Langmuir 2003, 19, 3797-3804
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High Temperature Microelectrophoresis Studies of the Rutile/Aqueous Solution Interface Mark V. Fedkin,†,‡ Xiangyang Y. Zhou,† James D. Kubicki,§ Andrei V. Bandura,†,§ and Serguei N. Lvov*,†,‡ The Energy Institute, Department of Energy and Geo-Environmental Engineering, and Department of Geosciences, The Pennsylvania State University, University Park, Pennsylvania 16802
Michael L. Machesky Illinois State Water Survey
David J. Wesolowski Oak Ridge National Laboratory Received November 18, 2002. In Final Form: February 11, 2003 A recently developed high temperature microelectrophoresis cell was employed for ζ-potential measurements at the rutile/aqueous solution interface over a wide range of pH at temperatures of 25, 120, and 200 °C. Water, 0.001 mol kg-1 NaCl(aq), and 0.01 mol kg-1 NaCl(aq) solutions were tested at these temperatures. The desired pH values were attained by adding either HCl(aq) or NaOH(aq). The obtained experimental data allowed us to estimate isoelectric point pH values (pHiep) of 5.26 ((0.45) at 25 °C, 5.13 ((0.37) at 120 °C, and 4.50 ((0.55) at 200 °C. This decrease in pHiep values with increasing temperature agrees with the decease in point of zero net proton charge (pHznpc) pH values (as determined by potentiometric titration) observed for similar rutile powders in our previous studies. ζ-potential data were combined with the proton charge results and rationalized using a surface complexation modeling approach. Modeling results indicate that ζ-potentials are expressed at a distance that is generally equal to (within error) the so-called diffuse double layer thickness (κ-1).
Introduction Microelectrophoresis is one of the electrokinetic techniques that can be used to study metal oxide/water interface chemistry and aid in deciphering the structure of the electrical double layer (EDL). Conversion of measured electrophoretic mobilities into ζ-potentials (ZP ) ζ) results in a potential associated with the EDL. The ZP can be broadly defined as the potential at an ill-defined slipping plane between the bulk solvent and relatively “immobile” ions and molecules associated with the EDL.1,2 The pH value at which the ζ-potential equals zero is termed the isoelectric point pH (pHiep) and is a significant characteristic of metal oxide/water interfaces. An analogous quantity is the pHznpc value, at which the net proton induced surface charge equals zero, as determined by potentiometric titration.3-6 For well-behaved oxide surfaces in the presence of so-called “indifferent” electrolytes, * Corresponding author. E-mail:
[email protected]. † The Energy Institute. ‡ Department of Energy and Geo-Environmental Engineering. § Department of Geosciences. (1) Hunter, R. J. Zeta Potential in Colloid Science-Principles and Applications; Academic Press: London, 1981. (2) Lyklema, J. Fundamentals of Interface and Colloidal Science, Vol. II. Solid-Liquid Interfaces; Academic Press: San Diego, CA, 1995; Chapter 4. (3) Huang, C. P. In Adsorption of Inorganics at Solid-Liquid Interfaces; Anderson, M. A., Rubin, A. J., Eds.; Ann Arbor Sci: Ann Arbor, MI, 1981; p 183-217. (4) Berube, Y. G.; De Bruyn, P. L. J. Colloid Interface Sci. 1968, 27, 305. (5) Fokkink, L. G. J. Ion adsorption on oxides-surface charge formation and cadmium binding on rutile and hematite. Ph.D. dissertation, Wageningen Agricultural University, The Netherlands, 1987.
pHiep ) pHznpc, whereas differential adsorption affinities for cations versus anions in the electrolyte medium result in a shift of these quantities in opposite directions.7,8 Experimental methods for determining ZPs and pHiep values under ambient conditions are based on different kinds of electrokinetic phenomena.1,9 The electrokinetic approaches can be divided into two major categories: the moving boundary method and the microelectrophoresis method. Two common examples of the moving boundary method are (1) the streaming potential drop or streaming current (measured in a fine capillary) and (2) the streaming potential and current measured between two ends of a powder bed or a porous plug. To date, very limited effort has been made to measure ZP and pHiep values using electrokinetic methods at elevated temperatures. Alekhin and coauthors10 studied H+ adsorption and electrokinetic potential on γ-Al2O3 and SiO2 at temperatures from 25 to 250 °C using the streaming potential technique. A similar method was used by Jayaweera and coauthors11,12 to determine the ZP and pHiep values of a number of oxides (6) Ridley, M. K.; Machesky, M. L.; Palmer, D. A.; Wesolowski, D. J. Colloids Surf., A 2002, 204, 295. (7) Lyklema, J. Pure Appl. Chem. 1991, 63, 895. (8) Stumm, W. Chemistry of the Solid-Water Interface; Wiley: New York, 1992. (9) Fernandez-Nieves, A.; de las Nieves, F. J. J. Non-Equilib. Thermodyn. 1998, 23, 45. (10) Alekhin, Yu. V.; Sidorova, M. P.; Ivanova, L. I.; Lakshtanov, L. Z. Kolloidn. Zh. 1985, 46, 1195. (11) Jayaweera, P.; Hettiarachchi, S. Rev. Sci. Instrum. 1993, 64, 524. (12) Jayaweera, P.; Hettiarachchi, S.; Ocken, H. Colloids Surf., A 1994, 85, 19.
10.1021/la0268653 CCC: $25.00 © 2003 American Chemical Society Published on Web 03/25/2003
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Figure 1. Schematic of high temperature zetameter.
at 25 and 235 °C. In one of our recent studies,13 the ZP on a ZrO2 capillary tube in acidic hydrothermal solutions was roughly estimated at temperatures up to 400 °C. The other common method used to determine ZP and pHiep values is microelectrophoresis. This involves measuring the velocity of suspended particles in an electrical field. A high temperature zetameter based on the microelectrophoresis method was recently developed and tested in our laboratory, and the first high temperature tests for the ZrO2/water interface have been carried out.14 In this paper, we describe our effort to study the TiO2/H2O interface using the same high temperature microelectrophoretic zetameter at temperatures up to 200 °C. In addition, ζ-potential data are combined with previously published surface charge results15,16 and rationalized using a similar surface complexation modeling approach. Experimental Approach High Temperature Zetameter. A high temperature zetameter was recently developed in our laboratory (Figure 1). The detailed description of the experimental system is given elsewhere.14 The design of the zetameter allows the establishment of a constant, uniform electrical field between two Pt electrodes and the observation of the movement of suspended particles in the electrical field at temperatures up to 200 °C and pressures up to 50 bar. The suspension was loaded into the suspension column, which was maintained at room temperature and a desired pressure. The particles were delivered from the suspension column to the cell by the flow of the solution from a high pressure pump. The internal pressure was adjusted with a pressure-relief valve. The cell was heated with three coil heaters wound around the cell and inlet and outlet tubes. A long-focus Stereomaster (Fisher Scientific) microscope (magnification ×250) was used to observe the moving particles inside the electrophoretic cell. To avoid the interference of the electroosmotic flows of the electrolyte in the cell, the microscope was focused on the stationary plane, which is located in a closed cylindrical capillary cell at 0.146 × i.d. from the cell wall.17,18 (13) Lvov, S. N.; Zhou, X. Y.; Macdonald, D. D. J. Electroanal. Chem. 1999, 462, 146. (14) Zhou, X. Y.; Wei, X. J.; Fedkin, M. V.; Strass, K. H.; Lvov, S. N. Rev. Sci. Instrum. (in press). (15) Machesky, M. L.; Wesolowski, D. J.; Palmer, D. A.; IchiroHayashi, K. J. Colloid Interface Sci. 1998, 200, 298. (16) Machesky, M. L.; Wesolowski, D. J.; Palmer, D. A.; Ridley, M. K. J. Colloid Interface Sci. 2001, 239, 314. (17) Shaw, D. J. Electrophoresis; Academic Press: New York, 1969. (18) Minor, M.; van der Linde, A. J.; van Leeuwen, H. P.; Lyklema, J. J. Colloid Interface Sci. 1997, 189, 370.
Fedkin et al.
Figure 2. Data of ac-impedance spectroscopy for a 0.1003 mol kg-1 NaCl(aq) solution at 120 °C and 14 bar. Different curves show repeated runs. Electrical Field Strength. The electrical field strength in the electrophoresis cell, E, was evaluated as
E)
V l
(1)
where V is the applied dc potential difference between the electrodes, and l is the effective interelectrode distance. The effective distance was determined experimentally by measuring the electrical resistance of a 0.1 mol kg-1 NaCl solution between the electrodes in the electrophoresis cell. For a uniform electrical field, the resistance of the solution in the cell between two electrodes is defined as follows:
R)
1 l KA
(2)
where R is the electrical resistance of the solution (Ω), A is the cross-sectional area of the cell (cm2), l is the length of the cell (cm), and K is the electric conductivity of the medium (Ω-1 cm-1). Because the conductivity of NaCl(aq) solution is well-known over a wide range of concentration, temperature, and pressure,19-21 the ac impedance measurements performed in the electrophoretic cell enable the determination of the effective interelectrode distance (l) from eq 2. Thus, the high temperature electrophoretic cell was filled with a 0.1 mol kg-1 NaCl(aq) solution, and the resistance of the solution was measured by an ac-impedance spectroscopy method over a range of frequency from 0.2 to 10 000 Hz. The Pt electrodes used in the measurements had a cylinder shape with diameter of 2 mm and flat smooth surfaces. The electrodes were placed inside the quartz capillary cell (3 mm diameter) and spaced several millimeters apart. The experimental solution resistance data were plotted versus the inverse square root of frequency and extrapolated to zero in order to determine the limiting resistance (Figure 2). The results of the resistance measurements, along with the obtained effective (eq 2) and physical interelectrode distances, are presented in Table 1. The conductivity values for the 0.1 mol kg-1 NaCl(aq) solution used in these calculations are K ) 0.011 Ω-1 cm-1 at 25 °C (ref 20), K ) 0.0360 Ω-1 cm-1at 120 °C and FH2O ) 0.944 g cm-3 (refs 20 and 21), and K ) 0.043 Ω-1 cm-1 at 200 °C and FH2O ) 0.867 g cm-3 (ref 19). The effective distances obtained from the impedance measurements and the actual interelectrode distances measured under the microscope were found to be in good agreement. This result suggests that, in this particular cell, the electric field strength between the electrodes can also be evaluated using the geometrical position of the electrodes in the cell with an average accuracy of 5%. (19) Ho, P. C.; Palmer, D. A.; Mesmer, R. E. J. Solution Chem. 1994, 23 (9), 997. (20) Noyes, A. A.; Coolidge, W. D. J. Am. Chem. Soc. 1904, 26, 134. (21) Quist, A. S.; Marshall, W. L. J. Phys. Chem. 1968, 72 (2), 684.
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Table 1. Electrical Resistance, R, of an NaCl Solution (0.1003 mol kg-1) and Effective Distance between the Electrodes Estimated by Two-Electrode ac Impedance Spectroscopy T, °C
R, Ω (at 10 000 Hz)
conductivity, Ω-1/cm
effective distance, cm
physical distance, cm
25 25 120 120 120 120
211.5 227.5 93.0 94.4 637.8 637.9
0.012 0.012 0.036 0.036 0.036 0.036
0.180 0.193 0.237 0.241 1.625 1.625
0.20 0.20 0.24 0.24 1.70 1.70
Preparation of Solutions. Pure water and NaCl(aq) solutions (0.001 and 0.01 mol kg-1) were used as background electrolytes for preparation of TiO2 (rutile) suspensions. In each experiment, the same solution was used to fill the cell and to deliver the suspension. Before the experiment, the pH of the solution was adjusted at 25 °C by titration with either 0.1 mol kg-1 HCl(aq) or NaOH(aq). The pH was monitored using a Cole Parmer high precision glass pH electrode ((0.005 pH units), which was calibrated against standard buffer solutions [Oakton, pH ) 4.01, 7.00, and 10.00 ((0.01) at 25 °C]. The electrode reading that did not change by more than 0.03 pH units within several minutes was considered an equilibrium value. After the experiment, a sample of experimental solution was taken from the system, and pH was checked again at 25 °C. For relatively acidic and neutral solutions, the difference between the starting and final pH values was less than 0.05 units. For relatively basic solutions, the pH shift could not be completely avoided, and the 0.1 unit difference was taken as tolerable. The ionic strength, I, of the background solution was determined in each run from the initial concentration of the NaCl(aq) solution and the amounts of added HCl(aq) or NaOH(aq) using the following equation:
1 I ) [mNa+zNa+2 + mCl-zCl-2 + mH+zH+2 + mOH-zOH-2] 2
(3)
where mi and zi are respectively molalities and valences of ions. Preparation of Suspensions. A titanium oxide powder obtained from KRONOS, Inc. (KRONOS 4020, Lot #60170) was used in this study. The commercial material was wet-sieved through a 66 µm stainless steel screen, and about one-third of the material passed through the screen. The recovered fine fraction was rinsed repeatedly with deionized water (Barnstead Nanopure), allowing the suspension to settle for about 1 h after each agitation in approximately 5:1 water/solid by volume, in a closed, polyethylene bottle. After many washings, a clear supernatant was observed after 1 h of settling, and the pH was confirmed to be the same as that of fresh deionized water. The resulting solid was resuspended in deionized water and heated in a lidded Teflon container within a pressure vessel at 220 °C for several days. This process was repeated four times, with suspension-settling-decanting steps between each hydrothermal treatment. The powder was then dried in a vacuum oven at 80 °C overnight. BET multipoint N2 surface area analysis gave a highly reproducible value of 2.914 ( 0.004 m2 g-1. SEM images indicate that the powder consists of 3-50 µm, subspherical aggregates composed of sintered, anhedral to subhedral grains ranging from 0.1 to 1 µm in diameter. High resolution X-ray diffraction analysis using a rotating anode instrument indicated that the material is well-crystallized rutile, with no detectable crystalline contaminants. The rutile powder was added to the background solution in the amount of approximately 1 g of solid per liter of the solution. The suspensions were ultrasonicated for 10-30 min for better dispersion of the particles. The light-scattering analysis of sonicated TiO2 suspensions showed the average particle size of 10 µm. Because the stability of the suspension varied with pH, the amount of solid phase and the time of ultrasonication were changed accordingly in order to provide the optimal translucency of the suspension under the microscope. High Temperature pH. The pH of the solutions and suspensions used in the measurements was estimated using a high precision glass pH electrode at 25 °C. At elevated temper-
Table 2. Theoretical and Experimental Parameters Used for the Calculation of pH and ZP at Different Temperatures parameter
25 °C
120 °C
200 °C
Am, kg0.5 mol-0.5 Bm, kg0.5 mol-0.5 A-1 C, kg mol-1 a°, Å γH+ in pure H2O γH+ in 0.001 mol kg-1 NaCl γH+ in 0.01 mol kg-1 NaCl diss const of water, Kw assoc const of HCl, KHCl assoc const of NaOH, KNaOH assoc const of NaCl, KNaCl viscosity,a η, Pa s relative permittivity,a
0.505 0.328 0 4.56 0.990 0.965 0.903 1.0 × 10-14 0.253 0.382 0.170 8.95 × 10-4 79.0
0.563 0.347 0.0317 4.56 0.987 0.961 0.894 9.12 × 10-13 0.182 1.000 0.242 2.30 × 10-4 50.7
0.781 0.363 -0.0485 4.56 0.978 0.947 0.856 6.77 × 10-12 0.454 1.887 0.502 1.40 × 10-4 34.9
a Parameters determined using the NIST/ASME Steam Properties software.37
atures, the pH of the medium changed due to respective changes of the activity coefficients of ions, the water dissociation constant (Kw), and the association constants of HCl and NaOH. The following steps were taken to calculate the high temperature pH. The activity coefficient of a proton, γH+, in the expression
pH ) -log(mH+γH+)
(4)
was evaluated at each temperature using the third approximation of the Debye-Huckel theory:
log γi ) -
AmxIm 1 + Bma°xIm
(
+ CIm - log 1 +
)
mtotMw 1000
(5)
where Im is the ionic strength, mtot is the sum of molalities of all dissolved species, Mw is the molecular mass of water, Am and Bm are the Debye-Huckel theoretical parameters on the molal scale, and C and a° are the Debye-Huckel empirical parameters. The methods for evaluation of these parameters were described elsewhere22 (Table 2). The ionic strength on the molal scale (Im) and the sum of molalities (mtot) were determined at each experimental point from the concentration of the background NaCl solution and the amounts and concentrations of added titrants (HCl or NaOH). The activity coefficients of hydrogen ions obtained through eq 5 for different temperatures and electrolyte concentrations are presented in Table 2. The molality of protons in the solution, originally measured at 25 °C, was re-evaluated at higher temperatures taking into account the change in water dissociation constant (Kw) and constants of other ionic equilibria present in the system using mass and charge balance relationships. The high temperature Kw values used in calculations, 9.12 × 10-13 at 120 °C and 6.77 × 10-12 at 200 °C, were taken from the literature.22,23 The procedure of calculation of the high temperature pH was described in detail elsewhere.13,22,24 Our calculations indicate that the influence of the increasing extent of surface protonation as temperature increases on estimated pH values is insignificant (500),1,2 where κ is inverse double layer thickness and a is the particle radius. This condition is normally met at relatively high ionic strengths and relatively large particle sizes. On the basis of the average particle size in experimental TiO2 suspensions (10 µm), the κa values were estimated equal to 520 and 1650 for Im ) 0.001 mol kg-1 and Im ) 0.01 mol kg-1, respectively. Thus, the Smoluchowski theory was accepted as an adequate approximation for the µ-ζ relationship for this particular experimental system.
Results and Discussion Electrophoretic Mobility and ζ-Potential. The values of pH, ionic strength, velocity, mobility, ζ-potential, and the standard deviation of the ζ-potential at each temperature are given in Tables 3-5. The electrophoretic mobility and ζ-potential shown at each pH were calculated as the average values of up to fifty repeated measurements made under identical conditions. The negative sign of the velocity and mobility indicates that the particles traveled
Table 3. Experimental Microelectrophoresis Data and Calculated ζ-Potentials for TiO2 Suspensions Measured at 25 °C and 1 bar
pHa
104I, mol kg-1
v, µm s-1
E, V cm-1
µ, 10-8 m2 V-1 s-1
ζ, mV
SD of ζ,b mV
4.00 5.00 5.40 7.00 8.00 9.40 2.90 3.30 4.00 4.60 5.25 6.00 6.70 7.75 9.00
0.30 0.25 0.17 0.05 0.10 0.27 12.08 11.12 10.86 10.50 10.25 10.18 10.68 10.44 11.02
20.1 8.6 0.5 -25.0 -31.4 -40.7 10.5 9.8 11.9 7.8 -2.0 -14.6 -17.1 -19.0 -20.6
7.5 7.5 7.5 7.5 7.5 7.5 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0
2.68 1.14 0.06 -3.34 -4.19 -5.43 2.11 1.95 2.37 1.55 -0.39 -2.92 -3.41 -3.80 -4.12
34.3 14.6 0.8 -42.7 -53.6 -69.5 27.0 25.0 30.4 19.9 -5.0 -37.4 -43.7 -48.6 -52.7
8.3 11.5 20.8 4.7 7.0 14.3 4.5 8.0 5.3 16.1 28.0 7.0 7.0 12.2 10.0
a The pH of the solutions was adjusted by adding HCl(aq) or NaOH(aq). b SD refers to standard deviation.
Table 4. Experimental Microelectrophoresis Data and Calculated ζ-Potentials for TiO2 Suspensions Measured at 120 °C and 14 bar
pHa
104I, mol kg-1
v, µm s-1
E, V cm-1
µ, 10-8 m2 V-1 s-1
ζ, mV
SD of ζ,b mV
3.40 4.11 4.15 4.40 5.85 5.94 6.03 6.17 6.18 6.25 6.69 7.36 3.54 4.34 4.62 5.48 5.90 6.01 6.02 6.07 6.44 4.05 4.57 6.01 6.06 7.09
0.84 0.47 0.47 0.43 0.27 0.13 0.69 2.30 0.96 0.56 1.14 1.52 11.66 10.68 10.48 10.10 10.11 10.22 10.80 10.26 10.45 100.86 100.39 100.49 100.64 100.49
81.4 27.3 40.2 41.3 -71.9 -71.3 -98.1 -80.5 -104.6 -75.0 -97.5 -100.0 87.2 136.2 21.3 -21.5 -60.4 -104.1 -139.6 -85.8 -99.8 67.0 81.5 -30.8 -34.9 -58.7
5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 12.6 18.8 8.0 8.0 11.3 12.6 18.0 8.9 8.9 10.4 14.1 10.4 10.4 13.8
16.28 5.46 8.03 8.27 -14.39 -14.27 -19.61 -16.10 -20.92 -15.01 -19.49 -20.00 6.91 7.25 2.66 -2.69 -5.32 -8.25 -7.76 -9.69 -11.25 6.43 5.80 -2.95 -3.35 -4.27
83.5 28.0 41.2 42.4 -73.8 -73.2 -100.6 -82.6 -107.3 -77.0 -100.0 -102.6 35.4 37.2 13.7 -13.8 -27.3 -42.3 -39.8 -49.7 -57.7 33.0 29.7 -15.1 -17.2 -21.9
25.2 26.5 25.0 15.0 5.8 9.5 8.4 12.6 13.7 5.3 10.4 14.6 7.2 8.5 5.0 26.0 10.0 10.0 8.0 8.3 22.1 10.7 7.4 10.0 6.3 12.0
a The pH of the solutions was adjusted by adding HCl(aq) or NaOH(aq). b SD refers to standard deviation.
in the direction opposite to the electrical field vector. The ZP data plotted versus pH at 25, 120, and 200 °C are shown in Figures 3-5. The relative errors of the ζ-potential tend to increase at the pH values closest to the isoelectric point (IEP) for a few reasons. First, due to the low magnitude of the ζ-potential, particles responded weakly to the electrical field and were more difficult to track visually. Second, the suspension probably contained both negatively and positively charged particles, which could simultaneously or alternately move in opposite directions. This might happen if some of the particles or particle aggregates had already changed their surface charge to the opposite sign, while others still had not. Since adsorption/desorption is a continuous dynamic process, we can suspect that, in the pH region close to IEP, the
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Langmuir, Vol. 19, No. 9, 2003 3801
Table 5. Experimental Microelectrophoresis Data and Calculated ζ-Potentials for TiO2 Suspensions Measured at 200 °C and 40 bar
pHa
104I, mol kg-1
v, µm s-1
E, V cm-1
µ, 10-8 m2 V-1 s-1
ζ, mV
SD of ζ,b mV
2.88 3.69 3.84 4.13 4.99 5.46 5.54 5.57 5.58 5.63 5.68 6.09 6.20 3.01 3.71 4.49 5.06 5.50 5.55 5.60 5.62
1.50 0.68 1.40 0.35 0.20 1.95 0.14 0.10 1.50 1.70 0.75 1.90 0.52 12.7 10.9 10.3 10.2 10.0 10.0 10.2 10.3
70.3 23.0 56.6 -17.3 -71.7 -52.9 -50.5 -83.8 -78.0 -77.8 -107.5 -110.2 -105.9 32.3 38.7 19.2 -16.1 -43.9 -45.3 -35.7 -71.8
7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0
9.37 3.06 7.55 -2.30 -9.56 -7.05 -6.74 -11.18 -10.39 -10.37 -14.33 -14.69 -14.12 5.38 6.46 3.21 -2.69 -7.32 -7.55 -5.95 -11.97
39.5 12.9 31.8 -9.7 -40.3 -29.7 -28.4 -47.1 -43.8 -43.7 -60.4 -61.9 -59.5 24.4 29.3 14.6 -12.2 -33.2 -34.3 -27.0 -54.3
14.2 23.7 23.4 24.6 24.7 18.7 17.6 19.3 18.2 18.7 18.7 15.7 20.2 22.6 19.3 19.9 20.5 21.0 18.6 13.1 21.1
Figure 4. ζ-potential at the rutile/aqueous solution interface as a function of pH measured at 120 °C and 14 bar. Background electrolyte: pure water (circles), 0.001 mol kg-1 NaCl(aq) (squares), and 0.01 mol kg-1 NaCl(aq) (triangles). The solid lines represent modeled ζ-potential values at 0.001 and 0.01 mol kg-1. The pH was adjusted by adding either HCl(aq) or NaOH(aq).
a The pH of the solutions was adjusted by adding HCl(aq) or NaOH(aq). b SD refers to standard deviation.
Figure 5. ζ-potential at the rutile/aqueous solution interface as a function of pH measured at 200 °C and 40 bar. Background electrolyte: pure water (circles), 0.001 mol kg-1 NaCl(aq) (squares). The solid line represents modeled ζ-potential values at 0.001 mol kg-1. pH was adjusted by adding either HCl(aq) or NaOH(aq). Figure 3. ζ-potential at the rutile/aqueous solution interface as a function of pH measured at 25 °C and 1 bar. Background electrolyte: pure water (circles) and 0.001 mol kg-1 NaCl(aq) (squares). The solid line represents modeled ζ-potential values for the 0.001 mol kg-1 data, as explained in the text. The pH was adjusted by adding either HCl(aq) or NaOH(aq).
particles have a surface charge slightly oscillating between negative and positive values rather than steadily fixed near zero. To this end, the bulk suspension can hardly be regarded as a perfectly uniform system with strictly defined IEP. One can rather consider the IEP range within which all particles in the system have to switch the sign of their surface charge. With increasing ionic strength of the background electrolyte, the magnitude of the ζpotential deceases slightly, and this is most obvious in the comparison of 0.001 and 0.01 mol kg-1 NaCl solutions at 120 °C. The increase of ionic strength to 0.01 mol kg-1 always caused stronger electrolysis at Pt electrodes and also resulted in more intense aggregation of the TiO2 particles. Both of these processes were unfavorable for consistent measurements of particle velocity; therefore, only a few experimental points at only one temperature (120 °C) were obtained in 0.01 mol kg-1 NaCl. The difference between the rutile suspensions based on water and 0.001 mol kg-1 NaCl is relatively small and, in most cases, remains within the error bars.
Isoelectric Points. Obtained experimental ζ data were treated with surface complexation models (as described in the next section), and the pHiep values for the TiO2/ NaCl(aq) interface were determined. These values are listed in Table 6. Experimentally obtained pHiep values of rutile at different temperatures compared with some previously published data are shown in Figure 6. The decrease of pHiep with increasing temperature agrees with previous surface charge titration studies, and this trend correlates with the temperature dependence of log Kw. Similar zerocharge points at 25 °C were found in some previous studies: 5.4,6,16 5.5,5 and 5.5.25 At the same time, many authors reported significantly higher pHznpc or pHiep values: 6.1,26 5.9,27 and 6.0.4 According to some studies,28,29 surface charging on rutile is very sensitive to the preexperimental hydration state of the particle surface. Depending on the thermal pretreatment procedure, dry(25) Golikova, E. V.; Rogova, O. M.; Shelkunov, D. M.; Chernoberezhskii, Yu. M. Colloid J. 1995, 57 (1), 25. (26) Kallay, N.; Colic, M.; Fuerstenau, D. W.; Jang, H. M.; Matijevic, E. Colloid Polym. Sci. 1994, 272, 554. (27) Jang, H. M.; Fuerstenau, D. W. Colloids Surf. 1986, 21, 236. (28) Parks, G. A. Chem. Rev. 1965, 65, 177. (29) Contescu, C.; Popa, V. T.; Schwartz, J. A. J. Colloid Interface Sci. 1996, 180, 149.
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Table 6. Relevant Experimental Quantities and Model Parametersa temp (I.S) m)b
25 °C, (0.001 120 °C, (0.001 m)c 120 °C, (0.01 m)c 200 °C, (0.001 m)b a
pHiep
SD
pHznpcb
SD
pHppzcc
DS (nm)
SD
κ-1
Cs
log KH1
log KH2
log KM
log Ka
MSCd
5.26 5.13 5.13 4.50
0.45 0.37 0.37 0.55
5.40
0.20
4.30
0.20
5.66 4.77 4.77 4.43
8.09 6.12 3.52 9.50
2.87 1.33 1.63 1.39
9.28 8.91 2.89 8.44
2.10 2.40 2.40 3.12
6.07 5.10 5.10 4.73
5.27 4.43 4.43 4.11
14.252 14.430 14.430 14.630
-2.700 -2.030 -2.030 -1.465
1.42 2.30 0.19 1.66
b
SD refers to standard deviation. Values from ref 16. c pHppzc adjusted to approximate measured pHiep values. (goodness of fit indicator).
d
Model selection criterion
Figure 7. Schematic of the basic Stern music model, including the slipping plane distance (DS) parameter. The various surface and Stern layer potential and charge terms are indicated by (ψ) and (σ), respectively. KH1 and KH2 refer to surface protonation constants, and KM and KA refer to electrolyte cation and anion binding constants, respectively. Nst is the total site concentration, and CS is the Stern layer capacitance. Figure 6. Experimental isoelectric points and zero net proton charge points for TiO2 (rutile) at the temperatures 25-250 °C.
ing, and storage conditions, the pHzpc of rutile at 25 °C can vary between about 4.2 and 6.8. Thus, the history of the powder is one of the reasons for the high scatter of experimental data on surface properties of TiO2 at ambient conditions. Bourikas and coauthors30 give a mean rutile pHzpc value at 25 °C of 5.9 ( 0.2, on the basis of the previous literature. Moreover, the 25 and 200 °C pHiep values obtained in this study are in fair agreement with pHznpc values determined by acid-base titrations of a similar rutile power.15 The high temperature pHiep of TiO2 reported by Jayaweera and Hettiarachchi,11 6.6 at 235 °C, is high when compared to the pHiep obtained in our electrophoretic study at 200 °C and to pHzpc values previously measured by Machesky and coauthors.15 At room temperature, the same TiO2 material showed the pHiep ) 8.9, which is much higher than typical rutile values.30 This fact and the absence of any information about the nature and treatment of the TiO2 powder used suggest that Jayaweera and Hettiarachchi’s pHiep values are atypical. Rationalization of ζ-Potential Values Using Surface Complexation Models. One use of ζ-potential data for surface complexation modeling is in the determination of pHiep values and how these pHiep values change due to the specific adsorption of ions.31 For example, the specific adsorption of alkaline earth cations by rutile shifts pHiep values progressively higher until ultimately ζ-potential values remain positive over the accessible pH range.27 Away from the pHiep, the ζ-potential is expressed at some ill-defined distance into the diffuse layer portion of the EDL.2 A useful way to quantify this distance within the context of a given surface complexation model is to consider this slipping plane distance as an additional model dependent fitting parameter.30,31 Ideally, this modeling (30) Bourikas, K.; Hiemstra, T.; van Riemsdijk, W. H. Langmuir 2001, 17, 749. (31) Dzombak, D. A.; Morel, F. M. M. Surface Complexation ModelingHydrous Ferric Oxide; Wiley: New York, 1990; Chapter 4.
exercise should be performed using titration and ζpotential data collected from the same solid in parallel or simultaneous experiments. For the present purpose, these data were collected on different rutile powders because a coarser-grained powder was needed for microscopic observation of the electrophoretic mobility, and this larger grain size interfered with the pH titration technique used by Machesky et al.15 An additional difference was the lower ionic strength range in the present investigation (10-4 to 0.01 mol kg-1, vs 0.03 to 1 mol kg-1). However, since the pHiep values obtained in this study are similar to the pHznpc values obtained with a finer-grained powder,15 it was considered reasonable to combine the results from both studies and to rationalize them with a common modeling framework. The specific surface complexation model used for this purpose is the temperature-compensated MUSIC model of surface protonation, in combination with the basic Stern representation of the EDL structure. A schematic of this model is given in Figure 7. The MUSIC model allows estimation of surface protonation constants, and the temperature-compensated MUSIC model is described in detail elsewhere.16 A necessary input parameter of the MUSIC model approach is the Ti-O bond length for protolyzable surface groups. Most previous applications (e.g. ref 32) have assumed that surface Ti-O bond lengths as well as the types and relative proportions of present surface groups are equal to those present on the bulk crystallographic planes expressed at the surface. Machesky et al.16 found it necessary to modify these assumptions in order to closely match predicted with experimental pHznpc values for their particular rutile sample, which was dominated by the (110) crystallographic plane.6 The proportion of singly to doubly coordinated surface oxygen groups was changed from the ideal ratio of 0.50:0.50 to 0.402:0.598, and the bond length of the singly coordinated oxygen was decreased from the bulk value of 1.98 to 1.94 Å, to obtain a predicted point of zero charge that matched the experimental value (5.40). (32) Hiemstra, T.; Venema, P.; Van Riemsdijk, W. H. J. Colloid Interface Sci. 1996, 184, 680.
Rutile/Aqueous Solution Interface
Figure 8. Rutile (110) surfaces as calculated with DFT were used to estimate (a) Ti-OH and (b) Ti-Obr bond lengths. These results are only estimates of the actual bond lengths because neutral surfaces were modeled and the experimental surfaces have a negative charge.
More recently, we have employed periodic density functional methods to calculate surface Ti-O bond lengths for use in the MUSIC model. A cell consisting of 1 × 2 rutile unit cells (1 cell in the x-direction and 2 cells in the y-direction) was created to model the (110) surface geometry (Figure 8). The (110) surface normal is in the z-direction, and the (110) faces in this direction were separated by a vacuum gap of 10 Å. The atomic positions of the central layer were fixed at the experimental crystal geometry to mimic the constraint of the bulk crystal structure. The slab was symmetric (space group P2) about this plane, which makes the calculations more efficient. All other atoms were allowed to relax, but the unit cell parameters were constrained to the experimental values. The minimum energy structures of the slab models were determined using the CASTEP module33 of Cerius-2 (Accelrys Inc., San Diego, CA). The generalized gradient approximation (GGA)34 and ultrasoft pseudopotentials were used, allowing us to apply a relatively small plane wave cutoff energy of 340 eV. The default CASTEP Monkhorst-Pack scheme35 was used for choosing k-points. Surface Ti-O distances calculated with periodic density functional methods were significantly different from the Ti-O distances in bulk rutile. For example, the calculated Ti-O bond length for a singly coordinated Ti-OH group on the surface was 1.90 Å (compared to 1.98 Å in bulk; Figure 8a), whereas an average bond length near 1.86 Å was calculated for the doubly coordinated Ti2-O surface group (compared to 1.94 Å in bulk; Figure 8b). The reader is cautioned that these bond lengths were calculated for a neutral surface of hydrated rutile (110) in a vacuum and that charging and solvation of the hydrated surface should change calculated Ti-O bond lengths. More fully hydrated models of negatively charged surfaces should be modeled in the future to provide more accurate predictions of surface Ti-O bond lengths. Use of the above-calculated Ti-O bond lengths along with a 0.50:0.50 distribution of singly and doubly coordinated surface sites in the MUSIC model results in a calculated point of zero charge of about 4.77, which is less than most experimentally determined values for rutile powders.30 A slight increase in these bond lengths to 1.916 Å for the singly coordinated surface site (e.g., Ti-OH) and 1.890 Å for the doubly coordinated surface site (e.g., Ti2-O) results in predicted point of zero charge pH values (33) MSI Molecular Simulations User’s Guide, CASTEP-Cambridge Serial Total Energy Package Version 4.2; San Diego, CA, 1999. (34) Perdew, J. In Electronic structure of solids ′91; Ziesche, P., Eschrig, H., Eds.; Akademic Verlag: Berlin, 1991. (35) Monkhorst, H. J.; Pack, J. D. Phys. Rev. 1976, 13, 5188.
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that closely match (to within 0.06 pH units) experimentally observed values over the range 10-250 °C.6,15 Thus, the CASTEP calculations were able to provide a first-order approximation to the surface Ti-O bond lengths that was useful in fitting the data. Increasing the model hydration of the surface, modeling negatively charged surfaces, increasing the cutoff energy in the calculation, and increasing the amount of relaxation allowed in the slab may be required before the model Ti-O bond lengths would be accurate enough without modification. These Ti-O bond lengths were readjusted to 1.925 and 1.89 Å, respectively, to more closely match the estimated pHiep values determined in the present study. The resulting pHppzc values are then within 1 standard deviation of measured pHiep values at all studied temperatures (Table 6). The surface charge data15 were fit to the basic Stern EDL model using revised surface protonation constants that result from the modified Ti-O bond distances. In addition, Na+ was assumed to bind in a tetradentate configuration (2 singly coordinated Ti-OH groups and 2 Ti2-O groups), on the basis of in-situ X-ray standing wave measurements on single-crystal rutile (110) surfaces.36 The resulting best-fit constants (Stern layer capacitance (Cs), Na+ binding constant (KM), and Cl- binding constant (KA)) were then held constant during the modeling of the ζ-potential data. Model parameter values at 120 °C were estimated from available 100 and 150 °C values, since surface charge titration data were not available at 120 °C. Consequently, the slipping plane distance, Ds, (from the head of the diffuse layer) was the only variable parameter for fitting the ζ-potential data. ζ-potential values consistent with the basic Stern EDL model (Figure 7) were calculated with the following equation valid for 1:1 electrolytes,
ζ)
[ [ ]
( )
]
Fψd 4RT arctanh tanh exp(-κDs) F 4RT
(8)
where ψd is the potential at the head of the diffuse layer, κ is the so-called Debye-Hu¨ckel parameter, Ds is the slipping plane distance from the head of the diffuse layer, and R, T, and F are the gas constant, absolute temperature, and the Faraday constant, respectively. In eq 8 the DebyeHu¨ckel parameter is given by
κ)
( [
x
2F2
]
mtotFw × 1000 1 + 0.001mtotMw 0RT
)
(9)
where Fw is the solution density, is the relative permittivity of the medium, and 0 is the permittivity of a vacuum. The term with square brackets in eq 9 converts molal to molar concentration units, as typically used for the GuoyChapman theory. The inverse of κ is the so-called double layer thickness (κ-1). ζ-potential values from Tables 3-5 were fitted by nonlinear least-squares regression using eq 8, relevant equations for the basic Stern EDL model,16 and the parameter values given in Table 6. The resulting curves of predicted ζ-potential versus pH are compared with the experimental results in Figures 3-5. Best-fit values of Ds extracted from the fitting exercise are given in Table 6, (36) Fenter, P.; Cheng, L.; Rihs, S.; Machesky, M.; Bedzyk, M. J.; Sturchio, N. C. J. Colloid Interface Sci. 2000, 225, 54. (37) Klein, S. A.; Harvey, A. H. NIST/ASME Steam Properties. Formulate for General and Scientific Use. NIST Standard Reference Database 10 - Version 2.0; U.S. Department of Commerce: 1996.
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along with the standard deviation of this parameter (SD) and the model selection criterion (MSC), which is a measure of the goodness of fit (larger is better). For the most part, fitted ζ-potential values are within 2 standard deviations of the experimental values. The least satisfactory fit occurs at low pH for the 0.01 mol kg-1 NaCl solution data at 120 °C. In this instance, the fit curve significantly underestimates experimental ζ-potential values. Note, however, that the experimental ζ-potential values for 0.01 and 0.001 mol kg-1 NaCl solutions are identical (within experimental error) at low pH, in contrast to the case of high pH, where the 0.01 mol kg-1 NaCl solution data are lower in absolute magnitude. This decrease is expected, since increasing ionic strength compresses electrical double layers. Consequently, the data rather than the model are probably responsible for the especially poor fit at low pH in 0.01 mol kg-1 NaCl solution. Best-fit Ds values are generally within one standard deviation of κ-1 values. At 25 °C, the empirical relation developed by Bourikas et al.30 would predict that Ds < κ-1. For example, in 0.001 mol kg-1 NaCl solution and at 25 °C, κ-1 is about 9.6 nm, while Bourikas would estimate Ds at about 6.7 nm. This latter value is also within one standard deviation of the best-fit value estimated in this study for the 0.001 mol kg-1 NaCl solution at 25 °C (8.09 ( 2.87 nm). There is not a clear trend in the value of Ds with increasing temperature at constant ionic strength, but there is no a priori method for predicting the position of the shear plane as a function of these variables, since it may depend on a complex interplay of ion binding constants at the Stern plane, diffusivity of water and ions within the EDL, changes in the dielectric constant and hydrogen bonding network of water with temperature, and changes in the effectiveness of counterion shielding with temperature. Clearly, more data from parallel ζ-potential and surface titration measurements on the
Fedkin et al.
same solids over a wide temperature and ionic strength range will be necessary to refine the relationship between Ds and κ-1. Conclusions This paper represents the first experimental-theoretical study of the ζ-potential of an oxide powder suspension in water ever reported over a wide range of temperatures, pH values, and ionic strengths extending into the hydrothermal regime. The ZP data obtained in this study by the microelectrophoresis technique are shown to be consistent with surface charge density and pHznpc data obtained by potentiometric pH titrations of similar powder suspensions of the same mineral (rutile) over a similar pH-temperature range.6,15,16 The combination of these results enables the location of the shearing plane to be estimated within the context of the electrical double layer and surface site complexation model, which was used to rationalize the combined data sets (basic Stern MUSIC). Further advances with this approach will be enhanced by improvements in the experimental apparatus, which will enable extending the range of temperature, electrolyte concentration, and particle size used for the high temperature electrophoresis technique. Acknowledgment. The authors gratefully acknowledge the financial support of this work by the U.S. Department of Energy (Contract #DE-AC05-00OR22725) and the National Science Foundation (Grant # EAR0073722). M.L.M also acknowledges the support of the Illinois State Water Survey and the Illinois Department of Natural Resources. Lawrence M. Anovitz is gratefully acknowledged for his generous help with the characterization of the rutile powder used in this study. LA0268653
