Modeling uranium(VI) adsorption onto montmorillonite under varying carbo- nate concentrations: A surface complexation model accounting for the spillover effect on surface potential

The prediction of U(VI) adsorption onto montmorillonite clay is confounded by the complexities of: (1) the montmorillonite structure in terms of adsorption sites on basal and edge surfaces, and the complex interactions between the electrical double layers at these surfaces, and (2) U(VI) solution speciation, which can include cationic, anionic and neutral species. Previous U(VI)-montmorillonite adsorption and modeling studies have typically expanded classical surface complexation modeling approaches, initially developed for simple oxides, to include both cation exchange and surface complexation reactions. However, previous models have not taken into account the unique characteristics of electrostatic surface potentials that occur at montmorillonite edge sites, where the electrostatic surface potential of basal plane cation exchange sites inﬂuences the surface potential of neighboring edge sites (‘spillover’ eﬀect). A series of U(VI) – Na-montmorillonite batch adsorption experiments was conducted as a function of pH, with variable U(VI), Ca, and dissolved carbonate concentrations. Based on the experimental data, a new type of surface complexation model (SCM) was developed for montmorillonite, that speciﬁcally accounts for the spillover eﬀect using the edge surface speciation model by Tournassat et al. (2016a). The SCM allows for a prediction of U(VI) adsorption under varying chemical conditions with a minimum number of ﬁtting parameters, not only for our own experimental results, but also for a number of published data sets. The model agreed well with many of these datasets without introducing a second site type or including the formation of ternary U(VI)-carbonato surface complexes. The model predictions were greatly impacted by utilizing analytical measurements of dissolved inorganic carbon (DIC) concentrations in individual sample solutions rather than assuming solution equilibration with a speciﬁc partial pressure of CO 2 , even when the gas phase was laboratory air. Because of strong aqueous U(VI)-carbonate solution complexes, the measurement of DIC concentrations was even important for systems set up in the ‘absence’ of CO 2 , due to low levels of CO 2 contamination during the experiment.


INTRODUCTION
Due to mining, milling and fuel processing operations, numerous sites have been contaminated with uranium in the past, with 38 proposed or final Superfund sites on the EPA National Priority List in the U.S. alone (NIH, 2016). In the future, the long-term storage of nuclear waste has the potential to create additional sources of uranium contamination affecting subsurface environments and drinking water resources. Chemically-induced, acute effects of uranium in humans, such as an inflammation of the kidneys (nephritis), have been reported (Hursh and Spoor, 1973), while chronic health effects and carcinogenicity are less well understood (World Health Organization, 2004). At this point in time, the World Health Organization has proposed a provisional guideline value of 15 lg UÁL À1 in drinking water (World Health Organization, 2004); the current U.S. EPA Maximum Contaminant Level (MCL) is set at 30 lg UÁL À1 (U.S. Environmental Protection Agency, 2001). A sound scientific understanding of uranium mobility is needed in order to evaluate risks to humans and the environment, to optimize the management of nuclear waste and to take appropriate remediation actions if necessary.
The most relevant factors controlling uranium transport in saturated porous media are uranium solubility in pore water solutions and uranium adsorption reactions to mineral surfaces. Uranium can exist at oxidation states of IV or VI, but U(VI) is the most relevant oxidation state in most surface waters and in oxic groundwaters (Choppin, 2006). In reducing environments, the low solubility of U (IV) mineral phases greatly decreases uranium mobility.
Numerous studies have demonstrated the impacts of pH, bicarbonate and calcium concentrations on U(VI) solution speciation, adsorption and transport behavior Curtis et al., 2004;Fox et al., 2006;Hartmann et al., 2008). Potential changes in chemical solution conditions and contaminant solution speciation over time and space are especially relevant for uranium, given the long half-lives of uranium isotopes and complex transport pathways in engineered systems and the natural environment. For instance, in nuclear waste repositories, pore water pH is buffered at values between 7 and 8 in the bentonite backfill material of engineered barrier systems surrounding waste canisters and/or in the clay host-rock (Muurinen and Lehikoinen, 1999;Bradbury and Baeyens, 2003;Wersin, 2003;Wersin et al., 2004;Tournassat et al., 2015c). However, more alkaline pH conditions are expected in close proximity to steel canisters (pH 8-11) due to corrosion processes (Bildstein and Claret, 2015), as well as in cementitious leachates at bentonite-concrete boundaries (pH > 13 for Ordinary Portland Cement and pH 9-11 for low alkali cement) due to the chemical degradation of cement (Savage et al., 1992;Gaucher and Blanc, 2006;Gaboreau et al., 2012b;Milodowski et al., 2016). Furthermore, dissolved calcium concentrations may also vary over time and space due to the progressive degradation of cementbased engineered barriers, the specific calcite contents in clay host rocks or changing concentrations in carbonate minerals along transport pathways (Hartmann et al., 2008;Gaboreau et al., 2012a;Adinarayana et al., 2013).
These chemical gradients in waste scenarios are important for the fate and transport of uranium, since U(VI) aqueous speciation is very complex. For instance, the uranyl cation (UO 2 2+ ) typically dominates speciation at low pH, while neutral and anionic U(VI)-hydroxyl and carbonate complexes become predominant at higher pH conditions. In a dilute U(VI) solution at pH 7 in the absence of carbonate, the predominant U(VI) species is the neutral UO 2 (OH) 2 0 . In comparison, for the same solution in equilibrium with atmospheric CO 2 , the predominant species is the anion (UO 2 ) 2 CO 3 (OH) 3 À (for a 1 mmolÁL À1 solution). However, groundwater solutions are typically in equilibrium with partial pressures of CO 2 (pCO 2 ) at 1 % or greater, and may contain considerable concentrations of calcium due to the presence of carbonate minerals. At 1 % pCO 2 , pH 7 and in the absence of Ca, U(VI) solution speciation is dominated by the anion UO 2 (CO 3 ) 2 2À ( Clay minerals are important minerals to consider in uranium contaminant transport because of the proposed use of bentonite or clay-rocks as a buffer material in engineered and natural barrier systems at future nuclear waste disposal sites (Tournassat et al., 2015b). Furthermore, there is the possibility that colloid-facilitated transport of uranium adsorbed on clay or bentonite particles may occur near granite waste repositories Schäfer et al., 2004;Missana et al., 2008). Last, clay contents in soils and sediments are often high at uranium-contaminated sites (Grawunder et al., 2009;Graham et al., 2011).
Sodium-montmorillonite is the focus of this study because this mineral is the major component of bentonite in barrier systems. Montmorillonite is a smectite, a 2:1layer-type dioctahedral phyllosilicate with a large specific surface area ($750 m 2 Ág -1 ) and cation exchange capacity ($1 mol c Ákg À1 ). Each montmorillonite layer has a thickness of $1 nm and carries negative surface charges due to isomorphic substitutions of Al(III) for Si(IV) and Mg(II)/Fe (II) for Al(III) in its phyllosilicate framework (Brigatti et al., 2013). Due to its crystal structure, montmorillonite provides two types of surfaces and surface site types: (1) cation exchange sites, with a permanent surface charge, on basal planar surfaces, and (2) surface complexation sites, with variable surface charges as a function of pH, on edge surfaces of clay particles (Borisover and Davis, 2015).
Many research groups have investigated the surface speciation of adsorbed U(VI) on montmorillonite with EXAFS spectroscopy (Dent et al., 1992;Chisholm-Brause et al., 1994;Giaquinta et al., 1997;Sylwester et al., 2000;Hennig et al., 2002;Catalano and Brown, 2005;Schlegel and Descostes, 2009;Marques Fernandes et al., 2012;Troyer et al., 2016). Analysis of the data obtained at various ionic strengths reveals the presence of U(VI) outersphere complexes at low pH and/or low ionic strengths, and of U(VI) inner-sphere complexes at other conditions. These interpretations of EXAFS data are in qualitative agreement with the duality of adsorption mechanisms on montmorillonite surfaces, i.e. cation exchange on basal planar surfaces at low pH/ionic strength and surface complexation on edge surfaces at other conditions, as also evinced by other spectrometric techniques for a range of different specifically adsorbed cations Chisholm-Brause et al., 2001;Kowal-Fouchard et al., 2004;Wolthers et al., 2006).
The formation of inner-sphere bonds of U(VI) with surface groups at montmorillonite edge sites at neutral pH and high ionic strength was deduced from the splitting of the U(VI) oxygen equatorial shell into two distinct contributions at $2.3 Å and $2.5 Å in EXAFS spectra. However, there is considerable uncertainty in the interpretation of second neighbor atoms involved in these surface complexes. Hennig et al. (2002) concluded that surface mononuclear bidentate complexes formed at aluminol sites. Schlegel and Descostes (2009) also proposed a U-Al shell, in agreement with Hennig et al. (2002). Additional Polarized-EXAFS (P-EXAFS) characterizations allowed them to conclude that the U complex was located on the particle edges and corresponded to a mononuclear bidentate complex. In contrast, Catalano and Brown (2005) suggested that the primary surface group second neighbors were Fe atoms, where Fe has substituted for Al in the octahedral sheets. In addition, Catalano and Brown (2005) fitted their data with a U-C shell and suggested that ternary uranylcarbonato species formed at the surface in the presence of carbonate. However, more recently, Marques Fernandes et al. (2012) and Troyer et al. (2016) concluded that it was not possible to conclusively distinguish between Fe, Al, and Si as second neighbor atoms in U(VI) EXAFS spectra. Furthermore, Marques Fernandes et al. (2012) did not find spectroscopic evidence for uranyl-carbonato complexes at the montmorillonite surface, despite the fact that their surface complexation model included the species. Troyer et al. (2016) were not able to confirm the presence of ternary uranyl-carbonato surface complexes from their EXAFS data either, but made a strong conclusion about the presence of such species from laser-induced fluorescence spectroscopy (LIFS) data. The LIFS results, however, were obtained at very high U(VI) equilibrium concentrations and high U(VI)/clay ratios. The total U(VI) concentration was 100 mmolÁL À1 and solid-to-liquid ratio was 0.2 gÁL À1 , leading to an equilibrium U(VI) solution concentration of $70 mmolÁL À1 . Although it is not known, these conditions might have favored the formation of uranyl carbonate complexes driven by a high total uranium-carbonate ratio.
An accurate prediction of uranium mobility in clay-rich environments is dependent upon the development of adsorption models that can capture: (1) the complex uranium solution and surface speciation as a function of chemical solution conditions, and (2) the complexity of montmorillonite and its implications for the conceptual description of adsorption processes. Surface complexation models (SCMs) have the ability to directly link U(VI) adsorption behavior with U (VI) solution speciation based on existing thermodynamic data, which allows the models to predict changes in adsorption as a function of chemical solution conditions over time and space. Several research groups have developed surface complexation models (SCMs) for the U(VI)montmorillonite system (Pabalan and Turner, 1996;Turner et al., 1996;Hyun et al., 2001;Baeyens, 2005, 2011;Marques Fernandes et al., 2012). Surface complexation modeling studies predict that U(VI) adsorption decreases at alkaline pH when carbonate anions are present, due to the formation of strong aqueous uranyl-carbonato complexes (see Fig. EA-1, and see the aqueous speciation diagrams in Davis et al. (2004) and Fox et al. (2006)). However, the impact of the aqueous carbonate complexes on U(VI) sorption depends on whether these complexes adsorb on the clay surfaces or not. For example, in the model of Marques Fernandes et al. (2012), the authors found it necessary to include ternary uranyl-carbonato surface complexes to describe U(VI) adsorption onto montmorillonite in the presence of various concentrations of aqueous carbonate. Analogous U(VI) surface species have also been proposed on iron oxides and imogolite (Waite et al., 1994;Villalobos et al., 2001;Arai et al., 2007). For U(VI) adsorption on montmorillonite, however, in the absence of clear spectroscopic evidence, the need to add such additional surface complexes was guided by the quality of the fit between the model and the data. This fitting criterion may however be impaired by inadequate hypotheses in the modeling exercise. For example, the model of Marques Fernandes et al. (2012) was a nonelectrostatic model, which means that the ionic nature of the sorbent and its interaction with the electrostatic potential field surrounding the montmorillonite particles is inherently not included. Given the complex U(VI) solution speciation described above, it is important to take into account that the interactions of cationic, neutral or anionic U(VI) solution species with the surface electrostatic field is influenced by their charge. Hence, an electrostatic model is needed in order to test the importance of the electrostatic interactions in quantifying U(VI) adsorption. Furthermore, the electrostatic model is needed to test whether it is necessary to include ternary uranyl-carbonato surface complexes in the model.
Currently available electrostatic surface complexation models for montmorillonite have been mostly based on the classical surface complexation models for oxides. These models are based on the hypothesis that surface charges are homogeneously distributed on a flat and infinite surface, which is an invalid assumption for clay minerals for the following two reasons. First, the edge surface is very different from a flat infinite surface in terms of its dimensions: while its length could be considered to be infinite, its width is always limited to 1 nm for individual layers dispersed in an electrolytic solution. Second, the surface potential developed by the permanent charges of the basal surfaces interacts with the surface potential at the edge surfaces with pHdependent charge (Secor and Radke, 1985;Chang and Sposito, 1994;Bourg et al., 2007;Tournassat et al., 2013Tournassat et al., , 2015aTournassat et al., , 2016a. This unique feature, called the spillover effect, must be taken into account in the development of an electrostatic model for montmorillonite edge surfaces.
Given the current uncertainties associated with results from spectroscopic studies and the modeling needs described above, the goals of this study are: (1) to improve the current mechanistic understanding of uranium(VI) adsorption onto montmorillonite as a function of chemical conditions, with a specific focus on the role of dissolved inorganic carbon; and (2) to develop an electrostatic surface complexation model that accounts for the impacts of the electricdouble-layer (EDL) spillover effect on U(VI) surface reactions.

MATERIALS AND METHODS
For the development of U(VI) surface complexation models, it is important to carefully characterize the compositions of experimental solutions, because various other solutes may affect U(VI) solution or surface speciation. Uranium(VI) adsorption onto Na-montmorillonite was investigated here as a function of total U(VI), dissolved carbonate, and calcium concentrations (Table 1). Experimental blanks, standards and sample suspensions were analyzed for U(VI), calcium and dissolved inorganic carbon (DIC), and monitored for elements that could indicate clay dissolution or inadequate solid-liquid phase separation (for U(VI) and Ca background values, see Electronic Annex; Si, Al, Fe, K, and Mg data not reported). In addition, analytical detection limits and experimental background values for DIC solution concentrations were determined as described in further detail below. Analysis of DIC concentrations in supernatant solutions was of particular importance in our experiments, given the relevance of carbonate for U(VI) speciation.

Materials
Glassware was cleaned by soaking in acid (10 % (v/v) HCl) over 12-24 h, followed by thorough rinsing with Nanopure water and air-drying. All aqueous solutions were prepared with Nanopure water (Barnstead ultrapure water system) using chemicals of reagent grade or better. Acids, bases and salt solutions used in adsorption experiments were of TraceSelect grade (Sigma Aldrich), in order to minimize calcium background concentrations in particular. Uranium(VI) solutions contained U-238, either from an in-house or a commercially available uranyl nitrate stock solution (1.30 mmolÁL À1 stock provided by Drs. David Singer and Wayne Lukens at Lawrence Berkeley National Laboratory, or various dilutions of a 1000 mg UÁL À1 Inorganic Ventures ICP-MS standard).
A well-characterized, standardized source clay (Namontmorillonite, SWy-2, Clay Minerals Society) was selected as the sorbent. Since this material is known to contain considerable impurities of quartz (8 %), feldspars (16 %) and calcite (Chipera and Bish, 2001;Costanzo and Guggenheim, 2001;Mermut and Cano, 2001), it was pretreated to avoid uncontrolled impacts of calcite dissolution on U(VI) solution speciation during adsorption experiments. The major purification steps, which have been described in detail elsewhere (Tinnacher et al., 2016), included: (1) dissolution of calcite impurities in 1 molÁL À1 sodium acetate/0.564 molÁL À1 acetic acid solution at pH 5, (2) conversion of the clay into its Na form, (3) separation of quartz and feldspar impurities from the <2 lm clay fraction by centrifugation, and (4) oven-drying of the clay mineral phase at 45°C. Afterwards, clay stock suspensions of 10 or 20 gÁL À1 were prepared in Nanopure water, and exact solid concentrations determined by weighing volume fractions before and after drying at 45°C.

Experimental protocol for batch adsorption experiments
Uranium(VI) adsorption onto Na-montmorillonite was characterized as a function of pH, and total U(VI), DIC, and calcium concentrations (Table 1).
Batch adsorption experiments were conducted at room temperature (22.5-23.5°C) at an ionic strength of 0.1, and a Na-montmorillonite concentration of 0.5 gÁL À1 (except for experiment 7 with a solid concentration, m s , of 0.24 gÁL À1 ). pH values ranged from 3.9 to 10.2. The reaction time was 48.5 h, which closely approached or was sufficient to reach steady-state conditions (see discussion of kinetic adsorption data in the Electronic Annex). This reaction time is comparable to reaction times of 20-72 h used in other, similar studies Hyun et al., 2001;Bradbury and Baeyens, 2005;Schlegel and Descostes, 2009). Total calcium concentrations varied from low micromolar background concentrations (see Electronic Annex) to the higher concentration of 2.1 mmolÁL À1 in the experiment with added Ca.
The main steps in the batch adsorption experiments were: (1) pre-equilibration of Na-montmorillonite with a background electrolyte solution at specific pH and chemical solution conditions, (2) U(VI) adsorption equilibration with the mineral phase, and (3) sampling and analysis of supernatant fractions after removal of the solid phase by centrifugation. In the initial preparation of the solution/clay suspensions, aliquots of Nanopure water,  Na-montmorillonite stock suspension, 1 M NaCl and 0.1 M CaCl 2 solutions, and 1 M or 0.1 M NaHCO 3 solution were transferred into 50 mL polycarbonate centrifuge vials to yield the intended solid concentrations and aqueous compositions in the final sample volumes. The polycarbonate vials ('Oakridge centrifuge tubes') were chosen as sample vials to minimize U(VI) wall adsorption effects. The pH values were then adjusted to the intended values for the adsorption experiments with small volumes of HCl or NaOH. During this initial preparation procedure, the solutions were exposed to one of three different gas phases: (1) atmospheric CO 2 in laboratory air ($0.04 %, 400 ppm), (2) CO 2 -''free" atmosphere (in a glove box, filled with 94.3 % N 2 /5.7 % H 2 gas mixture) and (3) elevated CO 2 atmospheres (intended to be 2 % CO 2 /98 % N 2 ). In the CO 2 -''free" experiment, the initial solutions used N 2 -purged Nanopure water and were prepared in an anaerobic glove box purged with a 94.3 % N 2 /5.7 % H 2 gas mixture. Two experiments involved exposure to elevated CO 2 atmospheres. In Experiment 6, the solutions were prepared in a disposable Sigma Aldrich glove bag purged with a 2 % CO 2 /98 % N 2 gas mixture, but it was found subsequently that the purging of the glove bag was incomplete to remove all air (see Experimental Results section). Solutions in Experiment 7 were exposed in a COY glove box to the same gas mixture, but again it was found after the experiments that the glove box had been insufficiently purged with the gas mixture. After the preparation of the solutions, they were generally pre-equilibrated in closed sample vials by shaking for 12-24 h; however, in the case of Experiment 7 the vials were left open and exposed to the glove box atmosphere for 15 h.
After pre-equilibration with the electrolyte solution, aliquots of acidified U(VI) stock solution were added to obtain the intended total U(VI) concentrations in the experiments. Because the U(VI) stock solution was acidic, it was necessary to add small amounts of NaOH immediately following the U (VI) addition to adjust the pH to the intended experimental value. The vials were then shaken for 48.5 h. Afterwards, final pH values were recorded while minimizing gas exchange during the pH measurement (discussed further below). The sample suspensions were centrifuged to remove particles larger than approximately 50 nm from solution, as calculated based on Stokes law (Beckman Coulter Allegra 64R, F0850 rotor, centrifugation at 26 900 g for 61 min). Aliquots of supernatant solution were collected and analyzed for metal concentrations by ICP-MS (Perkin-Elmer SCIEX ICP-Mass Spectrometer ELAN DRC II, after sample acidification with TraceSelect grade HNO 3 (2% v/v)), and DIC concentrations on a Shimadzu TOC-V CSH . Each experiment included experimental standards (in duplicate), in which the standards had the same volume of U(VI) stock solution added to a vial in the absence of the clay with pH adjusted to 2.0. In addition, electrolyte blanks (in duplicate) containing 0.1 molÁL À1 NaCl but no U(VI) or clay were used to determine calcium and uranium-238 background concentrations (see Electronic Annex).
The U(VI) adsorption results are reported as distribution coefficients (K D values, in LÁkg À1 ) and fractions of U(VI) adsorbed (f UðVIÞ ads in %). Adsorbed U(VI) fractions and K D values were computed based on concentration differences in supernatant solutions between experimental standards (C tot ) and samples (C eq ): where m s is the solid concentration in kgÁL À1 . The error bands were calculated as follows (Tournassat et al., 2013): where D values are the considered error bands, k is the coverage factor (taken at a value of k = 2), C tot , C eq , uC tot and uC eq are the total concentration, the equilibrium concentration and their associated uncertainties (we considered 2 % of the values) respectively. Uncertainty on m s was neglected.

Analytical detection limits and background values for dissolved inorganic carbon
The Method Detection Limit (MDL) and Minimum Level (ML) were determined to be 0.051 and 0.161 mgÁL À1 DIC (4.2Á10 À6 and 1.3 Á 10 À5 molÁL À1 DIC) for the specific setup of our DIC analysis, as described in detail in the Electronic Annex. The MDL represents the minimum DIC concentration that can be identified, measured and reported with a 99 % confidence that the concentration is greater than zero (U.S. EPA, 1995). The ML is defined as the smallest measured concentration of a constituent that may be reliably reported using a given analytical method. Potential DIC contributions from various sources in the CO 2 -''free" batch adsorption experiment, performed in the 94.3 % N 2 /5.7 % H 2 glove box environment, were quantified as described in detail in the Electronic Annex. Taking into account the offset due to DIC background concentrations in Milli-Q water (MQW), calibration curves showed linearity down to the lowest concentration standard at 0.025 mgÁL À1 (2.1 Á 10 À6 molÁL À1 ) of added DIC.

Dissolved inorganic carbon in experimental solutions
Because U(VI) aqueous speciation is strongly dependent on the DIC concentration , Fox et al. (2006), and see Figs. EA-1 and EA-2), it was very important in these experiments to determine DIC directly rather than calculate its concentration based on an assumed equilibrium with a gas phase.
The handling of open sample vials in the glove box atmosphere (5 % H 2 /95 % N 2 ) in the CO 2 -''free" adsorption experiment, centrifugation of close vials under atmospheric CO 2 conditions, and refrigeration of closed vials outside the glove box prior to DIC analysis were each evaluated for their potential to increase measured DIC concentrations (see Electronic Annex for details). Sample handling and centrifugation, which took place prior to supernatant sampling in the CO 2 -''free" adsorption experiment, resulted in 0.344 and 0.277 mgÁL À1 DIC (2.9 Á 10 À5 and 2.3 Á 10 À5 mol Á L À1 DIC) concentrations during the test experiment. Storage of solutions in the refrigerator, which occurred after supernatant sampling in the adsorption experiments, resulted in a concentration of 0.331 mgÁL À1 DIC (2.8 Á 10 À5 molÁL À1 DIC). Given the similarity of DIC contributions from these potential sources and the series of steps in the CO 2 -''free" adsorption experiment, it can be assumed that these DIC concentrations are representative of typical DIC ''contaminant" contributions to sample suspensions in our adsorption experiments. Furthermore, we can assume that measured DIC values represent DIC concentrations that were present in sample suspensions during the U(VI) sorption equilibration.

Measured DIC concentrations in batch adsorption experiments
Final dissolved carbonate (DIC) concentrations in the U(VI) sorption experiments were the result of several contributions: (1) background concentrations from reagents (e.g., NaOH), (2) addition of NaHCO 3 during initial solution preparation, and (3) ingassing and outgassing of CO 2 during exposure to various gas phases during the preparation of solutions for the U(VI) sorption experiments. A summary of measured DIC concentrations in the adsorption experiments is provided in Fig. 1.
Experiments carried out in the presence of laboratory air (Experiments 1-4) resulted in measured DIC concentrations generally greater than the values expected for this pCO 2 ($10 À3.45 atm) (Fig. 1, left panel). This was likely due to additions of DIC with reagents, especially during the adjustments of pH with NaOH. Samples from the CO 2 -''free" experiment (Experiment 5) had DIC concentrations similar to solutions observed under atmospheric conditions for pH < 6, suggesting CO 2 contamination during the experimental handling as described above. However, the samples at pH > 6 had DIC concentrations that were much lower than those under atmospheric conditions (Fig. 1, left panel), demonstrating that the contaminant CO 2 ingassing to the solutions was likely flux-limited at higher pH.
In the experiments with elevated CO 2 in the gas phase, the DIC results (Fig. 1, right panel) suggest that neither the gas bag (Experiment 6) or gas chamber (Experiment 7) was sufficiently purged with the 2 % CO 2 /98 % N 2 gas to achieve the intended equilibration with the 2% partial pressure of CO 2 . This was the case despite multiple purge volumes that were used to clear the bag and gas chamber in these experiments. In experiment 6, solutions up to a pH of 7.24 exhibited DIC concentrations that suggested equilibration with a gas phase composition closer to $1 % CO 2 . Samples from supernatants at higher pH values had DIC concentrations consistent with even lower partial pressures of CO 2 . This trend is most likely due to insufficient purging combined with a lack of fast CO 2 equilibration between the aqueous phase and the local atmosphere in the gas bag.
In experiment 7, the calculated low pCO 2 values at acidic pH suggest that the Coy gas chamber was not sufficiently flushed to achieve the target CO 2 partial pressure. Although the solutions contained added NaHCO 3 such that they would be equilibrated with a 2 % CO 2 gas phase, DIC data indicate that some CO 2 outgassed from solutions into the chamber atmosphere, driven by a pCO 2 value lower than 2 %.  Appelo, 1999, 2013) with the THERMOCHIMIE database (Giffaut et al., 2014).
Despite the problems equilibrating the solutions with the intended gas phases, DIC concentrations in the prepared solutions were constant in the U(VI) sorption experiments after the closing of the centrifuge tubes (calculated partial pressures of CO 2 in the centrifuge tubes are given in Fig. EA-6). By measuring DIC in all sample solutions, including those exposed to laboratory air, the equilibrium geochemical model determined the U(VI) aqueous speciation for each experimental data point rather than assuming a constant specific partial pressure of CO 2 in equilibrium with the aqueous phase. As will be discussed further below, this was very important in describing the observed U(VI) adsorption behavior in the SCM.

Effect of variable DIC
In experiments conducted in laboratory air (Experiments 1-4), U(VI)-montmorillonite K D values varied over four orders of magnitude as a function of pH (Fig. 2). At low pH, U(VI) adsorption is assumed to be limited due to its competition with protons at surface complexation sites (Stumm et al., 1992). At high pH, low uranium adsorption is attributed to increasing carbonate concentrations, leading to weakly sorbing or non-sorbing aqueous U(VI)carbonate complexes (Hsi and Langmuir, 1985;Waite et al., 1994;Davis et al., 2004). In the CO 2 -''free" system, U(VI) adsorption is very similar at weakly acidic pH values to that observed for the laboratory air atmospheric CO 2 systems. Above pH 6.5, however, U(VI) adsorption was much stronger at very low concentrations of CO 2 than in the laboratory air systems. The increase in U(VI) adsorption at high pH under these conditions can be attributed to much lower concentrations of aqueous U(VI)carbonate complexes that compete effectively with the edge site surface complexation reactions. The effect of aqueous carbonate complexes on U(VI) adsorption is further demonstrated by the U(VI) adsorption results in systems with elevated CO 2 concentrations (Experiments 6 and 7), where U(VI) adsorption decreased at pH values above 5.5 (Fig. 2).

Effect of variable calcium concentrations
Under laboratory air conditions, U(VI) adsorption appeared to be similar in the presence of 2.1 mmolÁL À1 CaCl 2 compared to Ca background concentrations (Fig. 2). However, upon closer inspection, the U(VI) K D value appeared to be lower at pH $ 8 by approximately a half an order of magnitude (compare Exp. 2 and 4 with similar total U(VI) concentrations). Nonetheless, it is difficult  to be certain of this effect because of differences in experimentally observed DIC concentrations. Calculations show that U(VI) aqueous speciation changes in this pH region in the presence of sufficient Ca because of the formation of aqueous ternary Ca-U(VI)-carbonate complexes at pH > 7.5 (Fig. 3). This effect is evaluated further in the modeling section, where calculations are made at a constant CO 2 partial pressure.

Surface complexation modeling strategy
An analysis of the literature shows that considerable uncertainty remains on the nature of inner-sphere complexes on montmorillonite edge surfaces. Surface complexation modeling cannot elucidate the nature of clay atoms present on surface sites, i.e. decipher the contributions of aluminol, silanol and Fe-substituted sites. However, modeling allows for an estimation of the likelihood of a reaction, such as the adsorption of uranyl carbonate complexes, and an understanding of the effect of Ca-CO 3 -U(VI) solution complexes on the extent of U(VI) adsorption in calciumrich environments. In the process, it is necessary to follow a parsimony rule, i.e. to build a model with the fewest adjustable parameters as possible in order to avoid correlations between fitting parameters. Accordingly, the chosen modeling strategy was based on a four-step approach, as follows. In a first step, U(VI) adsorption model parameters were fitted using experimental data from the CO 2 -''free" experiment. In a second step, we applied these parameters to predict the data obtained in the other experiments: a good match of the prediction with experimental data would suggest that formation of ternary uranyl-carbonato surface complexes is not important, while an underestimation of the adsorption extent would indicate that a uranylcarbonato surface complex must have formed (e.g., see the modeling approach of Waite et al. (1994)). In a third step, we applied the model to a large range of data obtained from the literature in order to test its robustness. In a fourth and final step, factors influencing U(VI) adsorption, such as pCO 2 or Ca 2+ concentrations, are discussed on the basis of predictive calculations with the model. A summary of experimental U(VI) batch sorption data is provided in the Electronic Annex in order to allow other researchers to test their modeling concepts.

Surface complexation model for montmorillonite edge surfaces
The objective of the modeling work presented here was to develop a model that was as mechanistic as possible, but without adding too many fitting parameters. Accordingly, the speciation model for SWy-2 edge surfaces was directly taken from Tournassat et al. (2016a). This surface complexation model explicitly takes into account the spillover effect of the basal surface potential on the edge surface potential. This effect is typical for layered minerals with structural charges and renders classical surface complexation models developed for oxide surfaces incorrect for modeling clay mineral edge surface properties (Bourg et al., 2007;Tournassat et al., 2013Tournassat et al., , 2015aTournassat et al., , 2016a. Briefly, the negative surface charge created by the isomorphic substitutions in the montmorillonite lattice creates a negative electrostatic potential field that interacts with the electrostatic field created by the amphoteric edge surface sites (Secor and Radke, 1985;Sposito, 1994, 1996). Consequently, if the edge surface charge is zero, the edge surface potential remains negative. This effect can be adequately captured by setting the relationship between surface charge (Q edge in CÁm À2 ) and surface potential (w edge in V) to: where A 1 , A 2 , and A 3 are fitted parameters, F is the Faraday constant (96 485 C mol À1 ), R is the gas constant (8.314 JÁK À1 Ámol À1 ) and T is the temperature (K). For montmorillonite at 25°C, Tournassat et al. (2013) refined the values of these parameters to: A 1 = 1.4-1.2 log I, A 2 = 11 + log I, and A 3 = À0.02 Â (Àlog I) 1.60 , where I refers to the ionic strength (unitless). This equation is comparable to the classic equation of the diffuse layer model (DLM) for oxides (Davis et al., 1978) that is implemented in most geochemical calculation codes , but that is not adapted to model the properties of clay edge surfaces (Tournassat et al., 2013(Tournassat et al., , 2015a(Tournassat et al., , 2016a: where ee 0 is the dielectric constant for water. The site densities, stoichiometries and protonation/deprotonation constants were taken from Tournassat et al. (2016a). Site densities were calculated from crystallographic considerations and structural formulas; protonation/deprotonation constants were obtained from the predictions of firstprinciple molecular dynamics calculations (Liu et al., 2013(Liu et al., , 2014(Liu et al., , 2015a. Edge surfaces with different crystallographic orientations exhibit amphoteric sites of different natures and with different site densities (Tournassat et al., 2016a). Two kinds of edge surfaces can be found in this model, corresponding to the AC and B chains that were first described by White and Zelazny (1988). The relative proportions of these two kinds of surfaces (AC and B) on SWy-2 particle edges and the total edge specific surface area ($14 m 2 Ág À1 ) were fitted from titration curves. The value of the edge specific surface area that was fitted by Tournassat et al. (2016a) compared well with the value measured by the lowpressure gas adsorption method ($19 m 2 Ág À1 ) (Duc et al., 2005). This value, however, was different from the SWy-2 N 2 -BET specific surface area value. N 2 -BET specific surface area measurements have been commonly used for the calibration of surface complexation models for clay minerals in the literature, even though these values are not representative of the edge specific surface area for the following reason. N 2 -BET measurements probe both edge and external basal surface areas of the particles, and the latter contribution always dominates over the first for montmorillonite particles (Tournassat et al., 2003(Tournassat et al., , 2013(Tournassat et al., , 2015a(Tournassat et al., , 2016a. None of the parameters of the above described surface model was changed during the modeling exercises, leaving only the speciation of U(VI) surface complexes and the related association constants as fitting parameters. Only U(VI) surface complexes on the B-chain surface type were considered in the model, in agreement with the results obtained with P-EXAFS on the orientation of the U(VI) surface complexes (Schlegel and Descostes, 2009;Marques Fernandes et al., 2012). In the absence of any supporting spectrometric evidence on the nature of the surface sites involved in U(VI)-specific adsorption, we hypothesized that the formation of U(VI) surface complexes took place on the most abundant, non-substituted Si T -Al Oc -Si T edge sites, where subscripts T and Oc refer to the tetrahedral and octahedral sheets of the layer respectively ( Table 2). Note that the influence of cation exchange reactions was negligible under our experimental conditions. An in-house version of PHREEQC, which was modified to handle Eq. (6), was used to carry out the calculations, together with the database THERMOCHIMIE v. 9b0 for thermodynamic parameters of solute species (Giffaut et al., 2014). This database is available in various formats including PHREEQC format at the following address: https://www.thermochimie-tdb.com/.

Calibration of the U(VI) surface complexation model in the ''absence'' of CO 2
Carrying out all the steps of an adsorption experiment in the complete absence of CO 2 is very difficult. The DIC measurements indicate that carbonate was not fully excluded from the solutions despite the efforts to achieve this goal. Despite the observed carbonate contamination, the adsorption results from the CO 2 -''free" experiments were qualitatively similar to other literature data for carbonate-free systems (Bradbury and Baeyens, 2005;Marques Fernandes et al., 2012), i.e. showing a sharp increase in U (VI) adsorption from pH 4 to pH 6 and a limited decrease of U(VI) adsorption at pH > 6 ( Fig. 2).
While measured DIC concentrations are usually not considered in CO 2 -''free" U(VI) adsorption models in the literature, they were specifically taken into account in the model calculations discussed here. Only three edge surface reactions were necessary to reproduce the data ( Fig. 4 and Table 2). The effect of cation exchange was negligible because of the effective competition between Na + and UO 2 2+ for cation exchange sites under our experimental conditions (0.1 M NaCl background electrolyte). The calculation made with the same reference model parameters, but using a zero DIC value instead of the measured one, illustrates how sensitive the calculation is to the consideration of actual DIC values (dashed line in Fig. 4) Even at the low DIC concentrations observed in the CO 2 -''free" experiment, dissolved carbonates provide highly competitive ligands for U(VI) complexation reactions relative to mineral surface sites.

Blind prediction of U(VI) adsorption in the presence of CO 2
The minimal set of adsorption parameters obtained from the fitting of CO 2 -''free" adsorption data were directly used to predict the results of experiments carried out under laboratory air conditions (Experiments 1-3). The individually measured DIC concentrations were used to calculate the aqueous composition and U(VI) speciation. The blind prediction of U(VI) adsorption data was good (Fig. 5). Furthermore, in the experiment at U(VI) tot = 0.1 mM, the NaHCO 3 aliquot addition was twice of what it should have been for the sample at pH = 7.34, due to an experimental error (see point circled in left panel of Fig. 5). The related decrease in U(VI) adsorption due to U(VI) aqueous complexation with carbonate was reproduced by the model, without a need for including the formation of uranylcarbonato complexes on the montmorillonite surface. This further supports doubts from spectroscopic studies on the existence of such ternary surface complexes (on montmorillonite) at atmospheric pCO 2 conditions. Furthermore, the experimental error in the NaHCO 3 addition for the sample at pH 7.34 also demonstrates that the solution was slow to re-equilibrate with the atmosphere outside of the closed sample vial, and confirms that the measured DIC values were constant during U(VI) sorption equilibration.
The robustness of the model was further tested as a function of ionic strength, and, again, the model predicted the data well (Fig. 6). Under the conditions of this experimental dataset, the influence of cation exchange reactions was negligible for pH > 5. The apparent effect of ionic strength on the extent of U(VI) adsorption is due to the changes in electrostatic potential as a function of ionic strength, as well as to small changes in pH values (see Fig. 6 caption).
At greater DIC concentrations (due to elevated pCO 2 ), U(VI) adsorption data were also correctly predicted by the model without changing fitting parameters or adding new surface complexes. The model underpredicted the measured values in percent U(VI) adsorbed by 15% or less (Fig. 7). However, it was not possible to enhance the quality of the fit by including a uranyl-carbonato surface complex without deteriorating the data fits obtained in laboratory air or CO 2 -''free" conditions. . From left to right, the total U(VI) concentration was 1.1 Á 10 À7 , 9.6 Á 10 À7 , or 2.55 Á 10 À6 molÁL À1 . NaHCO 3 aliquot addition was twice the intended amount for the sample at pH = 7.34 and 1.1 Á 10 À7 molÁL À1 U(VI) (circled experimental point in left panel). The model prediction was calculated for each data point taking into account individually measured DIC concentrations and pH values (5.6, 5.4, 5.2 at 0.002, 0.01 and 0.1 M NaCl, respectively). The solid concentration was 0.52 gÁL À1 ; the total U(VI) concentration was 9.5 Á 10 À7 molÁL À1 .

Model predictions of literature data
A wide range of literature data is available for U(VI) adsorption on montmorillonite (McKinley et al., 1995;Pabalan and Turner, 1996;Turner et al., 1996;Hyun et al., 2001;Bradbury and Baeyens, 2005;Marques Fernandes et al., 2015;Troyer et al., 2016). Thus, it was possible to test the predictive capabilities of the model over a wider range of conditions than those tested in the experiments described above. However, the limitations of this benchmarking approach are at least twofold. First, the origin and preparation of the clay material (fine fraction separation and further chemical purification) can influence adsorption results because of variations in reactive surface area and surface chemistry. Second, DIC concentrations were not reported in previous studies, while the results presented here demonstrate the importance of this parameter.
The following modeling and data presentation strategies were applied in order to avoid any misinterpretations regarding the quality of the model predictions. Data from the literature were first compared with a blind modeling prediction without any adjustment of model parameters given in Table 2 (reference model). In the case of experiments carried out under atmospheric conditions, a log 10 (pCO 2 ) value of À3.45 was assumed for these reference calculations. In case of CO 2 -''free" conditions, a log 10 (pCO 2 ) value of À99 was applied. In a second step, various hypotheses were tested to achieve a better fit of the data, if necessary. In particular, as our reference model did not include cation exchange reactions, it was necessary to include these reactions to reproduce U(VI) adsorption  Table 3 Cation exchange reaction parameters added to the reference model in order to reproduce literature data obtained at low ionic strength and low pH. a Surface reactions on montmorillonite basal surfaces Log 10 K X À + Na + = XNa 0 Cation exchange reactions with U(VI) species (as a function of literature data) Troyer et al. (2016), Hyun et al. (2001) 2 XNa + UO 2 2+ = X 2 UO 2 + 2 Na + 0.95 0.9 Pabalan et al. (1996) 2 XNa + UO 2 2+ = X 2 UO 2 + 2 Na + 0.75 1.2 McKinley et al. (1995) 2 XNa + UO 2 2+ = X 2 UO 2 + 2 Na + 1.2 0.8 Turner et al. (1996) 2 XNa + UO 2 2+ = X 2 UO 2 + 2 Na + 0.7 0.41 a Cation exchange reactions were modeled with a classic diffuse layer model that was already calibrated for Na + and Ca 2+ by Tinnacher et al. (2016). The total specific surface area for cation exchange reactions was set to the crystallographic surface area for montmorillonite, i.e. $750 m 2 Ág À1 (Tournassat and Appelo, 2011;Tournassat et al., , 2015bTournassat and Steefel, 2015). b Values measured in the reference papers. Fig. 7. U(VI) adsorption in the presence of elevated pCO 2 (symbols: data; line: model predictions). The model was calculated for each data point taking into account individually measured DIC concentrations. Solid concentrations were 0.52 gÁL À1 (left) or 0.24 gÁL À1 (right). Total concentrations of U(VI) were 8.1 Á 10 À7 molÁL À1 (left) and 9.8 Á 10 À7 molÁL À1 (right). data obtained at low ionic strength and low pH (pH < 4) conditions.

Data of Troyer et al. (2016)
The data of Troyer et al. (2016) were acquired in the presence of atmospheric pCO 2 on a clay material similar to the one used in this study (<2 mm fraction of SWy-2 montmorillonite), but in the presence of a 0.01 M NaCl electrolyte, thus promoting cation exchange reactions compared to our conditions. We tested the model on the authors' three adsorption isotherms obtained at pH 4, 6 and 8. Data obtained at pH 6 could be adequately reproduced without changing any parameter from the reference model (Fig. 8). Data obtained at pH 4 could be reproduced only by adding a cation exchange reaction to the reference model (Table 3). Data at pH 8 were not satisfactorily reproduced in the first calculations. However, a slight change in the pH value (7.8 instead of 8) or pCO 2 value (10 À3.7 atm instead of 10 À3.45 atm) made it possible to fit the data very well, again showing the great sensitivity of the system to pH/pCO 2 over this range of conditions. Some data at high U(VI) surface coverage could not be predicted by the model, even after changing some of the parameters. The origin of this problem can be understood by comparing the measured U(VI) surface coverage with the maximum available surface site density. If we consider a site density of 2.06 sitesÁnm À2 (Bourg et al., 2007;Tournassat et al., 2016a) and a specific surface area of 14 m 2 Ág À1 , the maximum adsorption capacity for U(VI) complexes should be $0.05 molÁkg À1 . If we further assume that no U multinuclear complexes form at the surface, this value decreases to $0.025 molÁkg À1 (perfect ordering). This value is similar to the maximum adsorbed concentration value measured in Troyer et al. (2016) at pH 6, but far lower than the maximum value measured at pH 8. Hence, the much higher measured than simulated extent of U(VI) adsorption cannot be explained by the formation of isolated mononuclear bidentate U(VI) surface complexes alone. These data must include additional uptake processes that are not described in the model developed here, and are beyond the scope of this study, e.g. polymerization on the surface, or precipitation. The latter cannot be fully ruled out at elevated U(VI) concentrations, since a supersaturation of schoepite was predicted at 1.3 and 62 lmolÁL À1 U(VI) at pH 6 and pH 8 respectively, based on the U(VI) aqueous speciation model of Troyer et al. (2016). Hyun et al. (2001) The data of Hyun et al. (2001) were also acquired in the presence of atmospheric pCO 2 on a clay material similar to the one used in this study (fine fraction of SWy-2 montmorillonite). U(VI) adsorption was characterized at two fixed total U(VI) concentrations (10 À7 and 10 À5 molÁL À1 ), with variable pH, and for two ionic strengths (I = 0.001 and I = 0.1), and at a relatively high solid concentration ($6-7 gÁL À1 ). The reference model provided a good prediction of the data (Fig. 9).

Data of
At low ionic strength, the addition of cation exchange reactions, with the same parameters as for the study of Troyer et al. (2016), had almost no influence on the results. At pH 4 and low ionic strength, the high level of adsorption is mainly due to the increase in the surface potential value at edge surfaces. At high pH, the disagreement between experimental data and model predictions could be attributed to the fact that carbonate concentrations were not constrained experimentally (Hyun et al., 2001). Pabalan and Turner (1996) reported that, under some conditions, an equilibration period of ten days with the atmosphere was necessary to reach equilibrium between DIC and   Pabalan and Turner (1996). Cation exchange parameters are given in Table 3. Solid concentration = 3.2 gÁL À1 ; total U(VI) concentration = 2 Á 10 À7 molÁL À1 . The results are presented in percentage adsorbed (left) and in log 10 K D values (right) for a better evaluation of model fits at low (left) and high (right) U(VI) adsorption. atmospheric CO 2 . Insufficient time of equilibration with the atmosphere in the experiments of Hyun et al. (2001) could have led to pCO 2 values that were lower than the atmospheric value considered in the calculations: fitted value were log 10 pCO 2 = À4.4 at pH 9 and À5.05 at pH 9.55 (blue 1 line in Fig. 9). Pabalan and Turner (1996) The data of Pabalan and Turner (1996) were obtained in the presence of atmospheric pCO 2 on a clay material, SAz-1, that was different from SWy-2. Experimental conditions were otherwise quite similar to those used in the present study. In particular, close equilibrium with atmospheric pCO 2 was ensured by the addition of bicarbonate to the solutions. Again, the predictions of the model were in very good agreement with the experimental data without any further adjustments (Fig.10), despite the different nature of the clay.

Data of McKinley et al. (1995)
McKinley et al. (1995) reported U(VI) adsorption data on the <2 mm fraction of Swy-1 montmorillonite as a function of pH and ionic strength. At first sight, these data were not satisfactorily reproduced by the reference model (Fig. 11). The addition of cation exchange reactions improved predictions at low pH, but U(VI) adsorption at pH > 5.5 was still overestimated. However, these discrepancies can be satisfactorily explained by taking into account that the edge specific surface area of the Swy-1 sample from McKinley et al. (1995) was lower than the area of the Swy-2 sample, i.e. 12.6 m 2 Ág À1 instead of 14 m 2 Ág À1 . Both values are within the range of montmorillonite edge surface area values reported in the literature, which vary from 5 m 2 Ág À1 to 25 m 2 Ág À1 (Tournassat et al., 2015a(Tournassat et al., , 2016a. Turner et al. (1996 reported U(VI) adsorption data on the <2 mm fraction of a smectite isolate from a sedimentary rock fraction (Kenoma scmectite). Kenoma smectite is a beidellite, meaning that most of its structural charge originates from tetrahedral isomorphic substitutions, instead of octahedral substitutions for montmorillonite. Despite this difference, U(VI) adsorption data could be fitted equally well using the same approach as for the data of McKinley et al. (1995). Only U(VI) adsorption data obtained at very low ionic strength (I = 0.001) were overestimated (Fig. 12). Since the solid/liquid separation was achieved by centrifugation, it may be possible that finer particles were not completely removed from solution at this ionic strength, causing a lower apparent extent of U(VI) adsorption. (At low ionic strength, separation of solids from solution based on density differences is more difficult, due to the increased intensity of electrostatic repulsive interactions between montmorillonite layers (Van Olphen, 1992)).

Data of
4.5.6. Data of Marques Fernandes et al. (2012) Marques Fernandes et al. (2012) conducted U(VI) adsorption experiments on the <0.5 mm fraction of a SWy-1 montmorillonite over a wide range of pH and total U(VI) concentrations while varying pCO 2 . Experimental data at pH > 7, in the presence and absence of atmospheric Fig. 11. Comparison of model predictions with U(VI) adsorption data of McKinley et al. (1995). For the blue curve, the total edge specific surface area was set to 12.6 m 2 Ág À1 instead of the reference model value of 14 m 2 Ág À1 . Cation exchange parameters are given in Table 3.  Turner et al. (1996) (symbols). Cation exchange parameters are given in Table 3. pCO 2 (actual DIC concentrations were not measured), were predicted satisfactorily by the reference model without further modifications (Fig. 13). Experimental data obtained at lower pH, however, had higher adsorption than predicted by the reference model. The position of the pH adsorption edge could only be reproduced by increasing the edge surface area by a factor 8. This is probably not a justifiable assumption, even if we consider that the authors used a finer clay fraction (<0.5 mm) than in most other reported studies (<2 mm). With the large edge surface area, U(VI) adsorption was also greatly overestimated at pH > 7 (Fig. 13). The SWy-1 montmorillonite material of Marques Fernandes et al. (2012) thus exhibits U(VI) adsorption properties that are significantly different from the SWy-1 material studied by McKinley et al. (1995) and all other montmorillonite materials studied in the literature, given the otherwise good agreement between experimental data and the model predictions presented here for a large number of other studies. Based on the quality of fit, Marques Fernandes et al. (2012) attributed the very high adsorption affinity of SWy-1 montmorillonite to ''strong sites", with a specific site density of $2 mmolÁkg À1 . However, if present, the influence of such strong sites should have been apparent in the many other studies discussed above, where the U(VI) to solid concentration ratio was lower than the putative ''strong site" density. Hence, it appears that, for most other solid materials previously studied, these strong sites either do not exist or are present at a far lower site density than the reported value of $2 mmolÁkg À1 (Marques Fernandes et al. (2012)). Differences in material preparation procedures could potentially explain this difference in reactivity; e.g., Marques Fernandes et al. (2012) acidified their clay sample to pH 3.5 to remove acid-soluble impurities, while pH 5 was used in this and other previous studies.
Marques Fernandes et al. (2012) also conducted U(VI) adsorption experiments in the presence of added NaHCO 3 in order to probe the adsorption of U(VI)-carbonate complexes at the surface. These data could be predicted with our model after an adjustment of the equilibrium DIC concentrations (Fig. 14). Our calculations led to the conclusion that the equilibrium DIC value was 30 % to 40 % lower than the initially guessed values. Since measured DIC values are not available from the above reference, it is not possible to give a definitive conclusion with regards to the adequacy of the model prediction with the data. However, the discrepancy between guessed and fitted DIC values is similar to the one that we recorded in our own experiments between guessed and measured values (see materials and methods section and Fig. 2). Hence, we believe that Marques et al. (2012) may have experienced similar, experimental problems.

Summary of modeling results
The reference U(VI) adsorption model presented here is based on a state-of-the-art description of the reactivity of montmorillonite clay edges that specifically takes into account the spillover effect of the basal surface potential on the edge surface potential (Bourg et al., 2007;Tournassat et al., 2013Tournassat et al., , 2015aTournassat et al., , 2016a. This model accurately predicts adsorption of U(VI) on montmorillonite surfaces over a wide range of experimental conditions, with  only one specific adsorption site, three different U(VI) complexes at the surface, and one cation exchange reaction.
Within the limits of data accuracy, there was no need to include the formation of uranyl-carbonato surface complexes in the model to simulate the experimental data. Including such a species would only be justified if: (1) the discrepancies between experimental data and model predictions (without including these surface complexes) were larger than the combined uncertainties associated with experimental errors and formation constants for aqueous U(VI)-carbonate complexes, and (2) if actual measurement data are available for all solution parameters, including DIC concentrations (or alternatively, alkalinity). Without these data, the uncertainties of assumed pCO 2 values are too large to draw any conclusions regarding the presence of ternary U(VI)-carbonato surface complexes.
For illustration, the effect of varying pCO 2 conditions on U(VI) adsorption is shown in Fig. 15. Based on these calculations with the reference model, at pH > 9 a ''true" absence of CO 2 can be interpreted only if it can be demonstrated that actual pCO 2 values are lower than 10 À6 atm. This partial pressure corresponds to 1 ppm CO 2 in the surrounding atmosphere, i.e. experimental conditions that could be met only with great difficulty in the laboratory, even in a specially equipped glove box. It can be concluded that an ''absence of CO 2 " at pH > 9 (ideally corresponding to pCO 2 = 10 À99 atm in Fig. 15), is, in fact, obtained because of slow gas exchange rates between degassed solutions and the surrounding atmosphere, and not a true equilibrium with the partial pressure of CO 2 in that atmosphere. Under these conditions, it is thus necessary to measure DIC concentrations to assess the exact concentrations in solutions exposed to low levels of pCO 2 . To our knowledge, this type of measurement has never been performed in previously reported U(VI) adsorption studies on montmorillonite. Most likely, this has sometimes led to false assumptions that previous experiments were conducted at pCO 2 levels that did not impact U(VI) adsorption.
For example Schlegel and Descostes (2009) reported U (VI) adsorption results in the ''absence of CO 2 " that clearly show evidence of pCO 2 at higher values than 10 À5 atm (compare their Fig. 1 with Fig. 15 of this paper). Even a precise interpretation of data obtained at atmospheric pCO 2 may be problematic. The value of atmospheric pCO 2 can fluctuate as a function of geographic location, season, and above all the presence of humans in an enclosed lab setting because of respiration and poor ventilation. In addition, a slight change in pH after pre-equilibration of a solution (e.g., due to reagent addition) can impact the final pCO 2 value in a reaction vessel if the time-frame of the pH re-adjustment is too short to allow for full gassolution re-equilibration. A pCO 2 of 10 À3.2 instead of 10 À3.45 atm has a significant effect on the prediction of U (VI) adsorption at pH > 7. Hence, even with a 'forced' pre-equilibration of background electrolyte solutions using NaHCO 3 additions for intended pH values, CO 2 exchange with the surrounding atmosphere and other experimental artefacts add a significant uncertainty to the modeling results, unless actual measured DIC concentrations are used during the model fitting process. This effect is well illustrated with the modeling of U(VI) adsorption data by Troyer et al. (2016) at pH $ 8 (Fig. 12).
While DIC concentrations are critical parameters in the evaluation of U(VI) adsorption, the combined presence of Ca and carbonate further increases the level of complexity and uncertainty in the model calculations. This is due to the formation of aqueous calcium-uranyl-carbonate complexes (Meleshyn et al., 2009), with unknown adsorption impacts (Fox et al., 2006). According to the reference model, the effect of the formation of this complex on U (VI) adsorption could be significant for Ca 2+ concentrations larger than 2 mmolÁL À1 , which is in agreement with our experimental results (Fig. 16).

CONCLUSIONS AND ENVIRONMENTAL IMPLICATIONS
Overall, we can summarize the major findings and implications of this study in the following: 1. We developed a new surface complexation model (SCM) that specifically accounts for the 'spillover' of the electrostatic surface potential of basal cation exchange sites on the surface potential of neighboring edge sites. This model allows us to simulate U(VI) adsorption onto Na-montmorillonite over a wide range of chemical solution conditions with a lower number of fitting parame- Fig. 16. Left: Predicted effect of Ca 2+ concentration on U(VI) adsorption using the reference model with a solid concentration of 0.5 gÁL À1 , a 0.1 molÁL À1 NaCl background electrolyte, a total U (VI) concentration of 10 À6 molÁL À1 , and a pCO 2 = 10 À3.2 atm. Solubility index (SI) for calcite is plotted for comparison. Right: Comparison of our experimental data with model results with and without taking into consideration the impact of Ca 2+ on U(VI) solution speciation. ters than previous SCM concepts, and without including a second site type or the formation of ternary U(VI)carbonato surface complexes. This SCM allows us to simulate U(VI) sorption onto montmorillonite as a function of chemical solution conditions, while minimizing the number of fitting parameters in subsequent uranium(VI) diffusion models. 2. Modeling results suggest that an accurate description of the unique characteristics of electrostatic surface potentials on montmorillonite edge sites is highly important, in order to accurately predict U(VI) sorption and transport behavior at larger field scales. Similar modeling approaches may also be useful for other chargeunbalanced, layered mineral phases. 3. Our modeling results further emphasize the strong influence of dissolved carbonate ligands on U(VI) sorption, which is driven by the competition between U(VI)-carbonate complexation reactions in solution and U(VI) surface complexation reactions on montmorillonite edge sites. As a consequence, predictive U(VI) transport models need to capture potential changes in dissolved inorganic carbon (DIC) concentrations over time and space, e.g. in case of variable contents in carbonate minerals along transport pathways and/or fluctuating pH conditions. For instance, calcite impurities in bentonite, the proposed buffer material at future nuclear waste repositories, may affect U(VI) sorption by providing a source of dissolved carbonate concentrations. 4. Lastly, a measurement of DIC concentrations appears to be crucial for accurate simulations of U(VI) aqueous speciation during the development and calibration of SCMs. Assumptions of a full exclusion of inorganic carbon from sample solutions in CO 2 -''free" adsorption experiments, or a complete solution equilibration with atmospheric/elevated CO 2 levels in the local atmosphere, may often not be justified. This is due to the generally challenging nature of CO 2 -''free" adsorption experiments, and the potentially slow CO 2 gas exchange between sample solutions and the local atmosphere under atmospheric/elevated CO 2 conditions. Hence, we recommend that DIC analysis or alkalinity titrations are included as routine measurements in future U(VI) adsorption studies. Furthermore, future experimental designs should also take into account the experimental challenges experienced in this study, with regards to achieving constant pCO 2 conditions across a series of sample solutions in a given adsorption experiment.