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Rupture of Hydrophobic Microcontacts in Water: Correlation of Pull-Off Force with AFM Tip Radius Hjalti Skulason and C. Daniel Frisbie* Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455 Received February 14, 2000. In Final Form: April 20, 2000 The purpose of this work was to investigate the functional dependence of the adhesion (pull-off) force on probe radius in AFM force measurements. Pull-off forces for hydrophobic AFM probes in contact with hydrophobic substrates were measured in water. Chemical functionalization of probes and substrates was accomplished by self-assembly of octadecanethiol on Au. Average pull-off forces for 10 SAM/Au-coated probes were measured and found to depend linearly on the probe tip radii, which were determined by scanning electron microscopy (SEM). Using the JKR contact mechanics model, the thermodynamic work of adhesion (Wad) determined from the pull-off forces was 110 ( 10 mJ/m2 which compares favorably with estimates of Wad based on reported interfacial energies. These results verify the linear dependence of the adhesive force on probe radius, as expected from contact mechanics models. They also verify that SEM can provide self-consistent and reproducible estimates of the probe radius.
Introduction In atomic force microscopy (AFM) studies the probesubstrate pull-off force depends on both the chemical functionality of the probe and the substrate as well as the solvent in which the measurements are performed.1 Frequently, a considerable variation is observed in the average pull-off force obtained for different probes measuring the same interaction.2 For example, the average avg ) for Au-coated probes and subpull-off force (Fpull-off strates functionalized with a monolayer of 11-mercapto1-undecanamide has been reported in separate papers as 0.211c and 1.81a nN under ethanol. One possible source of this discrepancy is the difference in the radius of curvature, R, between the different probes used in these experiments. A sharp probe with a small R is expected to give a smaller average pull-off force than a dull probe with large R. The common contact mechanics models used to analyze these pull-off force measurements, namely the Derjaguin, Muller, Toporov3 (DMT) and Johnson, Kendall, Roberts4 (JKR) models, predict that the pull-off force should scale linearly with the probe tip radius of curvature. According to the JKR model, the force required to separate a probe from adhesive contact with a flat substrate is
3πRWad Fpull-off ) 2
(1)
where Wad is the work of adhesion between the probe and * To whom correspondence should be addressed. E-mail:
[email protected]. (1) (a) van der Vegte, E. W.; Hadziioannou, G. Langmuir 1997, 13, 4357. (b) Wenzler, L. A.; Moyes, G. L.; Raikar, G. N.; Hansen, R. L.; Harris, J. M.; Beebe, T. P., Jr. Langmuir 1997, 13, 3761. (c) Sinniah, S. K.; Steel, A. B.; Miller, C. J.; Reutt-Robey, J. E. J. Am. Chem. Soc. 1996, 118, 8925. (d) Thomas, R. C.; Houston, J. E.; Crooks, R. M.; Kim, T.; Michalske, T. A. J. Am. Chem. Soc. 1995, 117, 3830. (e) Frisbie, C. D.; Rozsnyai, L. F.; Noy, A.; Wrighton, M. S.; Lieber, C. M. Science 1994, 265, 2071. (2) (a) Takano, H.; Kenseth, J. R.; Wong, S.-S.; O’Brien, J. C.; Porter, M. D. Chem. Rev. 1999, 99, 2845. (b) Noy, A.; Vezenov, D. V.; Lieber, C. M. Annu. Rev. Mater. Sci. 1997, 27, 381. (3) Derjaguin, B. V.; Muller, V. M.; Toporov, P. J. J. Colloid Interface Sci. 1975, 53, 2. (4) Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. London A 1971, 324, 301.
the substrate in a given solvent. The work of adhesion depends on interfacial energies,
Wad ) γ1,medium + γ2,medium - γ1,2
(2)
where 1 and 2 refer to the probe and the substrate, respectively. In cases where Wad is known for a particular system, eq 1 has been used to estimate indirectly AFM probe radii from pull-off force measurements.1c,5 Surprisingly, the applicability of continuum-based contact mechanics models to nanoscale contacts, in particular the linear dependence of the pull-off force on R, has not been investigated in detail.6 In the study described here, a principal objective was avg on probe to assess the functional dependence of Fpull-off radius. We chose the interaction between two hydrophobic surfaces in water as a model system to correlate measured pull-off forces with tip radii. Previous AFM force measurements have shown that hydrophobic forces in water are among the strongest interactions encountered between SAM tailored surfaces.2b Studying a strong interaction is important in order to maximize the effect that small variations in AFM probe sizes have on the pull-off forces. Numerous authors report measuring the radius of curvature of AFM probes,7 typically from SEM images.1a,d,8 In conjunction with force measurements, the average radius of curvature for all probes used in a particular experiment is usually reported, without noting the spread encountered. Consequently, a second objective of this study was to determine what the spread could be for commercial (5) Clear, S. C.; Nealey, P. F. J. Colloid Interface Sci. 1999, 213, 238. (6) Numerous studies have shown that Fpull-off correlates with expectations based on the JKR theory and estimated values of Wad. However, there has been only one study that has explicitly considered the variation of Fpull-off with R; see: Sugawara, Y.; Ohta, M.; Konishi, T.; Morita, S.; Suzuki, M.; Enomoto, Y. Wear 1993, 168, 13. (7) (a) Tsukruk, V. V.; Bliznyuk, V. N. Langmuir 1998, 14, 446. (b) Lio, A.; Morant, C.; Ogletree, D. F.; Salmeron, M. J. Phys. Chem B 1997, 101, 4767. (c) Carpick, R. W.; Agrait, N.; Ogletree, D. F.; Salmeron, M. Langmuir 1996, 12, 3334. (8) (a) Kidoaki, S.; Matsuda, T. Langmuir 1999, 15, 7639. (b) Vezenov, D. V.; Noy, A.; Rozsnyai, L. F.; Lieber, C. M. J. Am. Chem. Soc. 1997, 119, 2006. (c) Noy, A.; Frisbie, C. D.; Rozsnyai, L. F.; Wrighton, M. S.; Lieber, C. M. J. Am. Chem. Soc. 1995, 117, 7943.
10.1021/la000208y CCC: $19.00 © 2000 American Chemical Society Published on Web 06/23/2000
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Scheme 1. Schematic Representation of Au-Coated AFM Tip and Substrate Overlaid with SAMs of Octadecanethiol Interacting in Water
Figure 1. Histograms of pull-off forces recorded with two different SAM-modified AFM tips having radii of curvature of 15 nm (A) and 110 nm (B).
probes and whether SEM could be used reliably and reproducibly to determine R. Experimental Section Materials. Octadecanethiol (99%, ODT) and tetrahydrofuran (99.9%, THF) were obtained from Aldrich (Milwaukee, WI), and absolute ethanol was obtained from Aaper Alcohol and Chemical Co. (Shelbyville, KY). Gold (99.999%) was obtained from W. E. Mowrey Co. (St. Paul, MN), and chromium, from R. D. Mathis (Long Beach, CA). Silicon wafers were purchased from WaferNet (San Jose, CA), and standard Si3N4 triangular cantilevers were obtained from Digital Instruments (Santa Barbara, CA). Water (18 MΩ) was filtered using a Barnstead system. Monolayer Preparation. Silicon wafers were cleaned in boiling 5:1:1 H2O/H2O2/NH4OH, rinsed with distilled water and absolute ethanol, dried with flowing N2, and coated with Cr (5 nm) and then Au (100 nm) by thermal evaporation. Similarly, AFM cantilevers were coated with 3 nm of Cr and 40 nm of Au. Substrates and cantilevers were put immediately into a 5 mM solution of ODT in 4:1 ethanol/THF for a minimum of 24 h. Removal from solution was followed by extensive rinsing with the same solvent mixture and drying in flowing N2. Force Measurements. Force measurements were done on a Nanoscope III from Digital Instruments (Santa Barbara, CA) equipped with a fluid cell. Cantilevers with leg length of 100 µm and leg width of 35 µm were used, and the force constant of each lever was determined by the Cleveland method.9 Resonance frequencies of coated cantilevers varied from 50 to 54.1 kHz, with the corresponding variation of force constant between 0.23 and 0.28 N/m. Approximately 200 force curves were collected with each cantilever, each with a Z position sweep of 500 nm at a rate of 500 nm/s. Force curves were analyzed using routines written in Igor Pro (Wavemetrics Inc., Lake Oswego, OR). Scanning Electron Microscopy. Imaging of AFM tips was performed with a Hitachi S-800 field emission gun scanning electron microscope (FEG-SEM). Images were recorded with an operating voltage of 8 kV at 200 000× magnification. Tip radii were measured by drawing a circle on the images such that an arc of the circle coincided with the tip end. The error in the measurement was estimated by drawing a minimum and maximum possible arc radii to coincide with the tip. Grain Size Measurements. Topographic AFM images of the polycrystalline Au substrates were acquired using an oxidesharpened Si probe. The radii of curvature of 20 Au grains were estimated by measuring their height (h) and radius (r) and using R ) (h2 + r2)/2h. (9) Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. Rev. Sci. Instrum. 1993, 64, 403.
Figure 2. High-resolution SEM images of the AFM tips used to acquire the data shown in Figure 1. The circles were used to estimate radii of 15 nm (A) and 110 nm (B).
Results and Discussion For each of the 10 tips examined in this study, the average pull-off force was determined by acquiring approximately 200 force curves. The histograms in Figure 1 show the distribution of pull-off forces for two tips originating from the same wafer. There is a large (∼20 nN) difference in the mean pull-off force, which along with the relatively small spread for both tips results in completely separated distributions. Figure 2 shows high-resolution SEM images of the very end of the Au-coated Si3N4 AFM probes used for acquiring the data in Figure 1. The tip in Figure 2a was used to obtain the data in Figure 1a and has an estimated radius of curvature of 15 nm, represented by the drawn circle. This is the sharpest Aucoated Si3N4 probe we have encountered. In comparison, Figure 2b shows an extremely blunt tip used to acquire the Figure 1b data, with an estimated radius of curvature of 110 nm. An on-top view of the tip (not shown here) showed that the Au coating was intact, indicating that
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the bluntness of the tip was not a result of the force measurements. The Figure 1 and Figure 2 data show that in a qualitative sense the average pull-off force clearly depends on the probe radius, as has been noted in previous papers.2,8c In Figure 3a the average pull-off force is plotted as a function of the estimated tip radius for 10 probes. A significant variation in tip radius (15-130 nm) is observed, with eight of the probes evenly distributed between 15 and 60 nm. This variation clearly shows that assuming an average radius of curvature for measurements involving a single AFM probe can lead to significant errors (factors of 2-3 typically). Importantly, there is a remarkavg and R. Howably good linear correlation between Fpull-off ever, the linear fit has a nonzero intercept, which is not predicted by eq 1. Furthermore, calculating work of adhesion from the data in Figure 3a using eq 1 gives Wad ) 49 ( 19 mJ/m2, half of the expected value of 103 mJ/m2.10 The agreement with eq 1 is much better if the surface roughness is considered. The topological shape of the polycrystalline Au surface can be modeled as a two-dimensional array of spherical caps. Thus, the tip-substrate interaction can be approximated as a contact between two half-spheres of unequal radii. In this case, R in eq 1 is replaced by the reduced radius of the two spheres,
R1R2 R) R1 + R2
(3)
where R1 is the radius of curvature of the probe and R2 is the average radius of the spherical surface caps. From AFM images of the Au-coated substrate using oxide-sharpened Si AFM tips, Figure 4, we estimated the average radius of curvature for the Au grains to be 110 avg is plotted as a function of the nm. In Figure 3b, Fpull-off reduced radius of curvature, calculated from eq 3. It shows that the mean pull-off force also has a good linear dependence on the reduced tip radius. A linear fit of the data yields a slope of 0.52 ( 0.05 N/m and, importantly, an intercept of 0.2 ( 1.6 nN, indistinguishable from zero. These results are in good agreement with the functional form of eq 1. Furthermore, calculating the work of adhesion from the slope yields Wad ) 110 ( 10 mJ/m2, in excellent agreement with values based on published interfacial energies.10 The conclusion is therefore that the linear avg and R, as predicted by relationship between Fpull-off models such as JKR, can apply to AFM pull-off force measurements, which has not been shown previously. The relatively small scatter in the data points in Figure 3 indicates that the SEM method has good precision for estimating tip radii. Other methods for determining AFM probe radii have been developed, one of which involves scanning the tip over a step-edge11 or an apex having a much higher aspect ratio than the tip.12 Deconvolution of this image gives an estimated radius. The advantage of using SEM to determine R is the speed by which a large (10) Using reported values for the interfacial energies (see: Israelachvili, J. Intermolecular and Surface Forces; Academic Press: New York, 1992), the value for the thermodynamic work of adhesion between two methyl-terminated surfaces in water can be estimated from eq 2. These values are 52 and 0.9 mJ/m2 (ref 1c) for γmethyl-water and γmethyl-methyl, respectively, yielding W ) 103 mJ/m2. (11) (a) Ogletree, D. F.; Carpick, R. W.; Salmeron, M. Rev. Sci. Instrum. 1996, 67, 3298. (b) Glasbey, T. O.; Batts, G. N.; Davies, M. C.; Jackson, D. E.; Nicholas, C. V.; Purbrick, M. D.; Roberts, C. J.; Tendler, S. J. B.; Williams, P. M. Surf. Sci. 1994, 318, L1219. (12) (a) Atamny, F.; Baiker, A. Surf. Sci. 1995, 323, L314. (b) Bogdanov, A. L.; Erts, D.; Nilsson, B.; Olin, H. J. Vac. Sci. Technol. B 1994, 12, 3681. (c) Vesenka, J.; Miller, R.; Henderson, E. Rev. Sci. Instrum. 1994, 65, 2249.
avg Figure 3. (A) Plot of mean pull-off force (Fpull-off ) vs estimated tip radius (dots) for 10 tips. The solid line shows a linear leastsquares fit yielding a slope of 0.23 ( 0.09 N/m and an intercept of 5.2 ( 3.5 nN. The vertical error bars represent the standard deviation of the average pull-off force while the horizontal error bars are estimated maximum and minimum radius. (B) Plot of mean pull-off force vs reduced tip radius, taking into account roughness of the substrate. Linear least-squares fit yields a slope of 0.52 ( 0.05 N/m and an intercept of 0.2 ( 1.6 nN.
Figure 4. Topographic AFM image of 100 nm thick thermally evaporated Au coating on a Si wafer used in the measurements. The black line shows the position of the cross section shown on top of the image.
batch of tips can be analyzed. Our results demonstrate that SEM gives reliable measurements of R. The data also show that there is considerable spread in tip radii for commercial AFM probes. Some of this variation in R presumably can be attributed to the microstructure of the Au coating on the tip, but the underlying shape of the
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Si3N4 is also of key importance to the overall sharpness of the probe. It is interesting to estimate the variation in the tipsubstrate contact area for tips of different radii. According to the JKR model, the radius of the contact area at pull-off is
a)
(
)
RFpull-off K
1/3
(4)
where K is the elastic modulus of the two contacting objects.4 Assuming that the monolayers contribute negligibly to the overall elasticity,1e we consider contact of Au surfaces and obtain a value of 64 GPa for K. The contact areas for the two probes shown in Figure 2a,b are then 4 and 26 nm2, respectively. With an alkanethiol coverage13 of ∼4 molecules/nm2 this corresponds to 16 and 104 molecular pairs in contact at pull-off. Clearly, a significant difference in contact area can be associated with two identically functionalized AFM probes. Assuming an average radius of curvature determined from only a few probes can result in significant over- or underestimates of tip-sample contact area and Wad in pull-off measurements. The prediction of the JKR model and our finding that Fpull-off scales with R is at odds with a simple model in which adhesion arises from a certain number of identical bonds between the tip and substrate. Such a model would predict that Fpull-off would scale with R2/3 since the contact (13) (a) Dubois, L. H.; Nuzzo, R. G. Annu. Rev. Phys. Chem. 1992, 43, 437. (b) Nuzzo, R. G.; Fusco, F. A.; Allara, D. L. J. Am. Chem. Soc. 1987, 109, 2358.
area is proportional to R2/3 (refer to eq 4). The connection of the JKR model to a discrete bonding picture remains an important question for workers attempting to investigate intermolecular interactions in microcontact rupture experiments. In our studies, the adhesion between the hydrophobic tip and substrate in water is clearly not due to formation of discrete bonds between molecules on the tip and the substrate. Rather, the thermodynamic driving force for the adhesion stems from the large surface energy associated with the water-monolayer interface (see eq 2). A potentially important direction for further study would be to investigate the dependence of Fpull-off on R when strong discrete interfacial bonds can be formed. In summary, we have measured pull-off forces in water between octadecanethiol-modified Au-coated AFM tips and substrates. For each tip, the mean pull-off force was correlated with its radius of curvature, measured from high-resolution SEM images. By taking into account the roughness of the Au substrate, the pull-off force was found to scale linearly with the reduced tip radius in accordance with the JKR model. A considerable variation was found in probe radii with most probes having a radius of curvature in the 20-60 nm range. These findings are of importance to researchers using contact mechanics models to analyze AFM pull-off force measurements. Acknowledgment. This work was supported by the Center for Interfacial Engineering (CIE) at the University of Minnesota. H.S. and C.D.F. thank a reviewer for insightful comments on the scaling relationship between Fpull-off and R. LA000208Y
