Proton Binding by Hydrous Ferric Oxide and Aluminum Oxide

Acid−base titration data are fit to a continuous binding site model for the system represented as a pKa spectrum. The modified parameter fitting met...
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Environ. Sci. Technol. 2001, 35, 4637-4642

Proton Binding by Hydrous Ferric Oxide and Aluminum Oxide Surfaces Interpreted Using Fully Optimized Continuous pKa Spectra D. SCOTT SMITH† AND F. GRANT FERRIS* Department of Geology, University of Toronto, 22 Russell Street, Toronto, Ontario, Canada M5S 3B1

A modified regularized least squares pKa spectrum approach is proposed to determine proton stability constants and concentrations for binding sites on hydrous ferric oxide (HFO) and aluminum oxide surfaces. Acid-base titration data are fit to a continuous binding site model for the system represented as a pKa spectrum. The modified parameter fitting method optimizes simultaneously for both smoothness of the pKa spectrum and goodness-of-fit, whereas other methods optimize for goodness-of-fit given a fixed smoothness factor. The modified method is tested with aluminum oxide and recovers values consistent with theoretical values. The regularized pKa spectrum method optimized for smoothness is applied to prepared samples of two types of HFO. The prepared HFO samples differ only in the total iron concentration of the parent solution. The resultant pKa distributions are compared to proton binding constants from MUSIC model results for crystalline iron oxides. The types of binding sites in the HFO sample are consistent with theoretical binding site stability constants for crystalline iron oxides. Overall, the prepared HFO samples have binding constants most consistent with values for lepidocrocite and goethite.

Introduction Acid-base titrations are an excellent way to probe the surface structure and reactivity of natural sorbents with respect to protons. There are many ways to fit experimental titration data, including but not limited to linear programming (1), FITEQL (2), and regularized least squares (3). In addition, there are methods to obtain the distribution function of affinity constants directly from the data via derivative techniques combined with smoothing algorithms (4). The linear programming and regularized least-squares methods are examples of pKa spectrum methods that permit quantitative assessment of sorbent heterogeneity. In determining a representative pKa spectrum for a given sample, either a continuous or discrete model can be used depending on the needs of the investigator. Continuous pKa spectra are more realistic for natural heterogeneous systems and are advantageous because it is possible to algebraically manipulate spectra in order to make comparisons between samples, such as in the comparison of individual end member spectra to the spectrum for composite sorbent materials (5). * Corresponding author phone: (416)978-0826; fax: (416)978-3938; e-mail: [email protected]. † Current address: Department of Chemistry, McMaster University, 1280 Main Street West, Hamilton, ON, Canada L8S 4M1. 10.1021/es0018668 CCC: $20.00 Published on Web 10/23/2001

 2001 American Chemical Society

In general proton sorption is dependent on both direct chemical interactions and electrostatic interactions. Thus, the measured heterogeneity is a combination of both chemical heterogeneity and electrostatic effects. For many samples it is possible to separate the electrostatic and chemical parts of the sorption (6). Once electrostatic effects are removed, then titrations from several different ionic strengths should collapse onto one so-called master curve. This master curve approach has been used for bacteria cell walls (6) and for humic substances (7). This paper does not consider the electrostatic effects and focuses on how to extract apparent pKa spectra from titration data. There are many examples in the literature of apparent pKa spectra for mineral surfaces (3, 8, 9). Thus, the spectra presented here are ionic strength dependent, and more work must be done on electrostatic modeling before a complete picture of proton interactions at mineral surfaces can be addressed. A continuous binding model can be obtained using nonlinear least-squares regularized for smoothness (3). Regularized least-squares is like traditional least-squares with an added term corresponding to an a priori assumption about the system; in this case, the assumption that the pKa spectrum is a smooth continuous function. In the method of C ˇ ernı´k et al. (3) the best pKa spectrum regularized for smoothness is determined as the “smoothest” pKa spectrum that still describes the data statistically well. In this method it is assumed that the smoothest answer is the best answer as long as it describes the data reasonably well. In fact, in applying the regularized least-squares technique there should be a set of parameters that optimizes both the goodnessof-fit and the regularization function, i.e., smoothness (10). A method to determine the optimal answer for both goodness-of-fit and smoothness is presented here as the Fully Optimized ContinUouS (FOCUS) pKa spectrum method. An important reactive mineral in natural systems is twoline ferrihydrite or hydrous ferric oxide (HFO) (11). The surface structure of HFO is poorly defined (12-14), and there are conflicting data on its proton binding properties; for example, it is usually assumed that the proton reaction properties of HFO can be represented by a single amphoteric site (11) but existing structural models (14) and theoretical studies of other iron oxides (15) suggest that surface reactions should be more complex. Thus, the FOCUS modeling approach developed here is applied to address the possible heterogeneity of HFO surface binding sites, and results are compared to theoretical models for crystalline iron oxides. One problem with reproducibility of HFO titrations in the literature is that the structure of the HFO is sensitive to the preparation method (11). In this study we apply the FOCUS pKa spectrum method to look at two different HFOs that differ only in the initial total iron concentration which the HFO was precipitated from. One HFO corresponds to the recipe of Schwertmann and Cornell (16), which uses a high initial iron concentration, and the other HFO was prepared from an order of magnitude more dilute total iron, which is closer to iron levels in natural environments. In addition, aluminum oxide is investigated because it is a crystalline reference system to compare to theoretical predictions.

Experimental Method HFO and Al2O3 Preparation. Two types of HFO were prepared. The first HFO corresponds closely to the recipe of Schwertmann and Cornell (16) and is designated as HFO1. The second prepared HFO differed only in that the initial total iron concentration was approximately an order of VOL. 35, NO. 23, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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magnitude lower; this is designated HFO2. Both HFO types were prepared in the laboratory using a Metrohm GP 736 Titrino at 25 °C under a positive pressure of N2. Initially, 4.0 g of ferric nitrate for HFO1 or 0.4 g for HFO2 was dissolved in a known volume of ultrapure water, approximately 50 mL. This iron solution was equilibrated under N2 until a constant potential was measured for the glass electrode, and then the sample was titrated to pH 7 with 0.1 M NaOH. The resulting HFO gel precipitate was then centrifuged at 6000 rpm for 10 min and rinsed once with ultrapure water and twice with 0.1 M KNO3 by centrifugation at 6000 rpm for 10 min each time. The washed HFO gel was finally resuspended in 200 mL of 0.1 M KNO3 and ready for titration. After titration, the total mass of the sample was determined by filtration using a 0.2 µm filter (Pall Gelman Supor membrane), repeated washes with ultrapure water, and finally oven drying overnight at 60 °C. In addition, the Fe concentration of the solid was determined by digesting the filter in concentrated HCl and analyzing by atomic adsorption spectroscopy (Perkin-Elmer 4000). Each replicate titration corresponds to a separate preparation of HFO. Alumina, as γ-aluminum oxide, was obtained from Alcoa technical center and washed in the same was as HFO. Nitric acid was then added to the washed sample to bring the pH to around 3, and the final suspension was left stirring for 1 day in order to reach equilibrium before starting the titration. All samples were titrated in the same way as detailed in ref 17. Data Processing Method. To fit acid-base titration data some model for the system must be assumed. The simplest model that is applicable is to assume that the surface reactivity can be explained as a mixture of monoprotic sites. Polyprotic sites could of course occur on the surface, but in this type of modeling such sites would be represented as a mixture of an appropriate number of monoprotic sites. Thus, the amphoteric sites often proposed for HFO surfaces symbolized as S-OH2+, S-OH°, and S-O- (11) would be represented as two monoprotic sites both with the same concentration as an individual amphoteric site and each with a pKa value corresponding to the respective stepwise disassociation constant. After selection of a model for the system it is important to define an objective function, which is some definition of the error dependent on the difference between measured and calculated results. This objective (i.e., error) function is minimized in fitting the data. In acid-base titrations, -log[H+] is measured as a function of volume of acid and/or base titrant added. The measured pH data is not good for fitting purposes because the dominant determinant of the titration curve shape is the disassociation of water, thus the effects of interest are difficult to see in the raw titration data; it is better to transform the data before fitting so that effect of water is removed, and the effects of the deprotonation/ protonation reactions on the substrate of interest can be observed directly. In addition, pH data are on a logarithmic scale so errors at low or high pH are buffered; it is better to use a concentration scale because the site densities are in concentration units. Lu ¨tzenkirchen (18) points out that some literature fitting results for HFO using nontransformed data do not describe the data very well after the appropriate transformation. The usual transformation is shown below for the ith addition of acid (Ca) or base (Cb) titrant

bi ) Cbi - Cai ( [H ′]i - [OH-]i

(1)

where bi represents either the charge excess expression (2) or -bi is the number of protons consumed (19), depending on whether a charge balance or mass balance approach is used, respectively. Mathematically the two interpretations 4638

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are equivalent. The discussion here will use the charge formalism, rather than mass balance. For a monoprotic model, bi can be calculated as a function of the speciation parameters. These include the number of site types (m), the concentration of each site (LTj), the acidity constant of each site (defined as the disassociation constant) Kj, and a constant offset term S0. For the ith addition of titrant the expression to determine bcalc,i is given below: m

bcalc,i )

(

LTjKj

∑ K ( [H j)1

j

(

)

]i

( S0

(2)

The offset term, S0, is necessary in order to account for positive charges on the surface. The monoprotic model on its own can only account for negative charges, but many natural surfaces are positively charged at low pH (20); thus, a constant offset term is necessary to fit the data. If the monoprotic model is actually true for the system, then the offset term corresponds to the initial acid neutralizing capacity (ANC) for the system (1). Alternatively, the offset can be thought of as the initial protonation state of the system (3). The S0 term should not be overinterpreted; it is simply an additive term that allows fitting of the data, and it could correspond to ANC or to the difference between the sites that are always protonated and those that are always deprotonated over the course of the titration, but this would only be true if the monoprotic model is exactly true. The important thing to realize is that the shape of the pKa spectrum is independent of the S0 term, so the pKa values are representative of the system even if the monoprotic model for charging is not true. There are numerical difficulties in fitting the model given by eq 2 to the data represented by eq 1 in that the stability constant and site concentration terms are correlated parameters (18, 21). Also, it is desirable not to have to assume a value for m. Already we have to assume a form for the reaction; to minimize assumptions it is desirable to let the data determine the best number of sites. This is possible using the pKa spectrum approach (1, 3, 21, 22) which involves fixing a sequence of pKa values and assigning ligand concentrations to each, including zero values. Fixing the stability constants solves the parameter correlation problem mentioned above. Thus, if the K values are fixed, such as pKa ) (3, 3.2, 3.4, ..., 10.8, 11), then the problem can be rewritten in matrix form for n titration points and m sites

Ax - b where

A(i,j) )

LTjKj Kj ( [H (]i

for i)1..n and j)1..m

and

A(i,j))1 for i ) 1..n and j ) m ( 1

(3)

where A is an n ×(m+1) matrix, x is a (m+1) × 1 vector of site concentrations, and b is n ×1 vector containing the measured charge excess from the titration data. The final entry in x corresponds to the offset term S0. The form of this equation is common in the physical sciences, and there are many ways to solve for x. The nature of the matrices makes this an ill-posed problem though, and there is not one unique solution for x unless additional assumptions are made about the nature of the solution. Recently, C ˇ ernı´k et al. (3) applied a method for solving ill-posed problems to acid-base titration data and eq 3. The

approach they used was regularization (3, 10). Regularization involves using some a priori information about the system to constrain the results; this leads to less sensitivity to data changes and a more unique solution. One constraint imposed by the nature of the system is that all of the ligand concentrations must be positive. This is termed the nonnegativity constraint. In addition, the results can be regularized for a few discrete sites or for smoothness depending on if a discrete or continuous result is desired. This a priori assumption about the nature of the final result makes it possible to formulate the regularized least-squares optimization problem:

minimize SS ( λR where n

SS (

∑(b

calc,i(x)

- bmeas,i)2

i)1

and m-1

R(xl, ..., xm) )

∑ (x j-2

j-l

- 2xj + xj+l)2 such that xj g 0 for j ) 1...m (4)

The SS term is the usual sum of squares term for nonlinear regression and the regularization term is given by R. The value of both the SS and R terms are dependent on the parameter vector (x) and the regularization power is controlled by the constant λ. The regularization function is selected to impose some a priori information of the system. C ˇ ernı´k et al. (3) present many different regularization functions depending on if the fewest number of sites or a continuous distribution is desired. Here we utilize the regularization for smoothness function given by C ˇ ernı´k et al. (3), which corresponds to the sum of squares of finite difference approximation of the second derivatives. This regularization function, given in eq 4, is small for smoothly varying values of x and large if the values of x oscillate. The solution to eq 4 should be optimized in terms of both the smoothness and goodness of fit. Theoretically, there is an optimal answer that satisfies both criteria with a minimum of compromise in the other. Determining this optimal solution depends on the regularization strength given by the parameter λ. C ˇ ernı´k et al. (3) utilized statistical tests to select the smoothest answer (highest λ) that still gave a statistically good fit to the data. This approach assumes that the smoothest answer that still describes the data is the best. An alternate approach is to select the answer which best satisfies both the sum of squares and regularization criteria simultaneously. Thus, a way to optimize the parameter λ is developed below and this is termed the FOCUS pKa spectrum method. FOCUS pKa Spectrum Method. There are two criteria to be optimized in determining the best fit regularized for smoothness. These are the sum of squares of the residuals, which describes the goodness-of-fit, and the regularization term, which describes how close the data agree with the initial assumption about the nature of the answer. The minimum of SS can be determined using nonlinear regression with the constraint that the parameters must be positive. The minimum for R is zero when the entries in x are constant. Using these two values an origin can be defined with the position (minimum (SS), 0) in (SS, λR) - space. The values of x that satisfy both criteria optimally then are the values that occur at a minimum distance from this origin. A criteria for the optimal answer to both SS and R simultaneously can

now be written:

minimize d(λk) )

x(minimum(SS) - SSk)2 + (0 - λkRk)2 for k ) 1...K

(5)

Thus, to determine the FOCUS solution an initial fit is performed ignoring the regularization term (λ ) 0) and the minimum(SS) value is determined. Then the value of λ is varied for a total of K different values and for the kth value the sum of squares (SSk) and regularization Rk are determined. The length of the vector from the defined origin to the kth calculated point is then determined using eq 5 above. The optimal value for λ could be determined using standard nonlinear regression techniques, but for the current work the minimum value for d was determined by systematically varying λ and selecting the minimum value of d. Data Analysis Methods. All data were analyzed using Matlab (The MathWorks Inc., MA). Constrained optimization was used for all optimization problems using the BFGS algorithm (23). Tests for false local minima were performed by varying the initial guesses and accepting the answer that had the lowest error. In general, most data converged to the same answer independent of the initial guess. The discrete forms of the equations given above were used for fitting purposes but were converted to the integral forms (3) for plotting and concentration determinations. The pKa sequence was defined from one log unit outside the pH range of the titration at both the upper and lower ends. The step size for the grid was defined as 0.1 pKa units. In addition, for the optimization problem the pKa value just outside the pKa grid was assigned a value of zero concentration to force the pKa spectra to tend to zeros at the edges. This was used to prevent unrealistic concentrations being assigned at the ends of the pKa window (24) and is reasonable because a ligand one log unit outside the pH range can only be protonated or deprotonated by 10% of its total concentration. Moreover, the effects of ligands that are always protonated or deprotonated are included in the S0 term. This same reasoning has been used in previous work by other authors in determining the pKa values (24), but sufficient details are not always given.

Results and Discussion The HFO prepared from a dilute initial total Fe (HFO2) shows a higher proportion (66.8 ( 4.3%) of Fe in the final solid product, compared to HFO1 (58.5 ( 3.0%). These values for the relative amount of iron in the prepared samples are reasonable given the proportion of iron by mass calculated for defined iron oxides. For example, the percent iron by mass for goethite (FeOOH) is 62.6%, hematite (Fe2O3) is 69.8%, and for proposed two-line ferrihydrite formulas (8) the range is 57.9 (Fe5HO8‚4H2O) to 62.4% (Fe6(O4H3)3). The only unlikely stoichiometry is Fe(OH)3 which would have too few irons by mass (52%) to account for the measured %Fe in either of the samples. The proportion of iron in HFO1 matches closest with the usual stoichiometry proposed for HFO (Fe5HO8‚ 4H2O) and HFO2 matches closest to hematite. X-ray diffraction patterns of HFO1 (25) and HFO2 (26, 27) do not show any long range order though and correspond to twoline ferrihydrite (25, 14). The acid-base titration data transformed as the charge excess expression, eq 1, are shown in Figure 1. Each subplot shows a minimum of four replicate titrations for the HFO samples and a single titration for the alumina sample. The best-fit lines were calculated by fitting all the replicate titration data simultaneously. It can be seen that the models describe the data well and that there are no trends in the residuals (i.e., bcalc-bobs); the best-fit line runs through the middle of the cluster of data. The error values are sometimes higher for the acidic and basic ends of the titrations, but this is VOL. 35, NO. 23, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Acid-base titration data for (a) HFO prepared from a concentrated initial total Fe (HFO1), (b) HFO prepared from a more dilute starting initial Fe (HFO2), (c) aluminum oxide, and (d) all titration curves summarized on one plot. In subplot (d) the different line styles correspond to the subplots indicated on the attached legend. For each titration experimental data are represented by open circles, and the best-fit curves are shown as a solid lines. consistent with the error function shape determined by Monte Carlo simulations by Smith et al. (21), which shows that titration errors are larger at the ends of the titration. Figure 1d compares the best-fit lines for all titrations on one plot. This is to facilitate comparison of the different titrations and to demonstrate shifts in the apparent zero point of charge (zpc). The apparent zero point of charge is taken as the pH where the charge excess is zero. Strictly speaking this is not the actual zero point of charge which would have to be determined as the point of zero salt effect (11) from titrations at different ionic strengths. It can be seen that the shapes of the titration curve for both HFO samples are very similar except HFO1 has a higher apparent zpc. The apparent zero point of charge for HFO1 (8.0) is the same as the best value selected in the literature review by Dzombak and Morel (11) for HFO. Also, the apparent zpc for the aluminum oxide is 8.2 which corresponds exactly to the value reported by Stumm and Morgan (28), although there are a wide range of values reported for aluminum oxide in the literature. The zpc for HFO2 is more acidic than is usually observed for HFO having a value around 7.2 rather than the usual value of 8.0. This is because most HFO prepared in previous studies used a recipe similar to Schwertmann and Cornell (16) rather than the more dilute starting total Fe used for HFO2 here. The shape of the alumina titration curve matches those presented by Contescu et al. (19) in that there is an initial steep portion followed by more gradual charging behavior. Figure 2 shows how the optimal regularization solution was determined for HFO2. Values of λR versus SS for various values of λ are shown in Figure 2a. The shape of this curve follows the proposed shape of such curves presented by Press et al. (10). An optimal answer can be imagined as being the point on the curve that is closest to both the best value for SS and the best value for R. This would be the point closest to the origin defined as (minimum(SS),0) as discussed in the methods section above. The minimum value for SS was calculated by setting λ ) 0 and optimizing the values in x subject to the nonnegativity constraint. The resultant parameter values are shown in Figure 2c. With that definition for the origin, the distance for points determined with various values of λ can be calculated. A plot of λ versus distance is shown in Figure 2b and reveals a minimum at λ ) 0.69. The x vector corresponding to this minimum is selected as the 4640

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FIGURE 2. Optimal fitting of acid-base titration data regularized for smoothness. The data corresponds to Figure 1b. Subplot (a) is a plot of the sum of squares (SS) versus the regularization (λR) for various values of λ. Subplot (b) is the distance defined as in eq 5 versus the regularizing power, λ. Subplot (c) is the best-fit without regularization and subplot (d) is the optimal best-fit using FOCUS pKa spectroscopy (λ ) 0.69). The dashed lines in (d) correspond to six Gaussian shaped sites that were fit to the overall pKa spectrum. FOCUS pKa spectrum and is given in Figure 2d. Finally, the dashed lines in Figure 2d correspond to a discrete six-site model for the pKa spectrum assuming that the total spectra can be represented as a sum of Gaussian components. Figure 3 shows the FOCUS pKa spectra for the corresponding data given in Figure 1. The final subplot (Figure 3d) displays all three pKa spectra overlain on the same plot. Inspection of Figure 3 reveals that HFO1 has five peaks, HFO2 has six peaks, and γ-Al2O3 has three peaks. In the overlay plot, Figure 3d, it can be seen that the spectra for HFO1 and HFO2 are somewhat different. Not only does HFO2 have more peaks but also the positions are different. The most dramatic difference is that HFO1 has an acidic site with a pKa value around 3, whereas HFO2 only has a very small peak at such an acidic pKa value; the remaining peaks occur within an order of magnitude of each other for the two samples, and the peak widths are approximately the same. To summarize the FOCUS pKa spectra data and to facilitate comparisons with other literature, a discrete site model is also calculated for each pKa spectrum. This is done by assuming that the spectra can be approximated as a mixture of Gaussian sites which is reasonable considering the centrallimit theorem and the shapes of the spectra. A similar assumption has been used fitting titration data (29). These discrete sites, along with pKa confidence intervals estimated as the standard deviation of the calculated normal distribution, are given in Table 1. The associated ligand concentrations, calculated as the area under the individual curves, are given in Table 2. The total site density of the two HFO samples are very close to each other, with HFO2 having 86% of the concentration of HFO1 in units of moles per mass. The alumina sample has almost twice as many total sites by mass as the two HFO samples. The overall distribution of pKa values are different for the two HFO samples; HFO2 is only 6% the concentration of HFO1 when comparing the concentrations of the most acidic sites. In addition, HFO2 has a higher concentration for the most basic sites by 113% compared to HFO1. The intermediate pKa sites match up closely except HFO2 has a similar intermediate site density spread over an additional pKa value.

TABLE 1. Summary of pKa Valuesa sample

site1

site 2

site 3

site 4

site 5

site 6

Al2O3 HFO1 HFO2

3.39 ( 0.37 3.39 ( 0.41 3.01 ( 0.34

4.00 ( 0.35 5.22 ( 0.41 4.78 (0.34

7.21 ( 0.28 6.74 ( 0.54 5.73 ( 0.50

9.07 ( 0.41 8.12 ( 0.35 7.32 ( 0.44

10.0 ( 0.5 10.1 ( 0.5 8.75 ( 0.37

na na 10.4 ( 0.40

a For each site the column entries correspond to the pK value plus or minus the width of the pK value determined from a Gaussian model a a for the peak shapes (see text).

TABLE 2. Summary of LT Valuesa sample

site1

site 2 site 3 site 4 site 5

Al2O3 HFO1 HFO2

2.42 2.31 0.50 0.60 0.032 0.34

0.22 0.48 0.34

0.49 0.33 0.37

site 6

S0

total

0.50 na -5.00 5.94 0.94 na -1.69 2.85 0.30 1.06 -0.84 2.45

a Site densities are given in units of µmol/mg and calculated as the area of the Gaussian modeled peaks. The site labels correspond to the pKa values given in Table 1. The total column is the sum of sites 1-6, not including the offset term S0.

FIGURE 4. Aluminum oxide discrete spectrum (a) and the theoretical model of Contescu et al. (19) is shown in (b). Discrete pKa spectra for (c) HFO1, (d) HFO2 measured here compared to the MUSIC model results for (e) hematite, (f) lepidocrocite, (g) goetite, and (h) HFO according to Dzombak and Morel (11). The concentration for each spectra is normalized to the highest concentration peak so that the comparison is for spectral shape, not absolute values.

FIGURE 3. pKa spectra for (a) HFO prepared from a concentrated initial total Fe (HFO1), (b) HFO prepared from a more dilute starting initial Fe (HFO2), and (c) aluminum oxide. In subplot (d) the calculated pKa using the same line styles as above are shown on an overlay plot. Interpretation of the pKa Values. To assess the validity of the experimental and data processing methods used here, the results of crystalline aluminum oxide are compared to theoretical values for alumina surface reactions. The results of this comparison are shown in Figure 4 where the sites are shown as discrete peaks in subplot (a). The lowest pKa site was divided into two peaks because a single Gaussian peak was not able to completely describe the shape of lowest peak in the FOCUS pKa spectrum. The theoretical pKa values for aluminum oxide surface reactions given by Contescu et al. (19) are shown in subplot (b) for comparison. The concentrations in Figure 4 are plotted normalized to the highest concentration so that relative concentration changes can be compared. The two spectra compare quite well in that there are peaks in the same regions with the same relative magnitude. The highest concentration of sites occur in the acidic pKa range for both spectra, and in both cases these reactions are represented as two pKa values. The values of Contestcu et al. are, however, about 1 pK unit further apart then the values determined here. At intermediate pKa values both spectra have a single small peak that is about 0.5 pKa units higher in the results presented here but still consistent with the value from the study by Contescu et al. Finally, the most basic site presented by Contescu et al. at a pKa value of 9.8 is represented by two peaks at 9.1 at 10 in the results

presented here, but if both peaks are taken together the relative intensity is consistent with the single peak in the reference study. Overall, the two studies agree very well, and the peaks presented here could be assigned to the same surface reactions as presented by Contescu et al. (19). The surface structure of HFO is still unknown (14) so theoretical values for surface site protonation reactions cannot be calculated using the MUSIC (multisite complexation) model. These calculations have been performed for many other iron oxides with structures related to HFO (15). The relative pKa spectra for the HFO samples measured here and for reference iron oxides are shown in Figure 4. The objective is a comparison of pKa values and the relative intensities for concentrations. Overall, the pKa spectra for the two HFO samples prepared here show features in common with the spectra for crystalline iron oxides. In particular, goethite is similar in shape to HFO2 in that the lowest concentration sites are the most acidic, followed by intermediate pKa sites, and finally the most basic sites are the most concentrated. The main difference is that the pKa values for goethite occur a lot less spread out than the values for HFO2. The two prepared HFO samples are more similar to each other than they are to any one crystalline iron oxide, but there are not any peaks in the HFO samples that do not have a closely corresponding value in at least one of the crystalline iron oxide spectra. This implies that the same types of reactions and the same types of surface sites exist in HFO as exist in the more crystalline solids. In fact, HFO has been proposed to be built up in part by ultradispersed hematite grains (30) and also has been proposed to have a structure similar to goethite (13). Note that the comparisons presented here are qualitative only. The FOCUS spectra are VOL. 35, NO. 23, 2001 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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conditional on ionic strength, whereas the MUSIC model results are for hypothetical zero ionic strength. Finally, the model of Dzombak and Morel (11) shown in Figure 4h looks completely different from any crystalline iron oxide and is dramatically different from the results reported here. Although the model of Dzombak and Morel can recover experimental data for HFO titrations, it should not be interpreted as representing rigorous chemical equilibrium conditions. Thus, if a more chemically realistic model of HFO surface-proton reactions are required, or for mineral surfaces in general, then the FOCUS pKa spectrum method can be used. This method recovers values consistent with the different types of surface groups that exist in iron oxides, whereas the model of Dzombak and Morel, although it describes data, is not consistent with the heterogeneous nature of HFO interface reactivity.

Acknowledgments This work was funded by a Natural Sciences and Engineering Research Council (NSERC) of Canada grant to F.G.F. In addition, the authors would like to thank Spencer Smith from McMaster University for very helpful discussions on the data fitting method and Hongying Jiang for assistance with the acid-base titrations.

Literature Cited (1) Brassard, P.; Kramer, J. R.; Collins, P. V. Environ. Sci. Technol. 1990, 24, 195. (2) Westall, J. C. FITEQL: a computer program for determination of chemical equilibrium constants from experimental data; Report 82-01; Department of Chemistry, Oregon State University: Corvallis, OR, 1982. (3) C ˇ ernı´k, M.; Borkovec, M.; Westall, J. C. Environ. Sci. Technol. 1995, 29, 413. (4) Nederlof, M. M.; van Riemsdijk, W. H.; Koopal, L. K. Environ. Sci. Technol. 1994, 28, 1037. (5) Smith, D. S.; Ferris, F. G. Environ. Sci. Technol. 2001, submitted for publication. (6) Plette A. C. C.; van Riemsdijk, W. H.; Benedetti, M. F.; van der Wal, A. J. Colloid Int. Sci. 1995, 173, 354. (7) Kinniburg D. G.; van Riemsdijk, W. H.; Koopal, L. K.; Benedetti, M. F. In Adsorption of Metals by Geomedia: Variables, Mechanisms and Model Applications; Jenne, E. A., Ed.; Academic Press: New York, 1998; Chapter 23. (8) C ˇ ernı´k, M.; Borkovec, M.; Westall, J. C. Langmuir 1996, 12, 61276137.

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Received for review November 10, 2000. Revised manuscript received August 27, 2001. Accepted August 29, 2001. ES0018668