Diffuse layer model adsorption, 378 surface

TABLE 10.9 Diffuse-layer model surface compiexation (intrinsic) constants for adsorption of species by hydrous ferric oxide (HFO) at 25°C... 

With the diffuse-layer model and the sweep option in MINTEQA2, calculate the adsorption of zinc onto HFO at 0.5-pH-unit increments between pH 4 and 8.5 and determine corresponding surface speciation. Comment on the relationship of surface speciation to the pHpzNpc and on the behavior of surface charge and surface potential around the pHpzNPc- Finally, compute and plot for zinc adsorption from pH 4 to 8.5. Assume the same system conditions as in the previous problem, but with a total added zinc concentration of 10 M. System conditions include I = 0.01 M, Sa = 600 mVg, Cj = 8.9 x 10 g/L, and F = 2 x 10" mol active sites/L. 

In this problem we use the diffuse-layer model to compute the adsorption of orthophosphate species by goethite between pH 3 and 10. Intrinsic constants for the adsorption reactions are available in the MINTF.QA2 file,/ o-d/w.f/6r. Similar calculations have been discussed and performed by Hohl etal. (1980). (a) Assume 0.6 g/L of goethite in suspension, with a surface-site density of 1.35 x 10 moles of sites per... 

In this problem you are to compare the predicted adsorption of phosphate by goethite as computed using the constant capacitance and diffuse-layer models. Assume the same general system conditions as given in Problem 12. In other words, there are 0,6 g/L of goethite in suspension. The surface-site density of goethite equals 1.35 x 10 mol sites/g, and its surface area is 45 m /g. Total phosphate is 1.0 x 10 M and SNa = 3.0 X 10-3 M. 

Also the choice of the electrostatic model for the interpretation of primary surface charging plays a key role in the modeling of specific adsorption. It is generally believed that the specific adsorption occurs at the distance from the surface shorter than the closest approach of the ions of inert electrolyte. In this respect only the electric potential in the inner part of the interfacial region is used in the modeling of specific adsorption. The surface potential can be estimated from Nernst equation, but this approach was seldom used In studies of specific adsorption. Diffuse layer model offers one well defined electrostatic position for specific adsorption, namely the surface potential calculated in this model can be used as the potential experienced by specifically adsorbed ions. The Stern model and TLM offer two different electrostatic positions each, namely, the specific adsorption of ions can be assumed to occur at the surface or in the -plane. 

The discrepancies between K values (characterizing specific adsorption) calculated for different sets of parameters of the model of primary surface charging are less significant with models having fewer adjustable parameters than TLM. The I pK-diffuse layer model was combined with the model of Pb adsorption assuming 1 proton released per one adsorbed Pb (inner sphere). In this model the ionic strength effect on the uptake curves is rather insignificant (Fig. 5.120). 

Figure 5.132 presents the ionic strength effect on the model uptake curves calculated for one proton released per one adsorbed Pb, using the diffuse layer model Kosmulski, for model parameters cf. Table 5.13). The model curves are significantly steeper, and the ionic strength effect is less significant than in the analogous Pb adsorption model (inner sphere, one proton released) combined with TLM (Fig. 5.126). The calculated stability constant of the surface complex is higher by three orders of magnitude for the diffuse layer model (Table 5.28) than for TLM (Table 5.27).

Figure 6.6. Fit of the diffuse layer model to copper adsorption by hydrous ferric oxide. The solid line represents the optimal ht for these data. The dashed line represents the fit corresponding to the best overall estimate of the Cu surface complexation constant obtained from 10 Cu adsorption edges. (From Dzombak and Morel. 1990.)...

In the diffuse layer model, all intrinsic metal surface complexation constants were optimized with the FITEQL program for both the strong and weak sites using the best estimates of the protonation constant, log X +(int) = 7.29, and the dissociation constant log K-(int) = —8.93 obtained with Eq. (6.61) (Dzombak and Morel, 1990). Thus, individual values of log A . (int) and log A . (int) and best estimates of log (int) and log A j (int) are unique in that they represent a self-consistent thermodynamic database for metal adsorption on hydrous ferric oxide. 

Another standardized database for the diffuse layer model was developed for montmorillonite by Bradbury and Baeyens (2005). Surface complexation constants for strong and weak sites and cation exchange were fit to adsorption data for various metals using constant site densities and protonation-dissociation constants in a nonelectrostatic modeling approach. Linear free energy relationships were developed to predict surface complexation constants for additional metals from their aqueous hydrolysis constants. 

Bostick et al. (2002) studied Cs+ adsorption onto vermiculite and montmorillonite with EXAFS and found that Cs+ formed both inner-and outer-sphere complexes on both aluminosihcates. The inner-sphere complexes bound to the siloxane groups in the clay structure. Combes et al. (1992) found that NpOj adsorbed onto goethite as a mononuclear surface complex. Waite et al. (1994) were successful in describing uranyl adsorption to ferrihydrite with the diffuse layer model using the inner-sphere, mononuclear, bidentate surface complex observed with EXAFS. 

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 purely electrostatic diffuse layer model often underestimates the affinity of the counterions to the surface. In the Stem model, the surface charge is partially balanced by chemisorbed counterions (the Stem layer), and the rest of the surface charge is balanced by a diffuse layer. In the Stern model, the interface is modeled as two capacitors in series. One capacitor has a constant capacitance (independent of pH and ionic strength), which represents the affinity of the surface to chemisorbed counterions, and which is an adjustable parameter the relationship between a, and Vd in the other capacitor (the diffuse layer) is expressed by Equation 2.18. A version of the Stern model with two different values of C (below and above pHg) has also been used. The capacitance of the Stem layer reflects the size of the hydrated counterion and varies from one salt to another. The correlation between cation size and Stern layer thickness was studied for a silica-alkali chloride system in [733]. Ion specificity of adsorption on titania was discussed in terms of differential capacity as a function of pH in [545]. The Stern model with the shear plane set at the end of the diffuse layer overestimated the absolute values of the potential of titania [734]. A better fit was obtained with the location of the shear plane as an additional adjustable parameter (fitted separately for each ionic strength). Chemisorption of counterions can also be quantified within the chemical model in terms of expressions similar to the mass law (Section 2.9.3.3). 

This model is considered a particular case of the diffusion layer model for the interaction of solutions with high ionic strength and surfaces with low potential (less than 25 mV). It is easy to use and is usually applied for the quantitative description of metal ions and anions adsorption on the oxide surface. 

For the use of the diffusion layer model are ne ed parameters of active centre concentration and acidity constants Kp and Kd on the mineral s surface and also equilibrium constants of all specific complexation reactions. This model was successfully used at analysis of adsorption of such ions as Na+, SO or Cl poorly adsorbed on the surface of iron oxide type minerals. 

The interaction of an electrolyte with an adsorbent may take one of several forms. Several of these are discussed, albeit briefly, in what follows. The electrolyte may be adsorbed in toto, in which case the situation is similar to that for molecular adsorption. It is more often true, however, that ions of one sign are held more strongly, with those of the opposite sign forming a diffuse or secondary layer. The surface may be polar, with a potential l/, so that primary adsorption can be treated in terms of the Stem model (Section V-3), or the adsorption of interest may involve exchange of ions in the diffuse layer. 

The physical meaning of the g (ion) potential depends on the accepted model of an ionic double layer. The proposed models correspond to the Gouy-Chapman diffuse layer, with or without allowance for the Stem modification and/or the penetration of small counter-ions above the plane of the ionic heads of the adsorbed large ions. " The experimental data obtained for the adsorption of dodecyl trimethylammonium bromide and sodium dodecyl sulfate strongly support the Haydon and Taylor mode According to this model, there is a considerable space between the ionic heads and the surface boundary between, for instance, water and heptane. The presence in this space of small inorganic ions forms an additional diffuse layer that partly compensates for the diffuse layer potential between the ionic heads and the bulk solution. Thus, the Eq. (31) may be considered as a linear combination of two linear functions, one of which [A% - g (dip)] crosses the zero point of the coordinates (A% and 1/A are equal to zero), and the other has an intercept on the potential axis. This, of course, implies that the orientation of the apparent dipole moments of the long-chain ions is independent of A. 

Some emphasis is given in the first two chapters to show that complex formation equilibria permit to predict quantitatively the extent of adsorption of H+, OH , of metal ions and ligands as a function of pH, solution variables and of surface characteristics. Although the surface chemistry of hydrous oxides is somewhat similar to that of reversible electrodes the charge development and sorption mechanism for oxides and other mineral surfaces are different. Charge development on hydrous oxides often results from coordinative interactions at the oxide surface. The surface coordinative model describes quantitatively how surface charge develops, and permits to incorporate the central features of the Electric Double Layer theory, above all the Gouy-Chapman diffuse double layer model. 

According to this model, and in the absence of specific adsorption, the adsorbed solvent molecules are located in the inner Helmholtz plane, the thickness of which is determined by the radius of the molecule. At the same time, solvated ions define the location of the outer Helmholtz plane. Other ions, charged oppositely to the surface charge, are smeared out in the diffuse layer. 

The electrode roughness factor can be determined by using the capacitance measurements and one of the models of the double layer. In the absence of specific adsorption of ions, the inner layer capacitance is independent of the electrolyte concentration, in contrast to the capacitance of the diffuse layer Q, which is concentration dependent. The real surface area can be obtained by measuring the total capacitance C and plotting C against Cj, calculated at pzc from the Gouy-Chapman theory for different electrolyte concentrations. Such plots, called Parsons-Zobel plots, were found to be linear at several charges of the mercury electrode. ... 

Although each SCM shares certain common features the formulation of the adsorption planes is different for each SCM. In the DDLM the relationship between surface charge, diffuse-layer potential, d, is calculated via the Gouy-Chapman equation (Table 5.1), while in the CCM a linear relationship between surface potential, s, is assumed by assigning a constant value for the inner-layer capacitance, kBoth models assume that the adsorbed species form inner-sphere complexes with surface hydroxyls. The TLM in its original... 

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