Constant capacitance model metal adsorption

The site binding model based on reactions (1), (2), (14) and (15), often called surface complexation model (SCM), was, beside the simple site binding models (for example two layer model or constant capacitance model) readily applied to a description of the edl on the metal oxide-electrolyte solution interface. Reactions (14) and (15) describe the adsorption of so-called back-... 

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... 

The intent of this chapter is not to survey noninvasive surface spectroscopy but to illustrate briefly how it is applied to resolve the Stummian issue of whether inner-sphere surface complexes form. For this purpose, the application of electron spin resonance (ESR), electron nuclear double resonance (ENDOR), and electron spin echo envelope modulation (ESEEM) spectroscopies to elucidate metal cation speciation and the use of extended X-ray absorption fine structure (EXAFS) spectroscopy to detect surface anion species will be described. Emphasis will be on the interpretation of spectra. Sample preparation and instrumentation details were reviewed in recent volumes edited by Hawthorne (55) and Perry (27). Because the constant capacitance model was developed in the context of adsorption by hydrous oxides, these... 

Figure 10,26 Correlation plot for some metal cations, of their first hydrolysis constants ( /fii) versus intrinsic surface complex constants i Ku) for their adsorption by Si02(am) assuming the constant capacitance model. The equation of the solid line is log = 0.09 -( 0.62 log A. Hydrolysis and adsorption reactions are written A,i -t- H2O = +...

Most studies of metal ion complexation rely on the two-pKH model. Schindler and Stumm [59, 69, 78, 82, 87] combine the two-pKH constant capacitance model with stoichiometric reactions of the metal ions with surface hydroxyls. Huang et al. [62] and Dzombak and Morel [63] tabulate ion affinity constants on the basis of the two-pKH GC model. Leckie and co-workers [88-90] combine the model cation and anion adsorption with the two-pKH TL model. Hayes makes a distinction between strongly and weakly adsorbing ions [89, 90]. A series of reviews on s.a. using the two-pKH model can be found in [91]. 

Figure 6.5. Fit of the constant capacitance model to metal adsorption on silica. (From Schindler et al., 1976.)...

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... 

Some adsorption models attempt to adjust for the nonconstant nature of the equilibrium constants. The constant-capacitance model uses K values for dissociation and metal complexation that are adjusted for the efiect of the electrical potential at the surface, employing the empirical reaction... 

METAL CATION ADSORPTION. The formation of inner-sphere surface complexes involving metal cations is typically described in the constant capacitance model with the chemical reactions ... 

Adsorption, 167-169 See Double layer effect Metals on organic matter, 137 Metals on clays, 167,171 Organic compounds, 181, 355 Oxyanions, 190 Inner-sphere coordination, 169 Outer-sphere coordination, 168 Models, 178,186 Constant capacitance, 186... 

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). 

The method developed here for the description of chemical equilibria including adsorption on charged surfaces was applied to interpret phosphate adsorption on iron oxide (9), and to study electrical double-layer properties in simple electrolytes (6), and adsorption of metal ions on iron oxide (10). The mathematical formulation was combined with a procedure for determining constants from experimental data in a comparison of four different models for the surface/solution interface a constant-capacitance double-layer model, a diffuse double-layer model, the triplelayer model described here, and the Stem model (11). The reader is referred to the Literature Cited for an elaboration on the applications. 

When represents a metal cation not in the background electrolyte, the intrinsic constants are determined by fitting the triple layer model to adsorption edge data. This fitting entails a surface speciation calculation with previously measured values of the intrinsic constants in Eq. 5.61, the capacitance parameters Ci and C2, and the parameter Af. The computation includes Eqs. 5.58, 5.59, and 5.69, as well as surface charge and mole balance equations imposed as constraints. " ... 

Most of the research on metal sorption at the mineral/water interface has dealt with equilibrium aspects. Numerous studies have used macroscopic approaches such as adsorption isotherms, empirical and semi-empirical equations (e.g., Freundlich, Langmuir), and surface complexation models (e.g., constant capacitance, triple layer) to describe adsorption, usually based on a 24 hour reaction time. 

The electric field or ionic term corresponds to an ideal parallel-plate capacitor, with potential drop g (ion) = qMd/4ire. Itincludes a contribution from the polarizability of the electrolyte, since the dielectric constant is included in the expression. The distance d between the layers of charge is often taken to be from the outer Helmholtz plane (distance of closest approach of ions in solution to the metal in the absence of specific adsorption) to the position of the image charge in the metal a model for the metal is required to define this position properly. The capacitance per unit area of the ideal capacitor is a constant, e/Aird, often written as Klon. The contribution to 1/C is 1 /Klon this term is much less important in the sum (larger capacitance) than the other two contributions.2... 

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. 

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