Langmuir 1999, 15, 8045-8051
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Effect of Different Crystal Faces on Experimental Interaction Force and Aggregation of Hematite Tjisse Hiemstra* and Willem H. Van Riemsdijk Department of Environmental Sciences, Sub Department of Soil Science and Plant Nutrition, Wageningen Agricultural University, P.O. Box 8005, 6700 EC Wageningen, The Netherlands Received March 26, 1999. In Final Form: July 22, 1999
Charging is a basic property of the solid/solution interface of minerals. The charging at different crystal faces depends on the surface chemical composition, that is, the type and number of proton-reactive surface groups. Atomic force microscopy has provided direct information on the pH-dependent charging properties of individual crystal faces (Eggleston and Jordan, Geochim. Cosmochim. Acta, 1998) of hematite (001 face) and quartz (101 face). This promising scanning force technique may enable the testing of structurereactivity relations as applied in the MUlti SIte Complexation model (MUSIC). The published pH-dependent variation of the interaction forces has been evaluated. The large experimental difference in the pH dependence of the interaction force is in accord with the expected proton affinity behavior of both crystal faces, as predicted with the MUSIC model. The reactivity of the 001 face of hematite is quite exceptional, because the surface groups only charge at extremely high or low pH values in contrast to the generally observed (overall) charging behavior of hematite. The difference in reactivity of the crystal faces of hematite has implication for the rate of aggregation. The presence of the 001 face leads to a less pH-dependent rate of aggregation below the point of zero charge, in accord with experimental observations (Schudel et al., J. Colloid Interface Sci., 1997). Model analysis further shows that the interaction forces acting on the 001 faces of hematite are sensitive to the presence of surface defects, in contrast to the forces acting on the 101 faces of quartz.
Introduction Charging is a basic property of the solid/solution interface of oxides. It affects surface processes such as adsorption,1-6 particle-particle interaction resulting in coagulation,7-10 and mineral dissolution and precipitation.11-14 Traditionally, particle charge has been measured mainly by using titration methods and electromobility measurements. These methods have the disadvantage that they only provide information about the chemical affinity of the surface as a whole. Circumstantial evidence is present that reactivity of crystal faces and sites may be quite different.15-22 This has led to the development of the * To whom correspondence should be addressed. (1) Hingston, F. J. In Adsorption at Solid-Liquid Interfaces; Anderson, M. A., Rubin, A. J., Eds.; Ann. Arbor Science Publishers: Ann Arbor, MI, 1981; Chapter 2. (2) Dzombak, D. A.; Morel, F. M. M. Surface Complexation Modeling: Hydrous Ferric Oxide; John Wiley: New York, 1990. (3) Davis, J. A.; Kent, D. B. In Mineral-Water Interface Geochemistry. Reviews in Mineralogy; Hochella, M. F., White, A. F., Eds.; Mineral Society of America: Washinghton, DC, 1990; Vol. 23, p 177. (4) Stumm, W. Chemistry of the Solid-Water Interface; John Wiley & Sons: New York, 1992. (5) Hiemstra, T.; Van Riemsdijk, W. H. J. Colloid Interface Sci. 1996, 179, 488. (6) Hiemstra, T.; Van Riemsdijk, W. H. J. Colloid Interface Sci. 1999, 210, 182. (7) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1992. (8) Schudel, M.; Behrens, S. H.; Holthoff, H.; Kretzschmar, R.; Borkovec, M. J. Colloid Interface Sci. 1997, 196, 241. (9) Behrends, S. H.; Borkovec, M.; Schurtenberger, P. Langmuir 1998, 14, 1951. (10) Waltz, J. Y. Adv. Colloid Interface Sci. 1998, 78, 119. (11) Pulver, K.; Schindler, P. W.; Westall, J. C.; Grauer, R. J. Colloid Interface Sci. 1984, 101, 554. (12) Furrer, G.; Stumm, W. Geochim. Cosmochim. Acta 1986, 48, 2405. (13) Hiemstra, T.; Van Riemsdijk, W. H. J. Colloid Interface Sci. 1990, 136, 132. (14) Weidler, P. G.; Hug, S.; Wetche, T. P.; Hiemstra, T. Geochim. Cosmochim. Acta 1998, 62, 3407.
MUlti SIte Complexation (MUSIC) framework,5,6,23,24 which explicitly may account for the difference in behavior of the various types of surface sites and crystal faces. An important aspect of the applicability of the MUSIC approach is the availability of proton affinity constants for the individual types of surface groups. Several theoretical approaches have been used to estimate the proton affinity constants of individual types of sites, ranging from a bond valence analysis of surface sites24 to molecular dynamic and mechanic calculations of clusters.25,26 In these approaches the model results are empirically related to known affinity constants. The most recent approaches include the presence of H bonds and solvent.24,26 Unfortunately, it is very difficult to get information about the behavior of individual sites or even crystal faces, restricting the testing of surface structure-reactivity relations. Experimental assessment of reactivity of one particular type of crystal face can only be done if the (15) Russell, J. D.; Parfitt, R. L.; Fraser, A. R.; Farmer, J. C. Nature 1974, 248, 220. (16) Parfitt, R. L.; Atkinson, R. J.; Smart, R. St. C. Soil Sci. Soc. Am. Proc. 1975, 39, 837. (17) Van Riemsdijk, W. H.; Lyklema, J. Colloids Surf. 1980, 1, 33. (18) Hiemstra, T.; Van Riemsdijk, W. H.; Bruggenwert, M. G. M. Neth. J. Agric. Sci. 1987, 35, 281. (19) Colombo, C.; Barro´n, V.; Torrent J. Geochim. Cosmochim. Acta 1994, 58, 1261. (20) Spadini, L.; Manceau, A.; Schindler, P. W.; Charlet, L. J. Colloid Interface Sci. 1994, 168, 73. (21) Bargar, J. R.; Brown, G. E.; Parks, G. A. Geochim. Cosmochim. Acta 1997, 61, 2639. (22) Sugimoto, T.; Wang, Y. J. Colloid Interface Sci. 1998, 207, 137. (23) Hiemstra, T.; Van Riemsdijk, W. H.; Bolt, G. H. J. Colloid Interface Sci. 1989,133, 91. (24) Hiemstra, T.; Venema, P.; Van Riemsdijk, W. H. J. Colloid Interface Sci. 1996,184, 680. (25) Rustad, J. R.; Felmy, A. R.; Hay, B. P. Geochim. Cosmochim. Acta 1996, 60, 1563. (26) Rustad, J. R.; Wasserman, E.; Felmy, A. R.; Wilke, C., J. Colloid Interface Sci. 1998, 198, 119.
10.1021/la9903604 CCC: $18.00 © 1999 American Chemical Society Published on Web 09/30/1999
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mineral has one really dominant crystal face. Some preparations of goethite with a dominant 110 face may be a reasonable candidate. Studying the behavior of mineral preparations in which the relative contribution of two dominant faces is varied may be another option, as has been used lately for hematite22 and gibbsite.27 Very recently a considerable contribution has been made using a scanning force microscope (SFM) approach on welldefined surfaces of cleaved single crystals.28 In potency the SFM enables the assessment of the charging properties of individual crystal faces of minerals in situ. Eggleston and Jordan28 have determined the pH-dependent particleparticle interaction on the 001 face of a single crystal of hematite and on the 101 face of quartz. The use of these two materials has the advantage that they are chemically stable, in contrast to single crystals of corundum (R-Al2O3), which may transform into aluminum hydroxide.29,30 Another advantage of the presented approach is the use of cleaved crystals, which may avoid cleaning with, for instance, heat treatment (dehydration) and its corresponding surface changes. The SFM has been used as a device to measure the attractive and repulsive forces between a tip and sample. In principle these forces can be evaluated using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, provided that, for instance, the exact topography of the tip and sample are known. Because of the uncertainties, Eggleston and Jordan28 suggested to evaluate the SFM data by comparing them semiquantitatively with the results of the DLVO theory, that is, mainly the pH dependency is evaluated. We will follow this approach. The electrostatic potential plays a crucial role in the interaction. This potential will be calculated with the MUSIC model (basic Stern approach). This will be done for the 101 face of quartz (SiO2) and especially for the 001 face of hematite (Fe2O3). The surface structure and surface sites of both faces will be discussed briefly. Recently the rate of aggregation of hematite particles has been determined as a function of pH and ionic strength.8 Below the point of zero charge (PZC) the rate of aggregation was found to be much less pH dependent, showing that the interaction forces are different in this pH range. This phenomenon may be related to the presence of the 001 face. This will be evaluated. Surface Structure Crystal faces may have different types of sites. One of the most prominent reasons for the difference in chemical behavior of the surface groups is the variation in the number of metal ions that coordinate to surface oxygens. A variable number of coordinating metal ions may lead to a difference in charge neutralization of the surface oxygens. The charge neutralization can be evaluated using the Pauling bond valence approach31 as applied in the MUSIC concept.23,24 We demonstrate this for quartz. The Si4+ ion in SiO2 is coordinated to four oxygens, resulting in a charge neutralization of one valence unit (v.u.) per bond. The valence of the oxygens in the bulk (-2 v.u.) is neutralized by two Si ions (#Si2O0), each contributing +1 v.u. At the surface, some oxygens may become singly coordinated as result of the absence of one Si. The resulting (27) Hiemstra, T.; Han Yong; Van Riemsdijk, W. H. Langmuir, in press. (28) Eggleston, C. M.; Jordan, G. Geochim. Cosmochim. Acta 1998, 62, 1919. (29) Larson, I.; Drummond, Chan, D. Y. C.; Grieser, F. Langmuir 1997, 13, 2109. (30) Pedersen, H. G. Langmuir 1999, 15, 3015. (31) Pauling, L. J. Am. Chem. Soc. 1929, 51, 1010.
Hiemstra and Van Riemsdijk
undersaturation of charge can be neutralized by the uptake of one proton, leading to the formation of a #SiOH0 group. Analysis of the surface structure of the 101 face of quartz reveals a site density of 6.1 sites/nm2 for #SiOH0 .32 The singly coordinated surface groups are believed to be the proton-reactive type of surface group on silica and quartz. At high pH #SiO- groups are formed. At very low pH #SiOH2+ will be formed. The pH with equal amounts of both charged surface groups (#SiO-1 ) #SiOH2+1) is called the point of zero charge (PZC). For quartz the experimental PZC is 2.33 The protonation reactions can be formulated as:
#SiO- + H+ 〈)〉 #SiOH0; logK1
(1)
#SiOH0 + H+ 〈)〉 #SiOH2+; logK2
(2)
and
Attempts have been made to predict the proton affinity of the surface groups. Hiemstra et al.24 found values of 7.7 and -4, respectively, for the first and second protonation step. They used a bond valence approach. Recently Rustad et al. 26 predicted a value of 8.5 for the first protonation reaction with molecular mechanics of gas-phase clusters and slabs, previously applied to goethite. With this approach a too-high logK2 value (logK2 ) 5.9) is found, that is, a small ∆pK is predicted. However, introduction of nanosolvation in the approach led to the conclusion that logK2 must be very small,26 although no logK2 could be calculated. From the predictions we conclude that the protonation of the 001 face of quartz is characterized by a two-step protonation reaction with a large difference in proton affinity, that is, a large ∆pK is predicted. In the given approaches no attempts have been made to distinguish more than one type of hydroxyl, such as isolated, vicinal, and germinal sites. For quartz a rather unique situation exists, in the sense that one is able to assess the proton affinity constant (logK1 of reaction 1) from ordinary titration experiments. This is possible because the surface has only one main type of proton-reactive group and because the difference in logK values between the first and second protonation steps is large (about 10-12 logK units); that is, the second step is quantitatively not relevant in the experimental pH range. A compilation of literature data on the charging of silica and quartz has been given by Sahai and Sverjensky.34 Schindler and Kamber35 found for amorphous silica a logK1 value of 6.8 and Hiemstra et al.36 found a value of logK1 ) 7.5 for the data of Bolt.37 The latter value will be used in calculations in this paper. The bond valence analysis can also be applied to the 001 face of hematite. In the solid the Fe3+ ion is hexacoordinated with oxygens, leading to a Pauling bond valence of 0.5 v.u. It implies that on average four Fe ions are needed to neutralize the oxygen valence. This is the situation in the bulk of hematite. The 001 face of hematite is rather unique. The surface oxygens have only one type of coordination, that is, all groups are doubly coordinated (32) Yates, D. E. The Structure of the Oxide/Aqueous Electrolyte Interface. Ph.D. Thesis, University of Melbourne, Melbourne, Australia, 1975. (33) Kosmulski, M. Langmuir 1997, 13, 6315. (34) Sahai, N.; Sverjensky, D. A. Geochim. Cosmochim. Acta 1997, 61, 2801. (35) Schindler, P. W.; Kamper, H. R. Helv. Chim. Acta 1968, 15, 1718. (36) Hiemstra, T.; De Wit, J. C. M.; Van Riemsdijk, W. H. J. Colloid Interface Sci. 1989, 133, 105. (37) Bolt, G. H. J. Phys. Chem. 1957, 61, 1166.
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(#Fe20-1). The site density of the surface groups is 13.7 nm-2.38 The undersaturation of the oxygen charge (-1) can be compensated by the uptake of a proton, yielding #Fe2OH0. This proton can be removed at sufficiently high pH. At low pH the #Fe2OH2+ species may be formed. The reactions are:
# Fe2O- + H+ 〈)〉 #Fe2OH0; logK3
(3)
# Fe2OH0 + H+ 〈)〉 # Fe2OH2+; logK4
(4)
and
A closer look at the structure of hematite shows that the Fe ions are not symmetrically located in the octahedron.24,25 The ions are distorted. This leads to differences in Fe-O bond length. This difference in length can be translated to a difference in charge distribution of the Fe over the surrounding oxygens. It gives a difference in bond valence as defined by Brown40 and Brown and Altermatt.41 With the bond valence approach for estimation of the proton affinity,24 this can be been taken into account. For the doubly coordinated surface groups at the 001 face it implies that one Fe-O bond length is large and one is relatively short. The corresponding bond valences are respectively 0.4 and 0.6 v.u. and the sum is 1.0 v.u. Fortunately the sum is precisely the same as that found with the Pauling bond valence approach where one assumes an equal bond length. It implies that a relaxation of the surface layer, as supported by the work of Eggleston and Hochella,42 will not influence the charge attribution and our predictions of the proton affinity constants. The estimated logK values for the protonation of the #Fe2Oand #Fe2OH0 (eqs 3 and 4) are respectively 11.9 and 0.0 if one explicitly accounts for the formation of H bonds with the solvent.25,43 No other estimates for these logK values exist at present for hematite. It is noted that the molecular mechanical calculations of Rustad et al.25 predict a logK for the protonation of Fe2O- and Fe2OH0 being respectively logK1 ) 9.0 and logK2 ) 5.9 for the 110 face of goethite. Later these values were slightly adjusted: logK1 ) 10 and logK2 ) 7.8.44 The calculations point to a relatively small difference in affinity, ∆logK value ) 2.2. This contrasts with our predictions. Especially, the value for protonation of Fe2OH0 is totally different from our estimate (logK ) 0). It is noteworthy that very recently Rustad et al.45 assumed in their assessment of the proton affinity a priori that only surface species with a sufficiently small bond valence charge will be stable ( 2). However, this may change in the constant potential approximation into a relatively large attraction at small distances (e.g., κh < 1), even if the potentials at the head end of the DDL are in both cases negative.46,48 The difference between the constant charge and the constant potential approach is quite large at small distances of approach (κh < 2). Moreover, the forces at small distances are subject to large uncertainties due to, for instance, surface roughness, as discussed by Ducker et al.,49 Zhmud et al.,50 and Waltz.10 In our calculations we will assume for the particle-particle distance at contact a value of h ) 6 nm (κh ≈ 2 in 0.01 M electrolyte solution) and use the constant potential approach because this expression is more accurate.48 Silica Tip over the 101 Face of Quartz In Figure 3 the data of the force at contact28 are given as a function of pH. Low interaction forces are present at low pH, where one expects the PZC of silica and quartz. At high pH a large interaction force is observed. We have calculated the pH dependence of the force. We assumed that tip and crystal have the same charging behavior. We omitted the van der Waals attraction. The potential at the head end of the DDL depends on the assumption of the formation of ion pairs. It has been shown that for silica the ion pair formation is rather weak.36,51 We have used a logK value of -1.8 for the reaction #SiO+ Na+ 〈)〉 #SiO- - Na+, which was found 36 as the best (49) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Langmuir 1992, 8, 1831. (50) Zhmud, B. V.; Meurk, A.; Bergstro¨m, L. J. Colloid Interface Sci. 1998, 207, 332. (51) Sonnefeld, J. Colloid Polym. Sci. 1995, 275, 932.
Interaction Force and Aggregation of Hematite
Figure 3. Force at contact between a tip (oxidized Si wafer) and the 101 face of quartz as sample measured by Eggleston and Jordan.28 The presented data were obtained in 0.01 M NaCl. The line is calculated (constant potential approach) assuming that tip and sample have the same reactivity. For comparison, the constant charge approach is also given (dotted line). The distance at contact is set at h ) 6 nm. The radius of the tip is set at 0.1 µm. The site density is 6.1 nm-2, logKH ) 7.5, logKNa ) -1.8. The Stern layer capacitance is 2.5 F/m2.
fit for the charging data of Bolt.37 The Na+ ion is located in the outer plane of the basic Stern model. The corresponding Stern layer capacitance is 2.5 F/m2. The calculated potentials at the head end of the DDL are assumed to be the potentials during interaction (eq 6). This is known as the constant potential or constant charge approximation.7,46 The calculated force is approximately constant over a relatively large pH range around the PZC because the development of the potential with change of pH is relatively small. This is known as non-Nernstian behavior and has been experimentally observed measuring directly the surface potential of a SiO2-ISFET.52 This behavior is typical for surfaces of, for instance, silica, latex, and humic acids, etc.53 It is noticed that many other (hydr)oxide surfaces behave often near-Nernstian, that is, silica and quartz are rather atypical.23 Another exception is the 001 face of hematite, which we predict to behave like silica and quartz. One should be rather careful with the interpretation of the data in Figure 3. We do not have information over the SiO2 wafer tip. The size (radius) is unknown, as is its reactivity. We analyzed literature data on the interaction between a glass sphere and a SiO2 wafer.49,50 The reactivity (tip or sample or both) is quite different from classical silica behavior. The apparent site densities are found to be extremely low, and the analysis showed that the change in potential with pH is very different from what is expected for silica and quartz. From this point of view, the use of a crystal with a known reactivity as tip seems to be preferred. Hematite Tip over the 001 Face of Hematite The experimental force at contact on the 001 face of hematite is, as in the case of quartz, clearly variable in the experimental pH range (Figure 4). At a pH value >10 the interaction is highly repulsive. Around a pH of 8 a minimum is found. In the lower pH range the interaction force is either indistinguishable from zero (data not shown, measured in NaNO3) or the force is slightly increasing (52) Van Hal, R. E. G.; Eijkel, J. C. T.; Bergveld, P. Adv. Colloid Interface Sci. 1996, 69, 31. (53) Healy, T. W.; White, L. R. Adv. Colloid Interface Sci. 1978, 9, 303.
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Figure 4. Force at contact between a tip (a shard of crushed hematite) and the 001 face of cleaved hematite as sample measured by Eggleston and Jordan.28 The lines are calculated (constant potential approach) assuming that tip and sample react respectively like colloidal hematite particles and 001 face (full line), 001 face and 001 face (dashed line), or colloidal hematite-hematite particles (dotted line). The distance at contact is set at h ) 6 nm. The radius of the tip is set at 1 µm. For parameters of the charge model see Figure 1.
with the proton concentration (data given in Figure 4, measured in NaCl). We have calculated the expected pH dependency pattern. We assumed that the tip has a reactivity equivalent with the overall behavior of colloidal hematite particles. The charging reaction of the tip is represented by eq 5 and the parameter values for hematite given by Schudel et al.8 are used. For the sample (001 face) the calculated reactivity has been based on the estimated log K values of the protonation (eqs 3 and 4) of the doubly coordinated groups.24,43 For tip and sample, symmetrical ion-pair formation has been assumed, using the ion-pair formation constants of Schudel et al.8 The result is shown in Figure 4. The calculated curve (full line) does not show a significant development of force over a large pH range
