Evaluation of internally consistent parameters for the triple-layer model by the systematic analysis of oxide surface titration data

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1 Pergamon PI1 SOO ( 97) Geochimica et Cosmochimica Acta, Vol. 61, No. 14, pp , 1997 Copyright Elsevier Science Ltd P&ted in the USA. All rights reserved /97 $ OO Evaluation of internally consistent parameters for the triple-layer model by the systematic analysis of oxide surface titration data NITA SAHAI* and DIMITRI A. SVERJENSKY The Morton K. Blaustein Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland 21218, USA (Received November 19, 1997; accepted in revised form March 12, 1997) Abstract--Systematic analysis of surface titration data from the literature has been performed for ten oxides (anatase, hematite, goethite, rutile, amorphous silica, quartz, magnetite, S-MnO,, corundum, and -y-alumina) in ten electrolytes (LiNO 3, NaN03, KNOX, CsN03, LiCl, NaCl, KCl, CsCl, NaI, and NaC104) over a wide range of ionic strengths (0.001 M-2.9 M) to establish adsorption equilibrium constants and capacitances consistent with the triple-layer model of surface complexation. Experimental data for the same mineral in different electrolytes and data for a given mineral/electrolyte system from various investigators have been compared. In this analysis, the surface protonation constants (K,,, and KS,,) were calculated by combining predicted values of ApK( log KS,* - log KS,, ) (Sverjensky and Sahai, 1996) with experimental points of zero charge; site-densities were obtained from tritium-exchange experiments reported in the literature, and the outer-layer capacitance (C,) was set at 0.2 F. mm*. This scheme permitted us to retrieve consistent sets of values for the inner layer capacitance (C, ), and for the electrolyte adsorption constants (Ks,Lm and K+,+) corresponding, respectively, to the equilibria and >SOH: + Lag = >SOH: - L- >SO- + M,, = >SO- - M+ Aqueous activity coefficients were calculated using the extended Debye-Huckel equation (Helgeson et al., 1981), which is valid to high ionic strengths (>OS M). Systematic analysis of the data reveals important trends and differences between triple-layer model predictions and experimental data and between data for the same mineral/electrolyte from different investigators. Furthermore, the analysis yields an internally consistent set of triple-layer parameters which will be used in developing a predictive model for electrolvte adsomtion based on Born solvation and electrostatic theory (Sahai and Sverjensky, 1997a). Copyright Elsevier Science Ltd 1. INTRODUCTION Geochemical systems are characterized by complex assemblages of minerals and solutions of widely varying compositions ranging from dilute Ca-HC03-H4Si04-bearing riverwater and shallow groundwaters through saline Na-Cl-Mg- SO,-rich seawater to the concentrated Na-Ca-Cl brines of sedimentary basins (Drever, 1988). The chemistry of such aqueous solutions and minerals can be altered by processes involving adsorption of dissolved ions such as ion-exchange in clays and metal scavenging in surface waters. In laboratory experiments of adsorption, the ionic strength of the aqueous medium is usually set by a dominant electrolyte, which is often referred to as the swamping or background electrolyte (henceforth, referred to simply as electrolyte ). The electrolyte used is often a simple 1: 1 electrolyte such as NaCl or IWO,. Adsorption of protons and ions results in the accumulation of a net of excess of charge near the mineral surface. Surface charge is a function of ph, the concentration (ionic strength), and the identity of the * Presenr address: Department of Geology, Arizona State University, Tempe, Arizona 85287, USA. electrolyte (Yates, 1975; Sprycha, 1984, 1989). In addition to affecting surface charge at equilibrium, alkali metal cations present as the electrolyte are also thought to catalyze the dissolution rate of some minerals such as amorphous silica and quartz (Dove and Crerar, 1990; Bennett, 1991). The extent of the catalyzing effect depends on the identity and concentration of the cation and the temperature of the system (Dove and Crerar, 1990; Bennett, 1991). Thus, adsorption of electrolyte ions may affect both reaction equilibria as well as kinetics. From the above considerations, it is clear that the quantitative description of adsorption equilibria and kinetics requires a thermodynamic model capable of dealing with chemical variability in terms of both ( 1) the specific identity and concentration of the electrolyte and (2) the identity of the underlying mineral. The most widely used models of the mineral-solution interface are the surface complexation models such as the constant capacitance model (Schindler and Kamber, 1968; Hohl and Stumm, 1976), the diffuse double layer model (Stumm et al., 1970; Huang and Stumm, 1973; Dzombak and Morel, 1990), the triple-layer model (James and Healy, 1972; Yates et al., 1974; Yates, 1975; Davis et al., 1978), and the various four-layer models (Bowden et al., 1980; 2801

2 2802 N. Sahai and D. A. Sverjensky Bousse and Meindl, 1986; Charmas et al., 1995). All these models treat adsorption reactions as analogous to aqueous complexation reactions. The models assume that the electrolyte ions balance the local excess charge on the surface by forming a diffuse swarm of counterions near the surface. The diffuse layer of ions is considered to be held by electrostatic forces only. The difference between the models lies in their description of the electric double layer (Westall and Hohl, 1980; Davis and Kent, 1990). In particular, the triplelayer and four-layer models explicitly account for specific electrolyte ion adsorption, by assigning a specific equilibrium constant for the adsorption reaction of each ion. The surface complexation models require several model parameters. The triple-layer model, in particular, requires seven parameters. In most previous studies, these parameters were obtained by fitting surface titration data. The sets of parameters so obtained are not necessarily unique (Westall and Hohl, 1980), making it difficult to compare results from different experimental studies. Therefore, some method for consistent estimation of model parameters is required. Schindler and Stumm ( 1987) attempted to compare equilibrium constants for surface protonation and organic adsorption reactions with the corresponding reactions in aqueous solution. However, the correlation for surface acidity suggested by Schindler and Stumm ( 1987) is not applicable to silica, a common geological mineral. Hiemstra et al. ( 1989a) developed theoretical correlations between the aqueous acidities of dissolved metals and the physical properties of the system such as the Pauling bond strength per unit bond length. But they had to add correction terms to their correlation in order to apply the correlation to surface protonation. Other workers (e.g., Sprycha and Szczypa, 1987; Sprycha, 1989) have advocated the use of experimental electrokinetic data together with potentiometric titration data for surface protonation and electrolyte adsorption equilibrium constants. However, few studies report complementary surface titration and electrokinetic experiments on the same oxide/electrolyte systems, making it difficult to follow the recommendation of Sprycha and Szczypa ( 1987) and Sprycha ( 1989). There have also been attempts to estimate surface complexation model parameters by consistent analysis experimental surface titration data (Davis et al., 1978; James and Parks, 1982; Dzombak and Morel, 1990; Hayes et al., 1991a). Dzombak and Morel ( 1990) made a comprehensive study of the literature on hydrous ferric oxide, but their study is limited to a single solid phase. Hayes et al. ( 1991a) constrained values of the surface protonation constants by using the definition of the point of zero charge and ApK (see definition below), in conjunction with a sensitivity analysis of surface titration data to establish recommended values for the triple-layer model parameters. But their study was limited to three oxides (rutile, corundum, goethite) in a single electrolyte ( NaNOX) over the range of ionic strengths, M-0.1 M. James and Parks ( 1982) applied the triple-layer model to surface titration data for a number of oxides and electrolytes. Additional data has been published since their work which could extend their analysis and aid in the development of a theoretical model with general predictive capability. Some recent papers in the literature have critiqued the assumptions and performance of the triple-layer model (e.g., Rudzinski et al., 1992; Charmas et al., 1995) and the assumptions made when extracting values of K,,,, Kb,2, KS,M +, and KS,L- from experimental data by the single-extrapolation method (e.g., Sprycha, 1984, 1989; Sprycha and Szczypa, 1984, 1987) (Details of the single-site extrapolation method can be found in Davis et al., 1978 and in James and Parks, 1982). Models with a more complicated, heterogeneous nature of the mineral surface (e.g., Rudzinski et al., 1992) or a more complicated structure of the electrical double layer such as the four-layer models (Bowden et al., 1980; Bousse and Meindl, 1986; Charmas et al., 1995) have been suggested. However, a systematic analysis of a large amount of experimental data has not been reported before suggesting the need for a more complicated model. Clearly, there is a need for a systematic analysis of available surface titration data for a variety of oxides and electrolytes. The main objectives of this study, therefore, are ( 1) to compare experimental surface titration data for a variety of oxides and electrolytes over a wide range of ionic strengths, (2) to compare experimental data for a particular mineral/ electrolyte system from different investigators, and (3) to retrieve an internally consistent set of parameters for the triplelayer model by a systematic analysis of the data. We have chosen to use the triple-layer model because it allows for specific electrolyte adsorption while assuming a less complicated structure of the electric double layer compared to the four-layer models. Thus, the systematic analysis of surface titration data should reveal trends or differences between experimental data and model predictions. The resulting dataset was also used in developing a model for predicting electrolyte adsorption (Sahai and Sverjensky, 1997a). 2. REVIEW OF THE SINGLE-SITE TRIPLE-LAYER MODEL According to the triple-layer model (Yates et al., 1974; Yates, 1975; Davis et al., 1978), protons and hydroxide ions adsorb directly at the surface or O-plane (Fig. l), resulting in surface charge, co (Coulombs. me*). It is assumed that the ions, M+ and L-, of the ML-th electrolyte adsorb at the P-plane, resulting in charge, crii (Coulombs * mm*). To neutralize the overall charge, ( gu + gp), there is a diffuse layer of counterions in the aqueous solution that has a closest distance of approach defined as the d-plane. Associated with each plane of charge are corresponding electric potentials (Volts) $0, Iclu> and (cld. These three layers of charge and potential are modeled as a parallel-plate capacitor of capacitances (Farads. mm2), C, and CZ (Fig. 1). Adsorption is assumed to occur at specific sites on the mineral surface. All sites are considered to be energetically equivalent; that is, the adsorbing species does not prefer any one site over any other. It is further assumed that adsorption at the surface can be described by chemical equilibria analogous to aqueous complexation reactions. For instance, to form the positively charged site, the adsorption of a proton on a generic surface site, >SOH, may be represented by (e.g., Schindler and Stumm, 1987)

3 Evaluation of internally consistent parameters for the triple-layer mode S-A z a-. Compact layer of specifically adsorbed ions of counterions Bulk solution DISTANCE, x (meters) P-plane (M+, L- adsorption) (AlVER WESTALL, 1986) Fig. 1. Schematic representation of potential, I,!I, as a function of distance, x, from the surface according to the triple-layer mode1 (Davis et al., 1978). Protons and hydroxide ions adsorb at the surface or O-plane; electrolyte metal ion (M+) and ligand (L-) are assumed to adsorb at the P-plane. Closest distance of approach of counterions is defined by the d-plane. The three layers of potential separated by intervening regions of dielectric constant t, and tz are modeled as a parallel plate capacitor of capacitances C,, C, (after Westall, 1986). >SOH + H,+, = >SOH: where the equilibrium constant is defined by ( 1) (2) 96,485 Coulombs * mole -, R is the ideal gas constant equal to J*mol- OK-, and T is the absolute temperature ( K). Similarly, adsorption of the electrolyte (M+L-) ions at the P-plane is represented by the reactions >SOH: + Liq = >SOH; - L- (5) and addition of a proton to a negatively charged site is represented by >SO- + H,+, = >SOH where the equilibrium constant is defined by & = a>soh. ~(pj2.303rt ads0-ah,t4 The symbol > signifies that the surface site is attached to the underlying bulk mineral, the subscript aq represents a species in aqueous solution, and aj represents the activity of the j-th species. The power term on the right-hand side of Eqns. 2 and 4 is related to the amount of electrostatic work done in moving the species from bulk solution to the charged surface, where F is Faraday s Constant equal to (3) (4) with corresponding equilibrium constant and KG- = a>soh;ml P~ii/2.3 3RT (6) &SOH;aL; >SO- + Ma, = >SO- - M+ with corresponding equilibrium constant a>som-m+. 1()Fl/Jp3 3R7 GM+ = a,so -amtq where the power term on the right-hand side of Eqns. 6 and 8 is related to the amount of electrostatic work done in moving an ion from bulk solution to the /?-plane, and Gp is (7) (8)

4 2804 N. Sahai and D. A. Sverjensky the potential at the P-plane. Alternatively, adsorption of anion L- can be represented by adding Eqns. 1 and 5 such that >SOH + H,+, + L;s = >SOH: - L- (9) where the corresponding equilibrium constant is defined by F co = - (C,SO& + c>soh;~l - c>.so - c>sc -M ) (15) AC, and charge at the P-plane is given by F mfi = - (C>SO -M - c>soh; -1. ) AC, (16) Charge balance requires that the sum of the charges at the 0-, p-, and d-planes be equal to zero, such that co + 0p + LT<, = 0 (17) and adsorption of cation M can be represented by adding Eqns. 3 and 7 such that >SOH + M:, = >SO- - M+ + H,;, (11) where the corresponding equilibrium constant is defined by By assuming that the mineral-water interface behaves like a parallel-plate capacitor, the electric potential associated with each plane of charge (Fig. I ) is given by 00 = C, ($,o - $0) (18) O</ = CZ(IcId (19) The standard state for the aqueous species is the hypothetical 1 molal solution. The standard state chosen for surface species is a concentration of 1 molal for the adsorbed species and zero surface potential. The reference state for aqueous species is chosen as infinite dilution and, for surface species, the reference state is zero surface potential. This choice of standard and reference states results in electric potentials equal to zero, at the standard state. Note that Hayes and Leckie (1987) used different standard and reference states for aqueous species than the ones defined in the present study. The ratio of the activity coefficients for surface species in reactions represented by Eqns. 2 and 4, 6 and 8, and 10 and 12 are assumed to cancel (Chan et al., 1975). In most studies, aqueous activity coefficients have been calculated using the Davies equation. In the present study, however, we used the Helgeson et al. ( 198 1) version of the extended Debye-Huckel equation which has been calibrated to high ionic strengths (Helgeson et al., 198 1). The site-density, N, (sites * nm-*), determines the maximum concentration of adsorbed species. The total number of sites, Nr (moles. liter- ), is related to the site-density through Nr = N, x A x C, x + x 10 (13) 4 where A is the specific surface area ( m2 * g - ) of the mineral, C, is the concentration (g.l- ) of solid mineral in the aqueous dispersion, NA is Avogadro s number, and the factor lo * converts nm2 to m2. Mass balance on surface sites requires that the total concentration of sites (moles.liter - ) be a constant where C, is the concentration of the j-th species. Surface charge (Coulombs*m~*) is calculated from the concentrations (moles. liter _I ) of the surface species by For a 1: 1 electrolyte, potential (*Cl) and charge (cm) in the diffuse layer are related by Gouy-Chapman theory through (e.g., Sposito, 1984) or, = (8e,c,RTI) * sinh %Z 2RT Thus, seven parameters are required to describe adsorption according to the triple-layer model: the equilibrium constants (K,,,, K,,,, K,,,, KS,,,, t ), the site density (N,), and the capacitances of the inner layer (C, ) and outer layer (C) Equations I-20 can be solved numerically to determine surface and aqueous speciation (e.g., Westall, 1979, 1982; Westall et al., 1976; Papelis et al., 1988; Herbelin and Westall, 1994). In this study, the speciation calculations were performed using the surface and aqueous speciation program GEOSURF (Sahai and Sverjensky, 1997b), which is based on MINEQL (Westall et al., 1976) and HYDRAQL (Papelis et al., 1988). In most studies, the parameters are obtained only by fitting experimental surface titration data, which results in nonunique values for the parameters (Westall and Hohl, 1980). Therefore, it would be useful to have a consistent method for evaluating the triple-layer model parameters from experimental data. Furthermore, it would be useful to have a theoretical model for estimating the parameter-values for systems where experimental data are incomplete or lacking. A new thermodynamic model for predicting electrolyte adsorption based on solvation and electrostatic theory as applied to the triple-layer model has recently been developed (Sahai and Sverjensky, 1997a). The theory permits model parameters to be related to known physical and chemical properties of the mineral/solution system. For example, the equilibrium constant (K,,,) for adsorption of the j-th electrolyte ion (j = M + or L- ) on the k-th mineral surface is related to the inverse dielectric constant of the mineral ( I /Q) by (Sahai and Sverjensky, 1997a) log K,., = ~ ST 1 0 ti + b K::,, (21)

5 Evaluation of internally consistent parameters for the triple-layer model 2805 where Afl, (kcal * mole- ) is the interfacial Born solvation coefficient of the ion, related to the charge and effective electrostatic radius of the adsorbed ion, and log Kii,, is the ion-intrinsic contribution related to the effective electrostatic radius of the aqueous ion. However, in order to determine the values of Anj and KE,,, for a given ion, Eqn. 21 needs to be calibrated on internally-consistent values of log KS,,, obtained from experimental surface titration data. This was an additional motivation for the present study. 3. STRATEGY FOR SYSTEMATIC ANALYSIS OF SURFACE TITRATION DATA The problem at hand is to obtain a consistent set of values for the model parameters in order to calibrate theoretical equations such as Eqn. 21 for predicting Ks.L-, Ks,M+, and C,. Our strategy, then, is to estimate as many triple-layer model parameters as possible independently of surface titration data. As described in detail below, we have estimated values of N, from isotopic-exchange data, KS,, and Ks,2, from the surface protonation model (Sverjensky and Sahai, 1996) and set C, constant at 0.2 F - rn- (Yates, 1975; Davis et al., 1978; James and Parks, 1982). The remaining parameters (&.L- > K,M+ 1 and C, ) will be retrieved by fitting surface titration data. In this paper, we present the consistent method developed for analyzing surface titration data, along with our fits to the data for retrieving values of Ks,L-, Ks,M+, and C, Estimation of Site-Densities All surface complexation models rely on the assumption that ions adsorb at specific sites on the mineral surface. It is generally recognized that mineral surfaces are heterogeneous, i.e., microstructural topography, the termination of bulk crystal structure at the surface, and chemical impurities result in sites that are energetically distinct from each other. There have been some attempts (e.g., Hiemstra et al., 1989a,b; Dzombak and Morel, 1990; Contescu et al., 1993, 1994, 1996; Cemik et al., 1995; Westall, 1995) to model the multi-site nature of surfaces. However, the development of most multi-site models requires a knowledge of all the surface sites present, their distribution and population on relevant crystal faces, and the relative surface areas of these crystal faces for a particular mineral. Such information is rarely available. Therefore, the simplifying assumption is made for most surface complexation models that all surfacesites are energetically identical (i.e., a single-site approach). In order to perform mass balance surface speciation calculations using the triple-layer model, one must know how many sites are available per unit surface area of the mineral (Nh). For the purposes of this study, we consider a surface site to be any atom capable of adsorbing or desorbing a proton. In other words, N, is an estimate of the total number of exchangeable hydrogen atoms on the mineral surface. Attempts to theoretically estimate site-density based on crystal structure (Yates, 1975; James and Parks, 1982, and references therein; Sposito, 1984; Hiemstra et al., 1989b; O Day, 1992; Barron and Torrent, 1996; Koretsky et al., 1997) are hampered by the general lack of information regarding crystallinity, grain size, and morphology of the mineral samples used in most adsorption studies. Realizing the complexity of the problem in estimating site-densities, especially for modeling natural systems, a constant value of N, has been suggested by some workers (e.g., Dzombak and Morel, 1990; Davis and Kent, 1990; Hayes et al., 1991). Dzombak and Morel (1990) suggested a value of 2.31 sites * nm- for hydrous ferric hydroxide, while Davis and Kent ( 1990) and Hayes et al. (1991) suggested values of 2.31 sites/nm-* and 10 sites/nm-*, respectively, for all minerals. This is a pragmatic approach which has the advantage of providing consistency when modeling natural systems. However, we also feel that the value of N, should reflect the crystal structure in some way. Therefore, we have adopted different values of N, for different minerals. Numerous experimental methods have been used to estimate the site-densities for oxides and hydroxides. These include (James and Parks, 1982, and references therein) chemical reactions with various adsorbates (e.g., fluoride adsorption isotherms), acid-base titrations of minerals, weight-loss methods, infra-red and H,O-adsorption/desorption studies, and isotopic (tritium or deuterium) exchange. However, estimates from different techniques have often resulted in quite different values for the same mineral, sometimes differing by almost an order of magnitude. For example, Boehm ( 1971) obtained a value of 4.5 sites/nm* for hematite by chemical reaction whereas Yates ( 1974) obtained 22.4 sites/nm* from isotopic-exchange methods. The method of using chemical reactions with various adsorbates to estimate site-density probably underestimates the total number of exchangeable protons because it determines only the number of sites that are reactive towards the particular adsorbate used in the chemical reaction (James and Parks, 1982; Dzombak and Morel, 1990). Further, the number of reactive sites for each adsorbate would be different, yielding a different value of N, for a single mineral. The use of acid-base titration data for obtaining site-densities is based on the assumption that all the available surface sites are occupied (ionized) by adsorbed of H or OH-. However, most acid-base titrations are not performed at the extreme phs or at high ionic strengths, where ionization of all sites is expected. Therefore, acid-base titrations probably result in underestimating site-density. Even if the titrations were performed at extreme phs, the results of titrations at these extreme phs are of questionable accuracy (Contescu et al., 1996). Acid-base titrations probably also result in underestimates of site-density at low ionic strengths, where only a small fraction of the surface sites is ionized (Dzombak and Morel, 1990). Weight-loss methods involving extensive heating may result in surface restructuring and loss of stoichiometric hydroxyls for minerals such as goethite. Temperature adsorption/desorption studies may be unreliable because the rehydration of a surface is not perfectly reversible (e.g., Berube and de Bruyn, 1968a; Yates, 1975). Such variations resulting from different techniques lead to considerable uncertainty in estimates for site-density. The isotopic-exchange method involving the use of deu-

6 2806 N. Sahai and D. A. Sverjensky terated (e.g., Zhuravlev and Kiselev, 1962; Davydov et al., 1964) or tritiated water (e.g., Berube et al., 1967; Yates, 1975; Yates et al., 1977; Riese, 1982) has been used widely to determine the extent of surface hydration. The extent of H20-D20 exchange between water and DzO-labeled oxide or the extent of H-3H exchange between water and Hlabeled oxide is determined. The result is used to calculate the amount of exchangeable H on the surface. Both methods assume that outgassing for long periods at room temperature removes physically adsorbed water without removing chemically adsorbed water and without causing crystallization of the hydrolyzed layer (Yates, 1975). The method uses the adsorbate of interest (i.e., H) for determining sitedensity in terms of the number of exchangeable protons per unit surface area and yields estimates for N, that do not depend on ph. Further, a recent molecular statics study (Rustad et al., 1996) indicates that there are about sites * nrn-, on average, for the surface of goethite. This value is very close to the value of 16.4 sites - nrn- obtained by tritium-exchange (Yates, 1975). Thus, following Davis et al. ( 1978) and James and Parks ( 1982), we believe that tritium-exchange presents the best experimental estimate for number of exchangeable H. It should be noted that the isotopic-exchange technique, as well as theoretical methods for counting sites based on crystal structures, probably results in maximum values for site-density. We have used values of N, determined by isotopic-exchange where available, as summarized in Table 1. In the case of any mineral where such information was not available, we have estimated the site-density by comparing the crystal structure of the mineral with a mineral of the same or similar structure for which Ns is known by isotopic-exchange. For instance, the site-density for rutile by tritium-exchange is determined as 12.5 sites * nm- (Yates, 1975; Yates et al., 1977). But there is no data for N, by the isotopic exchange method for anatase. Since anatase and rutile are closely related in structure, we have assumed a value of 12.5 sites * nrn-* for anatase. Similarly, hematite has N, equal to 22.0 sitessnm- Table 1. Triple-layer model obtained for the mineral/electrolyte systems included in this study. Values of K,,I and K,,* predicted from experimental ph,,, and from ApK (Eqn. 31). N, from isotopic exchange experiments or estimated (see text). Values of log K&,4, log Kh- and C, obtained by fitting experimental surface titration data. N, (sites. PHWC &K log K\., log K1.2 C, Mineral Electrolyte nme2) iexpt) (pred.) (talc.) (talc.) log K$,,* log KzL- log KI,M- log Kqy (F.m- ) Anatase Anatase Anatase Hematiteb Hematite Hematite Hematit& Hematite Goethite Goethite Rut@ Rut&? Rutile Rutileh Rutile Am. Silica (Ludoxy Am. Silica (Degussa Aerosil) Am. Silica (Degussa Aerosil) Am. Silica (Pyrogenic CAB-O-XL) Am. Silica (Pyrogenic CAB-0-SIL) Am. Silica (Pyrogenic CAB-0-SIL) Am. Silica (B. D. H. ppted)b Magnetite &MnO, (IC12) CorundumP y-aluminaq,, y-aluminay LiCl NaCl NaI KNOl KNO3 LiCl CsCl NaCl NaC104 NaCl LiN03 KNO, KNO3 Nai% NaClO, NaCl NaCl NaC104 KC1 LiCl CsCl KNO? KN03 LiNOi NaNO? KNOX CsNOx NaIW NaCl NaCl I X I i PO t f f t il f il I I I * 0.8 * 1.oo * 0.6 * 0.95 * 0.9 * I.50 * 1.3 * 1.20 * 1.1 * 1.30 * 1.4 * I.55 * 0.9 * * 3.86 * 1.60 * 3.56 * I.30 * 3.26 * 1.10 * 3.06 * s.o Sources of surface titration data: Sprycha (1984), byates (1975), Fokkink (1987), dbreeusma (1973), Liang (1988), Van Geen et al. (1994), glumsdon and Evans (1994), hberube and de Bruyn (1968a), Berube and de Bruyn (1968b), Bolt (1957), Casey (1994), Brady (1992). Abendroth (1970). Blesa et al. (1984), Tamura et al. (1996), PHayes et al. (199la), qhuang (1971), Huang and Stumm (1973), James and Parks (1982), estimate from crystal structure, this study, H-exchange (Yates, 1975; Yates et al., 1977), 3H-exchange (Zhuravlev and Kiselev, 1962; Davydov, 1964; Madeley and Richmond, 1972), Infra-red method (Peri, 1966), Svejensky and Sahai (1996), %prycha (1989) * See caveat in text regarding K*,Lm for amorphous silica, quartz and 6-MnO*.

7 Evaluation of internally consistent parameters for the triple-layer model 2807 (Yates, 1975)) which we have assumed also holds for corundum because hematite and corundum are isostructural. It should be noted that A13+ in corundum has a somewhat different size than Fe3+ in hematite so that the unit cells of the two minerals are of slightly different dimensions. This implies that the site-density of two isostructural minerals is, actually, slightly different. However, the difference is assumed to be small and we have neglected such differences Estimation of Surface Protonation Equilibrium Constants According to Eqns. 2,4, and 15, surface charge associated with proton adsorption can be described completely by two surface protonation constants, KS,, and Ks,2. The sum of these two constants is related to an important physical property of the mineral, the ph of the pristine point of zero charge (~Hprzc) given by ~Hrrzc = 0.5 (log KS.2 + log KS.2 1 = lois & (22) which corresponds to the equilibrium >SOH + 2H,+, = >SOH; (23) where, at the point of zero surface charge (Sverjensky and Sahai, 1996), Kz = a>soh: a>s0sq (24) The difference between the surface protonation constants is defined as which corresponds ApK = log K,, = (log Ks,2 - log KS,,) to the equilibrium (25) >SO- + >SOH: =2>SOH (26) where (Sverjensky and Sahai, 1996) K,, = &.soe a>so-a>soh: (27) From Eqns , it is apparent that if we can find a way to estimate (phppzc) and ApK, then we can solve Eqns. 22 and 25 for KS,, and Ks,2. A model for predicting phppzc and ApK from physical and chemical properties of the system has been developed in Sverjensky and Sahai ( 1996). Here, we will only summarize briefly the main relationships developed in the Sverjensky and Sahai (1996) model for estimating surface protonation constants. By combining the Born solvation theory for surfaces first proposed by James and Healy ( 1972) and the electrostatic theory of Parks (1965, 1967) and Yoon et al. (1979), Sverjensky ( 1994) showed that the (phppzc) can be estimated from the inverse dielectric constant of the mineral ( l/ck) and from the Pauling bond strength per unit bond length ( s/r,s.oe) (A) of the central metal cation in the metal oxide according to (Sverjensky, 1994) ~Hppzc = -0.5(&#) -BZ i s r>s-oh > + log K;;+,z (28) where AR,,, Bz, and Kh+,= are assumed to be constants for all solids and are characteristic of Eqn. 28 (Sverjensky, 1994; Sverjensky and Sahai, 1996). An2,, is the interfacial Born solvation coefficient and is related to the contribution from solvation to the free energy of surface protonation. Bz is an electrostatic constant, and Kk+,z is related to the ion-intrinsic contribution. ck represents the dielectric constant of the k-th solid. The equation was calibrated using experimental points of zero charge from the literature (Bolt, 1957; Parks, 1965, 1967; Tewari and Campbell, 1976; Evans et al., 1979; Balistrieri and Murray, 1982; Sprycha, 1982; Blesa et al., 1984; Hiemstra et al., 1987; Carrol-Webb and Walther, 1988; Zeltner and Anderson, 1988; Davis and Kent, 1990; Wogelius and Walther, 199 1; Blum and Lasaga, 1991) resulting in (Sverjensky and Sahai, 1996) = (d) (k) (29) It should be noted that the values reported in the literature for the points of zero charge are usually the common intersection point of titration curves at different ionic strengths or are the isoelectric points from electrophoretic mobility measurements. As pointed out by Lutzenkirchen et al. ( 1995), in principle, the use of the common intersection point as the value for the phppzc is inconsistent with the definition of the phppzc (Eqn. 22). However, in practice, we are limited by the experimental difficulty of measuring a true pristine point of zero charge, which would be the point of zero charge if the electrolyte ions were not specifically adsorbing. The important point is that, in principle, the phppzc can be obtained from Eqn. 29. Using solvation and electrostatic theory, Sverjensky and Sahai ( 1996) have also shown that the difference between the protonation constants ( ApK) can be related to the dielectric constant of the mineral and to the s/r term, according to where AR,,, B,, and KL+,n are characteristic of Eqn. 30 (Sverjensky and Sahai, 1996) and defined analogously to the corresponding terms in Eqn. 28. Values of ApK used in calibrating Eqn. 30 were taken from Davis et al. (1978), resulting in (Sverjensky and Sahai, 1996) ApK = s (31) ( Y>S-OH > From Eqn. 30, it is expected that ApK be a function of both 1 /cl and s/r,s_oh. The actual calibration of the equation however (see Eqn. 3 1) shows that ApK appears to be inde-

8 2808 N. Sahai and D. A. Sverjensky pendent of et and is a function of s/r,s_or, alone. (Eqn. 31). It is possible that the difference in solvation for the species in the reaction of Eqn. 26 (surface species only) is not significant compared to reactions involving both aqueous and surface species such as Eqn. 23 (Sverjensky and Sahai, 1996). The reader is referred to Sverjensky and Sahai ( 1996) for a complete description of the assumptions made in and the theoretical and physical underpinings of Eqns Here, we only point out that the values of ApK used in calibrating Eqn. 30 and resulting in Eqn. 31 were obtained from values of KS,, and KS,* obtained by Davis by the singleextrapolation method (Davis et al., 1978; James and Parks, 1982). Sprycha and Szczypa (1984, 1987) indicate that in the presence of specific adsorption, the single extrapolation technique may result in inaccurate values of KS,, and Ks,2. These authors advocate the use of electrokinetic data in addition to surface titration data for determining adsorption constants. Although, in principle, we agree with Sprycha and Szczypa ( 1984, 1987) that data from different experimental techniques should be analyzed, there are very few studies in the literature where both electrokinetic and surface titration experiments were performed for the same mineral/solution system. Therefore, lacking better experimental means of determining accurate values of ApK, we believe that Eqn. 31 can be used in conjunction with values of phppzc for calculating surface protonation constants. In contrast to other attempts at relating surface protonation equilibrium constants with corresponding aqueous complexation constants (e.g., Schindler and Stumm, 1987; Hiemstra et al., 1989b), the surface prototontion model of Sverjensky and Sahai (1996) predicts KS,, and Ksk2 based on the properties (dielectric constant and Pauling bond strength per unit bond length) of the bulk mineral alone. Note that in the present study, we have used experimental points of zero charge (rather then the values predicted by Eqn. 29) in conjunction with predicted values of ApK (Sverjensky and Sahai, 1996) to obtain surface protonation constants (see below ) 4. ANALYSIS OF SURFACE TITRATION DATA FOR RETRIEVING INTERNALLY CONSISTENT VALUES OF &,+, Ks,~m, AND Cr The next step is to analyze surface titration data on a variety of mineral/electrolyte systems in a consistent manner. Since the studies of Davis et al. (1978) and James and Parks ( 1982), attempts to analyze the published results of surface titration experiments have been severely hampered by a lack of tabulated experimental surface titration data that would facilitate comparisons between different minerals and different investigators. With a few exceptions, most researchers have provided only graphical display of their results of surface titrations. Consequently, in the present study, surface titration data were retrieved from graphs in the literature using a CALCOMP 9000 digitizer. Surface titration data for hematite in LiCl and CsCl (Breeusma, 1973) and for 5- MnOl in the alkali nitrates (Tamura et al., 1996) were retrieved manually. The only data tabulated in the original papers were for amorphous silica in NaCl (Bolt, 1957) and for goethite in NaClO, (Van Geen et al., 1994); D. G. Lums- don and L. J. Evans (pers. commun.) kindly provided us with their original data for goethite in NaCl (Lumsdon and Evans, 1994). Hayes et al. (1991a) surface titration data for corundum in NaN03 were provided by David Ward (pers. commun.). For the convenience of future researchers, we have tabulated the digitized data used in the present study in an appendix to this paper. In choosing the sets of data, we have tried to include a wide variety of oxides, electrolytes, and ionic strengths that would enable comparison and theoretical analysis of the results. Also, because of the range of minerals, electrolyte, and ionic strengths analyzed, the results from this paper can be used in calibrating a theoretical model for electrolyte adsorption (Sahai and Sverjensky, 1997a). In some cases, we were able to find and include surface titration data for the same mineral/electrolyte system from different workers (e.g., hematite and rutile in KN03 from both Yates, 1975, and Fokkink, 1987; silica in NaCl from Bolt, 1957, and (a) 0.2 B.E.T. = l6rn*.g- ; solid cont. = 20 &I- Experimental data: spycha (1984) Best fit curves: this study -01 in - (a) AxL&&Cl 1 (b) -.- * n 0.2 I-.. (b) AnataseMaCl 4 --._ - 5. _ M 0 67 i si t? -0.2 :a+$$ O.OlM --.. BET.= 16 m2.gs1; solid cow.= 20 g.l-1. Expenmenlal data: Sprycha (1984) Best lit CUNES: this study -0.4 w P B.E.T. = 16 m*.gl: solid cont. = 20 g.l- Experimental data: Sprycha (1984) Best fit curves: this study Fig. 2. Model fit (curves) to surface titration data (symbols) on anatase (Sprycha, 1984) in M to 0.1 M (a) LiCl (b) NaCl (c) NaI log K,,, = C2.8, log K,,* = +9.2, N, = 12.5 sites*nm-, estimated; C, = 0.2 F. m-*. Data are fit for values of K$_-, K,*M+, and Cl. PH

9 Evaluation of internally consistent parameters for the triple-layer model 2809 ( w 0.25 O.OOlM (c) Hematite/LiCI B.E.T. = 32 g-, sohd cont. = 20 g.l- Ex~&~~~ental data: Yates (1975) Best lit curvw this study B.E.T. = 34 n&g-, solid cont. = 10 g.le Experimental data: Breeusma (1973) Best fit curves: this study PH (W (d) HematiWCsCI B.E.T. = 29 rn2.g-, solid cont. = 20 g.l B.E.T. = 34 m2.g-l, solid cont. = 10 g.le Experimenti dam: Brewsma (1973) Best 81 curves: this study I PH ( M (e) HemdWhkCI &- k e a" B.E.T. = 80 m2.g., s&d cow. = IO g.l- t I Experimental data: Liang (1988) Best tit curves: lhis studv -1 I PB Fig. 3. Model fit (curves) to surface titration data (symbols) on hematite in (a) M to 0.1 M KNOz (Yates, 1975), (b) M to 0.2 M KN03 (Fokkink, 1987), (c) M to 0.1 M LiCl (Breeusma, 1973), (d) M to 0.1 M CsCl (Breeusma, 1973), and (e) M to 0. I M NaCl (Liang, 1988). Filled symbols for forward titrations, empty symbols for backward titrations. For (a) and (e), log IV,,, and log K,.? equal to +5.7 and , respectively; for (b), log K,,, and log K,,, equal to +6.0 and , respectively; for (c) and (d), log K,,, and log K,,> equal to +5.6 and , respectively; NS is nm -, from H-exchange experiments (Yates, 1975); C? = 0.2 F.rn-. Data are fit for values of K,T,-, K&+, and C,. Casey, 1994; silica in NaC104 from Brady, 1992, and Schindler and Kamber, 1968). Data for silica from Bolt (1957) and Abendroth ( 1970) and data for rutile from Yates ( 1975) were also fitted by Davis et al. ( 1978)) whose values for ApK have been used in calibrating our model for surface protonation (see section 3.2, and Svetjensky and Sahai, 1996). The following sets of data were fitted-anatase in M to 0.1 M LiC1, NaCI, NaI (Fig. 2a,b,c) (Sprycha, 1984); hematite in M to 0.1 M KNOl (Yates, 1975) (Fig. 3a), hematite in M to 0.2 M KNOX (Fokkink, 1987) (Fig. 3b), hematite in M to 0.1 M LiCl (Breeusma, 1973) (Fig. 3c) and in 0.01 M to 1.0 M CsCl (Breeusma, 1973) (Fig. 3d), hematite in M to 0.1 M NaCl (Liang, 1988) (Fig. 3e); goethite in 0.01 M to 0.1 M NaC104 (Van Geen et al., 1994) (Fig. 4a) and in M to 0.1 M NaCl (Lumsdon and Evans, 1994) (Fig. 4b); t-utile in M to 1.0 M LiNO? (Yates, 1975) (Fig. 5a) and in KNOl from M-2.9 M KNOX (Yates, 1975) (Fig. 5b), rutile in M to 0.2 M KNO? (Fokkink, 1987) (Fig. 5c), rutile in M to 2.0 MNaNO? (Berube and de Bruyn, 1968b)

10 2810 N. Sahai and D. A. Sverjensky b-4 (W T. = 45 n12.g~~. solid cone. IO g.l-1 rimenlal data: Van Geen et al. (1994) PH O.lM (b) GocthiteMaCl B.E.T.= 86 m2.g1, solid cont.= 10 g.1. Experimental data: Lumson and Evans (1994) Best tit cuves: Uds study PH Fig. 4. Model fit (curves) to surface titration data (symbols) on goethite in (a) 0.01 M to 0.1 M NaClO, (Van Geen et al., 1994); log K,.I and log K>.?, equal to and +I 1.71, respectively, and (b) M to 0.1 M NaCl (Lumsdon and Evans, 1994); log K,,, and log K,,* equal to +6.3 and -11.9, respectively. N, = 16.4 sites * nrn-, from %exchange experiments (Yates, 1975); Cz = 0.2 F. m-* Data are fit for values of KTL-, K&, +, and C I. retrieved by fitting the data. Also included in Figs. 2-8 are the B.E.T. surface areas and the solid concentration of the mineral samples as reported in the original source of the experimental data. In some cases where the solid concentration was not reported in the original source, we have used an assumed value. Additional surface titration data for corundum in KC1 (Yopps and Furstenau, 1964) and in NaN03 (Carroll, 1989), silica in M NaCl (Bolt, 1957)) hematite in 1.0 M LiCl (Breeusma, 1973 ), natural cassiterite in KN03 (Ahmed and Maksimov, 1969), natural quartz in 1.O M KN03 (Ahmed, 1966), natural quartz in NaNOX (Riese, 1982), and natural quartz in KCI-NaOH (House and Orr, 1992) were also retrieved digitally but are not included in this study for the following reasons. Titration data for corundum from Yopps and Furstenau (1964) could not be used because they did not report a value for BET surface area for their sample. Additional data for corundum (Carroll, 1989) could not be analyzed because the data show two common intersection points and the accuracy of the data is in question (S. A. Carroll, pers. commun.). Bolt s data for amorphous silica at the lowest ionic strength ( MNaCl) is probably inaccurate due to changes in ionic strength upon addition of titrant (Kent et al., 1986). In the case of hematite titration in LiCl (Breeusma, 1973), a common intersection point was obtained at ph 8.5 for the titration curves at 0.01 M and 0.1 M; however, the titration curve at 1.0 M does not have a common intersection point with the curves at the other ionic strengths, and the triple-layer model was unable to produce a good fit to the data. Therefore, we have disregarded the data at 1.0 M LiCl for further analysis. We also analyzed surface titration for natural cassiterite in KNOX ( Ahmed and Maksimov, 1969) and natural quartz in 1.O MKNOJ (Ahmed, 1966), but the triple-layer model does not fit the data well. Therefore, these data were excluded from further analysis in this study. For these two cases of cassiterite (Ahmed and Maksimov, 1969) and quartz ( Ahmed, 1966)) the possible reasons for the discrepancy between data and model fits are the presence of some major impurity in the sample, inaccurate data, or inadequacy of the triple-layer model. Given the success of the triple-layer model in the literature as well as in the present study (Figs. 2-8), we believe that the first two reasons are probably responsible for the cases where the model fits to experimental data are unsatisfactory. Titration curves at different ionic strengths for natural quartz in NaNOz (Riese, 1982) apparently intersect at more than one point. Therefore, we believe that this dataset is inaccurate and have not included it in our analysis. House and Orr ( 1992) used KC1 as their swamping electrolyte, but they used NaOH to adjust ph so that the resulting solution was a mixture of Na- and K-electrolytes. Our study does not account for mixed electrolyte systems. Therefore, we have not used the House and Orr ( 1992) data for quartz. (Fig. 5d), and rutile in M to 1.0 M NaClO, (Berube and de Bruyn, 1968a) (Fig. 5e); amorphous silica (Ludox) in 0.01 M to 1.O M NaCl (Bolt, 1957) (Fig. 6a), amorphous silica (Degussa aerosil) in 0.01 M to I.O M NaCl (Casey, 1994) (Fig. 6b), amorphous silica (Degussa aerosil) in 1.0 M NaCIO, (Brady, 1992) and 0.1 M NaClO, (Schindler and Kamber, 1968) (Fig. 6c), amorphous silica (pyrogenic, CAB-0-SIL M7) in M to 0.1 M KC1 (Abendroth, 1970) (Fig. 6d) and in 0.1 LiCl and 0.1 MCsCl ( Abendroth, 1970) (Fig. 6e), amorphous silica (B. D. H. precipitated) in 0.1 KN03 (Yates, 1975) (Fig. 6f); natural quartz (Minu-sil) in molal to 1.O molal NaCl (Riese, 1982) (Fig. 7a); magnetite in M to 1.0 MKNO-( (Blesa et al., 1984) (Fig. 7b) and 6-Mn02 in 0.1 M LiN03, NaN03, KNOX, and CsN03 (Fig. 7~); corundum in NaNOX (Hayes et al., 1991) (Fig. 8a); y-alumina in M to 0.1 M NaCl (Huang, 1971; Huang and Stumm, 1973; Sprycha, 1989) (Figs. 8b) and y-alumina in M to 1.0 M NaCl (Sprycha, 1989) (Fig. 8~). The optimized set of parameters for each mineral/electro- Finally, we would like to point out that in some of the lyte system are reported in Table 1, and the corresponding following analyses of experimental titration data, the values fits to experimental data are shown in Figs Note that for electrolyte adsorption constants and inner-layer capaciin Figs. 2-8, we have shown the values of the logarithm of tances were obtained from studies where data for only one the adsorption constant for each electrolyte cation and anion ionic strength was reported (e.g., pyrogenic silica in 0.1 M as defined by Eqns. 10 and 12 and the inner-layer capacitance LiCl, Aerosil silica in 1.O M NaC104, B. D. H. precipitated

11 Evaluation of internally consistent parameters for the triple-layer model 2811 (a) Ct = 1.25 F.m-2 10gK ~, K+ = -6.2.losK*,. NO.,- = 4.8 B.E.T. = 51.0 rn*.g-l, solid cont. = g.l- Experimental data: F&kink ( 1987) Best tit curves: this study 0.005M (d) OM PH (d) RutilhaNO3 B.E.T. = 43.0 m2.g. solid cont. = g.1. Experimental data: Beruk & d+z Bnqn (1968a) O.OOlM (e) 0.2 (e) RutiWNaClO C, = 1.45 F.II-~ logk s, = -6.6.logK*,, C,04- = 4.6 L? 0 k G t? -0.2 r -0.4 B.E.T. = 43.0 m2.g.i, solid cant. = 20.0 g.~- 0.03M 1 Experimental data: Bemk and de Bmyn (1%8b) 1.0M Best tit curves: this study Fig. 5. Model fit (curves) to surface titration data (symbols) on mtile in (a) M to 1.0 M LiNO? (Yates, 1975), (b) M to 2.9 M KNO, (Yates, 1975), (c) M to 0.2 M KN09 (Fokkink, 1987); for (a), (b), (c), and (d), log K,,, and log Ks,2 are equal to +2.6 and +9.0, respectively; (d) Or001 M to 2.0 M NaNO, (Berube and de Bruyn, 1968a) and (e) M to 1.0 M NaC104 (Berube and de Bruyn, 1968a); for (e), log KS,, and log K,,2 are equal to +2.7 and +9.1, respectively. Filled symbols for forward titrations, empty symbols for backward titrations. N, = nm-*, from H-exchange experiments (Yates, 1975); C, = 0.2 F. mm. Data are fit for values of K,T,-, K&+, and C,. PH silica in 0.1 M KN03, and 6-Mn02 in 0.1 M LiN03, NaN03, KNO,, and CsNO-,). Therefore, the accuracy of the retrieved values of Ks,M +, Ks,L-, and Ci for these cases is probably less than that for the cases where data were available at more than one ionic strength. All triple-layer model surface speciation calculations reported here were performed using the computer program, GEOSURF (Sahai and Sverjensky, 1997b), which is based on MINEQL (Westall, 1976) and HYDRAQL (Papelis et al., 1988). In most studies, the errors on the measured surface charge and ph are not reported. Therefore, we did not consider it essential to base the algorithm in GEOSURF on an optimization routine such as FITEQL (Westall, 1982; Herbelin and Westall, 1994), so that the fits in Figs. 2-8 are estimated by eye only. GEOSURF has the following distinguishing features: ( 1) the extended Debye-Huckel equation (Helgeson et al., 198 1) is used for calculating aqueous activity coefficients which has been calibrated to high ionic strengths ( >0.5 M) (Helgeson et al., 1981). This allows us to perform surface and aqueous speciation calculations over a wide range of ionic strengths (0.001 M-2.9 M) (2) GEOSURF is linked to two separate thermodynamic databases for aqueous and surface species. The data file for surface species contains the results of our fits to titration