Factors Affecting the Height and Phase Images in Tapping Mode

were examined with tapping mode atomic force microscopy (AFM) using various values ... and phase images of PPO/PES blend samples, the relative contras...
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Langmuir 1997, 13, 3807-3812

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Factors Affecting the Height and Phase Images in Tapping Mode Atomic Force Microscopy. Study of Phase-Separated Polymer Blends of Poly(ethene-co-styrene) and Poly(2,6-dimethyl-1,4-phenylene oxide) G. Bar,* Y. Thomann, R. Brandsch, and H.-J. Cantow Freiburger Materialforschungszentrum, Stefan-Meier-Strasse 21, D-79104 Freiburg, Germany

M.-H. Whangbo* Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204 Received January 29, 1997X Blends of two polymers, poly(ethene-co-styrene) (PES) and poly(2,6-dimethyl-1,4-phenylene oxide) (PPO), were examined with tapping mode atomic force microscopy (AFM) using various values of the driving amplitude A0 and set-point amplitude ratio rsp ) Asp/A0, where Asp is the set-point amplitude. In height and phase images of PPO/PES blend samples, the relative contrast of chemically different regions depends sensitively on the rsp and A0 values. As the tip-sample force is increased from small to large, both phase and height images of PPO/PES blend samples can undergo a contrast reversal twice. This makes it difficult to assign the features of height and phase images to different chemical components without performing additional experiments. Phase and height images were interpreted by analyzing several factors that affect the dependence of phase shift and amplitude damping on rsp and A0.

1. Introduction Since its invention, atomic force microscopy (AFM)1 has become a very powerful tool for studying surface structures from the micron scale to the atomic scale.2 In contact mode AFM, the probe tip is mounted on a cantilever and scans over the surface of a sample while maintaining a contact with the surface. The “topographic” information about the surface is then deduced by measuring the cantilever deflection during scanning. However, the tip can exert considerable forces to the sample surface, thereby causing sample deformation, so that the height images may not represent the true topographic information of the sample surface. For soft samples such as polymers or biological specimens, the tip-force may induce an irreversible destruction of the surface so that imaging itself might become impossible.3 To overcome such difficulties, tapping mode AFM was introduced.4 In this method the cantilever oscillates vertically near its resonance frequency, so that the tip makes contact with the sample surface only briefly in each cycle of oscillation. As the tip is brought close to the sample surface, the vibrational characteristics of the cantilever vibration (e.g., the amplitude, resonance frequency, and phase angle of vibration) change due to the tip-sample interaction. Usually, the feedback mechanism of tapping mode AFM is controlled by the set-point amplitude ratio rsp ) Asp/A0, where A0 is the amplitude of the free oscillation and Asp is the set-point amplitude such that during scanning the observed amplitude of oscillation is maintained at Asp by X

Abstract published in Advance ACS Abstracts, June 15, 1997.

(1) Binnig, G.; Quate, C. F.; Gerber, C. Phys. Rev. Lett. 1986, 56, 930. (2) For reviews, see: (a) Burnham, N. A.; Colton, R. J. In Scanning Tunneling Microscopy and Spectroscopy; Bonnell, D. A., Ed.; VCH: New York, 1993; Chapter 7. (b) Magonov, S. N.; Whangbo, M.-H. Surface Analysis with STM and AFM; VCH: Weinheim, 1996. (c) Sarid, D. In Scanning Force Microscopy; Lapp, M., Stark, H., Eds.; Oxford University Press: New York, 1991. (3) (a) Weisenhorn, A. L.; Maivald, P.; Butt, H.-J.; Hansma, P. K. Phys. Rev. B 1992, 45, 11226. (b) Hoh, J. H.; Hansma, P. K. Trends Cell. Biol. 1992, 2, 208. (4) Zhong, Q.; Innis, D.; Kjoller, K.; Elings, V. B. Surf. Sci. Lett. 1993, 290, L688.

S0743-7463(97)00091-7 CCC: $14.00

adjusting the vertical position of the sample. Because of its advantages, tapping mode AFM has been used to measure many organic and biological samples.5 A recent development of tapping mode AFM allows one to detect shifts in phase angles of vibration when the oscillating cantilever interacts with the sample surface.6 The detection of phase angle shifts provides enhanced image contrasts, especially for heterogeneous surfaces. Recently, the tip-sample interaction leading to phase imaging in tapping mode AFM has been studied theoretically and experimentally.7-12 Since tapping mode AFM is widely used to examine polymer surfaces, it is essential to investigate how image contrasts depend on experimental conditions. In the present work, we probe this problem by studying blends of two polymers, poly(etheneco-styrene) (PES) and poly(2,6-dimethyl-1,4-phenylene (5) (a) Radmacher, M.; Tillmann, R. W.; Fritz, M.; Gaub, H. E. Science 1992, 257, 1900. (b) Umemura, K.; Arakawa, H.; Ikai, A. Jpn. J. Appl. Phys. 1993, 32, L1711. (c) Stocker, W.; Beckmann, J.; Stadler, R.; Rabe, J. P. Macromolecules 1996, 29, 7502. (d) Bustamante, C.; Keller, D. Phys. Today, 1995, December, 32. (e) Howard, A. J.; Rye, R. R.; Houston, J. E. J. Appl. Phys. 1996, 79, 1885. (f) Ho¨per, R.; Workman, R. K.; Chen, D.; Sarid, D.; Yadav, T.; Withers, J. C.; Loutfy, R. O. Surf. Sci. 1994, 311, L731. (6) Chernoff, D. A. High Resolution Chemical Mapping Using Tapping Mode AFM with Phase Contrast; In Proceedings Microscopy and Microanalysis, 1995. (7) Magonov, S. N.; Elings, V.; Papkov, V. S. Polymer 1997, 38, 297. (8) (a) Magonov, S. N.; Elings, V.; Whangbo, M.-H. Surf. Sci. Lett. 1997, 375, L385. (b) Whangbo, M.-H.; Magonov, S. N.; Bengel, H. Probe Microsc. in press. (c) Magonov, S. N.; Cleveland, J.; Elings, V.; Denley, D.; Whangbo, M.-H. Surf. Sci., submitted for publication. (9) (a) Spatz, J. P.; Sheiko, S.; Mo¨ller, M.; Winkler, R. G.; Reineker, P.; Marti, O. Nanotechnology 1995, 6, 40. (b) Winkler, R. G.; Spatz, J. P.; Sheiko, S.; Mo¨ller, M.; Reineker, P.; Marti, O. Phys. Rev. B 1996, 54, 8908. (10) (a) Sarid, D.; Ruskell, T. G.; Workman, R. K.; Chen, D. J. Vac. Sci. Technol., B 1996, 14, 864. (b) Sarid, D.; Chen, D.; Workman, R. K. Comput. Mater. Sci. 1995, 3, 475. (c) Chen, D.; Workman, R. K.; Sarid, D.; Ho¨per, R. Nanotechnology 1994, 5, 1999. (11) Anczykowski, B.; Kru¨ger, D.; Fuchs, H. Phys. Rev. B 1996, 53, 15485. (12) Burnham, N. A.; Behrend, O. P.; Oulevey, F.; Gremaud, G.; Gallo, P.-J.; Gourdon, D.; Dupas, E.; Kulik, A. J.; Pollock, H. M.; Briggs, G. A. D. Nanotechnology in press.

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oxide) (PPO), with tapping mode AFM. This work is focused on the question of how to interpret contrast variations in images of tapping mode AFM. The blending behavior of PES with PPO and the morphologies observed for the blends will be discussed elsewhere. 2. Experimental Section The PES copolymer was prepared using the procedure described elsewhere.13 The PES we prepared has a styrene content of about 30 mol %. A high molecular weight PPO sample was purchased from BASF. PES/PPO polymer blends (70:30 wt %) were prepared from a solution of both components in xylene (10% concentration) at 130 °C. The solution was then deposited on a glass substrate and dried under vacuum for 24 h at 150 °C. The estimated thickness of the resulting films was several microns as judged from light microscopy. The flat surfaces of films on the side of the film-glass interface were examined by AFM. These surfaces, after being mounted on the sample support, were dried again under vacuum at room temperature to remove contaminants on the surface. To investigate the miscibility of PES with PPO, the prepared samples were examined using differential scanning calorimetry, optical microscopy, and wide angle X-ray scattering. These measurements indicate that although polystyrene is miscible with PPO at all blend ratios,14 PES and PPO are not miscible but compatible. AFM experiments were performed with a Nanoscope III scanning probe microscope. AFM images were obtained under ambient conditions while operating the instrument in the tapping mode and contact mode. We used commercial Si cantilevers with force constants of 0.02-0.7 N/m for contact mode AFM measurements and those with force constants of 13-70 N/m for tapping mode AFM measurements. Height, amplitude, and phase images were recorded simultaneously using tapping mode AFM. Images were taken at the fundamental resonance frequency of the Si cantilevers. The relative phase shifts (with respect to the phase angle of the free cantilever at the resonance frequency ω0) were measured as a function of the set-point ratio rsp ) Asp/A0 at several different A0 values. Images were recorded with typical scan speeds of 1/2 - 1 line/s using a scan head with a maximum range of 170 × 170 µm2 or 16 × 16 µm2 showing the same results. Data presented here were obtained on the same surface area using a scan head with a maximum range of 170 × 170 µm2.

3. Dependence of Relative Image Contrast on A0 and rsp Height and phase images recorded for a surface of a two-component sample exhibit contrast variations which depend on the experimental parameters A0 and rsp in a rather complex way. Understanding these variations will allow us to assign different contrast regions of an image to different material components on the sample surface. To achieve this objective, it is necessary to examine height and phase images as a function of A0 and rsp systematically. The height and phase images recorded with A0 ≈ 15 nm are shown in Figure 1. At light tapping (rsp ) 0.8), the height image does not show the presence of any structures, while the phase image reveals the presence of domain structures in dark contrast (Figure 1a). At moderate tapping (rsp ) 0.7-0.4), both the height and phase images show domain structures in dark contrast (Figure 1b). At hard tapping (rsp ) 0.2), the contrast difference between the domain structures and their surrounding is enhanced in both the height and phase images (Figure 1c). Figure 2 shows the height and phase images recorded with A0 ≈ 45 nm. At light tapping, the contrast of the phase image is similar to that recorded with A0 ≈ 15 nm (Figures 1a and 2a), but the presence of domain structures (13) (a) Sernetz, F. G.; Mu¨lhaupt, R.; Waymouth, R. M. Macromol. Chem. Phys. 1996, 197, 1071. (b) Y. Xu.; Sernetz, F. G.; Thomann, R.; Kressler, J.; Mu¨lhaupt, J. Macromol. Chem. Phys., in press. (14) MacKnight, W. J.; Karasz, F. E.; Fried, J. R. In Polymer Blends; Paul, D. R., Newmann, S., Eds.; Academic Press: San Diego, CA, 1978; p 234 ff.

Figure 1. Height (left) and phase (right) images of a PES/PPO sample using A0 ) 15 nm: (a) rsp ) 0.8; (b) rsp ) 0.4; (c) rsp ) 0.2. In the height images the contrast covers height variations in the 5 nm range in parts a and b, and in the 10 nm range in part c. In the phase images the contrast covers phase angle variations in the 5° range in part a, and in the 30° range in parts b, and in c. The images were subjected to a plane fitting procedure. The scan size was 1.8 µm × 1.8 µm.

is seen in the height image. At moderate tapping, the domain structures appear brighter than the surroundings in the phase image, and the contrast difference between the domain structures and the surroundings is lost in the height image (Figure 2b). At hard tapping, the domain structures appear dark in both the height and phase images (Figure 2c). The height and phase images recorded with A0 ≈ 75 nm are presented in Figure 3. At light tapping the height and phase images are similar to those recorded with A0 ≈ 45 nm (Figures 2a and 3a). At moderate tapping the domain structures appear bright in both the height and phase images (Figure 3b). At hard tapping the image contrast is reversed in both the height and phase images (Figure 3c). As shown above, the relative contrast of chemically different regions depends sensitively on the rsp and A0 values. This makes it difficult to assign the features of height and phase images to different chemical components, unless additional experiments are carried out. It is most striking that, as a function of rsp, both phase and height images can undergo a contrast reversal twice. 4. Assignment of Image Features To determine whether the domain structures of phase images correspond to the PES or PPO component, we

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Figure 2. Height (left) and phase (right) images of a PES/PPO sample using A0 ) 45 nm: (a) rsp ) 0.8; (b) rsp ) 0.4; (c) rsp ) 0.1. In the height images the contrast covers height variations in the 5 nm range in parts a and b and in the 10 nm range in part c. In the phase images the contrast covers phase angle variations in the 5° range in part a and in the 30° range in parts b and c. The images were subjected to a plane fitting procedure. The scan size was 1.8 µm × 1.8 µm.

Figure 3. Height (left) and phase (right) images of a PES/PPO sample using A0 ) 75 nm: (a) rsp ) 0.85; (b) rsp ) 0.4; (c) rsp ) 0.1. In the height images the contrast covers height variations in the 5 nm range in parts a and b and in the 10 nm range in part c. In the phase images the contrast covers phase angle variations in the 5° range in part a and in the 30° range in parts b and c. The images were subjected to a plane fitting procedure. The scan size was 1.8 µm × 1.8 µm.

proceed as follows: PPO and PES have glass transition temperatures (Tg) of 210 and 6 °C, respectively. These two Tg values were confirmed for samples of PES/PPO blends prepared in our work. Furthermore, in the 50:50 blend of PES/PPO, the PPO component was found to crystallize. Thus, PPO and PES are the rigid and compliant components of the blends, respectively. To determine which region, the domain structure or the surrounding, is rigid, force-versus-distance curves (hereafter referred to as force curves) were determined for the two different regions. (Force curves are obtained by monitoring the cantilever’s deflection as the cantilever is brought toward and then away from the sample surface.) The slope and shape of the repulsive part of force curves provide information about the local contact stiffness of the examined sample surface.15 Typical force curves determined with the tip located over a domain structure and over a surrounding are shown in parts a and b, respectively, of Figure 4. The curve for the domain structure (Figure 4a) is much steeper than that for the

surrounding (Figure 4b). The tip-induced local indentation of a sample surface is larger on a compliant region than on a rigid region. Therefore, the force curve should be less steep on a more compliant region because, for the cantilever to feel a certain level of indentation force and hence reach a certain level of deflection, the cantilever must travel more toward the surface on a more compliant region. Figure 4b shows a strong hysteresis between the loading and unloading curves typical for compliant materials15 caused by the larger tip indentation and elastic/ plastic deformation of the sample. Consequently, the domain structures correspond to the rigid component of a PES/PPO blend, i.e., PPO. Further the compliant component shows a larger pull-off force than the rigid component.

(15) (a) Burnham, N. A.; Kulik, A. J.; Gremaud, G. In Procedures in Scanning Probe Microscopy; Colton, R. J., Ed.; Wiley: New York, in press. (b) Hues, S. M.; Draper, C. F.; Colton, R. J. J. Vac. Sci. Technol., B 1994, 12, 2211. (c) VanLandingham, M. R.; McKnight, S. H.; Palmese, G. R.; Eduljee, R. F.; Gillespie, J. W.; McCullough, R. L. J. Mater. Sci. Lett. 1997, 16, 117.

5. Factors Influencing the Image Contrast To gain insight into why the image contrast depends on A0 and rsp as described in section 3, it is necessary to examine how the cantilever’s vibrational characteristics are affected by tip-sample interactions in tapping mode AFM. A freely oscillating cantilever is characterized by the spring constant k, the quality factor Q, the driving amplitude A0, and the resonance frequency ω0.16 The amplitude of a freely oscillating cantilever, Af(ω), has a

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mechanism of tapping mode works in such a way that a surface region of larger amplitude damping is recorded as higher in topography and hence brighter in height image. In considering a heterogeneous surface, it is important to recall that the relative amplitude damping on different surface regions is determined by the tip-sample force interaction discussed above and by their height differences. The phase angle of the free cantilever, φf(ω), is a steadily increasing function of ω with an inflection point at ω0. The phase angle of the interacting cantilever, φi(ω), is the same as φf(ω) except that its inflection point is at ωeff. Therefore, when measured at ω0, the phase shift, ∆φ(ω0) ) φf(ω0) - φi(ω0), is negative when σ < 0 and positive when σ > 0. When σ is very small in magnitude compared with k, the phase shift ∆φ(ω0) is given by8

∆φ(ω0) ≈

Qσ k

∝ x〈A〉E*

Figure 4. Force curves recorded on the (a) dark and (b) bright regions visible in Figure 1b. They show the cantilever’s deflection (vertical axis) as the cantilever is brought toward and then pulled away from the sample surface (horizontal axis).

peak centered at ω0 with the peak height A0. To examine how the tip-sample interaction modifies the vibrational characteristics of the cantilever, we consider several limiting cases. A. Large A0 and Large rsp: Weak Tip-Sample Interaction. During each tapping cycle under ambient conditions the tip may go through several tip-sample force regimes (e.g., van der Waals and capillary forces, which are attractive, and the indentation force, which is repulsive). When both A0 and rsp are large, the tip-sample interaction is weak, and it is reasonable to assume that the tip-sample force interaction changes the force constant of the cantilever to an effective value keff ) k + σ.8,17 Here σ is the sum of the force derivatives of all attractive and repulsive forces acting on the cantilever.8 That is, the tip-sample interaction alters the resonance frequency of the cantilever to a new resonance frequency ωeff. To a first approximation, the amplitude of the interacting cantilever, Ai(ω), is obtained by shifting the peak of Af(ω) to a higher frequency (ωeff > ω0) when σ > 0 and to a lower frequency (ωeff < ω0) when σ < 0.8,17 Thus, when measured at ω0, the amplitude damping, ∆A(ω0) ) Af(ω0) - Ai(ω0), is written as18

(Qσ/k)2 ∆A(ω0) ) A0 ≈ A0(Qσ/k)2 2 1 + (Qσ/k)

(1)

where the approximate relationship holds if Qσ is much smaller in magnitude than k. Thus the amplitude damping ∆A(ω0) increases with an increasing the difference between keff and k; i.e., σ ) k - keff. The feedback (16) Rao, S. S. Mechanical Vibrations, 3rd ed.; Addison-Wesley: New York, 1995. (17) (a) Martin, Y.; Williams, C. C.; Wickramasinghe, H. K. J. Appl. Phys. 1987, 61, 4723. (b) Du¨rig, U.; Zu¨ger, O.; Stalder, A. J. Appl. Phys. 1992, 72, 1778. (c) Babcock, K.; Dugas, M.; Manalis, S.; Elings, V. Mater. Res. Soc. Symp. Proc. 1995, 355, 311. (d) Pethica, J. B.; Oliver, W. C. Phy. Scr. 1987, T19, 61. (18) Salmeron, M.; Neubauer, G.; Folch, A.; Tomitori, M.; Ogletree, D. F.; Sautet, P. Langmuir 1993, 9, 3600.

(2a) (2b)

where eq 2b is valid when σ > 0. E* is the effective modulus of the tip-sample system, which is close to Young’s modulus of the sample when the tip is much stiffer than the sample, and 〈A〉 is the contact area A over one cycle of oscillation. B. Small A0: Effect of the Contamination Layer. Under ambient conditions, the contamination layer mainly composed of water is present on all surfaces and leads to a capillary force which attracts the cantilever to the sample surface.2b Thus for small A0 and small rsp, the cantilever’s motion may be dominated by the attractive force, and the tip may become trapped on the sample surface. Oscillating the cantilever under these conditions will make tapping mode AFM similar to force modulation microscopy (FMM). Then, the amplitude of the cantilever vibration will be larger on a stiff than on a compliant region so that, as far as the feedback mechanism is concerned, the stiffer region is lower in height (i.e., darker in height image). C. Large A0 and Moderate/Small rsp: Strong TipSample Interaction. As rsp is reduced at large A0 the cantilever’s behavior is largely dominated by the indentation force and hence by the tip-sample stiffness. For moderate rsp, the more compliant surface region will experience a greater indentation when the cantilever approaches the surface. To maintain a constant amplitude decrease, therefore, the cantilever has to be closer to the sample on a more compliant than on a less compliant surface region. Thus the more compliant surface region will appear lower in height image as far as the feedback mechanism is concerned. When rsp is reduced further (e.g., 0.1), the tip-sample interaction is large and the tip spends a substantial portion of its time in contact with the sample surface, thereby making tapping mode AFM similar to FMM. Then, the stiffer region would be lower in height (i.e., darker in height image), as in the case of small A0. For large A0 and small rsp, the phase shift is determined by the indentation force and hence by the tip-sample stiffness. As tapping mode AFM behaves more like FMM, the phase shift should decrease toward zero because the phase angle of the cantilever oscillation would become closer to that of the driving oscillation. As discussed above and elsewhere,8 the stiffness depends on both the effective Young’s modulus E* and the tip-sample contact area 〈A〉. For large A0 and small rsp, the contribution of the contact area probably dominates over that of E*. Then the compliant region is likely to provide a greater phase shift than does the stiff region.

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Recently it was suggested19 that major factors affecting phase shifts of soft materials are viscoelastic properties and adhesion forces with little participation from elastic properties. However, the relaxation frequencies of viscoelastic polymers are significantly lower than the tapping frequencies typically employed. The location of the transition zone between the rubberlike and glasslike states on the frequency scale is identified where the storage modulus G′ ) 108 dyn/cm2.20 For PES this value for G′ is found at a frequency below 10 kHz. Therefore, it is expected that soft polymers behave as an elastic solid as far as tapping experiments are concerned, and the phase shifts are governed by their stiffness.8b To measure viscoelastic properties of soft materials, measurements should be performed with tapping frequencies which are comparable to their relaxation frequencies (e.g., a few kilohertz as in force modulation and other related modes).21 6. Image Analysis A. Dependence of the Phase Shift on A0 and rsp. Figure 5summarizes how the phase shifts ∆φ(ω0) over the PPO (rigid) and PES (compliant) regions of a PPO/PES blend are affected by the amplitude A0 and the set-point ratio rsp. Every ∆φ(ω0) versus rsp plot of Figure 5 was obtained by averaging ∆φ(ω0) versus rsp plots recorded at several different places on the PES or PPO region. In general, the phase shifts on the two regions become more positive as A0 increases from 15 to 45 to 75 nm, because at a larger amplitude A0 the indentation force contributes more to the phase shift than do attractive forces. At A0 ≈ 15 nm the phase shift is negative on PES and on PPO so that the overall force on the cantilever is attractive (Figure 5a). The phase shift is more negative on PPO than on PES for entire rsp values. The latter means that the PPO region leads to stronger attractive interactions than does the PES region, which is reasonable because the PPO region provides a greater capillary force (Note that the PPO region is more hydrophilic than the PES region due to the oxygen atoms). The ∆φ(ω0) versus rsp curves have a “V” shape. For rsp < ∼0.4, ∆φ(ω0) increases with decreasing rsp most likely because the effect of the indentation force becomes enhanced although this effect is overshadowed by the attractive forces. For rsp > ∼0.4, ∆φ(ω0) decreases with decreasing rsp, most likely because the cantilever becomes more strongly trapped to the surface by the contamination layer, but the effect of the indentation force is negligible. At A0 ≈ 45 nm the phase shift is positive on PPO for ∼0.25 < rsp < ∼0.65 but negative for other rsp values (Figure 5b). On PES the phase shift is negative for rsp > ∼0.25 but positive for rsp < ∼0.25. For ∼0.25 < rsp < ∼0.65, the phase shift is higher on PPO than on PES, thereby suggesting that the stiffness (due to the indentation force) is the primary factor governing the cantilever’s response in this region. At A0 ≈ 75 nm the phase shift behavior is similar to that at A0 ≈ 45 nm, except that the phase shift is positive on PPO and PES for rsp < ∼0.8 and larger on PPO for a much wider range of rsp values (Figure 5c). B. Image Analysis. We first examine the rsp dependence of the phase images in Figures 1-3 by analyzing the data recorded at A0 ≈ 45 nm. For rsp > ∼0.65 the phase shift is negative on PPO and PES and is more negative on PPO (Figure 5b), so that ωeff(on PPO) < ωeff(on PES) (19) Tamayo, J.; Garcia, R. Langmuir 1996, 12, 4430. (20) Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; Wiley: New York, 1980. (21) Overney, R. M.; Leta, D. P.; Pictroski, C. F.; Rafailovich, M.; Liu, Y.; Quinn, J.; Sokolov, J.; Eisenberg, A.; Overney, G. Phys. Rev. Lett. 1996, 76, 1272.

Figure 5. Plots of the phase shift versus set-point amplitude ratio rsp on PES and PPO recorded with (a) A0 ) 15 nm, (b) A0 ) 45 nm, and (c) A0 ) 75 nm.

< ω0. The latter means that the PPO region leads to more attraction than does the PES region. Since ωeff(on PPO) < ωeff(on PES) < ω0, the PPO region is predicted to be darker than the PES region in phase image according to eq 2a (for negative σ), in agreement with experiment (Figure 2a, right). As rsp is decreased, the phase image undergoes a contrast reversal twice (at rsp ≈ 0.25 and 0.65) (see Figures 2b and c and 5c). In the region ∼0.25 < rsp < ∼0.65, the phase shift is more positive on the stiff PPO region. This suggests that the effect of the indentation force is more strongly felt on the stiff PPO region and that the stiffness is mainly determined by the effective Young’s modulus. In the region rsp < ∼0.25 the phase shift is more positive on the compliant PES region, which suggests that the effect of the indentation force is more strongly felt on the compliant PES region and that the stiffness is mainly determined by the contact area. As discussed in section 5B for small rsp, the tip will be more affected by the attractive capillary force over the PPO region, further reducing the phase shift. When rsp varies from large to small values, the phase images determined at large A0 (∼75 nm) undergo an image reversal twice, as in the case of A0 ≈ 45 nm. However, at large A0 (∼75 nm), the contribution of the indentation force is larger for a much wider range of rsp values. The phase images recorded

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at A0 (∼15 nm) do not show image reversal. This means that the phase shift is dominated by the attractive tipsample forces. Let us now analyze the rsp-dependence of the height images in Figures 1-3 using the data recorded at A0 ≈ 45 nm. For rsp > ∼0.65, ωeff(on PPO) < ωeff(on PES) < ω0, as already mentioned. Thus the PPO region is predicted to be brighter than the PES region in height image according to eq 1, in disagreement with experiment (Figure 2a, left). This discrepancy can result if the PPO region is lower in topography than the PES region, which is possible because the mounted films were dried in vacuum at room temperature (see Experimental Section); during the drying process, the PES part is likely to ooze out slightly on the surface, since its Tg is below room temperature. At rsp ) 0.4 where the height image of Figure 2b was recorded, Figure 5b suggests that ωeff(on PPO) > ωeff(on PES) > ω0. According to eq 1, therefore, the PPO region is expected to be brighter than the PES region. However, the PPO and PES regions have no contrast difference in height image (Figure 2b, left). This is consistent with the view that the PPO region is lower in topography than the PES region (see above). When A0 is increased from ∼45 to ∼75 nm, the height images indeed show that the PPO region is brighter than the PES region for all rsp values 0.1 < rsp < 0.85 (Figure 3b, left). This suggests that the effect of the indentation force is strong enough to surmount the effect of the topographic difference between the PPO and PES regions, and the more compliant region appears lower in height because of the larger deformation, as already discussed in section 5C. This reasoning is reasonable because, at rsp ) 0.4 and A0 ≈ 75 nm, ωeff(on PPO) > ωeff(on PES) would be much higher than ω0 (Figure 5c). Finally, it is noted that for very small rsp ) 0.1 (at A0 ≈ 45 and 75 nm) the stiff region PPO is darker in height image (Figures 2c and 3c, left). As discussed in section 5C, this is explained if tapping mode AFM behaves like FMM under these conditions. When A0 is very small (∼15 nm), the stiff region PPO is also darker in height image (Figures 1b and c, left). As discussed in section 5B, this is explained if tapping mode AFM behaves like FMM because the cantilever is trapped on the surface due to the contamination layer.

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7. Concluding Remarks Our tapping mode AFM study shows that in height and phase images of polymer samples with heterogeneous surfaces, the relative contrast of chemically different regions depends sensitively on the rsp and A0 values. As rsp varies from a large to a small value, both phase and height images of PPO/PES samples can undergo a contrast reversal twice. This makes it difficult to assign the features of height and phase images to different chemical components unless additional experiments are carried out. The dependence of phase shift on rsp and A0 can be qualitatively discussed using eq 2 derived under the assumption that the tip-sample force interaction is weak. The dependence of amplitude drop on rsp and A0 is more complex; eq 1 derived under the assumption that the tipsample force interaction is weak has a limited applicability. The amplitude drop can be more strongly affected by factors other than the resonance peak shift induced by the tip-sample interaction. These factors include surface topography and tapping conditions. At very small A0 as well as at very small rsp and large A0, a stiff surface region appears darker than a compliant region; tapping mode AFM becomes similar to FMM under these conditions. Our study indicates that, to obtain images close to the “true” topography of a sample surface, the images should be recorded using a sufficiently high amplitude (e.g., A0 ≈ 45 nm) and as high rsp values as possible. Use of high amplitudes A0 and moderate rsp values provides image contrast caused mainly by the stiffness of a sample surface. In characterizing heterogeneous polymer samples, it is necessary to record height and phase images by systematically varying the driving amplitude and set-point ratio. Otherwise, interpretation of observed image features can become misleading. Acknowledgment. Work at North Carolina State University was supported by the Office of Basic Energy Sciences, Division of Materials Sciences, U.S. Department of Energy, under Grant DE-FG05-86ER45259. LA970091M