Investigation of Nanoscale Frictional Contact by Friction Force

Results 5 - 14 - Beijing 100080, People's Republic of China. Received ... be entirely subject to linear law, especially when the loads were kept low. ...
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Langmuir 2001, 17, 3945-3951

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Investigation of Nanoscale Frictional Contact by Friction Force Microscopy Zhongqing Wei, Chen Wang, and Chunli Bai* Institute of Chemistry and Center for Molecular Sciences, The Chinese Academy of Sciences, Beijing 100080, People's Republic of China Received August 17, 2000. In Final Form: February 19, 2001 Organsilane self-assembled monolayers (SAMs) deposited on mica (APTES/mica and OTS/mica) were investigated by friction force microscopy in air. The frictional force as a function of load was found not to be entirely subject to linear law, especially when the loads were kept low. The JKR model, the DMT model, and the transition regime between these two can be employed to describe the nanoscale contacts. We analyzed and fitted the measured frictional data using the modified Carpick’s transition equation. The transition parameter, R, extracted from the fitting was used to determine which model should be used to describe the contacts. We found that the frictions both for the tip-APTES/mica system and the tip-OTS system could be described by the transition regime between JKR and DMT models. In addition, using the Carpick’s transition equations, we determined the adhesion energies for the tip-sample contacts. This study implies a method to identify the accuracy of a particular continuum model to describe the nanoscale contacts. Considering that many previous studies assumed the contacts were completely subject to either the JKR model or the DMT model, we believe that this work will provide us with more realistic information concerning the nanoscale contacts.

Introduction The study of tribology has been extended to truly atomic and molecular levels since the emergence of friction force microscopy (FFM).1-3 As an extension of atomic force microscopy (AFM),4 FFM combines lateral imaging with lateral force measurements down to the nanometer scale. Many striking experimental results5-14 obtained with FFM demonstrated that FFM shows promise to provide a fundamental understanding of tribological phenomena at the atomic scale.15 With numerous friction measurement results arising, more theoretical efforts should be paid to clarify these experimental results. This is because the analyses and interpretations of these measurements as well as the understanding of fundamental issues in tribology require the development of tribological theories at the nanometer scale (usually referred to as nanotribology). Unfortunately, * To whom correspondence should be addressed. Telephone: +86-10-62568158. Fax: +86-10-62557908. E-mail: clbai@ infoc3.icas.ac.cn. (1) Mate, C. M.; McClelland, G. M.; Erlandsson, R.; Chiang, S. Phys. Rev. Lett. 1987, 59, 1942. (2) Meyer, G.; Amer, N. M. Appl. Phys. Lett. 1990, 57, 2089. (3) Marti, O.; Colchero, J.; Mlynek, J. Nanotechnology 1990, 1, 141. (4) Binnig, G.; Quate, C. F.; Gerber, C. Phys. Rev. Lett. 1986, 56, 930. (5) Kim, H. I.; Koini, T.; Lee, T. R.; Perry, S. S. Langmuir 1997, 13, 7192. (6) Lu¨thi, R.; Meyer, E.; Haefke, H.; Howald, L.; Gutmannsbauer, W.; Guggisberg, M.; Bammerlin, M.; Gu¨ntherodt, H.-J. Surf. Sci. 1995, 338, 247. (7) Lio, A.; Charych, D. H.; Salmeron, M. J. Phys. Chem. B 1997, 101, 3800. (8) Lio, A.; Morant, C.; Ogletree, D. F.; Salmeron, M. J. Phys. Chem. B 1997, 101, 4767. (9) Barrena, E.; Kopta, S.; Ogltree, D. F.; Charych, D. H.; Salmeron, M. Phys. Rev. Lett. 1999, 82, 2880. (10) Hu, J.; Xiao, X.-d.; Ogletree, D. F.; Salmeron, M. Surf. Sci. 1995, 327, 358. (11) Clear, S. C.; Nealey, P. F. J. Colloid. Interface Sci. 1999, 213, 238. (12) Tsukruk, V. V.; Bliznyuk, V. N. Langmuir 1998, 14, 446. (13) Artsyukhovich, A.; Broekman, L. D.; Salmeron, M. Langmuir 1999, 15, 2217. (14) Qian, L.; Xiao, X.; Wen, S. Langmuir 2000, 16, 662. (15) Carpick, R. W.; Salmeron, M. Chem. Rev. 1997, 97, 1163.

the progress of nanotribology cannot keep pace well with experiments, and not much work has been done concerning nanotribology theories.15 While macroscopic theories agree with experiments that friction force is proportional to applied load (where the constant of proportionality is defined as the friction coefficient), microscopic (nanometer scale) experimental results exhibit complicated time, temperature, load, and velocity dependencies and cannot be properly described in terms of a single parameter such as “friction coefficient” or “shear stress”.16,17 The frictional behavior at the nanometer scale has been shown to differ substantially from bulk behavior, and the gap between macroscopic tribology and nanotribology is large.15 The nanotribological theories associated with FFM involve many issues such as the calibration of the FFM cantilever force spring constant, the determination of the geometry, atomic structure, and chemical composition of the FFM tip,18 the contact area between the FFM tip and the sample, atomic scale stick-slip behavior, wear processes, and so on. The complex nature of these mentioned factors led to the tardiness and difficulties of the development of the nanotribological theories. One of the most important issues concerning nanotribology is the role of contact area in friction determination. FFM measurements are related to nanometer-sized elastic single-asperity contact with the sample being probed if externally applied loads are kept low,17 while macroscopic frictional measurements involve multiple asperity contacts and plastic deformation. Although many studies reported the measurements of the frictional coefficient at the nanometer scale, Carprick et al.17 have demonstrated that the concept of a friction coefficient is not valid in the elastic single-asperity regime for nanometer-sized contacts between mica and Pt measured in UHV. (16) Heuberger, M.; Luengo, G.; Isralelachvili, J. N. J. Phys. Chem. B 1999, 103, 10127. (17) Carpick, R. W.; Agraı¨t, N.; Ogletree, D. F.; Salmeron, M. Langmuir 1996, 12, 3334. (18) Carpick, R. W.; Agraı¨t, N.; Ogletree, D. F.; Salmeron, M. J. Vac. Sci. Technol. B 1996, 14, 1289.

10.1021/la001185q CCC: $20.00 © 2001 American Chemical Society Published on Web 05/23/2001

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Rather, at low loads, the frictional force varies with load in almost exact proportion to the area of contact.18 The variation of contact area with load between adhesive elastic bodies depends on the effective range of attractive surface forces. Surface forces for long and short range can be described by the DMT (Derjaguin-Mu¨ller-Toporov) model19 and the JKR (Johnson-Kendall-Roberts) model,20 respectively.21 Thus, the contact areas can also be described by these two models. The intermediate case between these two limiting cases has been discussed in detail by Maugis using the Dugdale model.22 More recently, Carpick et al.21 simplified the Dudale’s transition model and presented a simpler generalized equation (we shall refer to this equation as Carpick’s transition equation) to describe the JKR-DMT transition. A transition parameter in this equation, R, is used to determine which model should be applied to the system concerned. The Carpick’s transition equation shows the variation of contact area with load. However, the transition model is appropriate for isotropic, linear, elastic materials. It was not designed to account for anisotropic substrates such as mica. Also, it was not designed to account for a thin film, or materials with viscoelastic behavior, which is the case for SAMs. Unfortunately, a model for such anisotropic materials or SAMs has not yet been developed. In a previous report, however, Lio et al. discussed the transition regime and applied it to AFM measurements on self-assembled monolayers of n-alkanethiols on gold.8 In this work, we have studied the variation of frictional force with externally applied load for the FFM tips in contact with the surfaces of alkylsilanes/mica. The collected friction force data were fitted with a modified Carpick’s transition equation. The extracted transition parameter R from the fitting was used to determine which contact model (JKR, DMT, or “transition regime” between these two) is more realistic for the systems concerned. Then, using R and related equations (see below), we derived adhesion energies between contact bodies. To our knowledge, this is the first investigation that combines the theoretical Carpick’s transition equation with the studied system to explore the suitability of a contact model for a given contact. Considering that many previous studies assumed that the contacts were entirely subject to either the JKR model or the DMT model, we believe that this work will provide us with more realistic information concerning the nanoscale contacts. Experimental Section Materials and Instrumentation. (3-Aminopropyl)triethoxysilane (APTES, 99.99%, ACRO) and octadecyltrichlorosilane (OTS, 95%, ACRO) were used as reagents for self-assembled monolayer deposition on mica. Toluene (99.99%, HPLC grade, ACRO) was employed as a solvent to solubilize alkylsilanes. Ultrapure water (18.2 MΩ‚cm) was obtained with a Mill-Q filtration system and was used throughout the experiments. All other chemicals used in chemical manipulations were of reagent grade or better. A simple home-built hygrometer was used for relative humidity (RH) appraisement. Monolayer Preparation. Mica was used as a substrate for SAM deposition. Prior to modification with a SAM, the mica was pretreated in order to obtain a SAM with high quality. Freshly cleaved mica was heated to 120 °C in an oven for 2 h. The purpose (19) Derjaguin, B. V.; Muller, V. M.; Toporov, Y. P. J. Colloid Interface Sci. 1975, 53, 314. (20) Johon, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. London A 1971, 324, 301. (21) Carpick, R. W.; Ogletree, D. F.; Salmeron, M. J. Colloid Interface Sci. 1999, 211, 395. (22) Maugis, D. J. Colloid. Interface Sci. 1992, 150, 243.

Wei et al. for doing this was to produce a silanol group as much as possible on the mica surface. The mica was then moved into a nitrogenfilled glovebox and dried in a stream of N2 for at least 30 min at room temperature. Then, the pretreated mica was separately immersed in APTES/toluene (v:v, 1:200) solution and OTS/toluene solution (v:v, 1:2000) (toluene is a better solvent for OTS deposition than other solvents23) for 20 min, subsequently rinsed with toluene and water, heated at 120 °C for 30 min, cooled at room temperature, and finally stored in water until use. Scanning Force Measurements. Topography and force measurements were carried out using a commercial multimode Nanoscope III (Digital Instruments, Santa Barbara, CA). All measurements were performed in ambient air using a contact mode tip. A tip scan speed of 5 µm/s was used for force measurements. The spring normal and lateral constants of the cantilever were calibrated according to the procedures shown in the Appendix. For the purpose of comparisons, experimental data in this report were acquired using the same tip throughout the experiments. After good images were collected, frictional loops with trace and retrace scanning were recorded while the tip scanned across the sample along the X direction (perpendicular to the long axis of the cantilever) with Y direction (parallel to the long axis of the cantilever) scanning disabled. By convention, the sample surface is taken as the X-Y plane with the Z coordinate lying along the surface normal. The deflection of the cantilever in the Z direction was recorded as the normal force (FN), that is, the total load, which is the total of external applied load FE and adhesion force Fad (total of capillary force and molecular interactions) between the AFM tip and the sample. The zero point of the total load is defined as the point where the tip breaks contact with the surface, that is, the free position of the cantilever. Both load and friction signals were recorded, while the force measurements were performed by scanning the tip repeatedly back and forth over the same line. We began the measurements at a negative load (higher than the pull-off force) which was increased to a chosen load (loading half cycle), followed by decreasing the load (unloading half cycle) until the tip pulled out of contact with the samples. Negative loads corresponded to the tip being pulled off the surface. The plot of friction versus load can then be obtained.

Results and Discussion Characterization of SAMs. According to the procedures discussed above, we prepared the SAMs of APTES and OTS deposited on mica. Figure 1 shows the topographical (a) and frictional (b) images of APTES/mica acquired simultaneously at the same sample location. The value of rms roughness for this SAM in Figure 1a is 0.532 nm. The frictional loop (Figure 1d) and the corresponding z-profile (Figure 1c), taken along the dashed line in parts b and a separately, are also shown. Likewise, Figure 2 shows the topographical (a) and frictional (b) images of OTS/mica collected simultaneously at the same sample location. The rms value for the OTS SAM in Figure 2a is 0.304 nm. The frictional loop and the corresponding z-profile, taken along the dashed line in Figure 2b and a, are shown in parts d and c, respectively. Dark areas in frictional images correspond to low frictions. Modification of Carpick’s Generalized Transition Equation. Carpick’s transition equation describes the range of surface contact force between the tip and the surface of the sample. One of its applications is to determine which model is suitable for describing the elastic contact. This equation is given as follows:21

(

)

R + x1 - FE/FPO a ) a0 1+R

2/3

(1)

where a is the contact radius at external applied load FE, (23) McGovern, M. E.; Kallury, K. M. R.; Thompson, M. Langmuir 1994, 10, 3607.

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Figure 1. Topographical (a) and frictional (b) images of APTES/mica collected simultaneously at the same sample location. The scan sizes are 1.8 µm × 1.8 µm. Parts d and c are the friction loop and the corresponding z-profile, taken along the dashed line in parts b and a, respectively.

a0 is the contact radius at zero load, R is Carpick’s transition parameter, and FPO is the pull-off force (FPO ) -Fad), given by

FPO ) kN

∆VPO SN

∆VL FL ) kL SL

(2)

where kN is the cantilever spring constant in the normal direction, ∆VPO is the difference of the deflection voltage between the zero point and the pull-off point, and SN is the sensitivity of the piezotube in the normal direction, which was determined by measuring the slope of the normal force signal versus the z-displacement curve on a hard surface. Here, R is used to describe the range of surface contact forces. R ) 1 corresponds exactly to the JKR case, R ) 0 corresponds exactly to the DMT case, and 0 < R < 1 corresponds to the intermediate case, that is, the transition regime. Assume that the friction force (FL) is directly proportional to the contact area, that is, FL ) τπa2,24 where τ is the constant interfacial shear strength. This is expected to be true for single-asperity contacts and in the absence of wear if the shear strength is constant. Meanwhile, the materials must be homogeneous, isotropic, and linearelastic. Herein, we assume that this equation can also be applied to our SAMs systems. Thus, eq 1 can then be modified to the following form:

(

where FL,0 is the friction force when the external applied load FE is zero. FL can be associated with the cantilever spring constant in the lateral direction (kL) by the equation

)

R + x1 - FE/FPO FL ) FL,0 1+R

4/3

(3)

(24) Bowden, F. P.; Tabor, D. Friction and lubrication of solids: Part 1; Oxford University Press: 1964.

(4)

where ∆VL is the lateral deflection signal in voltage (equal to half the difference between the average trace and retrace voltages in the friction loop) and SL is generally difficult to obtain. Ogletree et al.25 presented a quite general procedure to determine the ratio of the lateral and normal force calibration factors, from which SL can be obtained. SL can also be calibrated from lattice-resolution images of mica and Au(111).8 However, the use of SL can be avoided in this work. Since Carpick’s equation is expressed in nondimensional form, we can represent forces in raw, uncalibrated voltage units and apply the equation to our data. Equation 3 can be modified into the following form:

(

)

R + x1 - ∆VE/∆VPO ∆VL ) ∆VL,0 1+R

4/3

(5)

where ∆VL,0 is the lateral deflection signal in voltage at zero load and ∆VE is the external applied voltage exerted on the piezotube, which is equal to the setpoint voltage subtracted by the baseline deflection voltage. This equation shows a relationship between ∆VL (friction force in voltage unit) and ∆VE (external applied force in voltage unit). Clearly, using this modified Carpick’s transition equation to fit experimental measurements of friction (25) Ogletree, D. F.; Carpick, R. W.; Salmeron, M. Rev. Sci. Instrum. 1996, 67, 3298.

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Figure 2. Topographical (a) and frictional (b) images of OTS/mica acquired simultaneously at the same sample location The scan sizes are 2.0 µm × 2.0 µm. Parts d and c are the friction loop and the corresponding z-profile, taken along the dashed line in parts b and a, respectively.

forces under different external applied loads, we can obtain a plot of ∆VL versus ∆VE. Thus, R can be easily extracted from the fitting. Other parameters including ∆VL,0 and ∆VPO can also be extracted simultaneously. Obviously, this modified equation avoids the use of a cantilever spring constant and eliminates the possible errors caused by the determinations of spring constants. The extracted R is surely independent of calibration factors. However, other parameters, such as the adhesion energy, are dependent on the calibration factors. Analysis of Force Measurements. Many papers reported the frictional measurements by FFM concerning various systems. Further, a more recent study26 focused on the quantitative measurements of frictional properties of n-alkanethiols on Au(111). It is well-known that the spring contants kN and kL must be calibrated, if one wants to replace force measurement data in units of voltage with those in units of Newton. So far, several methods have been proposed for accomplishing this calibration. These methods include the resonance detection method,27 the two-slope method,25 and the FEA (finite element analysis) and PBA (parallel beam approximation) methods discussed by Sader et al.28-33 and others.34,35 Ideally this (26) Li, L.; Yu, Q.; Jiang, S. J. Phys. Chem. B 1999, 103, 8290. (27) Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. Rev. Sci. Instrum. 1993, 64, 403. (28) Sader, J. E.; White, L. J. Appl. Phys. 1993, 74, 1. (29) Sader, J. E. Rev. Sci. Instrum. 1995, 66, 4583. (30) Albrecht, T. R.; Akamine, S.; Carver, T. E.; Quate, C. F. J. Vac. Sci. Technol. A 1990, 8, 3386. (31) Neumeister, J. M.; Ducker, W. A. Rev. Sci. Instrum. 1994, 65, 2527. (32) Senden, T.; Ducker, W. Langmuir 1994, 10, 1003. (33) Sader, J. E.; Larson, I.; Mulvaney, P.; White, L. R. Rev. Sci. Instrum. 1995, 66, 3789. (34) Noy, A.; Frisbie, C. D.; Rozsnyai, L. F.; Wrighton, M. S.; Lieber, C. M. J. Am. Chem. Soc. 1995, 117, 7943.

calibration is performed in situ. In this work, such a calibration was not available, so we performed the calibration according to the procedures discussed in the Appendix. We used the values of Young’s modulus (E ) 140 GPa) and the Poisson ratio (ν ) 0.3) for Si3N4 from the literature33 and the dimensions measured from SEM to estimate spring constants. We obtained kN ) 0.126 N/m and kL ) 121 N/m. However, these calibrated values can only be regarded as estimated ones. For the purpose of accuracy, in most cases we directly utilized the force data in units of voltage rather than in units of Newton to carry on the following discussions. The frictional data (∆VL) reported in this paper were the averages of 10 separate voltages from the friction loops at specific external load (∆VE) taken from randomly distributed points over the same sample area. Figure 3 shows the plot of frictional signal ∆VL versus external applied load ∆VE over scanning lines on the surface of APTES/mica. The scan was carried out with decreasing load (unloading half cycle) at RH ∼ 55%. We can see from the figure that the variation of friction with load is nonlinear, especially near the pull-off point. The data points were not fitted with Amoton’s macroscopic linear law because of the convex curve in the low load regime (< ∼ -7.5 V). Instead, we can fit these points with the modified transition equation (eq 5). The extracted parameters from the fitting were as follows: ∆VL,0 ) 0.2431 V, R ) 0.8339 ( 0.0644, and ∆VPO ) -9.680 ( 0.1587 V. Recalling the above discussion, we considered that the value of R indicated the contact between the tip and APTES/mica cannot be simply described by either the JKR model or the DMT model. Instead, it corresponded to the intermediate case. Therefore, we can discuss the contact (35) Hazel, J. L.; Tsukruk, V. V. Thin Solid Films 1999, 339, 249.

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Figure 3. Plot of frictional signal ∆VL (in voltage) versus external applied load ∆VE (in voltage) over scanning lines on the surface of APTES/mica. The scans were carried out with decreasing load (unloading half cycle) at RH ∼ 55%.

Figure 4. Plot of frictional signal ∆VL (in voltage) versus external applied load ∆VE (in voltage) over scanning lines on the surface of OTS/mica. Both loading (+) and unloading (O) half cycles are shown. The scans were carried out at RH ∼ 55%.

behavior according to the transition regime presented by Maugis et al.22 and simplified by Carpick et al.21 Another conclusion can be derived from this fitting that the shear strength is constant and independent of load for this system. To derive the adhesion energy γ between the FFM tip and APTES/mica with the extracted parameters, we first introduce three equations21 presented by Carpick et al. into the discussion:

γ)

FPO πRF′PO

(

(6)

)

7 1 4.04λ1.4 - 1 + 4 4 4.04λ1.4 + 1

(7)

λ ) -0.9241 ln(1 - 1.02R)

(8)

F′PO ) -

where F′PO (nondimensional units) is the simple parametrization of FPO, λ is Maugis’ transition parameter, and R is the curvature radius of the tip. Substituting R ) 0.8339 into eq 8 gives λ ) 1.756. F′PO, -1.551, can then be calculated from eq 7. To obtain γ from eq 6, we should also know the value of R. The latter can be estimated from the apparent width w of the monatomic steps on Au(111) of height b by using the formula R ) w2/2b.8 However, this method was not available while our measurements were performed. Many previous studies have measured the radius of curvature of AFM tips from SEM images.34,36 More recently, Skulason et al. have demonstrated that SEM could be used reliably and reproducibly to determine R.37 Herein, from the SEM image analysis, we obtained an estimated radius of curvature of 80 ( 8 nm. Substituting this value of R into eq 6 yields a value of γ ) 0.1565 ( 0.0821 J/m2 for the tip-APTES/mica contact. For the tip-OTS/mica system, we also collected a plot of frictional signal ∆VL versus external applied load ∆VE at RH ∼ 55%, as we did for the tip-APTES/mica system. Both loading and unloading half cycles are shown in Figure (36) (a) Thomas, R. C.; Houston, J. E.; Crook, R. M.; Kim, T.; Michalske, T. A. J. Am. Chem. Soc. 1995, 117, 3830. (b) Vezenov, D. V.; Noy, A.; Rozsnyai, L. F.; Lieber, C. M. J. Am. Chem. Soc. 1997, 119, 2006. (c) Kidoaki, S.; Matsuka, T. Langmuir 1999, 15, 7639. (d) van der Vegte, E. W.; Hadziioannou, G. Langmuir 1997, 13, 4357. (e) Burnham, N. A.; Dominguez, D. D.; Mowery, R. L.; Colton, R. J. Phys. Rev. Lett. 1990, 64, 1931. (37) Skulason, H.; Frisbie, C. D. Langmuir 2000, 16, 6294.

Figure 5. Plot of frictional signal ∆VL (in voltage) versus external applied load ∆VE (in voltage) over scanning lines on the surface of OTS/mica. Both loading (O) and unloading (b) half cycles are shown. The scans were carried out at RH ∼ 67%.

4. We can see from the figure that there was no significant difference between these two half cycles under the conditions where this plot was collected. However, in some cases, we did find a gap between these two cycles. Figure 5 shows an integral cycle for the tip-OTS/mica system at RH ∼ 67%. This finding of a gap probably can be explained by the contact hysteresis between the tip and the sample surface. Yoshizawa et al.,38 Cohen et al.,39 and Kiely et al.40 (with IFM) have reported this phenomenon previously. Fitting data points of the unloading half cycle in Figure 4 with the modified Carpick’s transition equation, we extracted the parameter R ) 0.2648 ( 0.142. Likewise, fitting the data points of the unloading half cycle in Figure 5 gives R ) 0.2537 ( 0.1200 and VPO ) -5.480 ( 0.3739 V, resulting in γ ) 0.0509 ( 0.0105 J/m2 calculated from eqs 6-8. These fittings also indicate that the shear strength is constant and independent of load for this tipOTS system. We failed to find any reported adhesion energy of OH(tip)∼CH3(OTS) contact measured in ambient air. However, because the van der Waals force for OH∼CH3 contact is nearly identical to that for CH3∼CH3 contact, (38) Yoshizawa, H.; Chen, Y.-L.; Israelachvili, J. J. Phys. Chem. 1993, 97, 4128. (39) Cohen, S. R.; Neubauer, G.; McClelland, G. M. J. Vac. Sci. Technol. A 1990, 8, 3449. (40) Kiely, J. D.; Houston, J. E. Langmuir 1999, 15, 4513.

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we thus assumed that these two contacts should have similar adhesion energies. This point has been demonstrated by the comparison between our result (γ ) 0.0509 ( 0.0105 J/m2 for OH∼CH3 contact) and the previous reported value (γ ) 0.030 ( 0.016 mJ/m2 for CH3∼CH3 contact) measured by Thomas et al. with IFM.36a These two values are in agreement within an order of magnitude. So far as the values of adhesion energies are concerned, several points should be mentioned. First, we cannot quantitatively compare our adhesion energy for OH(tip)∼CH3(OTS) with other measurements. We failed to find any reported adhesion energy of OH(tip)∼CH3(OTS) contact, obtained under the condition of ambient air. Second, we have noticed the difference in the adhesion energies between the CH3-terminated monolayer (OTS) and the amine-terminated monolayer (APTES). The adhesion energy for the tip-APTES (OH∼NH2) contact is obviously larger than that for the tip-OTS (OH∼CH3) contact. This can be easily explained by the chemical effect in the adhesion energies. In addition to the capillary contribution, the adhesion energy can be resolved into a component due to van der Waals forces, γvdw, and a component due to pairwise interactions such as hydrogen bonding, γH-bond. Since the capillary contributions are about the same for these two contacts, and the van der Waals component for the pair OH∼NH2 is nearly identical to that for the pair OH∼CH3, the difference of adhesion energies mainly originates from the difference of pairwise interactions. Obviously, hydrogen bonds formed across the OH∼NH2 interface due to the large polarities of NH2 and OH can account for the higher adhesion energy of the OH∼NH2 interface. Also, the polar and hydrophilic amine group is easily wetted by ambient water, leading to the increase of adhesion energy. The last point we should also point out is that because a contact model for an ultrathin organic film has not yet been developed, these results of adhesion energy calculations may be significantly affected by this limitation. Except for the above-discussed R, it is significant to calculate Tabor’s parameter µ, another transition parameter which is commonly used to describe where one sits in the JKR-DMT spectrum of contact behavior. This transition parameter is defined as21

µ)

( ) 16Rγ2 9K2z03

1/3

(9)

where z0 is a parameter representing the equilibrium separation of the surfaces in contact, usually taken as 0.2 nm,8 and K is the combined elastic modulus of the tip and the sample, given by

4 K ) [(1 - ν12)/E1 + (1 - ν22)/E2]-1 3

(10)

where ν1 and ν2 are the tip and sample Poisson ratios, respectively, and E1 and E2 are the tip and sample Young’s moduli, respectively. Because the layer thickness of the SAM is very small compared to the tip radius and the elastic SAM will recover much faster under negative load, we assumed that the SAM did not influence the elastic behavior of the tip-substrate ensemble. In other words, the contribution of the SAM to the elastic behavior of the substrate was negligible. The constants for the Si3N4 tip (E1 ) 140 GPa, ν1 ) 0.3)8,33 and mica (E2 ) 56.5 GPa, ν2 ) 0.098)17 were taken from the literatures. If µ > 5, the JKR model applied, and if µ < 0.1, the DMT model applied. Values between 0.1 and 5 corresponded to the “transition regime” between the JKR and DMT models. We obtained

Table 1. Summary of Parameters for the Tip-SAMs Contactsa calibrationdependentb results

calibrationindependent results

tip-SAM combination

γ

Tabor’s parameter µ

R

tip-APTES tip-OTS

0.1565 0.0509

0.524 0.248

0.8339 0.2537

γtip-TPTES/ τtip-APTES/ γtip-OTS τtip-OTS 3.07

1.876

a The errors of R and γ were not taken into account for these results. b “Calibration-dependent” means “dependent of calibration factors”.

µ ) 0.524 for the tip-APTES contact and µ ) 0.248 for the tip-OTS contact. Evidently, both values of µ indicated that these two contacts corresponded to the intermediate case, in accordance with the conclusions drawn from R. However, as to the calculations of µ, the following points should also be pointed out: (a) This calculation did not consider the modification to the contact problem introduced by an elastic layer (APTES or OTS SAM) on a mica substrate. If the elastic compression of the SAM is taken into account, the low modulus of the monolayer would reduce the value of K, leading to a larger µ. (b) The error of the R value may be introduced by the SEM image analysis, leading to a possible error in the value of γ. (c) The exact value of z0 is unknown and thus somewhat arbitrary for using an atomic bond length assumption. The increase of the z0 value will decrease µ, leading to tip-sample contact closer to that of the DMT regime. So far, from the above results we are able to extract a ratio of the adhesion energies for tip-APTES versus tipOTS. Likewise, a ratio of the shear strengths for tipAPTES versus tip-OTS can also be extracted. We summarize these parameters in Table 1. Additionally, we have noticed the changes of pull-off forces and frictional forces at different experimental conditions. On one hand, under the same (the same tip, same RH ∼ 55%) experimental conditions, the friction force (0.2431 V, see Figure 3) at zero external load between the tip and APTES/mica is larger than that (0.098 65 V, see Figure 4) between the tip and OTS/mica. It is reasonable to suggest that the higher friction of APTES (with short chain) is due to poor packing or disorder of the molecules. The resulting numerous kinks and defects may provide many excitation modes to efficiently absorb energy and give rise to a high value of friction.7,41 The abovementioned chemical effect is also probably responsible for the higher pull-off force of APTES. On the other hand, it is worth noticing the difference of pull-off forces at zero loads at different RH values. For the tip-OTS/mica system, the absolute pull-off force (5.480 V) at RH ∼ 67% is smaller than that (9.680 V) at RH ∼ 55%. At this stage, we cannot give a satisfactory explanation for this observation. A similar phenomenon for the tip-mica contact has been reported previously.10,42 Finally, it is important to note the following points. First, the Carpick’s generalized transition equation is applicable for elastic, single-asperity contacts. Several reports10,17-18,43-44 have demonstrated that the FFM tip can form a single-asperity contact with the sample surface. Second, the external applied load must be kept low to (41) Xiao, X.; Hu, J.; Charych, D. H.; Salmeron, M. Langmuir 1996, 12, 235. (42) Xu, L.; Salmeron, M. Langmuir 1998, 14, 2187. (43) Putman, C. A. J.; Igarashi, M.; Kaneko, R. Appl. Phys. Lett. 1995, 66, 3221. (44) Meyer, E.; Lu¨thi, R.; Howald, L.; Bammerlin, M.; Guggisberg, M.; Gu¨ntherodt, H.-J. J. Vac. Sci. Technol. B 1996, 14, 1285.

Nanoscale Frictional Contact

Langmuir, Vol. 17, No. 13, 2001 3951

the JKR and DMT models. This result is consistent with the conclusions drawn from R. Acknowledgment. This work was supported by the financial support of the Chinese Academy of Sciences and the National Science Foundation of China. The authors thank the reviewer for insightful comments on our original manuscript. Appendix Determinations of the Cantilever Spring Constants kN and kL. The calibrations presented here are in reference to Figure 6. We combined the improved PBA (parallel beam approximation) method presented by Sader32 with the method presented by Noy et al.37 to determine kN and kL. According to the improved PBA method, the normal spring constant kN is given as Figure 6. Scheme of cantilever with a tip: J, the overall width of the arm; H, the tip vertical height; θ, the angle between the cantilever arm and the substrate; L, w, t, E, and ν, the length, width, thickness, Young’s modulus, and Poisson ratio of the cantilever arm.

avoid wear; thus, the tip-sample interaction during frictional sliding is believed to be completely elastic. In our experiments, after each run of frictional force measurements, we imaged in topographic mode the contacted sample area to check for wear. No wear was observed for any load reported in this paper. Third, on the basis of the above two points, we have assumed that friction was directly proportional to the contact area. This is untenable for multiple-asperity contacts or in the presence of wear.

kN )

}

]

It is important to emphasize that this equation is valid only when we assume the load is applied to the end tip of the cantilever. The lateral spring constant kL can then be determined using the method presented by Noy et al. The torsional spring constant kt can be expressed as

Conclusions 1. The wearless frictions of two tip-alkylsilane/mica systems were investigated by using FFM. In the low load regime, the frictional properties were not completely subject to the macroscopic linear law. 2. The Carpick’s generalized transition equation was used to fit frictional measurements. The direct use of voltage units for the plot of frictional signal versus load avoids the possible errors in using force units introduced by the calibrations of the cantilever spring constant (kN, kL) and the sensitivity (SN, SL) of the piezotube. 3. The parameter R, extracted from the fitting, can be employed to describe the range of surface force between the FFM tip and the sample. It can also be used to determine which model (JKR, DMT, or “transition regime” between these two) is suited for describing the nanoscale contact. Our results indicated that the frictional properties for both the tip-APTES/mica system and the tip-OTS/ mica system cannot be described by either the JKR model or the DMT model. Instead, the transition regime between these two models should be used to describe the contact behaviors for the two mentioned systems. Also, force measurements under the conditions of our experiments indicated that the shear strength is constant and independent of load for these systems. 4. The calculated values of Tabor’s parameter also indicated that the contact behaviors for the two concerned systems corresponded to the transition regime between

{ [

Et3w 4w3 cos(90° - θ) 1 + 3 [3 cos(90° 3 2(L sin θ) J -1 -1 Et3w 4w3 θ) - 2] ) 3 1 + (3 sin θ 2) 2L (sin θ)2 J3 (A1)

kt )

[

]

Ewh3 1 L 6(ctgθ)2 + 3(1 + ν)(sin θ)2

(A2)

Then,

kt ) kN

[

4w3 (3 sin θ - 2) J3 6(ctgθ)2 + 3(1 + ν)

2L2 1 +

]

(A3)

The relationship between kt and kL is given as

kL ) kt/H2

(A4)

Therefore,

[

kL )

LA001185Q

]( )

4w3 (3 sin θ - 2) J3 L2 kN 2 6(ctgθ) + 3(1 + ν) H

2 1+

(A5)