Langmuir 2000, 16, 8153-8158
8153
Investigation of Humidity-Dependent Capillary Force Xudong Xiao* and Linmao Qian Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China Received May 31, 2000. In Final Form: July 21, 2000 Due to the strong capillary condensation, the adhesion force between a Si3N4 atomic force microscope (AFM) tip and silicon oxide was observed to first increase and then decrease with an increase of humidity. In contrast, due to weak capillary condensation, the adhesion force between the AFM tip and the N-octadecyltrimethoxysilane (OTE, CH3(CH2)17Si(OCH2CH3)3) self-assembled monolayer (SAM) was found to be almost independent of humidity. It was found that the formulation commonly used for macroscopic objects fails to explain our data. Using an accurate formulation and an assumed tip shape, we can explain the observed decrease of adhesion for SiO2 at high humidity as being due to the decreased capillary pressure force when the dimension of the meniscus becomes comparable with the tip size. However, the observed late onset of adhesion of SiO2 cannot be understood within the framework of the classical continuum theory. We attribute this late onset to the properties of an ultrathin water film at molecular thickness. The new formulation predicts a vanishing water meniscus between the AFM tip and OTE over the entire humidity range and can also fully account for the humidity-independent adhesion results for OTE.
1. Introduction The interaction of particles with solid surfaces is of importance in many scientific and industrial fields.1,2 Revived interest in the subject recently is due to the use of the atomic force microscope (AFM).3-8 To study the interaction of an AFM tip with a substrate surface in air, the water capillary force is inevitably present and may play an important role.9 Capillarity is a general phenomenon that occurs between two contacting surfaces in a vapor environment. The quantitative study of capillarity can be traced back to the nineteenth century and the work of Young and Laplace.10 For a sphere-on-plane geometry (refer to the top left inset in Figure 3), assuming that (i) the radii of the solid-liquid contact lines are much smaller than the radius R of the sphere, (ii) the radii of the two contact lines are equal, (iii) the distance between the sphere surface and the flat surface is very small compared with the radius of the contact line, and (iv) the radius of the meniscus in a radial cross section is much smaller than the radius of the contact lines, the capillary force is given as9-11
Fc ) 4πγR cos θ
Figure 1. Distribution of measured adhesion force together with a Gaussian fit for OTE/SiO2 at 37% humidity. The inset shows a typical approach-retract force-distance curve with the hysteresis of the piezotube corrected.
(1)
where γ is the surface tension of the liquid and θ is the contact angle, which is assumed to be the same on the two solid surfaces. Under the above assumptions, the capillary force is surprisingly humidity independent. * Corresponding author. E-mail:
[email protected]. Fax: (852)2358-1652. Telephone: (852)2358-7494. (1) Visser, J. In Surface and Colloid Science; Matijevic, E., Ed.; John Wiley & Sons: New York, 1976; Vol. 8, p 3. (2) Heim, L. O.; Blum, J. Phys. Rev. Lett. 1999, 83, 3328. (3) Mate, C. M.; Novotny, V. J. J. Chem. Phys. 1991, 94, 8420. (4) Binggeli, M.; Mate, C. M. Appl. Phys. Lett. 1994, 65, 415. (5) Binggeli, M.; Mate, C. M. J. Vac. Sci. Technol. B 1995, 13, 1312. (6) Fujihira, M.; Aoki, D.; Okabe, Y.; Takano, H.; Hokari, H.; Frommer, J.; Nagatani, Y.; Sakai, F. Chem. Lett. 1996, 499. (7) Marmur, A. Langmuir 1993, 9, 1922. (8) de Lazzer, A.; Dreyer, M.; Rath, H. J. Langmuir 1999, 15, 4551. (9) Israelachvili, J. Intermolecular and surface forces, 2nd ed.; Academic Press Inc.: San Diego, 1992. (10) McFarlane, J. S.; Tabor, D. Proc. R. Soc. (London) 1950, A202, 224. (11) Orr, F. M.; Scriven, L. E.; Rivas, A. P. J. Fluid Mech. 1975, 67, 723.
Figure 2. Measured adhesion force as a function of humidity for SiO2 and OTE/SiO2 against a Si3N4 AFM tip.
It is believed that eq 1 holds for most macroscopic measurements, while its validity has not been verified for microscopic objects. For macroscopic spheres with surface roughness, a strong humidity dependence was often observed with reduced capillary force at low humidity. This was interpreted as being due to the multiasperity nature of the contact. With the effective radii of the
10.1021/la000770o CCC: $19.00 © 2000 American Chemical Society Published on Web 09/13/2000
8154
Langmuir, Vol. 16, No. 21, 2000
Figure 3. Various contributions to the adhesion force as a function of humidity calculated by eqs 4-8: (a) surface tension force; (b) capillary pressure force; (c) total capillary force; (d) van der Waals force; (e) adhesion force. In the upper-left corner inset, we show the geometry of a sphere-on-plane contact, with the relevant parameters used in eqs 4-8. In the central inset, the thickness of the water film at the contact line as a function of humidity is shown.
asperities much smaller than the sphere radius R, the capillary only formed around these asperities at low humidity, in contrast to the high humidity condition under which the capillary formed around the sphere.10 According to eq 1, the resulting capillary force at low humidity must be much smaller than that at high humidity because of the different radius. For smooth microscopic spheres, typical models for AFM tips with a single asperity, it was already clear from earlier AFM studies that a strong humidity-dependent adhesion force existed between the tip and the substrate surfaces.4-6,12,13 This apparent disagreement with eq 1, however, was never accounted for quantitatively or even semiquantitatively. With the help of two recent theoretical papers 7,8 that have examined the assumptions involved in obtaining eq 1, we report a semiquantitative comparison between our adhesion measurement and theory at different humidities. The adhesion of two sample surfaces, one hydrophilic SiO2 and one hydrophobic N-octadecyltrimethoxysilane (OTE)/ SiO2, to a Si3N4 AFM tip as a function of humidity was measured. While humidity has no effect on the hydrophobic sample, we found a strong humidity dependence for SiO2. As the humidity increases, the adhesion force, which includes the capillary force, between the AFM tip and SiO2 started to increase only above 30% humidity to a maximum at ∼70% humidity, followed by a decrease at higher humidities. The decreased adhesion for SiO2 at very high humidities is a result of the decrease in capillary force according to a modified theory. Semiquantitative agreement between the theory and the experiment can be obtained when the tip shape is considered. For the increase of adhesion for SiO2 in the low humidity region, however, the theory predicts a much earlier capillary force onset than observed experimentally. We interpret the disagreement as due to the failure of the continuum theory for molecularly thin water films. For OTE/SiO2, the observed humidity-independent adhesion can be fully explained by the modified theory as a result of no formation of a water meniscus. 2. Experimental Method The silicon wafers were cleaned according to well-established procedures,14 from which a hydrophilic SiO2 surface was obtained (12) Thundat, T.; Zheng, X.-Y.; Chen, G. Y.; Warmack, R. J. Surf. Sci. 1993, 294, L939. (13) Sugawara, Y.; Ohta, M.; Konish, T.; Morita, S.; Suzuki, M.; Enomoto, Y. Wear 1993, 168, 13.
Xiao and Qian with a water contact angle of ∼4°. The preparation of OTE monolayers on hydrophilic SiO2 was carried out as described previously.15-17 Briefly, 0.2 g of the OTE (Aldrich Chemical, Inc., Milwaukee, WI) and 5 mL of 1 N hydrochloric acid were added to 20 mL of tetrahydrofuran (THF) to prepare the prehydrolysis solution. The solution was stirred at room temperature for 4 days. Prior to self-assembly, the hydrolysis solution was filtered through a 0.2 µm PTFE membrane. Following this treatment, the solution was diluted to 1:20 in cyclohexane and then added to a clean Petrie dish container. The cleaned silicon wafers were immersed into the diluted solution for 10 min at room temperature. Samples were then rinsed with fresh cyclohexane for many cycles. Finally, they were baked at 120 °C for 2 h. According to refs 15-17, this procedure can produce high-quality OTE monolayers on both mica and SiO2 substrates. The water contact angle on the OTE monolayer was measured as ∼108°. The measurements were carried out in a home-built atomic force microscope with an RHK electronic controller (RHK Technology, Rochester Hills, MI). Commercially available Si3N4 cantilevers with a nominal force constant of 0.5 N/m (Park Instruments, Sunnyvale, CA) were employed. With the feedback loop of the AFM electronics disabled, the force-distance curve can be measured by ramping a voltage on the piezotubes to vertically displace the cantilever probe. A typical force-distance curve for SiO2 including approach and retraction is shown in the inset of Figure 1. For a sample much stiffer than the cantilever, such as silicon, the cantilever deflection is basically equal to the vertical displacement of the piezotube, and the force exerted on the cantilever is given by
F ) kc∆Zp
(2)
where kc is the force constant of the cantilever and ∆Zp is the vertical displacement of the piezotube. The hysteresis of the piezotube usually displaces the retraction part of the forcedistance curve from the approach part. In the inset of Figure 1, we have corrected this effect by adjusting the slope of the retraction part of the curve so that the force signal in the retraction part overlaps with that of the approach part in the repulsive force regime. The pull-off force in such a force-distance curve is then taken as the adhesion between the AFM tip and the surface. To reduce the statistical error, we have measured the adhesion force at 80 different locations on the sample at each humidity. By choosing a bin width of 1 nN, we can count the number of measurements with the adhesion force falling into a given bin. In Figure 1, this is plotted as a function of adhesion force for OTE/SiO2 at 37% relative humidity. The distribution can be fitted by a Gaussian function, from which the mean value and the standard deviation of the adhesion force can be obtained. For the example shown in Figure 1, they are 28.2 ( 1.0 nN.
3. Theoretical Background In general, the adhesion force between an AFM tip and a sample surface should include the capillary force (Fc) as well as the solid-solid interactions, consisting of van der Waals forces (FvdW), electrostatic forces (FE), and the chemical bonding force (FB)4
Fad ) Fc + FvdW + FE + FB
(3)
Since the tip and sample sit in air for a relatively long time (on the order of a few hours), no net charges are expected to remain. Thus, FE ) 0. The chemical bonding force can also be neglected, since the surfaces of the tip and sample are saturated with chemical bonds. Thus, no (14) Sunada, T.; Yasaka, T.; Takakura, M.; Sugiyawa, T.; Miyazaki, S.; Hirose, M. Jpn. J. Appl. Phys. 1990, 29, L2408. (15) Kessel, C. R.; Granick, S. Langmuir 1991, 7, 532. (16) Schwartz, D. K.; Steinberg, S.; Israelachvilli, J.; Zasadzinski, J. A. N. Phys. Rev. Lett. 1992, 69, 3354. (17) Xiao, X.-D.; Liu, G.-y.; Charych, D. H.; Salmeron, M. Langmuir 1995, 11, 1600.
Humidity-Dependent Capillary Force
Langmuir, Vol. 16, No. 21, 2000 8155
ionic or covalent bonds are expected to form during contact. We shall then focus on the first two terms of eq 3. For a sphere/plane geometry (see the inset of Figure 3 for definitions of the symbols), the capillary formed in a humid environment has been well studied. For macroscopic spheres, where r1 . r2 and φ ∼ 0, the commonly used formula for the capillary force is eq 1 (Fc ) 4πγR cos θ)9-11 when the contact angles on both surfaces are the same, and this is modified to Fc ) 2πγR(cos θ1 + cos θ2) when the two contact angles are different. In our case, the approximation used above is expected to fail, since the AFM tip radius is very small. At relatively low humidity, r1 is comparable with r2. At high humidity, the small tip radius translates into a large filling angle φ. Therefore, to correctly account for the experimental conditions, a better theoretical analysis has to be performed. Assuming that the meniscus shown in the cross section can be described by an arc of a circle (circular meniscus surface assumption), the capillary force exerted on the tip by the meniscus comes from both the capillary pressure (pressure difference ∆p outside and inside the meniscus due to the curvature) and the surface tension: Fc ) Fp + FS,11 with
Fp ) -πr12∆p )
(
πγR -sin φ +
)
cos(θ1 + φ) + cos θ2 2 sin φ (4) a + 1 - cos φ R
FS ) 2πγr1 sin(θ1 + φ) ) 2πγR sin φ sin(θ1 + φ) (5) where θ1 and θ2 are the contact angles of the liquid with the tip and the sample, respectively. Here, the term a/R in eq 4 is very small and is typically ignored for macroscopic spheres. We want to point out that keeping a finite a/R in eq 3 is in principle important, since only with it can a vanishing capillary force at zero humidity (φ ) 0) be obtained. Taking a ) 0 first and then φ ) 0 would reduce eq 4 to Fc ) 2πγR(cos θ1 + cos θ2) even at zero humidity, obviously an unphysical result. This is largely irrelevant for most of the macroscopic measurements without atomic smooth surfaces, since the roughness introduces additional effects to render eq 1 useless at low humidity, as already mentioned in the Introduction. For atomically smooth mica surfaces used in a surface force apparatus (SFA), however, the effect due to roughness is not present and the point raised above should be important. Unfortunately, this fine point was often ignored even in the SFA studies. As discussed by Israelachvili, a finite value of a for two contacting surfaces is needed for correctly evaluating the van der Waals force between two macroscopic objects9 (see below). For a similar reason, we believe a finite a is needed for correctly evaluating the capillary force between two contacting objects in order to apply the macroscopic continuum fluid theory at the atomic scale. When two surfaces are in contact, the definition of the separation a is not clear, however. In the case of the van der Waals force, Israelachvili suggests that a separation of the order of 2 Å be used for most cases.9 We would use similar values for our capillary force calculation. At thermal equilibrium, the filling angle φ is determined by the Kelvin equation 9,11
(
)
1 p 1 kT ln ) ∆p/γ ) ) γv0 ps r1 r2 cos(θ1 + φ) + cos θ2 1 (6) R sin φ a + R(1 - cos φ)
where v0 is the molecular volume and p/ps is the relative vapor pressure (relative humidity for water). From eqs 4-6, the liquid film thickness at the contact line and the capillary force can be calculated. 4. Results and Discussion A. Experimental Results. In Figure 2, the mean values of adhesion force measured with an AFM Si3N4 tip against SiO2 and OTE/SiO2 are plotted as a function of humidity. On silicon oxide, the adhesion force remains basically constant between 5% and ∼25% relative humidity and then increases by about a factor of 2 from 25% to 67% humidity and finally decreases sharply from 80% to 98% humidity. For OTE/SiO2, however, the adhesion force is almost independent of humidity. All the adhesion force data in this figure were taken at a loading/retracting rate of 10 nN/s. The adhesion force as a function of humidity for SiO2 and OTS/SiO218 has been studied previously by Fujihira et al.6 using a Si3N4 AFM tip, except the measurement was limited to a maximum of ∼60% humidity. Their results are qualitatively in agreement with ours; namely, no obvious change is found for the organic monolayer, but an increase of adhesion for SiO2 is observed as the humidity increases from 10% to 60%. Using a W tip, Binggeli et al.4,5 measured the SiO2 adhesion indirectly by extrapolating a friction versus load curve linearly to zero friction. That is, assuming the friction force f is proportional to the total load L + Fad, including both the adhesion (Fad) and the external applied load (L), the curve f(L) can then be used to deduce Fad. The dependence of adhesion on humidity was found to be small up to 75% humidity and to decrease by about a factor of 2 from 75% to 98% humidity. The decrease of adhesion in the high-humidity region is consistent with our observation. One possible reason for the difference in the low-humidity region is that the tip materials used in the two experiments are different, although we have to caution that the method used by Binggeli et al. is rather indirect and strongly depends on the validity of the assumption of f ) µ(L + Fad). Similar adhesion behavior to that of our measurement has also been observed for other systems, for example a Si3N4 AFM tip on mica,19,20 where the adhesion first increases from low to medium (∼50%) humidity and then drops at high humidity. B. Adhesion between the Si3N4 Tip and the SiO2 Surface. To simulate the result for the SiO2 surface, let us take the AFM tip radius as R ∼ 100 nm, the sphereplane separation as a ) 2.5 Å, θ1 ) 60° 21 and θ2 ) 0°, γ ) 73mJ/m2, and v0 ) 0.030 nm3.9 We can then calculate the filling angle φ by eq 6 and the water film thickness at the contact line by h ) a + R(1 - cos φ), which is shown as a function of humidity in the central inset of Figure 3. Using eqs 4 and 5, the capillary force together with the contribution from the capillary pressure and the surface tension can be calculated. The results are plotted in Figure 3. It is seen that the contribution from surface tension (curve a) at low humidity is small but increases very quickly above ∼80% humidity. The contribution from capillary pressure (curve b) increases from zero quickly (18) The OTS, octadecyltrichlorosilane (C18H37SiCl3), layer used in ref 6 is the same as the OTE (C18H37Si(OC2H5)3) layer used in this study except the starting molecules are slightly different. (19) Hu, J.; Xiao, X.-D.; Ogletree D. F.; Salmeron, M. Surf. Sci. 1995, 327, 358. (20) Xu, L.; Lio, A.; Hu, J.; Ogletree, D. F.; Salmeron, M. J. Phys. Chem. B 1998, 102, 540. (21) Ito, T.; Namba, M.; Buehlmann, P.; Umezawa, Y. Langmuir 1997, 13, 4323.
8156
Langmuir, Vol. 16, No. 21, 2000
Xiao and Qian
to a somewhat saturated value at intermediate humidity and then drops quickly when the humidity is above ∼80%. The total capillary force (curve c) therefore increases at low and intermediate humidity and decreases only at very high humidity (>90%). Because of the mutual compensation of the contributions from surface tension and capillary pressure, the decrease of capillary force is not as dramatic as the contribution from capillary pressure. The above behavior is in strong contrast to the macroscopic case. For a sphere of R ∼ 1 mm, the filling angle at 97% humidity is ∼1° and has a negligible contribution from the surface tension (eq 5). The capillary pressure makes the dominant contribution to the capillary force and basically remains constant at high humidity, consistent with eq 1. Although qualitatively the calculated capillary force as a function of humidity has the same basic features as the experimentally observed adhesion, in its details the shape of the curve is very different. Let’s examine the deviations one by one. First, the calculated capillary force at low humidity (
