Short-Range Forces between Glass Surfaces in Aqueous Solutions

Langmuir 2008, 24, 4881-4887

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Short-Range Forces between Glass Surfaces in Aqueous Solutions Sergio M. Acun˜a† and Pedro G. Toledo* Chemical Engineering Department and Surface Analysis Laboratory (ASIF), UniVersity of Concepcio´ n, P.O. Box 160-C, Correo 3, Concepcio´ n, Chile ReceiVed December 11, 2007. In Final Form: January 21, 2008 We found that the force between glass surfaces measured with an atomic force microscope (AFM) has universal character in the short range, less than ∼1 nm or about 3-4 water molecules, independent of solution conditions, that is, electrolyte ion size, charge and concentration and pH. Our results suggest that the excess DLVO force, obtained by subtracting the DLVO theory with a charge regulation model from the AFM force data, essentially does not change with the electrolytes Na, Ca, and Al, in the range of concentration from 10-6 to 10-2 M and the range of pH from 3.1 to 7.9. Single force curves for a glass-silica system in a 10-4 M aqueous NaCl solution at pH ∼5.1 show oscillations with a period of about 0.25 nm, roughly the diameter of a water molecule. We postulate that the excess force between glass surfaces arises from a surface-induced solvent effect, from the creation of a hydrogen-bonding network at the surface level, rather than from a solvent-induced surface steric hindrance.

Introduction The origin of short-range forces between surfaces in liquids is a subject of current and vivid debate. This complex interaction force, which is in excess of continuum van der Waals and electrical double-layer DLVO forces,1,2 is probably the most important yet the least understood of all forces in liquids. Such a force was originally advocated as short-range hydration repulsion by Parsegian and co-workers in the 1980s, on the basis of force measurements between lipidic bilayers.3-4 Incisive clarifying reviews and data compilations are available.5-7 Here we focus on the interaction of glass surfaces in water solutions. For a number of researchers, hydrophilic surfaces remain well-separated in water, because they experience monotonic repulsive forces arising from the structuring of water molecules in their close vicinities.8-18 This idea has had such echo in the literature that the excess DLVO force very frequently is referred to as a hydration force, “primary” when hydration water is directly removed and * Corresponding author. E-mail: [email protected]. † Present address: Department of Food Engineering, University of BioBio, Chilla´n, Chile. E-mail: [email protected]. (1) Derjaguin, B. V.; Landau, L. Acta Physicochim. URSS 1941, 14, 633-662. (2) Verwey, E. J. W.; Overbeek, J. Th. G. In Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948. (3) LeNeveu, D. M.; Rand, R. P.; Parsegian, V. A. Nature 1976, 259, 601603. (4) LeNeveu, D. M.; Rand, R. P.; Parsegian, V. A.; Gingell, D. Biophys. J. 1977, 18, 209-230. (5) Butt, H.-J.; Cappella, B.; Kappl, M. Surf. Sci. Rep. 2005, 59, 1-152. (6) Fro¨berg, J. C.; Rojas, O. J.; Claesson, P. M. Int. J. Miner. Process. 1999, 56, 1-30. (7) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1992. (8) Israelachvili, J. N.; Adams, G. E. J. Chem. Soc. Faraday Trans. 1 1978, 74, 975-1001. (9) Pashley, R. M. J. Colloid Interface Sci. 1981, 83, 531-546. (10) Rabinovich, Y. I.; Derjaguin, B. V.; Churaev, N. V. AdV. Colloid Interface Sci. 1982, 16, 63-78. (11) Peschel, G.; Belouschek, P.; Mu¨ller, M. M.; Mu¨ller, M. R.; Ko¨nig, R. Colloid Polym. Sci. 1982, 260, 444-451. (12) Israelachvili, J. N. Chem. Scr. 1985, 25, 7-14. (13) Horn, R. G.; Smith, D. T.; Haller, W. Chem. Phys. Lett. 1989, 162, 404408. (14) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991, 353, 239241. (15) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Langmuir 1992, 8, 18311836. (16) Grabbe, A.; Horn, R. G. J. Colloid Interface Sci. 1993, 157, 375-383. (17) Chapel, J.-P. Langmuir 1994, 10, 4237-4243. (18) Colic, M.; Fisher, M. L.; Franks, G. V. Langmuir 1998, 14, 6107-6112.

“secondary” when hydrated adsorbed species are removed. The mechanism is that water forms strong hydrogen bonds with silanol groups on the interacting surfaces. Klier and Zettlemoyer19 showed that the water molecules “sit” on the silanol groups with the oxygens pointing downward to the surface, implying that, in forming a hydrogen bond between water and silanol groups, the water molecule acts as a base and the silanol as an acid. In contrast to the electrostatic double-layer force, hydration forces reported tend to become stronger and longer ranged with increasing salt concentration, especially for multivalent cations. Israelachvili and Wennerstro¨m suggested a different interpretation in which hydration forces are attractive or oscillatory but not repulsive and where the repulsion has a completely different origin.20 According to these authors, experiments from Vigil et al. suggest that a correct understanding of the way short-range repulsive forces arise requires focusing on the detailed structure and properties of the interacting surfaces rather than on the structure of the intervening solvent.21 In passing, this statement disregards theoretical efforts centered in the water modeling near surfaces, in particular the phenomenological work of Marc¸ elja and collaborators, widely mentioned whenever short-ranged monotonic repulsions appear.22,23 Silica is a solid with uncharged silanol groups (tSi-OH) and charged silicic acid groups (t Si-O-) at the surface.24 According to Israelachvili and Wennerstro¨m, protons can be dissociated from the surface silanol groups, generating a long-range repulsive DLVO double layer type force. In addition, the surface of the silica is generally amorphous and clearly not molecularly smooth, being covered with molecularly thin silica “hairs”.21 These hairs push the electric double layer repulsion farther out from the silica massive surface than does the van der Waals attraction, at the same time that a short-range steric repulsion is generated from the interaction of protuberant silica hairs. Such protruding surface groups should not be considered as fixed or rigid but rather as a superficial layer of polymer-like flexible segments that expand or collapse on the (19) Klier, K.; Zettlemoyer, A. C. J. Colloid Interface Sci. 1977, 58, 216-229. (20) Israelachvili, J. N.; Wennerstrom, H. Nature 1996, 379, 219-225. (21) Vigil, G.; Xu, Z.; Steinberg, S.; Israelachvili, J. N. J. Colloid Interface Sci. 1994, 165, 367-385. (22) Marc¸ elja, S.; Radic´, N. Chem. Phys. Lett. 1976, 42, 129-130. (23) Gruen, D. W. R.; Marc¸ elja, S. J. Chem. Soc. Faraday Trans. 2 1983, 79, 225-242. (24) Iler, R. K. The Chemistry of Silica; Wiley: New York, 1979.

10.1021/la703866g CCC: $40.75 © 2008 American Chemical Society Published on Web 03/28/2008

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surface upon simply varying the solution pH. This suggests that the force is steric more than hydration in origin and that it becomes stronger and longer ranged with increasing hair extensions.20,21 Recent molecular dynamic studies, however, reveal that the interaction between perfectly flat hydrophilic surfaces with a relaxed distribution of surface charges displays strong repulsion at close distances followed by oscillations when the distance is within two water molecules.25 Here we offer extensive data that add a new and perhaps key element to the discussion on the origin of the short-range repulsive force between hydrophilic mineral surfaces. The force between glass surfaces measured with an atomic force microscope has universal character in the short range, less than ∼1 nm or about three or four water molecules, independent of water conditions; electrolyte ion size, charge, and concentration; and pH. Methods Glass microslides (B&C) typically 1 × 1 cm2 were used. The flat substrates were glued to AFM stubs before use. Glass colloidal probes were prepared by gluing a 20 µm diameter sphere (Duke Scientific Corp.) to the end of a tipless, V-shaped, 100 µm long, 0.6 µm thick Si3N4 cantilever (Veeco) with Norland Optical Adhesive 61 (Norland Products). A simple adaptation of Huntington and Nespolo protocol for attaching spheres to AFM cantilever tips was implemented in a Dimension 3100 (Veeco) atomic force microscope.26 The size of the microsphere was determined by SEM (ETEC, Autoscan). Probes were UV-heated enough to secure the microsphere-cantilever bonding. Spring constants of individual cantilevers were determined by the method of standards (standards provided by Park Scientific) with the Dimension 3100 AFM microscope and were typically 0.14 N/m. Probes were thoroughly rinsed first with bidistilled water and then with ethanol before use. SEM and AFM images verified the quality of the modified cantilevers. Prior to force measurement, the mineral surfaces, substrate, and sphere were thoroughly rinsed in high-purity water (18.6 MΩ/cm). Surface roughness, assessed by AFM imaging with the Dimension 3100, was typically subnanometer in size both for substrate and microsphere. Surfaces were characterized by X-ray photoelectron spectroscopy (Escalab 220i-XL, VG Scientific) and contact angle (Rame´-Hart goniometer) for purity. Force measurements between AFM probes and substrates as function of separation were conducted using an SPM-3 (Veeco) multimode atomic force microscope equipped with a Nanoscope IIIa SPM control station, fluid cell (0.1 cm3), silicone pad for vibration isolation, and acoustic enclosure. Samples were manipulated with tweezers to avoid contamination. Once substrate and probe were appropriately mounted, the cell was flushed repeatedly first with high-purity water and then with the electrolyte solution of interest prior to equilibration and force measurement. The system was allowed to reach equilibrium for few minutes before probe and substrate were approached one to another. For one key aspect, this was expected to reduce the presence of air microbubbles. Measurement of a typical force curve took less than 1 h; during this time frame, the AFM roughness of the substrate remained unaltered. AFM allows continuous measurement of cantilever deflection vs position as probe and substrate approach, commonly named extension, or separate, commonly named retraction. Data were provided by Nanoscope IIIa DI v4.42 instrument software (Veeco). Sample displacement was determined with a Z-piezoelectric crystal that was calibrated frequently with height standards of varying heights. To convert these data into force vs separation curves, we used the wellestablished method of Ducker et al.14,15 implemented in commercial software and our own routine. A brief review of the procedure follows. As the sample surface was driven toward the colloidal probe, the cantilever of known spring constant was deflected, and this was measured using a laser reflected off the cantilever onto a positionsensitive photodiode. Conversion of the diode-voltage vs sample (25) Lu, L.; Berkowitz, M. L. Mol. Phys. 2006, 104, 3607-3617. (26) Huntington, S.; Nespolo, S. Microsc. Today 2001, 1-3, 32-33.

Figure 1. (a) Examples of tip deflection versus Z-piezo displacement data from the Nanoscope IIIa software for the interaction between a flat glass substrate and a silica-glass sphere in water and in aqueous 10-2 M NaCl solution at 20 °C and pH ∼5.1. The zero of force occurs where the tip deflection is constant. The region of constant compliance is clearly seen in the figure where tip deflections are the highest. (b) Data from part a converted into force versus Z-piezo displacement. (c) Data from part b converted to force normalized by the silica probe radius as a function of separation of substrate and probe. The inset in part c displays the zero of distance, the position at which substrate and probe come in contact and the region where the repulsive force becomes vertical. displacement data to a force vs surface separation curve requires definition of zeros of both force and separation. The zero of force was chosen at the point where the deflection was constant (where

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Figure 2. Force curves between a flat glass substrate and a silica-glass microsphere at separations less than 5 nm in a range of solutions at 20 °C and pH ∼5.1. Each curve represents the average of three independent AFM measurements in exactly the same position on the substrate. Electrolytes are NaCl, CaCl2, and AlCl3. Concentrations range from 10-4 to 10-2 M.

the interacting surfaces were far apart). The zero of separation was defined from the force profile at high force, at the onset of the constant compliance region where the diode output becomes a linear function of the surface displacement, that is, where the probe is in contact with the surface. The constant compliance region was used to convert the diode signal into cantilever deflection, which in turn was used to determine surface separation. The force acting between the probe and the flat surface was determined from the deflection of the cantilever according to Hooke’s law. Extension and retraction driving speeds were low in order to minimize hydrodynamic contribution to the measured force. Typically, four or five force data points per nanometer were acquired. To examine the force curves closely in the last 2 nm before contact, roughly 10 force data points per nanometer were taken. Force curves were first verified to be independent of position on the substrate; measurements were always highly reproducible. Curves reported here correspond to the mean of at least three force curves measured in the same position. Standard deviation increases with electrolyte charge and concentration, although it always remains small and negligible. Forces are reported normalized by the microsphere probe radius, that is, as an interaction energy between flat surfaces by virtue of Derjaguin’s approximation, F(D) ) 2πRE(D),27 where F is force, D distance, R probe radius, and E energy per unit area. (27) Derjaguin, B. V. Kolloid Z. 1934, 69, 155-164.

Results and Discussion Examples of extension force-displacement curves for a flat glass substrate and a silica-glass sphere interacting in water and in aqueous 10-2 M NaCl solutions are shown in Figure 1. Figure 1a displays the output from the photodiode, corresponding to cantilever or tip deflection, versus the distance over which the Z-piezoelectric is moved. The linear region of constant compliance is clearly seen in both curves. Figure 1b displays data from Figure 1a converted into force versus separation between substrate and probe. Figure 1c shows data from Figure 1b converted into force normalized by the probe radius as a function of substrate-probe separation. Figure 1 displays zeros of both force and position and also the region where the repulsive force becomes vertical. In the following analysis, we consider force data right up to the contact between substrate and probe. Figures 2 and 3 display corresponding extension forceseparation curves measured in a range of aqueous NaCl, CaCl2, and AlCl3 solutions, with concentrations ranging from 10-6 to 10-2 M and pH from 3.1 to 7.9. As expected, the force is repulsive in all cases and decreases with electrolyte concentration and notably with counterion size and acidic pH. Figure 2 for AlCl3 shows that the trivalent Al3+ ion reduces the repulsion roughly in the same (high) proportion with respect to Ca2+ and Na+ for

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Figure 3. Force curves between a flat glass substrate and a silicaglass microsphere at separations less than 5 nm in NaCl 10-4 M solutions at 20 °C and pH 3.1, 5.1, and 7.9. Each curve represents the average of three independent AFM measurements in exactly the same position on the substrate.

Figure 4. DLVO fits to force curves between a flat glass substrate and a silica-glass microsphere in water at 20 °C. Constant charge, constant potential, and surface charge regulation models are compared. Hamaker constant is 0.85 × 10-20 J. Charge-regulated surface potential at infinite separation is used in all three models. Parameters are summarized in Table 1.

any of the concentrations tested, no matter how low, except in the short range where other mechanisms operate. The repulsion in the long range originates in the entropic confinement of counterions. In water, the repulsion is purely electrostatic. Surface charge screening in the presence of AlCl3 is so high that, in the long range at the highest concentrations studied here, the interaction turns into attraction. For many systems, particularly minerals, the continuum DLVO theory has been found to describe satisfactorily the surface interactions down to separations of 1-2 nm. Key features of the theory are the repulsive electric double-layer force and the attractive van der Waals force that operates in the long range over 1-2 nm. This is precisely so for our mineral surfaces, as Figures 4-6 show. Nonretarded van der Waals attractions between glass and silica were calculated through the Lifschitz theory with a Hamaker constant of 0.85 × 10-20 J (Meagher and others have

Acun˜ a and Toledo

used this value).28 Repulsive double-layer interactions for the same system were calculated by solving the nonlinear PoissonBoltzmann equation with the precise numerical algorithm of Chan et al.29 At small separations, the force predicted by DLVO theory depends on boundary conditions for the surface charge. Here, as appropriate for glass and silica above the isoelectric point, we use the so-called site dissociation model.30 The dissociation equation is tSi-OH T tSi-O- + H +. The surface charge of silica is thus determined by the number of dissociated silanol groups at the surface. Surface charge and surface potential are coupled, thus providing a model for surface charge regulation as the silica surfaces approach under a given solution ambient. The equilibrium constant is pK ) 7.5 and the total number of active dissociable sites is 8/nm2.31 For glass surfaces at large separations in 10-6 M NaCl solution, the charge regulation value calculated here for the surface potential is -118 mV, a value too high compared with values in the literature. In 10-4 M NaCl solution, the charge regulation value for the surface potential is -74.6 mV, in accordance with values in the literature ranging from -61 mV (Weise et al.32) to -83 mV.15 In 10-3 M NaCl solution, the potentials in the literature vary from -32 to -67 mV,13,32 a range that includes the regulated value of -55.4 mV calculated here. In 10-2 M NaCl solution, the potentials vary from -28 to -43 mV,13,14 excluding the somewhat higher value of -51.3 mV calculated here. For asymmetric electrolytes, such a comparison is not possible, due to a lack of data. However, our calculated surface potentials follow the expected trend, i.e., increasing the counterion valence decreases the surface potential. Table 1 summarizes charge regulation parameters used in Figures 4 and 5 and the minimum separation distance for which DLVO applies. The water used was bidistilled with a conductivity of 18.6 MΩ/cm and a concentration roughly estimated to be 10-6 M from material dissolved from the glassware. The use of downadjusted concentrations at high electrolyte concentrations to purposely improve data fit is routinely employed and justified on the ground that DLVO works better at low concentrations. Adjusted concentrations here are lower than the actual concentrations already at 1 mM salt. Table 2 summarizes corresponding charge regulation parameters used in Figure 6. Constant surface charge and constant surface potential models respectively overpredict or underpredict the interaction force, a well-known fact. For the analysis here, we prefer the charge regulation model that works better down to the shortest separation distances, as the insets in Figures 4-6 demonstrate. Analysis of measured force curves in the short range requires an act of faith in the DLVO theory, particularly on the assumption of the algebraic addition of forces and on the validity of doublelayer and van der Waals forces, both long-range by definition. This way one can isolate the “extra” DLVO repulsion by subtracting the theory from the data measured at short range. In favor is the known fact that DLVO works amazingly well at short distances, on the order of 2-5 nm, by a fortuitous cancellation of two or more opposite effects, however, leaving many observations unexplained. Figure 7 shows “extra” DLVO repulsive force curves for a flat glass substrate and a silica-glass sphere immersed in a range of aqueous NaCl, CaCl2, and AlCl3 solutions, with concentrations from 10-6 to 10-2 M and pH from 3.1 to 7.9. The various force curves surprisingly collapse in a single curve for surface (28) Meagher, L. J. Colloid Interface Sci. 1992, 152, 293-295. (29) Chan, D. J. Colloid Interface Sci. 2002, 245, 307-310. (30) Healy, T. W. Pure Appl. Chem. 1980, 52, 1207-1219. (31) Behrens, S. H.; Borkovec, M. Phys. ReV. E 1999, 60, 7040-7048. (32) Weise, G.; James, R.; Healy, T. Discuss. Faraday Soc. 1971, 52, 302311.

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Figure 5. DLVO fits to force curves between a flat glass substrate and a silica-glass microsphere in a range of solutions at 20 °C. Constant charge, constant potential, and surface charge regulation models are compared. The Hamaker constant is 0.85 × 10-20 J. Charge-regulated surface potential at infinite separation is used in all three models. Parameters are summarized in Table 1. The first row is for NaCl, the second for CaCl2, and the third for AlCl3. The first column is for 10-4 M, the second for 10-3 M, and the third for 10-2 M.

Figure 6. DLVO fits to force curves between a flat glass substrate and a silica-glass microsphere in a range of solutions at 20 °C. Constant charge, constant potential, and surface charge regulation models are compared. The Hamaker constant is 0.85 × 10-20 J. Charge regulated surface potential at infinite separation is used in all three models. Parameters are summarized in Table 2. The electrolyte is NaCl, the concentration is 10-4 M, and the pH is (from left to right) 3.1, 5.1, and 7.9.

separations below ∼2 nm. The higher the electrolyte valence, the shorter the range of the repulsive force; however, the intensity of the force remains the same for the various electrolytes. At separations larger than 2 nm, the data exhibit considerable dispersion following the electro-osmotic order, i.e., for each electrolyte, a higher concentration reduces the magnitude of the interaction. The absence of dispersion at short separations marks the transition from continuous DLVO type forces to discrete short-range forces. Similar observations as early as in 1982 went virtually unnoticed;10 authors found that within the range below ∼3 nm the values of the “excess” repulsion for glass filaments

interacting in KCl solutions with concentrations ranging from 10-4 to 10-2 M fell on a single curve. Later, Grabbe and Horn reported short-range repulsion between silica surfaces immersed in NaCl solutions at various concentrations and pH.16 They found no systematic force variation with electrolyte concentration and pH or with various surface treatments over the range below 0.5 nm. As in here, these authors found no reason to argue that silica hairs or silica gel were important in their experiments, and yet the short-range repulsion clearly existed. Chapel reported shortrange repulsion between two pyrogenic silica sheets immersed in a series of CsCl, KCl, NaCl, and LiCl electrolytes at a

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Table 1. Electrolyte, Real and Adjusted Concentration, pH, and Charge Regulation Surface Potential (ψ0) Used to Obtain the Best Curve Fits to the Force Data in Figures 3 and 4a electrolyte type

concentration (M)

adjusted (M)

pH

ψ0 (mV)

Dc (nm)

noneb NaCl

∼5 × 10-6 1 × 10-4 1 × 10-3 1 × 10-2 1 × 10-4 1 × 10-3 1 × 10-2 1 × 10-4 1 × 10-3 1 × 10-2

2.0 × 10-5 1.0 × 10-4 5.5 × 10-4 4.2 × 10-3 1.0 × 10-4 6.8 × 10-4 5.5 × 10-3 1.0 × 10-4 7.0 × 10-4 6.5 × 10-3

5.70 6.00 5.60 5.75 5.55 5.45 5.65 4.65 4.95 5.30

-118.0 -74.6 -55.4 -51.3 -50.8 -42.0 -30.3 -18.4 -15.4 -11.6

13 5 7 8 5 4 7 11 3 5

CaCl2 AlCl3

a DLVO theory is valid down to surface separations Dc. b Bidestilled water.

Table 2. NaCl Concentration, pH, and Charge Regulation Surface Potential (ψ0) Used to Obtain the Best Curve Fits to the Force Data in Figure 5a electrolyte type

concn (M)

pH

ψ0 (mV)

Dc (nm)

NaCl

1 × 10-4

3.1 5.1 7.9

-47.8 -74.6 -108.2

8 5 3

a

Figure 7. Excess repulsive force between a flat glass substrate and a silica-glass microsphere at separations less than 5 nm in a range of solutions at 20 °C. The excess force is obtained by subtracting the DLVO theory, with a charge regulation model, from the AFM force data. The solid line is an empirical double-exponential fit to the data. The force in the inset shows two exponential decay lengths.

DLVO theory is valid down to surface separations Dc.

concentration ranging from 10-4 to 10-1 M.17 Curiously, however, the author was more interested in the differences in the repulsion force at ranges above ∼0.5 nm rather than in the clear collapse of the curves below this range. Chapel also excluded compression of silica hairs as a possible explanation for the short-range repulsion. The excess repulsive force in the short range can be reasonably well represented with an empirical double exponential law. Force curves in Figure 7 conform to the “universal” law F/R ) 473.1 exp(-D/0.07) + 20.5 exp(-D/0.37), where F/R is in mN/m and D in nm, which correctly represents at least up to 10-1 M every force data point for a range of solution variablesselectrolyte, concentration, and pHsbelow 1 nm. Prefactors and decaying lengths are not significantly sensitive to electrolyte type, concentration, and pH. The force data in Figure 7, right inset, show two types of repulsion, one that decays rapidly in the very short range, 0 to ∼0.7 nm, and another that decays more slowly at distances between 0.7 and 1.5 nm. The tempting explanation based on short silica hairs growing rigid and orthogonal to the silica surface due to electrostatic repulsion is simply inadequate, because our silica surfaces remain unaltered during the experiments. The rapidly decaying repulsion originates rather from an inner molecular hydration layer, a couple of water molecules thick, highly ordered, and tightly bound to the silica surfaces. The slowly decaying repulsion originates from an outer hydration layer, less ordered and bound to the surface yet different from bulk water. This universal character of the short-range repulsive force for the low concentration solutions examined here is new and at variance with results established for symmetric silicasilica systems. We have attributed the short-range repulsive force to layer-by-layer dehydration of surfaces, or counterions if involved, when surfaces are pushed together. Figure 8 shows three carefully measured extension force curves between a glass substrate and a silica-glass sphere in a 10-4 M aqueous NaCl solution at pH ∼5.1. These force curves, which are denser than previous ones, were acquired at a rate of about 10 force data points per each nanometer of separation. The force data in Figure 8 exhibit a trend that is accentuated by the

Figure 8. Carefully measured actual force curves for a glass-silica system in a 10-4 M aqueous NaCl solution at pH ∼5.1. The solid line is simply a guide to the eye. Oscillations have a period of about 0.25 nm, roughly the diameter of a water molecule.

overlapping of the various force curves. In contrast, at large separations such overlap removed any fluctuation in the force. The solid line in Figure 8 is a guide to the eye only and should not be considered as more than that; however, at the short range below 1 nm it is unavoidable to acknowledge that the measured forces reveal oscillations in the force with reproducible periods of ∼0.25 nm, roughly the diameter of a water molecule. These oscillations, measured for the first time in a system including glass and silica surfaces, are similar to those measured earlier between mica surfaces.33 Notably, high-amplitude oscillations are limited to three or four in both systems, suggesting a shortrange ordering for the water that extends no more than 1 nm. The oscillations in the force reveal water structuring induced by the (33) Israelachvili, J. N.; Pashley, R. M. Nature 1983, 306, 249-250.

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Figure 9. Marc¸ elja and Radic´ model20,21 fits (solid lines) to excess repulsive force (data points) between a flat glass substrate and a silica-glass microsphere at separations less than 5 nm in 10-4 M NaCl solutions and pH 3.1, 5.1, and 7.9, and in a range of water solutions at pH ∼5.1. The electrolytes are NaCl, CaCl2, and AlCl3 with concentrations ranging from 10-4 to 10-2 M. The excess force is obtained by subtracting the DLVO theory, with a charge regulation model, from the AFM force data.

Figure 10. Attard and Batchelor model31 fits (solid lines) to excess repulsive force (data points) between a flat glass substrate and a silica-glass microsphere at separations less than 5 nm in 10-4 M NaCl solutions and pH 3.1, 5.1, and 7.9, and in a range of water solutions at pH ∼5.1. The electrolytes are NaCl, CaCl2, and AlCl3 with concentrations ranging from 10-4 to 10-2 M. The excess force is obtained by subtracting the DLVO theory, with a charge regulation model, from the AFM force data.

interacting surfaces and arise simply from the sequential squeezing out of two or three water layers. The fact that the excess repulsive force measured in the short range is independent of the conditions of the various solutions considered here may suggest some sort of compression or elastic deformation of the interacting surfaces as the origin of the force. We soon disregarded this possibility on the grounds of compression and deformation calculations performed by Ducker et al. on silica asperities and beads15 (with a Young modulus of 70 × 109 N m-2); the forces measured here are simply too small to account for the compression forces calculated by Ducker. Shifting the position of the plane of surface charge was also disregarded as an explanation for the excess short-range force; the shifts calculated are at least 3 nm, a value that exceeds by far the subnanometer roughness of our interacting surfaces. Next, we intend to rationalize our force data to the light of two existing theoretical efforts. First, we use the phenomenological hydration theory of Marc¸ elja and Radic´ that originated from Landau’s phenomenological theory of transitions.22,23 The hydration force for the plate-sphere configuration according to Marc¸ elja and Radic´ is given by F(D)/R ) 2πaη20D/sinh2(KD/2), where D is the separation distance, η(z) is the order parameter, which is zero in the bulk and maximum at the surfaces, η0, and K ) xa/c, where a and c are positive constants. Figure 9 shows the result. The theory correctly reproduces the short-range repulsion. Parameter values aη20 ) 94.8 mN/m2, related to the intensity of the hydration force, and K/2 ) 6.6 nm-1, related to the inverse of the force range, obtained for all the force curves are indistinguishable from those obtained by applying the theory to single force curves for three electrolytes, Na, Ca, and Al, for concentrations ranging from 10-6 to 10-2 M and pH ranging from 3.1 to 7.9. Of course, if the aim is simply to fit the data, then the double exponential law should be preferred. Second, we use the model of Attard and Batchelor in which the hydration force is a result of the disruption and deviation of a water hydrogen-bond network from that found in bulk water.34 Attard and Batchelor modeled water arranged on a two-dimensional square lattice between plates and obtained an expression for the

hydration force as a function of a free parameter (w) related to the Boltzmann weight of the Bjerrum defects. The hydration force between a plate and a sphere is F(D)/R ) (4πdkT/Vw)f(w) exp[-(D/d)g(w)], where Vw is the volume occupied by a water molecule, d is a lattice constant, f(w) ) (1 + w)(1 + 2w)/{(1 w)2 ln[3(1 + w)/(1 - w)]}, and g(w) ) 3(1 + w)/(1 - w). Typical values for these parameters are Vw ) 0.03 nm3 and d ) 0.3 nm. The value of the parameter w ) 0.93 obtained for all the force curves is indistinctive from those obtained for individual curves for the range of electrolytes, concentrations, and pH used here. However, the quality of the fit is poor according to Figure 10; the theory overestimates the intensity of the repulsion in the short range, a result likely related to the low dimensionality of the model.

(34) Attard, P.; Batchelor, M. T. Chem. Phys. Lett. 1988, 149, 206-211.

Conclusions The short-range repulsive force between glass and silica surfaces measured with an atomic force microscope (AFM) has universal character in the short range, less than ∼1 nm or about three or four water molecules, independent of electrolyte type, concentration, and pH. The oscillations in the force reveal water structuring induced by the interacting surfaces and arise simply from the sequential squeezing out of two or three water layers. The phenomenological model of Marc¸ elja and Radic´ based on polarization of water molecules by surface charges and dipoles correctly represents our data; the model of Attard and Batchelor based on breakage of hydrogen bonds predicts too slow a variation of the force with surface separation. Thus, we postulate that the excess DLVO force between glass and silica surfaces arises from a surface-induced solvent effect, from the creation of a hydrogenbonding network at the surface level, rather than from a solventinduced surface steric hindrance. Acknowledgment. Financial support from CONICYT-Chile through project FONDECYT 1060912 and from the Research Direction of University of Concepcio´n through project DIUC 203.096.057-1.0 is greatly appreciated. LA703866G