Surface Hydroxyl Site Densities on Metal Oxides as a Measure for the Ion-Exchange Capacity

Surface Hydroxyl Site Densities on Metal Oxides as a Measure for the Ion-Exchange Capacity

Journal of Colloid and Interface Science 209, 225–231 (1999) Article ID jcis.1998.5877, available online at http://www.idealibrary.com on Surface Hyd...

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Journal of Colloid and Interface Science 209, 225–231 (1999) Article ID jcis.1998.5877, available online at http://www.idealibrary.com on

Surface Hydroxyl Site Densities on Metal Oxides as a Measure for the Ion-Exchange Capacity Hiroki Tamura,1 Akio Tanaka, Ken-ya Mita, and Ryusaburo Furuichi Laboratory of Materials Chemistry, Graduate School of Engineering, Hokkaido University, Sapporo, 060-8628 Japan E-mail: [email protected] Received June 29, 1998; accepted September 17, 1998

Hydroxyl groups on metal oxide in water are the sites for ion exchange, and the surface hydroxyl site density on oxides is a measure of the ion-exchange capacity. Here, the Grignard reagent method was applied to determine the surface hydroxyl site density of oxide samples. The results were similar to those reported for different oxides with other methods (dehydration by heating, tritium exchange, crystallographic calculations, etc.), and they are comparable with those calculated from the closest packing of hydroxide ions. A mechanism of hydroxylation is proposed: lattice oxide ions (extremely strong bases) are exposed to aqueous solutions and are neutralized by water to become hydroxide ions. Also, the saturated deprotonation method was applied to hematite, and it was found that all the acid hydroxyl groups on hematite were deprotonated in very high concentrations of alkali solutions (;5 mol dm23 NaOH), and from the saturated amount of OH2 consumed by deprotonation, the same result as that by the Grignard method was obtained. It is shown that all hydroxyl groups take part in ion exchange and that the unusually small values reported elsewhere with the saturated (de)protonation method may contain errors. Hetero- or homogeneity of hydroxyl groups in contact with water as ion-exchange sites is also discussed. It is suggested that intensely hydrated layers at the oxide/water interface may result in homogeneous discrete sites. The development of microstructures in the oxides was suggested from the measured values of specific surface areas, and the effect of the microstructure environments on the reactivity of internal surface hydroxyl sites is discussed. © 1999 Academic Press Key Words: metal oxide; surface hydroxyl groups; ion-exchange capacity; Grignard method; water neutralization; hydration; discrete affinity; micropore.

INTRODUCTION

The surface of metal oxides in aqueous solutions is hydroxylated due to dissociative chemisorption of water molecules, and the surface hydroxyl groups adsorb ions from solution by the exchange with hydroxyl protons or hydroxide ions (1–5). Due to this, the amount of surface hydroxyl groups on metal oxides per unit area (surface density) provides a measure for the ion-exchange capacity of the oxide. Many methods have been 1

To whom correspondence should be addressed.

proposed to measure the hydroxyl site densities on metal oxides: (a) reaction with Grignard reagents (6 – 8); (b) surface acid– base, ion-exchange reactions for saturation (9 –12); (c) dehydration by heating (7, 8, 13, 14); (d) IR spectroscopy (15–18); (e) tritium exchange with hydroxyl protons (19, 20); and (f) crystallographic calculations (19, 21). Among these, method (b) sometimes gives far smaller values than those with the other methods (9, 12), and this poses the following questions: (i) which value is the most realistic, and (ii) do all the hydroxyl sites measured take part in the ion exchange? In this paper, the surface densities of hydroxyl sites on metal oxide samples measured by the authors mainly with method (a) are compared with those by other investigations to establish realistic values. The mechanism of hydroxylation and the reactivity of hydroxyl groups as ion-exchange sites are discussed on the basis of these established values. The surface densities of hydroxyl sites established here were quite similar for different oxide samples, and they are comparable to the calculated value for the closest packing of hydroxide ions. Other investigations except for some with method (b) also report values close to ours, and it is likely that all surfaces are hydroxylated. The results here do not agree with the commonly made assumption that the dissociative chemisorption of water molecules occurs only at the lattice metal ion site acting as a Lewis acid (1–5). For this assumption to hold, there would be different hydroxyl site densities for oxides with different numbers of metal ions due to their different valences. To explain the similar hydroxyl site densities for different oxide samples, an alternative mechanism is suggested, where lattice oxide ions are exposed to water at the oxide/water interface. Oxide ions are very strong bases and unable to exist unchanged in aqueous solutions, and they are neutralized by water to become hydroxyl groups. The surface density of hydroxyl sites on hematite (a-Fe2O3) measured at high concentrations of NaOH (;5 mol dm23) with method (b) showed the same hydroxyl site density as that obtained by the Grignard method (a), and surface saturation seemed to be attained (22). However, saturation of surface deprotonation is very difficult to attain within the pH range common in acid–base

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titrations. This behavior has been interpreted elsewhere with the Frumkin isotherm as being due to suppressive lateral interactions between formed charged sites, which increase in extent with the progress of the deprotonation (23). The dissolution of oxide samples in acids or bases consumes protons or hydroxide ions from the solution. Method (b) corrects for this, but when the amount of protons or hydroxide ions consumed by dissolution is very large at pH where the surface density of hydroxyl site is measured with surface acid– base or ion-exchange reactions, this correction causes large errors. Further, some surface (de)protonation models choose the surface hydroxyl site density as a model parameter determined by fitting the model equations to acid– base titration data, which are extrapolations to saturated values. If the extent of (de)protonation by titration at commonly used pH is low, the extrapolation provides model dependent results (24, 25), which may be erroneous or misleading. This suggests that the results obtained with method (b) may not always represent saturated values. There are many studies of the chemical reactivity of surface hydroxyl groups in relation to applications like catalysts, adsorbents, as well as ion exchangers. The presence of hydroxyl groups with different energies has been established with IR spectra (15–18), and it has been suggested that the surface hydroxyl groups on oxides are heterogeneous. For surface hydroxyl groups as ion-exchange sites, some research considers several types of discrete sites with different reactivities or sites with continuously varying reactivities, which can be expressed by site affinity distribution functions (SADF) (26 –32). However, most ion-exchange models explain the ion-exchange behavior by assuming identical sites with electrostatic interactions (1–5, 9 –12, 19, 20, 24, 25, 33–35) or with general lateral interactions by the Frumkin isotherm (22, 23, 36 –38). The lateral interactions (including electrostatic ones) between adsorbed ions increase in extent with the progress of a reaction, and the reactivity of the originally identical sites changes with the progress of the reaction. As a result, there are two approaches to explain the ionexchange behavior: one assumes the site affinity to distribute continuously, and the other considers the original site affinity to be discrete but the lateral interactions after the ion-exchange reaction alter the site affinity. It is very difficult to determine whether the affinity of an original surface prior to ion exchange is discrete or continuous. This paper discusses the hetero- or homogeneity of hydroxyl groups in water by considering the formation of intensely hydrated layers at the oxide/water interface. The metal oxide samples used here have internal surfaces like micropores, crevices, or flaws, since their specific surface areas measured by the BET method are far larger than those calculated from the particle size and shape observed by electronmicroscopy. Elsewhere it was reported that the suppressive lateral interactions described above are strong for oxides with large internal surfaces (37). In this paper it is suggested that

lateral interactions would be different due to differences in micropore numbers, shapes, and sizes. MATERIALS AND METHODS

Materials The alumina (JRC-ALO-4, g-Al2O3), silica (JRC-SIO-1), and titania (JRC-TIO-5, rutile) used here are the reference catalysts supplied from the Catalysis Society of Japan. Titania (Kanto, anatase, aggregates of smaller particles with diameters less than 1 mm), silica (Kanto, amorphous-SiO2), chromia (Kanto, corundum-type Cr2O3), hematite (Kanto A and B, a-Fe2O3, rectangular with dimensions several to 10 mm), and magnetite (Kanto, Fe3O4) are all commercial reagents (Kanto Chemical Co., Tokyo). Magnetite (Sphere, Fe3O4) was synthesized as spherical particles with a diameter of 1.0 mm by partial oxidation of iron(II) hydroxide gel with nitrate (36). The manganese dioxides (MnO2) are the International Common Samples IC1, IC12, and IC22 for batteries supplied from the IC Sample Office (Cleveland, OH), and the synthetic spinel type l-MnO2 (hMnIV 2 O4) with lattice vacancies (h). The IC samples consist of particles with diameters up to several tens of mm, prepared by electrolytic (IC1) and chemical (IC12, IC22) oxidation of manganese ions, and the crystal structure is g-type. The l-MnO2 was prepared by the following process (39): spinel-type LiMnIIIMnIVO4 was synthesized by reaction between Mn2O3 and Li2CO3 at 850°C, and then Li1 ions were removed with HNO3 solution, concomitantly lattice Mn(III) ions showed disproportionate decomposition to Mn(IV) and Mn21. This oxide consist of rectangular particles with dimensions of several to more than ten mm. The Al2O3, SiO2, Cr2O3, and Fe3O4 particles were cleaned with water, and the MnO2, TiO2, and Fe2O3 particles first with 0.1 mol dm23 HNO3 and then water. The washed oxide samples were dried at 110°C overnight and kept in a desiccator. Methyl magnesium iodide, a Grignard reagent, is commercially available as a diethyl ether solution (0.82 mol dm23, Kanto Chemical Co., Tokyo) and was used as received. Measurement of the Specific Surface Area of Oxide Samples The specific surface area, S BET, of the samples was measured by the BET method with N2 adsorption. Measurement of the Amount of Surface Hydroxyl Groups The amount of surface hydroxyl groups on oxide samples was measured mainly by the Grignard reaction method as shown next. For Fe3O4 (Sphere) and Fe2O3 (Kanto A), the saturated deprotonation method in alkali solutions was applied. The surface hydroxyl groups on metal oxides (2OH) react with methyl magnesium iodide (CH3MgI) to evolve methane according to the following reaction (6 – 8):

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SURFACE HYDROXYL SITE DENSITIES ON METAL OXIDES

FIG. 1. Apparatus for the determination of the amount of surface hydroxyl groups on metal oxides by the Grignard method: 1, reaction flask; 2, constant temperature water bath; 3, spoon; 4, CH4 gas cylinder; 5, magnetic stirrer; 6, dry ice trap; 7, pump to circulate the constant temperature water; 8, three direction valve; 9, gas buret; 10, NaCl saturated solution.

2OH 1 CH3MgI 3 2OMgI 1 CH41.

[1]

The amount of surface hydroxyl groups was determined by measuring the amount of evolved CH4 with an apparatus shown in Fig. 1. The procedure is as follows: a. The reaction flask 1 and the gas buret 9 are kept at 25°C by circulating constant temperature water 2. b. Put 150 cm3 of ether into the flask. c. Take up to ;5 g of metal oxide powder sample on the spoon 3 inserted into the flask. d. Inject 10 cm3 of CH3MgI– ether solution (0.82 mol dm23) into the flask, and stir with the magnetic stirrer 5. e. Open the valve 8 to air and flow CH4 from the tank 4 through the solution and the gas flow system to saturate the solution with CH4. Both ether vapor from the reaction flask and water vapor from the gas buret are trapped by the dry ice trap 6. f. Adjust the pressure of both the flask and the gas buret to atmospheric pressure, and turn the valve so it is closed to air and open between the flask and the gas buret. g. After the meniscus of the buret becomes stable, add the oxide sample by turning the spoon. h. Make the pressure in the buret equal to atmospheric pressure by adjusting the water level of the NaCl solution 10, and read the meniscus. RESULTS AND DISCUSSION

Figure 2 shows the volume (STP) or amount of methane evolved by the Grignard reaction as a function of the weight of silica (Kanto, amor-SiO2). There is a good linear relation, and the slope of the straight line gives the amount of hydroxyl sites per unit weight of this oxide. The amount of surface sites per unit surface area, the hydroxyl site density N s (mol m22), can be obtained by dividing the slope by the specific surface area

FIG. 2. Volume or amount of methane evolved by the Grignard reaction as a function of the weight of silica.

S BET (m2 g21). The N s values of oxide samples thus obtained are listed in Table 1 together with the S BET values. The S BET values differ widely for different oxides from 1.09 m2 g21 for Cr2O3 (Kanto) to 245 m2 g21 for SiO2 (Kanto). Even with the same oxide, it varies by several to ten times depending on the preparation conditions like for MnO2. However, the N s values are quite similar for these oxide samples, and the maximum difference is about one-third of an order of magnitude. The N s values have also been reported by other investigators with different methods. For TiO2 Yates (19) obtained 2.07 3 TABLE 1 Specific Surface Areas SBET and Hydroxyl Site Densities Ns of Metal Oxide Samples Sample

S BET/m2 g21

N s/1025 mol m22

Method

Al2O3 (ALO-4) Cr2O3 (Kanto) Fe2O3 (Kanto A) Fe2O3 (Kanto B) Fe3O4 (Kanto) Fe3O4 (Sphere) MnO2 (IC1) MnO2 (IC12) MnO2 (IC22) l-MnO2 SiO2 (SIO-1) SiO2 (Kanto) TiO2 (TIO-5) TiO2 (Kanto)

155 1.09 15.9 5.60 4.32 1.73 43.0 80.0 45.1 7.70 92.6 245 2.60 21.5

3.20 2.69 2.38 2.36 3.31 1.08 2.25 2.35 2.41 1.46 1.60 0.954 1.80 1.16

Grignard Grignard NaOH Grignard Grignard NaOH Grignard Grignard Grignard Grignard Grignard Grignard Grignard Grignard

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1025 mol m22 with method (e), method symbol in the Introduction above, and 2.02 3 1025 mol m22 with method (f). For Al2O3, Kummert (20) obtained 1.41 3 1025 mol m22 with method (e) and Peri (21) 2.08 3 1025 mol m22 with method (f). Sigg (40) obtained 2.82 3 1025 mol m22 for goethite (a-FeOOH) with method (e). Morimoto et al. (7, 8, 13) applied methods (a) and (c), and reported their results in figures, plotting the number of OH groups per nm2 against the heattreatment temperature (7, 8). The following results (in mol m22) were read from these figures for 100°C: for MgO 1.6 3 1025 with (a), for ZnO 1.3 3 1025 with (a) and 3.9 3 1025 with (c), for Al2O3 1.5 3 1025 with (a) and 2.0 3 1025 with (c), for SnO2 1.7 3 1025 with (c), for SiO2 (silica gel) 0.40 3 1025 with (a) and 0.42 3 1025 with (c), for SiO2 (porous silica glass) 0.58 3 1025 with (a) and 0.78 3 1025 with (c), and for SiO2 (aerosil) 0.43 3 1025 with (a) and 0.40 3 1025 with (c). For the metal oxide samples including SiO2 with large differences in origin, porosity, and surface area, Morimoto et al. showed that the Grignard method provides about the same results as the dehydration by heating method and concluded that the two methods are equally reliable. However, much smaller values have been reported for Al2O3 with method (b): Al2O3 showed values of 0.22 3 1025 mol m22 (9) and 0.171 3 1025 mol m22 (12), about one-tenth the values above; these are, however, proton or hydroxide ionexchange capacities and not the total hydroxyl site densities like above. Here, much Al2O3 dissolved without use of very high concentrations of acid and base, and corrections were made for the amount of H1 and OH2 ions consumed by this dissolution. Method (b) has also been used to measure the surface hydroxyl site density of hematite (Kanto A) (22). The procedure was as follows: 0.3–70 g of hematite powder was dispersed in 50 cm3 of 0.01– 6.4 mol dm23 NaOH solutions at 25°C, and the suspensions were shaken for more than 4 h. The oxide and solution were separated by filtration or centrifugation, and the supernatants were titrated with an HNO3 standard solution. Here, there was no dissolution of hematite, and the NaOH concentration of the supernatant decreased due to the reaction with acid hydroxyl groups 2OH(a) according to 2OH(a) 1 Na1 1 OH2 3 2O2 z Na1 1 H2O.

[2]

Figure 3 shows the amount of OH2 ions consumed by reaction [2] per unit surface area of hematite as a function of the free OH2 ion concentration [OH2]. Saturation is attained at [OH2] higher than about 4 mol dm23, and the total acid hydroxyl site density is 1.19 3 1025 mol m22. According to Boehm (41), the acid and base hydroxyl groups are equal in number, and the total surface hydroxyl site density is then 2.38 3 1025 mol m22. This agrees well with the 2.36 3 1025 mol m22 obtained for hematite for another batch (Kanto B) with the Grignard method (Table 1).

FIG. 3. Amount of OH2 consumed per unit surface area of hematite vs free OH2 ion concentration.

It may then be concluded that method (b) provides similar surface hydroxyl site densities as those obtained by other methods and that all surface hydroxyl groups take part in ion exchange. The far smaller values reported elsewhere (9, 12) may be erroneous due to either large corrections for dissolution or insufficient attainment of surface saturation, as suggested in the Introduction. The surface hydroxyl site densities established here by us (Table 1) and by others are quite similar for various oxides with di-, tri-, and tetravalent lattice metal ions as shown above (except for the SiO2 samples). However, a commonly made assumption that the dissociative chemisorption of water molecules occurs only at the lattice metal ion site acting as a Lewis acid (1–5) would lead to differences in hydroxyl site densities, as the number of lattice metal ions in oxides changes with valence. A different model or mechanism of surface hydroxylation must be developed to explain the findings here. Oxide surfaces usually terminate in oxide ions due to their large size and little polarizing power (41). The oxide ion O22 in oxides is an extremely strong base and cannot exist unchanged in aqueous solution. If the oxide ion is brought into an aqueous solution as a free ion, it would be neutralized by water to become two hydroxide ions (42), as O22 1 H2O 3 2OH2.

[3]

All the surface oxide ions of metal oxides exposed to aqueous solution may undergo such water neutralizing to become hy-

SURFACE HYDROXYL SITE DENSITIES ON METAL OXIDES

FIG. 4. Closest packing of hydroxide ions with radius r in two layers indicated by solid and broken circles.

droxyl groups, and the water molecules become the other type of hydroxyl group by losing protons. A decrease in the electric charge of oxide anions and hence an increased number of hydroxide anions leads to a more symmetrical and better neutralization of the cationic charge. These two kinds of hydroxyl groups are conjugate acids (a) of lattice oxide ions and conjugate bases (b) of water molecules, and their chemical natures are different. This hydroxylation reaction can be described by 2O 1 H2O 3 2OH(a) 1 2OH(b).

[4]

These two kinds of hydroxyl groups are considered to form two layers. Figure 4 illustrates this situation, it shows a top view of hydroxide ions with the radius r closely packed in two layers (solid and broken circles). The area S of the hexagon in Fig. 4 is S 5 6 =3r 2 . Within the hexagon there are 6 hydroxide ions in two layers, and with the Avogadro constant N A, the amount of hydroxide ions per unit area (surface density) becomes N s 5 1/( =3r 2 N A). The radius of a hydroxide ion is 1.45 Å (1.45 3 10210 m) (43), and N s becomes 4.56 3 1025 mol m22, somewhat larger than the measured values. The ionic radius of hydroxide ions was obtained for bulk ions in ionic crystals where hydroxide ions alternate with lattice cations. On the oxide surface, terminal hydroxyl groups lie adjacent to each other, and their electric charges are not neutralized symmetrically by lattice cations due to the local imbalance of anion and cation arrangements at the surface. As a result, there would be electrostatic repulsion between hydroxyl groups, leading to a looser packing. This could explain

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why the measured values of N s are smaller than the calculated result here. This mechanism of surface hydroxylation would explain the observed results that metal oxides have similar surface hydroxyl site densities corresponding very nearly to the closest packing of hydroxide ions irrespective of the valence of the lattice metal ions. The hetero- or homogeneity of hydroxyl groups as ion-exchange sites in aqueous solutions is not established, as pointed out in the Introduction. So far, solid surfaces have been studied extensively in vacuum or dry atmospheres, because various methods of spectroscopy can be applied only under these conditions. The results obtained in this manner show that the surface is heterogeneous depending on surface topology (kinks, steps, terraces, and other irregularities), crystal planes exposed, compositional changes, and others. It is commonly considered that the affinity of sites is continuously distributed and there are infinitely many different sites on the surface. These findings have explained the deviation of adsorption behaviors from the Langmiur isotherm and have been useful to better understand catalysis, corrosion, gas adsorption, and so on. The reactivity of surface hydroxyl groups in contact with water as ion exchange sites, however, may be different from what has been observed on dry, bare surfaces, since the wet surface is intensely hydrated. It has been proposed that water molecules attached to surface hydroxyls form an “ice-like” structure in several layers, and it has been suggested that this structuring may confer uniform properties to surface hydroxyl groups (44). If the site affinity is homogeneous, the deviation of adsorption behaviors from the Langmiur equation may be ascribed to lateral interactions, as most ion-exchange models have been successful to reproduce the observed ion-exchange behavior in this manner (see the Introduction). The homogeneous sites do not mean that surfaces have only one type of sites, as definite numbers of discrete sites with different affinities have commonly been assumed to model adsorption properties of surfaces: the presence of acid and base hydroxyl sites is generally accepted. Two types of acid hydroxyl groups have been assumed for the exchange of Na1 with silanolic protons on silica (45). Polyfunctionality of ion exchange resins has been explained by assuming a total of three types of carboxyl sites with different reactivities due to different internal pore environments (46 – 48). For metal oxides several types of hydroxyl sites due to different crystal planes have been proposed (26 –29). In this modeling, lateral interactions have been assumed for each type of site, and each type of site with a discrete affinity occurring at a surface has been called a homogeneous “subsurface” by Riemsdijk et al. (26). The hydroxyl groups on oxides established here may have this kind of homogeneous discrete reactivities. The distinction between the discrete and continuous affinities may be made by analyzing experimental adsorption isotherms with theoretical equations. The Frumkin equation was developed by considering progressively increasing lateral in-

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SUMMARY

FIG. 5. Lateral interactions between Na1 ions adsorbed on outer and inner surfaces: (a) flat outer surface; (b) inner surface of tunnel-like pore; (c) inner surface of closed pore.

teractions between adsorbed species at uniform sites. Temkin considered sites of continuously varying adsorption affinity and derived an equation apparently not different from the Frumkin equation (49). The problem of discrete or continuously varying affinity cannot be solved by this analysis, as the two approaches provide essentially the same results. Attempts to distinguish the discrete and continuous affinities are still progressing with various site affinity distribution functions (30 –32). The existence of internal surfaces in oxides is obvious from the comparison between the outer surface area calculated from the size and shape of oxide particles observed by electronmicroscopy with the total surface area measured by the BET method. The magnetite (Sphere) sample here has a calculated outer surface area of ;1.2 m2 g21, while the BET area is 1.73 m2 g21, and a very small degree of porosity was suggested (36). However, the other oxide samples with much larger BET surface areas (Table 1) must have very large internal surfaces possibly due to micropores, crevices, or flaws (50). Figure 5a– c illustrates micropores in oxides and possible interactions between adsorbed ions on the internal surfaces of micropores. On flat surfaces (a) there is only the interaction between adjacent neighbors, while there are also interactions between neighbors on opposite inside walls of tunnel-like pores (b) and closed pores (c). The reactivity of internal hydroxyl sites at some coverages would be decreased differently by different lateral interactions depending on the extent of development of such micropores, i.e., number, shape, and size. Evaluation of differences in suppression due to different pore structures may be difficult with the electrical double layer models, because they assume the hydroxyl sites to be located on infinite flat surfaces. Such evaluation has been made elsewhere, however (37), with the Frumkin isotherm which assumes only thermodynamic relations of adsorption, where a strong suppression for oxides with large internal surfaces was established.

(1) The surface density of hydroxyl sites on metal oxides was measured by the Grignard reaction method, and the results are close to those by tritium exchange, dehydration by heating, crystallographic calculations, and others. (2) The hydroxyl site densities are similar for different oxides and they are comparable with that calculated from the closest packing of hydroxide ions. (3) The mechanism for surface hydroxylation proposed assumes that lattice oxide ions (extremely strong bases) are exposed to water and are neutralized by water to become hydroxide ions. (4) The saturated deprotonation method was also applied to hematite with very high concentrations of alkali solutions (;5 mol dm23 NaOH), and the same results as (1) were obtained. It is suggested that all hydroxyl groups take part in the ion exchange and that the small values reported elsewhere with this method may be erroneous. (5) Hetero- or homogeneity of hydroxyl groups in contact with water as ion exchange sites was discussed. Intensely hydrated layers at the oxide/water interface may result in homogeneous discrete sites. (6) The micropore structure in oxides is suggested, and different lateral interactions in different micropores were discussed. REFERENCES 1. Schindler, P., in “Adsorption of Inorganics at Solid–Liquid Interfaces” (M. A. Anderson and A. J. Rubin, Eds.), p. 1. Ann Arbor Science, Ann Arbor, MI, 1981. 2. James, R. O., and Parks, G. A., in “Surface and Colloid Science” (E. Matijevi’c, Ed.), Vol. 12, p. 119. Plenum, New York, 1982. 3. Schindler, P. W., and Stumm, W., in “Aquatic Surface Chemistry” (W. Stumm, Ed.), p. 87. John Wiley & Sons, New York, 1987. 4. Dzombak, D. A., and Morel, F. M. M., “Surface Complexation Modeling.” John Wiley & Sons, New York, 1990. 5. Stumm, W., “Chemistry of the Solid–Water Interface.” John Wiley & Sons, New York, 1992. 6. Fripiat, J. J., and Uytterhoven, J. J., J. Phys. Chem. 66, 800 (1962). 7. Morimoto, T., and Naono, H., Bull. Chem. Soc. Jpn. 46, 2000 (1973). 8. Naono, H., Kadota, T., and Morimoto, T., Bull. Chem. Soc. Jpn. 48, 1123 (1975). 9. Hohl, H., and Stumm, W., J. Colloid Interface Sci. 55, 281 (1976). 10. Schindler, P. W., Fu¨rst, B., Dick, R., and Wolf, P. U., J. Colloid Interface Sci. 55, 469 (1976). 11. Mu¨ller, B., and Sigg, L., J. Colloid Interface Sci. 148, 517 (1992). ¨ hman, L.-O., Nordin, J., and Sjo¨berg, S., J. Colloid Interface 12. Laiti, E., O Sci. 175, 230 (1995). 13. Morishige, K., Kittaka, S., and Morimoto, T., Bull. Chem. Soc. Jpn. 53, 2128 (1980). 14. Egashira, M., Nakashima, M., Kawasumi, S., and Seiyama, T., J. Phys. Chem. 85, 4125 (1981). 15. Peri, J. B., J. Phys. Chem. 69, 211 (1965). 16. Erkelens, J., and Linsen, B. G., J. Colloid Interface Sci. 29, 464 (1969). 17. Van Veen, J. A. R., J. Colloid Interface Sci. 121, 214 (1988). 18. Gorski, D., Klemm, E., Fink, P., and Ho¨rhold, H.-H., J. Colloid Interface Sci. 126, 445 (1988).

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