated for any pH using the appropriate adjustable parameters (Table 5.1). For input into some of the computer models it is often necessary to prepare the input problem in an EPM format an example of this is shown for the TLM in Table 5.9. 

Silicic acid species adsorption reactions are written SOH + H4Si04 = SH3S1O4 + H2O and SOH + H4Si04 = SH2SiOj + H+ + H2O. 

Source Anderson and Benjamin (1990a, 1990b). Schindler and Stumm (1987). Goldberg and Sposito (1984). 

MINTEQA2 assumes that adsorbed and OH occupy the zero plane, but allows the user to position other adsorbed species in either the zero or beta plane in the TL model, consistent with their probable behavior as just described. However, most of the extensive published literature and reported values for the TL model have been derived assuming that only and OH occupy the zero plane 

An example of the positions of adsorbed species and general structure of the double layer in the TL model is. shown schematically in Fig. 10.19. Assuming that n-2, the net surface charge in the zero plane equals 

The charge-balance calculation for the zero plane ignores species A and in the beta plane and considers only the zero plane species to which these ions are adsorbed, plus unfilled adsorption sites (SO sites) and sites occupied by specifically adsorbed protons (SOHJ sites). With A and assigned to the beta plane, the net charge of that plane is given by 

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Triple-layer model Of limited value because of the complexity of adsorption sites, unpredictable... 

Wu CH, Shang LL, Cheng FL, Chao YK (2001) Modeling competitive adsorption of molybdate, sulfate and selenate on y-Al203 by the triple-layer model. J Colloid Interf Sci 233 259-264... 

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. This model developped by Yates et al. (1974) and Davis et al. (1978) uses a similar idea as the Stern model the specifically adsorbed ions are... 

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. 

Stern used this simplification in his calculations. The simplified model with only one Helmholtz capacitance is commonly referred to as the Stern model (Figure 4b), while the "extended" Stern model (Figure 4a) is designated the triple layer model. 

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. 

An extension of this method has been developed for the triple layer model which allows data obtained at several values of ionic strength to be considered simultaneously (7, 13.). However, this "double extrapolation technique" involves the same sort of approximation. 

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... 

The constants and parameters required for making triple layer model (TLM) computations (e.g.,, K, Clt C2, and... 

Table I. Triple Layer Model Parameters and Values...

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. 

Microscopic Subreactions and Macroscopic Proton Coefficients. The macroscopic proton coefficient may be used as a semi-empirical modeling variable when calibrated against major system parameters. However, x has also been used to evaluate the fundamental nature of metal/adsorbent interactions (e.g., 5). In this section, macroscopic proton coefficients (Xj and v) calculated from adsorption data are compared with the microscopic subreactions of the Triple-Layer Model ( 1 ) and their inter-relationships are discussed. 

Table IV. Subreactions and Constants Used in Triple-Layer Model Dalculations for CdCl /a-A O ...

A specific example of the relationship between the microscopic subreactions required to model experimental observations of metal removal and the macroscopic proton coefficient is shown for the case of Cd(II) adsorption onto a-A f (Figure 3). One variation of the surface coordination concept is used to describe the system subreactions the Triple Layer Model of Davis et al., (1,20). The specific subreactions which are considered, the formation constants and compact layer capacitances, are shown in Table IV. Protons are assigned to the o-plane (the oxide surface) and Cd(II) surface species and electrolyte ions to the 8-plane located a distance, 8, from the o-plane. 

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.

Fig. 5-8. An interfadal double layer model (triple-layer model) SS = solid surface OHP = outer Helmholtz plane inner potential tt z excess charge <2h = distance from the solid surface to the closest approach of hydrated ions (Helmluritz layer thickness) C = electric capacity.

Figure 4.11. Triple-layer model (Grahame) IHP, inner Helmholtz plane OHP, outer Helmholtz plane (, water dipole +, positive end of the dipole).

Fitting parameter for Triple-layer model 600-700 Davis and Leckie, 1978... 

In the triple layer model, the potential determining ions are located at the oxide surface with the specifically adsorbing ions and the ion pairs in the inner Helmholz... 

Some stability constants for ion pairs on Fe oxides are listed in Table 10.4. This model was applied by Davis and Leckie (1978, 1980) to adsorption of various cations and anions on ferrihydrite. The extended triple layer model of Sahai and Svenjensky (1997) incorporates recent advances in aqueous electrolyte chemistry which enable aqueous activity coefficients for electrolytes to be calculated over a wide range of ionic strengths. The model also considers the free energy of adsorption of an ion to be the sum of the contributions from an electrostatic term, a Born solvation term and a ion intrinsic term. This extended model has been applied to adsorption of Co and Cd on goethite. 

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