Defining reactive sites on hydrated mineral surfaces: Rhombohedral carbonate minerals

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Geochimica et Cosmochimica Acta 73 (2009) 4326–4345 www.elsevier.com/locate/gca

Defining reactive sites on hydrated mineral surfaces: Rhombohedral carbonate minerals Adria´n Villegas-Jime´nez a,*, Alfonso Mucci a, Oleg S. Pokrovsky b, Jacques Schott b b

a Earth and Planetary Sciences, McGill University, 3450 University Street, Montre´al, Que., Canada H3A 2A7 Ge´ochimie et Bioge´ochimie Expe´rimentale, LMTG, UMR 5563, Universite´ de Toulouse – CNRS, 14, Avenue Edouard Belin, 31400 Toulouse, France

Received 20 January 2009; accepted in revised form 22 April 2009; available online 12 May 2009

Abstract Despite the success of surface complexation models (SCMs) to interpret the adsorptive properties of mineral surfaces, their construct is sometimes incompatible with fundamental chemical and/or physical constraints, and thus, casts doubts on the physical–chemical significance of the derived model parameters. In this paper, we address the definition of primary surface sites (i.e., adsorption units) at hydrated carbonate mineral surfaces and discuss its implications to the formulation and calibration of surface equilibria for these minerals. Given the abundance of experimental and theoretical information on the structural properties of the hydrated (10.4) cleavage calcite surface, this mineral was chosen for a detailed theoretical analysis of critical issues relevant to the definition of primary surface sites. Accordingly, a single, generic charge–neutral surface site („CaCO3H2O0) is defined for this mineral whereupon mass-action expressions describing adsorption equilibria were formulated. The one-site scheme, analogous to previously postulated descriptions of metal oxide surfaces, allows for a simple, yet realistic, molecular representation of surface reactions and provides a generalized reference state suitable for the calculation of sorption equilibria for rhombohedral carbonate minerals via Law of Mass Action (LMA) and Gibbs Energy Minimization (GEM) approaches. The one-site scheme is extended to other rhombohedral carbonate minerals and tested against published experimental data for magnesite and dolomite in aqueous solutions. A simplified SCM based on this scheme can successfully reproduce surface charge, reasonably simulate the electrokinetic behavior of these minerals, and predict surface speciation agreeing with available spectroscopic data. According to this model, a truly amphoteric behavior is displayed by these surfaces across the pH scale but at circum-neutral pH (5.8–8.2) and relatively high RCO2 (P1 mM), proton/bicarbonate co-adsorption becomes important and leads to the formation of a charge–neutral H2CO3-like surface species which may largely account for the surface charge-buffering behavior and the relatively wide range of pH values of isoelectric points (pHiep) reported in the literature for these minerals. Ó 2009 Elsevier Ltd. All rights reserved.

1. INTRODUCTION Surface complexation models (SCMs) have been extensively applied to the interpretation of adsorption and surface reactivity data on a large number of minerals in aqueous solutions. Their relative simplicity and capacity

*

Corresponding author. E-mail address: [email protected] (A. Villegas-Jime´nez).

0016-7037/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.gca.2009.04.036

to incorporate fundamental concepts of thermodynamics, crystallography, and inorganic and colloid chemistry make them suitable tools for the description of the adsorptive properties of minerals under a wide range of chemical conditions. Nevertheless, despite the success and refinements achieved by many of these models, many shortcomings remain to be addressed before their applicability to natural systems and their validation at the molecular level can be established (e.g., Westall and Hohl, 1980; Goldberg, 1991; Sahai and Sverjensky, 1997; Kallay and Zˇalac, 2000; Zuyi

Defining primary surface sites at rhombohedral carbonate surfaces

et al., 2000; Lu¨tzenkirchen, 2002). Among these, the definition of the surface sites (hydrated adsorption units) that serve as reference species (hereafter referred to as ‘‘primary surface sites”) for the formulation of surface reactions is at the heart of a realistic description of adsorption processes (Healy and White, 1978; Pivovarov, 1997; Kulik et al., 2000; Kulik, 2002). These can be formalized in terms of discrete chemical units of given chemical composition and charge, in analogy to functional groups of ionic and molecular aqueous species. However, they differ from their aqueous analogs because primary surface sites have a fixed density per unit area and cannot be diluted infinitely on the surface (Kulik, 2002). These properties affect the definition of standard states for surface species and reflect on the values of the intrinsic formation constants (Kint) of surface species (Kulik, 2002; Sverjensky, 2003). Other distinctions include stereochemical, structural, and electrostatic conditions at the mineral/water interface that influence the energetics of the primary surface sites (Sposito, 1989; Zachara and Westall, 1999). Two major ion binding schemes (or models) have been postulated for the formulation of SCMs: one-site and multi-site complexation. One-site schemes assign an average ‘‘macroscopic” reactivity to all atoms present at the mineral surface, whereas multi-site schemes formalize the reactivities of individual surface atoms in terms of their chemical identity, coordination environment and hydrogen bonding configuration (Hiemstra et al., 1989, 1996; Barrow et al., 1993). Despite their generic nature, one-site schemes are simple, practical and powerful predictive tools based upon well established statistical mechanical grounds (Borkovec, 1997) and are, despite their disregard of the complexities inherent to real-world sorbents (chemical heterogeneity), the foundation of numerous electrical double-layer models that describe the charge–potential relationship at the mineral/water interface (Sposito, 1983). On the other hand, multi-site schemes are more realistic insofar as they reflect, semi-quantitatively, the compositional ‘‘heterogeneity” of the predominant mineral surfaces (Hiemstra et al., 1989; Hiemstra and van Riemsdijk, 1991, 1996; Scheidegger and Sparks, 1996). Nevertheless, the quantitative characterization of the reactivity of individual primary surface sites is far from trivial because the proper calibration of these multi-site, multi-reaction models requires: (i) uniform and/or well-characterized mineral surfaces in terms of chemical composition and microtopography (Barrow et al., 1993; Piasecki et al., 2001), (ii) suitable and sufficient experimental data arising from various independent sources and carrying sufficient information to properly resolve the energetic contributions of individual surface sites (Rudzin´ski et al., 1992, 1998; Piasecki et al., 2001), and (iii) the application of sophisticated mathematical treatments (Chandler, 1987; Ja¨ger, 1991; Borkovec and Koper, 1994). For instance, it is well known that, because of compensating effects, the composite adsorption (or surface charge) isotherms obtained from titration experiments that are typically used for the calibration of adsorption chemical models, are largely insensitive to surface energetic heterogeneity, and therefore, additional data (e.g., potentiometric, electrokinetic, radiometric, calorimetric) are

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required to properly discriminate among potential heterogeneity models and prevent misleading over-interpretations of available data (van Riemsdijk et al., 1987; Blesa and Kallay, 1988; Cernı´k et al., 1995; Rudzin´ski et al., 1992, 1998; Lu¨tzenkirchen, 2005). Furthermore, the presence of surface irregularities (e.g., steps, kinks and dislocations), chemical micro-heterogeneities, and multi-domain crystal surfaces, difficult to characterize experimentally, add to the complexity of multi-site models, so that the physical–chemical significance of the derived model parameters and their application to natural systems is seriously questioned (Lu¨tzenkirchen, 1997). It follows that simpler models are expected to remain predominant in the quantitative modeling of equilibrium adsorption phenomena (Lu¨tzenkirchen, 2002) and kinetic dissolution processes (Bandstra and Brantley, 2008). Despite the lack of scientific consensus with regards to the application of one-site vs. multi-site schemes to describe sorption reactions, it is generally agreed that primary surface sites must contain sufficient information about the sorbent phase for the accurate description of its surface reactivity while allowing for a simple and realistic representation of sorption equilibria (Kulik, 2002). Furthermore, because Law of Mass Action (LMA)-based sorption modeling approaches (Morel and Morgan, 1972; Westall and Hohl, 1980; Golderg, 1995), frequently incorporated in widespread computer codes (e., MINEQL, HYDRAQL, PHREEQC, FITEQL, etc.), are subjected to charge and mass balance constraints, the definition of primary surface sites in terms of their residual charges and elemental stoichiometry is critical for the reliable estimation of model parameters (i.e., intrinsic formation constants of surface species, capacitances, site densities) and the solution of surface speciation (sorption) equilibria. This issue is the focus of the present study within the context of rhombohedral carbonate minerals. We begin by highlighting critical aspects relevant to the definition of the residual charges and the elemental stoichiometry of primary surface sites. Later, the discussion focuses on the (10.4) cleavage calcite surface, as a model for all rhombohedral carbonate minerals, to rationalize the available theoretical and experimental evidence and formalize a realistic primary surface site for these surfaces. Accordingly, new surface equilibria are derived, calibrated, and evaluated against published experimental data (i.e., surface charge, electrokinetic and/or spectroscopic) for two common rhombohedral carbonate minerals: magnesite and dolomite. 2. DEFINITION OF PRIMARY SURFACE SITES 2.1. Charge assignment Atomic charges are not physical properties that can be readily defined accurately (Chandra and Kollman, 1984), and hence, their assignment to primary surface sites at mineral surfaces is problematic. Typically, either a ‘‘zero residual charge” or a ‘‘fractional residual charge” scheme is assigned to primary surface sites in surface complexation studies. Whereas the former is based on simple, yet realistic,

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chemical stability grounds (charge dissipation upon surface hydration), the latter is based upon Bond Valence concepts: ‘‘Pauling’s Electrostatic Valence Principle” (Pauling, 1929) or ‘‘Bond Valence Theory” (Brown, 1981). These concepts were originally developed and calibrated to bulk structures and were later applied to idealized, unrelaxed, unreconstructed metal oxide surfaces (neither bond stretching or contraction nor perturbation of the Coordination Number) for the estimation of the unsatisfied valence of surface atoms which was considered as an approximate measure of their residual charge (Yoon et al., 1979; Hiemstra et al., 1989, 1996; Bleam, 1993). It should be noted that Bond Valence Theory, a semi-empirical approach based upon central atom valences, coordination number and bond lengths, must not be confused with Valence-Bond Theory that complements Molecular Orbital Theory and involves fundamental quantum chemistry concepts where bonding is accounted for in terms of atomic valences and hybridized orbitals (Gallup, 2002). Depending on the residual charge and relative abundance of the primary surface sites, the unreacted hydrated mineral surface will carry a neutral, positive, or negative ‘‘reference charge density” (rREF), as described by (Hiemstra and van Riemsdijk, 1996): X rREF ¼ F zj N j ð1Þ where zj and Nj represent, respectively, the charge and density (in mol m2) of the j primary surface site and F is the Faraday constant. In other words, rREF represents the net charge of the surface when only primary surface sites are present. It is the resultant of crystal truncation (generating ‘‘dangling bonds”) and mineral hydration which, in turn, may lead to the re-organization of bonds (e.g., bond relaxation, bond breaking, and/or bond making) at the mineral surface and the establishment of ‘‘unknown” residual charges at the primary surface sites. rREF contributes to the net surface charge density (r0, C m2) as follows: r0 ¼ rH þ rIS þ rPS þ rREF

ð2Þ

where rH is the net proton surface charge density (F(CHþ  COH ), CHþ and COH are, respectively, the net surface H+ and OH adsorption densities in mol m2), rIS is the net charge density resulting from the total charge of ions (excluding H+ and OH) bound by inner-sphere surface coordination, and rPS is the net permanent structural surface charge arising from isomorphic substitutions exhibited by some minerals (Chorover and Sposito, 1995). For simplicity, we will focus our discussion exclusively on minerals without permanent structural charge (rPS = 0) and only within the context of adsorption at the 0-plane (surface). The calibration of intrinsic formation constants (Kint) by LMA approaches (Herbelin and Westall, 1996) is constrained by proton and, if applicable, inner-sphere ion adsorption data (CH and CIS, respectively) and is subjected to the following charge equality constraint: F RDzi ½ i0  þ rREF ¼ relect 0 SA

ð3Þ

where A is the specific surface area (m2 g1), S is the solid to solution ratio (g L1), Dzi is the net charge transfer of the

reaction producing surface species i, [i0] is the molar concentration of species i adsorbed at the surface (plane-0), and represents the electrostatically-derived net surface relect 0 charge density (an a priori unknown) computed from an electrostatic interfacial model (EIM) describing the surface charge–potential relationship (Westall and Hohl, 1980) and the iteratively-optimized surface potential (w0). The lefthand term in Eq. (3) represents the ‘‘net surface charge” and requires a definition of rREF and computation of the ‘‘apparent surface charge” (rapp 0 , first left-hand term of Eq. (3)) from the surface speciation predicted by the iteraare tively-optimized Kint values. Because Kint and relect 0 interdependent (Eq. (3)), their optimization is a function of two fixed experimentally-accessible quantities (CH and CIS, non-trivial measurements for some minerals) and one ill-defined quantity (rREF). In addition, the latter affects the Kint values via the estimated surface potentials since these depend on the adjusted relect values and the selected 0 EIM. Any modification in the values of w0 is reflected in the electrostatic correction necessary to reference apparent constants, Kapp, to a zero potential standard state for the calibration of Kint values:   DZ i F w0 K app ¼ K int  exp ð4Þ RT where R is the gas constant and T is the absolute temperature. The main corollary to this discussion is that the selected rREF may impact the calibration of the intrinsic formation constants via LMA approaches, and therein lies the importance of assigning appropriate charges to primary surface sites. 2.2. Elemental stoichiometry The selection of the elemental stoichiometry of the primary surface sites is also critical because it influences the molecular representation of surface reactions and participates in the mass balance constraint imposed by LMAbased approaches (total crystallographic site density) in the modeling of sorption equilibria (Kulik, 2002). The simplest scenario is to consider individual surface atoms (hydroxylated or hydrated) as the primary surface sites. However, electrostatic and steric interactions between neighboring surface species may arise and affect the energetics of the sorption processes. For instance, vicinal surface atoms may both interact with the same sorbate (bidentate adsorption; Ludwig and Schindler, 1995) or, upon reaction with a sorbate, adjacent surface atoms may be inactivated (Benjamin, 2002). In both cases, two adjacent surface atoms could be formalized as one surface site. These premises were championed by Pivovarov (1997) who, based upon crystallographic considerations, proposed the elemental stoichiometry of two generic types of charge– neutral primary surface sites for the hydrated hematite surface, („FeOH)2(OH2)+ and („O3H)2(H2O), assuming that H2O molecules physically adsorbed to hydroxylated vicinal surface metal and oxygen atoms represent a single ‘‘ adsorption center ” whereupon surface reactions occur. This approach yielded surface OH group densities in close agreement with experimental values (Morimoto et al.,

Defining primary surface sites at rhombohedral carbonate surfaces

1969). A similar definition of the elemental stoichiometry of one generic primary surface site for all metal oxides („O0.5H) was postulated by Kulik (2002) under the assumption that primary surface sites at mineral surfaces comprise H2O molecules from the adsorbed water monolayer. This definition of surface sites was influenced by results of wet chemical, spectroscopic, and molecular modeling studies that confirmed the presence of OH groups at metal oxide surfaces (Morimoto et al., 1969; Davis and Kent, 1990). The proposed one-site scheme considers the bidentate coordination of a H2O molecule to one surface metal and one surface oxygen and yields two vicinal charge–neutral hydroxyl groups (i.e., „MeOH and „OH) of which either only one is reactive (Kulik, 2002) or both participate simultaneously in the adsorption processes and are thus conceptualized as a single site (Pivovarov, 1998). This scenario allowed the modeling of sorption equilibria by both LMA (Pivovarov, 1998) and Gibbs Energy Minimization (GEM, Kulik, 2002) approaches and provided a suitable molecular representation of surface reactions at the metal oxide/H2O interface. It follows that the application of identical criteria for the definition of elemental stoichiometries for other mineral surfaces is warranted. 3. RHOMBOHEDRAL CARBONATE MINERALS 3.1. Case of the (10.4) calcite surface 3.1.1. Evidence from spectroscopic and molecular modeling studies The (10.4) calcite surface has been extensively studied (e.g., Stipp and Hochella, 1991; de Leeuw and Parker, 1997; Fenter et al., 2000; Wright et al., 2001; Geissbu¨hler et al., 2004). This surface is of great interest because it represents the most stable and predominant crystallographic face displayed by this mineral in aqueous solutions and it serves as a model for other rhombohedral carbonate minerals such as magnesite, dolomite, siderite, rhodocrosite, and gaspe´ite. The ideal (10.4) cleavage surface configuration displays a stoichiometric number of adjacent cations and anions that carry an equivalent but opposite residual charge per surface unit cell and corresponds to the atomic plane where strictly ionic (metal–oxygen) and no covalent bonds (carbon–oxygen) are broken. The preponderant stability of this atomic configuration over others was confirmed using a simple crystal lattice truncation protocol (based upon Bond Valence concepts) devised to determine the most stable atomic configuration of oxide mineral surfaces according to charge and bond strength minimization criteria (Koretsky et al., 1998). Numerous surface-sensitive instrumental techniques have been employed to characterize the (10.4) calcite surface under wet and/or vacuum conditions, such as X-ray Photoelectron Spectroscopy (XPS, Stipp and Hochella, 1991; Stipp, 1999), Low Energy Electron Diffraction (LEED, Stipp and Hochella, 1991; Stipp, 1999), Time-OfFlight Secondary Ion Mass Spectroscopy (TOF-SIMS, Stipp, 1999), Infrared Spectroscopy (IR, Neagle and Rochester, 1990), Fourier Transform Infrared Spectros-

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copy (FTIR, Kuriyavar et al., 2000), Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFT, Pokrovsky et al., 2000), Attenuated Total Reflection-Fourier Transform Infrared Spectroscopy (ATR-FTIR, AlHosney and Grassian, 2005), Atomic Force Microscopy (AFM, Rachlin et al., 1992; Stipp et al., 1994; Liang et al., 1996; Stipp, 1999), X-ray Reflectivity and Scattering (SXR, Chiarello et al., 1993; Fenter et al., 2000; Geissbu¨hler et al., 2004), and Grazing Incidence X-ray Diffraction (GIXRD, Magdans et al., 2006). These techniques revealed that the outer-most atomic layer relaxes and the surface undergoes a certain degree of reconstruction upon hydration. The presence of OH groups was detected near the cleaved (10.4) calcite surface exposed to moistened conditions (e.g., Stipp and Hochella, 1991; Fenter et al., 2000) and the formation of a hydration monolayer was confirmed (e.g., Fenter et al., 2000; Magdans et al., 2006). These findings established that water constituents are chemically associated to the surface, allowing for the formation of hydrated surface species. Furthermore, ‘‘chemisorption” of water on the calcite surface was also demonstrated by earlier thermogravimetric studies (Morimoto et al., 1980; Ahsan, 1992). Nevertheless, it is not yet possible to ascertain, by any of these analytical techniques, whether hydration occurs through adsorption of dissociated or undissociated water molecules because these are unable to detect hydrogen atoms, and thus, hydroxyl ions cannot be distinguished from adsorbed H2O molecules. In other words, it is not possible, for instance, to distinguish whether the primary surface site: „Ca(H2O) or „CaOH° (or both) form at the calcite surface. Consequently, water dissociation products cannot be ascribed to specific surface atoms. The only conclusion that can be drawn from these data is that the internal coordinates (i.e., O–H bond lengths and H–O–H angle) of undissociated water molecules are possibly modified upon adsorption but it is unknown to what extent. To ascertain whether H2O dissociates to its hydrolysis products (H+ and OH) upon adsorption on the calcite surface, additional information is needed. Theoretical studies provide information on the structure, energetics, and atomic bonding relationships at the hydrated mineral surface. Computer-assisted Atomistic Simulations (e.g., de Leeuw and Parker, 1997, 1998; de Leeuw et al., 1998; Kuriyavar et al., 2000; Hwang et al., 2001; Wright et al., 2001; Kerisit et al., 2003; Kerisit and Parker, 2004), Molecular Dynamics (Kerisit et al., 2003, 2005a; Kerisit and Parker, 2004; Perry et al., 2007), ab initio Density Functional Theory (Parker et al., 2003; Kerisit et al., 2003, 2005b; Archer, 2004), and Roothan–Hartree– Fock Molecular Orbital Theory (Villegas-Jime´nez et al., 2009a) were used to investigate the interactions of H2O monomers with the (10.4) calcite surface. All these studies reveal that the internal coordinates of water monomers remain essentially unchanged upon adsorption and, that associative adsorption of H2O on the (10.4) calcite surface is energetically favorable (over dissociative adsorption) where one H2O monomer bonds to one calcium atom and is hydrogen-bonded to either one (Archer, 2004; VillegasJime´nez et al., 2009a) or two neighboring surface oxygen atoms of carbonate groups (de Leeuw and Parker, 1997;

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Wright et al., 2001; Kerisit and Parker, 2004; Perry et al., 2007). In other words, each adsorbed H2O monomer (at the first hydration layer) interacts simultaneously with one cationic and at least one anionic center, and hence, charge and mass discretization of hydrolysis products among individual surface atoms is problematic. Clearly, a suitable formalism must be adopted for mass and charge assignment of water constituents among individual surface atoms in the definition of primary surface sites. Extension of these Atomistic Simulations to other hydrated (10.4) carbonate surfaces, such as magnesite and dolomite, reveals that H2O also adsorbs associatively on these surfaces according to a 1:1 H2O:MeCO3(surface) stoichiometry where each adsorbed H2O molecule interacts with one metal center (Mg for magnesite and Mg or Ca for dolomite) and at least one neighboring O surface atom (de Leeuw and Parker, 2001, 2002; Wright et al., 2001; Parker et al., 2003; Kerisit et al., 2005a; Austen et al., 2005). This information strongly suggests that, regardless of the specific orientation of adsorbed H2O molecules relative to the mineral surface, all (10.4) single- and mixed-metal carbonate surfaces are subjected to similar hydration processes where water remains undissociated upon adsorption. 3.1.2. Single generic primary surface site Based upon the results of spectroscopic and molecular modeling studies, a generic primary surface site for the (10.4) cleavage calcite surface can be defined as: „(CaCO3)H2O, where the constituents in parentheses represent surface atoms and at least one H2O molecule is associated

with the surface atoms and at least one H2O molecule is associated with the surface atoms. This reactive surface site reflects the elemental stoichiometry of the (10.4) hydrated surface unit cell: two neighboring surface atoms, one metal atom and one carbonate group, interacting with one undissociated water molecule (Fig. 1a). This scheme is equivalent to those of Pivovarov (1997) and Kulik (2002) for metal oxides insomuch as the adsorbed H2O molecules are considered as the reactive elemental units at the surface, whereupon surface reactions occur. Because a stoichiometric number of divalent cationic (Ca atoms) and anionic (CO3 groups) surface sites are present at the idealized (10.4) cleavage calcite surface (and of all rhombohedral carbonate minerals to that matter), and regardless of the residual charge displayed by individual surface atoms (following bond re-organization on hydration), charge–neutrality should be preserved at the idealized stoichiometric unit, „(CaCO3), and maintained upon adsorption of neutral H2O monomers. Accordingly, a neutral charge can be assigned to the newly defined primary surface site: „(CaCO3)H2O0. Whether more than one water molecule are associated with this primary surface site (e.g., Villegas-Jime´nez et al., 2009a) is unimportant to the definition of the primary surface site since attached water molecules do not affect mass or charge discretization. In contrast to earlier multi-site SCMs that assume the formation of primary surface sites of type „MeOHd and „CO3Hd, (d = residual charge), the one-site scheme circumvents the problem of mass and charge discretization allowing for a generic, yet realistic, mass and charge

Fig. 1. (A) Plan view of the hydrated surface unit cell at the idealized (10.4) calcite surface. Two primary surface sites, „(CaCO3)H2O are present per surface unit cell (shown in ovals). One H2O monomer interacts with one Ca and one O atom (see short arrows). Shaded tones distinguish atoms present within the surface unit cell but formally associated to neighboring surface or subsurface cells. (B) Schematic representation of non-overlapping and overlapping arrays of surface sites. The former is based upon specific atom partners, whereas the latter is established among any pair of nearest neighbor atoms.

n.r.: No additional reaction needed for full equivalency with the one-site scheme. Note that, although carbonate reactions (5a, 6a, 5b and 6b) are written in terms of the CO32 ion, the HCO3 ion is the dominant carbonate species in solution over the experimental range.

H+/HCO3 coadsorption (One-site) HCO3/OH exchange (two-site) n.r. Me Me 6a BhCO  H2 Oi þ 2Hþ þ CO3 2 () BhCO  H2 CO3 i þ H2 O 6b BMeOH0 þ 2Hþ þ CO3 2 () BMeHCO3 þ H2 O 3 3

HCO3 adsorption (one-site) CO32/OH exchange (two-site) n.r. 5b BMeOH0 þ Hþ þ CO3 2 () BMeCO3  þ H2 O Me Me  H2 Oi þ Hþ þ CO3 2 () BhCO  HCO3 i þ H2 O 5a BhCO 3 3

Me2+/H+ exchange 4b BCO3 H0 þ Me2þ () B CO3 Meþ þ Hþ n.r. Me Me 4a BhCO  H2 Oi þ Me2þ () BhCO  MeOHiþ þ Hþ 3 3

Ionization (protonation) n.r. 3b BMeOH0 þ Hþ () BMeOH2 þ Me Me 3a BhCO  H2 Oi þ Hþ () BhCO  H3 Oiþ 3 3

1b BCO3 H0 () BCO3  þ Hþ Ionization (two-step protolysis) 2b BMeOH0 () BMeO þ Hþ Me Me 2a BhCO  H2 Oi () BhCO  Oi2 þ 2Hþ 3 3

Anionic site

1b BCO3 H0 () BCO3  þ Hþ Ionization (one-step protolysis)

# Cationic site Amphoteric site #

Me Me  H2 Oi () BhCO  OHi þ Hþ 1a BhCO 3 3

#

Two-site One-site

Table 1 Equivalencies of generic surface reactions formulated in terms of one-site and two-site schemes.

n.r.

Type of reaction

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localization at the primary surface site, rather than at individual surface atoms. This yields a rREF = 0, identical to that of earlier multi-site SCMs for single- and mixed-metal rhombohedral carbonate surfaces (Van Cappellen et al., 1993; Pokrovsky et al., 1999a,b; Pokrovsky and Schott, 2002; Wolthers et al., 2008) and consistent with the reference level of zero net charge typically adopted by 2-pK models (Sposito, 1998). Detailed structural information of hydrated (relaxed) carbonate surfaces from independent studies (e.g., molecular modeling, Fitts et al., 2005; Kubicki et al., 2008) is required to determine realistic bond lengths, coordination environments, and hydrogen bonding arrangements of surface atoms for the derivation of more accurate d values (and rREF), as emphasized by earlier workers (Bickmore et al., 2004; Villegas-Jime´nez et al., 2005; Wolthers et al., 2008). 3.2. SCM reactions: One-site vs. two-site scheme The one-site scheme is analogous to the one describing non-overlapping bidentate adsorption, where pairs of specific neighboring surface sites (rather than pairs of random neighboring surface sites, as for overlapping bidentate adsorption), react with a given sorbate to produce a bidentate surface complex (Benjamin, 2002), and thus, two neighboring sites are inactivated for further reaction (see Fig. 1b). For carbonate minerals, polydentate adsorption is wellexemplified by the interaction of aspartate with calcium ions on the calcite surface (Teng and Dove, 1997), leading to a large perturbation of the local molecular surface geometry, significant steric effects, and the inactivation of adjacent sites (see also the ‘‘Umbrella effect”, Kovacˇevic´ et al., 1998). This contrasts with the two-site scheme where, with the exception of synergistic effects related the development of the macroscopic electrical potential, each site is independent, and thus, it is assumed that adsorption at one site does not affect the macroscopic reactivity of any of its neighbors. Earlier workers described the charging behavior of single-metal carbonate minerals with six or more generic reactions (ionization and constituent ion adsorption reactions) based upon a two-site (Van Cappellen et al., 1993; Pokrovsky et al., 1999a; Pokrovsky and Schott, 2002) or a multi-site scheme (Pokrovsky et al., 1999b; Wolthers et al., 2008). Similarly, analogous reactions can be derived for the one-site scheme (see Table 1). Although reactions are equivalent in terms of charge and mass transfer, the participating individual species in both schemes carry a distinct stoichiometry and different ‘‘conceptual” mechanisms are implied in each case. Fig. 2 illustrates ionization reactions conceptualized at the molecular-level for the one-site scheme. The main distinction between the one-site and the two-site models is revealed upon reaction of the primary surface sites. In the case of the protonation reaction for calcite (reactions 3a and 3b, Table 1), the one-site model conceptually involves the participation of both „CO3H0 and „CaOH0 sites to produce the protonated, positively-charged specie: „(CaCO3)H3O+. In contrast, according to the two-site scheme, only one cationic site reacts to produce the protonated, positively-charged specie: „CaOH2+ while leaving one anionic site, „CO3H0, available for further reaction. In other words,

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Fig. 2. Conceptual molecular representation of possible ionization reactions (protonation/deprotonation) at the (10.4) surface of rhombohedral carbonate minerals according to the one-site scheme. Equivalent reactions defined in terms of two surface sites are also shown for comparison. Note that this is a simplified conceptual scheme since more than one undissociated water molecule could be associated with the surface and may participate to surface reactions.

in both cases, one positive charge is transferred to the surface per mole of primary surface site reacted but, whereas only one primary surface site is available for further reaction in the one-site model, „(CaCO3)H2O0 (on a surface unit cell basis), three sites remain available according to the two-site model, one „CaOH0 and two „CO3H0. Once surface equilibrium is established, the charge density of the surface unit cell will depend on whether additional reactions took place at the surface (e.g., constituent ion adsorption). Clearly, multi-site schemes allow for a multitude of reactions that can lead to surface charge acquisition and may equally reproduce experimental surface charge data, at the expense of a larger number of unknown parameters (that must be adjusted or arbitrarily selected, see below) than for the one-site scheme. This has important consequences in the calibration of intrinsic formation constants and directly reflects on surface speciation predictions, as discussed in Section 4.2. In Fig. 3, the availability of ‘‘unreacted” primary surface sites at a generic single- or mixed-metal (10.4) carbonate surface is illustrated as a function of the proton occupancy for ionization (protonation/deprotonation) reactions formulated for the one-site (reactions 1a–3a, Table 1) and two-site (reactions 1b–3b, Table 1) schemes. 3.3. Mixed-metal carbonate minerals In mixed-metal rhombohedral carbonate minerals, two different types of constituent cations (i.e., Me1 and Me2)

alternate along the (10.4) surface. Thus, for the one-site scheme, two types of generic primary surface sites, (Me1CO3)H2O0 and (Me2CO3)H2O0 would be required to formulate equivalent surface reactions to those of the earlier four-site SCM model for dolomite that involves twelve surface reactions (Pokrovsky et al., 1999b). The Kint values describing these reactions, however, would be difficult to calibrate without a combination of suitable experimental data (e.g., titration, calorimetric, radiometric, electrokinetic) acquired over a wide range of solution compositions and use of suitable mathematical strategies that would allow resolution of the contribution of individual surface reactions (through their intrinsic formation constants) to the development of surface charge (see Section 1). Unfortunately, because of their reactivity (fast dissolution/precipitation kinetics, Pokrovsky and Schott, 2002), the experimental characterization of the sorptive properties of carbonate minerals is typically constrained to a relatively narrow range of solution compositions (pH, RMe and/or RCO2, solid:solution ratios) which complicates the quantitative evaluation of the intrinsic formation constants. This type of calibration would be even more problematic within the Charge Distribution MultiSite Ion Complexation (CDMUSIC) approach as it requires the fitting and/or arbitrary selection of a larger number of parameters (Wolthers et al., 2008). Other approaches, such as molecular modeling techniques (Rustad et al., 1996; Wasserman et al., 1999), may be required to establish critical theoretical constraints for the

Defining primary surface sites at rhombohedral carbonate surfaces

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Fig. 3. Idealized extent of proton occupancy of primary surface sites on a generic single- or mixed-metal (10.4) carbonate surface unit cell as dictated by ionization reactions (protonation/deprotonation), according to one-site and two-site schemes. Because rREF is identical in both cases, charge densities are also identical (on a surface unit cell basis and neglecting the presence of additional sorbing ions and/or further ionization of primary surface sites). Note that, except from very high pH conditions where all primary surface sites have reacted in both schemes, the number of ‘‘unreacted” primary surface sites is distinct for each model at each extent of proton occupancy.

accurate evaluation of the individual reactivity of multiple primary surface sites at carbonate surfaces. An alternate treatment for mixed carbonate minerals is to formulate surface reactions in terms of a single charge– neutral surface site that reflects half the stoichiometry of the hydrated (10.4) surface unit cell: (MeCO3)H2O0 where MeCO3 represents generically Me1 or Me2 (e.g., Ca or Mg for dolomite). Under this scheme, the number of intrinsic formation constants is reduced by at least a factor of two with respect to previous multi-site models (i.e., dolomite: Pokrovsky et al., 1999b; Wolthers et al., 2008), which renders the model more mathematically tractable. This formalism is justified by the inadequacy of the available experimental data for the proper calibration of multiple surface reactions and largely disregards the attribution of too much mechanistic meaning (e.g., surface site heterogeneity) to composite charging curves or adsorption isotherms (see Lu¨tzenkirchen, 1997). The newly-formulated surface reactions can be generalized for single- and mixed-metal carbonate minerals as shown in Table 1, the only difference being that, for mixed-metal carbonate minerals, one additional cation adsorption reaction (reaction 4a, Table 1) is required to express the individual affinity of Me1 and Me2 towards (MeCO3)H2O0. One corollary to this single charge–neutral surface site formalism is that an average reactivity is assigned to the generic surface site,

and hence, whether surface reactions formally take place at (Me1CO3)H2O or (Me2CO3)H2O remains undefined. In other words, the individual reactivities of these sites are averaged out during model calibration and expressed in terms of the formation constant, a reasonable approximation considering that the individual site reactivities in mixed-metal carbonate minerals are hard to decouple experimentally. That Ca2+ and Mg2+ ions adsorb in nearstoichiometric ratios on dolomite surfaces over a wide range of pH, RCa/RMg, ionic strength, and pCO2 (Bra¨tter et al., 1972; Brady et al., 1996) suggests that both primary surface sites exhibit similar reactivities. 4. EVALUATION OF THE ONE-SITE SCHEME 4.1. Re-calibration of surface reactions for magnesite and dolomite Despite all the arguments provided in favor of the onesite scheme, it is important to test the relevance of the derived reactions against experimental data. To this end, the calibration of one-site-based SCMs for magnesite and dolomite was performed using experimental surface charge data from Pokrovsky et al. (1999a,b). These data were obtained using a modified limited residence time (LRT) reactor where the pH was varied by additions of NaOH or HCl.

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Given the experimental difficulties involved in the experimental protocol, only a limited number of data points could be obtained for each acid–base titration (13) under a range of chemical conditions selected at the beginning of each experiment (i.e., magnesite: RMg = 0.8–7 mM and RCO2 = 0.9–29 mM; dolomite: RMg = 0.07–3.8 mM, RCa = 0.03–5.7 mM; RCO2 = 0.6–13 mM). Unfortunately, the one-site scheme cannot be tested for calcite because of the dearth of reliable data characterizing the proton and constituent ion sorptive properties of this highly reactive carbonate mineral (see Villegas-Jime´nez et al., 2009b). In earlier multi-site SCMs models for carbonate minerals (Van Cappellen et al., 1993; Pokrovsky et al., 1999a,b; Pokrovsky and Schott, 2002), a single set of surface reactions (reactions 1b–6b) was used in model calibration. Additional reactions were considered in a recent SCM to account for the reactivity of primary surface sites at terraces, corners, and edges and consider the formation of a new surface species: „CO3H2+ (Wolthers et al., 2008). Given the nature of the available experimental data (composite surface charge or electrokinetic data rather than adsorption data) and because of the large number of unknown parameters (Kint’s, capacitances, etc.), numerical optimization using commercially-available computer codes such as FITEQL (Herbelin and Westall, 1996) was not attempted by earlier workers (Van Cappellen et al., 1993; Pokrovsky et al., 1999a,b; Pokrovsky and Schott, 2002; Wolthers et al., 2008). Conversely, in the present study, we tested the one-site scheme for both minerals against different sets of reactions (Models) which were alternatively calibrated via stochastic numerical optimization using an in-house MatlabÓ subroutine. The latter incorporates a powerful search and optimization stochastic technique, the genetic algorithm (GA), that can perform the simultaneous optimization of a large number of parameters within a pre-established solution space and allows tackling complex optimization problems (Gen and Cheng, 2000). The application of GAs to estimate intrinsic formation constants of surface species has been described and successfully tested on a number of cases of varying degrees of complexity where adsorption data and/or surface charge data are used for SCM calibration (Villegas-Jime´nez and Mucci, in press). Because of the stochastic nature of GA optimizations, the GA parameters (i.e., population size, number of generations, type and probability of crossover and mutation probability) must be carefully selected and the optimization repeated to verify the reproducibility of the adjusted quantities. If poor reproducibility in the optimized values is observed upon multiple optimizations, the adopted model is incorrect and/or the data are inadequate for model calibration. All GA optimizations described below were run in triplicate with the following GA parameters: population of 500 chromosomes, 100 generations, a single-point crossover probability of 0.25, and a mutation probability of 0.02. All associated MatlabÓ subroutines can be obtained upon request to the lead author. The predictive power of each model (selected set of surface reactions) was evaluated on the basis of three criteria: (i) its ability to reproduce surface charge (used to perform the model calibration), (ii) its capacity to simulate, at a

semi-quantitative level, published electrokinetic data acquired over a wide range of solution conditions, and (iii) the compatibility of the predicted surface speciation with available spectroscopic information. The latter two are a posteriori SCM validation criteria independent of model calibration, key steps to consider in inverse modeling work. Our starting point was to calibrate the ionization reactions (generic reactions 1a–3a, Table 1) independently (Model I). To this end and for each mineral, surface charge data obtained from independent titrations at identical ionic strengths (I = 0.01 M for dolomite and I = 0.1 M for magnesite) and moderatively low RCO2 and RMe concentrations (magnesite: RCO2 < 1.7 mM, RMg < 1 mM; dolomite: RCO2 < 1 mM, RCa < 0.5 mM, and RMg < 0.8 mM) were combined into a single data set for each mineral and used in model calibration. In these data sets, pH was the master variable controlling the chemical speciation (covering the range: 5 6 pH 6 10 for both minerals) while RCO2 and RMg were kept at relatively low concentrations, minimizing the influence of constituent ions on surface charge development. This allowed us to examine the influence of ionization reactions on surface charge development and obtain initial estimates of their corresponding Kint values (reactions 1a–3a, Table 1). Following the procedure applied in earlier studies (Van Cappellen et al., 1993; Pokrovsky et al., 1999a,b; Pokrovsky and Schott, 2002), we used the Constant Capacitance Model (CCM) to describe the surface charge–potential relationship, where the surface is assumed to behave as a flat capacitor with the potential varying linearly away from the surface (Sposito, 1984; Goldberg, 1993): r0 w0 ¼ ð5Þ C where C is the specific integral capacitance (F m2) of the electrified interfacial layer (EIL). In this model, the capacitance is a function of the ionic strength and was described earlier by Van Cappellen et al. (1993): C¼

I 1=2 a

ð6Þ

where I is the ionic strength and a is an adjustable parameter related to the physical properties of the EIL that reconciles working units (m2 M½ V C1). In the CCM formulation, all surface species are assumed to adsorb chemically at the surface plane (0-plane), allowing for the formation of inner-sphere surface complexes. This is compatible with the premises implied by the limited residence time (LRT) experimental protocol (or Flow-through reactor technique originally developed by Charlet et al., 1990) that allocates ion charge imbalances recorded in solution (excluding the background electrolyte) at each titration point to the 0-plane (charge imbalance in filtered solution = surface charge). Surface species are treated in mol kg1 units referenced to the 1 m standard state, whereas aqueous species are given in molar concentrations under the constant ionic medium convention (Sposito, 1984). Ion pair formation and aqueous complexation were considered in model calibration and surface complexation using the formation constants listed in Table 2. Note that

Defining primary surface sites at rhombohedral carbonate surfaces

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Table 2 Equilibrium formation constants and mass balance equations used in thermodynamic calculations in this study. Log10 K° (25 °C)

Equilibria +



6.35a 10.33a 1.27a 0.25a 2.92a 1.01a 3.20a 1.27a 11.44b 12.85b

H + HCO3 () H2CO3* H+ + CO32 () HCO3 Na+ + CO32 () NaCO3 Na+ + HCO3 () NaHCO3 Mg2+ + CO32 () MgCO3 Mg2+ + HCO3 () MgHCO3+ Ca2+ + CO32 () CaCO3 Ca2+ + HCO3 () CaHCO3+ Mg2+ + H2O () MgOH+ + H+ Ca2+ + H2O () CaOH+ + H+ Mass balance equations RCa = [Ca2+] + [CaOH+] + [CaHCO3+] + [CaCO3(aq)] RMg = [Mg2+] + [MgOH+] + [MgHCO3+] + [MgCO3(aq)] RCO2 = [H2CO3*] + [HCO3] + [CO32] + [CaHCO3+] + [CaCO3(aq)] + [NaHCO3] + [NaCO3] RNa = [Na+] + [NaHCO3] + [NaCO3]

Brackets represent molar concentrations of the specified chemical species; [H2CO3*] = [CO2(aq)] + [H2CO3]. a Values from NIST (1998). b Values from Stumm and Morgan (1996).

because the LRT technique produces composite adsorption data (it involves protons, hydroxyls and constituent ions), the computation of net sorption densities upon referencing of apparent sorption densities to the Point of Zero Net Proton Charge (PZNPC), as recommended by some authors (e.g., Chorover and Sposito, 1995; Sposito, 1998), is not applicable to the data used in our study (Pokrovsky et al., 1999a,b). Unfortunately, to date, no method can unambiguously characterize the surface charge of a carbonate mineral suspension prior to titration (electrokinetic measurements yield potentials at the shear plane which can only be related to surface charge by an electrostatic model). Thus, the common assumption is to assign a ‘‘zero” surface charge to the carbonate mineral surface (rREF = 0, Eq. (2)) prior to titration, rendering apparent surface charge densities identical to net surface charge densities (e.g., Charlet et al., 1990; Van Cappellen et al., 1993; Pokrovsky et al., 1999a,b). This is based on the assumption that once a MeCO3 suspension in pure water (or in an ‘‘inert” background electrolyte) has reached equilibrium, the mineral surface must approach the Point of Zero Net Charge, PZNC (Charlet et al., 1990). Intrinsic constants were referenced to a zero potential standard state by performing the electrostatic correction to the mass law expression as defined by Eq. (4). We fixed the site densities of both minerals to their respective crystallographic values (9.8  106 for magnesite and 8.9  106 mol m2 for dolomite). In all cases, the value of a was adjusted simultaneously for capacitance values comprised between 0.1 and 100 F m2 (note that high capacitances were considered based upon earlier SCMs). In contrast, a large solution space was chosen for all log10 Kint values (25 to 25) to perform an exhaustive search for the set of Kint values that best reproduced the experimental data. All attempts to fit magnesite and dolomite data with the simplest electrostatic model, the generalized double-layer model (DLM, Davis and Kent, 1990) were unsuccessful. After the DLM, the CCM is the simplest elec-

trostatic model describing the surface charge–potential relationship and, is hence, a reasonable framework to rationalize adsorption data acquired by the LRT experimental protocol. There is little point in testing more sophisticated electrostatic models (e.g., Basic Stern Model, Triple Layer Model; Davis and Kent, 1990) and add complexity to our interpretation without having at our disposal individual, self-consistent sets of proton and constituent ion adsorption data at different ionic strengths that would serve to better define the affinity and type of interaction (innersphere vs. outer-sphere) of constituent and background electrolyte ions with the surface. Additional surface-sensitive spectroscopic data such as that of Pokrovsky et al. (2000) will be key in distinguishing between these types of interaction. Upon calibration, Model I (see Tables 3 and 4) provided reasonable fits of surface charge data for both minerals but the optimized Kint values of magnesite and dolomite could not simulate the zeta potential measurements of Pokrovsky et al. (1999a,b), particularly at high RCO2 (>0.01 M). This was expected given that Model I does not account for carbonate adsorption. Furthermore, the pH of isoelectric point (pHiep) of dolomite and magnesite, reported to range from pH 6 to 8.8 and 6.8 to 8.5, respectively (Pre´dali and Cases, 1973; Pokrovsky et al., 1999a,b; Chen and Tao, 2004; Gence and Ozbay, 2006), were poorly predicted by the optimized model parameters. These observations led us to perform further calibrations whereupon additional reactions (i.e., ionization and constituent ion adsorption) were considered. Given the known dependency of zeta potential values on RCO2 and RMe (Pokrovsky et al., 1999a,b), we tested, individually, the influence of constituent ion (Me2+ and CO32) adsorption on the development of surface charge. To this end, specific sets of surface reactions for both minerals and selected data points for each mineral were used in subsequent optimizations. For the calibration of ionization and constituent anion adsorption reactions (Model II, reactions

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4336

Table 3 SCM parameters for magnesite surfaces in 0.1 M NaCl solutions as estimated using various sets of surface reactions (see text for details). Values are averages of three stochastic GA-optimizations. Errors correspond to the 95% confidence intervals. Log10 Kint (25°)

Surface equilibria

Model I¥

Mg Mg BhCO  H2 Oi () BhCO  OHi þ Hþ 3 3 Mg BhCO 3

 H2 Oi ()

Mg BhCO 3

2

 Oi

þ 2H

þ

Mg Mg BhCO  H2 Oi þ Hþ () BhCO  H3 Oiþ 3 3 Mg BhCO 3 Mg BhCO 3

2þ

 H2 Oi þ Mg

()

Model IIIà

Model IV*

Two-site Model§

8.80 ± 0.32

8.50 ± 0.25

8.70 ± 0.1

8.65 ± 0.1

24.39 ± 1.82

22.08 ± 1.44

23.87 ± 0.42

22.95 ± 0.72

6.84 ± 0.16

8.30 ± 0.36

6.73 ± 0.13

7.0 ± 0.13

10.60 ± 0.15

17.25 ± (>4)

10.32 ± (>7)

2.20 ± 0.15

n.i.

n.i

4.65 ± 0.15 16.65£ ± 1

 MgOHiþ þ Hþ

Mg  H2 Oi þ Hþ þ CO3 2 () BhCO 3 Mg  HCO3 i þ H2 O BhCO 3 Mg BhCO3  H2 Oi þ 2Hþ CO3 2 () Mg BhCO 3

Model II 

n.i.

12.90 ± 1.37

n.i.

n.i.

21.80 ± 0.72

n.i.

14.40 ± 0.15

8.57 ± (>10) 18.85 ± 0.21

22.40 ± 0.5

 H2 CO3 i þ H2 O

Capacitance (F m2)

31.6 ± (<0.1)

31.6 ± (<0.1)

31.6 ± (<0.1)

31.6 ± (<0.1)

98.8

Intrinsic constants with large uncertainties in bold (see text for details). Optimization performed using data set at following conditions: (¥) RCO2 < 1.7 mM, RMg < 1 mM; ( ) 1 < RCO2 < 10 mM and 1.2 < RMg < 3 mM (optimization subsequently repeated with full data set); (à) 0.9 < RCO2 < 3.6 mM and 1 < RMg < 7 mM; (*) Full data set. (§) Log10 Kint values for two-site-based equivalent reactions taken from Pokrovsky et al., 1999a. (£) Value reflects full surface protolysis (cationic + anionic site). n.i. = reaction not included in the model. Note that these values cannot be directly compared with those of Wolthers et al. (2008) because their Log10 Kint values correspond to a ‘‘hybrid” CCMCD-MUSIC model. These authors only calibrated ionization constants (generic reaction 1a–3a, plus a novel reaction involving the doubledprotonated carbonate corner site: >CO3H2+) according to the CD-MUSIC-Triple-Plane model, whereas all constituent ion adsorption reactions (generic reaction 4a–6a) were taken from Pokrovsky et al. (1999a) (CCM approach) without further adjustment.

Table 4 SCM parameters for dolomite surfaces in 0.01 M NaCl solutions as estimated using various sets of surface reactions (see text for details). Values are averages of three stochastic GA-optimizations. Errors correspond to the 95% confidence intervals. Log10 Kint (25°)

Surface equilibria

Model I¥

Model II 

Model IIIà

Model IV*

Four-site Model§ (Ca)

Me BhCO 3 Me BhCO 3

 H2 Oi ()

Me BhCO 3

 H2 Oi ()

Me BhCO 3



þ

 OHi þ H 2

 Oi

þ 2H

þ

Me Me BhCO  H2 Oi þ Hþ () BhCO  H3 Oiþ 3 3 Me BhCO  H2 Oi þ Ca2þ () 3

Me  CaOHiþ þ Hþ BhCO 3 Me  H2 Oi þ Mgþ () BhCO 3 Me  MgOHiþ þ Hþ BhCO 3 Me BhCO3  H2 Oi þ Hþ þ CO3 2 () Me BhCO  HCO3 i þ H2 O 3 Me BhCO  H2 Oi þ 2Hþ þ CO3 2 () 3 Me  H2 CO3 i þ H2 O BhCO 3 Capacitance (F m2)

8.83 ± 0.41

8.18 ± 0.35

24.89 ± 0.17

19.51 ± 1.02

6.41 ± 0.25

7.30 ± 0.43

8.22 ± 0.1 23.65 ± 0.14 6.40 ± 0.1

8.19 ± 0.1 17.23 ± 0.14

(Mg)

4.8 ± 0.2 £

16.8£ ± 2

16.8 ± 2

6.77 ± 0.59

11.5 ± 0.2

n.i.

n.i.

19.24 ± (>5)

15.26 ± (>4)

1.8 ± 0.2

n.i.

n.i.

16.97 ± (>4)

20.43 ± (>4)

n.i.

11.28 ± 1.92

n.i.

n.i.

21.60 ± 0.79

n.i.

18.5 ± (<0.2)

18.2 ± (<0.1)

18.6 ± (<0.2)

4.17 ± (>15) 17.91 ± 1.51

31.6 ± (<0.1)

4.8 ± 0.2

10.6 ± 0.2

2.0 ± 0.2 16.6 ± 0.2

15.4 ± 0.2

24.0 ± 0.5

23.5 ± 0.5

25

Intrinsic constants with large uncertainties in bold (see text for details). Me represents generically either Ca2+or Mg2+. Optimization performed using data set at following conditions: (¥) RCO2 < 1 mM, RCa < 0.5 mM, and RMg < 0.8 mM; ( ) 0.6 < RCO2 < 3 mM, 0.18 < RMg < 1.5 mM, and 0.06 < RCa < 1.5 mM (optimization subsequently repeated with full data set); (à) 2 < RCO2 < 2.7 mM, 1.1 < RMg < 2.7 mM, and 1.1 < RCa < 2.7 mM; (*) Full data set. (§) Log10 Kint values for four-site-based equivalent reactions taken from Pokrovsky et al., 1999b. (£) Value reflects full surface protolysis (cationic + anionic site). n.i. = reaction not included in the model. Note that these values cannot be directly compared with those of Wolthers et al. (2008) because their Log10 Kint values correspond to a ‘‘hybrid” CCMCD-MUSIC model. These authors only calibrated ionization constants (generic reaction 1a–3a, plus a novel reaction involving the doubledprotonated carbonate corner site: >CO3H2+) according to the CD-MUSIC-Triple-Plane model, whereas all constituent ion adsorption reactions (generic reaction 4a–6a) were taken from Pokrovsky et al. (1999b) (CCM approach) without further adjustment.

Defining primary surface sites at rhombohedral carbonate surfaces

1a–3a, 5a and 6a, Table 1), only data points with relatively low RMe concentrations (i.e., RMg < 3 mM for magnesite; RMg and RCa < 1.5 mM for dolomite) were used in the calibration. In contrast, constituent cation adsorption and ionization reactions (Model III, reactions 1a–4a) were calibrated using data with moderate to low RCO2 concentrations (i.e., <3.6 mM for magnesite and <2.7 mM for dolomite) and the highest RMe concentrations available. Although optimized SCM parameters are different among models (see Tables 3 and 4), all models reasonably reproduced the titration data of Pokrovsky et al. (1999a,b). One-way Analysis of Variance (ANOVA) tests (95% confidence) confirmed that all model fits are statistically identical. A final calibration (using all available surface charge data) including ionization and constituent ion adsorption reactions (Model IV, reactions 1a–6a) was performed for comparison. For both minerals, the estimated Kint values for the constituent cation adsorption reactions (Model III and IV) are very small and carry large uncertainties (suggesting that these are unnecessary to describe the data, see Tables 3 and 4), whereas the uncertainties of the Kint values of the ionization reactions are low. In contrast, constituent anion adsorption constants, optimized within Model II, carry relatively low uncertainties and are believed to be relevant in the description of the data. This suggests that the available experimental data are adequate to derive reliable Kint values for ionization and constituent anion adsorption reactions but may be insufficient to properly calibrate the Kint values of constituent cation adsorption reactions, and thus, additional experimental data (batch adsorption or LRT-based titrations experiments covering higher constituent cation

4337

concentrations) are required to accurately resolve their affinity for these surfaces. We recognize that, at high metal concentrations, adsorption of constituent metals will affect surface charge development on carbonate minerals but, in the absence of pertinent data to calibrate this reaction, its inclusion in the model is premature and, in fact, unnecessary to fit our data. In all cases and for both minerals, rather high specific capacitances (31.6 F m2 for magnesite and 18.2– 31.6 F m2 for dolomite) are needed to reproduce the experimental surface charge. High capacitance values (30–100 F m2) were also required in previous studies to simulate the surface charge and/or the electrokinetic behavior of these and other divalent carbonate minerals using either monolayer (CCM, Van Cappellen et al., 1993; Pokrovsky et al., 1999a,b; Pokrovsky and Schott, 2002) or multi-layer EIMs (Wolthers et al., 2008). All attempts to fit the data with smaller capacitance values, by further restricting the GA-optimization range of the adjustable parameter a, significantly decreased the quality of the fit. Although the estimated capacitance values for both minerals (except from Model IV for dolomite) are lower than those derived in earlier studies (Pokrovsky et al., 1999a,b; Pokrovsky and Schott, 2002; Wolthers et al., 2008) and are in better agreement with physical constraints (i.e., thickness of EIL), they lie outside the range typically assigned to metal oxides (0.1–2 F m2). High capacitances at carbonate surfaces were explained by the presence of a thin, highly structured, non-diffuse EIL by earlier workers (Van Cappellen et al., 1993; Pokrovsky et al., 1999a,b; Wolthers et al., 2008) but its strict physical interpretation would require a very high and unrealistic dielectric constant of the

Fig. 4. Surface charge of magnesite in 0.1 M NaCl solutions (RMg = 0.8–7 mM and RCO2 = 0.9–29 mM) as predicted by the one-site Model I (ionization reactions), one-site Model II (ionization + constituent anion adsorption reactions) and the two-site Model of Pokrovsky et al. (1999a) (Ionization + constituent ions adsorption reactions) at conditions: RMg = 2 mM and RCO2 = 3 mM. Experimental data from Pokrovsky et al. (1999a) used in model calibration are shown.

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interfacial water (Hayes et al., 1991). Alternatively, they could be interpreted as being related to the large experimental surface charge densities rather than to the absence/presence of multiple electrostatic layers, and hence, we prefer to assign a purely operational character to the capacitance. Accordingly, and in conformity with premises of the CCM, all derived model parameters are considered as operational surface speciation predictors (i.e., model fit parameters), applicable only to the chemical conditions of model calibration (pH, I, etc.).

Surface charge simulations for magnesite, performed at fixed solution conditions (RMg = 0.002 M and RCO2 = 0.003 M.) using Models I and II and the two-site SCM of Pokrovsky et al. (1999a), are shown in Fig. 4 and compared against experimental data. It is noteworthy that, at pH P 8.5, the large range of measured surface charge cannot be reproduced by any of the models. Under strongly alkaline conditions, slight differences in RCO2 concentrations may induce significant changes in surface charge via carbonate adsorption which are not properly described at the selected

Fig. 5. Zeta potentials taken from Pokrovsky et al. (1999a,b) compared against predicted surface potentials (solid, long-dashed, dash-dotted, short-dashed, and dotted lines) predicted by Model II for magnesite and dolomite for a range of chemical conditions. Ref. 1: Pre´dali and Cases (1973); Ref. 2: Chen and Tao (2004); Ref. 3: Gence and Ozbay (2006).

Defining primary surface sites at rhombohedral carbonate surfaces

solution conditions of our simulations. Consideration of the experimental RCO2 and RMg conditions (the latter influencing the aqueous carbonate ion activities upon ion pair formation) at each titration point is required to improve the agreement between experimental data displayed in Fig. 4 and surface charge predictions returned by our one-site-based Model II (or the two-site-based model of Pokrovsky et al., 1999a). In contrast, surface charge predictions of Model I would remain unchanged because no provision for carbonate and/or metal ion adsorption is made by this Model. Because the presence of a shear-plane is ill-defined in the CCM, predicted surface potentials (the potential at the 0plane) were compared with zeta potentials (f-potentials, measured at the shear-plane), but only at a semi-quantitative level. We found that Model II is the only one that provides reasonable predictions of surface potential for a range of chemical conditions (i.e., it follows the trend displayed by zeta potentials) and best reproduces the pHiep values measured for both minerals (see Fig. 5). The predicted surface potentials are in reasonable agreement with f-potentials measured at pHs < 8.5 but, at pH above 9, Model II consistently predicts more negative surface potentials for both minerals at all chemical scenarios of our SCM simulations (see conditions in Fig. 5). This observation is, nonetheless, compatible with the premise that the absolute potential measured at the shear-plane must be lower than the surface potential (Davis and Kent, 1990). Based upon the selected criteria for evaluating the predictive power of our Models (see also Section 4.3), the calibrated model parameters for Model II are considered as good operational predictors of the surface charge and the electrokinetic behavior and surface speciation (see Sections 4.2 and 4.3) of magnesite and dolomite surfaces in chemical systems whose composition (i.e., pH, ionic strength, RMe and RCO2) is similar to those under which the experimental data used for model calibration were acquired. Nevertheless, the optimized parameters should be used with caution for predictive purposes since adsorption reactions involving constituent cations may be significant under specific chemical conditions (e.g., high RMe) and may influence the development of charge at the surfaces of some carbonate minerals such as calcite (e.g., Siffert and Fimbel, 1984; Huang et al., 1991; Cicerone et al., 1992). Further experimental work (e.g., batch constituent ion adsorption experiments) is needed to verify the self-consistency of these parameters under different chemical conditions and to carefully evaluate the relevance of other surface reactions (e.g., constituent cation and background electrolyte adsorption) that may contribute to the development of the surface charge and the formation of a more sophisticated EIL than envisioned by the CCM. 4.2. Intrinsic formation constants and surface speciation Our selected set of log10 Kint values are significantly different from those derived from earlier surface complexation models for both minerals (Tables 3 and 4). This divergence is explained by the application of the one-site scheme in the formulation of surface equilibria and the different strategies

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employed in each study to estimate the intrinsic formation constants. In earlier studies, Kint values were either calibrated manually against surface charge or electrokinetic data on a trial and error basis using equilibrium constants of analogous reactions in aqueous solution as their starting point (Van Cappellen et al., 1993; Pokrovsky et al., 1999a,b; Pokrovsky and Schott, 2002) or by using theoretical schemes originally developed for metal oxides (Wolthers et al., 2008). It is noteworthy that the latter authors report Kint values for a ‘‘hybrid” SCM where ionization reactions were calibrated according to the CD-MUSIC-Triple-Plane approach developed for metal oxides (Hiemstra and van Riemsdijk, 1996), whereas the Kint values of constituent ion adsorption reactions were those of earlier CCM-based SCMs (Van Cappellen et al., 1993; Pokrovsky et al., 1999a,b). Clearly, comparisons between these Kint values and those derived in the present study are unwarranted. Interestingly, the one-site-based log10 Kint values obtained for the one-step protolysis reaction for both minerals (reaction 1a, Table 1) are in reasonable agreement with those of analogous reactions in aqueous solutions (NIST, 1998): CaHCO3 þ () CaCO3 þ Hþ CaHCO3 þ () MgCO3 þ Hþ

log10 K ¼ 8:40 log10 K ¼ 8:42

ð7Þ ð8Þ

In Fig. 6, we present the surface speciation predicted by Model II for magnesite and dolomite for the following chemical conditions: RCO2 = RMe = 1 mM, which largely contrasts with that predicted by multi-site-based SCMs for these minerals (Pokrovsky et al., 1999a,b; Wolthers et al., 2008). For instance, whereas the one-site scheme predicts the predominance of protonated and deprotonated species under very different pH regimes (acid and alkaline, respectively), as would be expected for a truly amphoteric surface (analogous to a polyprotic acid in solution), multi-site SCMs predict the simultaneous predominance of a double-protonated („MeOH2+ for the CCM or „MeOH2+1/3 at terraces for the CD-MUSIC) and a deprotonated species („CO3 for the CCM and „CO31/3 at terraces for the CD-MUSIC) over a wide pH range (5 to 9). In other words, according to multi-site SCMs, protonation and deprotonation reactions (1b and 3b, see Table 1) simultaneously occur over a wide pH range, suggesting that a large number (n) of these double-protonated species must be neighboring an approximately equal number (m) of deprotonated species. This is intuitively unrealistic because such a molecular scenario (i.e., n „MeOH2+ ffi m „CO3) would most likely result in the re-establishment of the global stoichiometry and charge of primary surface sites („MeOH2+ + „CO3 = „MeCO3H2O0), implying that a negligible net protonation or deprotonation (hence, a negligible net charge transfer) occurs at the mineral surface under these chemical conditions. Furthermore, it would be difficult to explain why the anionic primary surface site, „CO3H0 strongly deprotonates at pH  5, whereas the cationic primary surface site, „MeOH0, readily undergoes protonation under identical pH conditions. This is a direct consequence of assigning individual reactivities (e.g., acidities) to neighboring cationic and anionic surface sites and

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Fig. 6. Surface speciation predicted by Model II for magnesite in 0.1 M NaCl solutions (RCO2 = 1 mM, RMg = 1 mM) and dolomite in 0.01 M NaCl solutions (RCO2 = 1 mM, RMg = RCa = 1 mM).

performing a simultaneous (unconstrained) adjustment of their corresponding intrinsic ionization constants. This contrasts with the one-site scheme that, by assigning an average reactivity to the cationic-anionic primary surface site, allows for a realistic description of the amphoteric behavior of the carbonate surface, and hence, yields intuitively reasonable predictions of surface speciation. According to Model II, the predominance of the charge– neutral H2CO3-bearing surface species, „(MeCO3)H2CO30, and, to a lesser extent, of the ‘‘unreacted” primary surface site, „(MeCO3)H2O0, at conditions similar to those under which carbonate mineral studies are typ-

ically conducted: RCO2 ffi RMe ffi 1 mM; pH 5.5–8.5, accounts for the charge-buffering behavior displayed by magnesite and dolomite surfaces and may explain the relatively wide range of pHiep values reported in the literature for these minerals (Pre´dali and Cases, 1973; Pokrovsky et al., 1999a,b; Chen and Tao, 2004; Gence and Ozbay, 2006). 4.3. Comparison against spectroscopic information According to the one-site scheme (Model II), surface speciation and charge acquisition at the above conditions

Defining primary surface sites at rhombohedral carbonate surfaces

is dominated only by the protonated species at low pH (<5), whereas, at circum-neutral pH (5.8–8.2), the charge–neutral H2CO3-bearing surface species is predominant for both minerals. This is in agreement with results of DRIFT spectroscopic studies (Pokrovsky et al., 2000) and Knudsen flow reactor-based CO2(g) adsorption studies (Santschi and Rossi, 2006) that revealed the presence of carbonate-bearing species at the dolomite and calcite surface at pH P 5 and RCO2 P 103 M (Pokrovsky et al., 2000), and at hydrated calcite surfaces exposed to CO2(g) atmospheres (Santschi and Rossi, 2006). These findings dismiss the viability of models that make no provision for carbonate ion adsorption (Models I and III). Similarly, because of the low Kint values returned from the optimization of carbonate adsorption reactions (generic reactions 5a and 6a, Table 1) in Model IV, this model predicts negligible concentrations of carbonate-bearing species at the above conditions, in conflict with available spectroscopic information. Using X-ray Reflectivity, Fenter et al. (2000) investigated the surface speciation of calcite, under three different chemical scenarios (RCa, RCO2, I, pH) which, according to SCM predictions (Van Cappellen et al., 1993), represented either: (i) a ‘‘calcium-terminated” surface (RCa 1.4 M, RCO2 = 0.34 mM, pH = 6.83), (ii) a ‘‘water-terminated” surface (RCa 0.5 mM, RCO2 = 1.33 mM, pH = 8.25), or (iii) a ‘‘carbonate-terminated” surface (RCa 0.012 mM, RCO2 = 2.27 mM, pH = 12.1). Among these, the solution composition generating the ‘‘water-terminated” scenario most closely reflects the chemical conditions (RCa = RCO2 = 103 M) under which our speciation predictions (Fig. 6) were conducted, and thus, is best suited for comparisons. According to our one-site-based SCM calculations (Fig. 6), at a pH 6 8.2, the surface speciation of magnesite and dolomite is dominated by H3O+-, H2O-bearing and/or a carbonate-bearing species. The abundance of the former and the latter species abruptly drops as pH increases, and thus, the H2O-bearing and/or the OH-bearing species predominate at slightly higher pH. These two species are undistinguishable from each other given that protons are not detected by X-ray Reflectivity, and hence, under these pH conditions, the surface speciation predicted by Model II is consistent with Fenter and coworker’s conclusion that X-ray Reflectivity data and the implied surface speciation could be explained solely by protonation/deprotonation reactions (generic reactions 1a–3a). In other words, at pH > 8.2, the calcite surface is essentially dominated by hydroxyl-bearing surface species (be it as OH, OH2 and, to a lesser extent, OH3), and at very high pH, by deprotonated species, „(MeCO3)O2, which, within the multi-site scheme, can be interpreted as BCOd3 . Note that the latter is not considered as an adsorbed carbonate-bearing species but rather as a deprotonated primary surface site. According to our one-site SCM calculations (Model II) and assuming that the surface speciation of calcite is similar to that predicted for magnesite and dolomite, neither the ‘‘carbonate-terminated” nor the ‘‘calcium-terminated” scenarios examined by Fenter et al. (2000) are adequate to evaluate carbonate adsorption because the very high pH in the former (beyond the range of carbonate-bearing surface species) and the very high RCa in the latter (which sub-

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stantially decreases CO32 activities in solution upon ion pair formation) are unfavorable to the development of carbonate-bearing surface species. Hence, under both scenarios, surface speciation would be dominated by H3O+-, H2O-, and/or OH-bearing species (resulting from protonation/deprotonation reactions), in agreement with Fenter and coworker’s results. It should be noted, however, that the above comparisons should be revised when X-ray Reflectivity-based surface speciation studies are extended to magnesite and dolomite surfaces. 5. CONCLUSIONS The definition of primary surface sites in terms of their elemental stoichiometry and residual charge plays a critical role on the molecular representation of reactions at mineral surfaces and the calibration of surface complexation models via LMA approaches. Given the abundance of experimental and theoretical information for the (10.4) cleavage calcite surface, this surface was selected as a case study to revisit the definition of reactive surface sites on divalent rhombohedral carbonate minerals. A single primary surface site is proposed for calcite which is compatible with available spectroscopic data and molecular modeling results as well as with assumptions frequently implied in the construct of SCMs. In addition, it circumvents the problem of charge and mass discretization associated to earlier multi-site schemes developed for this mineral. The one-site scheme was extended to the surface of magnesite and dolomite and published surface charge data for both minerals were used in the calibration of the newly defined surface reactions. Several sets of one-site-based surface reactions, including ionization and/or constituent ion adsorption reactions can successfully simulate surface charge but only one can qualitatively reproduce the electrokinetic behavior displayed by both minerals while yielding intuitively reasonable predictions of surface speciation, consistent with available spectroscopic data, and reflecting the behavior of a truly amphoteric surface. The simplified model for both minerals, involving bicarbonate ion adsorption and proton/bicarbonate ion coadsorption reactions (in addition to ionization reactions), accounts for the surface charge-buffering behavior displayed by these minerals under circum-neutral conditions and offers a possible explanation to the relatively wide range of pHiep values typically reported in the literature. This is achieved with a reduced number of parameters (five log10 Kint values and one capacitance) which contrasts with more sophisticated multi-site schemes (such as the CDMUSIC model) that require many more parameters that must be manually adjusted on a trial and error basis (as taken from earlier CCM-based SCMs) and/or arbitrarily selected on the basis of multiple theoretical assumptions originally derived for metal oxides. Admittedly, as in earlier SCMs for carbonate minerals calibrated within single (CCM) or multiple (Triple Plane) electrostatic layer schemes, the physical interpretation of the adjusted capacitances is problematic, and hence, we prefer to consider all model parameters as operational surface speciation

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predictors (i.e., model fit parameters), applicable to the chemical conditions of model calibration (pH, I, etc.). Given its simplicity and compatibility with available experimental data, we propose that the one-site scheme is a convenient approach to use in the construct of SCMs for other rhombohedral carbonate minerals. As more experimental data from different sources (adsorption isotherms, calorimetric, radiometric, electrokinetic, etc.) become available, it might be possible to fine-tune these models and reliably incorporate multi-layer and multi-site adsorption concepts without expanding upon numerous assumptions. Additional theoretical constraints obtained from molecular modeling techniques and fundamental crystal and colloid chemistry will be key for the proper calibration of such sophisticated models. ACKNOWLEDGMENTS A.V.-J. thanks Dr. Luuk Koopal for critical discussions that inspired this investigation. We acknowledge the insightful reviews of Dimitri A. Sverjensky, Phillipe Van Cappellen, Marie¨tte Wolthers, and two anonymous reviewers. This research was supported by a graduate student grant to A.V.-J. from the Geological Society of America (GSA) and Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery grants to A.M. A.V.-J. also benefited from post-graduate scholarships from Consejo Nacional de Ciencia y Tecnologı´a (CONACyT) of Mexico and additional financial support from the Department of Earth and Planetary Sciences, McGill University and from Consorcio Mexicano Flotus-Nanuk.

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