Dynamic Study of Polymer Films by Friction Force ... - ACS Publications

This point of view is indeed supported by results of dynamic secondary ion mass spectroscopy16 and neutron reflectivity measurements.17Friction force ...
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Dynamic Study of Polymer Films by Friction Force Microscopy with Continuously Varying Load X. P. Wang,†,‡ O. K. C. Tsui,† and Xudong Xiao*,† Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China, and Department of Physics, Structure Research Laboratory, The University of Science and Technology of China, Hefei, 230026, China Received March 18, 2002. In Final Form: May 29, 2002 The friction behaviors of poly(tert-butyl acrylate) (PtBuA) thin films have been investigated at different temperatures (20-70 °C) and different scan rates (50 nm/s to 25 µm/s) by friction force microscopy. By variation of the external load, the friction responses at different depths of the film are also probed. On the basis of the shifting of data from different temperatures, a series of friction master curves (friction versus scan rate) can be constructed to span 7 orders of magnitude in scan rate. A friction peak, indicating the glass-to-rubber transition of the polymer film, is clearly distinguished in each friction master curve obtained at different loads. The load dependences of the friction peak positions in the master curves and in the friction versus temperature curves indicate that the heating effect is important at the sliding contact. All the results lead to a conclusion that the dynamic behavior of the PtBuA film is independent of the film depth and is the same as that of the bulk, showing no detectable enhancement of the molecular relaxation at the surface of the films.

Introduction Because of the widespread applications of polymer thin films as protective coatings, adhesives, and lubricants in industry, much attention has been brought to the understanding of their physical properties.1,2 The viscoelastic behavior of thin polymer films can vary considerably from that of the bulk due to changes in the chain conformations associated with confinement effects and interfacial interactions between the polymer chain and the substrate.3-7 For example, the glass transition temperature, Tg, of polystyrene (PS) films on a silicon substrate with a thin native oxide overlayer can be depressed with decreasing PS thickness.3,5,6 The associated change in the molecular mobility has been attributed to the different dynamical properties of the polymer segments at the interfaces.5-13 In particular, it is generally believed that the molecular * Corresponding author. E-mail: [email protected]. † The Hong Kong University of Science and Technology. ‡ The University of Science and Technology of China. (1) Physics of Polymer Surface and Interfaces; Sanchez, I. C., Ed.; Butterworth Heinemann: Boston, 1992. (2) Polymer at Interfaces; Fleer, G. J., Cohen, S. M. A., Scheutjens, J. M. H. M., Cosgrove, T., Vincent, B., Eds.; Chapman & Hall: London, 1993. (3) Keddie, J. L.; Jones, R. A. L.; Cory, R. A. Europhys. Lett. 1994, 27, 59. (4) Kajiyama, T.; Tanaka, K.; Takahara, A. Macromolecules 1997, 30, 280. (5) Keddie, J. L.; Jones, R. A. L.; Cory, R. A. Faraday Discuss. 1994, 98, 219. (6) Forrest, J. A.; Dalnoki-Veress, K.; Dutcher, J. R. Phys. Rev. E 1997, 56, 5705. (7) Forrest, J. A.; Dalnoki-Veress, K.; Stevens, J. R.; Dutcher, J. R. Phys. Rev. Lett. 1996, 77, 2002. (8) van Zanten, J. H.; Wallace, W. E.; Wu, W. L. Phys. Rev. E 1996, 53, R2053. (9) Dalnoki-Veress, K.; Forrest, J. A.; de Gennes, P. G. J. Phys. IV France 2000, 10, 221. (10) Forrest, J. A.; Mattsson, J. Phys. Rev. E 2000, 61, R53. Mattsson, J.; Forrest, J. A.; Bo¨rjesson, L. Phys. Rev. E 2000, 62, 5187. (11) Fukao, K.; Miyamoto, Y. Phys. Rev. E 2000, 61, 1743. (12) Tsui, O. K. C.; Russell, T. P.; Hawker, C. J. Macromolecules 2001, 34, 5535. (13) Xie, F.; Zhang, H. F.; Lee, F. K.; Du, B.; Tsui, O. K. C.; Yokoe, Y.; Tanaka, K.; Takahara, A.; Kajiyama, T. Macromolecules 2002, 35, 1491.

mobility is enhanced at the polymer-air interface (i.e., the free surface), which has found evidence in computer simulations14 and surface Tg measurements.15 But at the polymer-substrate interface, the molecular mobility can be enhanced or reduced depending on whether the interaction between the segments and the substrate surface is repulsive or attractive. If the polymer-substrate interaction is attractive enough, the overall segmental mobility of the film can be reduced, which is in keeping with the observed enhancement in the Tg of poly(methyl methacrylate)5 and poly(2-vinyl pyridine)8 thin films on silicon. This paper concerns the dynamical properties of the chain segments at the free surface. If the assumption of this mobility being higher is valid, it is reasonable to expect the distinctive dynamic behavior to lessen with the depth into the film. This point of view is indeed supported by results of dynamic secondary ion mass spectroscopy16 and neutron reflectivity measurements.17 Friction force microscopy (FFM) has recently become a popular tool for investigating surface relaxations of polymers,4,15,18-20 ascribable to its simple working principle and the widespread availability of atomic force microscopes (AFMs). In essence, the measured friction is directly related to the viscoelastic dissipation resulting from relaxations of the surface segments.4,16,21 By change of the external load (14) Mansfield, K. F.; Theodorou, D. N. Macromolecules 1991, 24, 6283. (15) Tanaka, K.; Takahara, A.; Kajiyama, T. Macromolecules 2000, 33, 7588. (16) Zheng, X.; Rafailovich, M. H.; Sokolov, J.; Strzhemechny, Y.; Schwarz, S. A.; Sauer, B. B.; Rubinstein, M. Phys. Rev. Lett. 1997, 79, 241. (17) Lin, E. K.; Kolb, R.; Satija, S. K.; Wu, W. L. Macromolecules 1999, 32, 3753. (18) Haugstad, G.; Gladfelter, W. L.; Weberg, E. B.; Werberg, R. T.; Jones, R. R. Langmuir 1995, 11, 3473. (19) Kajiyama, T.; Tanaka, K.; Satomi, N.; Takahara, A. Macromolecules 1998, 31, 5150. (20) Hammerschmidt, J. A.; Moasser, B.; Gladfelter, W. L.; Haugstad, G.; Jones, R. R. Macromolecules 1999, 32, 3360. (21) Scanning Probe Microscopy of Polymer; Ratner, B. D., Tsukruk, V. V., Eds.; ACS Symposium Series 694; American Chemical Society: Washington, DC, 1996.

10.1021/la020270q CCC: $22.00 © 2002 American Chemical Society Published on Web 08/09/2002

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applied to the FFM probe tip, penetration of the probe tip into the polymer is varied.22 Thus, any depth dependence in the surface dynamic behavior should be revealed in the friction signal as a function of different loads. In general, the viscoelastic behavior of the polymer depends on the temperature as well as the probing frequency, as described by the Williams-Landel-Ferry (WLF) theory.23 Although previous FFM studies of polymer films have investigated the temperature and probing frequency dependence, no systematic study has been performed on the depth dependence of the dynamic behavior. In this paper, the friction behavior of thin films of poly(tert-butyl acrylate) (PtBuA) is examined at different temperatures with various probe tip scan rates and external loads. By use of the WLF time-temperature superposition principle, friction master curves and shift factors of different external loads were obtained. Experiment The PtBuA polymer was purchased from Scientific Polymer Products, Inc., Ontario, NY. The average molecular weight is Mw ) 148K Da with polydispersity index Mw/Mn ) 17 by gel permeation chromatography. The bulk Tg of the polymer was measured to be 50 °C by differential scanning calorimetry (DSC) at a heating rate of 10 oC/min in dry nitrogen. Thin films of PtBuA were prepared by spin coating 2 wt % solutions of the polymer in toluene at 6000 rpm. Prior to measurement, the films were annealed in a vacuum oven at 120 °C overnight. Thickness of the films was about 62 nm according to ellipsometry. The AFM used in this experiment was home-built, equipped with RHK electronic controls (RHK Technology, MI). The sample temperature was controlled to (1 °C stability through adjustment of a dc current applied to a Peltier heater. A V-shaped silicon nitride integrated cantilever/tip (Parks Scientific Instruments, Sunnyvale, CA) with 0.5 N/m nominal force constant and tip radius R ∼ 50 nm was used in the experiment. To eliminate the capillary effect, the friction measurements were carried out in a glovebox under low humidity (∼10%). Control of the experimental environment is crucial to the reliability of the measured friction. For example, it has been found that an increase of water content in a gelatin film due to higher humidity could shift the friction peak to higher frequencies.24 Our AFM employs the conventional optical deflection design. The normal force () external load) applied to the cantilever is proportional to the laser intensity difference between the upper and lower halves of the quadrant photodiode; on the other hand, the lateral force () friction) is proportional to the laser intensity difference between the right and left halves.25 To reduce statistical error, every measurement was repeated for at least five different spots on the polymer surface. The external load was calculated from the cantilever force constant and the piezoelectric tube Z displacement. Since the cantilever torsional force constant was not calibrated, the friction data will be presented in relative scales. In many former FFM studies of polymer films, friction was deduced from friction loops obtained at fixed loads.4,18,19,24,26 In the present study, we adopt a different approach in which friction was recorded in real time as the load was varied. This enables a more detailed study on the load dependence of friction over a broad range of loads. As described elsewhere,25 the friction versus load data were obtained by scanning the tip back and forth on the polymer surface, with successive increase in the applied load on each completion of a back-and-forth cycle. Since the measurements are always started from low to high loads, possible wear of the sample surface caused by high loads will not affect the (22) Johnson, K. L.; Kendall, K. K.; Roberts, A. D. Proc. R. Soc. London, Ser. A 1971, 324, 301. (23) Ferry, J. D. Viscoelastic Properties of Polymers; Wiley & Sons: New York, 1980. (24) Hammerschmidt, J. A.; Moasser, B.; Gladfelter, W. L.; Haugstad, G.; Jones, R. R. Macromolecules 1996, 29, 8996. (25) Hu, J.; Xiao, X. D.; Ogletree, D. F.; Salmeron, M. Surf. Sci. 1995, 327, 358. (26) Kajiyama, T.; Tanaka, K.; Takahara, A. Polymer 1998, 39, 4665.

Figure 1. Friction vs external load for (a) PtBuA film at 45 °C and (b) silicon at room temperature with different scan sizes but a fixed scan rate of 1 µm/s. Note that the friction signal increases with scan size in (a). data of lower loads. The outlined measurement procedure has two advantages. First, the load dependence of friction can be directly obtained. Second, thermal drift that normally affects the electronic set point will have less effect on the friction data.

Results and Discussions A. Scan Size Effect. Commercial AFMs usually have a limitation on the dynamic range of the scan frequency (lines/second) of about 4 orders of magnitude. Correspondingly, that sets a limit to the dynamic range of the scan rate (nanometers/second), which equals scan frequency times scan range. The dynamic range of the scan rate (nanometers/second) can in principle be maximized by jointly varying the scan frequency and the scan size.4 This approach is suitable only if the measured friction is independent of the scan range for the same scan rate. We found this condition to fail in PtBuA. Shown in Figure 1a are plots of friction versus external load obtained with different scan sizes (30 nm to 1 µm) at a fixed scan rate of 1 µm/s from a PtBuA sample at 45 °C. As seen, for external loads greater than ∼15 nN, the measured friction increases with increasing scan size until the latter is ∼300 nm, whereupon the friction signal saturates. Moreover, the scan size effect is notably more significant with higher loads. We verified this effect to be intrinsic to the polymer surface rather than an artifact of the instrument, as it was absent from the friction data of a cleaned bare silicon surface (Figure 1b). Scan size effect in FFM had been reported previously in a study of gelatin films.18 Contrary to the present result, the friction force was found to decrease with increasing scan size (0.2-150 µm) for scan rates less than ∼500 µm/s. As the friction force increased with the number of friction loops from which the friction data were averaged, the authors attributed the scan size effect to sample heating due to energy imparted to the system from scanning. It was further demonstrated that the heating effect could cause position shifts in a friction peak (which was presumed to be due to the glass-to-rubber transition of the gelatin film) with which the observed reduction in friction force with increased scan size could be explained. While we also observed position shifts in a friction peak due to use of different scan sizes, an increase in friction force with increased scan size revealed by Figure 1 cannot

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Many experiments have found that the model of Johnson, Kendall, and Roberts (JKR)22 provided good approximation for the contact between two objects coming into contact.28,29 Here, we shall use the JKR model to approximate the contact area between the AFM tip (modeled to be an elastic sphere with radius R) and the flat polymer surface. Then the radius of the contact, a, is given by22

a3 )

R (L + 3πγR + x6πγRL + (3πγR)2 ) K

(3)

with

K-1 )

Figure 2. Friction vs external load for PtBuA film at various scan rates measured at (a) 45 °C, (b) 60 °C, and (c) 70 °C.

be explained by using the same mechanism proposed in ref 18. We postpone elaboration on this point until a later part of this paper. Unless otherwise stated, the scan size was fixed at 100 nm for all experiments reported herein. B. Load Dependence. We have measured the friction of the PtBuA films at different temperatures from 20-70 °C and scan rates from 50 nm/s to 25 µm/s. The limitation on the dynamic range of the scan rate comes from mechanical instability of the instrument although the RHK electronic controller was able to output signal over a frequency range comprising 4 orders of magnitude. Shown in Figure 2a-c are friction versus external load curves obtained at 45, 60, and 70 °C, respectively. Results obtained at temperatures below 45 °C look the same as those of 45 °C and hence were not shown. As seen, friction generally increases with the external load. However, the friction curves of temperatures below 50 °C appear notably different than those of higher temperatures (>55 °C). Specifically, the friction curves of low temperatures are, to good approximations, linear (Figure 2a). But those of high temperatures exhibit a sublinear behavior (Figure 2b,c). In general, the friction force, F, between the AFM tip and a sample surface can be written as27

F ) τA

(1)

where τ is the shear strength of the polymer and A is the contact area between the tip and the sample. Since τ generally depends on the pressure, P, experienced by the sample,28 which equals the sum of the external load, L, and the adhesion force, La, over the contact area, A, the friction force can also be written as

F ) (τ0 + RP)A ) τ0A + R(L + La)

(2)

with τ0 and R being constants. (27) Micro/Nanotribology and its Applications; Bhushan, B., Ed.; Kluwer Academic Publishers: Boston, 1996. (28) Gracias, D. H.; Somorjai, G. A. Macromolecules 1998, 31, 1269.

3(1 - υ12) 3(1 - υ22) + 4E1 4E2

(4)

Here, γ is the interfacial surface energy; E and ν are the Young modulus and the Poisson ratio, respectively. The subscripts, 1 and 2, denote silicon nitride (which made up the tip) and PtBuA, respectively. Since E1 (∼155 GPa) is much larger than E2 (e0.6GPa),30 the first term of eq 4 can be neglected. Since the adhesion force, La, is ∼3πγR/2,22 eq 2 can be rewritten as

F ) R(L + La) + τ1(xL + La + xLa)4/3 with

(

)

3R(1 - υ22) τ1 ∼ πτ0 4E2

(5)

2/3

(6)

Equation 5 shows that two terms, one linear and one sublinear, contribute to the total friction. According to eq 6, the smaller the sample elastic modulus, E2, the more important the sublinear term. We have model-fit our data to eq 5. Shown in Figure 3 are some representative results from fitting, with contributions from the linear and sublinear terms also displayed (the dotted and dotteddashed lines, respectively). Evidently, the linear term dominated at low temperatures (Figure 3a). But with increased temperature, the sublinear term gradually picked up (Figure 3c) and was even dominating (Figure 3b). Previous studies on PtBuA films showed that this polymer undergoes a glass-to-rubber transition near 55 °C whereat the sample elastic modulus decreases by more than 3 orders of magnitude.30 Below 50 °C, τ1 is small as E2 is large. Hence the second term of eq 5 is negligible, which accounts for the linear behavior exhibited by F versus L in Figure 2a. Using eq 6, we estimate that τ1 should increase by about 2 orders of magnitude from 45 to 60 °C, in consistency with the fitted results (Figure 2a,b). This may account for the nonlinearity displayed by the friction curves at high temperatures (Figure 2b,c). While R, the coefficient of the linear term, may also play a role, it is likely that it has a weaker temperature dependence than τ1 as it is given by the ratio τc /σc (where τc is the yield stress and σc is the penetration hardness of the polymer),31 with both τc and σc decreasing with increasing temperature. The linear term is often regarded as a correction to the sublinear term in most solids.25 But in the present (29) Aime, J. P.; Elkaakour, Z.; Odin, C.; Bouhacina, T.; Michel, D.; Curely, J.; Dautant, A. J. Appl. Phys. 1994, 76, 754. (30) Tsui, O. K. C.; Wang, X. P.; Ho, J. Y. L.; Ng, T. K.; Xiao, X. D. Macromolecules 2000, 33, 4198. (31) Persson, B. N. J. Surf. Sci. Rep. 1999, 33, 83.

Dynamic Study of Polymer Films

Figure 3. Typical fits of the friction data to eq 5. Demonstrations are given for measurement results of (a) 45 °C, (b) 60 °C, and (c) 70 °C, with the experimental data displayed as open marks and the fits as solid lines. Contributions from the linear (dotted lines) and sublinear (dotted-dashed lines) terms are also shown.

experiment, the linear term is more important than the sublinear term in the glassy state of PtBuA. Gracias et al. had compared the friction behavior of low- and highdensity polyethylene (LDPE and HDPE) and found that the linear term dominated in LDPE but the sublinear term dominated in HDPE. The authors pointed out that R could be larger for samples of lower mass density.28 From this point of view, one may appreciate why the linear term plays a significant role in polymers but not in most other solids. C. Scan Rate Dependence. To investigate the glassto-rubber transition, we have measured friction versus scan rate at different temperatures from 50 to 70 °C. The results, obtained under different loads (10-50 nN), are plotted in Figure 4. At low temperatures (e55 °C), friction of PtBuA exhibits a moderate decrease with increasing scan rate (see Figure 4a). At temperatures of g65 °C, on the other hand, it shows an appreciable rise with increasing scan rate (Figure 4c). At intermediate temperatures, a peak appears near 1 µm/s (Figure 4b). The result of Figure 4b is reminiscent of the FFM results of Kajiyama et al. who observed friction peaks of PS films resulting from the glass-to-rubber transition of the polymer surface.4,19 The distinctive scan rate dependence of friction noted in Figure 4 at different temperatures is attributable to the different viscoelastic characteristics of the polymer in the vicinity of Tg. To better reveal the glass-to-rubber transition by the dynamic friction data, it is desirable to have the data displayed over a wide range of scan rates. As mentioned above, however, the range the AFM is able to handle spans only about 2 orders of magnitude. With this limitation, we exploit the time-temperature superposition principle to extend the dynamic range of the data.23,30,32 This is done by rescaling the abscissa of each friction curve by a (32) Wang, X. P.; Xiao, X. D.; Tsui, O. K. C. Macromolecules 2001, 34, 4180.

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Figure 4. Friction vs scan rate of a PtBuA film at various external loads at (a) 50 °C, (b) 60 °C, and (c) 70 °C.

Figure 5. Friction master curves obtained at various external loads. The reference temperature, Tref, was chosen as 55 °C.

temperature-dependent shift factor, aT, leading to a friction master curve that covers a wider range of scan rate. The friction curve thus obtained corresponds to one that would be obtained by experiment at a temperature equal to Tref, whereat aT(Tref) is chosen to be 1.23,33 Figure 5 shows the friction master curves constructed from the data of Figure 4. Here, Tref was chosen to be ∼55 °C. As seen in Figure 5, the friction curve segments, taken from Figure 4, of temperatures higher than Tref were shifted to lower scan rates whereas those of temperatures lower than Tref were shifted to higher scan rates. This simply reflects the fact that aT(T) is a monotonically decreasing function of T. Physically, aT(T) is the temperature-dependent relaxation time of the system normalized to the relaxation time at Tref.30,32 The friction of a polymer is proportional to its loss modulus. Accordingly, there should be a friction peak associated with the glass-to-rubber transition.19,20,34 As discussed by Kajiyama et al.,4 the mechanism can be understood as follows. As an AFM tip scans on the polymer surface, the deformation of the polymer ahead of the tip results in a front rim in which the elastic energy can be (33) Strobl, G. The Physics of Polymers; Springer: Berlin, 1997. (34) Schmidt, R. H.; Haugstad, G.; Gladfelter, W. L. Langmuir 1999, 15, 317.

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stored. When the polymer is in the glassy state, the elastic deformation is quickly recovered and hence the elastic energy is replenished to the sliding tip. This results in little total loss of energy in the sliding process and thus a low friction. When the polymer is in the rubbery state, even though the deformation (mainly plastic) cannot recover quickly due to the long recovery time of the polymer, the friction still remains very small because less dissipation energy is needed to produce the front rim due to the small Young’s modulus. On the other hand, as the polymer undergoes the glass-to-rubber transition, the energy required to form the front rim is larger than that for the rubbery state, and this energy cannot be restored to the sliding tip during contact due the long recovery time. This leads to a friction peak at the transition between the glassy and rubbery states. The broad peaks discernible in the friction curves of Figure 5 resemble those observed in other polymer films.19,20 It is interesting to note that the peak position differs between curves obtained with different loads. In particular, the higher the load, the further the peak shifts toward the high scan rate side. D. Heating Effect at the Sliding Contact. Three causes may produce shifts in the position of the friction peak with external load. One is the presence of a surface layer that has lower Tg than the bulk.3 When the external load is increased, the AFM tip penetrates deeper into the film where the probed Tg progressively approaches the bulk value. In this picture, one expects the Tg to increase with increasing external load. Correspondingly, the friction peaks should shift to lower scan rates. But this is clearly contrary to the experimental observation. Therefore, a mobile surface layer cannot be responsible for the observed shift in the friction peak position. The second possible cause is a pressure effect, which may lead to suppression of molecular relaxations, resulting in an enhancement in the Tg of the polymer.33 This effect has been reported previously in AFM studies of polymer films. By correlating the nanowear patterns on a PS film surface induced by scanning to viscoelastic responses, Schmidt et al. deduced that the Tg of the PS film was increased by ∼26 °C under an effective tip pressure of 84 MPa.34 Independently, Gracias et al. also found evidence of up to a 20 °C increase in the Tg of polypropylene thin films when data obtained by sharp tips (radius ∼ 50 nm) were compared to data obtained by blunt tips (radius ∼ 100 nm).35 In accordance, one would expect the pressure effect to cause the friction peak to shift to lower scan rates with increased external loads. But again, the prediction is inconsistent with experiment. The absence of the pressure effect is not surprising as the maximum load used in this experiment, ∼50 nN, produces a pressure of only ∼6.4 MPa, which is 1 order of magnitude smaller than in the other experiments. The third possible cause is a heating effect, which comes from the friction work done by the tip to the sample surface that causes an elevation in the local temperature of the scanned area.18,36 The larger the load, the higher the increase in local temperature one should expect. Assuming that the Tg of the polymer film was unchanged by the tip pressure, if the external load is higher, the glass-to-rubber transition should occur at lower apparent temperatures and correspondingly the friction peak should shift to higher scan rates. This is in qualitative agreement with the experimental result of Figure 5. (35) Gracias, D. H.; Zhang, D.; Lianos, L.; Ibach, W.; Shen, Y. R.; Somorjai, G. A. Chem. Phys. 1999, 245, 277. (36) Haugstad, G.; Gladfelter, W. L.; Jones, R. R. J. Vac. Sci. Technol., A 1996, 14, 1864.

Wang et al.

Figure 6. (a) Friction data vs temperature at various loads. The dashed lines are Gaussian curves fitted to the data near the peaks. Note that the friction peak in each curve shifts to lower temperatures with increased load. (b) Main panel: Friction peak temperature vs external load for scan sizes of 300 and 100 nm. Inset: Friction peak scan rate deduced from Figure 5 vs friction peak temperature deduced from (a). Both are from measurements with scan size ) 100 nm. The dashed line is calculated from νpeak(59.0 °C) × aT(T)/aT(59.0 °C).

We provide further support for the significance of the heating effect on the position shift of the friction peak. Shown in Figure 6 are the results from the temperature dependence study of friction, plotted as a function of temperature for fixed scan rate. As one can see, friction peaks appear at temperatures slightly higher than Tg, accountable by the finite scan rate of the measurement. In a comparison of the friction curves obtained at different loads (Figure 6a), it is immediately evident that the peak position moves to lower temperatures with larger loads. The friction peak position as a function of external load was plotted in Figure 6b for scan sizes equal to 100 and 300 nm. Clearly, the peak position continuously shifts toward lower temperatures as the external load is increased. Moreover, at any given external load, the friction peak obtained from a larger scan size always occurs at a higher temperature, which strongly suggests sample heating to be associated with the observed scan size effect. The correlation between the peak temperature (from Figure 6a) and peak scan rate (from Figure 5) is depicted in the inset of Figure 6b (open squares). The fact that high peak temperatures are correlated to small scan rates is reminiscent of the time-temperature superposition relation. We have plotted in the same graph νpeak(T) ) νpeak(59.0 °C) × aT(T)/aT(59.0 °C) (dashed line). Good agreement with the experimental data (Figure 6b) provides compelling evidence that the heating effect is the origin of the peak position shifts. One may perceive the heating effect as in the following. As the AFM tip scans across the polymer surface at a constant scan rate, the heat dissipation produced by friction leads to a temporal increase in the temperature, ∆T, local to the point in contact with the tip. One expects ∆T to be independent of the scan size immediately after

Dynamic Study of Polymer Films

the tip moved past. This implies the local temperature of the point to be T ) T0 + ∆T, where T0 is the averaged temperature of the sample surface. During the elapsed time, t, before the tip returns to the same site, ∆T should decrease due to heat transfer to the nearby ambience.37 In this experiment, the elapsed time is the time it takes the AFM tip to complete one back-and-forth cycle. Obviously, the elapsed time is longer for a larger scan size if the scan rate is kept constant. As a result, as the scan size becomes smaller, a larger fraction of the temperature rise at a given site can propagate to affect subsequent friction measurements, and hence a bigger heating effect is produced. This explains why the friction peak obtained from a smaller scan size always occurs at a lower temperature T0 than that from a larger scan size for any given external load (Figure 6b). The heating effect at a sliding contact is a general phenomenon of the macroscopic world when the work from friction cannot be dissipated fast enough. However, the heating effect at microscopic sliding contacts has seldom been investigated even though its existence is generally recognized. To the best of our knowledge, Haugstad et al. were the first to report the heating effect from tribological measurements.18,36 In particular, the heating effect was demonstrated to cause position shifts in the friction peak, which the authors used to account for the scan size effects they observed in FFM measurements.18 While we have also found similar position shifts of the friction peak from different scan sizes (Figure 6a), a closer look will find these position shifts to be uncorrelated to the scan size effect displayed in Figure 1a; namely, a decreased scan size leads to reduction in the friction force. The use of large applied loads also resulted in suppression of the measured friction. For example, when the applied load was increased by 5 times, the peak friction was increased by only ∼3.5 times (Figures 5 and 6a). One possible explanation for this observation is the accumulation of the polymer onto the tip from repeated scanning causing changes in the nature of the sliding contact. It is, however, not obvious whether a change in the scan size should affect the accumulation of polymer onto the tip or produce any other effect that should lower the friction force. While the presently observed scan size effect certainly deserves further investigation, we shall leave it as the subject of a future study. E. Dynamics of the Polymer Film. Taking the friction peak temperature to be Tg, the above results show that many experimental parameters, such as scan size and external load, may have artificial influence on the measured Tg. From this point of view, merely taking note of the friction peak temperatures may not be sufficient. One should also look at the shift factors as they contain essential dynamic information about the sample, namely, the temperature dependence of the relaxation time. In Figure 7, the shift factors, aT, used to construct the friction master curve at a load of 40 nN were plotted versus 1/T (solid squares). To compare the dynamic behavior between the thin film and the bulk, the shift factors of the bulk polymer obtained from shear modulus measurements are also shown as a solid line.30 At first glance, there is a noticeable difference between the two data sets. This is in contrast to the shift factors we found for PtBuA thin films by AFM adhesion measurement, in which no significant difference between data of thin films and the bulk was found.30,32 The present difference is due to a subtle difference in the definition of the shift factors in the two cases. In the bulk case, aT is defined as aT(f) ∼ (37) Bejan, A. Heat Transfer; John Wiley & Sons: New York, 1993.

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Figure 7. Shift factor aT vs 1/T. The dashed-dotted line with filled squares is the aT(v) of a PtBuA film at a load of 40 nN. The open symbols denote aT(f) from FFM measurements at various external loads. The solid line is aT(f) of the bulk obtained by shear modulus measurements.

f(Tref)/f(T), where f(T) and f(Tref) are the (shear modulus) measurement frequencies at temperatures T and Tref, respectively. On the other hand, aT in the thin film case is defined as aT(v) ∼ v(Tref)/v(T), where v(T) and v(Tref) are the scan rates at temperatures T and Tref, respectively. It is meaningful only if the two definitions have identical temperature dependence.20,24 It has been pointed out that the measurement frequency in friction measurements is essentially f ∼ v/2a.4 Using eq 3 for the radius, a, of the contact area, we obtain the relationship between the two different definitions of the shift factor:

aT(f) )

f(Tref) f(T)

E21/3(Tref)

) aT(ν)

E21/3(T)

(7)

Since E2(T) (the elastic modulus of the polymer) decreases drastically when the polymer transfers from the glassy to the rubbery state, it is not surprising that the two sets of shift factors have notably different temperature dependences. According to eq 7, aT(f) is larger than aT(v) if T > Tref but is smaller than aT(v) if T < Tref. By use of the known elastic modulus data of PtBuA,30 a conversion from aT(v) to aT(f) can be made. However, we caution that the conversion is subject to uncertainty from the potential difference in mechanical properties between the polymer surface and the bulk. Nonetheless, the present attempt serves to show the qualitative effect due to the correction suggested by eq 7. The converted shift factors aT(f) from friction measurements at different loads are plotted in Figure 7 as various open symbols as labeled. It is apparent that all aT(f) values of the polymer film are nearly independent of the external load and become much better approximations to the bulk data after the conversion. It has been demonstrated that FFM is suitable for the detection of the glass-to-rubber transition of polymer films.4,19,20 In contrast to most previous work wherein only a single load was used,4,20 we have exploited a large range of external loads to investigate the depth dependence in the dynamics of the polymer. Assuming that the AFM has a spherical apex with radius R, the penetration depth of the tip into the polymer film, δ, is given by δ ) R - (R2 - a2)1/2. Obviously, a small external load would result in a small penetration. For example, with ν ) 0.5, E ∼ 0.6 Gpa, and γ ) 24 erg/cm2 for glassy PtBuA30 and R ∼ 50 nm, δ increases from 1.53 to 2.84 nm when the external load is increased from 10 to 50 nN. This indicates that a higher sensitivity on the dynamic behavior of the polymer film surface can be achieved by using smaller external loads. Thus, from the depth dependence (or the

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external load dependence) of the dynamical behavior, one should be able to distinguish the surface mobile layer if it existed.3 Kajiyama et al. have carefully studied the surface relaxation process of PS thin films.26 From the friction measurements of PS films with Mn ∼ 140K Da, they found that the friction peak occurred at 373 K and the activation energy for the glass-to-rubber transition was about 220 kJ/mol. Both values are smaller than those of the bulk.19,26 The friction studies on poly(methyl methacrylate) (Mn ∼ 60K Da) films by Hammerschmidt et al. have also reached similar conclusions.20 While both groups attributed their observations to the higher molecular mobility at the free surface due to enrichment of the polymer chain end groups, an enhancement in the molecular mobility at the free surface and hence a depression in the surface Tg is in fact circumstantial. For example, using shear modulated force microscopy, Ge et al. have found little enhanced molecular motion at the free surface of PS thin films with different thicknesses and different molecular weights.38 If the chain end group has a higher surface energy than the chain segment, the end groups will remain inside the film body so that no enhancement in the surface mobility from the chain end group can result.39 From results of the present dynamic friction measurements with different external loads on a PtBuA film (Figure 7), we conclude that there is no noticeable enhanced segregation of the polymer chain ends to the free surface, nor existence of a mobile surface layer in PtBuA. This finding is in agreement with our previous AFM adhesion measurements of the same system.30,32 (38) Ge, S.; Pu, Y.; Zhang, W.; Rafailovich, M. Phys. Rev. Lett. 2000, 85, 2340. (39) Tanaka, K.; Jiang, X. Q.; Nakamura, K.; Takahara, A.; Kajiyama, T. Macromolecules 1998, 31, 5148.

Wang et al.

Conclusion We have carried out a detailed FFM study on PtBuA thin films at various temperatures, scan sizes, scan rates, and external loads. The relationship between friction and external load shows a nearly linear dependence at low temperatures but a sublinear dependence at high temperatures. Such behaviors can be attributed to the drastic decrease in the elastic modulus of the polymer resulting from the transition to the rubbery state from the glassy state. A series of friction master curves with various external loads were obtained, in which a friction peak, indicating the glass-to-rubber transition of the polymer, was clearly discernible. Moreover, the friction peak was found to shift toward higher scan rates as the external load was increased. We also found similar friction peaks in the friction versus temperature plots, in which the friction peak shifted to the low-temperature side when the external load was increased or the scan size decreased. In all cases, the observed shifts in the friction peak are consistent with an effect from heating. By comparison of the shift factors of the polymer film with those of the bulk, the microscopic dynamic behavior of the film was found to be independent of the probe depth from the film surface, a result demonstrating no enhanced molecular motion at free surface of PtBuA, in keeping with our previous findings using AFM adhesion measurements. Acknowledgment. We acknowledge the financial support of the Hong Kong University of Science and Technology through the William Mong Solid State Cluster Laboratory and the High Impact Area Fund as well as from the Research Grant Council of Hong Kong through Grant No. HKUST6139/97P. LA020270Q