Potentiometric Titrations of Rutile Suspensions to 250°C

JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.

200, 298–309 (1998)

CS975401

Potentiometric Titrations of Rutile Suspensions to 2507C Michael L. Machesky,* ,1 David J. Wesolowski,† Donald A. Palmer,† and Ken Ichiro-Hayashi‡ *Illinois State Water Survey, 2204 Griffith Drive, Champaign, Illinois 61820-7495; †Chemical and Analytical Sciences Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6110; and ‡Institute of Mineralogy, Petrology and Economic Geology, Tohoku University, Sendai 980-77, Japan E-mail: [email protected] Received October 7, 1997; accepted December 30, 1997

A stirred hydrogen electrode concentration cell was used to conduct potentiometric titrations of rutile suspensions from 25 to 2507C in NaCl and tetramethylammonium chloride media (0.03 to 1.1 m). Hydrothermal pretreatment of the rutile improved titration reproducibility, decreased titration hysteresis, and facilitated determination of the point of zero net proton charge (pHznpc). These pHznpc values are 5.4, 5.1, 4.7, 4.4, 4.3 ({0.2 pH units), and 4.2 ({0.3 pH units) at 25, 50, 100, 150, 200, and 2507C, 1 respectively. The difference between these pHznpc values and 2 pKw (the neutral pH of water) is rather constant between 25 and 2507C (01.45 { 0.2). This constancy is useful for predictive purposes and, more fundamentally, may reflect similarities between the hydration behavior of surface hydroxyl groups and water. A three-layer, 1pKa surface complexation model with three adjustable parameters (two capacitance values and one counterion binding constant) adequately described all titration data. The most apparent trend in these data for pH values greater than the pHznpc was the increase in proton release (negative surface charge) with increasing temperature. This reflects more efficient screening by Na / relative to Cl 0 . Replacing Na / with the larger tetramethylammonium cation for some conditions resulted in decreased proton release due to the less efficient screening of negative surface charge by this larger cation. q 1998 Academic Press Key Words: rutile; metal oxide; surface complexation; potentiometric titration; adsorption; PZC.

INTRODUCTION

Many of the variables that influence adsorption of ionic species by oxide surfaces have been extensively studied, including pH, type of oxide surface, type and concentration of adsorbing species, ionic strength, and time (kinetics). Temperature can also profoundly influence ion adsorption, but studies at other than room temperature are rare, and for temperatures above 1007C adsorption studies are virtually nonexistent. The systematic study of adsorption phenomena 1

To whom correspondence should be addressed.

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0021-9797/98 $25.00 Copyright q 1998 by Academic Press All rights of reproduction in any form reserved.

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at elevated temperatures and over wide temperature ranges is important for both fundamental and practical reasons. First, variable-temperature adsorption data can be combined with adsorption models to yield adsorption equilibrium constants, as well as associated adsorption enthalpies, entropies, and heat capacities. This leads to a more complete thermodynamic description of ion adsorption than can be obtained from isothermal adsorption data alone. Adsorption phenomena also influence many geochemical processes including the transport and fate of contaminants, mineral dissolution and precipitation reactions, colloidal stability, and various oxidation–reduction reactions (1, 2). For example, adsorption processes are a dominant control of contaminant migration in surficial environments. Seasonal and daily temperature variations can approach 507C in these environments, and the influence of temperature can approach that of pH in affecting adsorption behavior (3, 4). Also, temperatures are expected to range from about 140 to 257C near the proposed high-level nuclear waste repository at Yucca Mountain, Nevada (5). The effect of this large temperature gradient on radionuclide sorption processes, and consequently on potential migration away from the repository, is unknown (6). On a more practical level, the formation and deposition of corrosion products and the behavior of potential corrosion inhibitors in fossil- and nuclear-powered steam generators is highly dependent on adsorption processes. For example, magnetite is a common corrosion product in these elevated temperature environments (7), and the extent of magnetite deposition (or fouling) will be critically dependent on the surface charge of magnetite relative to steam generator surfaces. Blesa et al. (8), Machesky (9), and Barrow (10) have summarized previous studies concerned with temperature as an adsorption variable. Of particular relevance is the almost complete lack of information for temperatures above 1007C. A few streaming potential investigations in this temperature regime exist (11–13), and a few mineral dissolution studies have monitored relevant adsorption phenomena (14). In addition, Schoonen (15) has extrapolated available (T õ 957C)

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point of zero charge pH (pHzpc) data for several oxides to 3507C, but warns that the uncertainty in these extrapolations increases rapidly above 1507C because experimental data are unavailable. The results of our first set of potentiometric titrations of rutile in NaCl media from 25 to 2507C were reported elsewhere (16). In the present study, the rutile starting material underwent hydrothermal pretreatment prior to the potentiometric titrations so that improved data precision could be attained. Furthermore, the results are rationalized with the aid of surface complexation theory. MATERIALS AND METHODS

The source rutile was the same as that used previously (Tioxide Specialities Ltd., Cleveland, UK) and it was subjected to similar numerous washing–boiling–decantation cycles to improve product purity. As an additional purification step, the rutile was then hydrothermally aged in a Teflon-lined reaction vessel for 13 days at 2007C in distilled–deionized water and subsequently dried at 1007C. The N2-BET surface area of this cleansed sample was 17 { 3 m2 /g and the XRD pattern revealed only well-crystallized rutile. Potentiometric titrations were performed in a stirred hydrogen electrode concentration cell (SHECC) located at Oak Ridge National Laboratory, where it was first developed in the early 1970’s. A diagram of this apparatus is shown in Fig. 1. The principal advantage of this cell is the ability to conduct potentiometric titrations to 3007C (limited by the

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temperature at which the Teflon reference and sample compartments begin to decompose) with excellent precision and accuracy. A recent review provides additional information, including a summary of previous studies conducted with the SHECC (17). Subsamples of rutile (1.45 { 0.05 g) and 45 { 2 g of electrolyte solution (0.001 m HCl / NaCl to produce total molalities of 0.03, 0.3 and 1.0 m) were added to the test compartment of the cell, while approximately 16 g of the same solution were added to the reference compartment. Then, the cell was equilibrated overnight (11–16 h with stirring) at 25, 50, 100, 150, 200, and 2507C. Next, 18–25 aliquots of NaOH / NaCl of equivalent ionic strength were titrated into the test compartment from a positive displacement pump, with 12 to 40 min allowed for equilibration between additions. At the end of this equilibration period, drift rates were always õ0.15 mV/min and usually much smaller than this. Using a second pump, back titration with HCl / NaCl was carried out immediately following the base titration for several of the initial titrations. A new subsample of rutile was used for each titration, and some runs were duplicated. In addition, tetramethylammonium chloride (TMACl) and tetramethylammonium hydroxide replaced NaCl and NaOH for some titrations performed at 100 and 1507C. Hydrogen ion activity (pH) was estimated from the computed H / concentration using the relation gH / Å (aW KW / QW ) 1 / 2 , where aW Å water activity, and KW and QW are the activity, and molal concentration products for water dissociation, respectively (18). This is equivalent to assuming that gH / Å ( gH / gOH 0 ) 1 / 2 . Unpublished values of QW in TMACl media, determined at Oak Ridge National Laboratory, were used as needed. Acid and base consumption due to rutile dissolution and associated hydrolysis reactions were taken as negligible. This is a reasonable assumption since dissolved titanium concentrations are expected to remain below 10 07 M for all conditions of this study (19). Corrections for other solution blank effects, liquid junction potentials, and systematic errors were made with in-house programs (17, 20). Net H / adsorption (acid titration) and desorption (base titration) data were then converted to net surface charge ( s0 , C/m 2 units) for analysis and modeling purposes. RESULTS AND DISCUSSION

FIG. 1. Schematic drawing of the ORNL stirred hydrogen electrode concentration cell.

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Figure 2 illustrates that titration hysteresis, that is, the difference between initial titration with base titrant and subsequent back titration with acid titrant, was markedly reduced by increasing the total titration time. From these results it was surmised that titration hysteresis could probably be largely eliminated with even longer total titration times. However, it was not practical to perform such long titrations for all conditions. Consequently, most titrations were performed only with base titrant, but with longer intervals be-

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FIG. 2. Surface charge ( s0 ) data for titrations conducted over nine ( j, dashed line) and 13 ( l, solid line) hour periods at 1507C, 0.03 m NaCl. Base titration (lower portion of each curve) was followed immediately by back titration with acid titrant (upper portion of each curve).

tween titrant additions allowed (if necessary) for EMF readings to stabilize. Also, titration hysteresis was generally reduced for our hydrothermally aged rutile relative to rutile which was not hydrothermally pretreated (16). Figure 3 presents another method by which titration hysteresis was assessed. Instead of the normal procedure of aging the rutile overnight in acidic test solution, aging took place in an alkaline test solution (0.001 m NaOH) with subsequent titration using acid titrant. The resulting titration curve is very similar to that for an initially acidic test solution down to pH 3.5. This demonstrates the inertness of the rutile surface, which is a primary reason that rutile is an ideal model oxide for this type of study. Representative titrations with hydrothermally aged and unaged (16) rutile are compared in Fig. 4. The aged and

FIG. 4. Surface charge ( s0 ) data for hydrothermally aged ( l ) and unaged ( j ) rutile in 1.0 m NaCl at 25, 150, and 2507C.

unaged curves are similar and parallel each other at 25 and 1507C, but there is considerable difference at 2507C. The initial negative surface charge value for unaged rutile at 2507C signifies that the rutile surface released protons. Thus, above 1507C, unaged rutile became a net source of protons. In contrast, the aged rutile adsorbed protons from the initial test solutions under all conditions. Moreover, the initial surface charge value (after overnight aging but before adding base titrant) is similar at all temperatures for a given ionic strength. Two possible mechanisms for the increase in starting solution acidity with increasing temperature were proposed in our previous study (16): condensation of surface hydroxyl (SOH) groups into bridged (S–O–S) configurations or leaching of an acidic impurity (probably HCl) from the rutile crystallites. The latter mechanism now appears more likely. Apparently, repeated boiling is not enough to remove all residual HCl from the synthesis process when the rutile is subsequently exposed to temperatures above 1507C. Earlier work with rutile of similar origin noted that repeated Soxhlet extraction or elevated heat treatments were necessary to cleanse the rutile surface (21). An additional beneficial effect of the hydrothermal pretreatment may have been to accelerate Ostwald ripening (15). Hydrothermal pretreatment has also been found to benefit hydrothermal dissolution studies (22). In any case, these results reinforce those of others who have cautioned that solid pretreatment procedures can have a large influence on experimental results (23, 24). Hence, any pretreatment procedures should be carefully documented. Base titration data were fitted with fifth-order polynomial equations of the form s0 (c/m2 ) Å (B5rpH 5 ) / (B4rpH 4 )

FIG. 3. Surface charge ( s0 ) data (2007C, 1.0 m NaCl) after overnight aging in acidic ( l ) and basic ( j ) test solutions.

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/ (B3rpH 3 ) / (B2rpH 2 ) / (B1rpH) / A.

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TABLE 1 Polynomial Coefficients and Applicable pH Ranges and Offset Values Temp, I

B5

B4

B3

B2

B1

A

pH range

Offset

25, 0.03 25, 0.3 25, 1.0

05.35191E-05 3.48179E-05 04.30830E-06

1.69271E-03 01.07642E-03 2.09268E-04

02.14620E-02 1.26332E-02 03.26422E-03

0.13246 00.07486 0.01722

0.42310 0.18317 00.07471

0.60283 00.04423 0.25388

2.86–10.56 2.96–10.67 3.00–10.75

00.00430 00.00430 00.00365

50, 50, 50, 50,

05.95610E-06 01.20235E-05 01.43787E-05 01.94706E-05

2.30408E-04 3.62276E-04 5.70082E-04 7.57675E-04

04.32829E-03 05.33857E-03 08.46588E-03 01.07589E-02

0.03592 0.03892 0.05347 0.06500

00.16115 00.16462 00.19192 00.22281

0.32272 0.32760 0.36996 0.42554

2.85–10.08 2.86–10.11 2.96–10.29 3.00–10.25

00.00496 00.00496 00.00496 00.00018

0.03(1) 0.03(2) 0.3 1.0

100, 100, 100, 100, 100,

0.03 0.3 1.0 0.03 TMACI 1.1 TMACI

3.35742E-05 03.18484E-05 04.02165E-05 08.96844E-05 1.49878E-04

07.80898E-04 1.26198E-03 1.41246E-03 1.84535E-03 04.32610E-03

4.83594E-03 01.86547E-02 01.86502E-02 01.35157E-02 4.82728E-02

00.00109 0.12175 0.10836 0.03983 00.26102

00.09684 00.41089 00.34181 00.05153 0.63762

0.27458 0.63104 0.54996 0.07402 00.48315

2.86–9.22 3.00–8.99 3.05–9.17 2.80–8.30 2.94–8.56

00.00696 00.00567 00.00276 0.00243 00.00765

150, 150, 150, 150, 150, 150,

0.03 0.3 1.0 0.03 TMACI 1.1 TMACI(1) 1.1 TMACI(2)

1.99754E-04 1.25453E-04 02.16884E-05 1.02534E-04 2.96532E-04 3.65380E-04

05.09342E-03 03.02798E-03 9.07800E-04 03.18938E-03 08.40541E-03 01.01908E-02

4.77363E-02 2.69918E-02 01.31719E-02 3.69993E-02 9.26005E-02 1.10389E-01

00.21192 00.11835 0.07714 00.20508 00.49698 00.58211

0.41946 0.20612 00.26342 0.51586 1.24618 1.44459

00.22618 0.01310 0.48587 00.39087 01.07283 01.25142

2.85–8.10 3.00–8.22 3.08–8.31 2.83–7.72 3.02–8.00 3.02–8.04

0.00351 00.00037 0.00223 0.03358 0.01658 0.02219

200, 200, 200, 200,

0.03 0.3 1.0(1) 1.0(2)

03.54113E-06 1.50257E-05 4.79651E-05 07.41264E-05

3.33416E-04 1.25699E-04 01.27123E-03 2.07652E-03

08.54113E-03 07.71814E-03 1.34231E-02 02.18115E-02

0.06883 0.06316 00.08273 0.09547

00.25723 00.25493 0.18844 00.24242

0.40329 0.46972 0.02346 0.41692

2.87–7.52 3.05–8.06 3.20–8.07 3.19–8.06

00.00074 00.00725 0.00555 0.00744

03.63426E-05 07.09367E-04 03.49461E-04

2.21025E-03 1.98131E-02 6.53916E-03

03.71595E-02 02.15661E-01 03.59244E-02

0.24739 1.12172 00.01167

00.75142 02.86477 0.46484

0.92527 2.98662 00.66392

2.92–7.53 3.13–7.28 3.30–7.78

0.01978 0.00077 00.00271

250, 0.03 250, 0.3 250, 1.0

The resulting coefficients and pH intervals are contained in Table 1, along with appropriate offset values for each titration. These offset values equal the measured surface charge value for a particular titration at the chosen point of zero net proton charge (pHznpc) for each temperature (25). Both the pH values corresponding to zero surface charge and the intersection points of titration curves at each temperature were used to arrive at these pHznpc estimates and the associated uncertainties. The chosen pHznpc values are 5.4, 5.1, 4.7, 4.4, 4.3 ( {0.2 pH units), and 4.2 ( {0.3 pH units) at 25, 50, 100, 150, 200, and 2507C, respectively. The comparatively few titrations conducted in TMACl media were not utilized for these pHznpc estimates. Subtraction of the appropriate offset value results in the relative surface charge values ( s0,rel ) depicted in Figs. 5a–5f and 6. These offset corrections ensure that the suite of curves at each temperature intersect exactly at the chosen pHznpc and zero surface charge for modeling purposes (26). The coefficients and offset values in Table 1 can be used to estimate the titration data contained in Figs. 5a–5f and 6 to within 0.01 C/m 2 over the applicable pH range. Also presented in Figs. 5a– 5f are the fits of the surface complexation model (discussed below) used to rationalize these results. At each temperature, the data are typical of metal oxide acid–base titrations (27).

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That is, H / desorbed increases with ionic strength due to increased counterion screening of surface charge. Finally, the pHznpc at 2957C is provisionally estimated to be 4.3 ( {0.3 pH units). This estimate is based on two titrations (in 0.03 and 0.3 m NaCl) which were conducted over a very limited pH range because the EMF readings became very unstable. Model Background Surface complexation modeling efforts utilized the 1pKa description of surface hydroxyl group ionization (28, 29). The 1pKa model offers several advantages over the more commonly used 2pKa description. First, the 1pKa model is the simplest representation of multisite surface complexation models (30–32), which explicitly consider the different types of surface hydroxyl groups that exist on oxide surfaces. Second, the protonation constant describing surface hydroxyl group ionization can be equated with the measured pHznpc. Consequently, the observed pHznpc and its temperature dependence can be directly related to thermodynamic quantities. Finally, the 1pKa model can usually describe surface charge data adequately with one less model-dependent fitting parameter than the 2pKa description.

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FIG. 5. Relative surface charge data ( s0,rel , symbols) and model fit (solid lines) for 0.03 ( j ), 0.3 ( l ), and 1.0 m ( m ) NaCl, as well as 0.03 ( j ) and 1.1 m ( m ) TMACl (c & d only). The vertical dashed line is placed at the chosen pHznpc, and the horizontal dashed line is placed at the zero surface charge value. a) 257C, b) 507C, c) 1007C, d) 1507C, e) 2007C, and f) 2507C.

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model, is presented in Fig. 7. Note that the diffuse layer is assumed to begin at the edge of the outer Stern plane. The original formulation of Bousse et al. (33) and more recent use by Charmas and co-workers (38, 39) include a fourth layer and corresponding capacitance value before the onset of the diffuse layer. A principal benefit of this additional layer is to better fit electrophoretic mobility data, but such data were not available for this study. Consequently, this fourth layer was not explicitly included. Model parameters are as follows. The surface site concentration is given by /2 Ns Å [TiOH 01 / 2 ] / [TiOH /1 ] 2 /2 / [TiOH 01 / 2 –M / ] / [TiOH /1 – A0] 2

FIG. 6. Relative surface charge data in 0.03 m NaCl ( s0,rel , solid lines) and TMACl ( s0,rel , dotted lines), referenced to the pHznpc (pHznpc-pH) at a particular temperature.

The 1pKa model was initially coupled with a basic Stern layer description of the electrical double layer (EDL) structure, given this combination’s success in describing room temperature metal oxide titration data with a single Stern layer capacitance value and two counterion binding constants as the only variable fitting parameters (26, 29). However, attempts to fit the experimental data with the basic Stern model did not produce satisfactory fits at all temperatures and conditions. The reason for this can be qualitatively illustrated with the aid of Fig. 6. This figure demonstrates that at constant ionic strength, H / desorption in NaCl media increases with temperature above the pHznpc. This effect is not as apparent below the pHznpc, although the accessible pH range is much more limited. Moreover, less H / is desorbed at 100 and 1507C above the pHznpc in TMACl than in NaCl media. Above the pHznpc, Na / and TMA / screen the development of negative surface charge that results from H / desorption, while below the pHznpc, Cl 0 screens positive surface charge development. Thus, Na / is more effective at screening with increasing temperature, but Cl 0 is not. This charging asymmetry was accounted for by allowing for separate capacitance values for Na / and Cl 0 . This type of two-Stern layer model was first used by Bousse et al. (33) and can be termed a three-layer model (34) to distinguish it from the more familiar triple-layer model (35). Figure 6 also illustrates that negative surface charge development is not temperature congruent (36). That is, with respect to the pHznpc, negative surface charge development increases with temperature. This contrasts with other studies that have observed temperature congruence for rutile and hematite (36, 37). However, these previous studies were conducted over a much more limited temperature range (5–507C) and in a different ionic medium (KNO3 ). A schematic of the charge and potential relationships, as well as the model parameters associated with the three-layer

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[2]

where [ ] Å concentration ( mmol/m 2 ), TiOH 01 / 2 and /2 TiOH /1 are unprotonated and protonated surface sites, and 2 /2 TiOH 01 / 2 –M / and TiOH /1 – A 0 represent unprotonated 2 and protonated surface sites which are bound to countercations and counteranions, respectively. Ns was fixed at 20.8 mmol/m 2 (12.5 sites nm02 ) which is the value recommended by Yates et al. (40) based on crystallographic considerations and tritium exchange and weight loss experiments. The surface protonation constant for the reaction /2 TiOH 01 / 2 / H / Å TiOH /1 2

[3]

is given by /2 KH Å [TiOH /1 ]/{[TiOH 01 / 2 ]{H / }b exp( 0zH FC0 /RT )} 2

[4] where {H / }b Å hydrogen ion activity (10 0pH ) in the bulk solution, zH Å hydrogen ion charge, F Å Faraday constant, C0 Å surface potential, R Å gas constant, and T Å temperature in Kelvin. The log KH value was fixed at the pHznpc value identified at a given temperature for modeling purposes. At this pH, and with the additional assumption that

FIG. 7. Schematic representation of the three-layer model. Terms are defined in the text.

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counterion adsorption is minor or at least compensatory, C0 Å 0 and pH Å log KH . The cation binding constant for the reaction TiOH 01 / 2 / M / Å TiOH 01 / 2 —M /

which is used to calculate Cd above, is typically formulated in terms of molar (per unit volume) concentration units. With reference to Fig. 7, the charge associated with each layer is defined as

[5] s0 Å surface charge

is defined as,

/2 s0 Å F([Ti–OH /1 ](z / zH ) 2 /2 / [TiOH /1 — A 0 ](z / zH ) / [Ti–OH 01 / 2 ](z) [12] 2

KM Å [TiOH 01 / 2 —M / ]/{[TiOH 01 / 2 ][M / ]b ( g{NaCl ) 1 exp( 0zM FCM /RT )}

where [M / ]b Å cation concentration (molal) in the bulk solution, g{NaCl Å mean molal stoichiometric activity coefficient of NaCl at a given ionic strength and temperature, taken from published sources (41), zM Å cation charge ( /1), and CM Å potential at the plane of countercation adsorption. The mean activity coefficient of TMACl was assumed to equal that of NaCl since comparable data were not available for TMACl. Similarly, the anion binding constant for the reaction /2 /2 TiOH /1 / A 0 Å TiOH /1 — A0 2 2

/ [TiOH 01 / 2 —M / ](z))

[6]

[7]

sM Å countercation charge sM Å F([TiOH 01 / 2 —M / ](zM )) sA Å counteranion charge /2 sA Å F([TiOH /1 — A 0 ](zA )) 2

sd Å uncompensated or diffuse layer charge /2 sd Å 0F([Ti–OH 01 / 2 ](z) / [Ti–OH /1 ](z / zH ) 2

/2 / [TiOH /1 — A0 ](z / zH / zA )), 2 /1 / 2 2

0

— A ]/{[TiOH

/1 / 2 2

][A ]b ( g{NaCl ) [8]

where [A 0 ]b Å anion concentration (molal) in the bulk solution, zA Å anion charge ( 01), and CA Å potential at the plane of counteranion adsorption. For the purposes of the modeling efforts presented below, we set KM Å KA , which reduces the number of fitting parameters by one. This has the effect of specifying that counterion binding is compensatory. Consequently, with this assumption the pHznpc is equal to the pHzpc (25). The capacitance values (F/m 2 ) for the inner (C1 ) and outer (C2 ) layers were the fitting parameters used to determine the potentials associated with the three-layer model. These potentials can be expressed as C0 Å ( s0 /C1 ) / ( sM / s0 )/C2 / cd

[9]

cM Å c0 0 ( s0 /C1 )

[10]

cd Å cA Å (2RT/F)arcsinh( 0 sd /(8RTe0eb Irs ) 1 / 2 ),

[11]

where e0 Å permittivity of vacuum Å 8.854 1 10 012 , eb Å bulk dielectric constant of water at a given temperature (42) and ionic strength (43), I Å stoichiometric molal ionic strength, and rs Å solution density, which was taken from tabulated properties of NaCl solutions (41). The solution density term is necessary since the Gouy–Chapman theory,

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0

1 exp( 0zA FCA /RT )}

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/ [TiOH 01 / 2 —M / ](z / zM )

is defined as KA Å [TiOH

[13]

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where z Å 00.5 (charge of the TiOH site). Finally, electroneutrality requires that s0 / sM / sA / sd Å 0.

[16]

Commercially available least-squares minimization software (SCIENTIST, Micromath, Inc., Orem, UT) was used to fit the relative surface charge data to the three-layer model with pH as the independent variable. The experimental errors associated with the relative surface charge values for a particular titration were used for weighting purposes during least-squares minimization. Relative weights were assigned to each data point as Wi Å (errormax ) 2 /(errori ) 2

[17]

where errormax is the maximum error value for a particular titration, and errori is the error associated with a particular titration point. Each titration curve was fit separately with KM ( Å KA ), C1 , and C2 as variable parameters. Model output included best-fit titration curves as well as parameter values and their standard deviations. Discussion of Model Results Best-fit surface charge curves are shown in Figs. 5a–5f and the associated parameter values and their standard devia-

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TABLE 2 Fixed (F), Variable ({1 SD), and Averaged ({1 SD) Parameter Values C1 (F/m2)

SD

C2 (F/m2)

SD

log KH(F)

Ns(F) (mmols/m2)

25, 0.03 25, 0.3 25, 1.0 Avg(NaCl)

1.90 1.92 1.94 1.92

0.13 0.04 0.05 0.022

4.10 2.42 2.66 3.06

1.76 0.14 0.15 0.91

5.40

50, 0.03(1) 50, 0.03(2) 50, 0.3 50, 1.0 Avg(NaCl)

1.72 1.84 1.89 1.81 1.81

0.07 0.08 0.03 0.02 0.07

4.88 5.25 2.25 2.31 3.67

1.47 1.96 0.08 0.15 1.62

5.10

100, 0.03 100, 0.3 100, 1.0 Avg(NaCl) 100, 0.03 TMACI 100, 1.1 TMACI

2.10 2.07 2.27 2.15 0.73 0.86

0.03 0.04 0.11 0.03 0.01

6.00 2.97 2.81 3.93 6.00 6.00

150, 0.03 150, 0.3 150, 1.0 Avg(NaCl) 150, 0.03 TMACI 150, 1.1 TMACI(1) 150, 1.1 TMACI(2)

2.29 2.33 2.32 2.31 1.05 0.97 0.94

200, 0.03 200, 0.3 200, 1.0(1) 200, 1.0(2) Avg(NaCl)

2.40 2.39 2.40 2.44 2.41

250, 0.03 250, 0.3 250, 1.0 Avg(NaCl)

2.92 2.92 2.92 2.92

Temp, I

0.06 0.03 0.02 0.02 0.01 0.01

2.13 3.02 3.00 2.72 6.00 6.00 4.19

0.29 0.16

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0.062 0.049 0.029 0.046

0.021 0.006 0.005 0.016

4.75 7.24 6.94 6.31

20.8

0.079 0.088 0.064 0.060 0.073

0.017 0.019 0.006

6.30 5.74 7.74 6.56 6.59

0.04 0.02

0.12 0.002

1.72 2.61 4.47 2.93

0.46 0.15 0.79 1.41

20.8

0.050 0.052 0.025 0.042 0.050 0.050

0.003 0.003 0.002 0.015

5.79 8.28 7.71 7.26 4.12 6.27

4.40

20.8

0.154 0.058 0.037 0.083 0.150 0.037 0.037

0.012 0.003 0.001 0.062

6.79 8.15 7.79 7.58 5.48 6.73 6.17

4.30

20.8

0.186 0.095 0.069 0.060 0.102

0.008 0.004 0.003 0.004 0.058

5.85 8.13 6.49 7.73 7.05

4.20

20.8

0.255 0.175 0.132 0.187

0.014 0.004 0.018 0.063

4.99 7.47 6.13 6.20

0.22 0.46

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0.013

4.70

0.72 0.44 0.15

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MSC

0.51

tions (SD) are contained in Table 2. Also included in this table is the Model Selection Criterion (MSC) value which is a measure of the goodness of fit (larger is better). Each titration curve was fit separately and model optimization strategy included fixing some of the parameter values at each temperature to ensure a closer agreement among these values for all ionic strengths. A blank entry for the SD value indicates a fixed parameter value. The fit of the 1pKa , three-layer model is good for all temperatures and ionic strengths. The most significant trend in the best-fit parameter values is the increase in the innermost capacitance value (C1 ) with increasing temperature, particularly above 1007C. Average (over all ionic strengths) C1 values in NaCl media increase from 1.92 at 257C to 2.92 at 2507C. This capacitance value can be related to the relative dielectric constant of the Stern layer ( er ) and the distance of charge separation (d) between both electrostatic planes of the Stern layer (44),

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0.12 0.14 1.80

2.50 3.09 3.50 3.44 3.13

0.03

KM Å KA

C Å e0er /d.

[18]

The value of er is not known, but its maximum possible value can be taken as eb , the bulk dielectric constant of water, as was assumed for the modeling efforts. If d is then taken as the ionic radius of the ion adsorbed at the Stern layer, it is then possible to calculate a maximum possible value for the Stern layer capacitance, which would correspond to inner sphere coordination. This helps to partially constrain the fitted capacitance values C1 and C2 . For example, given 1.02 1 10 010 m as the ionic radius of Na / (45), the maximum C1 values calculated using Eq. [18] at 25 and 2507C are 6.81 and 2.35 F/m 2 , respectively. This decrease is a direct result of the decrease in eb from 78.45 to 27.08 (42). Moreover, given the average best-fit C1 values at 25 and 2507C (Table 2), we can estimate that the plane of Na / countercharge is located about 3.62 1 10 010 and 8.82 1 10 011 m from the surface plane at 25 and 2507C, respectively.

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This corresponds to about 3.5 and 0.8 times the ionic radius of Na / . That the plane of Na / countercharge is estimated to lie at less than the ionic radius of Na / from the rutile surface at 2507C may indicate that Na / partially penetrates the surface. This explanation is often invoked to rationalize the large capacitance values that are usually necessary to describe the surface charge behavior of silica near room temperatures (44). In any case, the increase in C1 from 1.92 to 2.92 F/m 2 between 25 and 2507C represents a more significant decrease in the distance of charge separation than the absolute values of C1 suggest. Thus, Na / moves closer to the rutile surface with increasing temperature with the result that screening of negative surface charge development is enhanced. The capacitance values associated with Cl 0 binding (C2 ) are generally much more variable than the C1 values, as evidenced by the usually larger standard deviations associated with the averaged values. Thus, averaged C2 values are approximately constant at all temperatures. In NaCl media, the averaged counterion binding constant also appears to increase above 1007C although the variability is large. The counterion binding constant also tends to decrease with increasing ionic strength at each temperature. Usually, there is also a relatively strong negative correlation (typically õ 00.9) between the best-fit KM ( Å KA ) and C1 values. This means that a decrease (increase) in KM coupled with an increase (decrease) in C1 over a certain range of values, would also result in acceptable fits. The C1 values associated with TMA / binding are smaller than those associated with Na / , as expected for this larger cation, the radius of which is about 2.8 1 10 010 m (46). In addition, best-fit C2 values are fairly large ( ú3) in all instances, which signifies that the plane of the Cl 0 countercharge is close to that of Na / . Consequently, a basic Stern layer approach might also produce acceptable fits. However, the temperatures and ionic strengths studied in TMACl media were limited, and additional data are required before such trends can be confirmed. Previous studies have noted that surface charge development is screened more effectively by Na / than Cl 0 at room temperature (47), and this screening probably includes Na / and Cl 0 adsorption at the rutile surface (48–50). Moreover, ion association in solution is always favored with increasing temperature due to the lowering of the dielectric constant of water, resulting in greater net release of hydration-sphere water molecules from the associating species (51). The closer approach of Na / to the negatively charged rutile surface with increasing temperature can be rationalized similarly, although whether inner- or outer-sphere binding (or both) is involved is not determinable from our data. However, Berger et al. (14) suggested that Na / moved from outer- to inner-sphere coordination on the amorphous silica surface with increasing temperature, since Na / adsorption was less dependent on ionic strength at 150 than 257C in

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the absence of competing species such as Ca 2/ . This was attributed to the lower Na / hydration energy at 1507C. Thus, we hypothesize that association of strongly hydrated ions with oppositely charged hydrated surfaces would (in general) increase with temperature, because of the entropy increase associated with greater liberation of waters of hydration. If true, correlations between ion–ion and ion–surface reactions, which have been noted at room temperature (2, 52), could be extended to considerably higher temperatures as well. Clearly, further experimental work on ion–surface reactions at elevated temperatures is necessary to extend these correlations. Surface site speciation can be calculated using the parameter values in Table 2. Figures 8a and 8b present the results of these calculations for the end member conditions of our study, that is, 0.03 m NaCl at 257C and 1.0 m NaCl at 2507C. For both conditions (and all in between) the majority of surface sites are not associated with counterions, although a significant portion of negatively charged sites are associated with Na / above pH 7 in 1.0 M NaCl at 2507C. A consequence of the large fraction of unassociated surface sites and the large value of Ns used is that the calculated surface potential is pseudo-Nernstian ( ú86% of Nernstian) for all conditions (53). Measurements with TiO2-containing electrodes have also observed Nernstian or super-Nernstian surface potentials, both at room temperatures (54) and between 25 and 2507C (55). pHznpc Temperature Dependence Figure 9 summarizes the temperature dependence of rutile pHznpc values from this study, our previous work (16), and two earlier studies conducted over a much more limited temperature range (23, 36). Also included are 12 pKw (18), an extrapolation to 3007C of the Fokkink data (36) by Schoonen (15), and a fit of the pHznpc (or log KH ) values from this study to the equation (56) log KT Å 0 [ DH 7298 0 298DCp /2.303R]T 01 / [ DS 7298 0 DCp (1 / ln 298)/2.303 R] / ( DCp /R)log T,

[19]

where T is in Kelvin and DH 7298 , DS 7298 , and DCp are the standard enthalpy, entropy, and heat capacity changes associated with hydrogen ion adsorption. DCp is assumed to be independent of temperature. The estimated pHznpc value at 2957C was not included in this fit since it is based on very limited data. The best-fit DH 7298 , DS 7298 , and DCp values are 023.2 { 1.1 kJ/mol and 25.5 { 3.4 and 79.6 { 11.6 J/K/ mol, respectively (R 2 Å 0.9999), and the predicted pHznpc values are within the estimated uncertainty of our measured values at all temperatures including 2957C. Hydrogen ion adsorption enthalpies for rutile near the pHzpc have been

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TITRATIONS OF RUTILE SUSPENSIONS

FIG. 8. Surface species distributions for (a) 257C, 0.03 m NaCl and (b) 2507C, 1.0 m NaCl. The vertical dotted line is placed at the pHnzpc.

measured using titration calorimetry; an average value is near 022 kJ/mol (57, 58), which is very close to that estimated using Eq. [19]. A similar fit of our earlier pHznpc values (16) with DH 7298 fixed at 022 kJ/mol resulted in best-fit DS 7298 and DCp values of 35 { 3 and 94 { 33 J/K/ mol, respectively (R 2 Å 0.9992). Extrapolation of the Fokkink pHzpc data (36) by Schoonen (15) agrees more closely with the pHznpc data from this study rather than our earlier study, and the data from Berube and DeBruyn (23). In general, the pHzpc differences between these various studies likely reflect differences in sample origin, as well as pretreatment and experimental procedures. Hence, thermodynamic parameters associated with ion–surface reactions will never be as well constrained as those for homogeneous solution reactions.

Many previous thermodynamic analyses of hydrogen ion adsorption by oxide surfaces have assumed DCp Å 0, because of the limited temperature range investigated (8, 9). However, the approximate parabolic temperature dependence of the pHznpc values reported here suggests a significant positive heat capacity term is associated with the proton adsorption process. Moreover, this temperature dependence mirrors that observed for 12 pKW . That is, the difference between the pHznpc and 12 pKW is rather constant ( 01.45 { 0.2) between 25 and 2507C. This constancy was also observed in our previous study and can be more formally represented as an isocoulombic, or charge-balanced, form of the 1pKa model (59, 16) /2 / 12OH 0 K * Ti–OH 01 / 2 / 12H / / 12H2O Å Ti–OH /1 2

[20] where log K * Å log KH (or pHznpc) 0

FIG. 9. Variation in pHznpc (or log KH ) and 12 pKw (long dashed line) with temperature (0–3007C). Values from the present study ( l ), and our earlier work (16, j ) include error estimates. The fit of Eq. [19] to the values from this study (excluding the 2957C value ( s )) is represented by the solid line. Also included are data from Fokkink (36, 1 ), an extrapolation of these data by Schoonen (15, short dashed line), and data from Berube and De Bruyn (23, / ).

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1 2

pKW .

[21]

Changes in net hydration and electrostriction are minimized for charge-balanced reactions. This simplifies extrapolation to higher temperatures and pressures, because the resulting heat capacity and volume changes are rather small. Other studies have noted that pHzpc-12 pKW values for various metal oxides are rather constant with temperature (60), but some studies have not (23, 61, 62). However, this study and our previous work (16) encompass a much wider temperature range than previous studies. The relative constancy of pHznpc-12 pKW is very useful for predictive purposes since a single room temperature pHznpc measurement for rutile would be sufficient for estimating the pHznpc to at least 3007C to within 0.2 pH units. Studies of other well-behaved oxides over similar temperature ranges are necessary to determine if the relative constancy of pHznpc-12 pKW is a more universal phenomenon.

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However, the similar temperature dependencies of 12 pKW and log KH (or pHznpc) values may be based, more fundamentally, on similarities in the ionization behavior of surface hydroxyl groups and water. Fokkink et al. (37) have argued that attaching a proton to a surface hydroxyl group causes only about 12 of the net hydration state changes that accompany H / and OH 0 reactions in solution, because of the presence of the surface. Moreover, it is likely that surface hydroxyl groups themselves are hydrated, and the ionization of these hydration waters may be the true source of proton uptake and release, similar to the hydrolysis behavior of metal ions in solution (63). If this proves true, the relative constancy of pHznpc-12 pKW may have wider use in rationalizing, as well as predicting, changes in pHznpc values with temperature. SUMMARY

Potentiometric titrations of metal oxide suspensions can be extended well into the virtually unexplored hydrothermal regime with the SHECC. As has often been observed in similar studies at lower temperatures, pretreatment and other experimental procedures can greatly influence the resulting titration curves. A final hydrothermal pretreatment step resulted in much improved titration curves (less hysteresis, better definition of the pHznpc) compared with our earlier work (16), due to the greater leaching of impurities (probably HCl) from the rutile surface during hydrothermal pretreatment. A 1pKa , three-layer surface complexation model could adequately describe the data over the wide range of temperatures (25 to 2507C) and ionic strengths (0.03 to 1.1 m) studied. Other surface complexation modeling approaches would likely produce similar fits, but the present approach depends on relatively few (three) variable model parameters. The most significant trend in the best-fit parameter values is the increase in the innermost capacitance value with increasing temperature. This reflects the closer approach of Na / to the negatively charged rutile surface (more efficient screening) with increasing temperature, as was noted in our previous study (16). Negative surface charge development in the presence of the larger TMA / cation was reduced (relative to Na / ), whereas positive surface charge development was rather constant with increasing temperature. These effects likely reflect the size and hydration state of the ions involved. Na / is smaller than TMA / and can approach the surface more closely, resulting in greater negative surface charge development above the pHznpc. Na / is also more strongly hydrated than TMA / or Cl 0 at room temperature and, in general, the association of strongly hydrated species increases with temperature (51). Thus, the increased association of Na / with the rutile surface may also be observed for other cation–metal oxide surface reactions with increasing temperature. The surface protonation constant (log KH ) can be equated

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with the pHznpc under the 1pKa approach, and this provides a formal link to the thermodynamic analysis of the temperature dependence of the observed pHznpc values. The difference between the pHznpc values and 12 pKW remains rather constant for rutile ( 01.45 { 0.2) with temperatures to at least 2507C. This is useful for predictive purposes, and may reflect a more fundamental similarity in the hydration state changes that accompany H / and OH 0 reactions in solution, and the protonation of surface hydroxyl groups on the rutile surface. Clearly, additional work along several fronts is warranted. The SHECC can be used to study other solids in the presence of various electrolytes and this should include species prone to specific adsorption at room temperatures, as well as direct measurement of adsorbed amounts. Direct spectroscopic approaches, so useful in characterizing adsorption at the molecular scale at room temperature (64, 65), should be applied to higher temperatures as well. Finally, various theoretical approaches (66, 67) could be applied to help guide future experimental work and to provide useful estimates in those instances where experimental data are difficult or impossible to obtain. ACKNOWLEDGMENTS We thank Robert E. Mesmer for helpful discussions. Michael Caughey, Tom Holm, and Nita Sahai graciously reviewed earlier versions of the manuscript. Reviews by Willem van Riemsdijk and Rene Rietra uncovered an error in the modeling approach, as well as several other errors and inconsistencies in the manuscript. The comments of an anonymous reviewer were also appreciated. This research project was partially sponsored by the Office of Basic Energy Sciences, U.S. Dept. of Energy, under Contract DEAC05-96OR22464, managed by Lockheed Martin Energy Corporation.

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