Diffuse layer model complex constants

TABLE 5.23 Calculated Stability Constants of Alumina-Pb Surface Complex (inner sphere, I proton released). For I-pK-Diffuse Layer Model Parameters cf Table 5.12... 

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).

Also for other diffuse layer models (cf. Table 5.13) the calculated stability constant of silica-Pb surface complex is considerably higher than for their TLM counterparts obtained from the same experimental data. The difference between the highest and the lowest K in Table 5.28 by almost two orders of magnitude is more significant than the discrepancies between the stability constants calculated for different diffuse layer models obtained for alumina (cf. Table 5.22). In spite of different K, the course of the calculated uptake curves obtained for different diffuse layer models and one proton released per one adsorbed Pb with... 

TABLE 5.28 The Stability Constants of Silica-Pb Surface Complex (1 proton released) for Diffuse Layer Model Parameters cf. Table 5.13... 

The intrinsic equilibrium constants for the diffuse layer model are similar to those for the constant capacitance model where P is replaced by Equations (6.10) and (6.11) describe surface protonation and dissociation, respectively. Metal surface complexation is described by two constants similar to tliat defined in Eq. (6.12) for strong and weak sites ... 

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. 

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... 

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 specifics of surface complexation is associated with the participation of the surface and minerals electrostatic field whose potential depends on the structure of the dual electric layer. Due to this, there are several different models of surface complexation. Most commonly used are the constant capacitance model, dual diffuse-layer model and triple layer model. 

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. 

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. 

Furthermore, we will take all other properties as constant and independent of temperature. Due to the high temperatures expected, these assumptions will not lead to accurate quantitative results unless we ultimately make some adjustments later. However, the solution to this stagnant layer with only pure conduction diffusion will display the correct features of a diffusion flame. Aspects of the solution can be taken as a guide and to give insight into the dynamics and interaction of fluid transport and combustion, even in complex turbulent unsteady flows. Incidentally, the conservation of momentum is implicitly used in the stagnant layer model since ... 

Macroscopic experiments allow determination of the capacitances, potentials, and binding constants by fitting titration data to a particular model of the surface complexation reaction [105,106,110-121] however, this approach does not allow direct microscopic determination of the inter-layer spacing or the dielectric constant in the inter-layer region. While discrimination between inner-sphere and outer-sphere sorption complexes may be presumed from macroscopic experiments [122,123], direct determination of the structure and nature of surface complexes and the structure of the diffuse layer is not possible by these methods alone [40,124]. Nor is it clear that ideas from the chemistry of isolated species in solution (e.g., outer-vs. inner-sphere complexes) are directly transferable to the surface layer or if additional short- to mid-range structural ordering is important. Instead, in situ (in the presence of bulk water) molecular-scale probes such as X-ray absorption fine structure spectroscopy (XAFS) and X-ray standing wave (XSW) methods are needed to provide this information (see Section 3.4). To date, however, there have been very few molecular-scale experimental studies of the EDL at the metal oxide-aqueous solution interface (see, e.g., [125,126]). 

The elegance of the surface complexation approch lies in the fact that it can be incorporated into the thermodynamic speciation models used for soluble complexes. Consequently many of the computer models, e.g. SOILCHEM, HYDRAQL, MINTEQA2 and ECOSAT, include several different SCMs. Some commonly used SCMs are the diffuse-double-layer model, DDLM (Huang and Stumm, 1973 Dzombak and Morel, 1990), the constant capacitance model, CCM (Stumm et al., 1970 1976 1980 Schindler et al., 1976), the triple-layer model, TLM (Davis etal., 1978 Davis and Leckie, 1978,1980 Hayes and Leckie, 1987 Hayes et al., 1988) and the 1 pK basic Stern model (Bolt and Van Riemsdijk, 1982 Van Riemsdijk et al., 1986 1987). 

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... 

Using this model, one cannot forecast the adsorption of the background electrolyte ions because this model do not consider the reactions responsible for such a process. Zeta potential values, calculated on the basis of this model, are usually too high, nevertheless, because of its simplicity the model is applied very often. In a more complicated model of edl, the three plate model (see Fig. 3), besides the mentioned surface plate and the diffusion layer, in Stern layer there are some specifically adsorbed ions. The surface charge is formed by = SOHJ and = SO- groups, also by other groups formed by complexation or pair formation with background electrolyte ions = SOHj An- and = SO Ct+. It is assumed that both, cation (Ct+) and anion (A-), are located in the same distance from the surface of the oxide and form the inner Helmholtz plane (IHP). In this case, beside mentioned parameters for two layer model, the additional parameters should be added, i.e., surface complex formation constants (with cation pKct or anion pKAn) and compact and diffuse layer capacities. 

There is a range of equations used describing the experimental data for the interactions of a substance as liquid and solid phases. They extend from simple empirical equations (sorption isotherms) to complicated mechanistic models based on surface complexation for the determination of electric potentials, e.g. constant-capacitance, diffuse-double layer and triple-layer model. 

While CCM and DDLM assume that all ions are at one plane, the triple layer includes different planes, in which the surface complexes are bound. In the original version of Davis et al. (1978) the protons and hydroxide ions are bound at the layer (o-plane) close to the phase boundary, whereas inner-sphere complexes are bound in a (3-plane somewhat dislodged. Both planes are assumed as constant-capacity layers. The range outside the (3-plane containing the outer-sphere complexes is modeled as a diffuse layer (Fig. 14 c). 

As detailed above, the adsorption behavior of most actinides varies widely with solution pH, Eh, complexation, competitive adsorption and ionic strength, and the surface properties of sorbent phases. For this reason, many researchers have modeled actinide adsorption using surface complex-ation (SC) models that can quantitatively account for such variables. These models include the constant capacitance (CC), diffuse-layer (DL), and triple-layer (TL) models (Chap. 10). Much of the ra-... 

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