Constant-capacitance surface complexation

Anderson, P, R., and M. M. Benjamin. 1990a. Constant-capacitance surface complexation model. In Chemical modeling of aqueous systems //, ed D. C. Melchior and R. L. Bassett. Am. Chem. Soc. Symp. Ser. 416, pp. 272-81. Washington DC Am. Chem. Soc. 

The model used to evaluate surface chemistry in these systems is the constant capacitance surface complexation model. This model has been used to describe the adsorption of cations (41) and anions (4,8) onto oxides similar to those used in our experiments. A significant difference between those studies and the present study is that we have adapted the model to simulate some of the interactions that might occur between particles in a binary suspension. 

Details on the adsorbent preparation and experimental and analytical techniques are presented elsewhere (9). This paper briefly reviews the experimental results for the Fe(OH)3 and Si02 suspensions and describes a conceptual and mechanistic model for particle interactions which is qualitatively consistent with the experimental observations. Similar results were obtained for binary Al(OH)3 and Si02 suspensions (9). The constant capacitance surface complexation model is then used to test the mechanistic model and estimate the quantitative influence of the particle-particle interactions on adsorbate distribution. 

Some triple layer model intrinsic equilibrium constants for surface complexation in the o-plane are Eqs. (6.10) to (6.13) as in the constant capacitance model, where h is replaced by 1, . Possible intrinsic equilibrium constants for surface complexation in the (3-plane are... 

The equilibrium constants KNa+ and Kci- introduced here characterize the extent of counterion complexation that occurs. Two other constants characterize the potential generation that results from this complexation, namely the capacitances CNa+ and ( Cl-- These are the capacitances between the planes of counterion complexation and the surface plane where ao is located. The potentials rpNa+ and rpcl are the electrostatic potential at the location in the double layer where the ions adsorb and form a surface complex. 

As shown in Figure 1, the adsorption of Mn(II) on y-FeOOH can be successfully described using a constant capacitance model. In these calculations the hydrolysed surface complex =FeO-Mn-OH was not considered. The reason for not considering both the bidentate (sS0)2Mn and hydrolysed surface species is that both have virtually the same pH dependence, so it is impossible using the available data to make anything other than an arbitrary choice about the relative proportions of these two species. Based on the model calculations, in the pH range 8-9, the predominant Mn(II) species on the y-FeOOH surface is the bidentate surface complex or the hydrolysed surface complex. 

The main, currently used, surface complexation models (SCMs) are the constant capacitance, the diffuse double layer (DDL) or two layer, the triple layer, the four layer and the CD-MUSIC models. These models differ mainly in their descriptions of the electrical double layer at the oxide/solution interface and, in particular, in the locations of the various adsorbing species. As a result, the electrostatic equations which are used to relate surface potential to surface charge, i. e. the way the free energy of adsorption is divided into its chemical and electrostatic components, are different for each model. A further difference is the method by which the weakly bound (non specifically adsorbing see below) ions are treated. The CD-MUSIC model differs from all the others in that it attempts to take into account the nature and arrangement of the surface functional groups of the adsorbent. These models, which are fully described in a number of reviews (Westall and Hohl, 1980 Westall, 1986, 1987 James and Parks, 1982 Sparks, 1986 Schindler and Stumm, 1987 Davis and Kent, 1990 Hiemstra and Van Riemsdijk, 1996 Venema et al., 1996) are summarised here. 

The above surface complexation models enable adsorption to be related to such parameters as the number of reactive sites available on the oxide surface, the intrinsic, ionization constants for each type of surface site (see Chap. 10), the capacitance and the binding constants for the adsorbed species. They, therefore, produce adsorption isotherms with a sounder physical basis than do empirical equations such as the Freundlich equation. However, owing to differences in the choice of adjustable... 

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). 

The constant-capacitance model (Goldberg, 1992) assigns all adsorbed ions to inner-sphere surface complexes. Since this model also employs the constant ionic medium reference state for activity coefficients, the background electrolyte is not considered and, therefore, no diffuse-ion swarm appears in the model structure. Activity coefficients of surface species are assumed to sub-divide, as in the triplelayer model, but the charge-dependent part is a function of the overall valence of the surface complex (Zk in Table 9.8) and an inner potential at the colloid surface exp(Z F l,s// 7). Physical closure in the model is achieved with the surface charge-potential relation ... 

The characteristic features of parameter estimation in a molecular model of adsorption are illustrated in Table 9.9, taking the simple example of the constant-capacitance model as applied to the acid-base reactions on a hydroxylated mineral surface. (It is instructive to work out the correspondence between equation (9.2) and the two reactions in Table 9.9.) Given the assumption of an average surface hydroxyl, there are just two chemical reactions involved (the background electrolyte is not considered). The constraint equations prescribe mass and charge balance (in terms of mole fractions, x) and two complex stability constants. Parameter estimation then requires the determination of the two equilibrium constants and the capacitance density simultaneously from experimental data on the species mole fractions as functions of pH. 

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-... 

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. 

The evaluation of qAB is a formidable task if done exactly, but the constant capacitance model (as well as other surface complexation models) is the special case that results from equation 12 by a simple approximation (22) ... 

Nature of the Surface Complexes. The constant capacitance model assumes an inner-sphere molecular structure for surface complexes formed in reactions like equation 5a or 7. But this structure does not manifest itself explicitly in the composition dependence of Kc everything molecular is buried in which is an adjustable parameter. This encapsulating characteristic of the model was revealed dramatically by Westall and Hohl (13), who showed that five different surface speciation models, ranging from the Gouy-Chapman theory to the surface complex approach, could fit proton adsorption data on AL O., equally well, despite their mutually contradictory underlying molecular hypotheses [see also Hayes et al. (19)]. They concluded that "... no model will yield an unambiguous description of adsorption. .. . To this conclusion one may add that no model should provide such a description,... 

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 = +...

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-... 

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]. 

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 ... 

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). 

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... 

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