Silicate adsorption by goethite at elevated temperatures

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The thus derived molar heat of arsenate adsorption onto amorphous aluminum hydroxide, e.g., varies in a broad range of −3 to ... concentration was mixed with 250 ml of goethite suspension (2 g L− 1). ... temperatures indicated as fitted by the 1-pK BSM CD model. ... species relevant in the pH range 4–10, Si2O2(OH)5.
Chemical Geology 262 (2009) 336–343

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Chemical Geology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c h e m g e o

Silicate adsorption by goethite at elevated temperatures Michael Kersten a,⁎, Nataliya Vlasova b a b

Environmental Geochemistry Group, Institute of Geosciences, Johannes Gutenberg-University, Mainz 55099, Germany Institute of Surface Chemistry, National Academy of Sciences of Ukraine, General Naumov Str.17, 03164 Kiev, Ukraine

a r t i c l e

i n f o

Article history: Received 18 November 2008 Received in revised form 2 February 2009 Accepted 3 February 2009 Editor: J. Fein Keywords: Adsorption Enthalpy FITEQL Geothermal Goethite Silicate Temperature

a b s t r a c t Batch adsorption experiments with relatively low silica concentrations between 10 µM and 100 µM were conducted at three different ionic strength (0.01 − 0.1 M), and four different temperatures between 10 °C and 75 °C, yielding in a total of 550 experimental data points. The residual concentration of monosilicic acid is controlled by an adsorption equilibrium which is dependent on pH. The % Si adsorbed vs. − log[H+] curves reveal an upward bend with a maximum at about a pH of 9. With acidification below pH 9 the residual Si concentration in the suspensions steadily increases, as well as in the increasingly alkaline pH range. The slope of the latter is becoming steeper with increasing temperature. A basic Stern layer and charge distribution approach was used for modelling surface charge. The − log[H+]-dependent Si adsorption at the goethite surface was modelled involving a single-site approach for both neutral and hydrolyzed silicate inner-sphere surface complexes. For both a binuclear bidentate 2C complex was chosen according to spectroscopic information. Experimental data at all ionic strengths and temperatures are matched equally well by the adsorption model. The model output suggests a decrease in the pH where hydrolysis of the Si surface complex starts, and therefore an increasing importance of the hydrolyzed surface species with increasing temperature. The equilibrium adsorption constants could be well represented by a linear Van't Hoff logKT vs. 1/T plot, from which thermodynamic ΔrH298 and ΔrG298 values of the adsorption reactions were derived. Adsorption of the silicate on the goethite surface is exothermic (ΔrH298 = − 43.7 kJ mol− 1 for the dominating surface complex), and becomes therefore weaker with increasing temperature. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Silica is ubiquitous in natural waters, typically in the few mg L− 1 SiO2 concentration range for surface and ground waters. Hydrothermal waters, on the other hand, are not only chloride but often also silicate enriched, with concentrations commonly in the range 100–1000 mg L− 1 depending on the source temperature. In fact, estimation of underground source temperatures is commonly based on the silica content of water from hot springs (White et al., 1956; Fournier and Potter, 1982; Ragnarsdóttir and Walther, 1983; Gunnarsson and Arnorsson, 2000). By exposing this brine to the surface, silica may become supersaturated upon flushing (concentration effect) and pond cooling (prograde solubility effect). Quartz and other crystalline silica polymorphs exhibit slow precipitation kinetics, but amorphous silica tend to precipitate rapidly as scale deposits (Iler, 1979). According to Ellis and Mahon (1977), in freshly discharged thermal waters from high-temperature hot springs and geothermal wells, aqueous silica is almost always present in a monomeric form as H4SiO4. Cooled thermal waters show concentrations of monomeric silica, which decrease with time and approach a

⁎ Corresponding author. Fax: +49 6131 3923070. E-mail address: [email protected] (M. Kersten). 0009-2541/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.chemgeo.2009.02.002

value approximately equal to the steady-state concentration at equilibrium with amorphous silica at the actual temperature. The silica present in the water in excess of the amorphous silica solubility polymerizes through a series of reactions involving linear, cyclic and three-dimensional polymeric silica (e.g. Iler, 1979; Sjöberg, 1996; Ellis and Mahon, 1977). Thermal waters in the ponds are often blue-colored (e.g., the “Blue Lagoon” in Iceland) caused by Rayleigh scattering from the colloidal silica particles (Ohsawa et al., 2002). Less well established is that silicate in aqueous environments does not behave conservatively but is particle-reactive. Adsorption on oxide surfaces is a particularly important silicate mobility controlling reaction in the hydrogeologic environment. It influences Fe(III) hydrolysis and prevents colloidal hydrous ferric oxide (HFO) from coagulation and hence crystalline goethite or hematite formation (Cornell et al., 1987; Vempati and Loeppert, 1989; Schwertmann et al., 2004). Silicic acid is also known to be adsorbed efficiently onto iron oxide surfaces from batch adsorption equilibrium experiments. Sigg and Stumm (1981) were the first to formulate a surface complexation model (SCM) for sorption of a neutral monomeric Si(OH)4 to goethite. Formation of both neutral and negatively charged innersphere surface complexes was assumed for this adsorption modeling approach. Later more advanced SCM approaches were reported including even polymeric surface complexes (Hansen et al., 1994; Gustafsson, 2001; Davis et al., 2002; Luxton et al., 2006;

M. Kersten, N. Vlasova / Chemical Geology 262 (2009) 336–343

Hiemstra et al., 2007). FTIR, 29Si NMR and X-ray photoelectron spectroscopy studies have indicated that silicate forms innersphere complexes on the goethite surface (Vempati et al., 1990; Hansen et al., 1994; Glasauer et al., 1999; Doelsch et al., 2001). The relatively short Fe–Si distance found by X-ray absorption spectroscopy (EXAFS) of Fe(III)-silica interactions in aqueous solution is best explained assuming formation of bi-dentate bi-nuclear (C2) complexes composed of tetrahedrally coordinated Si attached to the corners of two adjacent Fe octahedra (Pokrovski et al., 2003). Formation of the same silica coordination on goethite surfaces, albeit not yet evidenced by direct measurements, is supported by quantum chemical molecular modeling (Hiemstra and Van Riemsdijk, 2006), and by chemical analogy to GeO2 adsorption by goethite which is less difficult to analyze by EXAFS (Pokrovsky et al., 2006). It would also agree to spectroscopic data on surface complexes of other oxyanions such as arsenate, phosphate, and selenate. What matters more with respect to hydrothermal conditions is the fact that despite a growing number of studies on surface complexation modeling, not much is known about the effect of temperature on adsorption of oxyanions common in geothermal water wells such as silicate. Since no equation of state (EoS) for surface species analogous to aqueous species has been suggested so far, data on temperature dependence must rely on appropriate reaction model formulation and temperature interpolation equations of the modelling results (e.g., Schoonen, 1994). Two experimental approaches for determination of the enthalpy of surface reactions are commonly used, (i) direct (flow) micro-calorimetric experiments, and (ii) measurements of temperature dependency of an equilibrium parameter, e.g., the point of zero charge and adsorption constants (Kovačević et al., 2007). The enthalpy change measured in the calorimeter is the sum of contributions not only of interfacial reactions, but also of the accompanying bulk solution processes. The thus derived molar heat of arsenate adsorption onto amorphous aluminum hydroxide, e.g., varies in a broad range of −3 to −66 kJ mol− 1 rather than yield in a unique value (Kabengi et al., 2006). This study relies therefore on the more common generic equilibrium constant vs. temperature dependency approach. The purpose of this study was to better understand the effect of increasing temperature on adsorption of silicate. The experimental data analysis allowed formulation of a surface complexation model that can predict many important aspects of silica sorption for conditions encountered in natural and engineered geothermal systems.

2. Materials and methods 2.1. Synthesis of goethite Synthetic goethite was prepared from ferric nitrate (Fe(NO3)3·9H2O, Merck, p.a. quality) solution under highly alkaline conditions according to the procedure described by Gerth (1990). In brief, 50 mL of a 1 M ferric nitrate solution was rapidly admixed to 650 mL of 0.5 M sodium hydroxide (NaOH, Merck, p.a.) solution under inert Ar atmosphere free of CO2, and heated to 70 °C. The suspension was kept at 90 °C for 7 days and shaken up once per day. This suspension ageing was necessary to prevent Ostwald ripening of goethite nano-particles during the experiments. Then, the suspension was dialyzed in cellulose tubing for another 7 days until concentration of sodium was less than 0.1 mg L− 1. All Table 1 Intrinsic equilibrium protonation and silicate adsorption constants for the experimental temperatures indicated as fitted by the 1-pK BSM CD model. Surface complexation reaction

logKint (± 0.10) 10 °C 25 °C 50 °C 75 °C

9.45a (8) ≡FeOH− 0.5 + H+ ↔ ≡ FeOH+0.5 2 1 (11) 2 ≡ FeOH− 0.5 + Si(OH)04 ↔ (≡FeO)2Si(OH)− 5.67 2 + 2H2O −2 +2H2O 6.32 (12) 2≡FeOH−0.5 +SiO(OH)− 3 ↔(≡FeO)2SiO(OH) a

Data from Kersten and Vlasova (2009).

9.10a 5.22 6.15

8.60a 4.58 5.85

8.20a 4.16 5.61

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chemicals were stored in plastic bottles, and all experiments were carried out in plastic vessels to avoid silica contamination. Deionised boiled and Ar-bubbled water of pH 5 was used to prepare all solutions and suspensions to avoid carbonate contamination, which may severely interfere with Si adsorption. The goethite suspension was pre-concentrated by slight centrifugation and careful decantation until a final suspension of 38 g L− 1 (volume fraction of about 0.9%) was reached. The stock suspension bottles were kept in a refrigerated desiccators under Ar at 4 °C to avoid microbiological activity. A suspension subsample was dried under Ar atmosphere at 60 °C for BET surface area measurement, which gave a value of 20 m2 g− 1. This relatively low value is in good agreement with dependence of the surface area of goethite on synthesis temperature, and indicates an advanced maturation of the goethite particles (Diakonov et al., 1994). Acidity in terms of pHPZC and charging behaviour of the goethite surface was determined by both potentiometric titration and electroacoustics as described in detail earlier (Kersten and Vlasova, 2009). X-ray diffraction (XRD) analysis of the dried precipitate confirmed ultimately its pure composition and good crystallinity without any XRD-detectable phase impurities. 2.2. Silicate adsorption experiments A stock suspension of goethite was diluted with silicate/NaNO3 stock solutions to yield in a suspension of 1 g L− 1 goethite in solutions of various total silicate and NaNO3 concentrations. All solutions were de-aerated by bubbling with Ar. For preparing of 500 mL suspension in CO2-free deionised water, 250 ml of Na2SiO3·9H2O stock solution (Merck p.a., acidified to pH 4.0) with twice the final Si and NaNO3 concentration was mixed with 250 ml of goethite suspension (2 g L− 1). The highest stock silicate solution concentration was therefore fixed at 200 µM, far below amorphous SiO2 solubility to avoid polymerization (Gunnarsson and Arnorsson, 2000). All suspensions were thus adjusted to contain total silicate concentrations of 10, 50, and 100 µM, and total NaNO3 concentrations of 10, 50, and 100 mM, respectively. Batch reactions were conducted in 50-ml polypropylene centrifuge tubes. In each of these tubes, 45 mL of well-stirred suspension were placed. Initial pH adjustments were carried out in batch mode by discrete additions under an Ar-flushed glove bag of diluted (0.1 M) HNO3 or NaOH prepared in HDPE bottles from standard stock solutions (Titrisol, Merck) in CO2-free deionised water. The pH of the suspensions was measured using Inolab Level 2P pH meter (WTW) equipped with a combination electrode (SenTix81) and temperature probe. The electrode was calibrated using a three-point calibration with commercial pH buffers (CertiPur, Merck) at the respective temperature and known temperature dependence of pH of buffers (Covington et al., 1985). Electrode readings were taken when a drift less than 0.002 pH units in 10 min was attained. All centrifuge tubes were then capped and placed in an Ar-bubbled water bath thermostat at the desired temperature in the range between 10 °C and 75 °C. After 24 h, the samples were centrifuged at 3500 rpm for 20 min, and the final pH was measured in the supernatants. The supernatants were then filtered through 0.2-µm membrane filters, and three subsamples were analysed for residual dissolved Si concentrations using the “molybdenum-blue” method. This method is sensitive for dissolved monomeric silicate only. The amount of adsorbed silicate was calculated as the difference between initial and apparent equilibrium concentrations (% relative adsorption scale). The 24 h reaction time was selected to assure the relatively rapid (hours range) initial adsorption equilibrium to be completed without initiating the slower long-term secondary sorption process that is known to occur at longer exposure times (days to weeks range), probably due to intraparticle diffusion, polymerization of the silicate sorbate, or other ageing effects (Hingston and Raupach, 1967; Huang, 1975; Davis et al., 2002). Reversibility of adsorption was checked by additional desorption experiments on representative amount of subsamples. For this new sodium chloride

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solutions were added to the samples after centrifugation and decantation, pH was adjusted, and after equilibration for one week silicate concentration was measured in this new suspension and compared with previous results.

2.3. Model calculations A prerequisite for a correct modelling of the surface speciation is an accurate model of ion pair formation and solution speciation. The calculations had to consider that the aqueous chemistry of silica is somewhat complicated due to polymers potentially formed as a function of pH and Si concentration (Dietzel, 2002). Based on extensive silica solubility data sets, the equilibrium constants for water–silica interaction are well known. The overall speciation of aqueous Si in solution with concentrations set by solubility of amorphous silica (b0.002 M, 25 °C) is described by the following equilibria: þ SiðOHÞ4 ¼ SiOðOHÞ− 3 þ H ; logβ−1;1 ¼ −9:82

ð1Þ

þ SiðOHÞ4 ¼ SiO2 ðOHÞ2− 2 þ 2H ; β−2;1

ð2Þ

2SiðOHÞ4 ¼ Si2 OðOHÞ6 þ H2 O; β0;2

ð3Þ

þ 2SiðOHÞ4 ¼ Si2 O2 ðOHÞ− 5 þ H þ H2 O; β−1;2

ð4Þ

þ 2SiðOHÞ4 ¼ Si2 O3 ðOHÞ2− 4 þ 2H þ H2 O; β−2;2 :

ð5Þ

Sjöberg (1996) suggested that the prevailing hydrolytic monomeric silicate species in natural water with pH less than 9 is the neutral Si(OH)04. We calculated solution speciation for the maximum of dissolved silicate concentration used in this study by the code GRFIT (Ludwig, 1992), and found that the proportion of the only dimer species relevant in the pH range 4–10, Si2O2(OH)− 5 formed by reaction (4), do not exceed 3% of total. This modelling result is in accordance with what is known from other modelling results and in-situ spectroscopic measurements (e.g., Cary et al., 1982). Therefore only the first reaction (1) was further considered for silicate adsorption modeling in the pH range 4–10. The temperature dependence of the first dissociation constant logβ− 1,1 has been refitted using the data by Busey and Mesmer (1977) to give a function of absolute temperature (T in Kelvin): logβ−1;1 ¼ −81:22−0:0329T þ 32:82  logT:

ð6Þ

A temperature correction function for the water dissociation constant was refitted using the data set provided by Marshall and Franck (1981): logKT ¼ −89:307−0:041  T−1702=T þ 37:67  logT þ 3158=T2 :

ð7Þ

The activity coefficients of all species used at different ionic strength were calculated using the extended Debye-Hückel equation with appropriate solvent parameters published by Nordstrom and Munoz (1994). Adsorption model parameterization was carried out using the general optimization code UCODE (Poeter et al., 2005) coupled to a modified version of FITEQL 2.1 (Westall, 1982), whereby the latter was used as the application code in UCODE. The combination of both codes goes far beyond the capabilities of even the latest FITEQL 4.0 version alone (Lützenkirchen et al., 2008). Data for one experimental series were grouped in one application input file, but this approach allows for the use of an arbitrary number of data sets and different data sources for simultaneously fitting any parameter to a certain model. The optimizations were carried out based on the relative fraction adsorbed, thus avoiding problems with weighting for data sets with different concentrations. The calculations for plotting the modeling results were done with the final optimization results at defined step

values of pH with the application code. The coupled code allows for use of the charge distribution (CD) model by entering two free parameters according to the description by Lützenkirchen (2006), i.e., the charge distribution value (Δz) and the affinity for the surface (logK). The parameters commonly used in this model are optimized by minimizing the difference between the calculated and experimental silicate adsorption data. A central parameter in the model is the distribution of the charge. According to this concept, adsorbed molecules have a physical size (i.e., they are not true point charges), and the charge of an innersphere complex can be delocalized throughout the compact part of the electrical double layer (Hiemstra and Van Riemsdijk, 1996, 2006). If the neutralization of anion charge is expressed on a per coordinated cation bond basis according to Pauling's rules, then surface hydroxyls may have noninteger charge. In the case of the adsorption of the uncharged silicic acid species Si(OH)04, half of the ligands of the Si surface complex will become common with the reactive surface hydroxyl groups. The other two of the oxygen's of the adsorbed tetrahedral oxyanion complex are at some distance from the sorbent surface. The charge distribution of the adsorbed neutral complex is determined from the surface proton stoichiometry. The surface acidity of goethite was assumed to be controlled by only two reactions: one for protonation of singly coordinated hydroxo sites (≡FeOH− 0.5), and one for protonation of triply coordinated oxygen (≡ Fe3O− 0.5). The surface site density on goethite available for protonation was assumed as sum of singly coordinated groups (3.6 sites nm− 2) and one third part of the triply coordinated groups (2.8 sites nm− 2) according to a recommendation by Lützenkirchen et al. (2002). The affinity constants of these two proton reactive sites are set equal as common, but in our pragmatic simplification both sites were also summed up to give a single hydroxyl site (≡FeOH− 0.5) contribution with site density of NS = 6.4 nm− 2 to the surface charge rather than a two site model as common. Primary charging behaviour of goethite by protonation of the surface sites was determined experimentally earlier, and is approximated by this generic single site 1-pK approach: ; ≡FeOH−0:5 þ Hþ ↔≡FeOHþ0:5 2

ð8Þ

with a logKH equal to the pristine point of zero charge (pHPPZC = 9.1 ± 0.05) determined for the goethite surface (Table 1). The ionic strength dependence of the surface charge for goethite was modeled by locating the electrolyte ion pairs in the outer plane of the electrical double-layer. Corresponding reactions were formulated assuming the presence of background electrolyte ion pairs in the outer Stern plane, comparable to outer-sphere point charge complexes with CD values of Δz0 =0 and Δz1 =±1: ≡FeOH−0:5 þ Naþ ↔≡FeOH−0:5 Naþ ; logKNa

ð9Þ

and þ0:5 þ NO− NO− ≡FeOHþ0:5 2 3 ↔≡FeOH2 3 ; logKNO3

ð10Þ

with fixed intrinsic equilibrium reaction constants logKNa =logKNO3 =−1.0 as recommended by Hiemstra and van Riemsdijk (1996). Stern layer capacitance C1 in the BSM option was fixed to the value of 0.97 F m −2 fitted from potentiometric titration data at 25 °C (Kersten and Vlasova, 2009). Both the change in electrolyte adsorption constants and in capacitance with increasing temperature could be neglected as discussed previously (Kersten and Vlasova, 2009). Upon fixation of all these parameters, only the intrinsic affinity constants of adsorbed silicate, in combination with its charge distribution, are together fitted from the experimental data. Actual proton concentration −log[H+] calculated from the measured pH value instead of the latter was used in all FITEQL adsorption model fits.

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3. Results and discussion 3.1. Silicate adsorption on goethite at 25 °C The experimental data for total silicate concentrations ranging from 10 to 100 µM as function of pH and ionic strength are shown in Fig. 1. The adsorption vs. −log[H+] curves are bent upward, with a maximum in silicate adsorption near the goethite pHPPZC value, and less silicate adsorbed at lower and higher pH values. Similar trends have been observed in previous studies (Anderson and Benjamin, 1985; Mayer and Jarrell, 2000; Davis et al., 2002; Dietzel, 2002; Hiemstra et al., 2007). Below that pH value, the speciation of the silicate ion in natural waters is very simple with only one dominating species, the neutral Si (OH)04. This implies that the pH dependency of the adsorption is due solely to the interaction of Si with the surface and is not due to a change in aqueous speciation as already discussed by Hiemstra et al. (2007). The pH dependency is then rather determined by the interaction of silicic acid with protons released from the surface (positive slope of the adsorption curve), the amount of which in turn is strongly linked to the structure of the innersphere complex that is formed. As discussed above, the structure of surface complexes is linked to an interfacial charge distribution that affects the electrostatic interaction at the surface, and is essential for understanding the corresponding adsorption properties and hence to interpret the adsorption data. Above that pH of maximum adsorption, the slope of the adsorption curve levels off. This is mainly due to significant contribution of the deprotonated silicic acid species, SiO(OH)− 3 , to the solution speciation in that alkaline pH range. The pH dependency of Si adsorption depicted in Fig. 1 is therefore determined by two factors, i.e., (i) the H+ co-adsorption (the

339

sole factor at low pH), and (ii) the solution speciation responsible for the larger decrease in adsorption at high pH. The percentage adsorbed depends also on the initial amount of silica in solution. In the pH range from 4 to 10 the amount adsorbed onto the goethite surface is 60–90% for 10 µM silicate initial solution; decreases to 40–65% for 50 µM initial solution, and to 25–40% for 100 µM initial solution, respectively. The concentrations of the latter solution were still low enough to prevent overloading of the sorbent. Actual sorption densities were b2.5 µmol m − 2 which is lower than the theoretical maximum monolayer silicate sorption capacity (2.7 µmol m − 2) calculated from the site density of goethite (5.3 µmol m − 2) if to assume that all proton reactive surface sites (6.4 nm − 2) are also reactive to silicate by formation of innersphere bidentate surface complexes. Note that this generic single site approach was chosen to reduce the amount of adjustable parameters, and is therefore not necessarily compatible with structural reality but merely the result of our fitting exercise. It is also not quite compatible with the original MUSIC model by Hiemstra and Van Riemsdijk (1996). The triply coordinated surface groups may not really be accessible for Si binding, but the doubly coordinated ≡Fe2OH0 sites may become a Si-reactive candidate of equal site density, forming ≡Fe2OSi(OH)03 surface complexes (Hiemstra et al., 2007). For a full MUSIC model the affinities of nominally identical sites are also affected by the choice of model crystal planes (Kosmulski et al., 2004; Villalobos and Pérez-Gallegos, 2008; Lützenkirchen et al., 2008), for which there is yet no exact information on a molecular level. Based on the hypothesis of a bi-dentate bi-nuclear innersphere surface complex formation in agreement to what is known from spectroscopic data, two adsorption reactions with the singly coordinated goethite surface groups were formulated corresponding to the two dominant neutral and deprotonated species of silicic acid in solution. Accordingly, the two dominant species forming at the goethite–water interface are expected to be ≡ (FeO)2Si(OH)2− 1 and ≡(FeO)2SiO(OH)− 2. The adsorption reactions may then be reformulated in terms of the charge distribution (CD) approach as suggested by Hiemstra et al. (2007): Δzβ

0 SiðOHÞ2 2≡FeOH−0:5 þ SiðOHÞ04 ↔≡ðFeOÞ−1þΔz 2

þ 2H2 O;

ð11Þ

logK1;FITEQL ¼ 9:19  0:05 −1þΔz0 2≡FeOH−0:5 þ SiOðOHÞ− SiOðOHÞΔzβ þ 2H2 O; 3 ↔≡ðFeOÞ2

ð12Þ

logK2;FITEQL ¼ 10:12  0:05:

Fig. 1. Silicate adsorption onto goethite as a function of −log[H+] at different ionic strengths: 0.01 (open triangles), 0.05 (black dots) and 0.1 M (open dots) NaNO3, for four different temperatures. The solid lines represent fitted model curves.

Fitting with FITEQL as described above ultimately yield in a unique set of CD parameters and surface complexation constants within an uncertainty of ±0.1 log units which was found to best reproduce the whole range of experimental data for −log[H+] and ionic strength variation. For reaction (11), the adsorbate species is the uncharged tetragonal species Si(OH)04, i.e., the sum of the charge distribution (CD) values must be zero (Δz0 + Δzβ = 0). A surface charge distribution was fitted of Δz0 = 0.24 v.u. (valence unit) at the 0-plane, and Δzβ = −0.24 v. u. at the β-plane. This is equal to an asymmetrical Si-charge distribution locating some of the negative charge of the deprotonated sorbent surface at some larger distance from the surface, but keeping the potential of the 0-plane still lower than that on the β-plane. For the hydrolyzed sorbate (reaction (12)), the sum of the CD values must be −1 v.u. (Δz0 + Δzβ = −1). The CD values were set as Δz0 = 0.24 v.u. at the 0-plane (same as of reaction (11)), and Δzβ = −1.24 v.u. at the β-plane (equal to −Δz0 − 1), respectively. This is equal to adding part of the deprotonated sorbent surface charge to the negative charge created by the hydrolyzed ligand at the surface into the β-plane. It might be argued that the hydrolysis is suppressed in a negative electrostatic field. However, in case of a negative particle charge above the pHPPZC of the sorbent, the potential at the 0-plane will become effectively lower than on the β-plane, and ligands with the same proton affinity that experience a less negative surface potential will hydrolyze easier as discussed also by Hiemstra et al. (2007).

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According to Hiemstra and Van Riemsdijk (2006), any fitted charge distribution can be verified from analysis of the proton co-adsorption data, provided that only one type of surface species is formed as in case of silicate in the circum-neutral to acidic pH range. The CD value found for the average experimental ratio of the absolute adsorption densities δΓH/δΓSi at −log[H+] = 6.0 and 8.0 is Δz0 = −Δzβ = 0.25 v.u. (Hiemstra et al., 2007). This number is within a hundredth v.u. equal to our fitted value, and slightly lower than the theoretical Δz = 0.29 ± 0.03 v.u. found by Hiemstra and Van Riemsdijk (2006) by applying the Brown bond valence concept to MO/DFT optimized geometries. The deviation can be explained by the uncertainty in the number of water molecules that interact with the ligands of the Si complex. Such a water dipole correction may contribute a few hundredth v.u. to the interfacial charge distribution (Sverjenski and Fukushi, 2006; Hiemstra and Van Riemsdijk, 2006; Hiemstra et al., 2007). The thus predicted amount of Si adsorbed is represented as a function of –log[H+] by solid lines in Fig. 1. On the absolute adsorption scale (ΓSi in µmol m− 2), the correlation between the 550 data points measured and those predicted by the adsorption model is R2 = 0.997. The thus excellent experimental validation of the adsorption model allows also the calculation of adsorbed silicate speciation as illustrated in Fig. 2, where the percentage of the two predicted surface complexes is plotted as a function of pH exemplary for the same temperature but different Si concentrations and ionic strenghths. These and all other distribution plots not depicted show that the predominant species at all pH values is the neutral bidentate binuclear double-corner (2C) surface complex 1 ≡(FeO)2Si(OH)− 2 . Increasing proportion of the hydrolyzed species in solution at alkaline pH leads to some contribution of the deprotonated surface complex ≡(FeO)2SiO(OH)− 2 with additional negative charge (Fig. 2). At higher surface loading the higher negative charge of the latter surface complex becomes significant, so that contribution of the hydrolyzed complex is increasing with decreasing silicate concentration. The increase of background electrolyte concentration results in a better screening of additional negative charge, i.e., less repulsion will occur at a higher ionic strength. The higher the ionic strength is the higher is also the proportion of the deprotonated complex at the same silicate surface

Table 2 Estimated standard partial molal isobaric thermodynamic constants (25 °C, 1 bar) for protonation and silicate complexation reactions of the goethite surface. Reaction equation (8) (11) (12) a

ΔrG0298 (kJ mol− 1) a

− 51.9 ± 0.6 − 30.1 ± 0.6 − 35.4 ± 0.6

ΔrH0298 (kJ mol− 1) a

− 49.6 ± 3 −43.7 ± 6 − 21.7 ± 3

ΔrS0 (J mol− 1 K− 1) 8a − 46 46

Data from Kersten and Vlasova (2009).

loading. The pH value at which hydrolysis of the silica surface complex is observed hence decreases with increasing ionic strength and decreasing silicate concentration (Fig. 2), which is commonly observed experimentally for acid group dissociation in aqueous solutions. The experimental data are matched quite well by the two adsorption reactions (Eqs. (11), (12)) and unique model parameters for all three ionic strengths and temperatures considered (Fig. 1). However, the constants for multidentate surface species are in fact not adequately represented in the original FITEQL code. As already discussed by Hiemstra and Van Riemsdijk (1996) in the Appendix to their classical paper, the constants for such reactions should be defined on a mole fraction instead of a mole balance basis. Gustafsson (2003) has developed a procedure how to perform the recalculation already during fitting with FITEQL 4.0 but which is not yet commonly used. The original FITEQL constants have therefore to be recalculated by a numerical scaling factor that relates the concentration dependent logKFITEQL values used in FITEQL to the mole fraction based intrinsic logKint values, which for bidentate reactions is given by Tadanier and Eick (2002): logKint ¼ logKFITEQL þ logðCS SA NS;j Þ

ð13Þ

where CS is the actual solid-solution ratio (1 g L− 1), SA is the specific surface area (20 m2 g− 1), and NS,j is the maximum molar site density of the reference surface component j (5.3·10− 6 mol m2). The thus by as much as −4 units corrected logKint values are compiled in Table 1. A thus recalculated logKint = 5.22 for reaction (11) at room temperature is by a half unit lower than the value of logKint = 5.85 recently reported for the

Fig. 2. Silicate adsorption by goethite as a function of −log[H+] for three different silicate concentrations and three different ionic strengths. Experimental data as black dots, adsorption model curves for the total and beneath for the two surface complexes separately (dotted line for the neutral, solid line for the deprotonated surface complex).

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Fig. 3. Silicate adsorption by goethite as a function of − log[H+] at four different temperatures, at an ionic strength of 0.1 M NaNO3, and a total silicate concentration of 50 µmol L− 1. Experimental data as open dots, adsorption model curves for the total and beneath for the two surface complexes separately (dotted line for the neutral, solid line for the deprotonated surface complex).

same surface reaction by Hiemstra et al. (2007). However, an agreement must not inevitably be the case bearing in mind that they used a different goethite preparation route producing a more reactive sorbent, different electrostatics, different pHPZC and ion pair formation constants, all of which usually lead to a calculated different electrostatic contribution and a different intrinsic constant rather than this fortuitous agreement. The 2C surface species (reaction (11)) which will induce the lowest amount of charge in the β-plane will be relatively favored in the pH range considered in the experiments. The calculated surface speciation showed also that mononuclear complexes are practically absent at the goethite surface for the present relatively low silicate surface concentration, because their fitted complex formation constants are very low (data not shown). As previously discussed, the concentration of silicate polymers in solution is negligible in the pH range considered, and the sorption density did not exceed theoretical monolayer coverage. However, some studies reported more than monolayer coverage indicating polymerization on the surface (e.g., Huang, 1975; Davis et al., 2002). Hiemstra et al. (2007) have recently shown by model parameter evaluation for the adsorption of silica polymers by goethite that their contribution can be neglected if the solution concentration is below about 10− 4 M (i.e., undersaturated with respect to quartz). Since the experimental data show that in the model no more than a monolayer of Si monomers is necessary to be allowed to adsorb, there is also no real necessity to consider such reactions for this study albeit theoretically possible at higher Si concentrations approaching equilibrium with amorphous silica solubility. 3.2. Silicate adsorption at elevated temperatures +

A similar behaviour of silicate adsorption as a function of –log[H ] and ionic strength is observed at other temperatures (Fig. 1). The

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higher the temperature, the less amount of silicate is adsorbed on the goethite surface at the same total Si concentration. The shapes of the curves are also changing in that the maximum is shifted along the decrease in the pHPPZC with temperature. This indicates some influence by the temperature dependent electrostatic properties of the goethite surface. The bent in the curves is becoming steeper with increasing temperature, in particular again at the lowest Si concentration. The experimental data at different temperatures have been fitted by assuming the same inner-sphere surface complexation reactions (11) and (12) as for room temperature. The capacitance value and constants of binding with cation and anion of background electrolyte were not changed. Halter (1999) and Kersten and Vlasova (2009) suggested that the capacitance change with temperature is negligible, and constants for background cation and anion binding are relative values with respect to pHPPZC of goethite. The charge distributions in the 0- and β-planes were not changed, but kept just the same as for the room temperature model for a best fit of the adsorption affinity constants at the different temperatures. Hydrolysis of silica is strongly temperature-dependent and decreases in pH with increasing temperature (Eq. (6)). It is therefore not surprising that the pH value at which hydrolysis of the silica surface complex is observed also decreases with increasing temperature (Fig. 3). The point at which both the Si surface species curves crosses decreases from pH 9.6 at 10 °C to pH 7.3 at 75 °C (Fig. 3). The intrinsic logKTint constants of both adsorption reactions change linearly with inverse temperature (Fig. 4). The slope of reaction (12) is steeper due to the additional temperature effect of silica hydrolysis. The linear trend is reasonable for temperatures below 100 °C, even if the aqueous species have not identical charges on either side, i.e. are nonisocoulombic. Nonetheless, with the reasonable assumption of zero heat capacity within the available temperature range, the temperature behaviour of intrinsic equilibrium constants can be well represented by a linear logKT vs. 1/T plot according to the common van't Hoff approach assuming constant ΔrS: logKT ¼ logK298 −ðΔr H0298 =2:3RÞð1=T−1=298Þ:

ð14Þ

where ΔrH0298 is the standard enthalpy of the respective surface complexation reaction, and R is the universal gas constant (8.314 J K − 1 mol− 1). Because there is only one adjustable thermodynamic parameter, the amount of four different temperature points is justified for the Van't Hoff fitting. This approach is equivalent with setting the heat capacity ΔCp=0 justified for extrapolations up to 100 °C. The limited experimental temperature range does therefore not allow derivation of a reliable value

Fig. 4. Van‘t Hoff logKT vs. 1/T plots. Black dots are the pHPPZC of goethite as a function of inverse temperature (data from Kersten and Vlasova, 2009). Black squares are the data for silicate adsorption reaction (11), open dots are the logKint data for logKint T T silicate adsorption reaction (12).

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for the heat capacity by a three-term extrapolation as discussed in detail by Kersten and Kulik (2005) and Kulik (2006). Using the values for log KT determined in the temperature range 10–75 °C, a linear least square fit yield values for ΔrH0298 as listed in Table 2. They do not change values for the irrespectively whether using the KTint or original KFITEQL T van't Hoff calculation, because the slope does not change upon correction with the constant of Eq. (13). The weighted standard error of estimate as average scatter of the points from the fitted curve is low (Fig. 1), but the error in the enthalpy translates from the change in slope of the fit by Eq. (14) due to an experimental error in logK298 of ±0.1. From the general relationship ΔrG0298 =2.3·R·298·pK298 =ΔrH0298 −298·ΔrS0, the standard energy and ultimately the standard entropy of the silicate adsorption reactions were determined as also listed in Table 2. Similar logKT vs. T curves were found for arsenate adsorption on hematite by Fokkink et al. (1989), for arsenate adsorption on alumina by Halter and Pfeifer (2001), and for arsenite adsorption on goethite by Kersten and Vlasova (2009). The magnitude of the values is of the order expected for a ligand exchange reaction on a hydroxylated surface. The negative enthalpy values suggest the exothermic nature of both adsorption reactions. Hence, the amount adsorbed at equilibrium must decrease with increasing temperature as evident from Fig. 1, mainly due to variation in the Si speciation with temperature (Fig. 3). Assessment of uncertainty in thermodynamic adsorption data has not been a routine exercise in water quality modelling. Uncertainty can be grouped into at least two main categories: (i) bias due to system definition, and (ii) uncertainties involved with data collection and reduction of experimental measurements. System definition is apparently unbiased as indicated by a nearly perfect correlation (R2 = 0.997, n = 550) between measured and predicted adsorption densities. Category (ii) relates to error in pH sensor, goethite BET surface, and Si concentration measurement. Errors in the sensor readings can be neglected at first approximation. Errors in the BET and Si concentration measurements are relatively dominating but low, and counterweighing to each other in that the error in Si concentration dominates at high sorption density due to low Si concentrations remaining in solution, whereas the error due to BET surface of goethite dominates at low sorption density. Maximum error of both parameters are about b5%. The associated uncertainty (1σ) propagation for the extrapolation in logKT follows from the two-term extrapolation with δlogKT = δlogK298 + [(T − 298)/2.3RT]δΔrS0. The first term follows from experimental uncertainty (±0.1 units), while the second term can still be neglected at 373 K (100 °C), which result in δlogKo −1 . Excel files with the entire T ≈ δlogK298 ≈ 0.1 or δΔrGT ≈ 0.6 kJ mol data set for any other model fit exercises is available from the first author upon request by email. 4. Conclusions As typical for the adsorption of oxyanions on oxides, adsorption of silicate on the goethite surface is exothermic (negative ΔrH0298) and becomes therefore weaker with increasing temperature. This is compatible with the observed decrease of pHPPZC from slightly alkaline to neutral values with increasing temperature as typical for Fe and Al oxides, which becomes quite significant below 100 °C (Schoonen, 1994). The surface speciation model output suggests a decrease in the pH where hydrolysis of the surface species starts. Our fitting results thereby clearly show the increasing importance of the hydrolyzed species with increasing temperature, although this result is merely a hypothetical one unless direct spectroscopic evidence is available. Another qualitative temperature effect albeit already observed in field is that silica may become highly enriched up to percentage values in Fe oxide-bearing sinter and scales deposited at those sites where the thermal water is rapidly cooling down (e.g., Schwenzer et al., 2001). An assessment of quantitative reliability in our thermodynamic adsorption enthalpy data is more difficult since very little experimental

data can be found in the literature on anion adsorption by oxides at elevated temperatures. Even for these scarce data sets, direct comparison is difficult because they depend on experimental conditions and adsorption model assumptions chosen. Unlike the situation for surface protonation and pHPZC values (Kulik, 2006), to our knowledge, predictive correlations for ΔrH0298 of oxyanion adsorption are also not yet available. The log KTint adsorption constants and ΔrH0298 enthalpy data for silicate adsorption can readily be applied in aqueous equilibrium speciation codes, which allow for implementation of enthalpy constants in SCM versions with 1-pK BSM and CD-MUSIC option (e.g., Gustafsson, 2009). Such a modelling code can be used to predict the temperature dependence of adsorption over a wide range of concentrations, surface coverage, pH values, and ionic strength, as exemplified in detail earlier for the case of arsenite (Kersten and Vlasova, 2009). Such calculations show, however, that the effect on geothermal waters saturated by equilibrium with solid silica phases and thus silicate concentrations in the order of mM is negligible. There is in fact a debate about critical aspects of using dissolved silica as geothermometer (Verma, 2000). Adsorption reactions at least of monomeric silica may not be advocated for the observed undersaturation with respect to amorphous silica within the temperature range studied in this paper, and probably also not beyond that. This may change if to consider polymeric Si adsorption which must not be considered at under-saturation with respect to quartz (b0.1 mM Si concentrations) and hence low surface loadings (less than monolayer coverage) as of this study. Acknowledgments This work was made possible by the Federal Ministry of Education and Research grant 03G0710A. The authors express their gratitude to Dmitrii A. Kulik and Johannes Lützenkirchen for the fruitful discussions and help during the modelling exercises, and the Associate Editor Jeremy Fein for organizing helpful reviews of our manuscript. References Anderson, P.R., Benjamin, M.M., 1985. Effects of silicon on the crystallization and adsorption properties of ferric oxides. Environ. Sci. Technol. 19, 1048–1053. Busey, R.H., Mesmer, R.E., 1977. Ionization equilibria of silicic acid and polysilicate formation in aqueous sodium chloride solutions to 300 °C. Inorg. Chem. 16, 2444–2450. Cary, L.W., de Jong, B.H.W.S., Dibble, W.E.J., 1982. A 29Si NMR study of silica species in dilute aqueous solution. Geochim. Cosmochim. Acta 46, 1317–1320. Cornell, R.M., Giovanoli, R., Schindler, P.W., 1987. Effect of silicate species on the transformation of ferrihydrite into goethite and hematite in alkaline media. Clays and Clay Miner., 35, 21–28. Covington, A.K., Bates, R.G., Durst, R.A., 1985. Definition of pH scales, standard reference values, measurement of pH and related terminology. Pure Appl. Chem. 57, 531–542. Davis, C.C., Chen, H.-W., Edwards, M., 2002. Modeling silica sorption to ironhydroxide. Environ. Sci. Technol. 36, 582–587. Diakonov, I., Khodakovsky, I., Schott, J., Sergeeva, E., 1994. Thermodynamic properties of iron oxides and hydroxides. I. Surface and bulk thermodynamic properties of goethite (α-FeOOH) up to 500 K. Eur. J. Mineral. 6, 967–983. Dietzel, M., 2002. Interaction of polysilicic and monosilicic acid with mineral surfaces. In: Stober, I., Bucher, K. (Eds.), Water-Rock Interaction. Kluwer Academic Publishers, Netherlands, pp. 207–235. Doelsch, E., Stone, W.E.E., Petit, S., Masion, A., Rose, J., Bottero, J.Y., Nahon, D., 2001. Speciation and crystal chemistry of Fe(III) chloride hydrolyzed in the presence of SiO4 ligands. 2. Characterization of Si–Fe aggregates by FTIR and Si-29 solid state NMR. Langmuir 17, 1399–1405. Ellis, A.J., Mahon, W.A.J.,1977. Chemistry and Geothermal Systems. Academic Press, New York, pp. 296–310. Fokkink, L.G.J., De Keizer, A., Lyklema, J., 1989. Temperature dependence of the electric double layer on oxides: rutile and hematite. J. Colloid Interface Sci. 127, 116–131. Fournier, R.O., Potter II, R.W., 1982. A revised and expanded silica (quartz) geothermometer. Geotherm. Resourc. Counc. Bull. 11, 3–12. Gerth, J., 1990. Unit-cell dimensions of pure and trace metal-associated goethites. Geochim. Cosmochim. Acta 54, 363–371. Glasauer, S.M., Friedl, J., Schwertmann, U., 1999. Properties of goethites prepared under acidic and basic conditions in the presence of silicate. J. Colloid Interf. Sci. 216, 106–115. Gunnarsson, I., Arnorsson, S., 2000. Amorphous silica solubility and the thermodynamic properties of H4SiO04 in the range 0° to 350 ° C at Psat. Geochim. Cosmochim. Acta 47, 941–946.

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