- Email: [email protected]
Tapping mode scanning force microscopy in water using a carbon nanotube probe
Ultramicroscopy 80 (1999) 237}246
Tapping mode scanning force microscopy in water using a carbon nanotube probe Katerina Moloni, Michael R. Buss, Ronald P. Andres* School of Chemical Engineering, Purdue University, West Lafayette, IN 47907-1283, USA Received in "nal form 17 February 1999
Abstract An improved technique for obtaining tapping mode scanning force microscopy (TMSFM) images of soft samples submerged in water is described. This technique makes use of a carbon nanotube several microns in length mounted on a conventional silicon cantilever as the TMSFM probe. The sample is covered by a shallow water layer and during imaging only a portion of the nanotube is submerged. This mode of operation largely eliminates the undesirable e!ects of hydrodynamic damping and acoustic excitation that are present during conventional tapping mode operation in liquids and leads to high-quality TMSFM images. Because of their low bending force constants, carbon nanotubes are ideal for gentle imaging of soft samples. Because of their small (5}20 nm) diameter and cylindrical shape they provide excellent lateral resolution and are ideal for scanning high aspect ratio objects. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: SPM; AFM; Carbon nanotube; Tapping mode
1. Introduction In tapping mode scanning force microscopy (TMSFM), the cantilever is vibrated as it is scanned over a sample so that the probe tip contacts the sample intermittently. As in other AC modes of operation, the oscillation amplitude of the cantilever is monitored and used for feedback. TMSFM is preferable to the more common continuous-contact mode of operation when imaging soft samples because of the absence of lateral forces between the probe tip and the sample surface [1]. However, when the tip of the probe impacts the sample
* Corresponding author. Tel.: #1-765-494-4047; fax:#1-765494-0805. E-mail address: [email protected] (R.P. Andres)
during each oscillation, damage to both the sample and the probe is still possible. One way to decrease the energy of this impact is to decrease the adhesive interaction between the probe and the sample by immersing both in a liquid [2]. Unfortunately, immersion of a conventional cantilever in a liquid signi"cantly changes its oscillatory behavior, producing a complex frequency response [3] and decreasing both the resonant frequency and the quality factor of the oscillator [4]. These undesirable e!ects arise from hydrodynamic drag on the cantilever and acoustic excitation of the liquid. One way to circumvent these problems is to redesign the TMSFM probe. Dai et al. [5] have suggested that mounting a carbon nanotube on a conventional silicon cantilever would provide an excellent probe for TMSFM. They point out that the small diameter, cylindrical shape, and large
0304-3991/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 9 9 1 ( 9 9 ) 0 0 1 0 7 - 2
238
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
aspect ratio of a carbon nanotube when coupled with its ability to buckle without su!ering irreversible damage make it an almost ideal TMSFM probe. Dai et al. [5] showed that by immersing the carbon nanotube in water while keeping the silicon cantilever in air they could eliminate the excessive drag and acoustic excitation usually associated with AC operation in liquids. However, in order to employ this technique for TMSFM, the depth of the liquid layer covering the sample must be approximately one micron or less. Thus, a reliable method for stabilizing a micron deep water layer against evaporation while at the same time allowing probe access must be developed. We propose such a scheme, outline the advantages of using a carbon nanotube probe for tapping mode scanning force microscopy in liquids, and present sample TMSFM images in water obtained with a carbon nanotube probe. 2. Theoretical model We will approximate the dynamics of a silicon cantilever on which a carbon nanotube has been mounted as that of a driven, damped, harmonic oscillator. In the absence of probe}sample interaction the vertical motion of the tip of the nanotube is governed by the following equation. m
d2z dz #c #k(z!a exp(iut))"0, dt2 dt
(1)
where z is the instantaneous position of the tip relative to its rest position, t is time, m is the e!ective mass of the cantilever, c is an e!ective drag coe$cient, k is an e!ective spring constant, a is the amplitude of an oscillator that drives the cantilever, and u is the frequency of the oscillator. Introducing the resonant frequency of the cantilever u "(k/m)1@2, 0 and a quality factor
(2)
Q"mu /c. 0 Eq. (1) can be rewritten in the form
(3)
A B
d2z u dz " 0 #u2 (z!a exp(iut))"0, 0 dt2 Q dt
(4)
and this equation can be solved analytically to yield the steady-state oscillation amplitude of the probe tip [6] a A" , (5) ((1!u2/u2 )2#(u2/u2 )(1/Q2))1@2 0 0 and the phase lag between the oscillating tip and the sinusoidal oscillator driving the cantilever
A
B
uu 1 0 tan /" . (6) Q u2 !u2 0 Eqs. (5) and (6) model the free oscillation dynamics of etched silicon cantilevers quite well. The mass of a carbon nanotube is so small that attaching one to a typical silicon cantilever has a negligible e!ect on the resonant frequency of the cantilever. More importantly, because of the small diameter and smooth cylindrical shape of a nanotube, the e!ective drag coe$cient in air of a cantilever with a nanotube attached is only slightly larger than before this modi"cation. Thus, the quality factors of modi"ed and unmodi"ed cantilevers in air are nearly identical. The free oscillation dynamics of a nanotube modi"ed cantilever, when the tip of the nanotube is submerged in a liquid, is also well described by Eqs. (5) and (6), however, both the resonant frequency and the quality factor of the cantilever are changed from their values in air. A constant capillary force is exerted by the liquid on the wall of the nanotube. If this force is directed downward, it serves to increase the e!ective mass of the cantilever thereby decreasing its resonant frequency and increasing its quality factor (see Eqs. (2) and (3)). If this force is directed upward, it serves to decrease the e!ective mass of the cantilever thereby increasing its resonant frequency and lowering its quality factor (this is the case for a carbon nanotube immersed in water). There is also an increased drag on the nanotube when it is immersed in liquid and this further lowers the quality factor of the probe (see Eq. (3)). The experimental frequency response of a typical silicon cantilever (k&1 N/m) with a carbon nanotube attached to it is plotted in Fig. 1. Two curves are shown. The "rst (Fig. 1a) is for the case in which both the nanotube and the cantilever are in air. The second (Fig. 1b) is for the case in which the
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
Fig. 1. Frequency response curves for a `softa cantilever (k"&1 N/m) nanotube probe. (a) Oscillation amplitude in air, u "80.96 kHz and Q"220. (b) Oscillation amplitude in 0 water, u "81.55 kHz and Q"175. 0
nanotube is partially submerged in water while the cantilever is still in air. The same driving amplitude was used for both cases. Both curves are well modeled by Eq. (5). The increase in resonant frequency observed when the nanotube is submerged is due to the capillary force (&5 nN) acting on the probe at the air/water interface. This force is directed upward and decreases the e!ective mass of the cantilever. The decrease in the quality factor of the probe is due to its smaller e!ective mass and the increased drag on the nanotube. Both the resonant frequency and the quality factor are quite insensitive to the immersion depth of the nanotube as long as the cantilever does not touch the water surface. The data in Fig. 1 con"rm that a carbon nanotube probe submerged in a shallow water layer does not display the complex acoustic interactions present when a conventional silicon probe is submerged in a liquid [7]. It is particularly signi"cant that the quality factor of the probe remains high. The larger the value of Q the more sensitive A and ' are to probe}sample interaction. Several authors have simulated the tapping mode impact between probe and sample by introducing position-dependent force and position-dependent damping terms in Eq. (1) (see Ref. [8] and references contained therein). This approach requires both an exact model for the abrupt impact and numerical integration of a sti! nonlinear di!erential equation. Instead of attempting to simulate the probe}sample collision in detail, Berg and Briggs [9] have proposed treating the impact as an
239
instantaneous momentum impulse in which the probe experiences a kinetic energy loss and abrupt velocity reversal. We will take this approach. The interaction of a nanotube probe and a substrate immersed in water will be divided into two parts: (1) a soft attractive interaction that can be modeled as a decrease in the e!ective spring constant of the cantilever as the probe approaches the sample [6] and (2) an instantaneous momentum impulse on impact that can be modeled as a kinetic energy loss and instantaneous velocity reversal. The qualitative features of the probe}sample interaction and their e!ect on probe dynamics can be understood without detailed simulation. The soft attractive interaction between the probe and the sample serves to decrease both the resonant frequency and the quality factor of the cantilever when z (the distance between the rest position 4!.1-% of the probe and the sample) is decreased. If the cantilever is oscillating at a frequency equal to or above its resonant frequency, A decreases and U increases as the sample is approached. If the cantilever is oscillating at a frequency below its resonant frequency, there is little change in A or U as the sample is approached. This situation continues until a critical point is reached at which the probe begins to impact the sample during each oscillation. From this point on the probe instantaneously reverses its velocity when it contacts the sample surface. Even if the kinetic energy loss on impact is negligible, the e!ect of this instantaneous velocity reversal is a linear decrease in the amplitude of oscillation as z is decreased. 4!.1-% The quantitative e!ect of the kinetic energy loss su!ered by the probe on impact is di$cult to estimate without detailed simulation. To avoid adhesive capture, however, the total energy of oscillation of the cantilever must be greater than this energy loss, i.e. 1 kA2'*E, (7) 2 where *E is the kinetic energy loss su!ered in an impact. This establishes a minimum oscillation amplitude, A , for stable tapping-mode operation .*/ A "(2*E/k)1@2. (8) .*/ The best TMSFM images (based on monitoring oscillation amplitude) will be obtained when A is
240
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
small but large compared to A . As both large .*/ k and small *E serve to decrease A , it is desir.*/ able to operate with a sti! cantilever and a small energy loss. Both of these conditions can be realized with a nanotube probe. Because a carbon nanotube buckles easily and is virtually indestructible, it can be mounted on a sti! cantilever without worrying about damaging the tip in a crash. Because of their small tip diameters and high elastic modulus, carbon nanotubes also exhibit relatively low-energy loss. There are two components to *E. Reversal of the probe's motion on impact produces a constant fractional loss of kinetic energy due to "nite momentum transfer to the sample [10}12]. The proportionality constant characterizing this energy loss is the coe$cient of restitution. The second contribution is independent of the kinetic energy of collision. It is caused by inelastic adhesive interactions between the tip and the sample. There are two major sources of these interactions: (1) capillary forces exerted by a liquid meniscus between the sample and the tip [13] and (2) adhesion forces which deform the tip and the sample in the contact region [14]. Energy losses due to capillary forces are eliminated if the sample and probe are either kept free of trace amounts of liquid (vacuum operation) or are both immersed in liquid (liquid operation). Energy losses due to adhesion forces are minimized by operating with a probe that has a low surface free energy, by immersing the sample and probe in a liquid that lowers the adhesion energy, and by decreasing the diameter of the probe. In summary, optimum TMSFM images are achieved when the quality factor and e!ective spring constant of the probe are high and when the kinetic energy loss on impact is low due to a high coe$cient of restitution and low adhesion forces between the probe and the sample. This optimum condition is closely approached by operating with a carbon nanotube probe immersed in water. The quality factor of a carbon nanotube probe in air is essentially that of the original silicon cantilever and can be made quite high. Immersing the nanotube in water reduces this quality factor only slightly. Nanotubes have a high coe$cient of restitution and can be used with sti! cantilevers. They are virtually indestructible. They buckle when over-
stressed and recover completely when the stress is removed. Finally, operating with a nanotube probe in water minimizes adhesion forces. If a nanotube probe is oscillating at a frequency just below its resonant frequency with su$cient amplitude to escape adhesive capture, its oscillation amplitude remains nearly constant as the sample is approached until the probe begins to impact the sample. Once this occurs, there is a reversible, monotonic decrease in its oscillation amplitude as the o!set between the rest position of the probe tip and the surface of the sample is reduced.
3. Experimental details A multi-mode Nanoscope III (Digital Instruments, Santa Barbara, CA) was used in its tapping mode con"guration. The cantilevers used were etched silicon cantilevers obtained from Digital Instruments. The `softa cantilevers (FESPs) had spring constants of 1}5 N/m and resonant frequencies of 60}100 kHz, while the `harda cantilevers (TESPs) had spring constants of 20}100 N/m and resonant frequencies of 200}400 kHz. The carbon nanotubes were multiwalled nanotubes (MWNTs) obtained from Rice University.1 These MWNT's were synthesized in a DC carbon arc and had diameters ranging from 5}20 nm [15]. They were mounted on the silicon cantilevers using a procedure developed by Dai et al. [5,16]. An optical bench consisting of an aluminum plate mounted on an inverted bright-"eld/dark"eld optical microscope (Nikon Epiphot 200) was constructed. The microscope was equipped with 15] binocular eyepieces, a 5] objective (NikonCF BD 5] Plan Achromat) and a 50] extended working distance objective (Nikon CF BD ELWD 50] Plan Objective). Two translation stages (Newport M-460A-XYZ) equipped with manual micrometers (Newport SM0.5) were used, one to manipulate the silicon cantilever and the other a piece of SEM tape stuck to a small metal plate. First, the SEM
1 We want to thank Richard E. Smalley and Hongjie Dai both for supplying the MWNT's used in this study and for aiding us in our initial attempts to mount the nanotubes onto cantilevers.
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
tape was sparsely coated with carbon nanotubes by touching it to a sample of loosely aggregated multiwall nanotubes. Then the cantilever was pushed against the tape and a small amount of adhesive was transferred to the cantilever tip. Next, the tip of the cantilever was brought into contact with one of the nanotubes sticking to the tape. Adhesion between the tip and the nanotube was monitored by measuring the electrical resistance between the cantilever and the plate. Once a nanotube was stuck to the cantilever, a 10}20 V DC bias was applied between the cantilever and the plate. The resulting electrical current severed the nanotube. Although care was taken to always select a single, uniform diameter, multiwall tube, this procedure sometimes resulted in a bundle of parallel nanotubes being glued to the cantilever. Especially long nanotube probes have a low buckling force and vibrate on impact with the sample. This results in poor quality TMSFM images. When this happens, the length of the probe can be reduced by applying a 10}20 V bias between the cantilever and a conducting substrate and tapping (sparking) the probe against the sample. This procedure is repeated until satisfactory TMSFM images are obtained. The typical probe used in the present study was approximately 2}4 lm in length with a single 5}20 nm diameter multiwall nanotube protruding at its tip. Because of the way the probes were fabricated the nanotubes are open ended and are terminated with a hydrophilic surface at the tip. Special silicon substrates were fabricated for imaging samples in liquid. Lithographically de"ned trenches 5}20 lm wide and 2 mm long were etched in a 200 nm thick oxide layer on a silicon wafer. The bottoms of these trenches were smoothed and hydrogen terminated by immersing the wafer in 1 : 1 H SO : H O solution for 15}20 min, rins2 4 2 2 ing in DI water, and immersing the wafer in BHF for 15}30 s. Finally, the trenches were etched to the desired depth (typically 1.5 lm) by immersing the wafer in a KOH solution. The wafer was diced into small 4 mm]4 mm chips which were glued using silver paint to a magnetic base and placed in the Nanoscope. Flooding the trenches in these silicon chips with a liquid produced a thin layer that could easily
241
be penetrated by the nanotube probe without submerging the silicon cantilever. For nonvolatile liquids this permitted TMSFM imaging of samples placed in the trenches. For water, however, rapid evaporation made such imaging di$cult and a way to control evaporation had to be devised. In order to control evaporative water loss, the Nanoscope head was completely enclosed in a plexiglass box and the atmosphere in the box was brought to stable &80% relative humidity. This humidity level was achieved by #owing a stream from a commercial room humidi"er into the box and maintained by placing open jars containing a supersaturated KBr solution in the box.2 The temperature of the silicon chip was lowered &3}4 K below the ambient temperature by means of a thermoelectric cooler3 in order to establish equilibrium saturation at the surface of the chip. The temperature of the chip was then controlled by manipulating the voltage to the thermoelectric cooler until there was no net evaporative loss or gain of water from the surface of the chip.
4. Cantilever dynamics and TMSFM images Fig. 2 presents two traces of the oscillation amplitude of a nanotube probe as a function of the o!set between the probe's rest position and the bottom of a water-"lled trench. The same driving amplitude was used for both traces. For the "rst trace (Fig. 2a) the frequency of oscillation was set at the resonant frequency of the probe in air. For the second trace (Fig. 2b) the oscillation frequency was set at the resonant frequency of the probe submerged in water. Contact with the air/water surface is seen to occur at approximately 1.5 lm. In the "rst case this causes a drop in the oscillation amplitude. In the
2 Supersaturated KBr has an equilibrium vapor pressure 84% that of pure water at 298 K. 3 For imaging in water a silicon chip containing the standard trenches was glued using silver paint onto a 4 mm]4 mm thermoelectric cooler (Marlow Industries). The thermoelectric cooler was then glued using silver paint onto a 1 mm thick nickel plate, which served as a heat sink and a magnetic base.
242
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
Fig. 2. Plots of the oscillation amplitude of the probe in Fig. 1 as it is brought close to a silicon substrate covered with a 1.5 lm deep layer of water. (a) u"80.96 kHz. (b) u"81.55 kHz.
second case it causes an increase in the oscillation amplitude. This behavior is due to the di!erence between the frequency response curves for submerged and unsubmerged probes (see the discussion of Fig. 1). The large hysteresis observed between incoming and outgoing traces at the air/water interface is typical. The attractive interaction between the hydrophilic probe tip and the free water surface produces surface waves. Once the probe tip penetrates the air/water interface its oscillation amplitude remains nearly constant until it impacts the bottom of the trench at 0.18 lm. There is an abrupt drop in the oscillation amplitude to zero over a distance comparable to the free oscillation amplitude prior to impact. When the probe}sample separation is decreased further the oscillation amplitude increases again due to buckling of the nanotube and the interaction of this elastic force with the oscillator driving the cantilever. The best TMSFM images were obtained with `harda cantilevers (u "200}400 kHz, Q" 0 400}750). The sample images shown in Figs. 3}5 were obtained using these cantilevers. The frequency of oscillation was set equal to the resonant frequency of the probe in air and the free oscillation amplitude of the probe in water was adjusted to be &20 nm, corresponding to an oscillation energy of &4]10~15 J. The amplitude set point was 90% of the free oscillation amplitude.
Fig. 3 is a TMSFM image in water of a small gold cluster.4 This image demonstrates the kind of lateral resolution achievable with a carbon nanotube probe. Mahoney et al. [17] have shown that preformed, nanometer-scale Au clusters deposited at room temperature on various #at substrates retain their spherical shape except for a small elastic #attening at the base. Thus, the height of an Au cluster obtained from its TMSFM image should be approximately equal to the cluster's diameter. Also, when a spherical cluster is imaged by a cylindrically symmetric #at tip, a TMSFM image of the cluster supported on a #at substrate should be that of a spherical cap with a base diameter approximately equal to the sum of the diameter of the cluster and the diameter of the tip. Allowing for the somewhat uneven surface of the trench bottom, the image in Fig. 3 con"rms that the probe tip is symmetric with a diameter of approximately 7 nm. Fig. 3 also illustrates the low adhesion forces exhibited by a nanotube probe, which permit TMSFM imaging of samples weakly tethered to a substrate. The gold cluster is only held in place on the silicon substrate by van der Waals forces. It is di$cult to image nanoscale gold particles with an scanning force microscope operating in air [18], and this is the "rst time we have been able to obtain a stable image of one in water. Some of the most exciting opportunities for TMSFM in water involve the imaging of biological samples. Fig. 4 is a TMSFM image of virons of the double-stranded DNA bacteriophage /29 in water.5 These particles are barrel shaped and are approximately 80 nm in height and 50 nm in diameter. They were assembled in vitro from puri"ed structural proteins and enzymes without the involvement of the infectious parental virus [19]. The virons were suspended in a TMS bu!er and the silicon substrate was #ooded with this suspension. No e!ort was made to tether the virons to the bottom of the trenches. Fig. 5 is a TMSFM image of the surface of a 1.2 lm. diameter particle of `fuzzya amaranth 4 These colloidal gold particles with an average diameter of 5 nm were obtained from BB International (UK). 5 We want to thank Peixuan Guo for supplying these virus particles and for aiding us in preparing a sample for imaging. These particles are suspended in a TMS bu!er (50 mM Tris, 10 mM MgCl , 100 mM NaCl, pH 7.8). 2
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
243
Fig. 3. TMSFM scan in water of 7 nm diameter gold cluster on a silicon substrate. Scan rate 5 Hz.
starch in water.6 This particle was prepared by treating amaranth starch with glucoamyalase. Although treating other types of starch with this enzyme produces porous particles, to date it has not been possible to observe pore openings at the sur-
6 We want to thank Professor Roy L. Whistler for supplying this sample of amaranth starch that has been treated with glucoamylase and for helpful discussions.
face of enzyme treated amaranth starch [20]. The TMSFM image in Fig. 5 shows a well de"ned `openinga 40}50 nm across that is of undetermined depth. These pore openings are distributed all over the particle's surface. The ability of a carbon nanotube probe to image pore openings in the surface of an amaranth particle illustrate two of its strengths. First, the ability of this probe to image a three-dimensional nanoscale object with a high aspect ratio. Second, the
244
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
Fig. 4. TMSFM scan in water of virus particles on a silicon substrate. Scan rate 5 Hz.
ability of a nanotube probe to obtain TMSFM images in water of soft samples. Using a conventional silicon probe or even the same nanotube probe in air, these openings in the particle's surface are not resolved because of the strongly adhesive interaction between the probe tip and the surface of the amaranth particle.
5. Summary and conclusions This work builds on the pioneering suggestion of Dai et al. [5] that mounting a carbon nanotube on a conventional silicon cantilever would produce an excellent probe for tapping mode scanning force microscopy, especially if it is desired to image samples in liquids. A simple qualitative model that describes the salient features of TMSFM with carbon nanotube probes is developed. This model is
used to illustrate the important advantages of TMSFM with a nanotube probe. The critical feature necessary for TMSFM imaging in water with a nanotube probe is a simple way to prevent evaporation from a shallow water layer. A practical method to accomplish this is proposed. Finally, three examples are presented of the experimental implementation of these ideas. These examples illustrate the strengths of a probe that permits high u , high Q, low *E, TMSFM imaging 0 in water. These examples also illustrate a weakness of probes based on open-ended MWNTs, i.e. limited lateral resolution. This is because the tips of these probes have a #at cylindrical endform that is typically 5 nm or more in diameter. Dai et al. [5] point out that a nanotube probe made using a single-wall carbon nanotube has the potential of decreasing the probe diameter to 1 nm.
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
245
Fig. 5. TMSFM scan in water of the surface of a `fuzzya amaranth starch particle. Scan rate 5 Hz.
Implementation of such a probe may be the next step in perfecting scanning force microscopy. [3]
Acknowledgements
[4] [5]
This research was supported by the NSF (CTS9522248). The MWNTs were supplied by R.E. Smalley of Rice University, the /29 virus particles were supplied by P. Guo of Purdue University, and the amaranth starch particles were supplied by R.L. Whistler of Purdue University.
References [1] Q. Zhong, D. Innis, K. Kjoller, V. Elings, Surf. Sci. 290 (1993) L688. [2] P.K. Hansma, J.P. Cleveland, M. Radmacher, D.A. Walters, P.E. Hillner, M. Bezanilla, M. Fritz, D. Vie,
[6]
[7] [8]
[9] [10] [11] [12] [13]
H. Hansma, C.B. Prater, J. Massie, L. Fukunaga, J. Gurley, V. Elings, Appl. Phys. Lett. 64 (1994) 1738. C.A.J. Putman, K.O. van der Werf, B.G. de Grooth, N.F. van Hulst, Appl. Phys. Lett. 64 (1994) 2454. G.Y. Chen, T. Warmack, T. Thundat, D.P. Allison, A. Huang, Rev. Sci. Instrum. 65 (1994) 2532. H. Dai, J.H. Hafner, A.G. Rinzler, D.T. Colbert, R.E. Smalley, Nature 384 (1996) 147. D. Sarid, in: Scanning Force Microscopy with Applications to Electric, Magnetic, and Atomic Forces, Oxford University Press, New York, 1991. T.E. Scha!er, J.P. Cleveland, F. Ohnesorge, D.A. Walters, P.K. Hansma, J. Appl Phys. 80 (1996) 3622. N.A. Burnham, O.P. Behrendt, F. Oulevey, G. Gremaud, P.-J. Gallo, D. Gourdon, E. Dupas, A.J. Kulik, H.M. Pollock, G.A.D. Briggs, Nanotechnol. 8 (1997) 67. J. Berg, G.A.D. Briggs, Phys. Rev. B 55 (1997) 14899. B. Dahneke, J. Colloid Interface Sci. 51 (1975) 58. S.J. Wall, W. John, H.-C. Wang, S.L. Goren, Aerosol Sci. Technol. 12 (1990) 926. R.P. Andres, Aerosol Sci. Technol. 23 (1995) 40. J. Israelachvili, in: Intermolecular and Surface Forces, Academic Press, New York, 1991.
246
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
[14] K. Johnson, in: Contact Mechanics, Cambridge University Press, Cambridge, 1985. [15] D. Colbert, J. Zhang, S. McClure, P. Nikolaev, Z. Chen, J. Hafner, D. Owens, P. Kotula, C. Carter, J. Weaver, A. Rinzler, R.E. Smalley, Science 266 (1994) 1218. [16] A detailed description of this procedure may be found at http://cnst.rice.edu/mount.html or in Buss, R.B., Ph.D. Thesis, Purdue University, 1998.
[17] W. Mahoney, D.M. Schaefer, A.N. Patil, R.P. Andres, R. Reifenberger, Surf. Sci. 316 (1994) 383. [18] D.M. Schaefer, R. Reifenberger, A.N. Patil, R.P. Andres, Appl. Phys. Lett. 66 (1995) 1012. [19] C.-S. Lee, P. Guo, J. Virology 69 (1995) 5018. [20] Whistler, R.L., Purdue University, private communication.
Tapping mode scanning force microscopy in water using a carbon nanotube probe Katerina Moloni, Michael R. Buss, Ronald P. Andres* School of Chemical Engineering, Purdue University, West Lafayette, IN 47907-1283, USA Received in "nal form 17 February 1999
Abstract An improved technique for obtaining tapping mode scanning force microscopy (TMSFM) images of soft samples submerged in water is described. This technique makes use of a carbon nanotube several microns in length mounted on a conventional silicon cantilever as the TMSFM probe. The sample is covered by a shallow water layer and during imaging only a portion of the nanotube is submerged. This mode of operation largely eliminates the undesirable e!ects of hydrodynamic damping and acoustic excitation that are present during conventional tapping mode operation in liquids and leads to high-quality TMSFM images. Because of their low bending force constants, carbon nanotubes are ideal for gentle imaging of soft samples. Because of their small (5}20 nm) diameter and cylindrical shape they provide excellent lateral resolution and are ideal for scanning high aspect ratio objects. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: SPM; AFM; Carbon nanotube; Tapping mode
1. Introduction In tapping mode scanning force microscopy (TMSFM), the cantilever is vibrated as it is scanned over a sample so that the probe tip contacts the sample intermittently. As in other AC modes of operation, the oscillation amplitude of the cantilever is monitored and used for feedback. TMSFM is preferable to the more common continuous-contact mode of operation when imaging soft samples because of the absence of lateral forces between the probe tip and the sample surface [1]. However, when the tip of the probe impacts the sample
* Corresponding author. Tel.: #1-765-494-4047; fax:#1-765494-0805. E-mail address: [email protected] (R.P. Andres)
during each oscillation, damage to both the sample and the probe is still possible. One way to decrease the energy of this impact is to decrease the adhesive interaction between the probe and the sample by immersing both in a liquid [2]. Unfortunately, immersion of a conventional cantilever in a liquid signi"cantly changes its oscillatory behavior, producing a complex frequency response [3] and decreasing both the resonant frequency and the quality factor of the oscillator [4]. These undesirable e!ects arise from hydrodynamic drag on the cantilever and acoustic excitation of the liquid. One way to circumvent these problems is to redesign the TMSFM probe. Dai et al. [5] have suggested that mounting a carbon nanotube on a conventional silicon cantilever would provide an excellent probe for TMSFM. They point out that the small diameter, cylindrical shape, and large
0304-3991/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 9 9 1 ( 9 9 ) 0 0 1 0 7 - 2
238
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
aspect ratio of a carbon nanotube when coupled with its ability to buckle without su!ering irreversible damage make it an almost ideal TMSFM probe. Dai et al. [5] showed that by immersing the carbon nanotube in water while keeping the silicon cantilever in air they could eliminate the excessive drag and acoustic excitation usually associated with AC operation in liquids. However, in order to employ this technique for TMSFM, the depth of the liquid layer covering the sample must be approximately one micron or less. Thus, a reliable method for stabilizing a micron deep water layer against evaporation while at the same time allowing probe access must be developed. We propose such a scheme, outline the advantages of using a carbon nanotube probe for tapping mode scanning force microscopy in liquids, and present sample TMSFM images in water obtained with a carbon nanotube probe. 2. Theoretical model We will approximate the dynamics of a silicon cantilever on which a carbon nanotube has been mounted as that of a driven, damped, harmonic oscillator. In the absence of probe}sample interaction the vertical motion of the tip of the nanotube is governed by the following equation. m
d2z dz #c #k(z!a exp(iut))"0, dt2 dt
(1)
where z is the instantaneous position of the tip relative to its rest position, t is time, m is the e!ective mass of the cantilever, c is an e!ective drag coe$cient, k is an e!ective spring constant, a is the amplitude of an oscillator that drives the cantilever, and u is the frequency of the oscillator. Introducing the resonant frequency of the cantilever u "(k/m)1@2, 0 and a quality factor
(2)
Q"mu /c. 0 Eq. (1) can be rewritten in the form
(3)
A B
d2z u dz " 0 #u2 (z!a exp(iut))"0, 0 dt2 Q dt
(4)
and this equation can be solved analytically to yield the steady-state oscillation amplitude of the probe tip [6] a A" , (5) ((1!u2/u2 )2#(u2/u2 )(1/Q2))1@2 0 0 and the phase lag between the oscillating tip and the sinusoidal oscillator driving the cantilever
A
B
uu 1 0 tan /" . (6) Q u2 !u2 0 Eqs. (5) and (6) model the free oscillation dynamics of etched silicon cantilevers quite well. The mass of a carbon nanotube is so small that attaching one to a typical silicon cantilever has a negligible e!ect on the resonant frequency of the cantilever. More importantly, because of the small diameter and smooth cylindrical shape of a nanotube, the e!ective drag coe$cient in air of a cantilever with a nanotube attached is only slightly larger than before this modi"cation. Thus, the quality factors of modi"ed and unmodi"ed cantilevers in air are nearly identical. The free oscillation dynamics of a nanotube modi"ed cantilever, when the tip of the nanotube is submerged in a liquid, is also well described by Eqs. (5) and (6), however, both the resonant frequency and the quality factor of the cantilever are changed from their values in air. A constant capillary force is exerted by the liquid on the wall of the nanotube. If this force is directed downward, it serves to increase the e!ective mass of the cantilever thereby decreasing its resonant frequency and increasing its quality factor (see Eqs. (2) and (3)). If this force is directed upward, it serves to decrease the e!ective mass of the cantilever thereby increasing its resonant frequency and lowering its quality factor (this is the case for a carbon nanotube immersed in water). There is also an increased drag on the nanotube when it is immersed in liquid and this further lowers the quality factor of the probe (see Eq. (3)). The experimental frequency response of a typical silicon cantilever (k&1 N/m) with a carbon nanotube attached to it is plotted in Fig. 1. Two curves are shown. The "rst (Fig. 1a) is for the case in which both the nanotube and the cantilever are in air. The second (Fig. 1b) is for the case in which the
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
Fig. 1. Frequency response curves for a `softa cantilever (k"&1 N/m) nanotube probe. (a) Oscillation amplitude in air, u "80.96 kHz and Q"220. (b) Oscillation amplitude in 0 water, u "81.55 kHz and Q"175. 0
nanotube is partially submerged in water while the cantilever is still in air. The same driving amplitude was used for both cases. Both curves are well modeled by Eq. (5). The increase in resonant frequency observed when the nanotube is submerged is due to the capillary force (&5 nN) acting on the probe at the air/water interface. This force is directed upward and decreases the e!ective mass of the cantilever. The decrease in the quality factor of the probe is due to its smaller e!ective mass and the increased drag on the nanotube. Both the resonant frequency and the quality factor are quite insensitive to the immersion depth of the nanotube as long as the cantilever does not touch the water surface. The data in Fig. 1 con"rm that a carbon nanotube probe submerged in a shallow water layer does not display the complex acoustic interactions present when a conventional silicon probe is submerged in a liquid [7]. It is particularly signi"cant that the quality factor of the probe remains high. The larger the value of Q the more sensitive A and ' are to probe}sample interaction. Several authors have simulated the tapping mode impact between probe and sample by introducing position-dependent force and position-dependent damping terms in Eq. (1) (see Ref. [8] and references contained therein). This approach requires both an exact model for the abrupt impact and numerical integration of a sti! nonlinear di!erential equation. Instead of attempting to simulate the probe}sample collision in detail, Berg and Briggs [9] have proposed treating the impact as an
239
instantaneous momentum impulse in which the probe experiences a kinetic energy loss and abrupt velocity reversal. We will take this approach. The interaction of a nanotube probe and a substrate immersed in water will be divided into two parts: (1) a soft attractive interaction that can be modeled as a decrease in the e!ective spring constant of the cantilever as the probe approaches the sample [6] and (2) an instantaneous momentum impulse on impact that can be modeled as a kinetic energy loss and instantaneous velocity reversal. The qualitative features of the probe}sample interaction and their e!ect on probe dynamics can be understood without detailed simulation. The soft attractive interaction between the probe and the sample serves to decrease both the resonant frequency and the quality factor of the cantilever when z (the distance between the rest position 4!.1-% of the probe and the sample) is decreased. If the cantilever is oscillating at a frequency equal to or above its resonant frequency, A decreases and U increases as the sample is approached. If the cantilever is oscillating at a frequency below its resonant frequency, there is little change in A or U as the sample is approached. This situation continues until a critical point is reached at which the probe begins to impact the sample during each oscillation. From this point on the probe instantaneously reverses its velocity when it contacts the sample surface. Even if the kinetic energy loss on impact is negligible, the e!ect of this instantaneous velocity reversal is a linear decrease in the amplitude of oscillation as z is decreased. 4!.1-% The quantitative e!ect of the kinetic energy loss su!ered by the probe on impact is di$cult to estimate without detailed simulation. To avoid adhesive capture, however, the total energy of oscillation of the cantilever must be greater than this energy loss, i.e. 1 kA2'*E, (7) 2 where *E is the kinetic energy loss su!ered in an impact. This establishes a minimum oscillation amplitude, A , for stable tapping-mode operation .*/ A "(2*E/k)1@2. (8) .*/ The best TMSFM images (based on monitoring oscillation amplitude) will be obtained when A is
240
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
small but large compared to A . As both large .*/ k and small *E serve to decrease A , it is desir.*/ able to operate with a sti! cantilever and a small energy loss. Both of these conditions can be realized with a nanotube probe. Because a carbon nanotube buckles easily and is virtually indestructible, it can be mounted on a sti! cantilever without worrying about damaging the tip in a crash. Because of their small tip diameters and high elastic modulus, carbon nanotubes also exhibit relatively low-energy loss. There are two components to *E. Reversal of the probe's motion on impact produces a constant fractional loss of kinetic energy due to "nite momentum transfer to the sample [10}12]. The proportionality constant characterizing this energy loss is the coe$cient of restitution. The second contribution is independent of the kinetic energy of collision. It is caused by inelastic adhesive interactions between the tip and the sample. There are two major sources of these interactions: (1) capillary forces exerted by a liquid meniscus between the sample and the tip [13] and (2) adhesion forces which deform the tip and the sample in the contact region [14]. Energy losses due to capillary forces are eliminated if the sample and probe are either kept free of trace amounts of liquid (vacuum operation) or are both immersed in liquid (liquid operation). Energy losses due to adhesion forces are minimized by operating with a probe that has a low surface free energy, by immersing the sample and probe in a liquid that lowers the adhesion energy, and by decreasing the diameter of the probe. In summary, optimum TMSFM images are achieved when the quality factor and e!ective spring constant of the probe are high and when the kinetic energy loss on impact is low due to a high coe$cient of restitution and low adhesion forces between the probe and the sample. This optimum condition is closely approached by operating with a carbon nanotube probe immersed in water. The quality factor of a carbon nanotube probe in air is essentially that of the original silicon cantilever and can be made quite high. Immersing the nanotube in water reduces this quality factor only slightly. Nanotubes have a high coe$cient of restitution and can be used with sti! cantilevers. They are virtually indestructible. They buckle when over-
stressed and recover completely when the stress is removed. Finally, operating with a nanotube probe in water minimizes adhesion forces. If a nanotube probe is oscillating at a frequency just below its resonant frequency with su$cient amplitude to escape adhesive capture, its oscillation amplitude remains nearly constant as the sample is approached until the probe begins to impact the sample. Once this occurs, there is a reversible, monotonic decrease in its oscillation amplitude as the o!set between the rest position of the probe tip and the surface of the sample is reduced.
3. Experimental details A multi-mode Nanoscope III (Digital Instruments, Santa Barbara, CA) was used in its tapping mode con"guration. The cantilevers used were etched silicon cantilevers obtained from Digital Instruments. The `softa cantilevers (FESPs) had spring constants of 1}5 N/m and resonant frequencies of 60}100 kHz, while the `harda cantilevers (TESPs) had spring constants of 20}100 N/m and resonant frequencies of 200}400 kHz. The carbon nanotubes were multiwalled nanotubes (MWNTs) obtained from Rice University.1 These MWNT's were synthesized in a DC carbon arc and had diameters ranging from 5}20 nm [15]. They were mounted on the silicon cantilevers using a procedure developed by Dai et al. [5,16]. An optical bench consisting of an aluminum plate mounted on an inverted bright-"eld/dark"eld optical microscope (Nikon Epiphot 200) was constructed. The microscope was equipped with 15] binocular eyepieces, a 5] objective (NikonCF BD 5] Plan Achromat) and a 50] extended working distance objective (Nikon CF BD ELWD 50] Plan Objective). Two translation stages (Newport M-460A-XYZ) equipped with manual micrometers (Newport SM0.5) were used, one to manipulate the silicon cantilever and the other a piece of SEM tape stuck to a small metal plate. First, the SEM
1 We want to thank Richard E. Smalley and Hongjie Dai both for supplying the MWNT's used in this study and for aiding us in our initial attempts to mount the nanotubes onto cantilevers.
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
tape was sparsely coated with carbon nanotubes by touching it to a sample of loosely aggregated multiwall nanotubes. Then the cantilever was pushed against the tape and a small amount of adhesive was transferred to the cantilever tip. Next, the tip of the cantilever was brought into contact with one of the nanotubes sticking to the tape. Adhesion between the tip and the nanotube was monitored by measuring the electrical resistance between the cantilever and the plate. Once a nanotube was stuck to the cantilever, a 10}20 V DC bias was applied between the cantilever and the plate. The resulting electrical current severed the nanotube. Although care was taken to always select a single, uniform diameter, multiwall tube, this procedure sometimes resulted in a bundle of parallel nanotubes being glued to the cantilever. Especially long nanotube probes have a low buckling force and vibrate on impact with the sample. This results in poor quality TMSFM images. When this happens, the length of the probe can be reduced by applying a 10}20 V bias between the cantilever and a conducting substrate and tapping (sparking) the probe against the sample. This procedure is repeated until satisfactory TMSFM images are obtained. The typical probe used in the present study was approximately 2}4 lm in length with a single 5}20 nm diameter multiwall nanotube protruding at its tip. Because of the way the probes were fabricated the nanotubes are open ended and are terminated with a hydrophilic surface at the tip. Special silicon substrates were fabricated for imaging samples in liquid. Lithographically de"ned trenches 5}20 lm wide and 2 mm long were etched in a 200 nm thick oxide layer on a silicon wafer. The bottoms of these trenches were smoothed and hydrogen terminated by immersing the wafer in 1 : 1 H SO : H O solution for 15}20 min, rins2 4 2 2 ing in DI water, and immersing the wafer in BHF for 15}30 s. Finally, the trenches were etched to the desired depth (typically 1.5 lm) by immersing the wafer in a KOH solution. The wafer was diced into small 4 mm]4 mm chips which were glued using silver paint to a magnetic base and placed in the Nanoscope. Flooding the trenches in these silicon chips with a liquid produced a thin layer that could easily
241
be penetrated by the nanotube probe without submerging the silicon cantilever. For nonvolatile liquids this permitted TMSFM imaging of samples placed in the trenches. For water, however, rapid evaporation made such imaging di$cult and a way to control evaporation had to be devised. In order to control evaporative water loss, the Nanoscope head was completely enclosed in a plexiglass box and the atmosphere in the box was brought to stable &80% relative humidity. This humidity level was achieved by #owing a stream from a commercial room humidi"er into the box and maintained by placing open jars containing a supersaturated KBr solution in the box.2 The temperature of the silicon chip was lowered &3}4 K below the ambient temperature by means of a thermoelectric cooler3 in order to establish equilibrium saturation at the surface of the chip. The temperature of the chip was then controlled by manipulating the voltage to the thermoelectric cooler until there was no net evaporative loss or gain of water from the surface of the chip.
4. Cantilever dynamics and TMSFM images Fig. 2 presents two traces of the oscillation amplitude of a nanotube probe as a function of the o!set between the probe's rest position and the bottom of a water-"lled trench. The same driving amplitude was used for both traces. For the "rst trace (Fig. 2a) the frequency of oscillation was set at the resonant frequency of the probe in air. For the second trace (Fig. 2b) the oscillation frequency was set at the resonant frequency of the probe submerged in water. Contact with the air/water surface is seen to occur at approximately 1.5 lm. In the "rst case this causes a drop in the oscillation amplitude. In the
2 Supersaturated KBr has an equilibrium vapor pressure 84% that of pure water at 298 K. 3 For imaging in water a silicon chip containing the standard trenches was glued using silver paint onto a 4 mm]4 mm thermoelectric cooler (Marlow Industries). The thermoelectric cooler was then glued using silver paint onto a 1 mm thick nickel plate, which served as a heat sink and a magnetic base.
242
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
Fig. 2. Plots of the oscillation amplitude of the probe in Fig. 1 as it is brought close to a silicon substrate covered with a 1.5 lm deep layer of water. (a) u"80.96 kHz. (b) u"81.55 kHz.
second case it causes an increase in the oscillation amplitude. This behavior is due to the di!erence between the frequency response curves for submerged and unsubmerged probes (see the discussion of Fig. 1). The large hysteresis observed between incoming and outgoing traces at the air/water interface is typical. The attractive interaction between the hydrophilic probe tip and the free water surface produces surface waves. Once the probe tip penetrates the air/water interface its oscillation amplitude remains nearly constant until it impacts the bottom of the trench at 0.18 lm. There is an abrupt drop in the oscillation amplitude to zero over a distance comparable to the free oscillation amplitude prior to impact. When the probe}sample separation is decreased further the oscillation amplitude increases again due to buckling of the nanotube and the interaction of this elastic force with the oscillator driving the cantilever. The best TMSFM images were obtained with `harda cantilevers (u "200}400 kHz, Q" 0 400}750). The sample images shown in Figs. 3}5 were obtained using these cantilevers. The frequency of oscillation was set equal to the resonant frequency of the probe in air and the free oscillation amplitude of the probe in water was adjusted to be &20 nm, corresponding to an oscillation energy of &4]10~15 J. The amplitude set point was 90% of the free oscillation amplitude.
Fig. 3 is a TMSFM image in water of a small gold cluster.4 This image demonstrates the kind of lateral resolution achievable with a carbon nanotube probe. Mahoney et al. [17] have shown that preformed, nanometer-scale Au clusters deposited at room temperature on various #at substrates retain their spherical shape except for a small elastic #attening at the base. Thus, the height of an Au cluster obtained from its TMSFM image should be approximately equal to the cluster's diameter. Also, when a spherical cluster is imaged by a cylindrically symmetric #at tip, a TMSFM image of the cluster supported on a #at substrate should be that of a spherical cap with a base diameter approximately equal to the sum of the diameter of the cluster and the diameter of the tip. Allowing for the somewhat uneven surface of the trench bottom, the image in Fig. 3 con"rms that the probe tip is symmetric with a diameter of approximately 7 nm. Fig. 3 also illustrates the low adhesion forces exhibited by a nanotube probe, which permit TMSFM imaging of samples weakly tethered to a substrate. The gold cluster is only held in place on the silicon substrate by van der Waals forces. It is di$cult to image nanoscale gold particles with an scanning force microscope operating in air [18], and this is the "rst time we have been able to obtain a stable image of one in water. Some of the most exciting opportunities for TMSFM in water involve the imaging of biological samples. Fig. 4 is a TMSFM image of virons of the double-stranded DNA bacteriophage /29 in water.5 These particles are barrel shaped and are approximately 80 nm in height and 50 nm in diameter. They were assembled in vitro from puri"ed structural proteins and enzymes without the involvement of the infectious parental virus [19]. The virons were suspended in a TMS bu!er and the silicon substrate was #ooded with this suspension. No e!ort was made to tether the virons to the bottom of the trenches. Fig. 5 is a TMSFM image of the surface of a 1.2 lm. diameter particle of `fuzzya amaranth 4 These colloidal gold particles with an average diameter of 5 nm were obtained from BB International (UK). 5 We want to thank Peixuan Guo for supplying these virus particles and for aiding us in preparing a sample for imaging. These particles are suspended in a TMS bu!er (50 mM Tris, 10 mM MgCl , 100 mM NaCl, pH 7.8). 2
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
243
Fig. 3. TMSFM scan in water of 7 nm diameter gold cluster on a silicon substrate. Scan rate 5 Hz.
starch in water.6 This particle was prepared by treating amaranth starch with glucoamyalase. Although treating other types of starch with this enzyme produces porous particles, to date it has not been possible to observe pore openings at the sur-
6 We want to thank Professor Roy L. Whistler for supplying this sample of amaranth starch that has been treated with glucoamylase and for helpful discussions.
face of enzyme treated amaranth starch [20]. The TMSFM image in Fig. 5 shows a well de"ned `openinga 40}50 nm across that is of undetermined depth. These pore openings are distributed all over the particle's surface. The ability of a carbon nanotube probe to image pore openings in the surface of an amaranth particle illustrate two of its strengths. First, the ability of this probe to image a three-dimensional nanoscale object with a high aspect ratio. Second, the
244
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
Fig. 4. TMSFM scan in water of virus particles on a silicon substrate. Scan rate 5 Hz.
ability of a nanotube probe to obtain TMSFM images in water of soft samples. Using a conventional silicon probe or even the same nanotube probe in air, these openings in the particle's surface are not resolved because of the strongly adhesive interaction between the probe tip and the surface of the amaranth particle.
5. Summary and conclusions This work builds on the pioneering suggestion of Dai et al. [5] that mounting a carbon nanotube on a conventional silicon cantilever would produce an excellent probe for tapping mode scanning force microscopy, especially if it is desired to image samples in liquids. A simple qualitative model that describes the salient features of TMSFM with carbon nanotube probes is developed. This model is
used to illustrate the important advantages of TMSFM with a nanotube probe. The critical feature necessary for TMSFM imaging in water with a nanotube probe is a simple way to prevent evaporation from a shallow water layer. A practical method to accomplish this is proposed. Finally, three examples are presented of the experimental implementation of these ideas. These examples illustrate the strengths of a probe that permits high u , high Q, low *E, TMSFM imaging 0 in water. These examples also illustrate a weakness of probes based on open-ended MWNTs, i.e. limited lateral resolution. This is because the tips of these probes have a #at cylindrical endform that is typically 5 nm or more in diameter. Dai et al. [5] point out that a nanotube probe made using a single-wall carbon nanotube has the potential of decreasing the probe diameter to 1 nm.
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
245
Fig. 5. TMSFM scan in water of the surface of a `fuzzya amaranth starch particle. Scan rate 5 Hz.
Implementation of such a probe may be the next step in perfecting scanning force microscopy. [3]
Acknowledgements
[4] [5]
This research was supported by the NSF (CTS9522248). The MWNTs were supplied by R.E. Smalley of Rice University, the /29 virus particles were supplied by P. Guo of Purdue University, and the amaranth starch particles were supplied by R.L. Whistler of Purdue University.
References [1] Q. Zhong, D. Innis, K. Kjoller, V. Elings, Surf. Sci. 290 (1993) L688. [2] P.K. Hansma, J.P. Cleveland, M. Radmacher, D.A. Walters, P.E. Hillner, M. Bezanilla, M. Fritz, D. Vie,
[6]
[7] [8]
[9] [10] [11] [12] [13]
H. Hansma, C.B. Prater, J. Massie, L. Fukunaga, J. Gurley, V. Elings, Appl. Phys. Lett. 64 (1994) 1738. C.A.J. Putman, K.O. van der Werf, B.G. de Grooth, N.F. van Hulst, Appl. Phys. Lett. 64 (1994) 2454. G.Y. Chen, T. Warmack, T. Thundat, D.P. Allison, A. Huang, Rev. Sci. Instrum. 65 (1994) 2532. H. Dai, J.H. Hafner, A.G. Rinzler, D.T. Colbert, R.E. Smalley, Nature 384 (1996) 147. D. Sarid, in: Scanning Force Microscopy with Applications to Electric, Magnetic, and Atomic Forces, Oxford University Press, New York, 1991. T.E. Scha!er, J.P. Cleveland, F. Ohnesorge, D.A. Walters, P.K. Hansma, J. Appl Phys. 80 (1996) 3622. N.A. Burnham, O.P. Behrendt, F. Oulevey, G. Gremaud, P.-J. Gallo, D. Gourdon, E. Dupas, A.J. Kulik, H.M. Pollock, G.A.D. Briggs, Nanotechnol. 8 (1997) 67. J. Berg, G.A.D. Briggs, Phys. Rev. B 55 (1997) 14899. B. Dahneke, J. Colloid Interface Sci. 51 (1975) 58. S.J. Wall, W. John, H.-C. Wang, S.L. Goren, Aerosol Sci. Technol. 12 (1990) 926. R.P. Andres, Aerosol Sci. Technol. 23 (1995) 40. J. Israelachvili, in: Intermolecular and Surface Forces, Academic Press, New York, 1991.
246
K. Moloni et al. / Ultramicroscopy 80 (1999) 237}246
[14] K. Johnson, in: Contact Mechanics, Cambridge University Press, Cambridge, 1985. [15] D. Colbert, J. Zhang, S. McClure, P. Nikolaev, Z. Chen, J. Hafner, D. Owens, P. Kotula, C. Carter, J. Weaver, A. Rinzler, R.E. Smalley, Science 266 (1994) 1218. [16] A detailed description of this procedure may be found at http://cnst.rice.edu/mount.html or in Buss, R.B., Ph.D. Thesis, Purdue University, 1998.
[17] W. Mahoney, D.M. Schaefer, A.N. Patil, R.P. Andres, R. Reifenberger, Surf. Sci. 316 (1994) 383. [18] D.M. Schaefer, R. Reifenberger, A.N. Patil, R.P. Andres, Appl. Phys. Lett. 66 (1995) 1012. [19] C.-S. Lee, P. Guo, J. Virology 69 (1995) 5018. [20] Whistler, R.L., Purdue University, private communication.