Triple layer model protonation

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. 

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. 

If a strongly adsorbing bivalent metal ion is added to the system described by Eqs. (39) and (40), in which competitive adsorption of protons and ions of basic electrolyte occurs, then according to the triple layer model [103-105] its addition can cause the formation of two kinds of surface complexes inner-sphere complexes SOM formed at the 0-plain of the triple layer and outer-sphere complexes SO M + formed at the, 3-plain. Some recent studies by Hayes and Leckie [142-145] suggest that the formation of the inner-sphere complexes is more probable for divalent cations like Cu, Pb, Cd" ", etc. than the formation of outer-sphere surface complexes. So, in general [142,143] ... 

In the triple layer model the surface reactions for protonation and dissociation of the surface functional group are Eqs. (6.6) and (6.7) as written for the constant capacitance model, where h is replaced by I, . The reactions for adsorption of the background electrolyte in the P-plane are... 

In the triple layer model, values for the intrinsic protonation and dissociation constants, as well as values for tlie intrinsic surface complexation constants for the background electrolyte, can be obtained from hnear, double, or electrokmetic extrapolations to zero surface charge and zero and infinite electrolyte concentration. Values of intrinsic protonation-dissociation constants and intrinsic surface complexation constants for background electrolytes obtamed for the triple layer model using the various extrapolations are compiled in Goldberg (1992). Use of graphical extrapolation methods has been criticized because the triple layer parameter values obtained are not unique (Koopal et al., 1987). 

Generalized composite approaches have also been used in application of the constant capacitance model to describe molybdenum (Goldberg et al., 1998) and arsenate adsorption by soil (Goldberg and Glaubig, 1988) and sediments (Gao et al., 2006) and the triple layer model to describe calcium and magnesium adsorption by soil (Charlet and Sposito, 1989). In these applications the electrostatic terms and protonation-dissociation reactions were retained. 

The triple-layer model (TLM) [753] considers surface protonation and deprotonation according to Reactions 2.21 and 2.22 (2-pA model) and two additional types of surface species ... 

The Triple Layer Model (TL) (Yates et al., 1974 Davis et al., 1978) Two different planes are assumed for the surface The innermost or o-plane does only incorporate protonation or deprotonation of surface sites. All other specifically adsorbed ions are assigned to the outer or b-plane. Therefore, each plane has its own charge and potential. The third layer (to justify the name of the model) is as in the above models the diffuse layer. In summary, this would give two electrostatic parameters (Capacities Ci and C2), but to reduce further the number of variable model parameters, C2 is generally fixed to 0.2, whereas Ci is a fitting parameter inside a range between 0.1 and 2.0, which is supported by theoretical considerations. 

THE NET PROTON CHARGE. In the triple layer model, the protonation and proton dissociation reactions in Eq. 5.41 are described by the conditional equilibrium constants... 

Kinetics of Selenium Adsorption. Zhang and Sparks 4G) examined selenate and selenite adsorption and desorption on goethite using pressure jump relaxation techniques. Selenate produced a single relaxation, that was interpreted as outer-sphere complexation with surface protonation based on fitting to the triple layer model. The forward rate constant was 10 L mol s Selenite adsorption was proposed to occur via two steps, an initial outer-sphere complex and subsequent replacement of a water molecule by formation of inner-sphere complexes of both HSeOj and SeOj, based on optimized fits using the triple layer model. The model optimized fit for the pK, of the surface species was approximately 8.7. Forward rate constants for the first step were on the order of 10 L -mor -s for HSeOj and 10 L -mor -s for SeOj. Forward rate constants for the formation of the inner-sphere complexes were 100 and 13 s respectively for HSeOj and SeOj. Agreement between the equilibrium constant obtained from batch and kinetic studies was taken as confirmation of the proposed reactions. 

Equations (l)-(4) are the foundations of electrical double layer theory and are often used in modeling the adsorption of metal ions at interfaces of charged solid and electrolyte solutions. In a typieal TLM, the outer layer capacitance is often fixed at a lower value (i.e., C2 = 0.2 F/m ), whereas iimer layer capacitance (Ci) can be adjusted to between 1.0 and 1.4 F/m [25]. It should be noted that the three-plane model (TPM) is a variation of the classical triple-layer model, in which the outer layer eapaeitanee is not fixed. Although the physical presentations of the TLM and TPM are identical as shown in Fig. 2, i.e., both involve a surface layer (0), an inner Helmholtz plane (p), and an outer Helmholtz plane d) where the diffuse double layer starts, a one-step protonation process (i.e., 1 piC approach) is, in general, assumed in the TPM, in eontrast to a two-step protonation process (i.e., 2 p/C approach) in the TLM. Another distinct difference is that pair-forming ions are assumed to be on the outer Helmholtz plane in the TPM but on the inner Helmholtz plane in the TLM. In our study, the outer layer capacitance is allowed to vary while the pair-forming ions are placed on the iimer Helmholtz plane with a complete set of surface eomplexation reactions being considered. Therefore, our approach represents a hybrid of the TPM and TLM. 

The adsorption of protons and hydroxyls necessarily leads to charges on the surface, which are balanced by counterions of opposite charge in the solution. Assumptions about the structure of the charged layers, which also contain other adsorbed species, lead to different models (i.e., double- or triple-layer models). 

FIGURE 12.2 Scheme of the triple-layer model. The 0 plane is where the surface charge resides (including protonic, inner-sphere complexes and, if any, permanent charge) the 1 or P plane is where outer sphere complex ions are located, and the 2 or d plane is the start... 

Recently, the extended triple layer model (ETLM) was introduced by Sveijensky and coworkers (Sverjensky 2005 Sveijensky and Fukushi 2006), incorporating prediction of intrinsic equilibrium constants based on crystal chemical, electrostatic, and thermodynamic theory, allowing the reduction of adjustable parameters. In the ETLM, proton sorption Reactions 12.2 and 12.3 are written as associations ... 

With respect to the mechanisms of ion binding, model e places all charges of adsorbed ions in the fi plane, except the protons, which are placed in the surface plane. This corresponds to the original application of the triple-layer model by Davis et al. [4], In the more recent interpretation this practice would mean that all ions are considered as outer-sphere complexes. The consequence is that competition between electrolyte ions (A , C ) and the other ions placed in the fi plane can be made substantial (this is also at least partially the case for charge distribution, which has actually been mentioned in these early papers). 

The 2-pK formulations of the triple layer model elearly have too many adjustable parameters. No unique parameter set ean be determined. With multiple parameter sets showing the same ability to describe experimental data, users are free to ehoose among these parameter sets. This results in different aeid-base parameters used for the same system by different groups, and, in prineiple, it eannot be exeluded that the subsequently modeled equilibria (like adsorption of in model f) will be affeeted by the choice of the acid-base parameters extreme eases of surfaees dominated either by the ion pairs or by the bare protonated and deprotonated surfaee speeies are possible. 

FIG. 5 Experimental points of net proton consumption from forward titration with 0.1 M KOH for purified 15-AI2O3 dispersed in nonindifferent electrolyte (KCI) solutions at room temperature. The continuous lines are numerically fitted [32] using the triple-layer model (Cj = 1.2-1.6F/m, ... 

The siuface complexes formed between surface sites and protons or hydroxide ions formed at the IHP are referred to as inner surface complexes. Surface complexes formed between surface sites and solutes other than protons and hydroxide ions at the SP are referred to as outer surface complexes. While these adsorption layers might at first suggest that adsorbed layer stracture might be determined from adsorption experiments, upon careful reflection, the assumption that proton and hydroxide ions complex with the same surface sites as do other solutes, but at different locations relative to the interface, seems curious at best. As a result of the arbitrary assignment of two adsorption planes it would seem that any information from the triple layer model about adsorbed layer stracture must be equally arbitrary. 

The pseudo-Stem model (and Stem model) differs from the triple layer model in that (1) the eleetrostatie potential remains constant between the OHP and the Stem plane in the former but decays linearly in this region in the latter [31], and (2) the pseudo-Stem model uses the BPD mass action equation (429). In the pseudo-Stem and triple layer models separate adsorption equations are used for adsorption of protons and hydroxide ions at the IHP and for adsorption of all other solute moleeules at the OHP. The amount of adsorption at both planes is then adjusted in order to be self-consistent with an electrostatic balance over Pq, P j and the diffuse layer. 

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). 

The subscripts on the electrostatic potentials are a result of models like the triple layer and pseudo-Stem models, which presume that protons and hydroxide ions adsorb at a siuface plane with electrostatic potential, T q, while all other solutes adsorb at a... 

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