Lateral Force Microscopy Study of the Frictional Behavior of Self

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Lateral Force Microscopy Study of the Frictional Behavior of Self-Assembled Monolayers of Octadecyltrichlorosilane on Silicon/Silicon Dioxide Immersed in n-Alcohols Susannah C. Clear and Paul F. Nealey* Department of Chemical Engineering, University of Wisconsin, Madison, Wisconsin 53706 Received May 4, 2000. In Final Form: October 11, 2000 Lateral force microscopy (LFM) was used to evaluate the frictional behavior of surfaces modified with self-assembled monolayers (SAMs) and immersed in n-alcohols (CH3(CH2)xOH where x ) 0-8,11) as a function of applied normal load, sliding velocity, and solvent chain length. SAMs were formed from octadecyltrichlorosilane (OTS) on silicon/silicon dioxide substrates. The objective was to investigate how the solvent environment affected the frictional behavior of OTS and to characterize the effectiveness of OTS as a boundary lubricant in liquid environments for applications such as fluidic self-assembly and microelectromechanical devices. Three characteristic frictional regimes were observed at low, intermediate, and high loads. Maxima as a function of the sliding velocity appeared in the frictional forces for intermediate applied normal loads of ∼20-40 nN for x ) 1-8. These maxima shifted to lower sliding velocities with increases in the applied normal load and with increases in the chain length of the solvent. The frictional maxima were interpreted by adapting concepts of viscoelasticity for bulk polymer systems to the twodimensional systems of SAMs. Maxima were interpreted to result from localized relaxation processes in the SAMs that depend on the extent of solvent partitioning in the compressed region under the tip. The characteristic relaxation times of the alkyl chains increased with increased applied normal load and with increased solvent chain length. The behavior as a function of x was consistent with both a mechanism of solvent partitioning controlled by the free volume distribution in the SAM and a mechanism of insertion into defects. The relaxation times of the alkyl chains were related to a molecular model of energy dissipation based on the adsorption and desorption of the chain tails from the surface of the atomic force microscopy tip. The total frictional forces was consistent with superposition of relaxation processes and viscous drag on the tip and plowing effects that become dominant at high applied normal loads.

Introduction Stiction and wear are two major design limitations of new micro- and nanoscale technologies such as microelectromechanical systems (MEMS) and fluidic selfassembly (FSA). Organic thin films, particularly selfassembled monolayers (SAMs) of alkylsiloxanes, are potentially useful as boundary lubricants, because their thicknesses are commensurate with the dimensions of the structures in both MEMS and FSA and because they have deposition chemistries that are compatible with the silicon or oxide surfaces that are common to MEMS and FSA. In this article we investigate the use of SAMs of alkylsiloxanes as boundary lubricants in liquid environments to determine the effects of solvent environment, sliding velocity, and applied normal load on the frictional behavior. Applications of MEMS in liquid environments include valves, micropumps, and micromotors.1 SAMs may be deposited on the surfaces of these devices to reduce capillary forces during release processes and limit friction between moving parts. Several authors have demonstrated that SAMs reduce adhesion and improve release and wear properties between surfaces in air in digital micromirror devices,2 polysilicon flange-bearing micromotors,3 and several test microstructures.4,5 The surface-to-volume * Corresponding author. E-mail: [email protected]. (1) Gad-el-Hak, M. J. Fluids Eng. 1999, 121, 5. (2) Maboudian, R.; Howe, R. T. J. Vac. Sci. Technol., B 1997, 15, 1. (3) Deng, K.; Collins, R. J.; Mehregany, M.; Sukkenik, C. N. Proceedings of the IEEE Micro-Electro-Mechanical Systems Workshop, Amsterdam, The Netherlands, 1995. (4) Alley, R. L.; Howe, R. T.; Komvopoulos, K. Proceedings of the IEEE Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1992.

ratios of the components are very large, so adhesive and frictional forces dominate inertial and gravitational forces. Molecularly thin SAMs are promising candidates to control adhesive and frictional forces because they are commensurate with the microscopic dimensions of the structures. SAMs are also commensurate with the dimensions of structures found in FSA, a novel technique developed by Smith and co-workers6-11 for the large-scale integration of dissimilar materials. In this process, suspensions of blocks with characteristic dimensions on the order of microns and with precise geometries are dispensed over a substrate that has pits of the same size and geometry as the blocks. The blocks slide over the substrate, and are positioned into the pits via fluid transport and collisions with other blocks. High frictional and adhesive forces between the surfaces of the blocks and the substrate reduce the efficiency and yield of FSA. In a previous article,12 we used chemical and lateral force microscopy to identify potential SAM-solvent combinations for use in FSA and MEMS. We investigated the (5) Houston, M. R.; Maboudian, R.; Howe, R. T. Proceedings of the IEEE Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1996. (6) Yeh, H.-J. J. Ph.D. Thesis, University of California, 1994. (7) Yeh, H. J.; Smith, J. S. IEEE Photon. Technol. Lett. 1994, 6, 706. (8) Tu, J. K.; Talghader, J. J.; Hadley, M. A.; Smith, J. S. Electron. Lett. 1995, 31, 1448. (9) Talghader, J. J.; Tu, J. K.; Smith, J. S. IEEE Photon. Technol. Lett. 1995, 7, 1321. (10) Verma, A. K.; Hadley, M.; Smith, J. S. Proceedings of the 45th Electronic Components and Technology Conference ‘95, Las Vegas, 1995. (11) Hadley, M. A. Ph.D. Thesis, University of California, 1995. (12) Clear, S. C.; Nealey, P. F. J. Colloid Interface Sci. 1999, 213, 238.

10.1021/la000650g CCC: $20.00 © 2001 American Chemical Society Published on Web 01/06/2001

LFM Study of Frictional Behavior of SAMs

effects of terminal functional groups and solvent environment on the adhesive and frictional forces between contacting surfaces that were modified with SAMs. We measured adhesive and frictional forces at a single sliding velocity between SAMs terminated with methyl or primarily carboxyl groups in a selection of solvents that represented a wide range of hydrogen-bonding ability. We found that SAMs of octadecyltrichlorosilane (OTS) in contact with both hydrophobic and hydrophilic SAMs exhibited low adhesive forces and small kinetic friction coefficients in simple n-alcohols such as ethanol. In this work, we systematically study a model system of SAMs of OTS in n-alcohols to explain the effects of solvent environment, applied normal load, and sliding velocity on the frictional behavior of SAMs. Friction at the molecular level in both dry and solvent environments is not well-understood.13-15 The frictional and elastic properties of several organic thin films including SAMs of alkylsiloxanes on Si/SiO2 or mica surfaces,16-20 SAMs of alkylthiolates on gold surfaces,21-28 and Langmuir-Blodget films13,29-36 have been the subjects of numerous atomic force microscopy (AFM) or surface forces apparatus (SFA) studies under dry conditions. Several authors have demonstrated that frictional force between surfaces modified with monolayers of surfactants correlates directly with adhesion hysteresis,35-37 which is a function of the physical state of the monolayer. With the SFA, Israelachvili and co-workers measured the frictional force between surfaces covered with monolayers of ammonium surfactants as a function of chain density and (13) Bhushan, B.; Kulkarni, A. V.; Koinkar, V. N.; Boehm, M.; Odoni, L.; Martelet, C.; Belin, M. Langmuir 1995, 11, 3189. (14) Bhushan, B.; Israelachvili, J. N.; Landman, U. Nature 1995, 374, 607. (15) Liu, Y.; Evans, D. F.; Song, Q.; Grainger, D. W. Langmuir 1996, 12, 1235. (16) Tian, F.; Xiao, X.; Loy, M. M. T.; Wang, C.; Bai, C. Langmuir 1999, 15, 244. (17) Lee, B.-W.; Clark, N. A. Langmuir 1998, 14, 5495. (18) Huang, J. Y.; Song, K. J.; Lagoutchev, A.; Yang, P. K.; Chuang, T. J. Langmuir 1997, 13, 58. (19) Xiao, X.; Hu, J.; Charych, D. H.; Salmeron, M. Langmuir 1996, 12, 235. (20) Reiter, G.; Demirel, A. L.; Peanasky, J.; Cai, L. L.; Granick, S. J. Chem. Phys. 1994, 101, 2606. (21) van der Vegte, E. W.; Subbotin, A.; Hadziioanou, G.; Ashton, P. R.; Preece, J. A. Langmuir 2000, 16, 3249. (22) Lee, S.; Shon, Y.-S.; Colorado, R.; Guenard, R. L.; Lee, T. R.; Perry, S. S. Langmuir 2000, 16, 2220. (23) Kiely, J. D.; Houston, J. E. Langmuir 1999, 15, 4513. (24) Zhou, Y.; Fan, H.; Fong, T.; Lopez, G. P. Langmuir 1998, 14, 660. (25) Kim, H. I.; Koini, T.; Lee, T. R.; Perry, S. S. Langmuir 1997, 13, 7192. (26) Kim, H. I.; Graupe, M.; Oloba, O.; Koini, T.; Imaduddin, S.; Lee, T. R.; Perry, S. S. Langmuir 1999, 15, 3179. (27) McDermott, M. T.; Green, J.-B. D.; Porter, M. D. Langmuir 1997, 13, 2504. (28) Lio, A.; Charych, D. H.; Salmeron, M. J. Phys. Chem. B 1997, 101, 3800. (29) Briscoe, B. J.; Evans, D. C. B. Proc. R. Soc., London Ser. A 1982, 380, 389. (30) Overney, R. M.; Meyer, E.; Frommer, J.; Guntherodt, H.-J. Langmuir 1994, 10, 1281. (31) Overney, R. M.; Bonner, T.; Meyer, E.; Ruetschi, M.; Luthi, R.; Howald, L.; Frommer, J.; Guntherodt, H.-J.; Fujihara, M.; Takano, H. J. Vac. Sci. Technol. B 1994, 12, 1973. (32) Overney, R. M.; Meyer, E.; Frommer, J.; Brodbeck, D.; Luthi, R.; Howald, L.; Guntherodt, H.-J.; Fujihara, M.; Takano, K.; Gotoh, Y. Nature 1992, 359, 133. (33) Meyer, E.; Overney, R.; Brodbeck, D.; Howald, L.; Luthi, R.; Frommer, J.; Guntherodt, H.-J. Phys. Rev. Lett. 1992, 69, 1777. (34) Tsukruk, V. V.; Bliznyuk, V. N.; Hazel, J.; Visser, D.; Everson, M. P. Langmuir 1996, 12, 4840. (35) Yoshizawa, H.; Chen, Y.-L.; Israelachvili, J. J. Phys. Chem. 1993, 97, 4128. (36) Yoshizawa, H.; McGuiggan, P.; Israelachvili, J. Science 1993, 259, 1305. (37) Chaudhury, M. K.; Owen, M. J. Langmuir 1993, 9, 29.

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temperature. They observed a maximum frictional force at a sliding velocity of 0.175 µm/s between two amorphous dihexadecyldimethylammonium monolayers. They proposed a ‘pseudo-phase diagram’ that accounts for the observed maximum in the frictional force and qualitatively explains the frictional force as a function of the chemical structure and packing density of the chains, the applied normal load, the temperature, and the sliding velocity. According to this model, monolayers that are at temperatures below a melting point, Tm, display solidlike behavior that is characterized by “Cobblestone” stick-slip friction and low friction. For T > Tm, monolayers are liquidlike with low frictional forces because alkyl chains readily adopt low-energy configurations in response to applied force. For T ≈ Tm, the monolayer is amorphous. frictional forces and energy dissipation are highest for amorphous monolayers because the time scale of the motion of the sliding surface across the surface of the monolayer is of the same order as the relaxation time of the alkyl chains. The relationship between the physical state of the monolayer and the frictional behavior was substantiated by recent AFM studies by Liu and co-workers15,38 and Tsukruk and co-workers34 for surfactant monolayers and LB films, respectively. For monolayers of double-chain quaternary ammonium surfactants, Liu and co-workers observed maxima in the frictional force as a function of sliding velocity for experimental temperatures less than 40 °C below the bulk melting temperature of the surfactant. They attributed these maxima to phase transitions within the film. With LB films, Tsukruk and co-workers demonstrated that the appearance of a maximum in the frictional force as a function of sliding velocity is also a function of the chain density of the film. Few studies in the literature have focused on the effects of the solvent environment on the frictional behavior of organic thin films. The solvent environment is expected to influence the frictional behavior of organic thin films through surface free-energy effects and solvent partitioning into the film. The effects of exposure to solvent vapor on the frictional behavior of organic thin films were reported only for hexane and water vapor for the surfactant systems studied by Israelachvili and co-workers35,36 and Liu and co-workers.15,38 They found that maxima in the frictional force shifted to higher sliding velocities when surfactant monolayers were exposed to hexane. At a given sliding velocity and applied normal load, the frictional behavior of a LB film or SAM depends on the ability of the monolayer to conserve order at the molecular level.33 For condensed or solidlike films, increases in disorder generally correlate with increased frictional forces. For SAMs in liquids, conservation of order is expected to be a function of the extent and nature of the solvent partitioning within the monolayer. In this article, we present a lateral force microscopy (LFM) study of the frictional behavior of solidlike35,39,40 SAMs of OTS chemisorbed to silicon/silicon dioxide (Si/SiO2) surfaces immersed in n-alcohols as a function of the sliding velocity and applied normal load. We used n-alcohols, CH3(CH2)xOH where x ) 0-8,11, as model solvents to probe the effect of the solvent environment at sliding velocities of 0.1-200 µm/s and applied loads of 1-40 nN. For these systems, the chain length of the solvent and the distribution of free volume determine the extent and mechanism of solvent partitioning in the (38) Liu, Y.; Wu, T.; Evans, D. F. Langmuir 1994, 10, 2241. (39) Wasserman, S. R.; Tao, Y.-T.; Whitesides, G. M. Langmuir 1989, 5, 1074. (40) Wasserman, S. R.; Whitesides, G. M.; Tidswell, I. M.; Ocko, B. M.; Pershan, P. S.; Axe, J. D. J. Am. Chem. Soc. 1989, 111, 5852.

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Figure 1. Schematic of the AFM used for LFM. The inset shows a schematic of the contacting silicon nitride tip and functionalized surface.

monolayer. We observed maxima in the frictional force for applied normal loads of ∼20-40 nN for n-alcohols CH3(CH2)xOH where x ) 1-8. We interpret these maxima with viscoelasticity arguments and a molecular model of the energy dissipation. Experimental Section Materials. Polished boron-doped 〈100〉 test grade silicon wafers were purchased from Tygh Silicon. Toluene (99.8%, anhydrous), chloroform (99%, anhydrous), hexadecane (99%), and OTS, [CH3(CH2)17SiCl3, 95%] were obtained from Aldrich and were used without further purification. Ethanol (dehydrated, 200 proof) was obtained from Pharmco and was used as received. Water was deionized with a Millipore Academic system to a resistivity of 18.2 MΩ-cm and a pH of ∼5.7. Si/SiO2 Substrate Preparation. Wafers were cleaned by immersion in a piranha solution at 90 °C [a mixture of 7:3 (v/v) 98% H2SO4 and 30% H2O2. Caution: Piranha solution reacts violently with organic compounds and should not be stored in closed containers] for 30 min. The wafers were then removed from the piranha solution and rinsed five to six times with copious amounts of deionized water. Wafers were blown dry with nitrogen and used immediately. Freshly cleaned substrates were wet completely by deionized water. Dry wafers were transferred to a glovebox filled with a nitrogen atmosphere. Deposition of SAMs of OTS. Complete monolayers of OTS were prepared on the freshly cleaned substrates from 0.5% (v/v) solutions of OTS in anhydrous toluene. Kinetic studies of the contact angles of water and hexadecane and the film thickness as functions of immersion time indicated that complete monolayers were obtained when dry Si/SiO2 wafers were immersed in an unstirred solution for 24 h. At the end of the immersion time, the wafers were removed from the silanizing solution, and were rinsed for about 30 s in chloroform. Wafers then were transferred to a stirred fresh chloroform bath for 2 min. Functionalized wafers then were removed from the nitrogen atmosphere and rinsed with absolute ethanol and deionized water. Substrates were blown dry with nitrogen and transferred to a 120 °C oven, where they were baked for 1 h. The completed substrates were stored for up to 6 weeks in sealed Petri dishes until use. Characterization of SAMs. Measurement of Contact Angles. The sessile contact angles, θ, steady-state advancing contact angles, θa, and receding contact angles, θr, of deionized water on the SAMs formed from OTS, and the advancing contact angles of hexadecane, were measured with a Rame´-Hart model 100-00 contact angle goniometer. The methods used to measure contact angles have been described elsewhere.41 The advancing and receding contact angles of water on the SAMs of OTS of 110 ( 2° and 97 ( 2°, and the advancing contact angle of hexadecane

on the SAMs of OTS of 43 ( 2° agreed well with reported values.39,40,42-44 The advancing contact angles for all the n-alcohols used in the measurements of frictionwere also measured on SAMs of OTS. The advancing contact angles for all the n-alcohols were less than 15° except for methanol, which had an advancing contact angle of 18 ( 3°. Ellipsometry. The thicknesses of the monolayers were measured with a Rudolf Research Type 43603-200E ellipsometer equipped with a He-Ne laser with a wavelength of 6328 Å set at an incident angle of 70°. Measurements of the thickness of the silicon dioxide layer were made within ca. 1 h of cleaning, and measurements of the alkylsiloxane surface were made within 1 day of deposition. Because it is not possible to determine both the thickness and the index of refraction of thin films simultaneously,45 the monolayer was modeled as a transparent medium with a refractive index of 1.45.39,46 The thicknesses were determined from averages of 10 separate measurements on different areas of the substrate. The thickness of the SAMs of OTS was 2.7 ( 0.2 nm, which agrees well with reported values published in the literature.39,40 Scanning Force Microscopy. Measurements of the friction and normal forces, as well as inspections of the topography of the monolayers, were done with a Nanoscope III MultiMode AFM from Digital Instruments equipped with a fluid cell. One hundredmicrometer, wide-legged cantilevers (Digital Instruments) were used for all experiments. A schematic of the experimental setup for chemical force microscopy is shown in Figure 1. The AFM was housed inside a sound and vibration isolation chamber. Before taking measurements, large areas of the substrate on the order of 25-100 µm2 were scanned in contact mode to ensure that a smooth monolayer had been formed without islands or other outstanding surface features. Only monolayers of alkylsiloxanes with mean roughnesses of less than 0.2 nm for areas of 1 µm2 were used in this work. After each experiment, the fluid cell was rinsed thoroughly with ethanol and acetone, and then washed with a dilute aqueous solution of Alconox with a Q-tip. It was then rinsed in copious amounts of deionized water and blown dry with nitrogen. Force-displacement curves were obtained at each setpoint voltage for the vertical deflection of the cantilever to determine the normal load applied to the sample. The raw voltage data were converted with Hooke’s law for small cantilever deflections (41) Ulman, A. An Introduction to Ultrathin Organic Films; Academic Press: San Diego, CA, 1991. (42) Laibinis, P. E.; Whitesides, G. M.; Allara, D. L.; Tao, Y.-T.; Parikh, A. N.; Nuzzo, R. G. J. Am. Chem. Soc. 1991, 113, 7152. (43) Laibinis, P. E.; Whitesides, G. M. J. Am. Chem. Soc. 1992, 114, 1990. (44) Maoz, R.; Sagiv, J. J. Colloid Interface Sci. 1984, 100, 465. (45) McCrackin, F. L.; Passaglia, E.; Stromberg, R. R.; Steinberg, H. L. J. Res. Natl. Bur. Stand., Sect. A 1963, 67, 363. (46) Nuzzo, R. G.; Allara, D. L. J. Am. Chem. Soc. 1983, 105, 4481.


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Figure 2. Trace and retrace of a single line on a sample. The x-axis corresponds to the lateral deflection of the piezoelectric tube, and the y-axis corresponds to the torsional signal recorded by the LFM photodiode. The torsion of the cantilever is proportional to the frictional forces between the tip and the sample as the sample moves laterally in a direction perpendicular to the principal axis of the cantilever, and the torsion is recorded as the lateral movement of the reflected laser beam on the photodiode. This voltage signal from the photodiode may be converted into frictional forces with appropriate calibration of the photodiode and the cantilever. as described elsewhere.12 The normal spring constants for cantilevers were calibrated with a gravimetric resonance detection method as described elsewhere.12,47 Variations in spring constant values from the same wafer do not exceed 20% and are typically only on the order of 10-15%.47,48 A value of ∼0.52 N/m was calculated for cantilevers that were obtained from the same wafer. The unweighted resonant frequency of each cantilever was measured before use, and all cantilevers that were used had a value of approximately 60 kHz. Frictional loops were obtained for sliding velocities of 0.1200 µm/s over scan areas that were 500 nm × 500 nm to 10 µm × 10 µm in area with applied loads of up to ∼40 nN. A representative friction loop is shown in Figure 2. After each run, topographic images of areas that were both larger and smaller than the experimental area were obtained to check for wear. No wear was observed for any load reported in this article. Hooke’s law was applied to convert the raw voltage data to frictional forces

∆V Flateral ) klat∆x ) klat Slat

(1)

where klat is the lateral spring constant, and Slat is the lateral sensitivity of the photodiode. We used the method of calibration presented by Noy and co-workers to estimate the lateral spring constant, klat.48 Slat was obtained from frictional traces over very small scan sizes, as described by Liu and co-workers,38 where the torsion of the cantilever is a linear function of the lateral movement of the tip for small twisting angles. The values of the frictional force reported in this article are averages of five separate data points obtained from different regions of the sample for each specific sliding velocity and applied normal load. Each of these individual data points was obtained from a single friction loop. The average of 512 voltages measured on the retrace was subtracted from the average of 512 voltages measured from the trace, and that difference was divided by two to determine the average LFM voltage.

Results Frictional Forces. We recorded frictional loops for sliding velocities of 0.1-200 µm/s and applied normal loads (47) Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. Rev. Sci. Instrum. 1993, 64, 403. (48) Noy, A.; Frisbie, C. D.; Rozsnyai, L. F.; Wrighton, M. S.; Lieber, C. M. J. Am. Chem. Soc. 1995, 117, 7943.

Table 1. Summary of Observed Maxima in the Frictional Forces in n-Alcohols solvent ethanol n-propanol n-butanol n-pentanol n-hexanol n-heptanol n-octanol n-nonanol

applied normal load (nN)

umax (mm/s)

25 28 42 21 24 25 38 29 34 21 26 26 33 24 32

133.1 100.0 96.9 133.2 120.5 79.6 78.7 89.4 79.5 52.3 41.0 7.6 6.0 1.9 2.2

of up to ∼40 nN in each of the n-alcohols studied. As discussed in the Experimental section, we calculated average frictional forces from these frictional loops. These frictional forces are plotted as functions of sliding velocity and load for each solvent in Figures 3a-j. The maximum load of ∼40 nN corresponded to a pressure of ∼0.6 GPa, assuming Hertzian contact and a radius of curvature of the tip of ∼60 nm, and this pressure likely caused the SAMs to deform elastically.49 Frictional maxima with respect to sliding velocity appeared for applied loads greater than ∼20 nN for n-alcohols CH3(CH2)xOH where x ) 1-8, as shown in Figures 3b-3i. No maxima appeared for any load considered in methanol or n-dodecanol, as shown in Figures 3a and 3j, respectively. Table 1 is a summary of all the velocities corresponding to the observed maxima in the frictional force, or umax for each applied normal load and solvent. The maxima reported in Table 1 were determined with Table Curve 2D curve-fitting software (Jandel Scientific), generally with polynomial and rational expressions for the fit of the data in the vicinity of the maximum. (49) Carpick, R. W.; Salmeron, M. Chem. Rev. 1997, 97, 1163.

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Figure 3. Frictional forces vs sliding velocity for SAMs of OTS immersed in (a) methanol, (b) ethanol, (c) n-propanol, (d) n-butanol, (e) n-pentanol, (f) n-hexanol, (g) n-heptanol, (h) n-octanol, (i) n-nonanol, and (j) n-dodecanol as a function of applied normal load. The lines are meant to guide the eyes. Error bars that are representative of the frictional data are included in one data set in each plot. The error was typically 7. For a given applied load, there was no obvious trend relating the relative magnitudes of the frictional forces to increasing solvent chain length. We do not compare absolute values of the frictional forces, because we recorded the data for different solvent with different AFM tips. Differences in the exact areas of contact and the alignment of the laser beam on each cantilever make comparisons of absolute values of the frictional force that are determined from different tips inaccurate.

Discussion The appearance of maxima in the frictional force as a function of sliding velocity in the intermediate-load regime suggests that the frictional behavior of SAMs in liquid environments may be analogous to the viscoelastic behavior of amorphous bulk polymer systems.50 In bulk viscoelastic systems near the glass transition temperature, the time scale of the experiment determines whether the response of the material is glasslike or rubberlike.51 The transition between the glasslike and rubberlike behavior occurs when the characteristic time associated with a relaxation process in the bulk is equal to the characteristic time scale of the experiment. The energy dissipation in the material goes through a maximum at the transition. Viscoelastic theory states that the characteristic relaxation times of amorphous polymers increase and the glass transition temperature increases with increased applied normal load. Plasticizers cause the glass transition temperature and the characteristic relaxation times to decrease by penetrating into the polymer matrix and increasing the mobility of the polymer chains.52-54 We expect that the characteristic relaxation time for the alkyl chains in a SAM of OTS also will increase with increases in the applied normal load and decrease with increases in the extent of solvent partitioning in the monolayer.38,35 Nature of Solvent Partitioning in SAMs. For SAMs to be plasticized by solvents, the solvent must partition into the monolayer. Partitioning of solvent into even wellordered SAMs has been reported. With simultaneous ellipsometry and quartz crystal microbalance (QCM) experiments on SAMs in situ, Blanchard and co-workers55 showed that methanol and hexane penetrate SAMs of octadecanethiolate (ODT) on Au when exposed to the (50) Ludema, K. C.; Tabor, D. Wear 1966, 9, 329. (51) Strobl, G. The Physics of Polymers; Springer-Verlag: Berlin, 1996. (52) Dimarzio, E. A.; Gibbs, J. H. J. Polym. Sci. A 1963, 1, 1417. (53) Dimarzio, E. A.; Castellano, C.; Yang, A. J. Polym. Sci. B 1996, 34, 535. (54) Wang, B.-G.; Yamaguchi, T.; Nakao, S.-I. J. Polym. Sci. B 2000, 38, 846. (55) Karpovic, D. S.; Blanchard, G. J. Langmuir 1997, 13, 4031.


solvent vapor. SAMs of OTS lack the long-range order of SAMs of ODT, so solvent partitioning is expected to occur to an equal, if not greater extent in SAMs of OTS than in SAMs of ODT. Solvent may partition into a monolayer either by occupying free volume in a monolayer or by insertion of individual molecules into defects. Both simulations and experimental results supported partitioning of solvent into SAMs which is governed by the distribution of free volume in the monolayer. Simulations of solute penetration into monolayers indicated that the concentration of solvent is highest near the free surface of the SAM and drops off with increasing depth in the SAM.56 The dispersion forces between adjacent alkyl chains and the covalent siloxane linkages that bind individual alkyl chains in the monolayer to adjacent chains and the surface limit the free volume available to the alkyl chains near the substrate. As the free volume decreases with increasing depth, the solvent concentration also decreases. Experimental results and simulations also suggested that the concentration profiles of the solvent in monolayers that are under low to moderate shear or that are compressed elastically , as they are by the AFM tip in our experiments, should remain similar to the concentration profile in uncompressed monolayers. For close-packed monolayers of long alkyl chains, both experimental data from sum frequency generation spectroscopy57 and simulation results58 showed that compression of SAMs in dry environments induces disorder that is limited to gauche distortions at the free ends of the molecules in the monolayer. The order within the monolayer, and consequently the distribution of free volume, is maintained under pressures that cause the monolayer to deform elastically. Simulation and experimental results of monolayers of long alkyl chains under shear further confirm that the extent of disorder decreases with increasing depth. For a close-packed monolayer of C18 alkane chains terminating in methyl groups, molecular dynamics simulations59 of the effect of shear showed that the root-meansquare fluctuations of the positions of the carbon atoms decrease exponentially with increasing depth in the monolayer and approach a constant value for depths greater than 7-8 carbon atoms from the free surface. Garrell and co-workers60 demonstrated experimentally that disordering of the alkyl chains occurs primarily near the free surface for both tetradecanethiolate and hexadecanethiolate monolayers with simultaneous thickness shear measurements and surface-enhanced Raman spectroscopy. They found that disordering in the interior of the SAMs occurred with increases in temperature as gauche rotamers appeared. If solvent can only partition into the SAM by this method, the concentration of partitioned solvent should decrease proportionally with the increasing chain length, or molar volume, of the solvent. Experimental results with chemically similar long-chain solvents and SAMs possessing defect sites suggested a second mechanism of solvent partitioning. Penetration of solvent molecules into the SAM may occur by insertion of single molecules into defect sites or disordered regions in (56) Dill, K. A.; Naghizadeh, J.; Marqusee, J. A. Annu. Rev. Phys. Chem. 1988, 39, 425. (57) Du, Q.; Xiao, X.-d.; Charych, D.; Wolf, F.; Frantz, P.; Ogletree, D. F.; Shen, Y. R.; Salmeron, M. Phys. Rev. B 1995, 51, 7456. (58) Siepmann, J. I.; McDonald, I. R. Phys. Rev. Lett. 1993, 70, 453. (59) Koike, A.; Yoneya, M. Langmuir 1997, 13, 1718. (60) Teuscher, J. H.; Yeager, L. J.; Yoo, H.; Chadwick, J. E.; Garrell, R. L. Faraday Discuss. 1997, 107, 399.

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the SAM.61 Cohesive van der Waals forces between solvent molecules with long alkyl chains and the alkyl chains make the insertion energetically favorable. Solvent partitioning that occurs according to the distribution of free volume should have an effect of the frictional force similar to the effect that plasticizers have on the viscoelastic behavior of bulk amorphous polymers. Solvent partitioning by this mechanism acts to increase the mobility of the alkyl chains in the SAM, just as plasticizers increase the chain mobility and decrease the glass transition temperature in bulk systems. Solvent partitioning that occurs by insertion of long-chain solvent molecules into defect sites should not have this effect. Instead, the inserted solvent molecules should increase the order of the SAM and reduce the mobility of the alkyl chains in the SAM. Exclusion of Solvent from SAMs Under Compressive Loads. As the AFM tip slides across the surface of the SAM, compressive stresses may partially or totally exclude the solvent from the compressed region under the tip. Both the extent that partitioned solvent is excluded from the compressed SAM and the extent of solvent partitioning in the uncompressed monolayer may determine the extent of plasticization and the frictional behavior of the SAM, and both likely depend on the mechanism of solvent partitioning. The possibility of two contributing mechanisms of solvent partitioning that affect the exclusion of solvent was supported by the distribution of values of umax as a function of solvent chain length. Peaks appeared for sliding velocities greater than 75 µm/s for n-alcohols CH3(CH2)xOH, x e 5, and sliding velocities of less than 5 µm/s for x > 6. We only observed frictional maxima at intermediate velocities for n-heptanol. Solventdependent changes in the abruptness of the transitions between two load-dependent frictional regimes at sliding velocities near umax, such as those illustrated in Figure 4, also suggested two mechanisms of solvent partitioning. For n-alcohols CH3(CH2)xOH, x < 5, the increase in the frictional force with increasing load was linear, and the transition in the slopes between the two regimes was distinct. For x > 5, the frictional force did not increase linearly with increasing load, and there was no distinct transition. It is possible to estimate the driving force for the exclusion of solvent from a thermodynamic analysis of the decrease in solubility with increased positive mean normal stress, even though the compressed region under the tip likely is not at equilibrium. For a SAM compressed under an applied normal load in solvent at equilibrium, the chemical potential of the solvent in the reservoir is necessarily equal to the chemical potential of the solvent partitioned in the compressed monolayer. In this case, the concentration of diluent in the monolayer, φ, at equilibrium as a function of the uniaxial compressive stress or mean normal stress, σ, is given by the ratio

(

)

σVpenetrant φ(σ) ) exp RT φ(σ ) 0)

(2)

where σ ) P/3, P is the Hertzian pressure, and Vpenetrant is the molar volume of the solvent,62-64 assuming ideal (61) Kallury, K. M. R.; Thompson, M.; Tripp, C. P.; Hair, M. L. Langmuir 1992, 8, 947. (62) Brown, H. R.; Argon, A. S.; Cohen, R. E.; Gebizlioglu, O. S.; Kramer, E. J. Macromolecules 1989, 22, 1002. (63) Brown, H. R. J. Polym. Sci. B 1989, 27, 1273. (64) Nealey, P. F.; Cohen, R. E.; Argon, A. S. Macromolecules 1994, 27, 4193.

728


mixing. The range of applied loads used in this study result in uniaxial compressive stresses at the apex of the tip of up to ∼0.2 GPa. Compression with the spherical tip results in a parabolic pressure distribution in the SAM, so this analysis predicts that φ(σ) should increase radially within the area of contact. As the chain length and partial molar volume of the solvent increase, the ratio of solubilities decreases more rapidly with increases in the applied normal load. As the applied normal load increases from 0 to 40 nN for SAMs of OTS, eq 2 predicts that the ratio of φ/φ(0) under the apex of the tip decreases by 2 orders of magnitude for methanol and 8 orders of magnitude for n-dodecanol. Consequently, this analysis suggests that uniaxial compressive stress results in a significant thermodynamic driving force for exclusion of solvent and that plasticization of the SAM by the solvent should be negligible at equilibrium at the highest applied normal loads of ∼40 nN for all solvents. If exclusion of solvent can occur within the time scale of sliding, the effect of the exclusion of solvent on the frictional behavior of the monolayer also likely depends on the solubility of the penetrant in the uncompressed SAM. As the molar volume increases with increasing solvent chain length, we expect that φ(0) should decrease because of steric effects. Thus, if φ(0) is negligible for longchain n-alcohols, the change in the mobility of the alkyl chains with increasing load that results from the exclusion of solvent is likely to be small compared with the change in the mobility that is determined by the increase in compressive stresses and confinement. If shorter-chain n-alcohols have a higher value of φ (0), the change in the solvent distribution in the film caused by increases in the load likely affects the mobility of the alkyl chains to a greater extent. In the time scale of sliding, the actual value of φ(σ) under the apex of the tip may be greater than that predicted by eq 2 ecause of kinetic limitations on diffusion. The kinetics of the diffusion depends on the chain density of the SAM, the specific interactions between solvent molecules and the alkyl chains of the SAM, area of contact and the thickness of the gap between the substrate and the AFM tip. Viscoelasticity arguments suggest that the effect of solvent exclusion on the frictional behavior of SAMs depends on the diffusion coefficient of the solvent in the compressed SAM and two time scales: a residence time and the characteristic relaxation time of the alkyl chains in the SAM. We define a residence time, τres, as the time that an alkyl chain tail is in contact with some portion of the surface of the tip. At applied normal loads of ∼25 nN, the diameter of the Hertzian area of contact is ∼9 nm, and the sliding velocities of 0.1-200 µm/s used in this work correspond to values of τres of 9 × 10-2 s to - 5 × 10-5 s. If τres is much longer than the relaxation time calculated from a Deborah number analysis and the time required for the solvent to be displaced from the compressed region, a quasi-steady-state of both energy dissipation and plasticization is reached under the tip. If τres, the relaxation time, and the time needed for exclusion are the same order of magnitude, the alkyl chains may experience a different local environment at the front than at the back of the tip. Deborah Number Analysis of Frictional Behavior of SAMs of OTS in Solvent. Like the viscoelastic behavior of bulk polymer systems, the frictional behavior of SAMs of OTS immersed in solvents can described qualitatively in terms of the characteristic relaxation times of the alkyl chains in the monolayers with a Deborah number analysis, as reported by Israelachvili and coworkers.35 With time-temperature superposition arguments, the ‘pseudo-phase diagram’ discussed in the

Clear and Nealey

Introduction, which Israelachvili and co-workers developed to describe the energy dissipation and frictional behavior as a function of temperature, may be extended to the frictional behavior of a monolayer as a function of the sliding velocity.35 These arguments suggest that the frictional force will go through a maximum with increasing sliding velocity for a given applied normal load and temperature of the experiment, and that the behavior of the SAMs will depend on the relative magnitudes of the characteristic relaxation time of the alkyl chains and the time scale of the experiment. This model predicts that the behavior of the SAMs will be liquidlike at very low sliding velocities, solidlike at very high sliding velocities, and amorphous at intermediate sliding velocities. Low frictional forces result at very low and very high sliding velocities; high frictional forces result at intermediate sliding velocities. A Deborah number, De, analogous to those that usually are defined for bulk polymer systems, may be defined for SAMs under shear as

De )

τ τi

(3)

where τ is the characteristic relaxation time of the alkyl chains in the monolayer and τt is the transit time, or the time required to travel a characteristic length, δ. The transit time is defined as

τt )

δ µ

(4)

where u is the sliding velocity. The maximum frictional force or energy dissipation occurs for amorphous monolayers at intermediate sliding velocities when τ ≈ τt, or when De ≈ 1. This Deborah number analysis suggests that increases in characteristic relaxation time of the alkyl chains shift maxima in the frictional force to lower sliding velocities, and vice versa. Decreases in the extent of solvent partitioning in the SAM that decrease the mobility of the alkyl chains and increase τ should cause maxima to shift to lower sliding velocities, just as Liu and co-workers38 observed when they compared the behavior of dry surfactant monolayers and those same monolayers exposed to hexane vapor. The molar volume of the solvent increases with x, so both φ (0) and the equilibrium value of φ/φ (0) at a particular mean normal stress should decrease with x, reducing the extent of solvent partitioning by both the free-volume-limited and insertion mechanisms. Solvent that partitions into the monolayer by the insertion mechanism also should act to increase τ with increasing x. These predictions are consistent with the observed decrease in umax of 2 orders of magnitude with increasing solvent chain length from x ) 1 to x ) 8 illustrated in Figures 3b-3i. Increases in the applied normal load decrease the mobility of the alkyl chains and decrease the equilibrium value of φ/φ (0), so they should shift maxima to lower sliding velocities as τ increases. This prediction is consistent with the peak data summarized in Table 1. Increases in the applied normal load shifted umax lower by as much as ∼15 µm/s for all solvents in which a maximum appeared except for n-nonanol, where the two peaks appeared at essentially the same sliding velocity. Based on the Deborah number defined above, the maxima occurred when the values of τ for SAMs of OTS in these n-alcohols were comparable with the transit times achieved in this study. We assume that δ is equal to the chain length of OTS of 2.7 nm. The values of τ for the


solvated alkyl chains in the SAMs of OTS at an applied normal load of ∼25 nN increased with increasing solvent chain length from a minimum observed value of 2 × 10-5 s in ethanol to maximum observed value of 2 × 10-3 s in n-nonanol. For comparison, the relaxation times calculated for the SAMs compare favorably with a value of 10-7 s calculated for amorphous bulk polyethylene from molecular dynamics simulation65 and with values of ∼10-6 s calculated for the β glass-rubber transitions of chlorinedecorated and lightly oxidized linear polyethylenes from dielectric measurements.66 No maxima were observed for methanol or n-dodecanol, so values of τ could not be calculated for these solvents. From the observed trend in umax, the value of τ in methanol is shorter than the transit times achieved in this study, and the value of τ in n-dodecanol is longer than the studied transit times. So, if a maximum appears for SAMs of OTS immersed in methanol, it should appear at sliding velocities greater than 200 µm/s, and a maximum in n-dodecanol should appear at sliding velocities less than 0.1 µm/s. The values of τres at umax and applied normal loads of ∼25 nN range from 7 × 10-5 s for ethanol to 1 × 10-3 s for n-nonanol. The similarity between the values of τres and τ suggests that if the diffusion coefficient of solvent in the compressed SAM is sufficiently large, exclusion of the solvent can occur in the residence time and the shift in umax may be attributable to local changes in the solvent environment as the tip passes over the chains. The shear stress induced by the tip also likely causes the chains ahead of the tip to tilt forward, so the exclusion of solvent may occur over a greater distance than what is traversed in the residence time and consequently a longer time frame. For the solvent to be displaced a distance of ∼1 nM during the residence time, τres, corresponding to the values of umax at ∼25 nN, the diffusion coefficient must be 1 × 10-10 cm2/s for ethanol to 2 × 10-12 cm2/s for n-nonanol. If shear stresses cause the chains to tilt forward ahead of the tip over a significant distance, particularly at high sliding velocities, these diffusion coefficients may be even smaller. The calculated diffusion coefficient for n-nonanol compares favorably with the value of 1 × 10-12 cm2/s that Vanderlick and co-workers reported for diffusion of pentane normal to the substrate in LB films of arachidic acid with molecular areas of 0.19 nm2/molecule based on uptake measurements with a QCM.67 For a well-ordered film, however, it is likely that the coefficient for lateral diffusion of the solvent is significantly smaller than the coefficient for diffusion normal to the alkyl chains. Thus, three possibilities exist: (1) solvent is not excluded significantly from the compressed region under the tip, (2) solvent is displaced only over an area smaller than the actual area of contact, and (3) disorder in the SAM that results in a network of defect sites cause the coefficient for lateral diffusion to be significantly larger than we would expect for a quasi-crystalline monolayer. Although we cannot rule out the first possibility completely, our estimates of the diffusion coefficients are consistent with the second and third possibilities. The second possibility is supported by the expected parabolic pressure distribution under the tip. The third possibility of “channeling” of solvent parallel to the substrate is supported because the surface density of SAMs of OTS typically is g0.21 nm2,40 and that SAMs of OTS do not possess long-range order.39,40,49 (65) Boyd, R. H.; Gee, R. H.; Han, J.; Jin, Y. J. Chem. Phys. 1994, 101, 788. (66) Graff, M. S.; Boyd, R. H. Polymer 1994, 35, 1797. (67) Hanley, C. M.; Quinn, J. A.; Vanderlick, T. K. AIChE J. 1996, 42, 1234.

Langmuir, Vol. 17, No. 3, 2001 729

The Deborah number analysis also may be applied to predict the frictional behavior of SAMs of OTS outside of the intermediate-load regime. No maxima appeared in the low-load regime; instead, the frictional force increased according to a power law with increasing sliding velocity. The frictional force increased more rapidly with increases in the applied load until an applied load was reached where an inflection point or a maximum appeared. The Deborah number analysis suggests that in the low-load regime, τ for the SAMs of OTS was shorter than the transit times achieved in this study. If maxima appear at these low loads, they appear at sliding velocities greater than 200 µm/s. In the high-load regime, the maxima disappear altogether from the range of studied velocities, as they did for ethanol at a load of 32 nN, n-butanol at a load of 32 nN, and n-heptanol at a load of 38 nN. This disappearance is not consistent with the Deborah number analysis that predicts that the maxima should shift to lower sliding velocities with increases in the load and that the frictional force should decrease with an increase in the sliding velocity. This inconsistency suggests that the frictional force is a superposition of contributions from the relaxation process and from a viscous drag arising from plowing, and that the plowing contribution becomes dominant as the load and the indentation depth increase. Mechanism of Energy Dissipation at the AFM Tip Surface. Greater insight into the observed frictional behavior may be gained with a molecular model of energy dissipation at the surface of the AFM tip. Subbotin and co-workers68 presented a mechanism for the energy dissipation caused by a hard surface shearing across an organic thin film, similar to the experimental setup in our LFM measurements. In this model, energy is dissipated as the ends of the alkyl chains adsorb to and desorb from the hard surface that contacts and travels across the upper surface of the SAM. Like the Deborah number analysis, this model predicts three distinct regimes of behavior that are functions of the sliding velocity. At extremely low sliding velocities, the thermally activated adsorption and desorption of the chains are the dominant mechanisms of energy dissipation, and many adsorption and desorption events can occur in the time scale of sliding. The energy dissipation and the frictional force in this regime are determined only by the net energy costs of forming and breaking multiple contacts between the chain ends and the surface of the rider as they move past one another. The second regime of energy dissipation and friction occurs when the sliding velocity increases above a critical value where adsorption and desorption are no longer the dominant mechanisms of energy dissipation. In this regime, the alkyl chains stretch until breakage of the contact between the tip and the chain tails of the alkyl chains occurs. In this regime, the time required for the tip to traverse a characteristic length is less than the time required for desorption to occur thermally. Thus, the energy dissipation and frictional force are determined by both the elongation of the alkyl chains and the net energy loss as the chain ends break away from the surface of the rider. A third regime occurs at high velocities above a critical value where the time scale of sliding is shorter than the time required for adsorption of the chain tails to the tips surface. In this regime, the fraction of chain tails that adsorb to the surface of the AFM tip decreases, as do the energy dissipation and the frictional force. This physical model of the energy dissipation is not described accurately in terms of a single relaxation time. (68) Subbotin, A.; ten Brinke, G.; Kulichikhin, V. G.; Hadziioannou, G. J. Chem. Phys. 1998, 109, 827.

730


Clear and Nealey

For adsorption to and desorption from a completely neutral surface, the characteristic relaxation time of a free segment is given by68

( )

τ ) τ* exp

Va kBT

(5)

where Va is the activation energy and τ* is the characteristic oscillation time of a segment in a local potential well. In the SAM-AFM tip system, an additional potential barrier, ∆Va, must be added to the model of tails of the alkyl chains adsorbing and desorbing from the surface of the rider. This potential barrier is associated with the change in the free energy of the grafted chain caused by adsorption or desorption, and depends on the correlation between the thickness of the adsorbed layer and the magnitude of the fluctuations of the chain tail. For a contact between a SAM and an AFM tip in solvent, ∆Va and the free energy of the chain are functions of both the extent of solvent partitioning and the order of the monolayer. When the tail of the chain adsorbs, it wins the energy ∆Va, so the characteristic time of adsorption is given as

(

τ+ ) τ* exp

)

Va - ∆Va kBT

(6)

Before the tail of the chain can desorb from the surface of the AFM tip, both the potential barrier and the barrier associated with the increase in free energy of the chain must be overcome. Thus, the characteristic time of desorption is given as

(

τ- ) τ* exp

)

Va - ∆Va kBT

(7)

For complex fluid and polymer systems,69 the net sum of the activation energy, Va, and the potential barrier, ∆Va, likely is a complex function of the temperature, sliding velocity and applied normal load, as well as the affinity of the tail to the surface of the rider and the solvent environment. The changes predicted for the values τ- , τ+, and Va, with changes in the applied normal load, extent of plasticization, or other variables are all the same as those predicted for τ in the Deborah number analysis. The rates of change of τ- and τ+ are functions of the dependence of ∆Va on the changing variable and the relative magnitudes of ∆Va and Va. The high frictional forces associated with frictional maxima are predicted to occur for the range of sliding velocities where a maximum number of the adsorbed chains are elongated before breakage of the contact between the chain tail and the AFM tip. This high frictional force regime is bounded by u1 ) ∆xmax /τ- and u2 ) ∆xmax/ τ+ where ∆xmax is the characteristic length (∆xmax) (L2 - H2)1/2, L is the contour length of the chain, and H is the thickness of the monolayer). The greater the difference, u2 - u1, the broader the maximum in the frictional force expected to be with respect to sliding velocity. If ∆Va , Va, then τ- ≈ τ+. In that special case, this physical model of energy dissipation also may be described by a single relaxation time as defined in eq 5, and the Deborah number analysis can be defined in terms of this τ and the transit time for the characteristic length, ∆xmax because τDeborah analysis ≈ τ- ≈ τ+. (69) Ferry, J. D. Viscoelastic Properties of Polymers, 3 ed.; John Wiley: New York, 1980.

Effect of Applied Normal Load on Frictional Behavior in Terms of the Molecular Model. The molecular model of energy dissipation provides insight into the three load-dependent frictional regimes discussed in the Results section. In the low-load regime, the molecular model suggests that we observed no maxima in the frictional force because both τ+ and τ- were less than ∆xmax/u for all sliding velocities, u, that were achieved in these experiments. At these loads, the energy dissipation and the frictional force likely resulted from thermal processes at all sliding velocities studied. The driving force for exclusion of solvent likely was small relative to its importance at higher applied normal loads. In the intermediate-load regime at loads of ∼15-25 nN, we observed inflection points followed by plateaus in the frictional force as a function of sliding velocity in n-alcohols CH3(CH2)xOH, x ) 0-8, and we did not observe a significant decrease in the frictional force with increasing sliding velocity. The molecular model suggests that plateaus in the frictional force occur if the potential barrier associated with the change in free energy of the chain during adsorption and desorption, ∆Va, is significant, so that τ- > τ+. At these loads, the value of τ- was within the range of the time scales of sliding achieved in these experiments, but τ+ was less than ∆xmax/u for all sliding velocities, u, that were achieved. The difference in the free energies of the alkyl chains in of the adsorbed and desorbed states may be attributable to nonzero concentrations of solvent in the compressed region under the tip. At velocities where a plateau in the frictional force occurred, the molecular model predicts that the energy dissipation and the frictional force were caused both the elongation of the alkyl chains and the breakage of the tail-tip contact. For loads in the intermediate regime above ∼20 nN for n-alcohols CH3(CH2)xOH, x ) 1-8, we observed frictional maxima as a function of sliding velocity instead of inflection points followed by broad plateaus. The molecular model predicts that the narrower the peak in the frictional force is, the more similar τ- is to τ+. Similar values for τand τ+ indicate that the change in free energy of the chain due to adsorption or desorption, ∆Va, is small or negligible, implying that the net free-energy cost of solvation on desorption also is low or negligible. The change in free energy with adsorption or desorption can be minimal if enough of the solvent is excluded so that the compressed region is largely homogeneous. Our estimates of the diffusion coefficients of solvent at ∼25 nN suggest that loads in the intermediate regime may be sufficient to exclude enough solvent from a compressed region near the apex of the tip to make that region essentially homogeneous. Thus, the transition from plateaus to maxima with increasing load that we observed is consistent with eq 2 that suggests that concentration of solvent should decrease with increasing load. For velocities in the vicinity of umax, the molecular model predicts that the energy dissipation and the frictional force are attributable both to the elongation of the alkyl chains and the breakage of the tail-tip contact. The decrease in umax for n-alcohols CH3(CH2)xOH where x ) 2-8 that resulted from slight increases in the applied normal load is consistent with the prediction of the molecular model that τ-, and τ+ should increase with applied normal load. Further evidence that the intermediate-load regime defines a transition in the compressed region between a state where alkyl chains experience a heterogeneous, plasticized environment within the SAM and a more compressed state where alkyl chains experience a homogeneous, unplasticized environment within the SAM


comes from an inspection of the two frictional regimes evident in plots such as Figure 4. The data in Figure 4 are for SAMs of OTS in n-pentanol at a sliding velocity of 76.3 µm/s, a velocity close to the values of umax reported for that system in Table 1, and that plot illustrates frictional behaviors that are characteristic for sliding velocities for SAMs of OTS near umax. In Figure 4, the friction coefficient is 0.75 for applied normal loads below ∼15 nN, but above that transitional load the friction coefficient increases by a factor of 2. This increase in the friction coefficient is consistent with a surface that is not plasticized by partitioned solvent. Influence of the Plowing Contribution to Frictional Behavior. The predictions of both the Deborah number analysis and the molecular model fail to explain both the inflection point and plateau that we observed at an applied normal load of 32 nN for SAMs of OTS in n-heptanol and the disappearance of the inflection points and maxima in the frictional force in the high-load regime that we observed for methanol, ethanol, n-butanol, and n-heptanol in Figures 3a, 3b, 3d, and 3g. The plateau in the frictional force cannot be attributed to a nonzero value of ∆Va, and is likely the sum of two counteracting effects: a reduction in the fraction of chain tails that adsorb to the AFM tip and an increased contribution from plowing at higher loads. The molecular model predicts that at sliding velocities higher than u2 ) ∆xmax/τ+, the frictional force decreases because the fraction of chain tails that adsorb to the rider decreases. The Deborah number analysis predicts that the frictional force should decrease with increasing sliding velocity when τ > τt. Both explanations do not account for a rider that is not a flat plane, so they neglect possible plowing effects. In AFM, the depth of indentation of the tip increases with increasing applied load. The plowing of the tip acts like a viscous drag, so the frictional force associated with it increases with increasing sliding velocity. The disappearance of the inflection points and plateaus or frictional maxima in the high-load regime is likely attributable to the superposition of the plowing contribution to the frictional force and the contribution resulting from the relaxation process. At high loads, the plowing contribution dominates the frictional behavior. This concept of the superposition of the contributions to the total frictional force suggests that the contribution associated with the relaxation process in the intermediateload regime at loads of ∼15-25 nN exhibited a broad peak in n-alcohols CH3(CH2)xOH, x ) 0-8, consistent with the predictions of the molecular model for a nonzero value of ∆Va. In this regime, we observed inflection points followed by plateaus in the frictional force at higher sliding velocities. The onset of the plateau occurred at sliding velocities that were as much as an order of magnitude lower than the observed values of umax, as illustrated by the friction data recorded at 16 nN in ethanol in Figure 3b. This behavior is not consistent with the superposition of a narrow peak associated with the relaxation contribution and the power law increase associated with the plowing contribution. In that scenario, the Deborah number analysis predicts that the onset of the plateau should occur at velocities similar to or greater than the values of umax observed in the intermediate-load regime, not sliding velocities that are lower than umax. The plowing contribution to the frictional force appeared to be responsible for most of the frictional behavior observed for methanol and n-dodecanol because they did not exhibit all of the characteristics associated with the three characteristic load-dependent frictional regimes that appeared for n-alcohols CH3(CH2)xOH, x ) 1-8. We did not observe maxima for methanol in the intermediate-

Langmuir, Vol. 17, No. 3, 2001 731

load regime, but we did observe inflection points at applied normal loads of 13-29 nN. In terms of the molecular model, the appearance of inflection points suggests either that both τ- and τ+ were shorter than the transit times achieved in these experiments, or that τ- > τ+ and τ- fell within the range of transit times achieved but τ+ did not. The first case suggests that maxima in the frictional force occurred at sliding velocities greater than 200 µm/s, if they appeared. The second case suggests that maxima did not appear with increases in the applied normal load before the plowing contribution to the frictional force became dominant. At all loads studied, we only observed a powerlaw frictional behavior for SAMs of OTS in n-dodecanol that was consistent with the plowing contribution and did not observe a maximum. This behavior suggests that τ- and τ+ were longer than any of the transit times achieved in this study and that the activation energy for the relaxation of the chain, Va, was large, due to either insertion of n-dodecanol into defect sites or severe limitation of the extent of solvent partitioning due to steric hindrance. Conclusions We used LFM in a fluid cell containing n-alcohols CH3(CH2)xOH, where x ) 0-8, 11, to probe the effect of solvent environment, applied normal load, and sliding velocity on the frictional behavior of SAMs formed from OTS. We observed three characteristic load-dependent frictional regimes for this system. In the intermediateload regime, we observed maxima in the frictional force with respect to sliding velocity in n-alcohols CH3(CH2)xOH where x ) 1-8. Increases in load shifted these peaks to lower sliding velocities, and increases in the chain length of the solvent generally shifted these frictional maxima to lower sliding velocities. With viscoelasticity arguments and a Deborah number analysis analogous to those used for bulk polymer systems, we interpreted the maxima in the frictional force as localized relaxation processes in the SAMs that depend on the solvent environment and the applied normal load. Thermodynamic and diffusion arguments suggested that the solvent that partitions into the uncompressed monolayer may be excluded by the compressive loads applied to the monolayer by the tip as the sample moves beneath the tip. This relaxation process is likely to occur in a localized region of the area of contact that is determined by both the magnitude of the diffusion coefficient of a solvent in the SAM and the parabolic pressure distribution that causes the ratio of φ/φ (0) to increase with increasing radial distance from the apex of the AFM tip. Solvent that partitions into the SAM is analogous to plasticizers that penetrate into an amorphous polymer and reduce the relaxation time of the polymer. As the extent of solvent partitioning decreases or the applied normal load increases, the characteristic relaxation time should increase as the solubility of the solvent in the monolayer decreases and the “plasticization” of the monolayer becomes less efficient. The shifts in the frictional maxima to lower sliding velocities with increases in load or solvent chain length were consistent with the expected increase in the characteristic relaxation time. A molecular model for the energy dissipation provided additional insight into the relaxation process of the alkyl chains in the SAM. The molecular model assumed that the tails of the chains adsorb to and desorb from the surface of the AFM tip, and that the characteristic relaxation time may be described with an Arrhenius relationship that accounts for both the activation energy associated with

732


the relaxation of the alkyl chains and the change in free energy associated with adsorption or desorption. The change in free energy is a function of the solvent environment that alkyl chains experience when adsorbed or desorbed. The appearance of inflection points and plateaus in the frictional force followed by the appearance of maxima with increasing normal load was consistent with the predictions of the model for a SAM that becomes more homogeneous as solvent is excluded. Both the Deborah number analysis and the molecular model failed to explain the frictional behavior in the highload regime. The nonplanar geometry of the tip made the plowing contribution to the frictional force important. The observed frictional behavior was a superposition of this plowing effect and contributions resulting from the relaxation process. This plowing effect increased in importance with increasing sliding velocity and applied normal load, and in the high-load regime, it dominated the frictional behavior. If SAMs of alkylsiloxanes such as those formed from OTS are used as boundary lubricants in solvent environ-

Clear and Nealey

ments for applications such as FSA or MEMS, it is necessary to determine how solvent partitioning affects the tribological properties of the SAM. The effectiveness and the lifespan of a device or process may be improved significantly if the range of sliding velocities achieved during operation does not include velocities near umax. Acknowledgment. This research was funded by the National Science Foundation (CTS-9703207), the National Science Foundation GOALI Program (CTS-9520403), the Office of Naval Research DOD AASERT program, the Shell Faculty Career Initiation Fund, and the 3M NonTenured Faculty Award. The authors would like to acknowledge the use of facilities at the University of Wisconsin - Materials Research Science and Engineering Center for Nanostructured Materials and Interfaces (NSF). The authors also would like to acknowledge helpful discussions with S. Kim (Parke-Davis) and J. Smith (University of California - Berkeley). LA000650G

Lateral Force Microscopy Study of the Frictional Behavior of Self

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