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Tapping Scanning Force Microscopy in AirsTheory and Experiment Joachim P. Spatz, Sergei Sheiko, and Martin Mo¨ller* Universita¨ t Ulm, Organische Chemie III-Makromolekulare Chemie, Albert Einstein Allee 11, D-89081 Ulm, Germany
Roland G. Winkler and Peter Reineker Universita¨ t Ulm, Abteilung Theoretische Physik, Albert Einstein Allee 11, D-89081 Ulm, Germany
Othmar Marti Universita¨ t Ulm, Experimentelle Physik, Albert Einstein Allee 11, D-89081 Ulm, Germany Received March 24, 1997. In Final Form: May 28, 1997X Ultrathin layers of micelles of a diblock copolymer with a polystyrene corona and a poly(2-vinylpyridine) core have been studied by tapping scanning force microscopy in air, probing the surface with varying forces depending on the setpoint of the probe and the tapping frequency. The compliance of the core of the micelles was varied by neutralization of the pyridine groups with HAuCl4 and incorporation of small particles. The apparent deformation of the globular micelles was compared with a simple model describing the probe as a forced oscillator which changes its effective spring constant depending on the direct contact with the surface. Consistent with the experiment, the model shows that the deformation and the shift in phase are minimized by tapping on the low-frequency side of the noncontact cantilever resonance.
1. Introduction Besides contact and noncontact scanning force microscopy (SFM) of the surface topography,1 a number of methods have been developed lately which allow probing the surface properties, i.e., lateral force or friction SFM,1 tapping SFM,2 chemical SFM,3 magnetic SFM,4 or peak force modulation SFM.5 In particular tapping scanning force microscopy, TSFM, has become a versatile and widely used technique for the investigation of soft materials and weakly adhering adsorbates.6 Oscillating the tip between contact and noncontact with the surface (tapping) allows the shear forces to diminish during lateral scan movements which are a major cause of destruction of the probed surface.2,6 Still, the interaction of the tapping probe with the surface can be rather strong, and the recorded images can be affected by the frequency and the force with which the surface is probed.7-9 Typically, interaction forces can be varied between 10-6 and 10-11 N.6,10 This can be used * Author to whom correspondence should be addressed. X Abstract published in Advance ACS Abstracts, July 15, 1997. (1) Martin, Y.; Williams, C. C.; Wickramasinghe, H. G. Appl. Phys. 1987, 61, 4723. (2) Zhong, Q.; Inniss, D.; Elings, V. B. Surf. Sci. 1993, 290, L688. (3) Akari, S.; Horn, D.; Keller, H.; Schrepp, W. Adv. Mater. 1995, 7, 549. Yokoyama, H.; Inoue, T. Thin Solid Films 1994, 33, 242. (4) Sarid, D. Scanning Force Microscopy With Applications to Electric, Magnetic, and Atomic Forces; Oxford Series on Optical Sciences; Oxford University Press: New York, 1991. (5) Rosa, A.; Hild, S.; Marti, O. ACS Polym. Preprints 1996, 1, 616. (6) Radmacher, M.; Tillmann, R. W.; Fritz, M.; Gaub, H. E. Science 1992, 257, 1900. Hansma, H. G.; Vesenka, J.; Siegerist, C.; Kelderman, G.; Morrett, H.; Sinsheimer, R. L.; Elings, V.; Bustamante, C.; Hansma, P. K. Science 1992, 256, 1180. (7) Spatz, J. P.; Sheiko, S.; Mo¨ller, M.; Winkler, R. G.; Reineker, P.; Marti, O. Nanotechnology 1995, 6, 40. (8) Winkler, R. G.; Spatz, J. P.; Sheiko, S.; Mo¨ller, M.; Reineker, P.; Marti, O. Phys. Rev. B 1996, 54, 8908. (9) Hoeper, R.; Workman, R. K.; Cheng, D.; Sarid, D.; Yadav, T.; Withers, J. C.; Raouf, O. R. Surf. Sci. 1994, 311, L731. Tamayo, J.; Garcı´a, R. Langmuir 1996, 12, 4430. (10) Magonov, S. N.; Whangbo, M.-H. Surface Analysis with STM and AFM; VCH: Weinheim, 1996.
S0743-7463(97)00311-9 CCC: $14.00
on purpose in order to discriminate local differences in the compliance and the adhesive interaction with the tip.4,10 In the present work we demonstrate variations in the images of a monolayer of globular block copolymer micelles as a function of the setpoint and the tapping frequency. The effective force applied to the surface gives an indication of the depicted deformation of the micelles and which can be compared with a simple model which we proposed recently.7,8 1.1. Model. TSFM is described as a forced oscillator which changes its effective spring constant twice each tapping period, where k*C ) kC is the spring constant of the cantilever system in the noncontact period and k* CS ) kC + kS is the effective spring constant during the contact period with kS refering to the surface stiffness of the specimen. The damping is introduced as dashpots with damping coefficients δC for the cantilever and δs for the sample. The model does not account for adhesive forces.4,13,14 Moreover, elastic deformation of the surface is described by a harmonic potential because the tip experiences attractive and repulsive forces upon approaching the surface. Thus, the model can only give a semiquantitative description of the forces acting onto the substrate. The mathematical description has been described before and can be found in the appendix.7,8 According to the model, the maximum force affected onto the substrate can be estimated by
Fdeformation ) ZdeformationkS
(1)
with
Zdeformation ) A(ω) - ZL A(ω) gives the amplitude of the oscillation without interaction with the substrate and ZL gives the displacement of the equilibrium position of the cantilever in contact with the substrate. © 1997 American Chemical Society
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Figure 1. Deformation of the substrate applied by changing the tapping frequency. The resonance frequency of the cantilever oscillation in air is at 360 kHz. The amplitude curves of the noncontact cantilever oscillation is indicated by the drawn lines. ZL indicates the distance between the equilibrium position of the noncontact cantilever oscillation and the substrate.
Figure 1 gives a numerical simulation of the sample deformation as a function of the tapping frequency. The distance ZL between the equilibrium position of the cantilever and the surface has been set according to the setpoint At, i.e., the amplitude at which the cantilever operates if in direct contact with the surface. Other parameters involved are the drive amplitude of the piezo a0, the stiffness of the substrate kS, and the quality factor of the cantilever QS which can be determined by knowing the resonance amplitude of the noncontact cantilever oscillation or have to be estimated respectively (see Table 1, Appendix). As shown in Figure 1, a different deformation of the surface is predicted, depending on which side of the resonance frequency the tapping frequency is set. This is caused by the increase of the effective spring constant upon contact of the cantilever with the surface and the corresponding shift of the resonance frequency to higher values. At high frequency, there is a step transition in the force and the effective cantilever amplitude at the point where the oscillation of the force cantilever gets too small to reach the surface. Decreasing the distance ZL between the equilibrium position of the cantilever oscillation in noncontact and the substrate from 60 to 55 or 50 nm shifts this transition to higher frequencies, and the surface deformation in contact becomes larger. Experimentally, this is realized by decreasing the tapping amplitude At, i.e., lowering the setpoint. Figure 2 shows the predicted dependence of the peak force and the elastic deformation of the sample, when the stiffness of the sample is increased covering the range between 1 and 10 000 N/m. 2. Experimental Section Sample Preparation. Polystyrene-b-poly(2-vinylpyridine) with DPS-DP2VP ) 300-300 was obtained by sequential anionic polymerization. Toluene selectively dissolves the polystyrene block yielding reverse micelles with a polystyrene corona and a poly(2-vinylpyridine) core. Micellar solutions were prepared by dilution of a stock solution of the block copolymer in absolute toluene to 5 mg/mL. The solution with the polystyrene-b-poly(2-vinylpyridine) micelles was stirred over night with 0.5 equiv of HAuCl4 per 2-VP unit. The gold acid protonates the 2-VP, and 11 the AuCl4 is bounded as a counterion.
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Figure 2. Forces (peak forces) and deformations applied to substrates of different stiffnesses by the oscillating tip during contact at different distances ZL. The left axis refers to the deformation of the substrate (solid signs). The right axis refers to the peak force onto the substrate (open signs).
Figure 3. Plain micelles scanned with minimized (top), high (middle), and again with minimized scan force (bottom). Parameters are: A0 ) 50 nm, Attop/bottom ) 35 nm, Atmiddle ) 20 nm, ft ) 359.570 kHz, fR ) 359.880 kHz. The high force was applied and released at the scan lines indicated by arrows (scan size ) 0.9 × 0.9 µm2). Aqueous gold solution were prepared by using sodium citrate as a reduction agent in water. A solution with block copolymer micelles was intensively mixed with the aqueous gold solution for 30 min, resulting in a pink-violet emulsion. To separate the phases again, the emulsions were allowed to stand overnight. A clear organic phase was obtained where aproximately 10% of the micelles contained a gold particle (φ = 10 nm) stabilized by the polymeric shell.12 Monofilms of the micelles were prepared by dipping a freshly cleaved piece of mica into the solution. Typically, the substrate (11) Spatz, J. P.; Roescher, A.; Sheiko, S.; Krausch, G.; Mo¨ller, M. Adv. Mater. 1995, 7, 731. Spatz, J. P.; Sheiko, S.; Mo¨ller, M. Macromolecules 1996, 29, 3220. Spatz, J. P.; Roescher, A.; Mo¨ller, M. Adv. Mater. 1996, 8, 337. Spatz, J. P.; Mo¨ssmer, S.; Mo¨ller, M. Chem. Eur. J. 1996, 2, 1552. (12) Roescher, A.; Mo¨ller, M. Adv. Mater. 1995, 7, 151. (13) Anczykowski, B.; Kru¨ger, D.; Fuchs, H. Phys. Rev. B 1996, 53, 15485. (14) 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, 1997, in press. (15) Chen, J.; Workman, R. K.; Sarid, D.; Ho¨per, R. Nanotechnology 1994, 5, 199.
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Figure 4. Deformation of block copolymer micelles by increasing the diminution of the tapping amplitude. High scan forces introduce a geometrical artifact as discussed in the text. (a) Minimized force and (b) high force of the same scan area of HAuCl4loaded micelles: fR ) 361.254 kHz, ft ) 360.800 kHz, ∆A(a) ) 15 nm, ∆A(b) ) 30 nm, and scan area ) 0.5 × 0.5 µm2. (c) Low force of partly loaded micelles, and (d) high force of partly loaded micelles: fR ) 365.320 kHz, ft ) 365.010 kHz, ∆A(c) ) 15 nm, ∆A(d) ) 30 nm, and scan area ) 1.5 × 1.5 µm2. was kept inside the solution for 20 min. The mica plate was taken out of the solution and immediately brought into contact with a piece of filter paper in order to remove the adhering liquid and to dry the surface rapidly.11 Scanning force microscopy was performed with a Nanoscope III (Digital Instruments, St. Barbara) in tapping mode. The Si-cantilever had a spring constant of about 50 N/m.
3. Results and Discussion According to the model described above and in the appendix the forces affecting a surface can be increased by increasing the differences between the amplitude of the noncontact oscillation A0 and the tapping amplitude At (∆A ) A0 - At) i.e. lowering the setpoint and/or by scanning on the high-frequency side of the noncontact oscillation (see Figure 1). Variation of the tip force can be demonstrated experimentally by imaging a heterogeneous material with small domains of different mechanical compliances being used
as “force sensors”. Examples are presented in Figures 3-5. The images depict thin films formed of densely packed micelles of a block copolymer from polystyrene (PS) and poly(2-vinylpyridine) (P2VP). Assembly to micelles in toluene solution and preparation of the thin films have been described elsewhere.11 The micelles consist of a P2VP core and a PS corona. Three different films have been studied: (i) the first film was formed of the plain micelles where the P2VP core has about the same compliance as the surrounding polystyrene shell (diameter of a micelle is about 18 nm);11 (ii) the second film consisted of a mixture of plain PS-bP2VP micelles and PS-b-P2VP micelles which contained a gold crystal of about 10 nm diameter. About 10% of the micelles were loaded by a rather stiff gold particle,12 (iii) the third film consisted of PS-b-P2VP micelles where the pyridine units had been partly neutralized by 0.5 equiv of HAuCl4.11 This way the polar block was loaded by inorganic ions, enhancing the stiffness of the core of all
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Figure 5. Scheme of micellar deformation: (a) deformation at the top and (b) reduced deformation if the tip is quenched between two micelles because of increased tip contact area.
micelles and increasing the overall micelle diameter to 25 nm with a core diameter of 19 nm measured by electron microscopy. Figure 3 shows a TSF micrograph of the plain PS-bP2VP micelles. The picture depicts three sections which were scanned under different conditions. The structure of the top and bottom section has been monitored with minimized peak force. The globular micelles are resolved as densely packed balls with an average diameter of 18 nm. In the middle part of the image, the peak force was increased by increasing the degradation ∆A ) A0 - At (A0 ) 50 nm, Attop/bottom ) 35 nm, Atmiddle ) 20 nm, ft ) 359.570 kHz, and fR ) 359.880 kHz), i.e., lowering the setpoint. The scan lines at the transition run through the centers of some of the micelles (indicated by arrows). Figure 4a and 4b demonstrate that TSFM can be used to detect a material contrast in compliance down to a material depth of several nanometers. Figure 4a shows HAuCl4-loaded micelles (sample iii) which were scanned with minimized peak force; Figure 4b shows the same scan area but they were scanned with increased peak force by increasing the degradation ∆A ) A0 - At (A0 ) 50 nm). Figure 4c shows a micellar film where some of the micelles contained an Au particle which can be clearly distinguished by increasing the tip force as shown in Figure 4d. Features appear larger than they are in reality which is explained by the relatively large radius of the probe apex and the interaction force. As schemetically drawn in Figure 5, two situations have to be distinguished for the tip in contact with the surface: (a) when the tip touches the micelle at the very top and (b) when the tip probes the interface between two micelles. Regarding case (a) the micelles are deformed if the core is soft. If the core is stiffened by the inorganic component, the deformation is reduced. In Figure 4b the tip reveals that all micelles contain a stiff grain, while Figure 4d shows that only some micelles were loaded with Au particles (indicated by arrows). Regarding case (b), it must be considered that the tip radius (∼15 nm) is large compared to the cleft between two micelles. The tip touches two micelles simultaneously which cannot move laterally. Because of the increased contact area, the tapping amplitude is decreased and the feedback system (constant amplitude) records the increased damping force as an apparent corrugation. Micelles at the edge of a micellar layer (marked by arrows in Figure 4b) do not show this geometrical artifact at the side where they are not enclosed by other micelles. Figure 6 displays an image of sample (iii) which was recorded by varying the tapping frequency and keeping the setpoint constant (At ) 35 nm). The image in Figure 6a was scanned with ft ) 346.820 kHz (A0 ) 50 nm, At ) 35 nm) on the low-frequency side of the noncontact resonance frequency of the cantilever, small apparent corrugations indicating a rather strong tapping force between some of the micelles. Turning to the highfrequency side, ft ) 347.380 kHz, the hills between micelles become much more pronounced (Figure 6b). This dem-
Figure 6. HAuCl4-loaded micelles scanned with constant tapping amplitude but different tapping frequency (scan size ) 0.9 × 0.9 µm2): (a) low-frequency side and (b) high-frequency side of the noncontact resonance curve. The increased tip force on the high-frequency side yields an enhanced distortion of the image. Parameters are fR ) 347.100 kHz, ft (low-frequency side) ) 346.820 kHz, ft (high-frequency side) ) 347.380 kHz, A0 ) 50 nm, and At ) 35 nm.
onstrates the asymmetrical variation of the tip force with the tapping frequency which was predicted by Figure 1.7,8 4. Conclusions In the example of “loaded” and “unloaded” block copolymer micelles it has been demonstrated how variations of the forces applied by the tip of a TSFM onto a surface can used to reveal structural details within a surface layer. Experimental observations on the dependence of the tip force from the amplitude (setpoint) and the tapping frequency have been shown to be consistent with a model describing the tip surface interaction by combination of two springs. The optimal operating point for
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nondestructive scans is as far as possible on the lowfrequency side while departing from these conditions the tip can be used as a “hammer” in order to introduce reversible and plastic deformations.
Table 1. Parameters Used for Calculating Figures 1 and 2 kC ) 50 N/m, kS ) 20 N/m QC ) 100, QS ) 100 ωC ω fC ) ) 360 kHz, f ) ) 361 kHz 2π 2π a0 ) 0.622 nm, ZL ) 40 nm
Acknowledgment. This work was supported by the Deutsche Forschungsgemeinschaft (SFB 239), Fond Der Chemischen Industrie, and by DEGUSSA AG.
Z ¨ (t) + 2δCSZ˙ + ωCS2Z(t) - ωC2ZL ) φC cos(ωt) (8)
Appendix The noncontact cantilever system is described by the differential equation:
Z ¨ (t) +
ωC Z˙ (t) + ωC2(Z(t) - ZL) ) a0ωC2 cos(ωt) QC
with
(1)
2δCS )
ωC ωS + ) 2δC ) 2δS QC QS
ωCS2 ) ω2 + ωS2
with
x
kC ) 2πfC m
(9) (10)
(2)
The solution of a transient resonant phenomenon of a forced, damped oscillation solves eqs 5 and 8:
being the Eigen frequency. The quality factor of the cantilever is denoted by QC; a0 and ω ) 2πf are the amplitude and the frequency of the driving piezo system, and ZL is the displacement of the equilibrium position of the cantilever above the surface. The zero level is located at the surface. Definition of the two parameters:
ZC(t) ) e-tδC{aC cos(ωeCt) + bC sin(ωeCt)} + AC cos(ωt - RC) + ZL (11)
ωC )
2δC )
ωC QC
ZCS(t) ) e-tδC{aCS cos(ωeCSt) + bCS sin(ωeCSt)} + ACS cos(ωt - RCS) + Z ˜ L (12)
(3) Ai )
δC is characteristic for the damping in the system cantilever, 2
φC ) a0ωC ) FC/m
(4)
a0ωC2
x(ωi2 - ω2)2 + 4δi2ω2
where A (i ) C, CS) is the amplitude of the stationary oscillation described by the particular solution (second part of eqs 11 and 12),
FC is the driving force and m the effective mass of the cantilever. Equation 1 can be written as
tan(Ri) )
Z ¨ (t) + 2δCZ˙ (t) + ωC2(Z(t) - ZL) ) φC cos(ωt) (5) Because of the surface contact once each cycle, the cantilever cannot reach a stationary oscillation state. Upon contact, the surface is assumed to deform according to a harmonic potential modeled by a spring with spring constant kS and a quality factor QS. The equation of motion for the cantilever in contact is given by
Z ¨ (t) +
(
x
(7)
being the Eigen frequency of the “massless” surface spring coupled to the cantilever mass. Equation 6 can be rewritten
ωi2 - ω2
ωei ) xωi2 - δi2
(14)
(15)
the Eigen frequency of the damped system, and
)
kS m
2δiω
the phase,
ωC ωS + Z˙ (t) + ωC2(Z(t) - ZL) + ωS2Z(t) ) QC QS φC cos(ωt) (6) ωS )
(13)
Z ˜L )
ωC2 ωCS2
ZL
(16)
the displacement of the equilibrium position of the CS system. ai and bi (i ) C, CS) are constants which have to be determined such that Z(t) and Z˙ (t) are continous. Parameters used for the simulation in Figures 1 and 2 are listed in Table 1. LA970311W
