Friction Coefficients Derived from Apparent Height Variations in

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Friction Coefficients Derived from Apparent Height Variations in Contact Mode Atomic Force Microscopy Images Junwei Li, Chen Wang, Guangyi Shang, Qingmin Xu, Zhang Lin, Jingjiao Guan, and Chunli Bai* Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, China Received December 22, 1998. In Final Form: April 23, 1999 Self-organized monolayer domains of liquid crystal (LC) on mica surface were investigated by contact mode atomic force microscopy (AFM) and friction force microscopy (FFM). By analyzing contributions of friction to the apparent height in AFM height images, we calculated the friction forces and the relevant friction coefficients. It is observed that the difference between the magnitude of the friction force on LC monolayers and mica was proportional to the normal load. The friction coefficients of the LC monolayers and bare mica were obtained as 0.076 and 0.094, respectively. In addition, frictional asymmetry of LC monolayers was observed in our study, which was attributed to the molecular tilt, and a possible explanation was proposed in terms of the stick-slip motion of the tip apex on the molecular scale.

1. Introduction Although friction phenomena is an old topic, the fundamental relationship between load (including adhesion) and friction remains1 an interesting issue to which the modern techniques of nanotribology, such as scanning probe microscopy (SPM),2-4 surface force apparatus,5 and computational simulating techniques6-8 have much to contribute. SPM techniques have emerged as a new tool for probing surface force and morphology with high normal and lateral resolutions.9-11 It was thus recognized that this technique could probe the nanoscale behavior of interactions between surfaces, such as friction, adhesion, lubrication, wear and so on.6 The advance of the applications of friction force microscopy (FFM) to study selfassembled (SAM) or Langmuir-Blodgett (LB) monolayers have yielded spectacular results in recent years.12 Since SAM or LB monolayers form densely packed and often ordered structures on solid surfaces, they are ideal to model lubricant films for fundamental studies of tribology.6,13,14 In typical imaging processes by atomic force microscopy (AFM) in contact mode, lateral force or friction may have significant contributions, especially for biological, organic, * To whom correspondence should be addressed. Tel: 86-1062568158. Fax: 86-10-62557908. E-mail: [email protected]. (1) Johnson, K. L. Langmuir 1996, 12, 4510-4513. (2) Schwarz, U. D.; Allers, W.; Gensterblum, G.; Wiesendanger, R. Phys. Rev. B 1995, 52, 14976-14984. (3) Erlandsson, R.; Hadziioannou, G.; Mate, C. M.; McClelland, G. M.; Chiang, S. J. Chem. Phys. 1988, 89, 5190-5193. (4) Liu, Y.; Evans, D. F. Langmuir 1996, 12, 1235-1244. (5) Yoshizawa, H.; Chen, Y.; Israelachvili, J. J. Phys. Chem. 1993, 97, 4128-4140. (6) Bhushan, A.; Israelachvili, J. N.; Landman, U. Nature 1995, 374, 607-616. (7) Matsuzawa, N. N.; Kishii, N. J. Phys. Chem. 1993, 97, 41284140. (8) Buldum, A.; Ciraci, S. Phys. Rev. B 1997, 55, 2606-2611. (9) Binnig, G. F.; Quate, C. F.; Gerber, C. Phys. Rev. Lett. 1986, 56, 930-933. (10) Bai, C. Scanning Tunneling Microscopy and Its Application; Springer-Verlag: Heidelberg, 1995. (11) Binnig, G. F.; Gerber, C.; Stoll, E.; Albrecht, T. R.; Quate, C. F. Europhy. Lett. 1987, 3, 1281-1286. (12) Carpick, R. M.; Salmeron, M. Chem. Rev. 1997, 97, 1163-1194. (13) Briscoe, B. J.; Evans, D. C. B. Proc. R. Soc. London A 1982, 380, 389-407. (14) Persson, B. N. Phys. Rev. B 1997, 55, 8004-8012.

and polymer samples.15 The investigation of the relationship between friction and load (including adhesive force) could help the interpretation of AFM images and understanding of the results of chemical force microscopy (CFM) at the molecular level.16-19 While many qualitative properties are revealed in topographic and friction data by AFM and FFM, quantitative understanding of these phenomena is still a nontrivial experimental task. The measured signals must be accurately calibrated to yield forces.12 Typical quantitative measurements of frictional properties by SFM were derived from friction loops in scope view.3-4,20-21 This requires, among other things, knowing accurately the lateral force constants of the cantilevers. Unfortunately, this is a rather complicated task, (especially for the commercially microfabricated “V” shaped cantilevers), and no standard method has yet emerged. So far, estimates can only be available from the formula given by Neumeister and Ducker.22 In the meantime, there are wellestablished methods to calibrate the normal force constants of the cantilevers,23 and the sensitivity of the cantilever in normal direction is easier to obtain, compared with that in lateral direction.24 It is therefore desirable to quantitatively study the friction behaviors on the basis of normal deflection of the cantilever. Here, we studied the frictional properties of liquid crystal monolayers on a mica surface with AFM. The (15) Radmacher, M.; Tillmann, R. W.; Frtz, M.; Gaub, H. E. Science 1992, 257, 1900-1905 and references therein. (16) Overney, R.; Meyer, E.; Frommmer, J.; Brodbeck, D.; Lu¨thi, R.; Howald, L.; Gu¨ntherodt, H. J.; Fujihira, M.; Takano, H.; Gotoh, Y. Nature 1992, 359, 133-135. (17) Fisbie, C. D.; Rozsnyai, L. F.; Noy, A.; Wrighton, M. S.; Lieber, C. M. Science 1994, 265, 2701-2704. (18) McKendry, R.; Theoclitou, M.; Rayment, T.; Abell, C. Nature 1998, 391, 566-568. (19) Green, J. D.; McDermott, M. T.; Porter, M. D. J. Phys. Chem. 1995, 99, 10960-0965. (20) Tsukruk, V. V.; Bliznyuk, V. N. Langmuir 1998, 4, 446-455. (21) Noy, A.; Frisbie, C. D.; Rozsnyai, L. F.; Wrighton, M. S.; Lieber, C. M. J. Am. Chem. Soc. 1995, 117, 7943-7951. (22) Neumeister, J. M.; Ducker, W. A. Rev. Sci. Instrum. 1994, 65, 2527-2531. (23) Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. Rev. Sci. Instrum. 1993, 64, 403-405. (24) Ogletree, D. F.; Carpick, R. W.; Salmeron, M. Rev. Sci. Instrum. 1996, 67, 3298-3306.

10.1021/la981750d CCC: $18.00 © 1999 American Chemical Society Published on Web 08/31/1999

Friction Coefficients Derived from Height Variation

monolayers have a clear reference surface (mica) that has different frictional properties from the LC monolayers. The friction force can be calculated by the apparent height of monolayers in trace and retrace images. By measuring the apparent height variation of the monolayers under different load, we found that the friction was proportional to the normal force, including the adhesive load. In addition, the friction coefficients of monolayers and mica were obtained. The adhesive force between tip and sample was measured by the force spectrum method. Moreover, the frictional behaviors of liquid crystal monolayers were also studied by friction signals in FFM. In our experiments, it is found that the coefficient of monolayers in the trace scan direction is not equal to that in the retrace scan direction, and the difference between them cannot be neglected. We attribute this friction asymmetry to the molecular tilt within the monolayers. A possible explanation of the asymmetry is given in terms of the lateral deformation of LC molecules within the monolayers during sliding. This paper is organized as follows. After introducing the experimental setups, we proceed to the discussion of the friction-induced apparent height variations, assuming the friction properties of LC monolayers to be isotropic. This is perceived as applicable to general systems. In the next section, we further look into the effect of the intrinsic molecular tilt within LC domains on the observed anisotropy of the friction behaviors. Finally, we provided an alternative method to study friction properties using FFM and the compare the merits for both methods. 2. Experimental Section In this section, we briefly explain the experimental setup and the data analyzing process. 2.1. Sample Preparation. The liquid crystal compound (4-pentyl-4′-methoxy-phenylbenzoate), with melting and phase-transition points of 310 and 302 K, respectively, was dissolved in an alcohol solution with the concentration of 1 × 10-8 (v/v). A drop of such solution (about 1 µL) was distributed onto the surface of the freshly cleaved mica. The sample was heated with a speed of 10 K/min to 373 K and subsequently cooled naturally to ambient temperature (300 K). 2.2. Imaging and Characterization of Friction. Friction behavior was characterized by the contrasts in height and friction images respectively with SPM (Nanoscope IIIa, DI) in contact mode. Two approaches will be illustrated later in detail. Height images in trace and retrace scan directions (indicated in the Figure 2) were obtained simultaneously when the scan angle was 0°. Friction images in trace and retrace scan directions were recorded when scan angle was 90°. All height images and friction images in contact mode were obtained at the same area of sample with the same tip (commercial triangular Si3N4 cantilever, 200 µm long, spring constant in normal direction 0.12 N/m). Tapping images were obtained with a Si cantilever. The imaging was under ambient condition with temperature 300 K and relative humidity 62%. A homemade sample stage was utilized to rotate the sample, to ensure that the same place was sampled after rotation. 2.3. Calculation of Imaging Load Force. Imaging load Fp exerted by the tip can be given as

Fp ) (T - T0)Kc/S where Kc is the cantilever spring constant in normal direction, T is the value of imaging setpoint, T0 is the

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Figure 1. Tapping mode AFM image of LC monolayer domains on mica surface along with a profile line.

value of deflection signal when the tip is in its free state, and S is the sensitivity of the tip in normal direction. T0 and S were determined by the force curve measurements. We measured the force curve right after every friction and height imaging in order to exclude the possible errors induced by systematic drift. 2.4. Statistical Measurement of Adhesive Force. Imaging area was divided into 1024 units, and the force curve was recorded in every unit. These 1024 force curves were analyzed to get the statistical distribution of the adhesive force in the imaging area. 3. Result and Discussion 3.1. Liquid Crystal Monolayer. Figure 1 is the height image of the sample measured with tapping mode. Because the tip contacts only intermittently with the sample in tapping mode, the friction effect on tip deflection is considered negligible. The apparent height in the tapping images is thus very close to the true film height. The higher domains in Figure 1 are liquid crystal films. During condensation, the liquid crystal molecules self-organized into an ordered structure4-5,25 at the mica/air interface due to their chemical structure: high concentration of rodlike species and amphipathic properties. The crosssectional profile in Figure 1 shows that the LC domains have uniform heights of 1.33 nm (although with a few defects in them), affirming that the arrangement of LC molecules is an ordered one. With the molecular mechanics calculation, the length from the polar head to the nonpolar end of an isolated liquid crystal molecule was 1.65 nm in minimum energy conformation. Therefore, the observed LC films were believed to be molecular monolayers, and the orientation of molecules had a tilt relative to surface normal. The tilt of molecular orientation has been reported earlier for self-assembly monolayers,26 LB films,27,28 and LC monolayers.29 The stability of the LC domains was tested by heating the sample to 373K for 2 h and then cooling it to ambient temperature. The tapping images of the sample did not show any significant differences comparing with those (25) Stupp, S. I.; Son, S.; Lin, H. C.; Li, L. S. Science 1993, 259, 59-63. (26) Poiruer, G. E.; Pylant, E. D. Science 1996, 272, 1145-1147. (27) Naselli, C.; Swalen, J. D.; Rabolt, J. F. J. Chem. Phys. 1989, 90, 3855-3860. (28) Meyer, E.; Overney, R.; Lu¨thi, R.; Brodbeck, D.; Howald, L.; Frommer, J.; Gu¨nther, H. J.; Wolter, O.; Fujihira, M.; Takano, H.; Gotoh, Y. Thin Solid Films 1992, 220, 130-137. (29) Dierker, S. B.; Pindak, R.; Meyer, R. B. Phys. Rev. Lett. 1987, 56, 1819-1822.

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Figure 2. Height images of trace (a) and retrace (b) in contact mode with imaging force of 8.3 nN when the scan angle was 0°.

Figure 3. Schematics of the contribution of lateral force to the bending deflection of the cantilever. Fn is the normal force of imaging, and Ff is the tangential force when tip slides on sample. L, h, and θ are described in text.

Figure 4. (a) Heights of the LC domain (marked in Figure 2a with a rectangle) in trace (solid squares) and retrace (solid circles) height images vs imaging force Fp exerted by scanning tip. (b) Values of ∆z (specified in eq 3) vs imaging force Fp.

prior to the heating. Therefore, the monolayers are stable in term of total energy. 3.2. Relationship between Friction and Load (Including Adhesive Force). Parts a and b of Figure 2 are the height images in trace and retrace scanning directions, respectively, obtained in contact mode when the scanning angle is 0°. The cross-sectional profiles of Figure 2a,b indicate that there is a significant difference between the apparent height in trace and retrace images. This difference is due to the contribution of lateral force to the deflection of the tip. As is suggested by many researchers, the apparent height za, which is measured in the experiment, has two contributions: one, z0, from the normal displacement of the tip and the other, zf, from the tilt of tip induced by the lateral force. Thus the apparent height has the form za ) z 0 + zf . The deflection of the cantilever needs to be examined in order to understand the effect of friction in imaging process. As shown in Figure 3, a tangential force Ff on the tip would result in a bending torque Mt ) hFf, where h is the perpendicular distance between the tip (point o) and the start point of cantilever (point c). Here, the length of the pyramid tip is negligible relative to h. The torque also contributes to the cantilever total deflection. Thus the lateral force leads to a pseudoheight zf, which is given by

where L is the length of cantilever and θ is the slope of cantilever. For the tip used in our experiment, θ is around 10°. It should be mentioned here that lateral forces arise not only from friction but also from local surface slopes.30 Since LC films studied here have uniform height, as shown in Figure 1, the tangential force was thus caused only by friction. So we can separate the contribution of friction from topology through bidirectional scans, trace and retrace. Because the friction changes its sign during trace and retrace scan, the apparent height in trace direction zT, and that in retrace direction zR can be given by

h zf ) Ff Kc ) (Ff/Kc)tan θ L

( )/

zT ) z0 + zf1 - zf2 ) (tan θ/Kc)(Ff1 - Ff2) + z0 (1) zR ) z0 - zf1 + zf2 ) (tan θ/Kc)(Ff2 - Ff1) + z0 (2) where zf1 and zf2 are the parts of the apparent monolayers height induced by friction on the LC monolayers and mica, respectively, and Ff1 and Ff2 are the friction on LC monolayer and mica, respectively. So the contribution of friction to the apparent height of monolayers, ∆z, can be separated by

2∆z ) zR - zT ) 2(tgθ/Kc)(Ff2 - Ff1)

(3)

Figure 4a shows the height of one monolayer domain in trace and retrace images versus the load exerted by the (30) Shang, G.; Qiu, X.; Wang, C.; Bai, C. Appl. Phys. A 1998, 66, 333-335.

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Table 1. Results of the Linear Fits for y ) A + Bx to the Data Set Shown in Figures 4 and 6 fig

fitting data line

value

A

4a 4a 4b 6a 6a 6b

trace zT retrace zR ∆z ) (zR - zT)/2 trace zT retrace zR ∆z ) (zR - zT)/2

1.016 2.109 0.5447 0.960 2.042 0.541

B sd

value

sd

0.0453 -0.0290 0.0019 0.0739 0.0236 0.00313 0.0514 0.0263 0.0022 0.0243 -0.0261 0.0012 0.0592 0.0315 0.00291 0.0360 0.0288 0.00177

relation coeff 0.963 0.871 0.944 0.978 0.918 0.961

tip, and Figure 4b is the calculated ∆z versus load specified in eq 3, along with linear regression analysis. To eliminate arbitrary errors caused by the measurements, we used bearing analysis method to measure the heights and voltage signals of the LC domain in the images.31 The friction behavior can be described in the general form2

Ff ) c1Fpm + c2Fp + c3

(4)

where Fp is the externally applied loading force and c1-c3 are material-dependent constants. The index m (0 < m 90°. In our study, the tip-sample configuration before and after rotation can be represented by (a) and (c), respectively.

during sticking is dissipated by creating a local nonequilibrium phonon density,41 as illustrated in Figure 7b. The following terms contribute to the total potential of the whole system: V1 is the interaction potential between the sliding tip and the terminal groups of LC molecules, V2 is the elastic potential of the sliding tip and LC molecules in the x-axis direction, and V3 is the elastic potential of LC molecules in the z direction. Thus E(x, z) ) V1 + V2 + V3. In our study, the changes of V1 and V3 in trace sliding are equal to that in retrace sliding, but V2 is different between trace and retrace sliding due to the molecular tilt. So, we only consider the lateral force depending on the deformation of molecules in x-axis direction. Here, as a simplification, we only analyze Fi, the lateral force between one chain unit and the sliding tip in association with V2. As shown in Figure 7c, during the sticking process, Fi can be given by

dFi ) k dx ) kLm sin φ d φ

The average value of Fi in trace sliding, Fi,T, and that in retrace sliding, Fi,R, can be given by 0

|Fi,T| )

0

∆φ

)

(

kLm sin φ0

∫φφ +∆φ dFi

1 - cos ∆φ ∆φ - sin ∆φ - cos φ0 ∆φ ∆φ

)

0

|Fi,R| )

0

∆φ

(

)

kLm sin φ0

1 - cos ∆φ ∆φ - sin ∆φ + cos φ0 ∆φ ∆φ

)

where φ0 is value of φ when there is no interaction between the chain units and sliding tip and ∆φ the change of φ during sticking. Now, we can explain our experimental results since the apparent friction coefficient can be given by µ ) FL/Fn, as specified in eqs 10 and 11. It is clear that the absolute value of Fi,T and Fi,R in trace and retrace is not the same, as long as φ0 is not equal to 90°; that is to say, the orientation of molecules has a tilt in monolayers. Three typical cases are shown in Figure 8: φ0 > 90° (cos φ0 < (41) Persson, B. N. Phys. Rev. B 1994, 50, 4771-4786.

0) and |Fi,T| > |Fi,R|, φ0 < 90° (cos φ0 > 0) and |Fi,T| < |Fi,R|, φ0 ) 90° (cos φ0 ) 0) and |Fi,T| ) |Fi,R|. Furthermore, the friction anisotropy observed by Liley et al.39,40 of chiral lipid monolayers with different orientations can also be accounted for by our model. From the above analysis, it is clear that the friction asymmetry can be induced by the molecular tilt. In practice, the calculation of the interaction potential involves hundreds of atoms at close proximity to the sliding object. This would require a further elaboration of the present model. The asymmetry of Fi can be given by

∆F ) (|Fi,R| - |Fi,T|)/2 )

(

kLm cos φ0 1 -

sin ∆φ 1 ≈ kLm∆φ2 cos φ0 ∆φ 6

)

The average friction in one scan loop can be given by

1 Fi(φ0) ) (Fi,T + Fi,R)/2 ) kLm∆φ sin φ0 2

where i ) 1, 2, ..., corresponding to the units involved in the chain, k is the spring constant perpendicular to the orientation of LC molecules, φ is the angle between LC molecular orientation and retrace sliding direction, 0 < φ < 180°, and Lm is the length of LC molecule.

∫φφ -∆φ dFi

Figure 9. Values of ∆F/(Fi)2 vs external load Fp.

Therefore,

∆F (Fi)2

)

cos φ0 3kLm sin2 φ0

Again, using our experimental results as a test, the calculated value of ∆F/(Fi)2 by eqs 1 and 2 can be found as approximately a constant with the change of load, as shown in Figure 9 (although there is large deviation when the load is very low). The constant is related to Lm, φ0, and k. k can be determined by surface tension. The asymmetry of lateral spring constants of tilt molecules proposed in our model is probably only one of the contributions to the friction asymmetry. Other material parameters, such as the molecular stiffness suggested by Liley et al.,39 would also contribute to this asymmetry. More experimental and theoretical work on the viscoelastic properties of monolayers will be needed before one could fully understand the friction asymmetry. Further quantitative studies of these phenomena will help to shed light on the physical nature of friction.13 3.4. Friction Behavior Studied by FFM. In this section, we illustrate the typical approach to characterizing friction using the friction signals in friction images. Friction images in trace and retrace scanning directions are shown in Figure 10a,b while the scanning angle is 90°. Figure 10 was obtained before the sample rotation. The friction signals, V, of LC monolayers in friction images are proportional to the difference between Ff1 and Ff2 of the form

V ) F(Ff2 - Ff1)

(12)

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Figure 10. Friction images of trace (a) and retrace (b) before the sample rotation with imaging force of 18.8 nN while the scan angle was 90°. A profile line was shown along with each image.

Figure 11. Friction signals were measured at different loads for the same LC domain as in Figures 4 and 6. (a) Values of friction signal of the LC domain in trace (solid squares) and retrace (solid circles) friction images vs imaging force Fp. (b) Values of ∆V vs imaging force Fp. ∆V is half of the difference between friction signal in retrace and that in trace friction images shown in part a. (c) Values of friction signal of the LC domain in trace (solid squares) and retrace (solid circles) friction images vs imaging forces Fp after sample was rotated 90°. (d) Values of ∆V vs imaging force Fp. ∆V is half of the difference between friction signal in retrace and that in trace friction images shown in part c.

where

F ) 1/(K|S|) K| is the cantilever force constant in lateral direction in unit of N/m and S| is the sensitivity parameter (m/v) relating the voltage signal to the distance that the tip moves in lateral direction.

Figure 11a,c shows the friction signals of the monolayers versus load in trace and retrace friction images before and after the sample rotation, respectively. Figure 11b,d gives ∆V, which was half of the difference between friction signals in trace and retrace images, versus load before and after the sample rotation, respectively, along with linear regression analysis. The same monolayer domain of LC was measured in Figures 4, 6, and 11. The linear

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Table 2. Results of the Linear Fits for y ) A + Bx to the Data Set Shown in Figure 11 fig 11a 11a 11b 11c 11c 11d

fitting data line

A

trace VT retrace VR ∆V ) (VR - VT)/2 trace VT retrace VR ∆V ) (VR - VT)/2

sd

value

sd

relation coeff

-0.0121 0.0165 0.0143 -0.0145 0.0135 0.00138

0.00116 0.00141 0.0008 0.00116 0.00141 0.0010

-0.00107 0.00104 0.00106 -0.00087 0.00091 0.0009

0.00004 0.00005 0.0003 0.00004 0.00005 0.0004

0.991 0.985 0.995 0.990 0.985 0.991

fitting results of Figure 11 are shown in Table 2. It can be concluded that the results from friction images before and after the sample rotation can both be described by eq 6. Combining the results in Table 2 and eqs 6 and 12, one could also obtain the values of µ1 and µ2, if the values of K| and S| are known. K| of the tip in our experiments is estimated to be 225 N/m, which can only be calculated by the dimensions of the tip.21 S| is given by4

S| )

3t A + B S 2L C + D

(

B

value

)

where A-D denote areas projected by the laser beam onto the corresponding photodiode windows and t is the tip height. The calculation of S| involves the measurements the value of A + B and C + D in situ, which requires the modification of SPM instrument. It is clear from above expressions that S| needs to be measured if one calculates the values of friction from the signals in friction images. This practice is deemed as an alternative to the study of friction behavior from SPM. From the fitting results in Tables 2, the absolute values of the slopes of friction signal versus load plots in trace and retrace scans show the same tendency as that from the height images, although the asymmetry is not obvious

due to the large value of the cantilever twisting constant (which is typically 3 orders of magnitude greater than the bending constant). 4. Conclusions In summary, it is demonstrated that friction will contribute significantly to the AFM height images in contact mode. Analyzing these contributions can be helpful to study the frictional properties of the surface on the nanoscale. This provides a method other than FFM to study surface friction with high accuracy. Adhesive force is shown to have a strong influence on the friction behavior. In our study, the quantitative analyses of the relationship between friction and normal force indicate that the difference between the magnitude of friction on LC monolayers and mica was proportional to the normal load (including adhesion). We attribute the observed appreciable friction asymmetry to the molecular tilt of monolayer, and a possible interpretation was given from the point of view of stick-slip motion. The results in our experiments indicate that the observed image contrast in both AFM and FFM are closely related to local chemical and physical properties. LA981750D