Ion Pair Formation and Primary Charging Behavior ... - ACS Publications

The primary charging behavior of titanium oxide (anatase, rutile, and P25) and the ion pair formation of the electrolyte ions with the surface groups ...
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Langmuir 2001, 17, 749-756

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Ion Pair Formation and Primary Charging Behavior of Titanium Oxide (Anatase and Rutile) K. Bourikas,† T. Hiemstra,* and W. H. Van Riemsdijk Department of Environmental Sciences, Wageningen University, P.O. Box 8005, NL 6700 EC Wageningen, The Netherlands Received June 8, 2000. In Final Form: November 11, 2000 The primary charging behavior of titanium oxide (anatase, rutile, and P25) and the ion pair formation of the electrolyte ions with the surface groups have been extensively studied. A large number of titration and electrokinetic data sets available in the literature have been successfully described, using the MUSIC (MultiSite Complexation) model with a Basic Stern double-layer option and applying the ion pair formation concept. The systematic analysis of the data, over a large number of different monovalent electrolytes and various ionic strength values, allowed the determination of a number of “best estimated” values for the ion pair formation constants. The values suggest that the interaction of the cations with the titania surface is stronger than that of the anions. This is in accordance with the observed shift of the IEP of titanium oxide to higher pH values, at high electrolyte concentrations. The binding of the cations follows the sequence Cs+ < K+ < Na+ < Li+ and that of the anions follows the sequence Cl- > NO3- > ClO4- > I-. Titanium oxide can be divided in two classes of materials, having a low (C ) 0.9 F m-2) and a high (C ) 1.6 F m-2) capacitance value, respectively. The low capacitance value corresponds with the low values found for well-crystallized gibbsite and goethite. On the basis of the low capacitance value and the absence of correlation with the dielectric properties of the solids, it is hypothesized that the first layer of physically adsorbed water has a unique relative dielectric constant  of about 40 on well-crystallized oxides. The high capacitance may correspond to a situation with a distorted water layer, which has bulk water properties ( ) 78). No other significant differences between the interfacial charging parameters of anatase and rutile were found.

Introduction The interface between titanium oxide and aqueous solutions is of great importance in many fields of chemistry. More particularly, a large number of studies in colloid chemistry, environmental chemistry, and catalysis deal with adsorption phenomena of this interface. Many researchers have focused on ion adsorption. It is wellknown that the surface complexation is strongly influenced by the development of surface charge, resulting in an electrostatic double layer present between the electrolytic solution and the oxide surface. The primary surface charge is determined by the reaction of protons with the surface. It is influenced by ion pair formation of the background electrolyte, which partly neutralizes the surface charge. The study of the primary charging of titanium oxide in relation to the electrolyte ion adsorption is the main aim of this work. A wide variety of models have been used to describe proton binding behavior at mineral/aqueous solution interfaces.1-14 Most site binding models are a combination * To whom correspondence should be addressed. † On leave from the Department of Chemistry, University of Patras and the Institute of Chemical Engineering and HighTemperature Chemical Processes, ICE/HT-FORTH, P.O. Box 1414, GR - 26500 Patras, Greece. (1) Schindler, P.; Stumm, W. In Aquatic Surface Chemistry; Stumm, W., Ed.; Academic Press: New York, 1987. (2) Davis, J. A.; James, R. O.; Leckie, J. O. J. Colloid Interface Sci. 1978, 63, 480. (3) Stumm, W.; Huang, C. P.; Jenkins, S. R. Croat. Chem. Acta 1970, 42, 223. (4) Hunter, R. J.; Wright, H. J. L. J. Colloid Interface Sci. 1971, 37, 564. (5) Yates, D. E. Ph.D. Thesis, University of Melbourne, 1975. (6) Schindler, P.; Kamper, H. R. Helv. Chim. Acta 1968, 51, 1781. (7) Healy, T. W.; White, L. R. Adv. Colloid Interface Sci. 1978, 9, 303. (8) Westall, J.; Hohl, H. Adv. Colloid Interface Sci. 1980, 12, 265. (9) Yates, D. E.; Levine, S.; Healy, T. W. J. Chem. Soc., Faraday Trans. 1 1974, 70, 1807.

of surface reactions and an electrostatic approach. Often these models are able to describe proton adsorption data quite satisfactorily. The physical chemical picture of the models used is however very different. As a result, an objective picture of the intrinsic properties of the titanium oxide/solution interface is difficult to obtain because each calculated set of the interfacial parameters depends on the specific model applied. Moreover, these parameter sets are not necessarily unique, making the comparison of results of different studies quite complicated. To improve the models, it is important to incorporate surface chemical information about the proton reaction of surface groups. A crystallographic analysis of the surface may provide the chemical surface composition. The corresponding relevant parameters should not be a priori available as fitting parameters. The analysis may also serve to define the chemical reactions. This approach can be combined with a systematic analysis of available surface titration and electrokinetic data over a large variety of different types of titanium oxide as well as of different electrolytes. It may provide a consistent set of parameters and may improve the knowledge of the solid/water interface of TiO2. A series of data sets concerning various minerals have been previously analyzed by Sahai and Sverjensky.15 They used the well-known homogeneous two-pK model for the surface charging mechanism.3,7,9,10 The homogeneous model is not connected to a detailed physical-chemical (10) Davis, J. A.; Leckie, J. O. J. Colloid Interface Sci. 1978, 67, 90. (11) Dzombak, D. A.; Morel, F. M. M. In Surface Complexation Modeling: Hydrous Ferric Oxide; Wiley: New York, 1990. (12) Bowden, J. W.; Posner, A. M.; Quirk, J. P. Aust. J. Soil Res. 1977, 15, 121. (13) James, R. O.; Parks, G. A. In Surfaces and Colloid Science; Matijevic, E., Ed.; Plenum: New York, 1982; Vol. 12, Chapter 2. (14) Bolt, G. H.; Van Riemsdijk, W. H. In Soil Chemistry B: Physicochemical Models; Bolt, G. H., Ed.; Elsevier: Amsterdam, 1982. (15) Sahai, N.; Sverjensky, D. A. Geochim. Cosmochim. Acta. 1997, 61, 2801.

10.1021/la000806c CCC: $20.00 © 2001 American Chemical Society Published on Web 01/11/2001

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picture of the oxide’s surface. Two types of reactive surface groups characterize the titanium dioxide surface. It is important to distinguish both, because they have a different reactivity with respect to for instance oxyanions16 and organic acids.17 For our analysis, we use the MultiSite Complexation (MUSIC) model37-39 in combination with the Basic Stern model for the double layer.37 In the present study, we will model a large number of surface titration and electrokinetic data sets available in the literature,17-36 concerning both types of crystalline titanium oxide, anatase17-28 and rutile.22,29-36 The main goals of our work are (i) the comparison of experimental charging data measured in a variety of monovalent electrolytes, over a wide range of ionic strengths, and (ii) the determination of a consistent set of parameter values, through a systematic analysis of the data, for the description of the anatase and/or rutile-electrolytic solution interface.

Bourikas et al.

of anions and cations shifts the PZC to a higher or lower pH value. The most widely used model for the description of the charging behavior of metal oxides has been the one-site/ two-pK model (e.g., refs 1-3). It assumes one hypothetical type of surface site, which may adsorb or desorb a proton, reflecting in a simple manner the amphoteric character of an oxide. However, no connection is made between the charging behavior and the actual presence of the various types of surface groups, known from spectroscopy.40 To make this connection, a new model, called the MUSIC (MultiSite Complexation) model,37-39 has been introduced. It explicitly accounts for the various types of surface groups, known from a surface structural analysis. The model uses the concept of local neutralization of charge as introduced by Pauling.41 If the charge of the metal ion in the solid is equally distributed over the surrounding ligands, the bond valence, ν, is defined as the charge z of the metal ion divided by its coordination number CN:

Surface Site Binding Model The charging of an oxide’s surface is due to its reaction with protons. It is well-known that metal oxides have an amphoteric character, able to adsorb and desorb protons, leading to a positive, neutral, or negative surface charge. The pH at which the surface is uncharged, in the absence of specifically adsorbed ions, is called the pristine point of zero charge (PPZC) or simply PZC. The surface charge is also dependent on the ionic strength. Titrations performed at different values of ionic strength give a common intersection point (CIP), when electrolyte ions have no specific influence. The pH that corresponds to the CIP is then called the PZC of the oxide. Unequal affinity (16) Bourikas, K.; Hiemstra, T.; Van Riemsdijk, W. H. Submitted for publication. (17) Giacomelli, C.; Avena, M. J.; De Pauli, C. P. Langmuir 1995, 11, 3483. (18) Kosmulski, M.; Gustafsson, J.; Rosenholm, J. B. J. Colloid Interface Sci. 1999, 209, 200. (19) Kosmulski, M.; Matijevic, E. Colloids Surf. 1992, 64, 57. (20) Janusz, W.; Kobal, I.; Sworska, A.; Szczypa, J. J. Colloid Interface Sci. 1997, 187, 381. (21) Janusz, W.; Sworska, A.; Szczypa, J. Colloids Surf., A 1999, 152, 223. (22) Sprycha, R. J. Colloid Interface Sci. 1984, 102, 173. (23) Spanos, N.; Georgiadou, I.; Lycourghiotis, A. J. Colloid Interface Sci. 1995, 172, 374. (24) Akratopulu, K. Ch.; Kordulis, Ch.; Lycourghiotis, A. J. Chem. Soc., Faraday Trans. 1990, 86, 3437. (25) Rodrı´guez, R.; Blesa, M. A.; Regazzoni, A. E. J. Colloid Interface Sci. 1996, 177, 122. (26) Foissy, A.; M’ Pandou, A.; Lamarche, J. M.; Jaffrezic-Renault, N. Colloids Surf. 1982, 5, 363. (27) Janssen, M. J. G.; Stein, H. N. J. Colloid Interface Sci. 1986, 111, 112. (28) Girod, G.; Lamarche, J. M.; Foissy, A. J. Colloid Interface Sci. 1988, 121, 265. (29) Yates, D. E.; Healy, T. W. J. Chem. Soc., Faraday Trans. 1 1980, 76, 9. (30) Fokkink, L. G. J.; De Keizer, A.; Lyklema, J. J. Colloid Interface Sci. 1989, 127, 116. (31) Be´rube´, Y. G.; De Bruyn, P. L. J. Colloid Interface Sci. 1968, 28, 92. (32) Gibb, A. W. M.; Koopal, L. J. Colloid Interface Sci. 1990, 134, 122. (33) Jang, H. M.; Fuerstenau, D. W. Colloids Surf. 1986, 21, 235. (34) Machesky, M. L.; Wesolowski, D. J.; Palmer, D. A.; IchiroHayashi, K. J. Colloid Interface Sci. 1998, 200, 298. (35) Szczypa, J.; Wasowska, L.; Kosmulski, M. J. Colloid Interface Sci. 1988, 126, 592. (36) Kallay, N.; C ˇ olic´, M.; Fuerstenau, D. W.; Jang, H. M.; Matijevic, E.; Colloid Polym. Sci. 1994, 272, 554. (37) Hiemstra, T.; Van Riemsdijk, W. H.; Bolt, G. H. J. Colloid Interface Sci. 1989, 133, 91. (38) Hiemstra, T.; De Wit, J. C. M.; Van Riemsdijk, W. H. J. Colloid Interface Sci. 1989, 133, 105. (39) Hiemstra, T.; Venema, P.; Van Riemsdijk, W. H. J. Colloid Interface Sci. 1996, 184, 680.

ν)

z CN

(1)

As a result, the charge of an oxygen can be calculated as the sum of its valences (-2 + the bond valences of all coordinating cations), which leads to a zero value for the bulk oxygens. However, surface oxygens may be coordinated to fewer metal ions than in the solid. This leads to an undersaturation of the surface oxygen charge. Binding of one or two protons can compensate the missing charge. The Pauling concept can be applied to titanium oxide. Both anatase and rutile have a structure with Ti4+-filled oxygen octahedra. The oxygens in the bulk of the solid are triply coordinated (Ti3O0), receiving from each Ti4+ a bond valence ν equal to 2/3 (each Ti4+ ion distributes its charge over six surrounding oxygens). The surface oxygens may be singly (TiO-4/3), doubly (Ti2O-2/3), and triply coordinated (Ti3O0), depending on the number of coordinating Ti4+ ions. It has been shown37-39 that the proton affinity of the TiO-4/3 group is so high that in contact with water it immediately changes into TiOH-1/3, which may adsorb a second proton, depending on the pH of the solution. The protonation reactions for singly and doubly coordinated surface groups can be given as KH1,2

TiOH-1/3 + H+ 798 TiOH2+2/3 KH2,1

Ti2O-2/3 + H+ 798 Ti2OH+1/3

(2) (3)

Protonation of the uncharged triply coordinated groups, Ti3O0, is not possible in the normal pH range. Therefore, these groups are considered to be inert and are not expected to influence the charging behavior of titania. The log KH values of the protonation reactions 2 and 3 have been estimated recently using a refined bond valence concept.39 According to this estimation, it is predicted that PZC values of the various ideal crystal planes are identical. Another interesting result of the approach is the prediction of relatively similar log KH values for reactions 2 and 3. On the basis of this result, we have simplified the protonation of the titanium oxide surface, assuming equal values for KH1,2 and KH2,1. For this assumption, it can be (40) Connor, P. A.; Dobson, K. D.; McQuillan, A. J. Langmuir 1999, 15, 2402. (41) Pauling, L. J. Am. Chem. Soc. 1929, 51, 1010.

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been shown that PZC and IEP may differ, which is an indication of a different interaction of cations and anions with the surface.44 We consider the above-presented Basic Stern model as the simplest physical realistic electrostatic model,45 which enables description of the variable charge as a function of the electrolyte ion concentration. It will be used in this paper for the description of the interface titanium oxide surface/monovalent electrolyte solution. Model Calculations

Figure 1. Basic Stern approach.

shown that log KH ) PZC in the case of symmetrical ion pair formation. Double-Layer Model Proton adsorption strongly depends on the electrostatic interaction with neighboring surface groups. The lateral interaction is generally modeled with a double-layer approach.42 Such an approach comprises at least the presence of a purely diffuse double-layer model. It is wellknown43 that the hydrated counterions of the background electrolyte have a minimum distance of approach of the surface. Application of this concept leads to the Basic Stern model.37,43 The empty space between the surface and the head end of the diffuse double layer (DDL) is treated as a plate condenser with a capacitance C (Figure 1). The last is determined by the distance of separation and the dielectric properties of the layer. The hydrated ions, located at the distance of minimum approach in the 1-plane (Figure 1), are generally treated as point charges and assumed to form ion pairs with surface hydroxyls. They are considered as outersphere complexes without forming strong chemical bonds with the surface groups. The corresponding reactions with the titania surface groups can be formulated as KC1

TiOH-1/3 + C+ 798 TiOH-1/3 - C+ KA1

TiOH2+2/3 + A- 798 TiOH2+2/3 - AKC2

Ti2O-2/3 + C+ 798 Ti2O-2/3 - C+ KA2

Ti2OH+1/3 + A- 798 Ti2OH+1/3 - A-

(4)

Results and Discussion

(5) (6) (7)

where C+ stands for the cation and A- for the anion. On the basis of the assumption of equal proton affinities for singly and doubly coordinated groups, we also assumed equal affinities for ion pair formation with cations (log KC1 ) log KC2 ) log KC) and with anions (log KA1 ) log KA2 ) log KA). The values of log KC and log KA are not set equal (symmetric ion pair formation), because it has (42) Borkovec, M. Langmuir 1997, 13, 2608. (43) Stern, O. Z. Elektrochem. 1924, 30, 508.

The MUSIC model with the Basic Stern option was used for the description of the titration data. Equations 2 and 3 were used for the protonation reactions of the surface sites and eqs 4,6 and 5,7 for the ion pair formation. They were handled using ECOSAT, a computer code for the calculation of chemical equilibria.46 The adjustable parameters of our approach are the protonation constant, KH, the ion pair formation constants, KC and KA, and the Stern layer capacitance C. We do not consider the site density, NS, as an adjustable parameter, because it is defined by the crystal structure of the oxide and the resulting chemical composition of the individual crystal faces. The site density value does not differ very much among the different crystal faces of anatase (5.27.0 sites nm-2) or of rutile (5.2-7.4 sites nm-2).39 We therefore assume an intermediate value of 6 for singly and 6 for doubly coordinated sites per nm2. The surface is treated as electrostatically homogeneous. It should be noticed that the charging behavior of titania is not very sensitive to the precise value of the total site density, as long as this value is relatively high. The limited number of adjustable parameters allows a more objective fitting of the experimental data as well as a closer observation of the influence of each parameter on the charging behavior of anatase and rutile. Anatase and rutile have the advantage that their charging behavior is quite sensitive to both log K values of ion pair formation because the PZC is in the middle of the experimental pH range. Titration data of each set were fitted simultaneously for all available salt levels. In some cases where the data were adequate and of good quality, a fitting program47 in combination with ECOSAT46 was used. In cases where the application of the fitting program led to completely unrealistic values for the charging parameters, we were forced to use a trial and error approach. After obtaining the parameter values from the modeling of titration curves, we modeled electrokinetic data in cases for which they were available.

In the analysis, we have evaluated the behavior of three types of titanium oxide which are usually found in the literature: anatase,18-23 rutile23,29-36 which usually has a lower surface area than anatase, and P25 titania17,23-28 which is a commercial product from Degussa. The last is the most commonly used titania in catalysis and colloid chemistry, and its patchwise structure is mainly anatase, having a small amount of rutile (less than 10%).17,23,25,48 (44) Hiemstra, T.; Yong, H.; Van Riemsdijk, W. H. Langmuir 1999, 15, 5942. (45) Hiemstra, T.; Van Riemsdijk, W. H. Colloids Surf. 1991, 59, 7. (46) Keizer, M. G.; Van Riemsdijk, W. H. ECOSAT: technical report of the department of Soil Science and Plant Nutrition; Wageningen University: Wageningen, The Netherlands, 1998. (47) Kinniburgh, D. G. FIT: Technical Report WD/93/23; British Geological Survey: Keyworth, U.K., 1993. (48) Contescu, C.; Popa, V. T.; Schwarz, J. A. J. Colloid Interface Sci. 1996, 180, 149.

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Figure 2. Charging behavior of rutile at various electrolyte levels. Solid lines correspond to calculated curves using the MUSIC and Basic Stern models, and points represent experimental data obtained from (a) Yates and Healy (ref 29) and (b) Be´rube´ and De Bruyn (ref 31).

Figure 3. Charging behavior of anatase at various electrolyte levels. Solid lines correspond to calculated curves using the MUSIC and Basic Stern models, and points represent experimental data obtained from Kosmulski et al. (ref 18).

Different preparation methods lead to materials with considerably different surface areas but only slight differences in their PZC values, indicating that the preparation method influences mainly the physical structure and porosity of the materials. Of course, impurities in the material can significantly influence the chemical surface behavior. In most cases, the description of the charging data was quite good using similar values for the parameters involved. This supports the validity of the approach used. From the 31 data sets used, some representative experimental data sets (points) and calculated curves are shown in Figures 2 (rutile), 3 (anatase), and 4 (titania P25). The parameter values retrieved from the modeling are presented in Table 1. For each parameter, a mean value has been calculated with a standard deviation (Table 2). The

Bourikas et al.

Figure 4. Charging behavior of titania P25 at various electrolyte levels. Solid lines correspond to calculated curves using the MUSIC and Basic Stern models, and points represent experimental data obtained from (a) Rodrı´guez et al. (ref 25) and (b) Giacomelli et al. (ref 17).

mean values can be considered as “presently best estimates”. The uncertainty reflects the influence of the differences of the used materials as well as the influence of the interaction between the electrolyte ions. In some systems, unusual deviation from the “normal” picture was observed, which can be due to a variety of reasons. The description of these data sets was poor. Detailed comments for each of these particular data sets are given in Table 1. Proton Affinity Constants. In the present application of the MUSIC model, the proton affinity constant would have been equal to the PZC in the case of equal affinity of the electrolyte ions for the titanium oxide surface (symmetrical ion pair formation). However, different affinities are found for the various electrolyte ions, which implies that the log KH is in principle not equal to the PZC. There, the log K value will be made adjustable. Slightly higher log K values than the value of the PZC have been calculated in some cases, because of a small asymmetry in the electrolyte ion affinity resulting in an asymmetrical titration curve and/or because of a small difference between the experimental PZC and IEP values. The data in Table 2 show that the proton affinity constant of rutile is a little bit lower than that of anatase. The mean log KH value is 5.9 for rutile compared to 6.3 for anatase, which corresponds to the slightly lower PZC values reported in the literature for rutile23,29-36 in comparison with those for anatase.17-28 We note that titanium oxide preparations may differ in the log KH because of imperfections in the crystal faces, resulting in a different chemical composition, that is, the ratio of singly and doubly coordinated groups.

Ion Pair Formation and TiO2 Surface Charging

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Table 1. Values of the Stern Capacitance C and the Protonation KH and Ion Pair Formation Constants KC and KA Calculated from the Analysis of the Corresponding Data Sets log KC Cs+

K+

Na+

log KA NH4+

Li+

I-

ClO4-

-0.5 -0.8

NO3-

Cl-

-1.0 -1.0 -1.0 -1.3

-0.2 -0.5 -0.7

-1.5 -0.6

-1.3 -1.4

-0.7 -0.6

-1.7

-0.7 -0.4

-1.3 -1.3

-0.4

-1.3

-0.6

-1.0 -0.4

-1.2

-0.5 -0.5 -0.8

-1.4 -1.2 -1.3 -0.5

-1.4

-0.6

-1.0 -0.6

-0.9 -0.9 -0.9 -0.9 -1.2 -1.4 -1.3

-0.8 -0.5 -0.5 -0.7 -1.1 -0.7 -0.7 -0.7

-1.7 -1.3 -0.3 -0.3 -0.4

-1.4 -0.3 -0.6

-0.1

-0.2

log KH

C/F m-2

material

ref

PZC

methoda

5.9 5.6 6.0 6.1 6.0 5.7 5.8 5.8 6.5 6.6 6.6 6.5 6.2 6.6 5.8 5.9 5.5 6.2 6.6 6.1 6.2 6.3 5.3 6.0 6.0 6.0 6.0 6.0 6.0 6.1 5.9

0.7 1.8 0.8 1.6 1.6 1.0 1.4 1.4 0.8 0.9 0.7 0.9 1.0 1.0 1.9 1.6 1.6 1.0 0.9 1.6 0.7 1.6 0.9 1.5 1.5 1.4 1.4 1.6 1.9 1.8 1.9

R* R R R R R A* A A(P25)* A(P25) A(P25) A A(P25) A(P25) R R R A(P25) A(P25) A A A R R R R R R A A A

29 30 29b 31 31 23 18 18 24 23 25 23 26 27c 32 33 34 17 28d 19d 20e,f 21e 35e 36 36 36 36 36 22g 22g 22g

5.8 5.6 5.9 6.0 6.0 5.64 5.7 5.7 6.4 6.1 6.5 6.14 6.2 6.6 5.8 5.9 5.4 6.0 6.6 6.0 6.2 6.2 5.35 6.0 6.0 6.0 6.0 6.0 6.0 6.0 5.8

f f te f f f f te f f f f te f f f te f te te te te te te te te te te f f f

a

* R, rutile; A, anatase; A(P25), titania P25 from Degussa. f, objective fitting; te, trial and error. b Data of ionic strength 1 M are not included in the analysis due to the observed strong asymmetry and large shift of the PZC. c A value of 50 m2 g-1 was used for the SSA of titania P25 (mean value in the literature) instead of 42.4 m2 g-1 measured in this study. d Poor fitting at low pH values. e Poor fitting due to strong asymmetry and/or very low salt dependency of the titration curves. f Data of titrations in CsCl were not used because of the unusual strong specific adsorption of the Cs+ ions and the large shift in the PZC. g Exceptional data because high log K values, for both cations and anions, were necessary for a good fitting of the titration curves. Table 2. Best Estimate Values of the Stern Capacitance C and the Protonation KH and Ion Pair Formation Constants KC and KA, Found from the Systematic Analysis of the Data Sets, for the Description of the Charging Behavior of Titanium Oxide parameter log KC

log KA

log KH (anatase) log KH (rutile) Clow/F m-2 Chigh/F m-2

Cs+ K+ Na+ NH4+ Li+ IClO4NO3Cl-

value

no. of studiesa

-1.1 ( ? -0.7 ( 0.1 -0.6 ( 0.1 -0.5 ( 0.1 -0.3 ( 0.1 -1.7 ( ? -1.6 ( 0.1 -1.2 ( 0.2 -1.1 ( 0.2 6.3 ( 0.3 5.9 ( 0.2 0.9 ( 0.1 1.6 ( 0.1

1 12 10 3 2 1 2 14 11 13 15 13 15

a Data of ref 22 are not included in the calculated mean values because exceptional high log K values, for both cations and anions, were necessary for a good fitting of the titration data. The reason was the unusual high charging behavior of the anatase used in that study.

Capacitances. We have made an important observation with respect to the capacitance. A close inspection of the various C values, reported in Table 1, shows that titanium oxide preparations can be divided into two main categories. The first consists of materials having a relatively low capacitance, 0.9 ( 0.1 F m-2 (e.g., Figures 2a and 4a,b), and the second group of materials is characterized by a relatively high capacitance, 1.6 ( 0.1

F m-2 (e.g., Figures 2b and 3). See also Table 2. This behavior is observed for both types of the oxide, anatase and rutile. A different capacitance leads to a different slope of the charging curves. A variation in the slope of the titration curves has previously been observed for goethite preparations.38,49 A correlation was found with the specific surface area (SSA) of the material and the crystallization.38 Well-crystallized materials had a low capacitance value. High values were related to imperfections and surface roughness.38 In the case of titanium oxide, no correlation between the capacitance and the SSA of the materials was found. The variation in C values indicates different doublelayer properties. The capacitance can be interpreted in terms of a distance, d, between the two electrostatic planes of the double layer, namely the solid surface (0-plane) and the head end of the DDL (1-plane) (see Figure 1). Considering a mean relative dielectric constant r in the Stern layer, the capacitance C is given by the following expression:

C)

0r d

(8)

where 0 is the absolute dielectric constant. Differences in capacitance can result from variation of d, for instance, because of surface roughness12 or protrusion of surface groups as found for silica.45 Another factor is the difference (49) Boily, J. F.; Lu¨tzenkrichen, J.; Balme`s, O.; Beattie, J.; Sjo¨berg, S. Colloids Surf., A, submitted for publication.

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in log KH between singly and doubly coordinated surface groups, which may affect the slope of the charging curve and the capacitance value obtained. The capacitance can also be affected by the relative dielectric constant r in the Stern layer. Assuming a Stern layer thickness of d ) 0.4 nm (approximately the radius of a hydrated ion) and using the r value equal to water (r ) 78) leads to a capacitance value of C = 1.7 F m-2. The value for C of 0.9 F m-2 points to a lower dielectric constant in the Stern region. A low value of C (0.9 F m-2) is not only found for anatase and rutile, but also for gibbsite44 and goethite,50 all modeled with a MUSIC approach. For the Al and Fe (hydr)oxides, it has been suggested44,50 that a lower dielectric constant of the Stern layer fits with the lower dielectric constant of the solid (r = 8-12). However, for rutile values of 86170 for the r have been reported.51 The similarity in capacitance for well-crystallized oxides with very different dielectric properties is probably not a coincidence. This may point to a unique capacitance value for wellcrystallized surfaces, independent of the dielectric properties of the solid. In that case, the value can be considered as characteristic of the first layer of physically adsorbed water on oxide surfaces. The relative dielectric constant r of this water layer equals about 40. The higher value of capacitance, as also found in various oxides (goethite,38 bayerite,44 and titanium oxide (this study)), could then reflect a distorted water layer which has properties close to those of bulk water. Ion Pair Formation. Electrolyte ions are adsorbed in two different ways. They are partly located in the diffuse double layer as counterions. In addition, some (hydrated) ions interact directed to the surface, forming outersphere complexes (Figure 1). Innersphere adsorption of the studied electrolyte ions (except maybe Li+) does not take place, and for this reason these types of electrolytes are sometimes called “indifferent” electrolytes. Indifference as a phenomenon is in accordance with the coincidence of PZC and IEP values if the electrolyte concentrations are relatively low. The development of electro-acousto-phoresis has recently shown that at high electrolyte concentrations, IEP shifts upward.52,53 The shift indicates a slightly stronger interaction of cations compared to anions.44 For this reason, we considered in our analysis the log K values for electrolyte ion pair formation as free adjustable parameters; that is, asymmetric ion pair formation is allowed. The calculated log K values of the ion pairs are also summarized in Table 1. No significant differences are found between the values corresponding to materials with an anatase structure and with a rutile structure. The results of our analysis (Table 1) show that the log K values of cations are higher than those of the anions in all cases. These results are in agreement with the abovementioned experimental phenomena. The data in Table 1 also show that the log K value depends on the type of the ion involved. For a particular ion, variation also exists between different types of materials. However, the differences are not systematic and are considered as part of the uncertainty. The mean values have been calculated taking into account almost all the available data. They are presented in Table 2 and are considered as the best estimates of the log K values for ion pair formation on the titania surface. (50) Hiemstra, T.; Van Riemsdijk, W. H. J. Colloid Interface Sci. 1996, 179, 488. (51) Shannon, R. D. J. Appl. Phys. 1993, 73, 348. (52) Kosmulski, M.; Rosenholm, J. B. J. Phys. Chem. 1996, 100, 11681. (53) Kosmulski, M.; Durand-Vidal, S.; Gustafsson, J.; Rosenholm, J. B. Colloids Surf., A 1999, 157, 245.

Bourikas et al.

Comparison of the log K values of the ion pair formation (Table 2) leads to some conclusions about the relative adsorption affinity of the electrolyte ions on titanium oxide’s surface. Concerning the cations, it seems that the adsorption strength follows the sequence Li+ > NH4+ > Na+ > K+ > Cs+. The series for the adsorption strength of anions is Cl- > NO3- > ClO4- > I-. The differences in the anion binding are less clear than those in the cation binding, because of quite weak adsorption of anions in the titania surface. This fact has also been noticed in a recent study of adsorption of electrolyte ions on the alumina surface.54 The above series are in good agreement with those reported in the literature. Be´rube´ and De Bruyn31 first measured the adsorption amount of some ions on the rutile surface. The cationic adsorption sequence that they found is Li+ > Na+ > Cs+, and the anionic one is Cl- ≈ ClO4- ≈ NO3- > I-. A similar trend on anatase was observed by Sprycha:22 Li+ > Na+ > K+ > Cs+ for cations and Cl- ≈ Br- > I- for anions. Dumont et al.55 found a similar trend for rutile with a PZC of 5.9. TiO2 materials with the unusual low PZC of 3-4.6 showed deviations. Studies of Yates et al.29 and Kallay et al.,36 concerning the binding of several cations on a rutile surface, led also to similar results. Similar affinity sequences have been found in other substrates, like alumina,54,56,57 hematite,58,59 and goethite.60 Finally, it should be mentioned that the adsorption behavior of Li+ is more complicated than that of the other ions. Titration experiments done in electrolyte solutions where Li+ was the cation of the electrolyte show a strong asymmetric behavior, without having a clear intersection point (e.g., refs 22 and 29). A significant shift of the PZC to lower values, as the ionic strength increases, is observed in most cases. This phenomenon has been found in several studies dealing with the binding of Li+ in various substrates,22,29,54,56,58 indicating strong binding of Li+ ions taking place on the (hydr)oxide’s surface. A possible explanation could be innersphere complex formation or the penetration of the Li+ ions in the solid surface because of their small size. As a result of this effect, the quality of the fitting, in the cases where Li+ was the electrolyte cation, is not so satisfactory, particularly at high salt levels where the phenomenon is strongest. ζ Potentials. Asymmetric ion pair formation influences the relation between the experimental PZC and IEP values. Recently, the electromobility was measured for anatase52 and a mixture of anatase and rutile,53 using the novel electroacoustic technique, which allows the measurement of electrokinetic parameters at very high ionic strength values. A significant shift of the IEP to higher pH values is observed at high electrolyte levels. At very high values of electrolyte concentration, a charge reversal is observed and the surface of titania becomes positively charged over the entire pH range. The above are an indication of a stronger interaction of the electrolyte cation compared to the corresponding anion, in accordance with (54) Johnson, S. B.; Scales, P. J.; Healy, T. W. Langmuir 1999, 15, 2836. (55) Dumont, F.; Warlus, J.; Watillon, A. J. Colloid Interface Sci. 1990, 138, 543. (56) Tschapek, M.; Wasowski, C.; Torres-Sanchez, R. M. J. Electroanal. Chem. 1976, 74, 167. (57) Sprycha, R. J. Colloid Interface Sci. 1989, 127, 1. (58) Breeuwsma, A.; Lyklema, J. Faraday Discuss. Chem. Soc. 1971, 52, 324. (59) Amhamdi, H.; Dumont, F.; Buess-Herman, C. Colloids Surf., A 1997, 125, 1. (60) Rietra, R. P. J. J.; Hiemstra, T.; Van Riemsdijk, W. H. J. Colloid Interface Sci. 2000, 229, 199.

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Figure 6. Empirical relation between the ionic strength and the apparent location of the shear plane, found from our analysis of the various titanium oxide data sets. Similar results found from Hiemstra et al. (ref 44) for aluminum (hydr)oxides are also presented. The location is expressed as the distance d from the head end of the DDL.

Figure 5. ζ potential of (a) rutile, (b) anatase, and (c) titania P25 at various electrolyte levels. Points represent experimental data obtained from (a) Kallay et al. (ref 36), (b) Kosmulski et al. (ref 18), and (c) Foissy et al. (ref 26). Solid lines correspond to calculated curves using the MUSIC model with the Basic Stern option, assuming an ionic strength dependent location of the shear plane, as given in Figure 6. Note that in Figure 5c, the ζ potential only differs in the negative branch of the curves for the various electrolyte levels used.

the measured electrolyte adsorption densities. Our model with asymmetric ion pair formation predicts this type of behavior in contrast to other approaches.34,61 The shift of the IEP at high ionic strength is a general phenomenon for oxides because it has also been observed experimentally for zirconia,52 gibbsite,62 and silica.63 (61) Charmas, R.; Piasecki, W. Langmuir 1996, 12, 5458. (62) Rowlands, W. N.; O’Brien, R. W.; Hunter, R. J.; Patrick, V. J. Colloid Interface Sci. 1997, 188, 325. (63) Kosmulski, M.; Matijevic, E. Colloid Polym. Sci. 1992, 270, 1046.

A quantitative description of ζ potentials is accompanied by uncertainties. An important reason is the theoretical complexity of the transformation of experimental electromobility data to ζ potentials, for nonideal particle suspensions. The IEP can be considered as the most reliable experimental result. The ζ potential is considered equivalent with the potential at the head end of the diffuse double layer. Adopting this assumption and using the Basic Stern approach in combination with an asymmetric ion pair formation, the trend of a decrease in the ζ potentials of titanium oxides as the electrolyte concentration increases as well as the shift in the IEP could be predicted. However, the absolute ζ potential values for TiO2 could not be described in a simple way, in contrast to for instance hematite64 and recent data for Al oxide.44,65 The experimental values for Ti oxide are quite low compared to the calculated ones. Lower potentials can be calculated if the shear plane is apparently located at a certain distance from the head end of the DDL.11,44 Following this empirical approach and using the BS option, we can describe the available electrokinetic data quite well, by fitting in each case the apparent location of the shear plane. Representative results are given in parts a (rutile), b (anatase), and c (titania P25) of Figure 5. The fitted location of the plane of shear for the present data sets depends apparently on the ionic strength. This was previously observed for gibbsite and a particular Al oxide.44 The apparent distance, d, between the shear plane and the head end of the DDL was found to be proportional to the square root of the ionic strength, I, of the solution (d ∼ I1/2). For these TiO2 data, we found the same (Figure 6). If the BS option with the plane of shear at the head end of the DDL is considered as reliable, the relation d ∼ I1/2 can be due to the uncertainty in the value of the conversion factor required to convert electrophoretic mobilities to zeta potentials. Increase of this factor with about 2 leads to “data” that coincide with the calculated ζ potentials. Conclusions The following conclusions can be drawn from the present study: (64) Schudel, M.; Behrens, H.; Holthoff, H.; Kretzschmar, R.; Borkovec, M. J. Colloid Interface Sci. 1997, 196, 241. (65) Johnson, B.; Russell, A. S.; Scales, P. J. Colloids Surf. 1998, 144, 119.

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Table 3. Surface Speciation of the Primary Charging of Titanium Oxide dissolved component

surface component

electrostatic component

surface species

H+

C+

A-

TiOH-1/3

Ti2O-2/3

exp(-FΨ0/RT)

exp(-FΨ1/RT)

log K

TiOH-1/3 Ti2O-2/3 TiOH2+2/3 Ti2OH+1/3 TiOH-1/3 - C+ Ti2O-2/3 - C+ TiOH2+2/3 - ATi2OH+1/3 - Asuma

0 0 1 1 0 0 1 1 ∑1

0 0 0 0 1 1 0 0 ∑2

0 0 0 0 0 0 1 1 ∑3

1 0 1 0 1 0 1 0 ∑4

0 1 0 1 0 1 0 1 ∑5

0 0 1 1 0 0 1 1 ∑6

0 0 0 0 1 1 -1 -1 ∑7

0 0 log KH log KH log KC log KC log KA + log KH log KA + log KH

a

See Appendix for definitions.

i. The charging behavior of the titanium oxide/ electrolytic solution interface can be described adequately, using both a multisite one-pK approach and the Basic Stern model in combination with the ion pair formation concept. ii. Interfacial charging parameters of anatase and rutile do not differ significantly, apart from the protonation constants that are slightly lower for rutile. iii. TiO2 materials can be distinguished based on a high (1.6 ( 0.1 Fm-2) and a low (0.9 ( 0.1 F m-2) capacitance value. The low value corresponds to similar values on well-crystallized goethite and gibbsite. iv. A low capacitance value points to a unique relative dielectric constant of about 40 for the first layer of physically adsorbed water, which is independent of the dielectric properties of the solid. v. A systematic analysis of surface charging data over a large number of different monovalent electrolytes and various ionic strength values allows the determination of values for the constants of ion pair formation of the electrolyte ions with the titania surface groups. Best estimates have been derived. vi. The values of the ion pair formation constants suggest stronger interaction of the cations with the titanium oxide surface compared to anions. vii. The affinity of the cations follows the sequence Cs+ < K+ < Na+ < Li+, and that of the anions follows the sequence Cl- > NO3- > ClO4- > I-. viii. The asymmetric ion pair formation of cations and anions is in accordance with the observed shift of the IEP of titanium oxide to higher pH values, at high electrolyte concentrations.

where Ck is the component’s concentration (mol L-1) and nk is the coefficient given in the table. The expression of log K is given in the last column of Table 3. By KH, KC, and KA, we denote the surface protonation constant and the pair formation constants of the electrolyte cations C and anions A, respectively. All log K values are based on intrinsic constants, adjusted for activity corrections in the case of I * 0. The activity coefficients were estimated with the Davies equation (constant ) 0.2).

Appendix

The parameters in the summation terms are: F, the solid solution ratio (kg L-1); A, the specific surface area (m2 kg-1); F, the Faraday constant (C mol-1); σ0 and σ1, the charge (C m-2) in the 0- and 1-planes, respectively; zj, the charge of the surface reference groups TiOH-1/3 and Ti2O-2/3; NS,j, the site densities (mol m-2) of the corresponding surface groups; Ψ0 and Ψ1, the electrostatic potential (V) of the 0- and 1-planes, respectively; C, the capacitance (C V-1 m-2) of the Stern layer between the 0and 1-planes; 0, the absolute dielectric constant (C V-1 m-2); r, the relative dielectric constant; R, the gas constant (J mol-1 K-1); T, the absolute temperature (K); Ci the concentrations of the dissolved electrolyte solution species with valence zi.

The primary charging of the titanium oxide interface is due to the presence of singly and doubly coordinated surface groups. The corresponding formation reactions (protonation and ion pair formation) have been defined in a table of species (Table 3). Each surface species consists of several components (columns), including surface (surface groups), dissolved, and electrostatic components (exp(-FΨi/RT)), with i ) 0, 1 standing for the corresponding planes). The concentration S (mol L-1) of a surface species can be calculated by reading the table horizontally and using the following general expression:

[Ck]n ∏ k

[S] ) 10logK

k

(A)

∑1 ) H+(t) - OH-(t) ∑2 ) C+(t) ∑3 ) A-(t) ∑4 ) FANS,1 ∑5 ) FANS,2 ∑6 ) FA/F(σ0 - ∑zjFNS,j) ∑7 ) FA/Fσ1 σ0 ) C(Ψ0 - Ψ1)

(A-1) (A-2) (A-3) (A-4) (A-5) (A-6) (A-7) (A-6a)

σ1 ) C(Ψ1 - Ψ0) ( 1 2

LA000806C

x

x80000rRT ∑Ci[exp(-ziFΨ1/RT) - 1]. i