Sorption Studies of Cobalt(II) on Colloidal Hematite Using Potentiometry and Radioactive Tracer Technique

Journal of Colloid and Interface Science 231, 326–336 (2000) doi:10.1006/jcis.2000.7149, available online at http://www.idealibrary.com on

Sorption Studies of Cobalt(II) on Colloidal Hematite Using Potentiometry and Radioactive Tracer Technique Magnus Gunnarsson,∗ Anna-Maria Jakobsson,† Stefan Ekberg,† Yngve Albinsson,† and Elisabet Ahlberg∗,1 ∗ Department of Chemistry, G¨oteborg University, SE-412 96 G¨oteborg, Sweden; and †Department of Nuclear Chemistry, Chalmers University of Technology, SE-412 96 G¨oteborg, Sweden Received April 3, 2000; accepted August 4, 2000

The sorption of Co(II) on colloidal hematite was studied as a function of pH, ionic strength, and Co(II) concentration. Two different techniques were used, yielding two different sets of information: (i) potentiometric titrations that provide information on the number of protons released as a function of pH owing to the sorption of Co(II) and (ii) measurement of the amount of cobalt sorbed on the surface as a function of pH using a radioactive tracer, 60 Co. At low Co(II) concentrations (10−8 M), the sorption was found to be independent of ionic strength but there seems to be a weak ionic strength dependence at higher Co(II) concentrations (10−4 M). The adsorption edge moved to higher pH with increasing Co(II) concentration. For the high Co(II) concentration, the number of protons released per cobalt sorbed increased from zero to approximately 1.5. The basic charging properties of hematite were modeled with four different surface complexation models. The 1-pK Basic Stern Model (BSM), with binding of electrolyte ions to the Stern plane, seems to be the most reasonable model if the ambition is to describe experimental data at different ionic strengths. The sorption of cobalt was modeled with the 1-pK BSM. By introducing a low concentration of high affinity surface sites for cobalt sorption it was possible to model the sorption in very wide cobalt concentrations, ranging from 10−8 M to 10−4 M. °C 2000 Academic Press Key Words: Co(II); hematite; sorption; protons released; surface complexation models; potentiometry; radioactive tracer.

INTRODUCTION

Iron oxides play an important role in the transport and accumulation of heavy metals and radioactive isotopes in natural water systems. They are also present as corrosion products in many industrial applications. Crucial to the processes in these systems is the sorption of ions from the solution onto the oxide surface. Here we have chosen to study the sorption of cobalt(II) on hematite (α-Fe2 O3 ) because of its relevance in the nuclear fuel process (1, 2). 60 Co contributes to the buildup of radioactivity on fuel rods and in the water cooling systems, and hematite is one of the many corrosion products present. In addition, both cobalt and hematite are present in the spent nuclear fuel that must be stored. 1

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Hematite is also very suitable for experiments on the laboratory scale. It is a very stable iron oxide and it is possible to obtain colloidal hematite with different particle size and geometry by changing the preparation conditions (3, 4). In this work, we synthesized hematite by forced hydrolyses of a FeCl3 solution at 100◦ C. The dominant particle shape was rounded off cubes and the mean diameter was 0.6 µm. Surface complexation models have been used for some decades to describe and understand the basic charging properties of mineral surfaces and adsorption mechanisms. A number of different models have thus far been developed and used to describe experimental data. To be able to model the sorption processes at mineral surfaces, it is important to first characterize the basic charging properties of the mineral under study. It is generally accepted that the potential determining ions for the oxide surface are H+ and OH− . This means that, if no other specific adsorbed ions are present, the basic charging properties can be determined by potentiometric titrations. The acid–base properties of hematite have been studied previously (5–10). Although the experimental data differ because of varying properties in the hematite used, the main difference between these studies is the choice of surface complexation model and the techniques used for determining model parameters. While this means that it is meaningless to compare different sets of model parameters obtained, there are some general properties of hematite that can be worth mentioning. First, the titrated surface charge of hematite has been reported at pH 4 and 25◦ C to be between 0.1 and 0.35 C/m2 (5–11) and is dependent on the electrolyte and the ionic strength. Second, the point of zero charge, pHpzc , for hematite at 25◦ C is between 7 and 9.5 (12). The pH dependence on the surface charge can also be studied with electrokinetic techniques where the particles are placed in an electric field. The sign and magnitude of the charge will determine the movement of the particles. The pH at which there is no movement equals the isoelectric point, IEP. If other potential determining ions than H+ and OH− are present in the system they will affect the measured IEP. In studies where both the pHpzc and IEP have been measured on hematite they are found to be almost the same (6, 13), indicating no specific adsorption of electrolyte ions.

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The sorption of cobalt on hematite has been the subject of several investigations (1, 14–23). Unfortunately, most of these studies contain only sorption data without making a connection to the basic charging properties of hematite. However, when the sorption is studied as a function of pH, the cobalt ions start to sorb between pH 5 and 7, and the sorption of cobalt is complete somewhere between pH 8 and 10. Although some attempts have been made to find a surface complexation model for the cobalt sorption on hematite based on titrations and sorption data (16) we would like to refocus on this issue. In the present study, we combined sorption data performed with a radioactive tracer technique in a wide cobalt concentration range with potentiometric titrations performed with and without cobalt being present in the hematite suspension. This combination yields information on both the amounts of cobalt sorbed on the surface and the number of protons released because of the sorption as a function of pH. MATERIALS AND METHODS

Reagents and Reagent Preparation The chemicals were all of professional analysis quality, and MilliQ or doubly distilled water was used for all solutions. Sodium hydroxide solutions (NaOH) were prepared from pellets obtained from Merck. A concentrated (≥10 M) NaOH solution was filtered through a glass membrane and diluted as needed. The NaOH was stored in a CO2 -free atmosphere in plastic bottles. Sodium nitrate (NaNO3 ), cobalt (II) nitrate (Co(NO3 )2 ) and nitric acid (HNO3 ) were obtained from Merck. Cobalt solutions for the radioactive tracer experiments were prepared using 60 Co from NEN, DuPont (>2.77 TBq/g Co). To remove any impurities of iron from the solution, the pH of the stock solution was increased to about 5, the solution was centrifuged for 30 min at 19,000g and the supernatant was used. The concentrations of the solutions used in the titrations were determined analytically by titrations against standard chemicals. Colloidal hematite particles were prepared by forced hydrolyses of a FeCl3 solution with a procedure almost similar to that reported by Matijevi´c (3, 4). A stock solution of 1.5 M

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FeCl3 (Merck) was prepared and filtered through a 0.45-µm Millipore membrane. Proper amounts of the FeCl3 stock solution and 1.0 M HCl (Merck) were mixed and diluted with preheated (∼98◦ C), doubly distilled water. The FeCl3 concentration obtained was then 0.040 M, and the HCl concentration 0.001 M. The solution was transferred to preheated (100◦ C) Pyrex bottles, closed tightly and sealed with Teflon tape. The bottles were stored in an oven at 100◦ C for 7 days and then cooled to room temperature. By removing the supernatant, the hematite suspension was concentrated to 15 g Fe2 O3 per liter and put in a 1-L plastic bottle. The hematite suspension obtained by this method contains considerable amounts of chloride ions and was therefore purified by gravitational sedimentation and subsequent removal of the supernatant. 0.1 mM HNO3 was added, and the suspension was shaken and placed in an ultrasonic bath for 5 min. This washing procedure was repeated over 20 times. A chloride ion concentration less than 2 × 10−7 M in the supernatant could then be established by adding 0.1 M AgNO3 . The acid environment was chosen to avoid the formation of carbonates in the suspension and to minimize coagulation by keeping the hematite particles charged. The synthesized particles were identified to be α-Fe2 O3 by X-ray diffraction analysis (Siemens D5000). Particle size and shape were studied with scanning electron microscopy (SEM) (Fig. 1). The mean particle diameter is 0.6 µm. The surface area, S, of the products was determined to be 6.36 m2 /g with BET nitrogen adsorption using an ASAP 2010 V4.00 instrument. Compared with area calculations based on the particle geometry obtained in the SEM image, the BET area is fully a factor of two larger. This is probably due to surface roughness and perhaps to some extent to a fraction of smaller particles. The BET area was used in all calculations. Potentiometric Titrations Potentiometric titrations on hematite suspensions (5–10 g/L) were performed at constant ionic strength in 0.05, 0.1, and 1.0 M NaNO3 electrolyte media. Titrations with and without Co(II) in the solution were compared to gain information on the protons released during cobalt sorption.

FIG. 1. SEM image of colloidal hematite particles synthesized and studied in this work.

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The titrations were performed on an automatic system constructed and designed at the Department of Inorganic Chemistry, G¨oteborg University. A computer program written in the TestPoint software was used to control the burette (Metrohm, 645 Multi-Dosimat), collect data, and specify equilibrium conditions. The temperature of the titration cell was kept at 25◦ C by using a temperature-controlled glass vessel. To maintain an inert atmosphere during the experiments, a stream of nitrogen was passed through the airtight titration vessel. Before the nitrogen entered the cell, it was first bubbled through solutions of 1 M NaOH and 1 M H2 SO4 to remove acid and alkaline impurities and then finally through ionic medium. The temperature of the washing solutions was 25◦ C. The free proton concentration was measured with a glass electrode (Metrohm 6.0726.100). An Ag,AgCl double junction electrode (Metrohm 6.0123.100) was used as reference. The electrodes were calibrated before and after each titration by measuring the potential from a solution with a known proton concentration, Eqs. [1] and [2]. Blank titrations with pure electrolyte solution in the titration vessel were done as an accuracy test of the solutions and the equipment. To eliminate carbonates nitrogen gas was bubbled through the acidified suspension (pH <4) for 1 h before each titration. The equilibrium condition was set to 0.001 pH units per minute, with a minimum of 10 min and a maximum of 1 h between each addition of acid or base. The solution was stirred with a mechanical stirrer at 500 rpm during the titrations. To examine whether solid Co(OH)2 was formed during the titrations and sorption experiments, samples were withdrawn from a titration at pH 9 and dried for transmission FTIR analysis using the standard KBr technique. This titration was performed in 50 mM NaNO3 under the same conditions as described above with a Co(II) concentration of 0.1 mM. A sample from a hematite suspension without Co(II) was taken as reference. Based on thermodynamic considerations Co(OH)2 is expected to precipitate in the absence of a solid adsorbent (24). Treatment of titration data. At 25◦ C the potential E (in mV) of the cell is given by E = E 0 + 59.158 · lg[H+ ] + E j ,

[1]

where E j (in mV) is the potential over the junction between the titrated solution and the outer reference solution. In this work, E j in a solution with ionic strength I was calculated as Ej =

24 · K w −51 · [H+ ] + I I · [H+ ]

[2]

where K w is the ionic product of water. This is an approximation of the results obtained by Sj¨oberg et al. (25). E 0 in Eq. [1] was determined from the measured potential in a solution with known [H+ ] and ionic strength. Note that the calibration routine used here will give measured concentrations of protons rather than the activity. Throughout this paper, pH will refer to −log[H+ ]. The H+ concentration in the hematite sus-

TABLE 1 pK w Values Used in this Study [NaNO3 ] (M)

pK w

0.05 0.1 1.0

13.83 13.79 13.70

pension was calculated at each titration point using Eq. [1]. The amount of adsorbed protons, n H+ , was determined from the measured free proton concentration, the total proton concentration known from the additions of acid or base and the experimentally determined pHpzc . The blank titrations were used to correct the data for nonlinear electrode response or liquid junction effects not accounted for by the calibration, Eq. [2]. The amount of adsorbed hydroxide ions, n OH− , was calculated by using an accurate value of K w . Unfortunately, very few accurate determinations of pK w (=−log K w ) in NaNO3 medium have been reported. The specific interaction (SI) theory (26) yields the values tabulated in Table 1 and are the values used in this work. They agree quite well with the values found in the literature for KNO3 and NaClO4 (27). Surface charge curves were calculated according to σo =

F(n H+ − n OH− ) , SA C V

[3]

where SA is the surface area in m2 g−1 , C is the hematite concentration in g L−1 , and V is the volume of the suspension before the first addition from the burette. Radioactive Tracer Studies The sorption of Co(II) was studied as a function of pH and cobalt concentration at constant ionic strength (0.05, 0.1, and 1 M NaNO3 ) using 60 Co. Samples were withdrawn at increasing pH from the same solution in a temperature-controlled glass vessel (25◦ C) under a nitrogen atmosphere. The pH was measured in the setup by an open junction reference electrode (K102, Radiometer) and a glass electrode (PHG201, Radiometer) calibrated against the H+ concentration using Gran calibration. After an addition of base, more than 10 min was allowed to pass before the sample was withdrawn into Beckman centrifuge tubes using a syringe. Before the liquid was separated from the solid by means of centrifugation at 15,000g the samples were allowed to equilibrate for varying times, up to 1 h. The 60 Co radioactivity was determined in both the samples with the aqueous phase and those with the solid phase using a NaI(Tl) gamma scintillation counter (Intertechnique CG 4000, France). The sorption of Co(II) was studied as a function of Co(II) concentration at two constant pH values (6.5 and 7.5) at 1 M NaNO3 by withdrawing samples at increasing Co(II) concentrations in the same setup as above. The Co(II) concentration was increased by adding Co(NO3 )2 .

SORPTION OF COBALT(II) ON COLLOIDAL HEMATITE

329

Electroacoustic Measurements The dynamic mobility of the hematite particles was measured with the AcoustoSizer (Matec Applied Science) at frequencies between 0.3 and 11.15 MHz. The principles of the technique and the theory behind the electroacoustic effect has been outlined by R. W. O’Brien (28, 29). The measurements were performed with a background electrolyte concentration of 1 mM (NaNO3 ), and the pH was varied between 4 and 10 by additions of NaOH. In this paper, the data from the measurements with the AcoustoSizer were used only to obtain an IEP. More experimental data from measurements on colloidal hematite and evaluations of elektrokinetic potentials will be presented in a related paper (in preparation). RESULTS AND DISCUSSION

The measurements of the dynamic mobility of the hematite particles as a function of pH in 1 mM NaNO3 gave an IEP of 8.3. Titrations of the Hematite Surface In the potentiometric titrations of the hematite surface, the electrode response was very quick and the potential drift between the additions was very small. Except for a few data points in the neutral pH region, the equilibrium condition (0.001 pH/min) was fulfilled within the minimum waiting time of 10 min. From a set of titrations performed at different ionic strengths the pHpzc could be determined to be 8.5 ± 0.3, which is in acceptable agreement with IEP obtained from the electroacoustic measurement. This indicates that H+ and OH− are the only potential determining ions, and the use of Eq. [3] for calculating the surface charge is therefore justified. When the surface charge curves were calculated, the pHpzc was locked to a value of 8.4. This is in good agreement with previously reported pHpzc for hematite (12). Almost straight surface charge curves were obtained for all three ionic strengths (0.05, 0.1, and 1.0 M) with a more pronounced curvature for the results from the titration in 1.0 M (Fig. 2). No clear saturation of protons on the hematite surface could be established. The surface charge measured at pH 4.0 in 1.0 M NaNO3 corresponds to a density of 2.6 protons adsorbed per nm2 .

FIG. 2. Surface charge curves obtained from potentiometric titrations of hematite particles in 0.05 M (s), 0.1 M (×), and 1.0 M NaNO3 (1).

sorption process at the oxide surface contains two processes, one quite fast reversible process and another slower process with a diffusion of cobalt ions into the particles. It is of course very difficult from these speculations to set a proper maximum time. From our results and those of the kinetic study of cobalt sorption on hematite by Todorovi´c et al. (19), we believe, however, that 1 h is long enough to capture the fast reversible process of the cobalt sorption. Differences between proton data from titrations performed with and without Co(II) in the hematite suspension are presented in Fig. 4 for two different Co(II) concentrations and in Fig. 5 for three different ionic strengths. The titration performed in 1.0 M NaNO3 was discarded because of anomalous potential drifts and coagulation problems. Repeated titrations with longer equilibrium times did not improve the experimental data. The measured proton differences reflect the protons involved in the sorption reactions of Co(II) onto the hematite surface and the protons

Titrations with Co(II) In the titrations involving Co(II), the potential drift between the additions was more pronounced in the region between pH 7 and 9.5, where the cobalt sorption takes place. The equilibrium condition was seldom fulfilled within the maximum waiting time of 1 h. Figure 3 shows the potential drift between two additions at pH 9. The data are taken from a titration performed on a hematite suspension containing 50 mM NaNO3 and 0.1 mM Co(NO3 )2 . From this result, it can perhaps be argued that longer equilibrium times should have been used. However, it is probable that the

FIG. 3. Potential drift at pH 9 during Co(II) sorption on hematite in a potentiometric titration performed in 50 mM NaNO3 ; [Co(II)]tot = 0.1 mM. NaOH was added at 10 and 70 min.

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Sorption Data from Radioactive Tracer Studies The distribution between the solid and aqueous phase with respect to the surface area, K a (m), is calculated from Ka =

FIG. 4. Difference between proton data from potentiometric titrations performed in 0.1 M NaNO3 , with and without Co(II) in the hematite suspension; (×) [Co(II)]tot = 0.1 mM; (s) [Co(II)]tot = 0.2 mM; hematite concentration 7.4 g/L.

[Cosorbed ] V · , [Coaq ] A

[4]

where [Cosorbed ] (mol dm−3 ) is the concentration sorbed on the solid, [Coaq ] (mol dm−3 ) is the concentration in the aqueous phase, V is the total volume (m3 ), and A is the area of the solid (m2 ). The results of the sorption studies are shown in Fig. 6 both as K a and percentage sorbed. It can be seen that the sorption takes place between pH 6.5 and 10 and that the amount sorbed increases with pH. As the concentration of cobalt is increased, the adsorption edge shifts to a higher pH. Further, the sorption is independent of ionic strength for low Co(II) concentrations, which is in agreement with work by Kobal et al. (15). However, there is an indication

involved in the hydrolysis of cobalt ions in the solution. The extent of the latter can be taken into account by using equilibrium constants for the cobalt hydrolysis taken from the literature. In some preliminary studies the maximum waiting time was set to 30 min and the data obtained in the titrations looked similar to those presented in Fig. 4. This justifies the notion that the reversible sorption process is covered within the maximum waiting time used in this study. Figure 4 shows that the amount of excess protons resulting from the presence of Co(II) is directly related to the amount of Co(II) in the suspension. A weak ionic strength dependence is indicated in the titrations at 0.05 and 0.1 M NaNO3 in Fig. 5. The possible formation of solid Co(OH)2 was investigated using transmission FTIR. Withdrawn samples at pH 9 showed no solid Co(OH)2 content.

FIG. 5. Difference between proton data from potentiometric titrations performed in 0.05 M (s), 0.1 M (×), and 1.0 M NaNO3 (1) with and without Co(II) in the hematite suspension; [Co(II)]tot = 0.1 mM.

FIG. 6. Sorption of Co(II) as a function of pH for different Co(II) concentrations and ionic strengths illustrated as (a) the distribution of cobalt between the solid and aqueous phases, K a , and (b) the percentage sorbed of the total concentration. (×) [Co(II)]tot = 4 × 10−8 M and 0.05 M NaNO3 . (1) [Co(II)]tot = 4 × 10−8 M and 1.0 M NaNO3 . (s) [Co(II)]tot = 0.9 × 10−4 M and 0.1 M NaNO3 . (+) [Co(II)]tot = 1 × 10−4 M and 1.0 M NaNO3 .

SORPTION OF COBALT(II) ON COLLOIDAL HEMATITE

331

tions. These results are in agreement with the study by Farley et al. (30). Evaluation of the Number of Protons Released per Cobalt Sorbed as a Function of pH

FIG. 7. The amount of sorbed Co(II) at different total concentrations of Co(II) for two different pH: 6.5 (+) and 7.5 (h). (a) The concentration of Co(II) sorbed on the solid phase as a function of the concentration in the aqueous phase. (b) The distribution of cobalt between the solid and aqueous phase, K a , as a function of sorbed Co(II) concentration.

of a dependence on ionic strength at the higher concentrations. This is consistent with the observations from the potentiometric titrations. The isotherms did not show Langmuirian behavior, and no saturation limit was reached. Figure 7a shows the concentration sorbed on the solid as a function of the Co(II) concentration in the aqueous phase. Up to a sorbed concentration of 10−6 , the slope is approximately 1 for the log [Cosorbed ] vs log [Coaq ]. Above a concentration of 10−4 , the slope is approximately 1 again. This can be seen more clearly in Fig. 7B, which plots the K a as a function of concentration sorbed. There is some kind of transition from a higher K a to a lower K a . The decrease in K a with increasing concentration ceases at a concentration of ∼1 × 10−5 M Co(II) or ∼0.15 Co(II)/nm2 . Above this concentration, the K a is approximately constant. The amount of measured cobalt sorbed on hematite never reaches a limit in the isotherms. Since the sorbed cobalt far exceeds the possible site concentration for Co(II) adsorption on hematite, we conclude that the Co(II) is surface precipitated at these high concentra-

The differences between the experimental conditions for the two techniques used in this study were kept to a minimum; however, even so, there were slight differences in the solid concentrations of hematite and the pHs at which the experimental results were obtained. It was therefore necessary to fit one of the experimental series to an empirical relation. In the sorption results obtained with the radioactive tracer technique for the ionic strength of 0.1 M, an empirical relationship was found between the distribution of cobalt between the phases per mass of hematite and the pH. This relationship was used to calculate the amount sorbed under the conditions in the titration and the number of protons released per Co(II) sorbed was found from this. The results are given in Fig. 8. It should be emphasized that the simultaneous proton release associated with the acid– base properties of the oxide surface has been subtracted and thus the proton release shown in Fig. 8 is entirely due to the cobalt sorption. It has been proposed that the H+ /Me(II) ratio can be extracted from a set of adsorption isotherms, similar to the ones given in Fig. 7a (31). However, in this case the proton release originates from both the cobalt sorption and the acid–base properties of the oxide and cannot be easily separated. As mentioned above, the protons are released both from the surface reactions and from the hydrolysis of cobalt. A correction for the protons released from the latter process is made using the hydrolysis constants in Table 2. When the adsorption data in Fig. 6b are compared with results in Fig. 8, it is clear how the number of protons released increases from zero to 1.5 between pH 7 and 9.5. This indicates that the sorption reaction does not involve the release of protons in the acid range, but when pH is increased, sorption reactions involving proton release dominate.

FIG. 8. The number of protons released per Co(II) sorbed as a function of pH in 0.1 M NaNO3 . The dotted line represents the contribution of protons from the hydrolysis of Co(II), (h) represents data not corrected for the hydrolysis and (+) represents data corrected for the hydrolysis.

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TABLE 2 Summary of Co(II) Hydrolysis at 298 K at Different Ionic Strengths (41) Used in this Work Species

log K (I = 0 M)

log K (I = 0.1 M)

log K (I = 1.0 M)

CoOH+ Co(OH)2 Co(OH)− 3

−9.65 −18.8 −31.5

−9.85 −19.0 −31.5

−10.0 −19.3 −31.7

Co(OH)2− 4

−46.3

−45.8

−45.6

It is interesting to note that more than one proton was released for each cobalt ion adsorbed at high pH. MODELING

The Hematite Surface The surface charge curves obtained from the potentiometric titrations were modeled using four different surface complexation models. The aims were to find a simple model that describes the basic charging properties of hematite and to critically evaluate the fitted parameters obtained. The least square fit program FITEQL 4.0 was used (32). If the particle surface is considered to be homogeneous, containing only one type of active surface site, the proton reactions at the surface can be described with either a 1-pK or a 2-pK model. The surface reactions in a 2-pK model are K a1

0 + ≡FeOH+ 2 ↔ ≡FeOH + H K a2

≡FeOH0 ↔ ≡FeO− + H+ ,

[5a] [5b]

where ≡FeOH0 denotes a general hydrolyzed species at the iron oxide surface and K a1 and K a2 are the corresponding equilibrium constants. In a 1-pK model, the surface reaction involving protons is described in a one-step charging process; i.e., 1/2 K a

≡FeOH2 ↔ ≡FeOH−1/2 + H+ .

[6]

This approach was introduced by Bolt and Van Riemsdijk (33, 34). The proton affinity constant, K a , in this model follows directly from the experimentally determined pHpzc of the oxide. To keep the number of adjustable parameters as low as possible, the surface site density was not optimized in this work. L¨utzenkirchen (35) showed that, when the site density is used as an adjustable parameter, high correlations between the parameters are obtained, which is an additional reason for using some estimate of this parameter. Here, a site density estimated from surface hydroxyl configuration data of various crystal faces of hematite (36) was used. Reeves and Mann (37) studied hematite particles synthesized by similar methods and found that the rhombohedral particles comprised six faces of the {104} form. According to the Multisite Complexation Model (MUSIC) (38, 39), only some of the surface groups are “active” in the titra-

ble pH range. Taking these things into account, we estimate that the site density is 5 nm−2 . (Site density here means the density of possible positions for proton adsorption on the neutral surface, i.e., at pHpzc. ) In the 2-pK formalism this corresponds to a concentration of 5 ≡FeOH0 groups per nm−2 and, in the 1-pK case, to a concentration of 10 ≡FeOH−1/2 groups per nm−2 . The value used here for the site density (5 nm−2 ) is to be compared with the proton density at the surface at pH 4 found from the titration in 1.0 M NaNO3 (2.6 nm−2 ). Since no saturation of the hematite surface was found in the titrations we believe that a reasonable value is 5 sites per nm2 . The assumption made in the modeling is that all surface groups have the same affinity for protons. The weights attributed to the experimental data point were all set to unity, and the goodness of fit parameter in this case is SOS/DF (sum of squares over degrees of freedom). The value of the capacitance, C, cannot be optimized directly by FITEQL and was therefore varied in separate runs until a minimum of SOS/DF was found. When the 2-pK concept was used the difference between pK a1 and pK a2 , i.e., 1pK a , was fitted directly and the pHpzc determined from the experiments was set to a fixed value of 8.4. In a recent paper by L¨utzenkirchen (35), FITEQL was used to study about 150 different data sets from the literature with the 2-pK constant capacitance model (CCM). Three distinguished patterns of the goodness of fit parameter, V , as a function of capacitance were proposed: (L1) A minimum of V occurs at a defined value of C: —it is possible to define a best fit parameter set —this is a satisfactory result. (L2) No minimum of V occurs over the whole range of C: —with decreasing C, V continues to decrease until no convergence is obtained in the optimization procedure —it is impossible to define a best fit parameter set based on V except by accepting the value at the lowest C at which convergence is possible (L3) A broad minimum occurs: —many parameter sets may yield statistically equal description of experimental data. Because of the linear shapes of the surface charge curves and the relatively high ionic strengths used in this work, it was reasonable to start with a constant capacitance model (CCM) (40). The possibility of finding a unique solution of fitted parameters for the 1-pK and the 2-pK CCM was compared. As the CCM is not applicable to data at different ionic strengths, only the experimental data in 0.1 M NaNO3 were used. The results are shown in Table 3 and classified as above. The surface charge curves obtained from these two models describe the experimental data at 0.1 M ionic strength well with a straight line through the experimental data points. In the 2-pK case, as indicated in Table 3, it was difficult to determine accurate unique values of the fitted capacitance and 1pK a . This is illustrated in Fig. 9a where the 1pK a values obtained and related NSOS/DF (normalised

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TABLE 3 Results of Fitting Experimental Titration Data on Hematite in 0.1 M NaNO3 to Four Different Surface Complexation Models Model 2-pK CCM 1-pK CCM 1-pK BSM (A) 1-pK BSM (B)

C of best fit (F/m2 ) Fitted 1pK a log K Na+ 1.49 1.49 4.26 1.50a

0.58 — — —

— — — 0.8

log K NO−

Class of pattern

— — — 9.2

L3 L1 L1 L2

3

Note. The site density was set to 5 nm−2 . Versions A and B of 1-pK BSM are the models without and with electrolyte ions adsorbed in the Stern plane, respectively. For the pattern classification, see text. a No minima occurred. The tabulated value is the value at the lowest C at which convergence was possible.

to SOS/DF of best fit) are plotted as a function of C. Note the large slope of the 1pK a curve in the broad minima of NSOS/DF. The corresponding results from the fitting to the 1-pK CCM are shown in Fig. 9b. In that case, the pK a value is fixed to the experimentally determined pHpzc (=8.4).

It is obvious from the results presented above that a 1-pK model has major advantages over a 2-pK model. This is similar to the findings of L¨utzenkirchen (41), who compared different surface complexation models on the basis of goodness of fit and uniqueness of estimated parameters. The conclusion drawn from this comparison between a 1-pK and a 2-pK model is based on the success of finding unique parameters and has nothing to do with the physical interpretation of the processes on the oxide surface. To be able to construct a model that is simultaneously applicable to different ionic strengths, it is necessary to use a more sophisticated surface complexation model than the CCM. The 1-pK basic Stern model (BSM) has been suggested by some authors as a first-choice model (41, 42) and is the model we will continue to use in this work. The BSM can be used with or without adsorption of electrolyte ions in the Stern plane (9, 42). The first case can be appropriate for ions that form outer sphere complexes with the surface sites or for ions that are strongly adsorbed to the surface but have no affinity for the proton sites located at the surface plane. If the adsorption of Na+ and NO− 3 into the Stern plane is taken into account, we have ≡FeOH−1/2 + Na+ ↔ ≡FeOH−1/2 Na+ , £ ¤ ≡FeOH−1/2 Na+ ¤ with K Na+ = £ [7] ≡FeOH−1/2 [Na+ ]d and − ≡FeOH−1/2 + H+ + NO− 3 ↔ ≡FeOH2 NO3 , £ ¤ 1/2 ≡FeOH2 NO− 3 ¤ , [8] with K NO−3 = £ + ≡FeOH−1/2 [NO− 3 ]d [H ]s 1/2

FIG. 9. Results of fitting model parameters to experimental titration data. (a) 2-pK CCM and (b) 1-pK CCM. (+) and (s) represent the obtained normalized SOS/DF and the fitted 1pK a , respectively. In the 1-pK model, the pK a was locked at 8.4.

where the lower case d and S denote the ion concentrations at the Stern and the surface plane, respectively. The surface charge curve obtained from potentiometric titration in 0.1 M NaNO3 was first modeled without electrolyte adsorption. The surface charge curves calculated from that model were typically s-shaped and gave a poor description of experimental data (Fig. 10). The capacitance of best fit was also unreasonable high (4.26 F/m2 ). Reactions [7] and [8] were then taken into account and the model curves obtained were found to be in good agreement with experimental data (Fig. 10). When K Na+ and K NO−3 were fitted as two different adjustable parameters, the correlation coefficient was almost unity (0.997), which implies that it is preferable to express these two constants as one in the calculations. K Na+ and K NO−3 were thus fitted symmetrically around the pHpzc (=8.4). The constants obtained are tabulated in Table 3. The log K Na+ value (0.8) determined from these model calculations is slightly higher than the results obtained by Schudel et al. (11) (logK Na+ = 0.3). However, a change in K Na+ of this magnitude does not influence the model calculations for cobalt adsorption.

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FIG. 10. Calculated surface charge curves obtained with the 1-pK BSM surface complexation model compared with experimental data (e) in 0.1 M ionic strength. The solids and the dotted line represent model calculations with and without electrolyte binding into the Stern plane, respectively. The surface site density was set to 5 sites/nm2 .

Co(II) Adsorption When the sorption of Co(II) on the hematite surface was modeled, the hydrolysis of cobalt was taken into account by using the constants determined by Baes and Mesmer (24) (Table 2). Since the cobalt sorption was studied at different ionic strengths, the most reasonable model to use is the 1-pK BSM with electrolyte ions located in the Stern plane. The constants obtained and presented in Table 3 were used and kept fixed when modeling the Co(II) sorption. Attempts were made to model the potentiometric titration data at 0.1 M NaNO3 with the following surface complexation reactions: K Co1

≡FeOH−1/2 + Co2+ ←→ ≡FeOHCo1 2 1

[9]

K Co2

≡FeOH−1/2 + Co2+ + H2 O ←→ ≡FeOHCoOH1/2 + H+ [10] ≡FeOH−1/2 + Co2+ + 2H2 O K Co3

←→ ≡FeOHCo(OH)2 −1/2 + 2H+ .

[11]

All cobalt complexes formed were put in the surface plane; i.e., an inner sphere complex formation was assumed. Since the experimental results show that the number of protons released ranges from zero to 1.5, a combination of at least two of these complexes was necessary. To successfully describe the titration and adsorption data it was necessary to introduce a low concentration of high-affinity sites (0.1 sites per nm2 ) for cobalt adsorption at the hematite surface. On these sites we allow the cobalt ions to adsorb without the release of protons, i.e., reaction [9]. The affinity for protons and the equilibrium constants for binding electrolyte ions into the Stern plane were the same for all surface sites. Together with reaction [9] at the high-affinity sites, reactions [10] and [11] were then allowed at all surface sites. When the titration data were used as input data in FITEQL, the optimization procedure

did not converge. Reaction [10] was therefore eliminated and it was possible to make a good determination of the remaining equilibrium constants. The model obtained was able to predict the number of released protons and the amount of sorbed cobalt found in the experiments. The surface complexation constants obtained for cobalt adsorption were extrapolated to zero ionic strength by calculating activity coefficients for species in solution using the SI theory (26). The ratio of the activity coefficients for the surface species was set to unity. The equilibrium constants obtained for the two surface reactions for cobalt included in the proposed model are tabulated in Table 4. Figure 11 compares the calculated distribution diagrams at 0.1 M NaNO3 with experimental data from both titrations and sorption studies. For high Co(II) concentration (1 × 10−4 M), the high-affinity sites will be saturated in the beginning of the pH region where adsorption takes place. As the pH increases the adsorption takes place at the other sites. When the Co(II) concentration is low (4 × 10−8 M), the high-affinity sites will take care of the adsorption. The proposed model was used for calculations at different ionic strengths but no significant ionic strength dependence could be established for the Co(II) sorption. The reason for this is that we did not use any outer-sphere surface complex for Co(II) in our model. Where outer-sphere complexes are introduced, a much larger ionic strength dependence is normally found than was observed experimentally in this work (43). Calculated model curves for the isotherm at pH 7.5 are compared with experimental data in Fig. 12. We have chosen in this figure to plot the concentration of adsorbed species and K a values as a function of total Co(II) concentration. Since no surface precipitation is included in the model the model curves deviate from experiments at high Co(II) concentrations (30). However, the potentiometric titrations and all sorption data except the isotherms are in the Co(II) concentration range where the model describes the data satisfactorily. With the same set of equilibrium constants it was difficult to quantitatively model the isotherm at pH 6.5. It should be noted that a very low fraction of Co(II) is sorbed at pH 6.5 and the model calculations becomes very sensitive to the constant for Co(II) adsorption at the high affinity sites. We thus paid greater attention to the pH 7.5 isotherm when the equilibrium constants in the presented model were determined. We have tried in the model work presented here to keep the number of parameters low and use quite a simple description TABLE 4 Equilibrium Constants Obtained for Cobalt Adsorption on Hematite (298 K) Surface complex 1

≡FeOHCo1 2 −1/2 ≡FeOHCo(OH)2

log K i

Sites

6.7 −13.9

High affinity All sites

Note. The constants have been extrapolated down to zero ionic strength.

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SORPTION OF COBALT(II) ON COLLOIDAL HEMATITE

of the processes taking place at the surface. Nevertheless, we believe that we have covered some main features of the sorption process of cobalt on hematite by combining sorption and −1/2 titration experiments. The formation of the ≡FeOHCo(OH)2 complex can be seen as a nonelectrostatic adsorption of the hydrolyzed species Co(OH)2 . In the hydrolysis of Co(II), the first hydrolyzed species Co(OH)+ is of secondary importance. This is consistent with the observation made here that a reasonable model fit could be obtained without the presence of the surface species ≡FeOHCoOH1/2 . Of course, the physical reality is much more complex than is described with this model. The trend in surface complexation modeling is toward model descriptions containing many different surface sites, species, and planes of adsorption in the stagnant liquid layer. However, without additional reliable experimental data, the incorporation of such complexity into the surface complexation model is questionable. SUMMARY

FIG. 11. Calculated distribution diagrams for the proposed model at 0.1 M NaNO3 compared with excess proton data from titration (×) and Co(II)aq concentrations from sorption experiments (h), (a) [Co2+ ] = 0.1 mM and (b) [Co2+ ] = 4 × 108 M. The dotted line in (a) represents the model prediction of the concentration of protons emerging from the presence of Co(II). The surface 1 complex FeOHCo1 2 relates to high-affinity sites.

It has been found that the sorption of cobalt (II) on hematite is independent of ionic strength at low Co(II) concentrations (10−8 M). At higher Co(II) concentrations (10−4 M), there seems to be a weak ionic strength dependence. The adsorption edge moved to higher pH with increasing Co(II) concentration. For the high Co(II) concentration, the number of protons released per cobalt sorbed increased from zero to approximately 1.5. The 1-pK Basic Stern Model (BSM), with binding of electrolyte ions to the Stern plane, was used to model experimental data. Two different sites were necessary to get a reasonable agreement between experiments and model calculations. At a low concentration of high-affinity sites, we modeled the cobalt(II) sorption without any proton loss. In addition, cobalt was allowed to adsorb at both kinds of sites involving 2 H+ release. With this model it was possible to model the sorption in very wide cobalt concentrations, ranging from 10−8 to 10−4 M. ACKNOWLEDGMENT Dr. Johannes L¨utzenkirchen is acknowledged for his valuable help with surface complexation modeling with FITEQL. Financial support from the Swedish Centre for Nuclear Technology (K.T.C.) is gratefully acknowledged.

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FIG. 12. Calculated adsorption isotherm with the proposed model at pH 7.5 in 1.0 M NaNO3 compared with experimental data. (e) Experimental data plotted as log [Co(II)]ads as a function of log [Co(II)tot ] and (×) represents the same data plotted as log K a as a function of log [Co(II)tot ].

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