domain: chim sde

text:
Johannes Lützenkirchen
email: johannes.luetzenkirchen@kit.edu

Remi Marsac

William H Casey

Gerhard Furrer

Tom Kupcik

Patric Lindqvist- Reis

The effect of monovalent electrolytes on the deprotonation of MAl 12 -Kegginions

Keywords: Keggin ions, cations, anions, potentiometry, fluoride

We study the deprotonation of MAl 12 -Keggin ions in monovalent electrolyte solutions of varying composition and concentration by potentiometric titration. The Keggins exhibit very steep deprotonation, where the singly coordinated aquo groups lose protons within a narrow pH-range. Once the deprotonation is substantial the Keggin ions start to aggregate by dehydration and linkage of terminal functional groups into hydroxo bridges. In the present study we address three aspects with our experiments. We test the cation-specificity, the anion-specificity and the overall effect of electrolyte concentration with respect to the deprotonation behavior. Our results show that the cation series in chloride systems does not show any ion-specificity and all the curves coincide for the 100 mM solutions whereas the anion series in sodium systems does. The most structure-making anion (bromate) used in this study causes aggregation of the Keggins prior to the onset of aggregation in the presence of borderline and structure-breaking anions (chloride, nitrate, perchlorate). For the latter, no significant difference is observed. The fluoride ion causes a completely different behavior. No significant deprotonation pH effect is observed where deprotonation occurs in the absence of fluoride. At even higher pH, massive consumption of hydroxide occurs. Some possible scenarios for the behavior of the fluoride-containing systems are discussed.

Introduction

Experimental investigation and modelling of interactions of trace components with metal-oxide substrates is of relevance in various areas [START_REF] Buerge-Weirich | Adsorption of Cu, Cd, and Ni on goethite in the presence of natural groundwater ligands[END_REF][START_REF] Muller | Interaction of Trace-Metals with Natural Particle Surfaces -Comparison between Adsorption Experiments and Field-Measurements[END_REF]Pavlova and Sigg 1988). In this respect the study of anion adsorption to such minerals and concomitant modeling has been pioneered by Laura Sigg [START_REF] Sigg | Die Wechselwirkung von Anionen und schwachen Säuren mit a-FeOOH(Goethit) in wässriger Lösung[END_REF][START_REF] Stumm | A Ligand-Exchange Model for the Adsorption of Inorganic and Organic-Ligands at Hydrous Oxide Interfaces[END_REF][START_REF] Sigg | The interaction of anions and weak acids with the hydrous goethite (α-FeOOH) surface[END_REF]. Since then the ligand exchange model has been continuously developed further and finds its application in modern surface complexation models [START_REF] Hernandez | Surface complexation of selenite on goethite: MO/DFT geometry and charge distribution[END_REF]). For such advanced models, it is invaluable to study well-defined surfaces and involve multiple experimental and theoretical approaches to constrain the stoichiometries of the surface complexes formed by ligand exchange [START_REF] Hiemstra | On the relationship between charge distribution, surface hydration, and the structure of the interface of metal hydroxides[END_REF]. One possibility is to study model colloids like goethite (see previous references) or single crystals [START_REF] Waychunas | Surface complexation studied via combined grazing-incidence EXAFS and surface diffraction: arsenate an hematite (0001) and (10-12[END_REF][START_REF] Waychunas | Surface complexation studied via combined grazing-incidence EXAFS and surface diffraction: arsenate on hematite[END_REF]) in attempts to gain full understanding and combine the molecular-level processes and the thermodynamic modelling. On colloids, the coordination chemistry at the surface is poorly known, while on single crystals charging phenomena were reported to occur that have not been previously discussed for particles (Lutzenkirchen et al. 2010b). In particular the charging on the oxide single crystals was interpreted to occur in the water film adjacent to the surface and not at the surface hydroxyls. More conclusive results that support this idea have been reported for silver halides [START_REF] Selmani | Surface and zeta-potentials of silver halide single crystals: pH-dependence in comparison to particle systems[END_REF]. Another suggestion has been to use large molecules as models for well-defined surfaces [START_REF] Casey | Large molecules as models for small particles in aqueous geochemistry research[END_REF][START_REF] Casey | Why small? The use of small inorganic clusters to understand mineral surface and dissolution reactions in geochemistry[END_REF] because in these molecules the coordination chemistry and speciation can be known with confidence.

The -Keggin ions [AlO 4 Al 12 (OH) 24 (OH 2 ) 12 ] 7+ (referred to as Al 13 ) and [GaO 4 Al 12 (OH) 24 (OH 2 ) 12 ] 7+ (referred to as GaAl 12 ) have been used in that sense. An initial explicit link between Al 13 and surface chemistry was published by [START_REF] Wehrli | Chemical mechanisms in the dissolution kinetics of minerals; the aspect of active sites[END_REF]. Subsequently Keggion-ions have been used to study in detail dissolution processes [START_REF] Furrer | On the chemistry of the Keggin Al13 polymer: Kinetics of protonpromoted decomposition[END_REF][START_REF] Amirbahman | Kinetics and mechanism of ligand-promoted decomposition of the Keggin Al13 polymer[END_REF][START_REF] Forde | Kinetics and mechanism of the reactions of the Al13 Keggin oligomer, [AlO4Al12(OH)24(H2O)]7+, with a series of phenolic ligands[END_REF][START_REF] Yamaguchi | Disappearance of Aluminum Tridecamer from Hydroxyaluminum Solution in the Presence of Humic Acid[END_REF]). Furthermore, the acid base behavior of the MAl 12 Keggin-ions has been studied in some detail experimentally [START_REF] Furrer | On the Chemistry of the Keggin Al13 Polymer .1. Acid-Base Properties[END_REF][START_REF] Lee | On the acid-base chemistry of the Keggin polymers: GaAl12 and GeAl12[END_REF] and by advanced calculations [START_REF] Rustad | Molecular dynamics simulation of the titration of polyoxocations in aqueous solution Geochim[END_REF]. A broad review on the role of the Keggin ions in the aqueous aluminium chemistry has also been published [START_REF] Casey | Large aqueous aluminum hydroxide molecules[END_REF]. Al 13 is metastable with respect to gibbsite, remains metastable in solution for very long times at its natural pH (pH 4.5, at this pH the Keggin-ion is expected to be fully protonated, see [START_REF] Furrer | On the Chemistry of the Keggin Al13 Polymer .1. Acid-Base Properties[END_REF][START_REF] Lee | On the acid-base chemistry of the Keggin polymers: GaAl12 and GeAl12[END_REF]), but slowly converts to the Al 30 oligomer over years (Furrer et al. 2002). Fully protonated, it bears seven positive charges. It has been found to adsorb to mineral surfaces (Lutzenkirchen et al. 2010a). Interestingly it has been observed during the transformation of boehmite to gibbsite [START_REF] Hernandez | Surface complexation of selenite on goethite: MO/DFT geometry and charge distribution[END_REF]. It is supposed to be toxic to plants [START_REF] Parker | On the Phytotoxicity of Polynuclear Hydroxy-Aluminum Complexes[END_REF]) but has been infrequently found in the environment (Furrer et al. 2002). NMR has been used to characterize this small ion to an amazing extent [START_REF] Phillips | Bonding and reactivity at oxide mineral surfaces from model aqueous complexes[END_REF]. Thus it is precisely known which kind of surface group is being deprotonated as the pH is increased. This reaction resembles the acid-base behavior of oxide minerals, but the deprotonation curve is extremely steep as shown in Figure 1. The data in that figure are taken from the literature, for Al 13 and Al 30 [START_REF] Casey | Large molecules as models for small particles in aqueous geochemistry research[END_REF], gibbsite with high charge [START_REF] Rosenqvist | Protonation and charging of nanosized gibbsite (alpha-Al(OH)(3)) particles in aqueous suspension[END_REF]) and low charge [START_REF] Adekola | Characterization of acid-base properties of two gibbsite samples in the context of literature results[END_REF]. Clearly the surface-charge densities of the various entities are in a similar range. Interestingly, the slope of the charge for Al 30 shows similarities to those of gibbsite with high charge around pH 5.5 to 6.5 and of Al 13 at pH > 6.5. The squares are data for the Keggin ions [START_REF] Casey | Large molecules as models for small particles in aqueous geochemistry research[END_REF], the triangles for gibbsite with high charge [START_REF] Rosenqvist | Protonation and charging of nanosized gibbsite (alpha-Al(OH)(3)) particles in aqueous suspension[END_REF]) and low charge [START_REF] Adekola | Characterization of acid-base properties of two gibbsite samples in the context of literature results[END_REF], see also [START_REF] Rustad | Molecular dynamics simulation of the titration of polyoxocations in aqueous solution Geochim[END_REF] Previous work on the deprotonation of these Keggin ions has shown that, depending on their concentration, the ions start to aggregrate at different charge conditions in a titration. At this point of aggregation, the deprotonation curves typically flattens as colloid formation inhibits further buffering of the pH. The lower the concentration of the Keggin ion, the higher the degree of deprotonation that can be achieved prior to the onset of aggregation. In the present work we have collected titration data in different ionic media of monovalent salts. This included study of cation effects, and we carried out a series of experiments in 100 mM chloride solutions. Recently, it has been shown that simple anions show specific effects on negatively charged sapphire single crystals [START_REF] Lützenkirchen | Specific Ion Effects at Two Single-Crystal Planes of Sapphire[END_REF]. Therefore, the occurence of a cation effect on a positively charged substrate cannot be excluded. In a second series of experiments a number of anions were tested in sodium systems while the background electrolyte concentration was kept constant at 100 mM. Ion-specific effects are of broad interest and have also been observed for the behavior of polyoxometallates. Thus [START_REF] Pigga | Selective Monovalent Cation Association and Exchange around Keplerate Polyoxometalate Macroanions in Dilute Aqueous Solutions[END_REF] observed very strong effects in the self-assembly off Keplarate ions. The negatively charged {Mo 72 Fe 30 } ions formed larger selfassemblies in the presence of the larger (structure breaking) monovalent ions in chloride systems. No study on the effects of co-ions was reported. Furthermore, we extended the previous work on variation of ionic strength [START_REF] Furrer | On the Chemistry of the Keggin Al13 Polymer .1. Acid-Base Properties[END_REF] to lower salt concentrations.

A priori, it is not clear if and how electrolytes and electrolyte concentrations will affect the behavior of the Keggin ions. One intent of the present paper is to report macroscopic data on this issue.

Another set of experiments was performed with fluoride. In this case the interest is in the stability of the Keggin ions after substitution of terminal surface groups (aquo-or hydroxo) with fluoride. The interaction of fluoride with mineral surfaces had already been studied in the course of Laura Sigg's Ph.D. thesis [START_REF] Sigg | Die Wechselwirkung von Anionen und schwachen Säuren mit a-FeOOH(Goethit) in wässriger Lösung[END_REF][START_REF] Stumm | A Ligand-Exchange Model for the Adsorption of Inorganic and Organic-Ligands at Hydrous Oxide Interfaces[END_REF][START_REF] Sigg | The interaction of anions and weak acids with the hydrous goethite (α-FeOOH) surface[END_REF]. Fluoride has often been considered as a ligand that allows the determination of the active surface sites. Unfortunately, complications will typically arise due to complex formation between fluoride and mineral constituents enhancing dissolution and potentially changing the surface. In this respect fluoride interaction with Al-bearing minerals has been extensively studied [START_REF] Nordin | Mechanisms for fluoride-promoted dissolution of bayerite [beta-Al(OH)(3)(s)] and boehmite [gamma-AlOOH]: F-19-NMR spectroscopy and aqueous surface chemistry[END_REF]. The interaction of fluoride with monomeric Al [START_REF] Phillips | Solvent exchange in AlFx(H2O)(6-x)(3-x) (aq) complexes: Ligand-directed labilization of water as an analogue for ligand-induced dissolution of oxide minerals[END_REF], Al 13 [START_REF] Allouche | Fluorination of the epsilon-Keggin Al-13 polycation[END_REF] and GaAl 12 [START_REF] Yu | Potentiometric and F-19 nuclear magnetic resonance spectroscopic study of fluoride substitution in the GaAl12 polyoxocation: Implications for aluminum (hydr)oxide mineral surfaces Geochim[END_REF] has been studied in much detail and the latter can be fluorinated. There is agreement that the aquo groups are first exchanged with aqueous fluoride. With time hydroxo bridges (µ-OH groups) become fluorinated, but no agreement exists as to whether the inter-vs. intra groups are concerned. Very recent theoretical work [START_REF] Jin | Effect of fluorine substitution on structures and reactivity of Keggin-Al13 in aqueous solution: an exploration of the fluorine substitution mechanism[END_REF]) was performed on this topic and [START_REF] Bino | Synthesis and structure of [Fe13O4F24(OMe)(12)](5-): The first open-shelf Keggin ion[END_REF] reported the structure of a fluoride-bridged Fe(III) Keggin structure. In the present work we try to relate the knowledge about the aqueous Al-F chemistry to interpret titration data in the presence of fluoride.

Material and Methods

Experimental

Solutions were prepared from 18.2 MOhm resistance water. Care was taken to remove carbon dioxide, which may have entered the solution after preparation, before starting titrations by flushing Argon over the solutions for extended times. The Argon was sent through washing bottles of sulfuric acid, sodium hydroxide and a solution containing the background electrolyte solution used in the experiment to avoid evaporation. The argon was flushed over the solution during the titration as well.

The Keggin ions were prepared as previously described (Lutzenkirchen et al. 2010a). The stock-solution has a total gallium concentration of 2.8 mM, which is basically identical to the resulting concentration of the Keggin ion. This stock solution contains chloride ions from the Al and Ga salts used in the synthesis as well as sodium ions from the NaOH solution used in the synthesis. The quantities of these ions are small compared to the major ionic medium ionic strength investigated for 25 µM MAl 12 (i.e. 100 mM) and amount to less than 1 mM. However, they do affect the ionic strength of the lower salt media studied here (1 mM and 10 mM added NaCl). The overall ionic strengths in those media arising from sodium and chloride ions are 2.6 and 11.6 mM, respectively. The MAl 12 concentration in these systems is 44 µM and the resulting contributions from the synthesis are therefore higher than in the previous case.

All systems were first acidified with HCl and subsequently titrated with NaOH solution. While this procedure introduces foreign sodium and chloride ions into the system, the quantities are rather low compared to the 100 mM background electrolyte concentrations and because the concentration of the Keggin ion were kept at 25 µM to have an extended range of Z B (as defined below). The ionic-strength dependence was studied in NaCl to avoid the presence of foreign ions in particular for the lowest ionic strength studied.

The pH electrode was calibrated daily against eight commercial buffer solutions. The voltage was recorded and transferred to pH and then to proton concentrations [H + ] using the Davies equation (linear coefficient 0.2) was used to calculate activity coefficients for the proton. Additionally the initial titration of the acidic solution with standardized NaOH was used to calibrate the apparatus before each titration. Both procedures produced the same results. The calibration parameters of the measurement system did not change significantly over the experimental period (in terms of slope and EMF o ). The good reproducibility observed when comparing the data makes us confident in our results.

The amount of protons reacted per Keggin ion was calculated according to the following equation

Z B = [(TOTH + -TOTOH  ) -([H + ] -[OH  ])]/TOTMAl 12
Here, TOTH + -TOTOH  is the concentration calculated from the amount of standardized acid and base solution added to the system. [OH  ] is calculated from the [H + ] values using the pKw for water at the respective ionic strength. Furthermore, in the above equation M is either Al or Ga. A value of Z B = 0 is taken as the refence point and corresponds to the initial charge of the Keggin ion (7+), while at Z B = 7 the charge of the Keggin-ion would vanish. The Keggin ion contains 12 aquo groups that can in principle be deprotonated. Thus Z B = 12 would mean deprotonation of all aquo groups. The µ 2 -OH groups can in principle also be deprotonated but this reaction is expected to take place at higher pH (as further discussed later). Before this deprotonation may occur the Keggin ions will aggregate. By this process the Keggin ions lose their model compound character.

Titrations were carried out at room temperature. Between the experiments the temperature did not vary by more than 2 degrees. High-precision titration data require better temperature control. However, in many cases such control is not possible and most oxide titrations have been carried out under conditions similar to ours. It is beneficial to the experimental work that the system is buffering so strongly during the deprotonation of the Keggin ions.

The titrations were carried out using a Metrohm Dosimat for supplying known volumes of standardized NaOH solution (0.1 M) to the reaction vessel. The set-up was calibrated in-situ by titrating an acidic solution (HCl) of the respective ionic medium of known volume with a standardized NaOH solution. At pH close to pH 4.5, which is the buffered pH achieved by dissolving millimolar concentrations of Keggin ions into these unbuffered solutions, a known amount of Keggin ion solution was added to the known volume of the respective electrolyte solution. The pH = 4.5 solution is reached when the Keggin ion is dissolved in water because of some terminal waters deprotonating. These were not accounted for in the calculations. Since the conditions were identical in all the titration runs, this procedure does not affect the comparison of the different. The solution was magnetically stirred at all the times and the stirring speed (about 600 rpm) was never changed during the series of experiments reported here. The pH of the resulting solution was about 4.5. After flushing purified argon over this solution for at least 2 hours, known volumes of standardized NaOH solution were added to the system. After two minutes the pH was recorded and another addition was made. In the flat initial region of the titration curve, the pH stabilized rapidly. On the steep part of the curve strong buffering was observed. The pH always decreased due to the release of protons from the Keggins. The decrease in pH slowed down with time. We did not attempt to achieve equilibrium but were interested in comparing different solutions. To assure comparability care was taken to carry out all the experiments following exactly the same protocol in terms of volume additions and waiting times. Once the buffering on the steep part of the titration curve in a given system stopped (i.e. the pH increased again significantly) some further additions were made and then the titration was stopped.

In the case where a sodium-fluoride-containing system was studied a fluoride-sensitive electrode was introduced. A separate blank titration for the same conditions (in terms of ionic strength, total Al and total F) has been carried. The electrode was calibrated against four solutions of known fluoride concentrations in the same medium as later used for the experiment. The ratio of fluoride to Keggin ion was much higher compared to the value used by [START_REF] Allouche | Fluorination of the epsilon-Keggin Al-13 polycation[END_REF], i.e. F/Al 13 = 2/1. We used a ratio of F/Al 13 = 25, which means that there is enough fluoride to replace all aquo groups and either all inter-or intra hydroxide bridges. To replace all aquo and all hydroxyl gropus would require a ratio of 36.. However, it is known that the replacing the hydroxide bridges is a slow process [START_REF] Yu | Potentiometric and F-19 nuclear magnetic resonance spectroscopic study of fluoride substitution in the GaAl12 polyoxocation: Implications for aluminum (hydr)oxide mineral surfaces Geochim[END_REF]) and we will discuss later that we expect the added fluoride replaces the aquo groups. The study of the fluoride-bearing system is delicate since it is not clear to what extent a fluorinated Keggin ion will persist under our conditions. Presumably, the ions will aggregate when enough fluoride anation has reduced the molecular charge and allowed colloid formation. However, during the addition of fluoride no visible aggregation occurred, which was always observable at the end of the titrations in the absence fluoride. Since for the fluoride-containing system no further studies were carried out involving e.g. NMR or other direct spectroscopies, our interpretation will accordingly be rather tentative but we hope that our results stimulate more research.

Calculations

Thermodynamic calculations were carried out using Phreeqc,version 2 (Parkhurst and Appelo 1999), ECOSAT (Keizer and van Riemsdijk 1994 ) and a modified version of FITEQL2 (Westall 1982).

The aim of the calculations was to evaluate the aqueous-phase behavior of the Al and Al/F systems and to test some hypotheses with respect to the reaction of the Keggins in the presence of fluoride with respect to their deprotonation. For the thermodynamic calculations stability constants were taken from the Minteq.v4 database provided with Phreeqc. The formation constant for Al 13 was taken from Öhman et al. (2006) and is selfconsistent with the hydrolysis constants for Al included in the Minteq.v4 data base. Relevant reactions are given in supplementary information. For the calculations on the deprotonation of Al 13 we adopted the reaction scheme previously proposed [START_REF] Furrer | On the Chemistry of the Keggin Al13 Polymer .1. Acid-Base Properties[END_REF]. Calculations were carried out to gain an idea in which direction the fluorination would drive the deprotonation of the Keggin ions. Recent theoretical work [START_REF] Jin | Effect of fluorine substitution on structures and reactivity of Keggin-Al13 in aqueous solution: an exploration of the fluorine substitution mechanism[END_REF]) on the substitution of various groups present on Al 13 by fluoride reported Al-O distances for various cases. We used those results for the Al-OH 2 groups for the bare Al 13 , for the substituted Al 13 cases F inter and F intra , in which 6 distinct hydroxide bridges were replaced by fluoride. The distances within the MUSIC framework [START_REF] Venema | Intrinsic proton affinity of reactive surface groups of metal (hydr)oxides: Application to iron (hydr)oxides[END_REF]) yield pK values for the protonation of one Al-OH (i.e. the first one). The respective values were then used to calculate all pK values within the 6x2 model by applying the same differences in the pK values as given previously for the bare Al 13 [START_REF] Furrer | On the Chemistry of the Keggin Al13 Polymer .1. Acid-Base Properties[END_REF]).

Results and discussion

Effect of NaCl concentration

Figure 2A shows the results of potentiometric titrations obtained in the GaAl 12 solutions for three different NaCl concentrations. The data show the expected steep deprotonation of Keggins around pH 6. The deprotonation reaches Z B = -6 (i.e. loss of 6 protons from the Keggin ion) before the curve starts to level off. This departure from the steep curve is indicative of agglomeration of the Keggin ions. The agglomeration is irreversible and its onset depends on the total concentration of Keggin ion [START_REF] Furrer | On the Chemistry of the Keggin Al13 Polymer .1. Acid-Base Properties[END_REF].

Several points are worth noting. First the shift of the deprotonation reactions to higher pH with increasing NaCl concentration agrees with the trend reported previously for Al 13 for a variation from 0.1 M to 1 M KNO 3 media [START_REF] Furrer | On the Chemistry of the Keggin Al13 Polymer .1. Acid-Base Properties[END_REF]. Second, we did not find any significant effect of the salt medium concentration on the aggregation process that can be tentatively associated to a departure from the steep deprotonation, which frequently occurs at Z B = -6 [START_REF] Furrer | On the Chemistry of the Keggin Al13 Polymer .1. Acid-Base Properties[END_REF]. If this was comparable to the related process in colloidal systems, higher salt concentrations should lead to aggregation at higher Z B values, corresponding to lower degrees of de-protonation or higher absolute charge. Our data do not concur with this expectation.

Figure 2A also includes model calculations based on the 2x6 model of [START_REF] Furrer | On the Chemistry of the Keggin Al13 Polymer .1. Acid-Base Properties[END_REF]. The model lines describe the Z B values between -3 and -6 very well. The data for Z B between 0 and -3 will be discussed in more detail elsewhere (Lützenkirchen et al., in preparation). From the model lines in Figure A we estimated the shift of the curves with decreasing ionic strength and plot them as a function of the square root of the difference in ionic strength on Figure 2B. The point to the right is from the paper of [START_REF] Furrer | On the Chemistry of the Keggin Al13 Polymer .1. Acid-Base Properties[END_REF] and fits exactly on a linear extrapolation of our two points. Since there are only three points, the trend is to be taken with caution. We did not attempt to include any model including ionic-strength correction to the de-protonation equations. Application of the Davies equation to an ion with a charge of +7 would induce huge changes that do not appear to be real based on the available results.

Effect of the nature of monovalent cations in chloride systems

In Figure 3 we present the results of the titrations in chloride systems with different monovalent cations at constant Keggin ion concentration and overall salt concentration of 100 mM. Our results do not display any significant difference between the various cations. In particular no difference in the onset of the agglomeration can be found. The data are highly reproducible and indicate as one would expect that changing the identity of the co-ion would not affect the deprotonation. For related Al-bearing systems, including sapphire-c single crystals [START_REF] Lützenkirchen | Specific Ion Effects at Two Single-Crystal Planes of Sapphire[END_REF] in chloride series and particulate aluminum oxide at low salt concentrations [START_REF] Johnson | The Binding of Monovalent Electrolyte Ions on α-Alumina. II. The Shear Yield Stress of Concentrated Suspensions[END_REF] in nitrate salts no cation-effects on zeta-potentials have been observed. At high salt concentrations (1 M) on particulate aluminium oxide in nitrate salts [START_REF] Johnson | The Binding of Monovalent Electrolyte Ions on α-Alumina. II. The Shear Yield Stress of Concentrated Suspensions[END_REF], and on sapphire-r single crystals [START_REF] Lützenkirchen | Specific Ion Effects at Two Single-Crystal Planes of Sapphire[END_REF]) cation effects in the chloride salts did occur and were of the same sequence, i.e. the structure-making ions showed weaker interaction. The hexagonal rings of ideal oxygen terminated sapphire-c are retrieved on the Keggin ions, which might explain the observed similarities in the behavior of the two latter. In general anion effects are rather expected on positively charged surfaces (e.g. [START_REF] Sprycha | Surface charge and adsorption of background electrolyte ions at anatase/electrolyte interface[END_REF] such as the Keggin ions (c.f. next section). In general, cationic counterions have a considerable effect on the stability and reactivity of polyoxometalate ions, but these are usually anionic. Here, for polyoxocations, one expects a large effect from counteranions, not cations, which is consistent with our observations. Unlike for the sapphire-c systems [START_REF] Lützenkirchen | Specific Ion Effects at Two Single-Crystal Planes of Sapphire[END_REF] we do not observe any effect of the co-ions. The difference between sapphire-c and the Keggin-ions might be in the differences of the intrinsic charges of both. While for sapphire-c the measurable negative electrokinetic charge mainly arises from physical hydroxide adsorption to the water film of a flat surface with low or zero charge at the plane of the surface hydroxyls [START_REF] Selmani | Surface and zeta-potentials of silver halide single crystals: pH-dependence in comparison to particle systems[END_REF]), the Keggin-ions have high intrinsic surface charge densities (see Figure 1). Thus on sapphire-c the unexpected co-ion effect would arise from competition between anions while the absence of the co-ion effect on the Keggin-ions is due to the intrinsic charge. In Figure 4 we present the results obtained with various monovalent sodium salts. Chloride, nitrate and perchlorate are typical anions used in "innocent" or "inert" background electrolytes. Bromate is a more unusual ion, known though to behave as a structure maker in colloidal-stability investigations [START_REF] Dumont | Stability of Ferric Oxide Hydrosols Discuss[END_REF]. As for the variation of the cations, no significant effect is observed in the solutions of common background electrolytes (Figure 4). Sodium solutions of chloride, nitrate and perchlorate yield nearly identical results. The data for the strongly structure-breaking perchlorate might be shifted a bit below the nitrate and chloride data, which do not differ from each other. This trend would be in line with the observation that the structure-making bromate ion causes different de-protonation behavior. Clearly the onset of agglomeration is slightly below Z B = -5. Independent evidence for strong interaction of iodate and bromate with aluminium oxides [START_REF] Franks | Ion-Specific Strength of Attractive Particle Networks[END_REF], corroborates our results and supports the idea that these ions are interacting with aluminium minerals beyond pure physical shielding of charge. Such interaction of fluoride with aluminium bearing systems is known [START_REF] Yu | Potentiometric and F-19 nuclear magnetic resonance spectroscopic study of fluoride substitution in the GaAl12 polyoxocation: Implications for aluminum (hydr)oxide mineral surfaces Geochim[END_REF]. From the extensive research conducted on polyoxometalate systems [START_REF] Hill | Introduction: PolyoxometalatesMulticomponent Molecular Vehicles To Probe Fundamental Issues and Practical Problem[END_REF], counter-ions are important if they coordinate to the oxygen-ring system in the molecule (for GaAl 12 the diameter of such a ring is about 5.25 Å) and thereby neutralize molecular charge. In some cases, the counter-ions form cationic bridges between anionic polyoxometalate ions, making for macromolecular structures in solution or dropping the molecules out of solution as insoluble solids, either crystalline or amorphous. Nominally inert counter-ions have a similar profound effect on the kinetics of isomerization [START_REF] Johnson | Dynamics of a Nanometer-Sized Uranyl Cluster in Solution[END_REF], electron exchanges [START_REF] Czap | Electrochemistry and homogeneous self-exchange kinetics of the aqueous 12-tungstoaluminate(5-/6-) couple[END_REF]) and ligand exchanges.

Related to the study of [START_REF] Pigga | Selective Monovalent Cation Association and Exchange around Keplerate Polyoxometalate Macroanions in Dilute Aqueous Solutions[END_REF] we find that the structure making anions have a more profound effect on the aggregation of the GaAl 12 ions. In their study the structure breaking cations had caused stronger selfassembly of their negatively charged Keplarate ions.

The influence of fluoride

Fluoride is known to act as a strong complexing agent that can enhance aluminium mineral dissolution as mentioned in the introduction. Aqueous solution speciation involves various Al-F complexes with up to six fluoride ions per aluminium ion. In this case all first-shell water molecules are then replaced by fluoride and the sign of charge of the ion is reversed because of the stepwise anation. The interaction of fluoride ions with the Albearing Keggin ions is complex and involves kinetics as discussed in the literature cited above. To obtain a first hint on the effect of fluoride on the deprotonation of the fluorinated Keggin ions we have carried out a tentative experiment. We believe that the results discussed below will merit further investigations. On Figure 5 we compare the titrations curves for 25 µM Keggin ion solutions in a bare NaCl system and in a system containing about 0.6 mM F  . The titration curve distinctly differs in the presence of fluoride. The complexity of the aqueous Al-F chemistry requires the discussion of various possible scenarios that might be relevant to the observations in the absence of further spectroscopic investigations:

1. The Keggin ion is destroyed by the excess of fluoride due to the formation of dissolved Al-F complexes.

This scenario was experimentally elucidated by a blank titration. 2. The hydroxo bridges of the Keggin ion are replaced by fluoride. This scenario was evaluated by MUSIC type calculations. They were in turn based on recent theoretical work on Al 13 [START_REF] Jin | Effect of fluorine substitution on structures and reactivity of Keggin-Al13 in aqueous solution: an exploration of the fluorine substitution mechanism[END_REF]).

We focus on the two extreme cases, i.e. the substitution of µ 2 OH inter-and intra-trimers of Al constituting the Keggin ion by F -(F inter and F intra ), shown in Table 1 in the respective publication [START_REF] Jin | Effect of fluorine substitution on structures and reactivity of Keggin-Al13 in aqueous solution: an exploration of the fluorine substitution mechanism[END_REF]. Fluoride replacement of µ 2 -OH has been spectroscopically confirmed by 19 F-NMR, but the concentrations were much lower than we employ here [START_REF] Yu | Potentiometric and F-19 nuclear magnetic resonance spectroscopic study of fluoride substitution in the GaAl12 polyoxocation: Implications for aluminum (hydr)oxide mineral surfaces Geochim[END_REF]). 3. The aquo groups of the Keggin ion are replaced. In this case the stability of the fluorinated Keggin ion is the relevant issue. Replacement of these terminal groups would be very fast on our experimental times scale. The rates of exchange of bound waters from the fully protonated forms of these structures fall into the millisecond time scale and these will accelerate as cationic charge is removed from the molecule by fluoride uptake. In contrast, the rates of isotopic exchange into µ 2 -OH are hours to weeks [START_REF] Casey | Large aqueous aluminum hydroxide molecules[END_REF].

The three scenarios are discussed in some detail in the subsequent sections.

Addition of fluoride leads to destruction of the Keggin ions

In Figure 6, a blank titration involving the same amounts of Al and F as in the respective titration curves where the Keggins are initially present is shown. In the absence of the synthesized Keggin ion, the titration results in a very different curve. Strong buffering occurs at much lower pH in the blank experiment. Therefore, this scenario is unlikely to explain the observed titration curve of the Keggin ions in the presence of fluoride, even though the blank titration was carried out in the absence of gallium. These results also show that the Keggin ion remains stable in the presence of F -for pH < 7 during the time of the experiments. The replacement of the hydroxo-bridges by fluoride shortens the Al-O distances for the aquo groups according to the theoretical calculations [START_REF] Jin | Effect of fluorine substitution on structures and reactivity of Keggin-Al13 in aqueous solution: an exploration of the fluorine substitution mechanism[END_REF]. This causes stronger deprotonation of the aquo groups compared to the unsubstituted Keggin ion. However, the contrary is observed experimentally (i.e. the titration curve with Keggin-ions in the presence of fluoride is shifted to higher pH compared to that of Keggin-ions in the absence of fluoride, Figure 5), suggesting that the substitution of the hydroxo-bridges plays a minor role in the present conditions, very likely because the aquo groups are substituted, as discussed below. Following the theoretical estimates for the distances on the unsubstituted Keggin-ion, its deprotonation occurs at much higher pH than experimentally observed. We therefore take the theoretical results as self-consistent input parameters to the calculations in Figure 7 that allow no more than comparison between the cases.

It appears that the intra-6-bridges have a more profound effect on the Al-O-distances of the aquo-groups than the inter-6-bridges (according to Table 1 in Jin et al.). This finds its repercussion in the MUSIC calculations in Figure 7. Several points would appear to support this scenario. First it is known that the substitution of the aquo groups is fast [START_REF] Allouche | Fluorination of the epsilon-Keggin Al-13 polycation[END_REF][START_REF] Yu | Potentiometric and F-19 nuclear magnetic resonance spectroscopic study of fluoride substitution in the GaAl12 polyoxocation: Implications for aluminum (hydr)oxide mineral surfaces Geochim[END_REF] resulting in a compound that is stable for some time [START_REF] Yu | Potentiometric and F-19 nuclear magnetic resonance spectroscopic study of fluoride substitution in the GaAl12 polyoxocation: Implications for aluminum (hydr)oxide mineral surfaces Geochim[END_REF]. The aquo groups are those that cause the deprotonation of the unsubstituted Keggin ion. Consequently once they are substituted they cannot deprotonate. The substitution (if complete) would cause the loss of positive charge and the Keggin ions would bear a negative charge of up to -5. Since the anation of the molecule causes a reduction of charge, the progressive replacement of bound waters might accelerate the aggregation since the electrostatic repulsion between molecules is reduced.

Based on the above it would be possible to understand, why the Keggin ions are not deprotonated in the usual pH-range (i.e. below pH 6.5). However, we also need to understand what causes the strong decrease in Z B at the higher pH. One possibility could be that the species is not stable at the high pH. Another possibility is that the fluoride is replaced by hydroxide ions.

Conclusions

We have studied the deprotonation of MAl 12 -Keggins under previously unexplored conditions. The observations can be summarized as follows:

(i) Variation of the ionic strength from 2.6 to approximately 100 mM NaCl background electrolyte caused a shift of the deprotonation curve to higher pH with increasing NaCl concentration. This agrees with previous measurements [START_REF] Furrer | On the Chemistry of the Keggin Al13 Polymer .1. Acid-Base Properties[END_REF]) (ii) Cation-specific effects do not occur in the simple monovalent electrolyte systems, as is expected. Because the MAl 12 -Keggins are polyoxocations, such results are to be expected based on simple shielding and lack of interactions beyond charge screening. . (iii) Anion specific effects appear to indicate that structure breaking anions primarily serve as charge screeners, while the structure making anion bromate promotes early aggregation in agreement with previous reports for particulate alumina systems.

(iv) The fluoride-containing system shows distinctly different behavior. We find fluoridation changes the acidbase chemistry of the molecule such that no deprotonation of the Keggin ion occurs. We inestigate possible interpretations concerning fluoridation of aquo and/or bridging hydroxo groups, that can be expected from previous spectroscopic studies by [START_REF] Yu | Potentiometric and F-19 nuclear magnetic resonance spectroscopic study of fluoride substitution in the GaAl12 polyoxocation: Implications for aluminum (hydr)oxide mineral surfaces Geochim[END_REF].The absence of deprotonation and the observed release of fluoride is best explained by fluoridation of the aquo-groups which is known to be fast. The release of fluoride at higher pH coincides with release of fluoride from gibbsite.

Fig. 1

 1 Fig. 1 Comparison of surface charge density as a function of pH between two gibbsite samples, Al 30 and Al 13The squares are data for the Keggin ions[START_REF] Casey | Large molecules as models for small particles in aqueous geochemistry research[END_REF], the triangles for gibbsite with high charge[START_REF] Rosenqvist | Protonation and charging of nanosized gibbsite (alpha-Al(OH)(3)) particles in aqueous suspension[END_REF]) and low charge[START_REF] Adekola | Characterization of acid-base properties of two gibbsite samples in the context of literature results[END_REF], see also[START_REF] Rustad | Molecular dynamics simulation of the titration of polyoxocations in aqueous solution Geochim[END_REF]

  Fig. 2 (A) Effect of variation of the sodium chloride concentration on the titration curve of GaAl 12. The lines are model calcuations that describe the Z B values between approximately -3 and -6. (B) pH -shift of the Z B curves as a function of the square root of the change in ionic strength.

Fig. 3

 3 Fig. 3 Titration results for 25 µM GaAl 12 solution in different chloride systems at 100 mM

Fig. 4

 4 Fig. 4 Titration results for 25 µM GaAl 12 solution in different sodium systems at 100 mM

Fig. 5

 5 Fig. 5 Titration of 25 µM GaAl 12 solution in 100 mM NaCl in the absence of NaF (open triangles) and in the presence of 0.63 mM NaF

Fig. 6

 6 Fig. 6 Titration of 0.32 mM Me 3+ (TOTGa + TOTAl) in 100 mM NaCl for solutions in which Keggins are initially present (squares) or absent (triangles)

Fig. 7

 7 Fig. 7 Calculated deprotonation of fluorinated Al 13 for two distinct cases (dotted and dashed lines) as compared to the pure Al 13 (full line) based on a MUSIC type approach[START_REF] Venema | Intrinsic proton affinity of reactive surface groups of metal (hydr)oxides: Application to iron (hydr)oxides[END_REF]). The inter-6 and intra-6 models correspond to the cases where 6 hydroxo-bridges (fast or slow) are replaced by fluoride. Input data to the MUSIC approach (bond distances) for these two cases have been recently published[START_REF] Jin | Effect of fluorine substitution on structures and reactivity of Keggin-Al13 in aqueous solution: an exploration of the fluorine substitution mechanism[END_REF]

Fig. 8

 8 Fig. 8 Predicted distribution of Al and F (left y-axis) and sodium hydroxide consumption (right y-axis) as a function of pH for the conditions of the experimental data shown in Figure 6 Top (a): Without F. Al 13 prevails and is a highly hydrolyzed Al-state (~Al(OH) 2.46 ). No consumption of OH -is needed below pH < 7 so the pH increases rapidly with NaOH addition. Above pH = 7, Al(OH) 4 -is formed, which consumes OH -. Bottom (b):With [F -] = 0.63 mM. The non-hydrolyzed Al-fluoro complexes prevail at low pH. Al 13 is formed when the pH increases, followed by Al(OH) 4 -, which consumes more OH -. This explains the different titration curves with or without F. No precipitation is considered. Calculations are based on the speciation scheme byÖhman et al. (2006).

Fig. 9

 9 Fig. 9 Fractional change in F-uptake in aqueous complexes (full line) on gibbsite (modelled and experimental) and in the Keggin ion system (measured by an ISE electrode)

Acknowledgements: WHC thank the US Department of Energy for support via grant DE-FG02-05ER15693.


text:
Johannes Lützenkirchen
email: johannes.luetzenkirchen@kit.edu

Remi Marsac

Dmitrii A Kulik

Timothy E Payne

Zhengrong Xue

Silvia Orsetti

Stefan B Haderlein

Treatment of multi-dentate surface complexes and diffuse layer implementation in various speciation codes

Keywords: Surface complexation model, speciation, multi-dentate surface complexes, Gouy-Chapman equation

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The uptake of chemical species on the surfaces of minerals from aqueous solutions, usually termed 'adsorption', plays a crucial role in the retention of hazardous cations and anions. The extent of adsorption is strongly dependent upon the local chemical environment, and it is therefore necessary to have realistic models for sorption processes to generate more defensible predictions. Such models can be developed utilising the same thermodynamic approaches as those applied in solution chemistry, using chemical reactions with associated stoichiometry and equilibrium constants, known as surface complexation models (SCMs). [START_REF] Kallay | Thermodynamics of the reactions at solid/liquid interfaces[END_REF] provided a recent overview of the thermodynamics of mono-dentate reactions at solid/ liquid interfaces.

Initially, surface reactions were determined on the basis of analogy with the structure of mononuclear aqueous complexes, and equilibrium constants were fitted against the macroscopic (experimental) sorption data. Nowadays, surface complexation reactions are being formulated with the input from spectroscopic studies or from detailed atomistic (mechanistic) models of the mineral-water interface.

With the advent of spectroscopic techniques that probe the structure of surface species [START_REF] Ponthieu | Metal ion binding to iron oxides[END_REF][START_REF] Sherman | Surface complexation modeling: Mineral fluid equilibra at the molecular scale[END_REF][START_REF] Sherman | Surface complexation of U(VI) on goethite (-FeOOH)[END_REF][START_REF] Sylwester | The structure of uranium(VI) sorption complexes on silica, alumina and montmorillonite[END_REF][START_REF] Machesky | Ion adsorption into the hydrothermal regime: experimental and modeling approaches[END_REF][START_REF] Zhang | Ion adsorption at the rutile-water Interface: Linking molecular and macroscopic properties[END_REF]and refs therein), many adsorbed cations were found to be coordinated not only to one but to two, three or four surface oxygens, and represented accordingly in SCMs as multi-dentate surface complexes. Such bi-, tri-or tetra-dentate surface species have been identified in many solid/liquid systems, encompassing both cation and anion adsorption to surface functional groups.

The treatment of multi-dentate surface complexes is possible in various ways. [START_REF] Wang | Mass action expressions for bidentate adsorption in surface complexation modeling: Theory and practice[END_REF] give a recent overview for bidentate surface complexes and related pitfalls in adsorption modelling. This discussion has some history [START_REF] Benjamin | Modeling the mass-action expression for bidentate adsorption[END_REF]. Furthermore, while the present manuscript was under review, [START_REF] Gustafsson | Comment on "Citrate adsorption can decrease soluble phosphate concentration in soils: Results of theoretical modelling[END_REF] showed how the wrong handling of bidentate surface complexes could induce unwarranted conclusions. In the present paper, we illustrate that different numerical formalisms have been implemented in available codes. Consequently, it would be helpful if the differences can be made transparent for the user community.

Another subtle detail is in the treatment of the diffuse part of the double layer in electrostatic models. While some codes document the use of the Gouy-Chapman equation (e.g. FITEQL), other codes have the general treatment implemented (e.g. ECOSAT). The difference is that the Gouy-Chapman equation is valid for symmetrical electrolytes only. This would mean that in general environmental settings, with a mixture of electrolytes, the diffuse part of the double layer cannot be correctly described with the Gouy-Chapman equation.

While the effect on the overall calculations of the surface equilibria is probably minor in most cases, it can be of more importance in certain cases.

The aim of the present paper is to make the reader aware of existing differences between codes in treatment of adsorption involving multi-dentate surface species, and to show that the treatment of the diffuse part of the double layer is not necessarily general.

Multi-dentate surface complexes

Formalism

A general surface complexation reaction can be written in two ways

d >SOH z + M x + wH 2 O  (>SO) d M(OH) w x+dz-w + (d+w)H + (1a) (>SOH z ) d + M x + wH 2 O  (>SO) d M(OH) w x+dz-w + (d+w)H + (2a)
>SOH denote surface sites, z and m denote charges, and d and w are stoichiometric coefficients. While the mass balance equations associated with both equations would be identical, the mass law equations will differ for "denticity" d > 1.

K M int,d = [(>SO) d M(OH) w x+dz-w ]×[H + ] d+w ×[>SOH z ] -d ×[ M x ] -1 (1b) K M int = [(>SO) d M(OH) w x+dz-w ]×[H + ] d+w ×[(>SOH z ) d ] -1 ×[ M x ] -1 (2b)
Here, K M int stands for the intrinsic equilibrium constant; we assume that the activity of water is constant, and use molarities instead of activities for the remaining species. Also we initially ignore the possibility of multi-nuclear complexes (in M x ) and omit the electrostatic factors.

The set of equations (1) will also be referred to as formalism 1, while the set of equations ( 2) will be referred to as formalism 2.

The important difference between formalism 1 and 2 is that in latter the ratio between concentration terms for surface species does not depend on the denticity d, while for the former it does. The consequence for formalism 1 is that a sorbent concentration term will ultimately appear, which involves correction of the stability constant in an appropriate way.

This has been known for a long time and is included in textbooks [START_REF] Sigg | Aquatische Chemie: eine Einführung in die Chemie wässriger Lösungen und natürlicher Gewässer[END_REF]1996;[START_REF] Sigg | Chimie des milieu aquatiques[END_REF]. Interestingly, in the textbook by Stumm and Morgan (1990), only formalism 2 is mentioned. A detailed derivation can be found in the recent review by [START_REF] Wang | Mass action expressions for bidentate adsorption in surface complexation modeling: Theory and practice[END_REF].

A debate about the formal treatment, i.e. eqs. (1) vs. (2), still exists. An argument in favor of 1 would be that multiple bonds on the surface must be formed, and that the adsorbing species M x has various possibilities to coordinate to available function groups on the surface. Such reasoning ultimately requires consideration of the surface structure (i.e. how the sites are arranged that are involved in the bonding). Arguments in favor of 2 would come from comparison to ligands like oxalate, where a single oxalate forms a bidentate complexe with metal ions in solution. This would never involve a square in the respective mass law equation.

On the surface, similar to a dissolved ligand like oxalate, the functionalities are pre-arranged.

No effect of solid concentration on the stability constant would result from eq (2).

In general, any treatment will fail when the surface coverage is high, and the possibilities for forming multidentate surface complexes become restricted. A simple mass law equation/mass balance treatment cannot handle this situation correctly if d > 1.

In case of eq (1), ultimately a second debate evolves about the best concentration scale to use, including molarities/molalities, mole fractions, or coverage fractions [START_REF] Kulik | Consistent treatment of 'denticity' in surface complexation models[END_REF][START_REF] Wang | Mass action expressions for bidentate adsorption in surface complexation modeling: Theory and practice[END_REF].

Consequences for the treatment in speciation codes

Formalism 2 is exclusively possible with codes that allow distinction between the mass action law equation and the mass balance coefficients.

Formalism 1, as implemented in a given code, is currently restricted to one of the concentration scales per code, though it could be made more general. For the ECOSAT code, for example, the precise treatment has been described by [START_REF] Venema | Multisite Adsorption of Cadmium on Goethite[END_REF]. In the ECOSAT implementation, the treatment is extended to multidentate surface species involving more than one kind of surface sites. While this seems to complicate the situation, because again various possible ways of defining the stability constants may exist, given that the implementation in the various codes and with respect to published parameters are known, the appropriate corrections can be made [START_REF] Kulik | Consistent treatment of 'denticity' in surface complexation models[END_REF].

In the present comparison, we apply the codes ECOSAT, FITEQL, PHREEQC, and VISUALMINTEQ (references to the codes can be fined in the REFERENCES section). We compare formalism 1 within different codes, starting with a single site model and continuing to the more general case where different kinds of surface sites contribute to a multidentate surface complex. In principle this may also extend to different kinds of surfaces that interact as described by [START_REF] Lützenkirchen | A new approach for modelling potential effects in cation adsorption onto binary (hydr)oxides[END_REF]. In particular, we compare the results obtained with the different codes on given examples to illustrate that the codes employ different implementations.

In some examples we also involve a comparison between the two formalisms for bidentate complexes using FITEQL. Formalism 1 will then be denoted as FITEQL (1) and formalism 2 as FITEQL (2).

Diffuse layer potential

Formalism

In most electrostatic surface complexation models, a distinct treatment of the diffuse part of the electrical interfacial layer (EIL) is included. The simplest treatment involves the Gouy-Chapman equation, which relates the potential of the onset of the diffuse layer ( d ) to the diffuse layer charge (σ d ), as given in equation 3.

σ d = (8000RTI) ½ sinh(zF d /2RT) (3)
In the above equation, R, T and F have their usual meaning, is the permittivity of the medium, which changes with composition under ambient conditions, and z is the valence of the symmetrical electrolyte, i.e. z = 1 for 1:1, z = 2 for 2:2 electrolyte, etc. I is the aqueous ionic strength, which has to be given in the appropriate units (molar or molal). I can be fixed at a given value by a background electrolyte (usually 1:1 electrolytes are used). Equation (3)

does not apply to asymmetrical electrolytes like 2:1 (such as CaCl 2 ) or to mixtures of symmetrical with asymmetrical electrolyes (i.e. general solution compositions). The codes typically allow for self-consistent calculation of the overall ionic strength, which would for example include changes in I due to pH adjustments in very acidic or basic regions, where the background electrolyte concentration is changed.

The general relation between the diffuse layer charge and potential as implemented in the ECOSAT code is reproduced in equation ( 4):

σ d = (2000RT) ½ {[i](exp(-z i F d /RT)-1)} ½ (4)
Here, [i] is the concentration of a dissolved species and z i is its charge.

Compared to equation (3), equation ( 4) always involves the full aqueous speciation in the sum, making the numerical solution of the overall equilibrium problem more complex.

Consequences for the treatment in speciation codes

The relevance of the diffuse layer for the equilibrium calculations is strongly dependent on the type of electrostatic model used. Using the purely diffuse layer model, it is expected that the effect is maximum. In this case, the relation between the surface charge and potential that directly affects the state of the adsorbed ions will be incorrect whenever the Gouy-Chapman equation ( 3) is used with asymmetrical electrolytes. For models including a Stern layer, the diffuse layer part is mainly associated to the overall electroneutrality condition, and the effect of using the inappropriate equation is probably minor. The important point that we want to make is that the users have to become aware of this problem, in particular because the generalized two layer models for hydrous ferric oxide [START_REF] Dzombak | Surface complexation modeling. Hydrous ferric oxide[END_REF], goethite [START_REF] Mathur | Surface complexation modeling. Goethite[END_REF] and gibbsite [START_REF] Karamalidis | Sorption modelling by Gibbs energy minimisation: Towards a uniform thermodynamic database for surface complexes of radionuclides[END_REF] use the purely diffuse layer model. These data sets are extensively applied to environmental settings with mixed electrolyte solutions. In the present code comparison, we will specify which equation is implemented in the codes ECOSAT, FITEQL, PHREEQC, and VISUALMINTEQ.

Examples of computations for multi-dentate surface complexes

The aim of the modeling exercises that are reported in the following was to illustrate the effects that arise from confusion of the intrinsic stability constants obtained using different codes or code combinations. The problem is related to the lack of knowledge about how the various codes operate, or how individual authors report stability constants.

Multi-dentate surface complexes involving one kind of surface site

We have selected a few examples. In one of them, we systematically compare the mono-dentate surface complexation calibration with higher denticity cases. To simplify the exercise, only one experimental adsorption edge is considered (i.e. the parameters are determined for a single set of experimental conditions). The basis for all modeling of metal ion adsorption is the acid-base model for the respective solid. This model, whenever required, was obtained from fitting the surface charge density vs. pH data to a single-site 1pK Basic Stern model involving electrolyte binding.

The first example system involves uranium(VI) adsorption on the quartz surface. For quartz, the classical 2pK scheme is in agreement with the MUSIC model, but one protolysis constant is sufficient to describe the titration results. In this first case, spectroscopy and theory suggest that bi-dentate complexes of uranyl are formed on silanol surface groups (Dent et al., 1992;[START_REF] Reich | Characterization of hydrous uranyl silicate by EXAFS[END_REF], 1998[START_REF] Greathouse | Molecular dynamics study of aqueous uranyl interactions with quartz (010)[END_REF]. In SCM calculations, we used the aqueous speciation database for uranium from NEA TDB (Guillaumont et al., 2003) with the Davies equation for aqueous activity coefficients:

(5)

where  j is the molal activity coefficient of individual aqueous species of charge z j , I has been defined above, and A  is the Debye-Hückel coefficient.

The second test case involves the Eu-TiO 2 system studied by [START_REF] Bouby | Sorption of Eu(III) onto titanium dioxide: Measurements and modeling[END_REF].

Their system-specific EXAFS data favor mono-dentate Eu binding, while X-ray standing waves results [START_REF] Machesky | Ion adsorption into the hydrothermal regime: experimental and modeling approaches[END_REF] support tetra-dentate binding of rare earth element (REE) cations to that rutile. To limit the model variants, we did not consider tetra-dentate binding of sodium in the acid-base model when fitting the surface charge and zeta-potential data of [START_REF] Bouby | Sorption of Eu(III) onto titanium dioxide: Measurements and modeling[END_REF]. The aqueous speciation database included hydroxocomplexes of Eu(III) with the following stability constants: log 1 = 6.8; log 2 = 12.9; log 3 = 15.8 used with the Davies equation, as in [START_REF] Bouby | Sorption of Eu(III) onto titanium dioxide: Measurements and modeling[END_REF]. Europium was considered to be equivalent to Americium, and consequently the critically evaluated hydrolysis data for Americium were used.

            I . I I z A γ j γ j 3 0 1 log 2 10
The third case treats the Cu-goethite system studied by [START_REF] Peacock | Copper(II) sorption onto goethite, hematite and lepidocrocite: A surface complexation model based on ab initio molecular geometries and EXAFS spectroscopy[END_REF] and [START_REF] Sherman | Surface complexation modeling: Mineral fluid equilibra at the molecular scale[END_REF], which put forward spectroscopic and structural arguments in favor of the corner-sharing bi-dentate and bi-nuclear tri-dentate Cu II surface complexes, and modeled the system with a 2pK-DLM using the FITEQL code. In this case, no refitting of acid-base parameters was required, and the parameters were taken from the above-cited references.

The last case in this section involves adsorption of Fe(II) to goethite with the formation of two bidentate surface complexes.

The uranyl -quartz system (mono-vs bi-dentate case)

This system is characterized by the following underlying acid-base model, as given by the reaction equations and the corresponding equilibrium constants.

Si-OH

0 ↔ Si-O ─ + H + log 10 = -7.90 (6) Si-OH 0 + Na + ↔ Si-O ─… Na + + H + log 10 = -6.93 (7)
The specific surface area was A S = 0.33 m 2 g -1 and solid concentration was c S = 100 g dm -3 . We used a site density N S = 4.6 nm -2 ( S = 7.6410 -6 mol m -2 ) and the fitted capacitance density (BSM) C 1 = 1.45 F m -2 . Assuming mono-dentate binding, the following reaction yielded the best-fit model obtained using FITEQL (Figure 1A).

Si-OH 0 + UO 2 2+ ↔ Si-OUO 2 + + H + log 10 = -0.64 (8)
In our simplified model, we did not attempt to achieve a better fit to the data by involving two or more reactions or by using Charge Distribution (CD). The black line on Figures 1A and 1B shows a complete CD-MUSIC benchmark model for this data set (scattered diamonds), calibrated for this system on a comprehensive experimental data set [START_REF] Lützenkirchen | Modelling uranyl adsorption to quartz -application of the CD-MUSIC concept[END_REF].

Using a FITEQL based code to fit a bi-dentate reaction to the data under the same premises results in an optimum description with the following reaction:

2(Si-OH 0 ) + UO 2 2+ ↔ (Si-O) 2 HUO 2 + + H + log 10 = 2.96 (9) 1 int, [] H K 1 int, [] Na K 1 int, [] U K 2 int, [] U K
Both models perform equally well (Figure 1A). In the next step, the two model variants were used with ECOSAT; the corresponding "blind predictions" are shown on Figure 1B, where the mono-dentate constant from eq (8) yields the same curve as on Figure 1A, whereas the bi-dentate constant from eq (9) results in a prediction of 100% adsorption in the whole pH interval. We see that direct application of the molar intrinsic constant = 10 2.96 in forward ECOSAT calculation results in a large over-prediction biased by 3.6 orders of magnitude, far more than any reasonable analytical or fitting error.

Rescaling the FITEQL-fitted bi-dentate constant to the surface mole fraction scale  concentration scale used in the ECOSAT input by applying the correction given by K int,2 (converted)

K int,1 K int,2 Experimental 1 int, K 2 int, K 2 int, [] U K 2 int, [] U K pH 3 4
K int,1
Benchmark CD model [START_REF] Venema | Multisite Adsorption of Cadmium on Goethite[END_REF] with total molar concentration of surface sites [] TOT = 2.52110 -4 M leads to the same value as that for the mono-dentate binding constant

2(Si-OH 0 ) + UO 2 2+ ↔ (Si-O) 2 HUO 2 + + H + log = -0.64 (10)
Use of this value (denoted as converted in Figure 1B) reproduces exactly the FITEQL result.

4.1.2. The Eu-rutile (TiO 2 ) system (mono-vs tetra-dentate case)

In the experiments (performed in 0.1 M NaClO 4 ), the specific surface area was A S = 50.6 m 2 g -1 and the solid concentration was c S = 0.1 g dm -3 ; the total Eu concentration was 1.23 10 -6

M. We used a single-site BS (basic Stern) model with the site density  S = 2.010 -5 mol m -2 (ca. 12 nm -2 ) and the fitted capacitance density C 1 = 0.71 Fm -2 . The surface protolysis reactions were written in a 'simple' 1pK fashion: The thin solid line on Figure 2A shows a benchmark CD-MUSIC model for the rutile surface using a mono-dentate Eu III surface species, which was calibrated on a large set of data for this experimental system [START_REF] Bouby | Sorption of Eu(III) onto titanium dioxide: Measurements and modeling[END_REF]. This FITEQL-optimized intrinsic constant leads to a model curve (green continuous line on Figure 2A) that is slightly shifted to the left from the "monodentate" curve, but has the same shape. This small shift may be due to the difference in the surface species charge.

Ti≡O ─½ + H + ↔
Application of the same constant with the same tetra-dentate reaction (12b) in an ECOSAT forward modeling run results in substantial over-prediction (see Figure 2B) at any pH. Re-scaling the constant with the total site molarity [] TOT = = 0.0001008 M results in a value log 10 = 9.14 (for the reaction 4(Ti≡O ─½ ) + Eu 3+ ↔ (Ti≡O) 4 Eu + ), with which the same forward-modeling curve is obtained in ECOSAT (Figure 2B) as that for log = 21.13 in FITEQL calculations.

Conversely, the bias in log value for this 4-dentate Eu surface complex relative to the log value was 12 orders of magnitude in this system. Adsorption studies of Cu(II) on goethite (-FeOOH) provides spectroscopic evidence for corner-sharing bi-dentate monomeric and tri-dentatedimeric Cu surface complexes [START_REF] Peacock | Copper(II) sorption onto goethite, hematite and lepidocrocite: A surface complexation model based on ab initio molecular geometries and EXAFS spectroscopy[END_REF][START_REF] Sherman | Surface complexation modeling: Mineral fluid equilibra at the molecular scale[END_REF]. These authors performed modeling using the FITEQL code with a DLM including the following surface species and intrinsic constants:

>SOH 0 + H +  >SOH 2 + logK a1 = 6.78 (13)
>SOH 0  >SO -+ H + logK a2 = -10.10 ( 14)

2>SOH + Cu 2+ + 2H 2 O = (>SOH) 2 Cu(OH) 2 + 2H + log = -3.1 (15) 3>SOH + 2Cu 2+ + 3H 2 O = (>SOH) 2 >SOCu 2 (OH) 3 + 4H + log = -5.25 (16)
In their experiments, specific surface area was A S = 32.73 m 2 g -1 ; solid concentration was c S = 3.33 gdm -3 ; the electrolyte concentration was 0.1 M NaNO 3 , and [Cu] TOT = 3.9310 -4 M. The site number density parameter for goethite was set to 6 sitesnm -2 ( S = 9.9610 -6 molm -2 ).

The aqueous hydrolysis constants for Cu 2+ are given in [START_REF] Peacock | Copper(II) sorption onto goethite, hematite and lepidocrocite: A surface complexation model based on ab initio molecular geometries and EXAFS spectroscopy[END_REF].

The goal of our numerical exercise was to find out whether (and how) this FITEQLfitted SCM can be reproduced with another speciation code (ECOSAT). The straightforward run (Figure 3A) of the pH adsorption edge in the ECOSAT with intrinsic constants taken from eqs (15, 16) resulted in ca. 1.3 units shift to lower pH relative to the experimental data.

However, after applying the correction with [>S] TOT = c S A S  S = 1.08610 -3 M, leading to intrinsic constants expressed in surface mole fraction scale , log 10 = -3.1 -2.96 = -6.06; log 10 = -5.25 -2.962 = -11.17 ( 17), the produced model curves were close to the original DLM of [START_REF] Peacock | Copper(II) sorption onto goethite, hematite and lepidocrocite: A surface complexation model based on ab initio molecular geometries and EXAFS spectroscopy[END_REF],

though not in perfect agreement (Figure 3B). The small discrepancies were probably not due to differences in the treatment of aqueous activity coefficients, but rather arise from the difference between pH and -log[H + ] scales in plotting the modeling results or in the fitting (this difference amounts to 0.11 log units for the ionic strength involved). Our fitting exercise

2 int, Cu K 3 int, 2 Cu K 2 int, Cu K  3 int, 2Cu K 
was done in the molar concentration scale for all species involved, and subsequently, the proton concentration was recalculated to proton activity. As seen from this example, the magnitude of the K int correction factor is about 3 log units for bi-dentate and about 6 log units for tri-dentate surface species.

Figure 3.

Copper pH adsorption edge in DLM for the Cu II -goethite system with bi-and tridentate species from [START_REF] Peacock | Copper(II) sorption onto goethite, hematite and lepidocrocite: A surface complexation model based on ab initio molecular geometries and EXAFS spectroscopy[END_REF]) (thin curves, scattered hexagons represent experimental data), re-modeled using the ECOSAT code (A) before and (B) after conversion of intrinsic adsorption constants.

Our modeling tests (which all keep the same EIL model parameters) demonstrate that in all cases, the numerical values of intrinsic adsorption constants may contain significant contributions related to the multiple denticity of surface complexes.

In this example, we also involve results obtained with VISUALMINTEQ and PHREEQC. The purpose was to determine which kind of formalism is implemented in these popular codes. According to the manuals, VISUALMINTEQ is exactly as ECOSAT.

PHREEQC does not involve the same treatment as ECOSAT but defines a correction term involving maximum coverage of all sites. For only one site involved in a multidentate surface complex this leads to a correction term corresponding to the denticity d. Here, x = 1, and y =1 for the singly co-ordinated sites (3.45 sites/nm 2 ) and x = 3, and y = 0for the triply co-ordinated sites (2.70 sites/nm 2 ). Capacitances for the two layers were 0.92 F/m 2 .

The Fe(II) adsorption model was designed as follows: 2>FeOH -0.5 + Fe 2+ = [(>FeOH -0.5 ) 2 ] +0.73 Fe II +1.27 logK Fe int,2 = 8.47 (21a) 2>FeOH -0.5 + Fe 2+ + 2H 2 O = (>FeOH -0.5 ) 2 +0.17 Fe III (OH) 2 -0.17 + 2H + logK FeOH int,2 = -9.31 (21b)

In our calculations, the specific surface area was A S = 78 m 2 g -1 ; solid concentration was c S = Figure 5A shows that in these calculations there is a shift of the PHREEQC calculation to higher pH compared to the ECOSAT results. According to Figure 5B FITEQL reproduces the ECOSAT calculations exactly within formalism 1 and an appropriate correction term.

Multi-dentate surface complexes involving two kinds of surface sites

In this section, we consider the CD-MUSIC model for Cd adsorption to the goethite (021)

face. According to the model by [START_REF] Venema | Multisite Adsorption of Cadmium on Goethite[END_REF] the reaction occurs via the following equation 2 FeOH -½ + Fe 2 OH° + Cd 2+ = [{(FeOH) 2 Fe 2 OH} +1.16-1 Cd +0.84 ] + log K Cd int,3 = 9.0

The ECOSAT inherent correction involves the term

log (S s + S d ) -2 log S s -log S d ( 23
)
where S is defined as product of suspension density (solid concentration), specific surface area and site density. We suspect that if included in the other codes (VISUALMINTEQ and PHREEQC)) these corrections may differ. They will depend on whether the multidentate surfaces are defined based on mole fractions (referenced either to individual sites or the total number of sites), surface coverage (again this might be referenced to the maximum coverage with respect to indivual site or all sites) or any other normalization. As pointed out above, these corrections may become huge. The correction term according to equation ( 22) for 1 g/l and 20 m 2 /g is 7.7 log units.

Figure 6A shows the results of straightforward application of the published parameters with the different codes. For FITEQL, the correction eq. ( 24) was used. According to Figure 6B PHREEQC as in the examples before does not reproduce those results. As pointed out before the corrections are different between PHREEQC and ECOSAT because according to the PHREEQC manual, the correction includes the denticity with respect to the surface sites as a denominator to the site concentration, in the case of a tridentate introducing a term log(3) = 0.478. This results in log K Cd int,3,PHREEQC = 9.48, which exactly reproduces the results obtained by the other codes. In the case of bidentates, the correction would be log(2) = 0.3. The denomitor in PHREEQC allows for the mole fraction of multidentate surface complexes to become unity. It is not clear how this is handled for binuclear, multidentate surface complexes like in eq. ( 16).

A B Figure 6. Cadmium adsorption as a function of pH in CD-MUSIC on goethite (021). A: Calculations using VISUALMINTEQ, ECOSAT and FITEQL. For FITEQL the ECOSAT based scheme was corrected. B: Calculations using ECOSAT and PHREEQC. PHREEQC (corrected) refers to a correction according to the PHREEQC manual.

Summary for multi-dentate surface complexes

To confirm the results of the previous two sections, we have built another series of calculations starting from monodentate surface complexes, and subsequently changing the system to a single bidentate complex on one site and subsequently on two sites. We use the example of Zn adsorption to HFO according to [START_REF] Dzombak | Surface complexation modeling. Hydrous ferric oxide[END_REF]. The databases or thermodynamic parameters were taken from [START_REF] Dzombak | Surface complexation modeling. Hydrous ferric oxide[END_REF].

Figure 7 summarizes the findings. While for the monodentate case, straightforward application of the codes yields the same outcome in all cases (Figure 7A), the previously noted differences are repeated in the cases of multidentate species.

In particular, ECOSAT and VISUALMINTEQ calculations coincide in all cases. Molar scale used within FITEQL yields different curves independently of the formalism used. In this case, the ECOSAT based constants need to be rescaled using the appropriate functions, such as eq. ( 23) for the Cd-goethite case in the previous section. PHREEQC always produces underestimates compared to the ECOSAT reference, caused by the additional correction.

Users of PHREEQC should refer to the documentation regarding the appropriate corrections.

In summary, the calculations have shown that huge differences in calculation results may occur when constants from the literature are used without prior correction. While this has been pointed out by [START_REF] Venema | Multisite Adsorption of Cadmium on Goethite[END_REF] for the rescaling of ECOSAT intrinsic equilibrium constant in surface mole fraction scale to that in molar scale (implemented in codes like FITEQL, MINEQL, SOLGASWATER), users have to make sure they either use a code with the same implementation or consult the manuals to do appropriate corrections. Our results

show that VISUALMINTEQ works exactly as ECOSAT, since in all cases the results from Note that the set-off in the calculations without correction is similar in all these cases. The situation is more complex if different sites participate in the multinuclear surface complex. In Conditions: A: 0.09 g/l HFO, 0.1 mM Zn; B: 0.09 g/l HFO, 0.1 mM Zn, C: 0.9 g/l HFO, 0.1 mM Zn; D: 0.09 g/l HFO, 0.1 µM Zn, E: 0.09 g/l HFO, 0.1 mM Zn; F: 0.9 g/l HFO, 0.1 mM Zn.

For applications to reactive transport modelling, the user has to make sure whether codes use automated scaling procedures for multidentate surface complexes or not. This is particularly important, since the huge solid to liquid ratio that will be involved in reactive transport in porous media will require substantial corrections, if the intrinsic constants are implemented in the molar scale. As with PHREEQC, the outcome will depend on the code and model implementation.

Diffuse double layer implementation

The aim of the following modeling exercises was to illustrate what kind of diffuse double layer equation is implemented in the different codes. To this end, we did calculations within a surface complexation model framework that involves the diffuse layer part. We used a 1:1 electrolyte and a 2:1 electrolyte, as well as mixed electrolytes. From the output, we separated the calculated diffuse layer potential and the diffuse layer charge and the overall ionic strength. All the codes give these distinct values that have to satisfy the respective implemented equation (i.e. either (3) or ( 4)). The diffuse layer potential and the ionic strength were then inserted in equation 3 to yield the diffuse layer charge inherent to symmetrical electrolytes, and compared to the value obtained by the codes. If the results coincided for the 2:1 and mixed electrolytes, it was concluded that equation 3, and not the more general case, was used in a given code.

Table 1 summarizes the results. While for ECOSAT and FITEQL the expected results were obtained (here the documentation is clear), for PHREEQC and VISUALMINTEQ users can take advantage of the results of our calculations to choose the code that is appropriate for their respective applications.

CONCLUSIONS

The problem of conversions between various kinds of intrinsic adsorption constants has previously been little addressed because, for mono-dentate surface complexation, the values of expressed in any concentration scale are the same. For the same set of experimental data, the value of depends only on the chosen site density parameter  S or site capacity q S , as already discussed in the literature [START_REF] Lützenkirchen | Surface complexation models of adsorption: a critical survey in the context of experimental data[END_REF][START_REF] Karamalidis | Sorption modelling by Gibbs energy minimisation: Towards a uniform thermodynamic database for surface complexes of radionuclides[END_REF]Kulik, , 2006[START_REF] Kulik | Thermodynamic concepts in modeling sorption at the mineral-water interface[END_REF][START_REF] Sverjensky | Standard states for the activities of mineral surface sites and species[END_REF]. But, although earlier studies have pointed to this issue (e.g. [START_REF] Venema | Multisite Adsorption of Cadmium on Goethite[END_REF], it has not yet been conclusively demonstrated how the large biases in This is a prerequisite for future thermodynamic sorption databases, which also require a conventional agreement on standard-and reference states for the activities of surface complexes and surface sites, which is still to be reached (Kulik and Lutzenkirchen, 2011).

The present paper contributes to the resolution of two long-standing problems around surface complexation models. The first is associated with the proliferation of specific model 1 int, M K 1 int, M K setups in the literature, used to describe individual sorption data sets. While an adequate fit is invariably achieved in each specific case, the conversion of computed parameter values without the necessity of refitting experimental data sets is relevant. Ultimately internally consistent sets of intrinsic and standard-state constants for general surface complex stoichiometries are required and we will describe an approach towards this in detail elsewhere.

The second issue is how to apply adsorption equilibrium constants to 'real' systems with non-zero electrostatic potential and significant surface coverage, site saturation and competition effects involving multi-dentate M surface species, possibly of different denticity, together with surface complexes of other ions. It is known that, at least for the electrolyte adsorption, fitted intrinsic adsorption constants depend on the choice of doubly layer model.

To what extent in such cases a variation of the site density parameter and denticity may affect capacitance and K int values required to obtain a comparable fit to the experimental data (in particular, surface charge data), still remains to be studied. The available information for the constant capacitance model (Lützenkirchen, 1999) would suggest such interdependencies, largely neglected so far. In a thermodynamic sense, the introduction of concepts of chemical potential, activity and activity coefficients, and consideration of activity-composition relationships could account for non-ideality effects. While Coulombic terms (electrostatic activity coefficients) are generally accepted, non-electrostatic surface site saturation and competition effects, mostly related to various types of adsorption isotherms, still remain largely controversial.

Figure 1 .

 1 Figure 1. Comparison of SCM fits for the uranyl-quartz system for mono-( , crosses) and bi-dentate cases. FITEQL fits for a simplified model (A), and forward ECOSAT calculations (B) without-and with re-scaled value of for U VI adsorption. Diamonds represent experimental data, thin solid curves -the 'benchmark' CD-MUSIC model.

Figure

  Figure2. Comparison of SCM fits for the Eu III -rutile system for mono-and tetra-dentate cases. FITEQL fits for a simplified model (A) and forward ECOSAT calculations (B) with the original and converted tetra-dentate intrinsic constant K int,4 . Scattered circles represent experimental data. See text for explanations.

  Cu II -goethite system (bi-+ tri-dentate case)

Figure 4 Figure 4 .

 44 Figure4shows that straightforward use of the published constants gives similar results

Figure 5 .

 5 Figure 5. Fe(II) adsorption as a function of pH in CD-MUSIC on goethite. A: comparison between a PHREEQC calculations (lines) and an ECOSAT calculation (lines with crosses). B: comparison between ECOSAT calculation (lines with crosses) and a FITEQL calculation after applying the appropriate correction term (squares).

  ECOSAT are exactly reproduced without adjustment of intrinsic constants.PHREEQC uses a different scaling. The transfer from ECOSAT to PHREEQC is simple if one site is involved in the multinuclear surface complex, and the user simply has to add the logarithm of the denticity to the ECOSAT constant. In the respective examples in Figure7this simple modification exactly reproduces the ECOSAT calculations. The correction term amounts to 0.3 in log units and allows to reproduce the ECOSAT calculations in Figures7 B, C, E and F.

Figure 7 DFigure 7 .

 77 Figure 7 D the set-off of the PHREEQC results compared to ECOSAT is much larger than in

K

  int values related to multiple denticity can be avoided by the appropriate scale conversions.Modeling examples considered in this contribution demonstrate significant magnitudes of 'denticity effects', visible by code comparison and benchmarking. The effects arise from different implementations of the law of mass action and mass balance. Our results emphasize that the set of intrinsic equilibrium constants for the formation reactions of surface complexes must be consistent for all types of surface species, including multi-dentate complexes. It is imperative to document precisely the concentration scales and the assumptions on denticity to clarify the interpretation of experimental and modeling results.

Acknowledgments.

  The authors are grateful to the sponsors and participants in the Sorption Forum of the Nuclear Energy Agency, which has facilitated the open discussion of the issues raised in this paper. Many aspects considered in this paper were discussed at the Discussion Meeting "Surface Reactions and the Electrical Interfacial Layer: Experiments and Models -Towards a Common Basis", Opatija, Croatia, in October 2007. The authors acknowledge the reviews by two anonymous referees, which helped improve the manuscript.

  2. Comparison of SCM fits for the Eu III -rutile system for mono-and tetra-dentate

					[]	K	int, Eu	4
					S c  S S A
						K	int, Eu	4
	[]	K	int, Eu	4
					K	int, Eu	4
				int,	4
				Eu

cases. FITEQL fits for a simplified model (A) and forward ECOSAT calculations (B) with the original and converted tetra-dentate intrinsic constant K int,4 . Scattered circles represent experimental data. See text for explanations.

Table 1 :

 1 Types of equations implemented in four different popular speciation codes.

	Code	ECOSAT	PHREEQC	VISUALMINTEQ	FITEQL
	Equation	4	4	3	3