Hydrophobic Surfaces Probed by Atomic Force Microscopy - American

Langmuir 2003, 19, 5357-5365

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Hydrophobic Surfaces Probed by Atomic Force Microscopy O. Teschke* Nano-Structures and Interfaces Laboratory, IFGW/UNICAMP, 13083-970 Campinas, SP, Brasil

E. F. de Souza Instituto de Cieˆ ncias Biolo´ gicas e Quı´mica, Pontifı´cia Universidade Cato´ lica de Campinas, 13020-904 Campinas, SP, Brasil Received January 10, 2003. In Final Form: April 4, 2003 We have measured the force acting on neutral tips as a function of distance to hydrophobic surfaces in aqueous solutions. The unusually large magnitude of this force is attributed to the electrostatic response of the aqueous fluid structure (hydration layer) at the interface. The local electric field in an interfacial region is a manifestation of the distribution of surface polar residues, and we have assumed that the polarization (hydration) of the hydrophobic surface immersed in water is predominantly driven by the direct water binding. The simplest electrostatic description of the coupling between the interfacial polarization charges and the corresponding polarization charges of the solvent molecules is expressed here as the spatially variable dielectric permittivity int. The exchange of a volume of the interfacial region with int by a tip with a dielectric constant tip is responsible for the tip attraction. The variable dielectric permittivity profiles for the following interfaces were measured in order to clarify the origin of the long-range attractive forces: water/air, water/CTAB covered mica, and water/hydrophobic silicon.

1. Introduction Knowledge about interfacial water structure near hydrophobic surfaces is crucial for the understanding of many important surface problems involving water. For instance, wetting or nonwetting is a familiar phenomenon, but there is not yet a clear physical picture of the phenomenon at the molecular level.1 Hydrophobic interactions are responsible for the formation of micelles and play an important role in organizing constituent molecules of living matter into complex structures such as membranes.2 Several studies have been recently devoted to the layering and orientation of water molecules on surfaces.3,4 The hydrophobic surface exhibits a strong attractive force in aqueous solutions. Although this strong force has been confirmed by a large number of experimental data,5-25 * To whom correspondence should be addressed. Address: UNICAMP/IFGW/DFA, Caixa Postal 6165, 13083-970 Campinas, SP, Brazil. Fax: (5519) 788-5376. E-mail: [email protected]. (1) Zisman, W. Adv. Chem. 1964, 43, 1. (2) Rehig, R. Annu. Rev. Phys. Chem. 1992, 46, 177. Tanford, C. The Hydrophobic Effect; Wiley: New York, 1980; pp 1-35. (3) Du, Q.; Freysz, E.; Shen, Y. R. Phys. Rev. Lett. 1994, 72, 238. (4) Porter, J. D.; Zinn, A. S. J. Phys. Chem. 1993, 97, 1190. (5) Israelachvili, J. N.; Pashley, R. M. Nature 1982, 300, 341. (6) Parker, J. L.; Yaminsky, V. V.; Claesson, P. M. J. Phys. Chem. 1993, 97, 7706. (7) Kekicheff, P.; Spalla, O. Phys. Rev. Lett. 1995, 75, 1851. (8) Craig, V. S. J.; Ninham, B. W.; Pashley, R. M. Langmuir 1998, 14, 3326. (9) Christenson, H. K.; Claesson, P. M. Science 1988, 239, 390. (10) Kurihara, K.; Kunitake, T. J. Am. Chem. Soc. 1992, 114, 10927. (11) Tsao, Y. H.; Evans, D. F.; Wennerstrom, H. Science 1993, 262, 547. (12) Wood, J.; Sharma, R. Langmuir 1995, 11, 4797. (13) Rabinovich, Y. I.; Yoon, R. H. Langmuir 1994, 10, 1903. (14) Meagher, L.; Craig, V. S. J. Langmuir 1994, 10, 2736. (15) Ishida, N.; Kinoshita, N.; Miyahara, M.; Higashitani, K. J. Colloid Interface Sci. 1999, 216, 387. (16) Podgonik, R. Chem. Phys. Lett. 1989, 156, 71. (17) Attard, P. J. Phys. Chem. 1989, 93, 6441. (18) Eriksson, J. C.; Ljunggren, S.; Claesson, P. M. J. Chem. Soc., Faraday Trans. 2 1989, 85, 163.

the strength and range do not coincide with each other. The mechanism for the attractive force has been a debated issue for almost 20 years, and depending on authors, this force could originate from (1) changes of the water structure in the thin layer between hydrophobic surfaces,26 (2) capillary forces due to cavitation in the vicinity of hydrophobic surfaces,27 (3) hydrodynamic fluctuations at a hydrophobic surface/water interface,28 (4) correlated dipole-dipole or dipole-charge interactions,17,29,30 and (5) dipole interactions associated with the large domains of ordered hydrocarbon chains.13 So, electrostatic,16,17 thermodynamic,18-20 and hydrodynamic28,31 points of view have been involved in explaining experimental results. Most consensus for the underlying physical mechanism has focused on long-range electrostatic forces. This idea and its various modifications17,29,32-34 all predict a strong dependence on the electrolyte concentration, which ex(19) Yaminsky, V. V.; Ninham, B. W. Langmuir 1993, 9, 3618. (20) Berard, D. R.; Attard, P.; Patey, G. N. J. Chem. Phys. 1993, 98, 7236. (21) Blake, T. D.; Kitchener, J. A. J. Chem. Soc., Faraday Trans. 1972, 168, 1435. (22) Israelachvili, J. N.; Pashley, R. M. J. Colloid Interface Sci. 1984, 98, 500. (23) Pashley, R. M.; McGuiggan, P. M.; Ninham, B. W.; Evans, D. F. Science 1985, 229, 1088. (24) Rabinovich, Y. I.; Derjaguin, B. V. Colloids Surf. 1988, 30, 243. (25) Christenson, H. K.; Claesson, P. M.; Berg, J.; Herder, P. C. J. Phys. Chem. 1989, 93, 1472. (26) Derjaguin, B. V.; Churaev, N. V. J. Colloid Interface Sci. 1974, 49, 249. (27) Yushchenko, V. S.; Yaminsky, V. V.; Shchukin, E. D. J. Colloid Interface Sci. 1983, 96, 307. (28) Ruckenstein, E.; Churaev, N. V. J. Colloid Interface Sci. 1991, 147, 535. (29) Podgornik, R. J. Chem. Phys. 1989, 91, 5840. (30) Podgornik, R.; Parsegian, V. A. J. Chem. Phys. 1991, 154, 477. (31) Vinogradova, O. I. Langmuir 1995, 11, 2213. (32) Tsao, Y. H.; Evans, D. F.; Wennerstro¨m, H. Langmuir 1993, 9, 779. (33) Miklavic, S. J.; Chan, D. Y. C.; White, L. R.; Healy, T. W. J. Phys. Chem. 1994, 98, 9022. (34) Spalla, O.; Belloni, L. Phys. Rev. Lett. 1995, 74, 2515.

10.1021/la0340450 CCC: $25.00 © 2003 American Chemical Society Published on Web 05/14/2003

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periments confirm7,24,25 and refute.14,35-37 The extreme range of the force (measurable at 300 nm 35) challenges conventional theories of surface forces and the liquid state. Recently, much attention has been paid to the role of bubbles and dissolved gas in aqueous solutions on the mentioned attractive force. These studies31,38,39 imply that the long-range interaction will be somewhat related with the gas phase, particularly in the case of hydrophobic surfaces with chemically bonded layers and solid polymer surfaces. Parker et al.35 and Carambassis et al.40 postulated that the long-range attractive force between silanated surfaces in aqueous solutions is attributable to the bridging between submicroscopic bubbles on surfaces. However, whether these submicroscopic bubbles are able to exist stably in bulk solutions or on solid surfaces has not been cleared thermodynamically.41-43 Previous studies using atomic force microscopy (AFM) were performed using large radii of curvature tips and flat surfaces;44 here we used flat macroscopic-size hydrophobized surfaces and nanosized ∼5 nm radius of curvature uncharged tips. Hydrophobic silicon and cetyltrimethylammonium bromide (CTAB) monolayers covering mica surfaces immersed in water and water/air interfaces were probed using the force acting on an uncharged tip when immersed in the hydration layer. This force is modeled by the gradient of the electrostatic energy variation involved in the tip immersion in this layer.

To measure the possible contribution of the water polarization effect at the interface, an attraction that exceeded the vdW attraction has to be present. The vdW attraction contribution is going to be discussed in the next paragraphs. The Hamaker constant was determined as follows: The calculations are based on the procedure outlined by Nir and Vassilieff.45 We used a generalization of Hamaker’s approach where the Hamaker constant takes into account dispersion interactions and is calculated by means of the microscopic approach and includes the correction for retardation effects in a vacuum. This correction depends on the shape of the interacting bodies. Nir and Vassilieff45 reduced the results from the macroscopic theory to the effective interaction between two bodies immersed in a third dielectric media. The Hamaker constant is then given by

(

The interaction energy associated with the vdW attraction is calculated by the expression below45,46

W(H,T) ) -

2A(H,T) (n - 2)(n - 3)

{∫

z)R (2R

- z)z

dz + (H + z)n-3 2 z)3κ-1-R-H[R + (tan R)z] dz z)0 (H + z)n-3 z)0

∫

2. van der Waals Force (vdW)

)

2

∞ Rn 3 A(H,T) ) An)0 + kT ∆L0∆R0 1 + rn + e-rn (1) 2 n)1 2

∑

Figure 1. Calculated Hamaker constant given by eq 1 as a function of the distance to the surface; for a silicon substrate and a silicon nitride tip immersed in water, where A0 ) 2.179 × 10-21 J.

(35) Parker, J. L.; Claesson, P. M.; Attard, P. J. Phys. Chem. 1994, 98, 8468. (36) Christenson, H. K.; Fang, J.; Ninham, B. W.; Parker, J. L. J. Phys. Chem. 1990, 94, 8004. (37) Christenson, H. K.; Claesson, P. M.; Parker, J. L. J. Phys. Chem. 1992, 96, 6725. (38) Karaman, M. E.; Ninham, B. W.; Pashley, R. M. J. Phys. Chem. 1996, 100, 15503. (39) Craig, V. S. J.; Ninham, B. W.; Pashley, R. M. J. Phys. Chem. 1993, 97, 10192. (40) Carambassis, A. C.; Jonker, L. C.; Attard, P.; Rutland, M. W. Phys. Rev. Lett. 1998, 80, 5357. (41) Ljunggren, S.; Eriksson, J. C. Colloids Surf., A 1997, 129, 151. (42) Attard, P. Langmuir 1996, 12, 1693. (43) Christenson, H. K. In Modern Approaches to Wettability: Theory and Applications; Schrader, M. E., Loeb, G., Eds.; Plenum: New York, 1992. (44) Ducker, W. A.; Xu, Z.; Israelachvili, J. C. Langmuir 1994, 10, 3279. (45) Nir, S.; Vassilieff, C. S. In Thin Liquid Films: Fundamental and Applications; Ivanov, I. B., Ed.; M. Dekker Inc.: New York, 1988; p 207.

}

(2)

and was previously calculated for silicon nitride tips/water/ mica substrates.47 The calculated Hamaker constant as a function of the separation between the substrate and the silicon nitride tip is shown in Figure 1 for A0 ) 2.179 × 10-21 J. 3. Experimental Section 3.1. Atomic Force Microscope Measurements in Water. The atomic force microscope is the most adequate equipment available for measuring interfacial force with a spatial resolution of a few angstroms in the scanned plane and 0.1 Å in the normal direction. If we use soft cantilevers with a spring constant of 0.03 N m-1, the force resolution in the normal direction to the scanned plane is 0.03 N m-1 × 0.1 × 10-10 m ) 0.3 pN. All force versus separation curves shown in this work are for approach. In our experiments a commercial AFM instrument, TopoMetrix TMX2000, was used where the movement of the cantilever was detected by the conventional deflection sensor using a fourquadrant detector enabling vertical as well as lateral force measurements. A special cell was built in order to perform observations in liquid media.45 The cell was made of Teflon, and the sample was fixed at its bottom and was moved in the x, y, and z directions with respect to a stationary tip. The laser beam enters and leaves the cell through a glass plate and thus does not cross the air/liquid interface, which is usually curved. The top-confining surface of the solution in the cell is far removed from the cantilever beam. In this geometry the displaced liquid follows a path that is perpendicular to the cantilever beam. Water (Milli-Q Plus quality, resistivity ∼ 15 MΩ/cm) was used in the cell. 3.2. Preparation of Aqueous Solutions. Deionized water was distilled once and then passed through a commercial Milli-Q system containing ion-exchange and charcoal stages. Solutions of cetyltrimethylammonium bromide were prepared using Sigma brand CTAB (99%) without further purification. The experiments were performed at 20 °C. Each curve presented was registered using at least five different samples of each interface and three (46) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: London, 1989; p 249. (47) Senden, T. J.; Drummond, C. J. Colloids Surf., A: Phys. Eng. Asp. 1955, 94, 29.

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Figure 2. Schematic diagram of the supertip used in this work. different tips with various approach velocities averaged using measurements at different points of the sample. Airborne contamination is minimized by preparing samples in a compact laminar flow cabinet and scanning samples in a clean air hood. Forces were measured between a commercial silicon nitride (Tip ) 7.4) and mica immersed in water for 1 h and for up to 5 h of immersion in water. Identical force versus distance curves were registered, consequently showing that we did not observe evidence of tip aging.46 3.3. Tips. We have obtained the best results in measurements with soft cantilevers with silicon nitride tips, typically ∼0.03 and 0.1 N m-1 (Microlever, type B, ThermoMicroscopes). Verifications of the spring constants of the cantilever by the method of Sader48 gave values not statistically different from the manufacturer’s values. Another procedure to calibrate cantilevers is to probe the interface and search for a region where the force gradient is larger than the spring constant. An instability will be registered at this region. The slope of the linear part of the force curve measured in this regions gives the spring constant value. The surface of a silicon nitride tip in aqueous solution is composed of amphoteric silanol and basic silylamine [secondary (silazane, -Si2NH2) and possibly primary (silylamine, -SiNH3) amines though the latter is rapidly hydrolyzed] surface groups49,50 at pH ∼ 6; with no added electrolyte the silicon nitride surface is either zwitterionic (zero net charge) or slightly negatively charged.51 The commercial silicon nitride tip surface has been found to be close to electrically neutral over a wide pH range (from at least pH 6 to 8.5), thus indicating equal densities of silanol and silylamine surface groups.46 To verify the surface charging behavior of the tips, force versus separation curves in solutions with pH between ∼5.2 and 6.8 were measured, and the isocharging point (icp) for silicon nitride was determined to be pHicp ≈ 6.3. 3.4. Tip Radius of Curvature Estimate. The radius of the tip was characterized by the observation of porous silicon structures and by comparing the size of the measured silicon particles by transmission electron microscopy (TEM) and AFM.52 This comparison allows us to estimate the distortion of the AFM images due to the finite size of the tip radius. The estimation of the radius is obtained by the deconvolution of the measured profile curve and the comparison with the particle diameter measured by TEM. The determined values are in agreement with the value given by ThermoMicroscopes technical information sheets. All the images were obtained with the contact mode using sharpened conical tips with an apex angle of ∼18° and an ∼200 nm height etched at the end of ∼3 mm height tips, as schematically shown in Figure 2. 3.5. Hydrophilic SurfacessMica. Mica is always negatively charged in water. When the mica basal plane is placed in water, (48) Sader, J. E.; Larson, I.; Mulvaney, P.; White, L. R. Rev. Sci. Instrum. 1995, 66, 3789. (49) Bergstro¨m, L.; Bostedt, E. Colloids Surf., A 1990, 49, 183. (50) (a) Harame, D. L.; Bousse, L. J.; Shott, J. D.; Meindl, J. D. IEEE Trans. Electron Devices 1987, 34, 1700. (b) Teschke, O.; Ceotto, G.; de Souza, E. F. Appl. Phys. Lett. 2001, 78, 6064. (51) Teschke, O.; Ceotto, G.; de Souza, E. F. J. Vac. Sci. Technol., B 2000, 18, 1144. (52) Teschke, O.; de Souza, E. F. Appl. Phys. Lett. 1999, 74, 1755.

Figure 3. AFM image of PTFE substrate. the mechanism for the formation of the double layer is assumed to be the dissolution of K+ ions as well as ion exchanging of K+ by H+ or H3O+ ions. It should be noted that the K+ ions initially held on the mica surface in the high resistivity water (15 MΩ/ cm, ∼5 × 10-6 M 1:1 electrolyte at pH ∼ 6) should be at least partially H+ ion-exchanged. Considering that the solvent volume of the cell was 300 µL and the mica exposed area was 1.13 cm2, if all K+ ions on the mica surface were exchanged into solution, the K+ concentration would be about 8.3 × 10-8 M, almost two orders smaller than the calculated concentration of the H+ present in the solution. 3.6. Hydrophobic SurfacessPreparation of Air Bubble. The first probed hydrophobic surface was an air bubble surface in water. A bubble was injected into the solution using a microsyringe, and photos of bubbles attached on the poly(tetrafluoroethylene) (PTFE) surface show that the contact angle of the bubble is ∼100°. Air bubbles of radii r ≈ 1 mm were formed from clean air and attached to a thermal treated PTFE surface. To prevent the three-phase line from moving laterally, thermal treated PTFE surfaces were used. The PTFE surface was modified by heating the sample in air at 384 °C. The topography of the polymeric surface of PTFE was imaged using AFM. The AFM image of the PTFE substrate is shown in Figure 3. This image shows well-defined boundaries for overlayers on bulk PTFE reflecting the ribbonlike morphology of PTFE substrate, following annealing. After this PTFE surface was placed in water, a small bubble was transferred from a microsyringe onto the hydrophobic surface where it remained attached. Bubbles trapped in this way were stable for many hours except for their radii, which increased slowly. The second probed hydrophobic surfaces were prepared by immersion of Si 〈100〉 optically polished substrates in 48% HF solution for 5 min, followed by extensive rinsing with Milli-Q water. Samples were then immersed in Milli-Q water and observed by AFM.

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Figure 4. Force vs absolute tip/substrate distance curve for a Si3N4 tip and a mica sample immersed in water. The full line indicated by DLVO corresponds to fitting by the DLVO theory for tip radii of curvature (R1 ) 5 nm and R2 ) 20 nm). The third hydrophobic surface probed was prepared by depositing a monolayer of CTAB on freshly cleaved mica surfaces by means of immersion of the substrate in a 10-5 M CTAB solution.51,52 When the mica basal plane is placed in 10-5 M CTAB solution, the mechanism for the formation of the double layer is assumed to be the dissolution of K+ ions as well as ion exchanging of K+ by (CH3)3-(CH2)15-CH2N + CH3-(CH2)14-CH2-N+(CH3)3, H+, or H3O+ ions. Then mica was removed from the solution followed by rising with Milli-Q water, and the contact angle was measured (∼90°).

4. Experimental Results 4.1. Tip/Hydrophilic Mica Forces in Water. Control experiments were performed using Si3N4 tips and mica substrates (hydrophilic surface) immersed in the Milli-Q Plus water. One of the force versus separation control curves is shown in Figure 4 (curve O). The full line indicated by DLVO corresponds to fitting by the DLVO theory for tip radius of curvature (R1 ) 5 nm and R2 ) 20 nm).53 Observe that the DLVO theory only fits well experimental points for distances far from the interfaces. 4.2. Tip/Bubble Forces in Water. Figure 5a shows the measured force between a neutral tip, mounted on a 0.03 N m-1 cantilever, and a ∼1 mm air bubble/water interface. At large distances, D > 300 nm, the force is negligible. At ∼250 nm from the interface, there is an attraction of the tip to the bubble until a repulsive force is experienced (∼5 nm). It is noteworthy that the force is much stronger and longer-ranged than the van der Waals attractive force. And since the cantilever deflection when pushed against a bubble and the bubble translation are equal in the force versus separation curves, we conclude that the bubble is undeformed for the set point specified force in these experiments. Figure 5b shows the measured force between a 0.1 N m-1 cantilever when the tip approaches a ∼1 mm air bubble/water interface. 4.3. Tip/Hydrophobic Silicon Surface Forces in Water. Figure 6a shows the force versus separation curve, acting on 0.03 N m-1 lever, 15 min (curve O) after the immersion of hydrophobic silicon surfaces in water; this curve is identical to the curve measured 2 min after the silicon wafer immersion in water. Observe that there is no long-range repulsive force acting on the 0.03 N m-1 cantilever with a characteristic Debye’s length (∼100 nm) associated with charged surfaces immersed in water, as shown for mica surfaces in Figure 4. The analysis of the force acting on the cantilever before immersion in the

Figure 5. (a) Force vs separation curves for the air bubble/ water interface measured 10 min after the bubble attachment to the PTFE substrate, measured with a 0.03 N m-1 spring constant cantilever. (b) Same as shown in Figure 5a, measured with a 0.1 N m-1 spring constant cantilever.

polarization layer was previously described.53,54 The attraction force range is in agreement with the published values for hydrophobic surfaces.44 Figure 6b shows the force versus separation curve for a 0.1 N m-1 cantilever. Measurements of the force versus separation curves for two different spring constants (κ ) 0.03 and 0.1 N m-1) shown in parts a and b, respectively, of Figure 5 provide complementary information. Soft cantilevers (κ ) 0.03 N m-1) have a high sensitivity and detect very small force values at the right part of the force curve (compare parts a and b of Figure 5), while 0.1 N m-1 cantilevers should give better results for high force values at the region close to the interface (separation ≈0). 4.4. Hydrophobic CTAB Monolayer on Mica Substrates. Hydrophobic mica, previously prepared by immersion in a 10-5 M CTAB solutions for ∼1 h and then washed in water, shows a contact angle > 90°. This surface was then immersed in water, and force versus distance curves were measured. The result is shown in Figure 7a for a 0.03 N m-1 cantilever. After a period of ∼15 min most of the surface was still covered by the CTAB adsorbed (53) Teschke, O.; Ceotto, G.; de Souza, E. F. Phys. Chem. Chem. Phys. 2001, 3, 3761. (54) Teschke, O.; Ceotto, G.; de Souza, E. F. Phys. Rev. E 2001, 64, 11605.


Figure 6. (a) Force vs separation curve for hydrophobic silicon surfaces measured 15 min after the silicon surface immersion in water, measured with a 0.03 N m-1 spring constant cantilever. (b) Same as shown in Figure 6a, measured with a 0.1 N m-1 spring constant cantilever.

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Figure 7. (a) Force vs separation curves for a mica surface covered by CTAB measured 15 min after the surface immersion in water, measured with a 0.03 N m-1 spring constant cantilever. (b) Same as shown in Figure 7a, measured with a 0.1 N m-1 spring constant cantilever.

layer. Desorption was observed in a few areas detected by measurements of the force versus separation curves, which show a characteristic behavior of hydrophilic surfaces53,55 (see Figure 4). Finally, for CTAB covered mica, we used a 0.1 N m-1 cantilever for measuring the force acting on the conical shaped tip when immersed in the water/CTAB/mica interface region. The result is shown in Figure 7b. 5. Hydrophobic Surface Model Recent experimental results of Shen et al.56 and Su et al.57 suggest that the water surface has a structure more ordered than the bulk and that this water structure is icelike, as seen in Figure 8. Ice has a variety of phases,58 but, in all cases, water molecules are held together by tetrahedral hydrogen bonding. The molecular orientations at the lattice points should obey the Bernal-Fowler(55) Ceotto, G.; Teschke, O.; de Souza, E. F. J. Mol. Catal. A 2001, 167, 225. (56) Shen, Y. R. Solid. State Commun. 1998, 108, 399. (57) Su, X.; Lianos, L.; Shen, Y. R.; Somorjai, G. A. Phys. Rev. Lett. 1998, 80, 1533. (58) Kamb, B. In Physics and Chemistry of Ice; Whalley, E., Jones, S. J., Gold, L. W., Eds.; Royal Society of Canada: Ottawa, 1973; p 28.

Figure 8. Schematic diagram of the hexagonal lattice structure at the ice/air surface.

Pauling (BFP) rule, which requires that each molecule donates two protons to two of the attached water molecules and accepts two protons from the other two.59 This, however, still leaves many possible ways to orient the

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water molecules in an ice lattice, giving rise to the residual entropy problem first tackled by Pauling.60,61 Ice has a tetrahedral hydrogen-bonding structure, with every monolayer composed of two submonolayers. At the surface, each molecule in the top submonolayer must have one of its four connecting hydrogen bonds broken.56 Obviously, the surface water molecules align the bulk water molecules into a more ordered hydrogen-bonding network. The icelike structure seems to apply to all water interfaces although the degrees of ordering may differ.56 We propose in this work that a surface is hydrophobic when there is no significant effect of ionic charges at the solid/liquid interface on the molecular alignment of bulk water in a layer close to the interface. The alignment of the superficial water molecules is due to the symmetry breaking associated with the surface, and the hydrogenbonding force is responsible for the alignment of the water molecules into a more ordered hydrogen-bonding network than in bulk. The hydrogen bonds broken at the interface associated with the hydrogen-bonding force will be described by an interfacial polarization charge distribution. On the other hand, hydrophilic surfaces have an ionic surface charge field strong enough to alter the water molecular alignment in the solution. The addition of charge into the solution, as present in various concentrations of NaCl, KCl, and so forth, has two effects: the first is associated with the surface adsorption of the ions in solution which modifies the surface interfacial charge, and the second is on the Debye length by modifying the ion concentration in solution. So the use of solutions of various concentrations of salt (NaCl, KCl, etc.) may affect both charge distribution in the bulk (changing the value of the Debye’s length) and surface charges due to the presence of adsorbed charge at the interface. These two variables characterize the so-called electrostatic effect. 6. Tip/Hydrophobic Interface Interaction Model


Figure 9. Conical shaped tip with a cone angle R and a flat end with an area of πR2 immersed in the polarization layer region; z is the integration variable of the elemental volume with a width ∆z, and d is the distance between the surface and the end of the tip. The hydrophobic water/air interface is described using an idealized model of ordering of water. The first few layers of water molecules are highly ordered, while, at some distance from the surface, the molecular distribution shows the normal undisturbed bulk structure.

region. The force is obtained by the gradient of the energy expression, that is, Fz ) -(∂/∂z)∆W, where

Let us apply our model to a polarization (hydration) layer attached to hydrophobic surfaces in water. In the absence of ions, the local electric field in an interfacial region is a manifestation of the distribution of the surface polar residues. The polarization distribution is driven by the direct water binding.3 For the simplest electrostatic description of the hydration layer, it is, consequently, enough to consider the coupling between the interfacial polarization charges and the corresponding polarization charges of the solvent molecules described here by the dielectric permittivity int. To estimate the size of the force acting on the tip, we assumed that the energy change involved in the immersion of the sharpened conical shaped tip inside the polarization layer is given by the product of the immersed tip volume times the dielectric permittivity variation and times the square of the electric field vector. The tip was defined to have a sharpened conical shape with one flat end with an area of πR2 (see Figure 9). The elemental volume (dv) of the sharpened conical tip immersed in the interaction region is given by dv ) π[R + (tan R)z]2 dz, where z is the integration variable of the conical volume and d is the distance between the surface and the end of the tip. The change in the electric energy involved in the exchange of the dielectric permittivity of the polarization layer by that of the tip is calculated by integrating the energy expression over the tip immersed volume in the polarization layer

The phenomenological description of the interfacial region is as follows: the polarization charge at the interface generates an electric field E with an exponential decay length λ, that is, E(z) ) E0e-z/λ, and orientation of the water molecules is described by a spatially variable dielectric permittivity given by the expression int(z) ) bulk - [bulk - (z ) 0)]e-(nz/λ),62 where n is an integer. The simple theory we presented models the macroscopic force acting on the tip as the gradient of the energy variation produced by the immersion of the tip in the water interface polarization layer. The surface introduces a “symmetry breaking” in the dielectric function. We cannot assume an homogeneous bulk medium; instead a variable dielectric permittivity as a function of the dimension perpendicular to the surface was assumed. In Attard’s work63 the dielectric function was derived by minimizing an approximate free energy density resembling a Landau expansion derived for an ice crystal. It has been then assumed that the canonical function describing a solid dielectric function may be applied to liquids; that is, it is assumed that polarization charges in the liquid can be described by the same function used for the organized charge arrangement of a solid. The main result of this

(59) Bernal, J. D.; Fowler, R. H. J. Chem. Phys. 1933, 1, 515. (60) Pauling, L. J. Am. Chem. Soc. 1935, 57, 2680. (61) Giaugue, W. F.; Stout, J. W. J. Am. Chem. Soc. 1936, 58, 1144.

(62) Podgornik, R.; Cevc, G.; Zeks, B. J. Chem. Phys. 1987, 87, 5957. (63) Attard, P.; Wei, D.; Patey, G. N. Chem. Phys. Lett. 1990, 172, 69.

∆W )

∫010λ-d(tip - int)E20π[R + (tan R)z]2 dz

1 2

(3)


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work is that the expansion in K-space of the dielectric function cannot be restricted to one component, that is, eiKz. We used the function eaz in real space to describe the dielectric function spatial dependence; observe that this function has more than one component in the K-space. We fitted the experimental curve (Figures 5a, 6a, and 7a, curves O) by adjusting the parameters E(z ) 0), (z )0), λ, and n in eq 3. Initially, we fitted the curve for points away from the interface where the parameters λ and E(z )0) are determined. Then, by adjusting the parameters (z ) 0) and n, it is possible to fit the curve for points close to the interface. 7. Experimental Data Fitting by the Hydrophobic Surface Interaction Model 7.1. Cantilever Spring Constant and Tip Radius of Curvature Measurements. To calibrate cantilevers (for each measured curve), we have probed the interface and have searched for regions where the force gradient is larger than the cantilever spring constant. An instability will be registered at this region. The slope of the linear part of the force curve measured in these regions gives the spring constant value. The measured spring constant (variations around 30% of the nominal value were measured) is used in the experimental curves fitting by the model. Measurement of the tip radius curvature has been previously described.51 The measured radius of curvature gave values between 3.5 and 5.0 nm. The effect of the uncertainty in calibration of the tip radius on the force curve fitting is shown in Figure 4 for two tip radii of curvature R1 ) 5 nm and R2 ) 20 nm. The force versus separation data in Figure 6a appear to be dominated by the spring constant of the weak cantilever (0.03 N m-1). We have repeated this measurement with stiff levers (0.1 N m-1); the results are shown in Figure 6b. The shape of the curves measured with the stiff cantilever changes substantially when compared to ones measured using a soft cantilever (see Figures 5a, 6a, and 7a). A stiff cantilever means loss of sensitivity, which is apparent in measured curves; that is, forces smaller than 0.05 nN were not detected, resulting in decreasing substantially the range of the measured force. However, at regions close to the interface where the force gradient exceeds the spring constant of the soft lever, the use of stiff cantilevers results in higher precision in the measurement of the attractive force spatial distribution. The measured experimental curves shown in Figure 5a show that the curve is not an artifact resulting from the choice of lever, since the curve does not show instabilities with a ∼0.03 N m-1 slope. The larger value of the measured attractive force at the curve minimum in Figure 5b is associated also with the large variation in the measured spatial distribution of the force values. For a curve with a lower gradient of attractive force than the cantilever spring constant, such as the one measured for the air/water interface, the stiff cantilever measurements do not add any information to the force curve. For hydrophobic silicon the curve that provides the best data without artifacts associated with the tip low spring constant value is shown in Figure 6a. This curve is fitted to eq 3. Finally, for CTAB covered mica we also used the curve measured with soft cantilevers (0.03 N m-1). To determine the precision of the fitting procedure, we have plotted the experimental and the fitted force versus separation curves for various dielectric permittivity spatial distributions (see Figure 10). The best fitting is given by

Figure 10. (a) Force vs separation curves shown in Figure 5 for various values of the dielectric permittivity () as a function of distance. Experimental points (curve O). (b) Dielectric permittivity spatial variation [(z)] as a function of distance to the solid/liquid interface. Curves correspond to the various fittings shown in part a.

the curve indicated by a full line, and an acceptable range of values is given by the curve indicated by the dotted line. 7.2. Tip/Air Bubble Interaction Model. Now let us analyze the force curve (see Figure 11) for the tip air/ water interface in more detail. It is apparent that the curve measured using the soft lever (Figure 5a) does not have an artifact associated with the low value of the cantilever spring constant. As far as the approaching force curves are concerned, no repulsive force appears. As for the probe, Lin et al.64 reported that the surface potential of the Si3N4 tip is nearly zero at pH ) 6.0. One may think that the tip surface might be wetted by air bubbles. If this is the case, we would observe the immersion of the tip in the air bubble. This is not observed in our experimental conditions. Hence, we consider that the tip surface is not wetted by air bubbles. The polarization profile was determined by experimental curve fittings shown in Figure 11. The calculated dielectric permittivity profile obtained by the experimental curve best fitting is shown in the inset. (64) Lin, X. Y.; Creuzet, F.; Arribart, H. J. Phys. Chem. 1993, 97, 7272.

5364



Figure 11. Tip air/water interface force.

Figure 13. Force vs separation curves for a CTAB monolayer covering mica surfaces. The full line indicates the curve calculated using eq 3. Inset: The full line corresponds to the dielectric permittivity spatial variation that results in the best fitting to the experimental points.

Figure 12. Force vs separation curves measured after 15 min of immersion of hydrophobic silicon surfaces in Milli-Q water. The full line indicates the curve calculated using eq 3, and the full line indicated by vdW corresponds to the calculated vdW attraction using eq 1. Inset: The full line corresponds to the dielectric permittivity spatial variation that results in the experimental points best fit by eq 3.

7.3. Tip/Hydrophobic Silicon Surface Interaction Model. Figure 12 shows the force versus separation curve, measured after 15 min of immersion of hydrophobic silicon surfaces in Milli-Q water, fitted by the model. The full line indicates the curve calculated using eq 3, and the full line indicated by vdW corresponds to the calculated vdW attraction using eqs 1 and 2. The curve shown in the inset corresponds to the dielectric permittivity spatial variation that results in the experimental points’ best fitting. The hydrophobic silicon surface can be described at the molecular level as follows: The silicon (100) surface is covered by hydrogen atoms. Due to the difference in the electroaffinity of the H atoms (0.754 eV) and the Si atoms (1.385 eV), an interfacial charge delocalization is created. Simultaneously, water molecules are ordered by the hydrophobic surface due to the geometric constraints of the surface, resulting in a region with a larger aligned molecular distribution than that in the bulk and described in this work by a spatially variable dielectric permittivity with a measured value of ≈11 at the interface (d ) 0) and

increasing to ∼80 in the bulk, as shown in the inset of Figure 12. If, arbitrarily, we assume the polarization layer width to be the one corresponding to half the amplitude variation of the dielectric permittivity in the inset of Figure 12, we obtain for the polarization layer width of hydrophobic silicon surfaces in Milli-Q water ∼4 nm. The calculated van der Waals attraction is shown by the full line and indicated by vdW. The interesting features of this curve are as follows: (a) It diverges at the interface (d ≈ 0) following a function ∼d-n, while the measured experimental curve seems to show a leveling in the force amplitude at d ≈ 0. (b) At ∼2 nm from the interface, the vdW force has decreased to a negligible value, in agreement with the ∼2 nm range of the vdW force shown in the literature.45 7.4. Tip/CTAB Covered Mica Surface Interaction Model. The experimental curve (Figure 7a) fitting by the model determines the polarization layer profile which is shown in Figure 13, and the respective calculated dielectric permittivity is depicted in the inset. In the case of a hydrophobic mica substrate prepared by surface coverage with a monolayer of tightly packed alkyl chains (CTA+ ions), water molecules appear to form a tight packed arrangement, resulting in an aligned hydrogen bonding network present at large distances from the interface. It is possible then to define hydrophobicity that previously could not be quantified by contact angle measurements, since hydrophobic silicon and a CTAB monolayer covering mica surfaces show a contact angle close to 90° by an electric field intensity value and the dielectric permittivity profile, as shown in Figures 11-13. However, comparisons between profile and electric field intensity at isolated points of the surface are not significant due to large variance in the measured values as a function of position. The spatial distribution (x,y) and E(x,y) we believe will be significant in defining the observed surface hydrophobicity. 8. Hydrophobic and Hydrophilic Interaction Ranges There are no adsorbed ionic charges on hydrophobic surfaces, but we have observed forces acting on a neutral tip immersed in the polarization layer that are of the same order of magnitude of the ones measured for ionic charged


hydrophilic surfaces53 (compare Figures 5-7 with Figure 4) which interact strongly with water molecules. The origin of the strong long-range hydrophobic field is the dipolar distribution of hydrogen broken bonds at the air/water interface and the hydrogen-bonding force. The energy associated with the hydrogen bonding is ∼7kT at room temperature18 while the orientational energy of water molecules is 0.5kT; consequently, a partial alignment (but larger than the one in the bulk) is observed up to ∼250 nm away from the interface. The hydrophobic attraction force which is based on the notion of enhanced hydrogen bonding for the water molecules close to hydrophobic surfaces is conceptually related to the theories of hydration forces proposed by Marcelja and Radic,65 Cevc et al.,66 and Eriksson et al.18 The surprisingly long range of the hydrophobic attraction would, according to the present theory, be due to a hydrogen-bond-mediated structural reorganization in the water/substrate interface. This points in the direction that we would need to know more about the molecular properties of liquid water and, in particular, perhaps about the conditions which favor the formation of hydrogen-bond-connected clusters of water molecules, before a full understanding of the hydrophobic attraction is within reach.18 Another point that has to be considered is that recently discontinuities or steps have been observed in the force curves measured at hydrophobic surfaces.35,40,66-70 It is suggested that these steps at the onset of the force are (65) Marcelja, S.; Radic, N. Chem. Phys. Lett. 1976, 42, 129. (66) Cevc, G.; Podgornik, R.; Zeks, B. Chem. Phys. Lett. 1982, 91, 193. (67) Ishida, N.; Inoue, T.; Miyahara, M.; Higashitani, K. Langmuir 2000, 16, 6377. (68) Yakubov, G. E.; Butt, H. J.; Vinogradova, O. I. J. Phys. Chem. 2000, 104, 3407. (69) Ishida, N.; Sakamoto, M.; Miyahara, M.; Higashitani, K. Langmuir 2000, 16, 5681. (70) Eriksson, J. C.; Ljunggren, S. Langmuir 1995, 11, 2325.

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due to the bridging of submicroscopic bubbles or cavities between the surfaces that causes the long-range attraction between hydrophobic surfaces. Here we do not observe steps on the force versus distances curve; consequently, we assume that there are no bubbles or cavities between the tip and the ∼1 mm diameter air bubble. No bubbles were observed on optically polished silicon surfaces previously immersed in HF solutions and surfactant covered mica surfaces. Hence, the interaction described in this work is not associated with microscopic bubbles that coalesce when the tip and substrate surfaces interact. 9. Conclusions In conclusion, we report AFM measurements made on three hydrophobic interfaces. One was a water/mica interface, where the mica was rendered hydrophobic by a monolayer coating of surfactant (CTAB), the second was a water/silicon interface rendered hydrophobic by immersion in HF solutions, and finally, the third was the water/air bubble interface. In all cases, the hydrophobic interaction was characterized by the appearance of an attractive force as the tip approached the interface. The force is associated with the exchange of a region of the polarization (hydration) layer with int by the tip with tip. We assumed that hydrophobic surfaces impose an alignment on the superficial water molecules due to the symmetric breaking of the bulk molecular arrangement associated with the surface. The hydrogen-bonding force is responsible for the alignment of the water molecules into a more ordered hydrogen-bonding network in a layer close to the interface. Acknowledgment. The authors are grateful to J. R. Castro and L. O. Bonugli for technical assistance and acknowledge funding support from FAPESP 98/14769-2. LA0340450

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