The titration of clay minerals

Journal of Colloid and Interface Science 273 (2004) 234–246 www.elsevier.com/locate/jcis

The titration of clay minerals II. Structure-based model and implications for clay reactivity Christophe Tournassat,a,b,∗ Eric Ferrage,a,b Christiane Poinsignon,c and Laurent Charlet a a LGIT-CNRS/UJF, University of Grenoble-I, P.O. Box 53, 38041 Grenoble, France b ANDRA, Parc de la Croix Blanche, 1/7 rue Jean Monnet, 92298 Châtenay-Malabry cedex, France c LEPMI-ENSEEG, University of Grenoble-I, P.O. Box 75, 38041 Grenoble, France

Received 10 July 2003; accepted 7 November 2003

Abstract The potentiometric titration and CEC data presented in part I are modeled in this paper, part II. Two models are compared: the two pK, three complexation sites plus exchange sites nonelectrostatic model developed by Baeyens and Bradbury and a model based on the MUSIC approach developed by Hiemstra and Van Riemsdijk. Both morphological and structural information is used to develop this new model. Morphological information is taken from the literature, while structural information is taken from the literature and constrained by supporting FTIR experiments. The Baeyens and Bradbury model is found to reproduce the general tendency of the titration curve, whereas the model based on the Hiemstra and Van Riemsdijk MUSIC approach provides a better fit to the experimental data. The former uses only 3 edge reaction sites, whereas the latter uses at least 27 edge reaction sites. Five main reactive sites are sufficient to fit the MUSIC model curve, but the model allows us to derive the properties of 22 other reactive sites. Logically, the greater the number of sites, the better the fit. Nevertheless, fewer adjustable parameters are necessary for the Hiemstra and Van Riemsdijk MUSIC model than for the Baeyens and Bradbury model, thanks to structural and morphological constraints. The precision of the potentiometric titration curve is insufficient to verify that the properties of the 27 sites given by the MUSIC model are effective. Thus, we coupled some properties of clay minerals, such as dissolution, to the modeled acid–base properties of these sites to assess our model. We then questioned the ability of simplified models such as the Baeyens and Bradbury model to predict the interactions between clay minerals and solutions in natural environments. In addition, we derived the cation exchange selectivity coefficients for CaCl+ ionic pairs and H+ from our CEC data and gave an estimate for the CaOH+ selectivity coefficient.  2003 Elsevier Inc. All rights reserved.

1. Introduction Sorption mechanisms on clay surfaces have been studied for decades. One distinguishes between (i) inorganic cation exchange in the interlayer and on basal plane surfaces [1] and (ii) specific pH-dependent sorption of cations and anions on the clay edges [2]. The edge sorption mechanism is a pH-dependent specific sorption on the clay edges [3–9]. It has already been well established that the proton surface charge density (σH ) on the clay edges depends on the physicochemical solution parameters (pH, ionic strength), which control the protonation state of the surface [3–9]. In contrast, * Corresponding author. Present address: BRGM, B.P. 6009, 3, avenue Claude Guillemin, 45060 Orléans cedex 2, France. E-mail address: [email protected] (C. Tournassat).

0021-9797/$ – see front matter  2003 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2003.11.022

cation exchange on basal planes is related to the permanent negative charge generated in the clay structure created by isomorphic substitutions in the lattice [1]. The density of exchange sites (σ0 ) can be derived from the structural formula, and is compensated for by “exchangeable cations,” which generally form outer sphere complexes in siloxane cavities [1,2]. In part I [10], we presented Na- and Ca-MX80 montmorillonite surface charge data obtained by combining potentiometric backtitration technique [7,11,12] with cation exchange capacity (CEC) measurements [13]. This is a powerful combination, as it can be used to identify each phenomenon that contributes to surface charge as a whole: dissolution processes, variations of the net proton edge surface charge, cation and proton exchange mechanisms, adsorption of ionic pairs, and precipitation of new phases.

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In the present paper (part II), we propose two models for the surface charge data. The first approach is a macroscopic surface complexation model [8]. The second is based on the bond valence principle (MUSIC, [14]). The first model is an empirical model, developed by fitting together titration and metal sorption data, the quality criterion being the best agreement between model and experimental data. The MUSIC model uses morphological and structural data to derive chemical properties of the solid. However, even with this more sophisticated approach, assumptions (e.g., on cation distribution) are necessary to build the surface clay chemical model. Supporting information obtained with Fourier transform infrared (FTIR) experiments help constrain these assumptions.

2. Structural input from FTIR measurements 2.1. Theoretical background Some sites present within the structure are a priori able to exhibit acid–base properties, as will be shown below, based on their affinity for protons. However, diffusion of H+ through the siloxane plane is doubtful. Hence, the first goal of the FTIR experiments was to refute the possible fast proton sorption within the clay structure and thus show that fast proton sorption occurs only on edge surfaces. Deuterium atoms (D, hydrogen isotope of atomic mass equal to 2) have the same chemical properties as hydrogen atoms. The use of D2 O for hydrothermal synthesis is a common method for identifying the IR absorption bands in clay minerals such as talc by the conversion of some, or all, of the OH groups to OD groups [15–21]. When D replaces H, the difference in atomic mass induces a shift of all vibrations of the OH groups toward lower wavenumbers by a factor R, close to 1.37 [22]. The deuterated OD stretching bands are present in the 2800–2500 cm−1 region. In the case of clay minerals, the degree of H–D exchange can easily be determined, since this region of the spectrum is free of other structural vibrations. In the present work, we apply the same technique to smectite to see whether D+ (and hence H+ ) diffuses into the mineral structure at 25 ◦ C. The second goal of the FTIR experiments was to learn more about the cation distribution inside the octahedral layer. The 950–750 cm−1 wavenumber range OH-bending region gives information on the cation distribution occurring in the octahedral layer [23]. By quantifying the area of the bands corresponding to the replacement of Al by Mg or Fe, it is possible to know if the cation distribution is ordered, random, or clustered. The procedure of Besson and Drits [24] was applied here to fit the OH-bending bands: the components were extracted, as pure Lorentzian curves, from the total curve together with the background. The bands deconvolution program uses a conjugated-gradient fitting procedure, taking into account Gaussian and Lorentzian functions.

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2.2. Preparation of the sample and measurement A Na-conditioned smectite was equilibrated for 90 days with a 40% D2 O, 60% H2 O, 0.01 mol l−1 NaCl solution, at 25 ◦ C. A 1-ml aliquot of suspension was deposited on a circular silicon support (25 × 2 mm, Eurolabo reference 1840) and was allowed to dry at room temperature. FTIR spectra of the clay film on support and support alone were recorded using a Nicolet 710 FTIR spectrometer (128 scans in the 4000–400 cm−1 domain, with a 4 cm−1 resolution). Spectra of the clay film were obtained by subtracting the support signal from the total signal. 2.3. Results Fig. 1 shows the results of the FTIR experiments. Characteristic deformation bands for montmorillonite can be seen in the region 1100–800 cm−1 [25]. Impurities of quartz are also visible (arrow on Fig. 1). The 3800–3200 cm−1 wavenumber region exhibits a single band relative to (Me1 Me2 )OH stretching vibration, where Me1 and Me2 denote octahedral cations (Al3+ , Mg2+ , Fe3+ , and Fe2+ ). This region is almost free from OH vibration of interlayer water, meaning that most of the water has evaporated. Therefore, OD vibration bands of interlayer deuterated water cannot overlap with the OD stretching bands characteristic of inner surface hydroxyl groups. While the (Me1 Me2 )OH stretching bands are usually observed at 3633 cm−1 , we did not observe any peak corresponding to the deuteration

Fig. 1. Transmission IR spectra of Na–D2 O-conditioned MX80 montmorillonite at 25 ◦ C using a silicon support (see text for details). Top: spectrum in the range 4000–400 cm−1 . Bottom: zoom on the OH stretching region (3700–3500 cm−1 ) and on the OD stretching region (3000–2500 cm−1 ). The arrow indicates the presence of quartz impurities.

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Fig. 2. Thick line: transmission IR spectrum of Na-conditioned MX80 montmorillonite in the OH-bending range (980–750 cm−1 ). Thin lines: decomposition of the spectrum (see text for details).

of the (Me1 Me2 )OD stretching bands in the region 2800– 2500 cm−1 . Hence, we can conclude that little H+ /D+ diffusion into the bulk of the smectite structure occurs at 25 ◦ C, and that (within 90 days reaction time) clay protonation does not involve structural smectite protons. This agrees with previous studies; on talc, for instance, H+ does not diffuse perpendicularly into the basal planes [26]. Based on these results, we used only surface reactions to explain the smectite titration data detailed in part I. Fig. 2 shows the deconvolution of the 950–750 cm−1 wavenumber region. As expected, three main bending bands are present (δAlAlOH, δAlFeOH , and δAlMgOH ) based on the structural formula of MX80 smectite clay [10]: 2+ (Si3.98 Al0.02 )(Al1.61 Fe3+ 0.13 Fe0.02 Mg0.24 )O10 (OH)2 Na0.28 .

Once the background was removed, the spectrum was fitted with three bending bands in the region 950–820 cm−1 corresponding to δAlAlOH (∼919 cm−1 ), δAlFeOH (∼882 cm−1 ), and δAlMgOH (∼848 cm−1 ). These vibration positions are in good agreement with those given by Vantelon et al. [23] for similar smectites. The position of the δAlFeOH band agrees well with the band position given for montmorillonite by Craciun [27] as a function of Fe content (calculated value

at 883 cm−1 ). Bands at 799 and 780 cm−1 are attributed to quartz [25]. Other bending bands, such as δAlFeIIOH and δMgMgOH bands, were not detected here due to low Fe(II) and Mg(II) content in the MX80 smectite octahedral layer. The areas under the δAlAlOH, δAlFeOH , and δAlMgOH bands are compared in Fig. 3 to theoretical areas, calculated on the basis of (i) the above structural formula, (ii) the assumed cation random distribution in the octahedral layer, and (iii) an assumed invariant absorption coefficient for the different OH groups [23–25,28,29]. For example, the δAlAlOH band should represent (1.61/2) × (1.61/2) × 100 = 64.8% of the total absorbance area. Fig. 3 shows how experimental points lie on the line corresponding to a random distribution. According to this result, the distribution of Al, Fe, and Mg cations within the octahedral layer is a near-random distribution. In the following section, this information is used to calculate the proportion of each edge surface functional group.

3. Modeling the titration data 3.1. Common mechanisms and code Two modeling approaches are compared in the present section. The first one is the macroscopic surface complexation model from Bradbury and Baeyens [8]. The second one is a model based on mineral structure and bond valence principle, according to the MUSIC approach [14]. Because proton uptake within the clay structure is not occurring even after 90 days, we considered only two proton sorption mechanisms: cation exchange on the basal/interlayer planes and specific sorption on clay edges. The electrostatic term is neglected, since proton surface charge density is independent of background ionic strength, as demonstrated in part I of this paper. Note that the absolute position of the titration curves is not known [10]. The titration data are therefore presented as H+ as a function of pH, H+ = H+ + A,

(1)

Fig. 3. Relative areas of the various OH-bending band contributions as a function of the theoretical areas derived from assuming a fully random distribution and schematic representation of cation distribution in the octahedral sheet [23],.(!) δAlAlOH , (1) δAlFeOH , (P) δAlMgOH .

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where H+ is the surface proton excess given by Eq. (3) in part I, and A is a constant. In the following section, we describe how we modeled H+ . A was assumed to be an adjustable parameter. A was chosen to ensure a best fit between the simulation and the experimental results. The Phreeqc2 code [30] was used for both approaches, as this versatile computer code is amenable to the various conventions used to describe cation exchange and surface complexation. The Llnl.dat [30] database was used to calculate the speciation in solution. 3.2. Bradbury and Baeyens model Simulation parameters used in this study are close to those used in the original study to describe titration data of saturated Na-montmorillonite [8]. Few parameters were changed with respect to cation exchange. We adjusted the CEC value to our theoretical value [10], which takes into account the stoichiometry of the clay and the dehydrated suspended clay concentration (0.76 eq kg−1 ). Table 1 summarizes these parameters. Vanselow’s convention was used to model cation exchange [31,32]. Cation exchange selectivity coefficients were fitted to our Na- and Ca-CEC data and to the CEC data previously published by Sposito et al. [13]. Table 1 Site types and sites capacities used in the simulation, based on the Bradbury and Baeyens model [8] Site types

Site capacities 2 × 10−3 mol kg−1a 4 × 10−2 mol kg−1a 4 × 10−2 mol kg−1a 0.76 eq kg−1b

Strong sites (≡Ss OH) Weak sites 1 (≡Sw1 OH) Weak sites 2 (≡Sw2 OH) Cation exchange sites (X− )

a Fixed. b Adjusted to the theoretical structural CEC value [10].

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The cation exchange of ion pairs such as CaCl+ and CaOH+ agrees well with Sposito et al. [13] and with results presented in part I [10]. 3.3. Hiemstra and Van Riemsdijk MUSIC model In the MUSIC model, the proton affinity of a surface group is calculated from the fractional charge of a surface oxygen and from the bond valence of all its ligands [14,33]. Initially created to model simple oxides such as quartz, alumina, titanium oxides, or iron (hydr)oxides [34,35], the MUSIC model has been refined several times [14,33,35,36]. In this study, we applied the updated version [14,33] to complex oxides, namely clay minerals. Proton affinity was computed using the formula [14]
  log K = −A (2) sj + V , j

where A is a constant set to +19.8 [14], V is the valence of the oxygen atom (V = −2), and j sj is the sum of all bond valences of the surrounding cations (j ) and H bonds,   sj = sMei + msH + n(1 − sH ), (3) j



i

where j sMei is the contribution of the i surrounding Mei ions, sH is the bond valence of the H donating bond (sH = 0.8), (1 − sH ) is the bond valence of the H accepting bond, and m and n are the number of donating and accepting H bridges, respectively, built with adsorbed water. The contribution of the surrounding Me ions (sMe ) is calculated according to Brown and Altermatt [37], sMe = e

(R0 −R) b

,

(4)

where R is the Me–O distance, R0 is the element-specific distance [37], and b is a constant (set equal to 0.37 Å). Ta-

Table 2 Site densities (sites nm−2 ) present on the lateral surfaces of clay particles Site density (sites nm−2 ) Direction

MeTd –O

MeOh –O

MeOh –O–MeTd

MeOh –O–MeOh

(MeOh )2 –O–MeTd

4.04 2.34 4.66 3.68

4.05 4.67 4.67 4.46

(100) (010) (110) Mean

4.05 4.67 4.67 4.46

2.02 3.50 2.34 2.62

AC type chains 2.02 1.17 2.34 1.84

(100) (010) (110) Mean

6.07 4.67 4.67 5.14

0 2.33 0 0.78

B type chains 4.05 2.33 4.67 3.69

4.04 2.34 4.66 3.68

4.05 4.67 4.67 4.46

(sites nm−2 ) (mmol kg−1 )

4.80 67.8

1.70 24.0

Mean of AC + B types chains 2.77 39.0

3.68 52.0

4.46 63.0

Td indicates a tetrahedral position whereas Oh indicates an octahedral position of the metal ion (Me). The calculation of the densities is based on the parameters shown in Figs. 1 and 2, the edge surface area given in Table 3, and a TOT layer thickness of 9.5 Å.

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ble 2 summarizes the calculated sMe values for MX80 montmorillonite. In Eq. (3), m and n remain the only free parameters to calculate the proton affinity of surface groups. Thus, these parameters were chosen, on the basis of steric considerations, after criteria set by Hiemstra et al. [14]. Singly coordinated surface groups interact with two donating or accepting hydrogen bonds (m + n = 2), except the singly coordinated tetrahedral Si–O surface groups, which interact with three hydrogen bonds (m + n = 3). Doubly coordinated surface groups interact with only one or two hydrogen bonds (m + n = 1 or 2). No criterion was given to choose between these two possibilities [14]. We chose an m + n value of 1, which fits our data better. Triply coordinated surface groups interact with only one hydrogen bond. Equation (1) can be used to derive the proton affinity constants of the surface groups based on structural information. Nevertheless, other parameters are needed to model the titration data, namely the number of each type of surface functional group. This can be calculated by multiplying the edge surface area (m2 kg−1 ) by the surface density of

edge sites (mol m−2 ). The different surface areas of the Na-montmorillonite MX80 in suspension [38] are summarized in Table 3. Since morphology of the montmorillonite platelets does not exhibit any kind of preferential crystallographic direction [38], it may be assumed that the number of sites can be determined based on the mean density of sites present in three different crystallographic directions, i.e., (100), (010), and (110). The calculation of site densiTable 3 Distances between the oxygen atom of the surface groups and their nearest metal neighbors (dMe–O ), specific distance relative to the ligand (R0 ) based on Brown and Altermatt [37], and calculated actual bond valence (sMe ) Si–O AlOh –O Mg–O Fe(III)–O Fe(II)–O

dMe–O (Å)

R0 (Å)

sMe

1.646a 1.93a

1.624 1.651 1.693 1.759 1.734

0.942 0.470 0.361 0.550 0.352

2.07b 1.98b 2.12b

a Based on the muscovite structure [39]. b Based on Drits et al. [65].

Fig. 4. Representation of the clay TOT layer structure. The figures on the left represent the octahedral layer. The figures in the middle represent the whole TOT layer structure seen from above basal plane. The figures on the right represent the two different layer termination types (A–C and B type chains; see text). Arrows and circles, as indicated by the inner caption, show different sites.

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ties can be achieved by assuming a muscovite structure [39], whose TOT layer has the same structure an the montmorillonite one. According to White and Zelazny [40], the edges can exhibit two types of terminations, which these authors call AC-type chains and B-type chains. In the case of ACtype chains, the termination of the platelet, composed of a Si tetrahedron, an Al octahedron, and a Si tetrahedron, is oblique compared to the crystallographic c axis. In the case of B-type chains, this termination is parallel to the crystallographic c axis. This difference of terminations leads to differences in site type densities. The structure of the montmorillonite is presented in the AC- and B-type chain configuration in Fig. 4 (top and bottom, respectively). The calculated site densities for these two types of configurations are summarized in Table 4. Since we have no information about the dominant configuration, we assumed the mean of the densities present on the AC and B chains. Table 4 shows that there is little difference in the total number of sites between the two types of edge chains. Thus, on the basis of Table 4 Surface area values for the Na-MX80 clay fraction in suspension [38] Basal and interlayer surface area (m2 g−1 ) Edge surface area (m2 g−1 ) Total surface area (m2 g−1 )

780 8.5 788

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the structural formula and assuming a random distribution of cations in the octahedral layer (see structural input from Section 2), it is possible to calculate the number of each type of surface functional group. Results are presented in Table 5, together with the proton affinity constant calculated according to Eq. (2). Considering that ≡SOHz represents one type of edge surface functional group with a z formal charge, the first protonation constant listed in Table 5 corresponds to the reaction ≡SO(z−1) + H+ ⇔ ≡SOHz

(5)

and the second protonation corresponds to the reaction ≡SOHz + H+ ⇔ ≡SOH(z+1) . 2

(6)

4. Results and discussion In this section, potentiometric titration data, given in part I, are simulated according to the two models described above: an empirical cation exchange plus three sites two pK model based on the Bradbury and Baeyens model [8], and a structural model based on 27 sites using the MUSIC approach [14]. The apparent CEC, which should match the measured CEC (based on ammonium acetate adsorption), is simulated by setting it equal to the calculated amount of Na

Table 5 List of the sites present on the lateral surface of the clay platelets with their m + n parameter, the site densities in mmol kg−1 and the proton affinity constants given by Eq. (2) Site SiTd –O AlOh –O  MgOh –O Fe(II)Oh –O Fe(III)Oh –O Al  Oh –O–AlOh AlOh –O–MgOh AlOh –O–Fe(II)Oh AlOh –O–Fe(III)Oh MgOh –O–MgOh MgOh –O–Fe(III)Oh MgOh –O–Fe(II)Oh Fe(III)Oh –O–Fe(III)Oh Fe(III)Oh –O–Fe(II)Oh Fe(II)Oh –O–Fe(II)Oh Al  Oh –O–SiTd MgOh –O–SiTd Fe(II)Oh –O –SiTd Fe(III)Oh –O–SiTd AlOh2 –O–SiTd AlMgOh –O–SiTd AlFe(III)Oh –O–SiTd AlFe(II)Oh –O–SiTd MgOh2 –O–SiTd MgFe(III)Oh –O–SiTd MgFe(II)Oh –O–SiTd Fe(III)Oh2 –O–SiTd

m+n

log K first protonation

log K second protonation

Number of sites (mmol kg−1 )

3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

9.1 → 8.2 22.4 24.5 24.7 20.8 17.0 19.2 19.3 15.4 21.3 17.6 21.5 13.8 17.8 21.7 7.7 → 7.2 9.8 10.0 6.1 −2.7 −0.4 −4.3 −0.3 1.8 −2.1 2.0 −5.9

−2.8 10.5 12.7 12.8 8.9 5.1 → 4.8 7.3 7.5 3.5 9.5 5.7 9.6 2.0 5.9 9.8 −4.2 −2.0 −1.9 −5.8 −14.5 −12.3 −16.2 −12.1 −10.1 −13.9 −13.9 −17.8

67.5 19.3 2.9 0.2 1.6 33.7 10.0 0.8 5.4 0.7 0.8 0.1 0.2 0.1 0.0 31.3 4.7 0.4 2.5 40.8 12.7 6.6 1.0 0.9 1.0 0.2 0.3

Bold values are those used in the simulation. Brackets indicate where several sites were grouped because of their similar proton affinity constants. The shaded sites are not taken into account in the simulation due to their low amount. Example of log K calculation is available upon request.

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Fig. 5. Experimental potentiometric titration data ([H+ ], top and middle) and CEC data (bottom) for three experiments described in part I and simulated by the three-sites, two-pK Bradbury and Baeyens model [8]. From left to right, experiments 1–3, respectively (see part I for experimental conditions). Experiment 1: 0.02 mol l−1 NaCl, 4.69 g l−1 ; experiment 2: 0.0068 mol l−1 CaCl2 , 3.03 g l−1 ; experiment 3: 0.05 mol l−1 CaCl2 , 1.53 g l−1 .

or Ca adsorbed onto the exchange position, plus the amount of H+ desorbed from the edges of the clay platelets as a function of pH. 4.1. Bradbury and Baeyens model Results of the simulations together with the experimental potentiometric data are shown in Fig. 5. The simulation parameters for edge surface complexation reactions are given in Table 6. The only fitted parameters in these simulations are the cation exchange selectivity coefficients. Fletcher and Sposito have already published a summary of exchange selectivity coefficients for montmorillonite [3]. We

had some difficulties fitting our data with these coefficients, in particular the CaCl+ ionic pair, whose selectivity coefficient depends on the equilibrium constant of the reaction Ca2+ + Cl− ⇔ CaCl+ and therefore on the thermodynamic database used for the simulation. We decided to fit the ini− tial data set (Na/Ca isotherms in ClO− 4 and Cl ionic back2+ ground) to model the binary and ternary Ca /CaCl+ /Na+ exchange reactions [13]. Fig. 6 shows the results of these simulations. For the Ca2+ /Na+ exchange isotherm obtained in a ClO− 4 ionic background, a sensitivity analysis shows that with a Ca2+ /Na+ selectivity coefficient value of 100.1 –100.6 we can fit the data well within the limit of the error bars Ca/Na (Kv = 100.17 in the Fletcher and Sposito review [3]).

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Table 6 Surface complexation reactions and associated protolysis constants (Kint ) of the simulation based on the Bradbury and Baeyens model [8] Surface complexation reactions

log Kint

Ss OH + H+ = Ss OH2 Ss OH = Ss O− + H+ Sw1 OH + H+ = Sw1 OH+ 2 Sw1 OH = Sw1 O− + H+ Sw2 OH + H+ = Sw2 OH+ 2 Sw2 OH = Sw2 O− + H+

4.5 −7.9 4.5 −7.9 6.0 −10.5

We chose a Ca2+ /Na+ exchange selectivity coefficient of 100.4 . The Ca2+ /CaCl+ /Na+ system can therefore be described with a CaCl+ /Na+ exchange selectivity coefficient between 102.2 and 102.8 . In agreement with these results and our results (Figs. 5 and 6), the exchange selectivity coefficients were fixed to the values indicated in Table 7. The 0.0 log K value for the H+ /Na+ exchange selectivity coefficient is very near the 0.1 log K value tabulated by Fletcher and Sposito [3] and it denotes an equal affinity of the exchanger for the two cations. Furthermore, it should be noted that the experimental data at high pH values are well simulated with a CaOH+ /Na+ exchange selectivity coefficient value equal to that of CaCl+ /Na+ . We therefore assume that ionic pairs may react with the clay surface with the same affinity, as in the case of either Me2+ –Cl− or Me2+ –OH− . Nevertheless, the precipitation of the Ca–Si phase (see part I) and the low number of experimental points at high pH prevent us from accurately defining the cation exchange selectivity coefficient for CaOH+ ionic pairs. Although the Bradbury and Baeyens model [8] reproduces the general tendency of the proton surface charge titrations and accounts for the apparent CEC increase, it fails to accurately predict the titration measurements.

Fig. 6. Fit of the Ca2+ /Na+ exchange data from Sposito et al. [13] in perchlorate (top) and chloride ionic background (bottom). PerchloCa2+ /Na+

= 0.4; thin dotted rate ionic background: thick line, log Kv 2+ + lines, log KvCa /Na varied from 0.1 to 0.6. Chloride background: thick 2+ + + + line, log K Ca /Na = 0.4 and log K CaCl /Na = 2.5; thin dotted lines, v

2+ /Na+

4.2. Hiemstra and Van Riemsdijk MUSIC model In the MUSIC model, we included both edge sites (Table 5) and cation exchange sites used in the Baeyens and Bradbury model. Furthermore, the cation exchange selectivity coefficients are the same as those listed in Table 7. Some edge sites were grouped together in the model and some sites were neglected due to the low number present at the particle edges (Table 5). The pK of the sites used in the simulation are marked in bold. Only three log K parameters were adjusted (Table 5). The slight adjustments correspond to a maximum dMe–O shortening of less than 0.01 Å; we do not allow the bonds to elongate. The shortening of the Me–O distances at the border of the layers is expected on the basis of the Pauling bond valence approach [37,41–43]. This model describes both the titration data and the apparent CEC variations very well as a function of pH (Fig. 7). Despite the numerous approximations relative to the different edge faces’ contributions and thus to the different edge surface group populations, the MUSIC approach can successfully model the surface proton charge of montmo-

log KvCa

v

+ + = 0.4 and log KvCaCl /Na varied from 2.2 to 2.8.

Table 7 Cation exchange reaction selectivity coefficients (Kv ) used in the simulations with both models Exchange reactions 2NaX + Ca2+ ⇔ CaX2 + 2Na+ NaX + H+ ⇔ HX + Na+ NaX + CaCl+ ⇔ CaClX + Na+ NaX + CaOH+ ⇔ CaOHX + Na+

log Kint 0.4a 0.0 a 2.5a 2.5b

a Adjusted (data from this study and [13]). + + b Set equal to K CaCl /Na (indicative value). v

rillonite. Nevertheless, some criticisms can be made on the choice of the m + n values [44]. We hope that studies such as molecular dynamic studies could help constrain these last parameters. To confirm the effectiveness of our approach, and of our choices for these questionable parameters, we tried to link some clay properties (surface potential, dissolution kinetics) to the protonation state of the edge sites, as given by our model.

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Fig. 7. Experimental potentiometric titration data (top and middle) and CEC data (bottom) from part I simulated by the Hiemstra and Van Riemsdijk MUSIC model [12,14]. From left to right, experiments 1–3, respectively. Experiment 1: 0.02 mol l−1 NaCl, 4.69 g l−1 clay content; experiment 2: 0.0068 mol l−1 CaCl2 , 3.03 g l−1 clay content; experiment 3: 0.05 mol l−1 CaCl2 , 1.53 g l−1 clay content.

4.3. Surface potential of clay minerals According to the model it is possible to calculate the pH at which the global edge surface charge is zero (point of zero charge, PZC). By setting the edge groups formal charge to the values given in Table 8, we found a pHPZC value of 7.45 (Fig. 8). At this pH, the edge contribution to the total charge of the clay should be 0, and the apparent CEC should be equal to the structural CEC. Fig. 7 shows that this is not the case: a positive difference of approximately 10% of the structural CEC is observed for experiment 1. Experiments 2 and 3 could be considered in this analysis because of the adsorption of CaCl+ ionic pairs. We estimate that a 10% error

in the measurement and calculation of the structural CEC is reasonable since many parameters, such as the Al content in the tetrahedral layer, are difficult to estimate and can significantly influence the theoretical structural CEC value. The clay edges’ PZC value also justifies, a posteriori, the habit of measuring the CEC at near-neutral pH [45]. We noted that the maximum variation of the edge surface charge value is smaller than 20% of the structural CEC. Since the charges created at the surface are also compensated by cations present in the solution, such as Na+ or Ca2+ , the effect of pH on the measured surface potential must be negligible. Many studies [9,46–49] have already shown that the zeta potential of montmorillonite is slightly negative and

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Table 8 Approximated formal charge of the edge surface groups of the clay Approximated formal charge Types of sites SiTd –O Me(III)Oh –O Me(II)Oh –O Me(III)Oh –O–Me(III)Oh Me(III)Oh –O–Me(II)Oh Me(II)Oh –O–Me(II)Oh Me(III)Oh –O–SiTd Me(II)Oh –O–SiTd Me(II)Oh2 –O–SiTd AlOh2 –O–SiTd AlMgOh –O–SiTd AlFe(III)Oh –O–SiTd

Deprotonation

First protonation

Second protonation

−1 N.A. N.A. N.A. N.A. N.A. −1/2 −2/3 −1/3 0 −1/6 0

0 −1/2 −2/3 0 −1/6 −1/3 +1/2 +1/3 +2/3 N.A. N.A. N.A.

N.A +1/2 +1/3 +1 +5/6 +2/3 N.A. N.A. N.A. N.A. N.A. N.A.

Surface sites are grouped into categories, where Me(III) indicates a trivalent cation and Me(II) a divalent cation.

Fig. 8. Calculation of the edge surface charge based on the parameters given in Table 5. Thick line: whole surface edge charge. Thin lines: individual contributions of the five main components, SiTd –OH (deprotonation, pK = 8.2, 67.5 mmol kg−1 ), AlOh –OH (double protonation, pK = 10.5, 19.3 mmol kg−1 ), AlOh –OH–AlOh (double protonation, pK = 4.8, 33.7 mmol kg−1 ), AlOh –OH–MgOh (double protonation, pK = 7.3, 10.0 mmol kg−1 ), and AlOh –OH–SiTd (double protonation, pK = 7.2, 31.3 mmol kg−1 ). The point of zero charge pH value is equal to 7.5.

that it remains constant between pH 4 and 9. We also argue that the clay in dilute suspension is almost completely dispersed [38,50]. Hence, the edge surface charge is expressed in only one dimension (the line represented by the perimeter of the platelet), decreasing the capability of the charges to create an electrostatic potential. And thus, we can assume the surface potential is zero. 4.4. Edge site protonation and clay particle dissolution Recent atomic force microscopy (AFM) studies clearly show that the dissolution of clays, such as nontronite and hectorite, occurs by edge retreat rather than by pit formation [51]. Dissolution rates of various oxides and silicates are controlled by the protonation state of surface functional groups [52,53]. In Fig. 9, the aqueous Si concentration is reported as a function of pH together with the protonation state

Fig. 9. Correlation between the deprotonation of tetrahedral and octahedral–tetrahedral surface sites and the dissolution of clay at high pH for experiments 1 (P) and 3 (E).

of the reactive edge sites, which involves a bond with an Si atom present in a tetrahedral position. It appears that the high rate of clay dissolution in the alkaline pH range correlates to the deprotonation of the OH groups bonded to at least one SiTd . This apparent clay dissolution can also be attributed to the presence of microcrystalline quartz or cristobalite in the clay suspension. Nevertheless, Cama et al. [54] showed that smectite dissolves congruently at pH 8.8, at 80 ◦ C. We think that part of the increased Si concentration observed at high pH can be attributed to clay dissolution. Conversely, the dissolution of the clay in the acidic pH range is correlated to a double protonation of Al surface groups. Fig. 10 shows the aqueous Al concentration as a function of pH together with the protonation state of reactive edge sites involving a bond with an Al atom in an octahedral position. Also, the ability of the clay to resist dissolution depends on the PZC position of the edge surface groups. Therefore, the edge sites protonation state given by the model is consistent with the dissolution pH range of the smectite. The pH range for dissolving clay minerals depends on clay type. Hectorite, a Mg2+ , Li+ trioctahedral smectite,

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Fig. 10. Correlation between the double protonation of dioctahedral surface sites and the dissolution of clay at low pH for experiment 3 (").

Fig. 11. Scheme of the protonation states of the hectorite main octahedral surface sites as a function of pH.

is less stable at low pH but more stable at high pH than montmorillonite [55]. In this structure, the main octahedral surface sites for proton adsorption should be the Mg2 –O– Si, the Mg–O, and the Mg–O–Mg sites. The approximate formal charges of these sites are presented as a function of pH in Fig. 11. Structurally, the presence of two Mg2 –O– Si sites should correspond to the presence of a Mg–O–Mg site. The Mg–O sites should be present to a lesser extent than the others. Thus, the global charge of the edges should mainly be controlled by the charge of the Mg–O–Mg site, since the Mg2 –O–Si site has the same charge over the entire pH range 4–9. Hence, the PZC should be shifted toward an alkaline pH value of approximately 10, in agreement with the observed differences in the stable pH range for montmorillonite and hectorite. 4.5. Implications The edge surfaces of smectite—and by extrapolation, of other clays—are very heterogeneous, and therefore, complicated systems. Nevertheless, the present structural and morphological model can be used to predict their reactivity toward protons. Only five main sites are necessary to model the titration data because the amounts of other sites are relatively too low to really affect the goodness of the

fit (Table 4). These main sites are SiTd –OH (deprotonation, pK = 8.2, 67.5 mmol kg−1 ), AlOh –OH (double protonation, pK = 10.5, 19.3 mmol kg−1 ), AlOh –OH–AlOh (double protonation, pK = 4.8, 33.7 mmol kg−1 ), AlOh –OH–MgOh (double protonation, pK = 7.3, 10.0 mmol kg−1 ), and AlOh – OH–SiTd (double protonation, pK = 7.2, 31.3 mmol kg−1 ). The deconvolution of the total edge surface charge is shown in Fig. 8. Only four adjusted parameters were necessary to quantify the numbers of these sites and their affinity for protons, namely three m + n values and the ratio between A–C and B type chains. Three pK values were slightly adjusted further to better fit the data, although they cannot be considered as freely adjustable parameters. This low number of adjustable parameters for a 27- (or more) sites model should be compared to the number of adjustable parameters for the 3-sites model of Bradbury and Baeyens [8]: three different site densities and six different affinity constants for protonation reactions were necessary to fit their data. This comparison shows the efficiency of a structurally and morphologically based model to predict clay surface reactivity with maximal precision and a minimal number of adjustable parameters. The clay proton affinity constants are often used to derive clay metal complexation constants [8,56–59]. But by considering the heterogeneity of the clay edges and the chemical properties of H+ and metallic cations, it becomes doubtful whether metal cations do sorb onto the same sites as H+ . Schlegel et al. [60] showed that Co2+ can form inner sphere complexes with hectorite edge surface sites and that Co2+ shares edges rather than corners with octahedral layer sites, meaning that Co2+ must bond to at least two oxygen surface groups. Since protons are linked to only one oxygen surface group, the classical empirical modeling approaches for metal complexation on clay minerals should be reexamined. For example, both Zachara et al. [5, 57] and Turner et al. [58,61] consider that the reactivity of clay edges can be modeled by considering the reactivity of alumina and silica and by using a triple layer model as an electrostatic model. In their studies they fitted the number of edge sites concomitantly with their metal adsorption data, but without titration data, or they calculated the number of sites on the basis of morphological information and of structural information given by White and Zelazny [40]. In this “alumina–silica” model, only Si–OH and Al–OH amphoteric sites were considered (2-pK model), according to White and Zelazny [40]. The sorption data were successfully fitted, but many hypotheses are not really justified. For instance, we show that AlOh –OH–SiTd sites could react with protons in the near neutral pH range, in contradiction to White and Zelazny [40]. Furthermore, the sites described in this study do not exhibit amphoteric behavior in the pH range usually considered for sorption experiments (i.e., pH value between 2 and 10).

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5. Conclusions

References

Natural clay systems are far more complex than clay systems studied in the laboratory. In natural or engineered systems, competition effects on sorption are expected (Tournassat et al., in preparation). To precisely model the effect of competition, it is necessary to constrain site densities and affinities available for competitive sorption. However, the oversimplification of the clay edge reactivity toward cations could make modeling the interactions between multisolute system and clay particles impossible. While surface complexation models such as the Bradbury and Baeyens model are an improvement over the Kd approach, we question their mechanistic approach and their effectiveness to model natural systems. First, the complexation pK values for cations are fitted relative to an “arbitrary” surface protonation pK value. Second, the complexation reactions are arbitrarily attributed to a single type of site. A very limited set of sites is considered in this type of simulation, although the structural heterogeneity of surface groups allows a large number of site configurations and available coordinations due to the morphology of the clay platelets and the chemical composition of the clay (especially the heterogeneous octahedral layer). And third, the complexation reactions involve only one site (e.g., via single corner sharing). We did not consider the possible interactions between two or more protonated sites and the cations (e.g., via double corner or edge sharing), as shown for Ni2+ by polarized EXAFS spectroscopy [60,62], or the nucleation processes of new phases as shown for Zn and Co on hectorite and montmorillonite [63,64]. In this study, we have shown that a model, based on sound morphological and structural information, is able to predict the reactivity of clay edge surfaces toward protons with better accuracy and with fewer free parameters than empirical three (or two) sites two pK models. This approach can be combined with the prediction of CEC variations as a function of pH. We hope that such an approach could be extended to other cation complexation reactions. In addition, we derived the cation exchange selectivity coefficient for CaCl+ and gave an estimation of the cation exchange selectivity coefficient for CaOH+ ionic pairs. These ionic pairs have similar, high affinity constants (log Kv = 2.5). We refer the reader to Sposito et al. [13] for an explanation of the high CaCl+ exchange constant. Finally, we confirmed the nonpreference of the clay exchanger for H+ and Na+ (log Kv = 0), and clearly distinguished this cation exchange from (simultaneously occurring) mineral dissolution.

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Acknowledgments This research was funded by the French National Radioactive Waste Management Agency (ANDRA). French Geological Survey is acknowledged for its editorial financial support.

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