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Influence of the Solvent Environment on the Contact Mechanics of Tip-Sample Interactions in Friction Force Microscopy of Poly(ethylene terephthalate) Films Claire R. Hurley and Graham J. Leggett* Department of Chemistry, UniVersity of Sheffield, Brook Hill, Sheffield S3 7HF, U.K. ReceiVed NoVember 23, 2005. In Final Form: February 28, 2006 Friction force microscopy measurements have been carried out on free-standing films of poly(ethylene terephthalate) in a variety of different media. In ethanol, the adhesion force was small, and the friction-load relationship was linear. In perfluorodecalin, nonlinearity was observed in the friction-load relationship, and the data have been found to fit the Johnson-Kendall-Roberts model of contact mechanics. The behavior in hexadecane was also characterized by a single-asperity contact model, but in this case, the data were found to fit the Derjaguin-Mu¨ller-Toporov model. It is suggested that these differences are due to the different strengths of tip-sample adhesion, which arise from the differences in the dielectric constants of the media: in ethanol, which has a high dielectric constant, the friction force varies linearly with the load, whereas in media of low dielectric constant, adhesion-limited behavior is observed.
Introduction Friction force microscopy (FFM)1-4 is a powerful tool for the surface analysis of organic materials. It offers nanometer-scale spatial resolution combined with sensitivity to variations in surface chemical composition,5-15 molecular organization,16-20 mechanical properties,21-23 and acid-base characteristics.24,25 A variety of approaches have been utilized in the quantification of FFM data. Amontons’ law
FF ) µFN
(1)
where FF is the friction force, µ is the coefficient of friction, and FN is the load, is among the most widely used, and its application * Corresponding author. E-mail:
[email protected]. (1) Overney, R.; Meyer, E. MRS Bull. 1993, May, 26. (2) Gnecco, E.; Bennewitz, R.; Gyalog, T.; Meyer, E. J. Phys. Condens. Matter 2001, 13, R619. (3) Carpick, R. W.; Salmeron, M. Chem. ReV. 1997, 97, 1163. (4) Leggett, G. J.; Brewer, N. J.; Chong, K. S. L. Phys. Chem. Chem. Phys. 2005, 7, 1107. (5) Frisbie, C. D.; Rozsnyai, L. F.; Noy, A.; Wrighton, M. S.; Lieber, C. M. Science 1994, 265, 2071. (6) Akari, S.; Horn, D.; Keller, H.; Schrepp, W. AdV. Mater. 1995, 7, 549. (7) Green, J.-B. D.; McDermott, M. T.; Porter, M. D.; Siperko, L. M. J. Phys. Chem. 1995, 99, 10960. (8) Noy, A.; Frisbie, C. D.; Rozsnyai, L. F.; Wrighton, M. S.; Lieber, C. M. J. Am. Chem. Soc. 1995, 117, 7943. (9) Beake, B. D.; Leggett, G. J. Phys. Chem. Chem. Phys. 1999, 1, 3345. (10) Clear, S. C.; Nealey, P. F. J. Colloid Interface Sci. 1999, 213, 238. (11) Zhang, L.; Li, L.; Chen, S.; Jiang, S. Langmuir 2002, 18, 5448. (12) Li, L.; Chen, S.; Jiang, S. Langmuir 2004, 19, 666. (13) Brewer, N. J.; Leggett, G. J. Langmuir 2004, 20, 4109. (14) Kim, H. I.; Houston, J. E. J. Am. Chem. Soc. 2000, 122, 12045. (15) Chong, K. S. L.; Sun, S.; Leggett, G. J. Langmuir 2005, 21, 2903. (16) Beake, B. D.; Leggett, G. J. Langmuir 2000, 16, 735. (17) Clear, S. C.; Nealey, P. F. J. Chem. Phys. 2001, 114, 2802. (18) Brewer, N. J.; Foster, T. T.; Leggett, G. J.; Alexander, M. R.; McAlpine, E. J. Phys. Chem. B 2004, 108, 4723. (19) Yang, X.; Perry, S. S. Langmuir 2003, 19, 6135. (20) Li, S.; Cao, P.; Colorado, R.; Yan, X.; Wenzl, I.; Schmakova, O. E.; Graupe, M.; Lee, T. R.; Perry, S. S. Langmuir 2005, 21, 933. (21) Hammerschmidt, J. A.; Moasser, B.; Gladfelter, W.; Haugstad, G.; Jones, R. R. Macromolecules 1996, 29, 8996. (22) Hammerschmidt, J. A.; Gladfelter, W. A.; Haugstad, G. Macromolecules 1999, 32, 3360. (23) Dinelli, F.; Buenviaje, C.; Overney, R. M. J. Chem. Phys. 2000, 113, 2043. (24) Marti, A.; Hahner, G.; Spencer, N. D. Langmuir 1995, 11, 4632. (25) Vezenov, D.; Noy, A.; Rozsnyai, L. F.; Lieber, C. M. J. Am. Chem. Soc. 1997, 119, 2006.
to FFM appears to be supported by a substantial body of work. However, Amontons’ law is generally regarded as being based upon a macroscopic understanding of friction in which energy is dissipated in contacts between multiple asperities on the sliding surfaces. Intuitively this seems to be an unlikely model to represent the interaction between the tip and sample in an FFM experiment. A priori, one might expect that a single-asperity contact mechanics model would be appropriate. If the surface forces are short-range compared to the elastic deformations they cause (compliant materials with strong adhesion and large tip radii), then the Johnson-Kendall-Roberts (JKR) model26 may be employed. In the JKR model, the friction force is expected to be proportional to the contact area, A, given by the expression
A)π
(KR)
(FN + 3πγR + x6πγRFN + (3πγR)2)2/3
2/3
(2)
where R is the radius of the probe, γ is the interfacial tension, and K is the elastic modulus. A number of authors have utilized this model to interpret FFM data from inorganic systems, but it has not been widely applied to organic materials. Alternatively, stiff materials with weak adhesion forces and small tip radii provide the alternative limit described by the Derjaguin-Mu¨llerToporov (DMT) model:27
A)π
(KR)
2/3
(FN + 4πγR)2/3
(3)
In both models, the friction force is proportional to the area of contact between the tip and the surface, but at loads approaching zero, the contact areas are considerably larger than those predicted by the Hertz model and tend toward a finite value. Paradoxically, the JKR model has been widely used to interpret pull-off force data for organic monolayers, although in many of these instances Amontons’ law has been used in the same studies to interpret friction data. This paradox urgently needs to be resolved because it is central to the interpretation of FFM data. (26) Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. London, Ser. A 1971, 324, 301. (27) Derjaguin, B. V.; Muller, V. M.; Toporov, Y. P. J. Colloid Interface Sci. 1975, 53, 314.
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A very significant contribution to this debate was made recently by Gao et al.,28 who conducted a systematic investigation of frictional forces on length scales ranging from the nanoscopic to the macroscopic. They examined the relationship between the friction force and the contact area. Although it is often assumed that the friction force is proportional to the area of contact, they argued that the area of contact is not a fundamental physical quantity; although it often provides a useful guide to the density of intermolecular interactions at an interface, it is actually the sum of all of the molecular interactions at the interface that determines the strength of the frictional interaction. They provided evidence that the JKR model may apply to situations where sliding is adhesion-controlled whereas Amontons’ law applies to situations in which nonadhesive sliding occurs. They also reported a transition from JKR-type behavior to a linear frictionload relationship following damage in a system that initially exhibits adhesive sliding. In the present study, we have explored the behavior of a polymer system, poly(ethylene terephthalate) (PET), as a function of the strength of the adhesive interaction between the tip and the sample. We have adopted an approach inspired by Spencer and coworkers,29 who have demonstrated that controlling the dielectric constant of the fluid medium influences the strength of the van der Waals interactions between a tip and a sample and hence the strength of the adhesion force. We set out to test whether the use of a fluid medium with a very low dielectric constant, perfluorodecalin, could enhance the adhesive interaction between tip and sample and examined the influence on the contact mechanics. We have found that the properties of the liquid medium exert a profound influence on the contact mechanics, with a linear friction-load relationship being observed in ethanol but adhesiondominated behavior being observed in media with low dielectric constants. These results are consistent with the arguments of Gao et al.28 Experimental Section FFM measurements were made on a commercially available Melinex OD film obtained from DuPont Teijin Films. Melinex OD is a 100-µm-thick, biaxially drawn poly(ethylene terephthalate) freestanding film material containing no additives. To remove dust, samples were blown with nitrogen. Measurements were taken either under ambient conditions or with the sample immersed in ethanol (Fischer HPLC grade), hexadecane or perfluorodecalin (Sigma Aldrich). Friction measurements were performed on a Digital Instruments Nanoscope IIIa Multimode atomic force microscope (Digital Instruments, Cambridge, U.K.) operating in contact mode. The probes were silicon nitride nanoprobes (Digital Instruments, Cambridge, UK) with a nominal force constant of 0.06 N m-1. The calibration of normal forces involved two steps. First, the photodetector sensitivity was calibrated by measuring a force curve for a very stiff sample. Mica was used because relative to the very flexible lever the stiffness of the mica is sufficiently large that it may be assumed that all deflection during the force measurement will be in the lever. Under these circumstances, the photodetector sensitivity is the gradient of a plot of photodetector signal versus displacement while measuring repulsive forces. Second, the spring constants of the levers were determined from their thermal spectra using a routine implemented within the microscope software (on our instrument, it is contained within the Digital Instruments PicoForce software) and based on the method of Hutter and Bechhoefer.30 This approximates the cantilever as a harmonic oscillator, the motion of which is driven (28) Gao, J.; Luedtke, W. D.; Gourdon, D.; Ruths, M.; Israelachvili, J. N.; Landman, U. J. Phys. Chem. B 2004, 108, 3410. (29) Feldman, K.; Tervoort, T.; Smith, P.; Spencer, N. D. Langmuir 1998, 14, 372. (30) Hutter, J. L.; Bechhoeffer, J. ReV. Sci. Instrum. 1993, 64, 1868, 3342.
Hurley and Leggett
Figure 1. Photodetector response as a function of the applied load for PET under ethanol. by thermal noise. Applying the equipartition theorem, Hutter and Bechoefer derived a relationship between the spring constant and the power spectrum of the cantilever response. Experimentally, the laser spot was focused on the apex of the cantilever, and the thermal fluctuations of the cantilever were measured and used to derive the power spectrum. Friction data were acquired with the fast scan direction perpendicular to the axis of symmetry of the cantilever. Measurements under fluid were taken using a liquid cell fitted with a silicone O-ring. Quoted loads are the products of the spring constants, detector sensitivities, and deflection set points. Friction force measurements were made from friction loops acquired by obtaining forwardreverse scan cycles along a single line with the microscope operating in scope mode. The friction signal was obtained by subtracting the mean signals in both directions, giving a resultant signal that was twice the frictional force. The load was first minimized to 0, and then the set point was increased stepwise to 40 nN to take measurements before being decreased in increments of 0.2 V until the tip pulled free of the surface. Above these forces, significant wear was observed, in line with previous reports.31 Data were acquired at five locations on the sample surface. Typical scan parameters were a scan area of 5 × 5 µm2 and 512 scan lines. Force curves were also obtained at 100 locations on the sample surface in each liquid. Pull-off forces were extracted from these using Carpick’s Toolbox.32
Results Figure 1 shows typical FFM data acquired for a sample of polyester film under ethanol. The lateral photodetector response, which measures the lateral deflection of the cantilever and is proportional to the frictional force, has been shown as a function of the applied load. The relationship is linear. The straight-line fit yields a regression coefficient of 0.997. Although the nonzero friction force at zero load is not consistent with Amontons’ law, it is consistent with a modified form of the law proposed by Derjaguin to take account of adhesion between the tip and sample.33 In this treatment, a constant internal load, Lo, is introduced in addition to the external load, FN, in eq 1 in order to account for intermolecular adhesive forces:
FF ) µ(L0 + FN) ) F0 + µFN
(4)
An alternative approach based upon the application of JKR contact mechanics has been described by Carpick and Salmeron.34 According to this approach, the friction force is proportional to the contact area (31) Beake, B. D.; Leggett, G. J.; Shipway, P. H. Wear 2004, 256, 118. (32) http://mandm.engr.wisc.edu/faculty_pages/carpick/toolbox.htm. (33) Derjaguin, B. V. Z. Phys. 1934, 88, 661. (34) Carpick, R. W.; Salmeron, M. Chem. ReV. 1997, 97, 1163.
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FF ) τA
(5)
where τ is the surface shear stress. The value of A is given by eq 2 above. If τ contains a pressure-dependent component
τ ) τ0 + RP
(6)
where τ0 is the surface shear stress at zero load, then we may write
FF ) τ0A + RFN
(7)
This equation describes a linear friction-load relationship. Upon the basis of the consideration of Figure 1 alone, it is difficult to evaluate which of these two approaches is the most appropriate. Pull-off forces were measured for PET samples under ethanol and perfluorodecalin (see Figure 2). In perfluorodecalin, a mean pull-off force of 3.08 ( 1.55 nN was measured, whereas in ethanol, a significantly smaller value, 0.18 ( 0.12 nN, was measured. The interfacial free energy of the tip-sample contact in the presence of a liquid medium depends on the properties of the liquid medium. For polymeric specimens, Feldman et al. have previously demonstrated that the magnitude of the pull-off force is determined by the properties of the liquid medium, which in turn influence the strength of the van der Waals interactions.35 For a sphere-plane interaction, the energy of interaction W is given by36
W)-
AR 6D
(8)
where R is the radius of the sphere, D is the separation, and A is the Hamaker constant. The liquid environment determines the strength of adhesion by influencing the strength of the van der Waals forces between the probe and sample surface. The Hamaker constant includes contributions from dispersion forces and from dipolar interactions. In media with low dielectric constants, the contributions to the Hamaker constant from dispersion interactions are increased relative to their magnitude in polar media. Perfluorodecalin, with its low dielectric constant (1.86) and refractive index,37 is thus expected to enhance the strength of the tip-sample dispersion forces compared to measurements made in ethanol, the dielectric constant of which (24.8) is much larger.38 Figure 3 shows the variation in the friction force as a function of load in perfluorodecalin. Data are shown for four different experiments. A larger number were carried out, but all were in general agreement. It is clear that the relationship between the friction force and the load is not linear. The nonlinearity is particularly clear under tensile loading but is evident at all loads. This is characteristic of the behavior predicted by a single-asperity contact mechanics model. Because adhesion plays a significant role in this system, there are two limiting cases, both derived from the Hertz model:39 the JKR and the DMT models. The fit of the experimental behavior to these models may be analyzed using the general transition equation (GTE) proposed by Carpick et al.,40 which can describe intermediate cases using an analytical solution based on the work of Maugis.41 (35) Feldman, K.; Tervoort, T.; Smith, P.; Spencer, N. D. Langmuir 1998, 14, 372. (36) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1992, Chapter 10. (37) Mesquida, P. Doctoral Dissertation, ETH Zurich, 1971. (38) CRC Handbook of Chemistry and Physics, 76th ed.; CRC Press: Boca Raton, FL, 1995. (39) Hertz, H. R. J. Reine. Angew. Math. 1881, 92, 156. (40) Carpick, R. W.; Ogletree, D. F.; Salmeron, M. J. Colloid Interface Sci. 1999, 211, 395. (41) Maugis, D. J. Colloid Interface Sci. 1992, 150, 243.
Figure 2. Representative force curves for PET measured under perfluorodecalin (left) and ethanol (right).
Figure 3. Variation in the photodetector response as a function of load for PET under perfluorodecalin.
Maugis approximated an actual interaction potential using a square-well potential to describe the attractive forces between contacting spheres. A constant adhesive stress σo was assumed to act between the surfaces. Maugis defined a parameter λ,
( )
λ ) 2σ0
R πγK2
1/3
(9)
where R is the equilibrium separation and K is the combined elastic modulus of the tip and sample. The value of λ describes the limits as (DMT)0.1 e λ e 5(JKR). The GTE provides a very close approximation to the Maugis-Dugdale model without the need for complicated statistical fitting. This form allows the “transition parameter” to be determined from the parameters of a fit allowing the range of surface forces to be described:
a a0(R)
)
(
)
R + x1 - L/Lc(R) 1+R
2/3
(10)
Here the transition parameter R is now used to determine the model employed: R ) 1 and 0 correspond to JKR and DMT models, respectively. Friction data obtained under perfluorodecalin were fitted using this equation, substituting the contact area for the friction force (because under the JKR and DMT models the friction force is proportional to the contact area) and keeping parameters F, Fo(R), and R free while constraining Lc. The data were fitted for loads of up to 25 nN. A transition parameter of 0.98 ( 0.05 was obtained using this treatment, which is indicative of JKR contact mechanics. The resulting fits are shown in Figure 3. It is clear that the data were modeled well by the JKR model (R2 ) 0.9938). The agreement between the fits to the four data sets is exceptionally good. The value of Lc determined from the GTE analysis was found to be 7.51 ( 1.65 nN, which is larger than
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Figure 4. Variation in the photodetector response as a function of load for PET under hexadecane.
Figure 5. Variation in the photodetector response as a function of load for PET under ambient conditions.
the experimentally measured value of 3.08 ( 1.55 nN. The reason for this discrepancy is not clear; however, the fit of the JKR model to the data in Figure 3 is certainly good. Because of the substantial difference in the behavior observed under ethanol and perfluorodecalin, measurements were made for samples immersed in hexadecane. The dielectric constant of hexadecane (2.04)38 is smaller than that of ethanol but slightly larger than that of perfluorodecalin (1.86).37 The resulting variation in the photodetector response as a function of the load is shown in Figure 4. Although the curvature in the friction-load relationship is less pronounced than that in Figure 3, application of the GTE yielded a value of R close to zero, suggesting that DMT contact mechanics applied. Fitting with a straight line was not as good, although within small ranges, data approximated to linear behavior. Measurements under ambient conditions also yielded a nonlinear relationship between the friction force and the load. Figure 5 shows the resulting experimental data together with fits made using the GTE. The data extended to substantial negative loads, reflecting the large size of the capillary force. Analysis of the data using the GTE yielded a value of R of 0.62, which is intermediate between the JKR and the DMT model.
Discussion Understanding the contact mechanics involved in FFM is critical to its exploitation in both fundamental studies of nanoscale tribological phenomena and in nanoscale surface analysis. In principle, FFM offers a uniquely powerful tool for surface analysis because it provides information on surface composition and molecular structure with nanometer spatial resolution. Recently, we have illustrated this through its application in the study of
Hurley and Leggett
the kinetics of surface chemical reactions.15 However, if the contact mechanics are not well understood then the interpretation of FFM data must remain subject to uncertainty. The data here shed light on some of the uncertainties associated with FFM contact mechanics. Self-assembled monolayers have been one of the most extensively studied systems by FFM. The majority of authors have utilized approaches based upon Amontons’ law (or Derjaguin’s modification of it) to model the data. Significantly, however, work by Houston and co-workers, using the interfacial force microscope (IFM), has suggested that tip-sample frictional interactions fit single-asperity contact mechanics. The frictionload relationships reported by these authors have typically exhibited distinct nonlinearity. They reported JKR-type behavior for alkanethiol monolayers,14,42 whereas for alkoxyl monolayers on the native oxide of silicon43 they reported JKR-type behavior for adsorbates with short chains and DMT-type behavior for longer adsorbates. Recently, we sought to analyze data for SAMs under compressive loading only using both the JKR model and Amontons’ law but were not able to determine with confidence which model fit the data properly. One concern in that study was that the range of loads accessible was too small to enable proper discrimination. However, a significant feature of the earlier work by IFM was that substantial adhesive interactions were reported. The IFM experiments of Houston and co-workers were conducted in air. The dielectric constant of air is small, and a more likely explanation for the discrepancies between their data and those of other workers, in light of the recent paper by Gao et al.,28 is that the contact mechanics in low dielectric media are different from those in media with higher dielectric constants. The present work sought to test this hypothesis, and the data reported here are in good agreement with the model of Gao et al. In ethanol, a linear relationship was observed between the friction force and the normal load. The data could not be fitted with a single-asperity contact mechanics model. Although the sample here was a polymer, this observation is consistent with the large body of data for SAMs that also reports linear frictionload relationships. According to the model of Gao et al.,28 this reflects load-controlled friction. The only caution in this interpretation is the nonzero intercept with the vertical axis. This requires further explanation. However, the general form of the behavior was clearly quite different from that observed in other media. The behavior in perfluorodecalin was rather different. It was consistent with JKR contact mechanics. The dielectric constant of perfluorodecalin is small, and this is expected to cause stronger dispersion forces between the tip and the sample. Dispersion interactions are likely to dominate at the PET-tip interface. As a result, larger adhesion (pull-off) forces were measured in perfluorodecalin. According to the analysis of Gao et al., the nonlinear friction-load relationship that we observed reflects adhesion-controlled friction. Such behavior is consistent with the data reported by Houston and co-workers using the IFM in air, where the low dielectric constant of the medium is also expected to lead to strong adhesive interactions. In hexadecane, a nonlinear relationship between the friction force and the load was also observed. The behavior was different from that observed in perfluorodecalin, with the GTE yielding a value of R close to zero, suggesting DMT mechanics. Generally, DMT mechanics are thought to apply to situations where adhesive (42) Burns, A. R.; Houston, J. E.; Carpick, R. W.; Michalske, T. A. Phys. ReV. Lett. 1999, 82, 1181. (43) Major, R. C.; Kim, H. I.; Houston, J. E.; Zhu, X.-Y. Tribol. Lett. 2003, 14, 237.
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interactions are weak. It is possible that the difference in contact mechanics observed here arises from a weakened adhesive interaction in this medium. Analysis of the data acquired in air using the GTE yielded a value for R that is intermediate between those for hexadecane and perfluorodecalin. Although air has a small dielectric constant, this is unlikely to be the explanation for the nonlinearity of the friction-load relationship because the data were acquired under ambient conditions (relative humidity ca. 40-50%) and a capillary was present between the tip and the surface. This was reflected in the measurement of a very substantial adhesive force (typically ca. 20 nN). In this case, therefore, the nonlinearity of the frictionload behavior has a different physical origin, although the measurement of a very large adhesion force probably means that the interaction between the tip and the surface was still adhesiondominated although not in the sense of the phrase as used by Gao et al. Considered together, these observations suggest the following interpretation. In media with high dielectric constants, such as ethanol, linear friction-load behavior is observed. In liquids with low dielectric constants, such as perfluorodecalin and hexadecane, adhesive interactions exert a varying degree of influence, and the friction-load relationship is nonlinear and may be modeled using single-asperity contact mechanics models. The work previously reported by Houston et al. using the IFM is consistent with such an interpretation, with the low dielectric constant of dry air yielding the strong dispersion interactions that cause the JKR-type behavior that they reported. Given the volume of work that has previously been reported for SAM systems, it is also important to examine their behavior as a function of the properties of the liquid medium to extend this analysis. However, it appears that the work of Gao et al. provides a very useful approach to understanding the frictional properties of PET. A practical conclusion to be drawn here is that the specification of the medium is a critical component of the FFM experiment. Not only will this influence the relative magnitude of the contribution of the adhesion force to the frictional interaction, but it could also mean that different contact mechanics will apply. There are three other questions that should be addressed. First, there has recently been speculation that under water, interphase layers form close to the sample surface and that the structure of these layers has an influence on the frictional interactions measured with an IFM.44,45 In the context of the present investigation, it is significant that water is an unusual liquid in some respects because of the strength of hydrogen bonding interactions. In air, the possibility of the formation of interfacial layers of condensed water does exist, but ethanol has much weaker intermolecular interactions, despite having a significant dipole moment, and perfluorodecalin has no polar interactions. On the basis of these considerations, it seems unlikely that solvent ordering, for example, occurs close to the polymer surface. Second, Kiely and Houston have demonstrated that a transition from JKR to Amontons-like behavior can occur in IFM experiments at high loads.46 This possibility was also discussed by Gao et al.28 Houston et al. suggested that for AFM
measurements of molecular-level friction a linear friction-load relationship has generally been reported because the energy dissipation process in a monolayer involves a thin film that can accommodate only a finite amount of strain; the zero-load strain is, they suggested, “sufficient to place the repulsive region under the thin-film, constant slope condition”.47 However, in the present study it is important to note that single-asperity behavior is observed in perfluorodecalin, the medium that yields the largest adhesion force and, by inference, the largest zero-load strain. According to the hypothesis of Houston et al., the contact mechanics should, if anything, be the reverse of what we have observed here: perfluorodecalin yielded the largest load and the largest frictional force, and hence one would have expected that it would be the least likely medium to yield JKR-type behavior, whereas the lower-adhesion medium, ethanol, would be more likely to yield area-dependent frictional forces. This is clearly not the case, and the conclusion must be that the linearity in Figure 1 is not explained by excessive strain. Instead, the proposal of Gao et al. that a linear friction-load relationship is to be expected except where the interaction is adhesion-dominated seems to fit the data better. A final question relates to the observation of a nonzero load under ethanol. This indicates that despite the observation of a linear friction-load relationship in this medium there is some adhesion between the tip and the sample. In perfluorodecalin, the strong adhesion observed modifies the friction-load relationship. Here, the effect is small and does not cause a nonlinear friction-load relationship. It is possible that the influence of this small adhesive force is significant only at small loads; moreover, the comparatively low moduli of polymers may mean that the contact area is larger at such small adhesive forces than is the case for other materials such as SAMs. These phenomena are worthy of some further investigation in the future.
(44) Kim, H. I.; Kushmerick, J. G.; Houston, J. E.; Bunker, B. C. Langmuir 2003, 19, 9271. (45) Fiebelman, P. J. Langmuir 2006, 22, 2136.
(46) Kiely, J. D.; Houston, J. E. Langmuir 1999, 15, 4513. (47) Houston, J. E.; Doelling, C. M.; Vanderlick, T. K.; Hu, Y.; Scoles, G.; Wenzl, I.; Lee, T. R. Langmuir 2005, 21, 3926.
Conclusions Under ethanol, the friction-load relationship for poly(ethylene terephthalate) during friction force microscopy was found to be linear. Under perfluorodecalin and hexadecane, two liquids with much smaller dielectric constants, the friction-load relationship was found to be nonlinear. It could be modeled effectively using single-asperity contact mechanics models. This was attributed to the stronger dispersion forces that act in these media, leading to adhesion-controlled friction. In the case of perfluorodecalin, in which the adhesion strength was the greatest, the JKR model was found to yield the best fit to the experimental data, whereas in hexadecane, which yielded a smaller adhesive interaction, the DMT model provided the best fit. Acknowledgment. C.R.H. thanks the Engineering and Physical Sciences Research Council (EPSRC) for a research studentship. G.J.L. thanks the EPSRC and the Royal Society of Chemistry Analytical Division for financial support. LA053176T
