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Atomic Force Microscopy at Solid-Liquid Interfaces S. J. O’Shea* and M. E. Welland Engineering Department, University of Cambridge, Cambridge CB2 1PZ, United Kingdom Received February 13, 1998. In Final Form: April 29, 1998 An atomic force microscope (AFM) operating in force modulation mode is used to study solvation forces at the interface between a graphite (HOPG) surface and the liquids octamethylcyclotetrasiloxane (OMCTS) and n-dodecanol. Simple analytical models are used that adequately describe the response of the cantilever as the modulation frequency and tip-sample interaction change. The analysis of AFM force curves yields the tip-sample interaction stiffness and damping. Hydrodynamic damping is significant for all the levers used and at present this limits the sensitivity of detecting weak tip-surface damping effects. The main results are: (i) Confinement of liquid between two surfaces can lead to oscillatory structural forces even when one of the surfaces has very high curvature. This could influence topographic images at the atomic level in liquids. In these experiments the typical radius for a sharp AFM tip is measured as Rtip ≈ 14 nm. (ii) The effective viscosity increases by ∼4 orders of magnitude for a sharp tip interacting with the OMCTS solvation layers nearest the surface. (iii) The AFM data are compared to published results obtained using the surface force apparatus (SFA). The AFM data for the interaction stiffness and damping are qualitatively similar to the SFA results, but the magnitude of the effects is smaller. This most likely arises from the limited interaction area over which the confined molecules can exhibit cooperative behavior (∼100 nm2). (iv) Oscillatory solvation forces can also be observed with very blunt tips (Rtip ≈ 350 nm), and the data suggest that in this case tip microasperities dominate the tip-sample interaction.
The forces acting between two solid surfaces in a liquid is of importance in many areas, including tribology and lubrication, adhesion, interactions between colloidal particles, and tip-sample interactions in scanning tunneling microscopy (STM) and atomic force microscopy (AFM). Much experimental understanding of the liquid-solid interface has been gained by use of the surface force apparatus (SFA), in which the force between two smooth mica surfaces is measured.1 An interesting problem studied using the SFA technique is the molecular ordering of a liquid induced by the presence of the nearby surface. Here oscillatory forces may be seen as the number of discrete molecular layers confined between the two approaching surfaces varies. Such behavior is clearly very different from that expected from continuum (e.g., van der Waals) force laws. More recently, the SFA method has been adapted to measure the shear forces acting as the two mica surfaces move laterally with respect to each other2. It is found that the shear can also depend on the discrete number of layers of molecules confined in the gap. AFM offers another means of studying forces between two surfaces at a molecular level, although a major difficulty is the chemical and geometrical characterization of the tip at the nanometer scale. Some previous AFM studies in liquid environments have shown how AFM can be used to measure long-range forces, such as the repulsive forces arising from the surface double layer in electrolyte solutions3 and the forces between long chain polymer brushes.4 Another research area is to directly measure the forces acting on colloidal particles by attaching the particle to the end of an AFM cantilever.5 Shorter range
forces, involving repulsive tip-sample interactions, have also been studied due to the promise of molecular scale chemical recognition and also because of the importance of such forces in understanding contact AFM imaging mechanisms. Examples include studies using tips and surfaces functionalized with chemically adsorbed molecules,6 which aim to either image site specific parts of the surface or to gain insight into the forces involved in molecule-molecule interactions. Similarly, the measurement of friction and adhesion using AFM also probes the localized surface chemistry.7 In this paper we are concerned with the measurement of short range forces in liquids using AFM. Specifically, we investigate the solvation forces acting near a graphite surface. This is a continuation of our previous AFM work in which solvation forces were observed by measuring either the normal force directly8 or by measuring the tipsample force gradient9 (i.e., the force derivative with respect to the separation, which is also called the stiffness or compliance). It transpires that the latter technique is considerably more sensitive. In this study we again use the compliance method to observe solvation effects but extend the work by considering the frequency response of both the magnitude and phase of the compliance signal as the tip-sample distance is varied. This allows a measurement of both the stiffness and damping at the tipsample junction. Also, much sharper tips are used, with the geometry of the tip apex measured directly using highresolution electron microscopy. These experimental additions lead to a fuller understanding of the behavior of realistic asperity contacts in liquids. The results and analysis will be used to illustrate general applications of AFM in liquid environments, such as imaging and nanome-
(1) Israelachvili, J. N. Intermolecular and Surface Forces; Academic: New York, 1986. (2) Van Alsten, J.; Granick, S. Phys. Rev. Lett. 1988, 61, 2570. (3) Butt, H.-J. Biophys. J. 1991, 60, 777. (4) O’Shea, S. J.; Welland, M. E.; Rayment, T. Langmuir 1993, 9, 1826. (5) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991, 353, 239.
(6) Frisbie, C. D.; Rozsnyai, L. F.; Noy, A.; Wrighton, M. S.; Lieber, C. M. Science 1994, 265, 2071. (7) Berger, C. E. H.; Vanderwerf, K. O.; Kooyman, R. P. H.; Degrooth, B. G.; Greve, J. Langmuir 1995, 11, 4188. (8) O’Shea, S. J.; Welland, M. E.; Rayment, T. Appl. Phys. Lett. 1992, 60, 2356. (9) O’Shea, S. J.; Welland, M. E.; Pethica, J. B. Chem. Phys. Lett. 1994, 223, 336.
Introduction
S0743-7463(98)00186-3 CCC: $15.00 © 1998 American Chemical Society Published on Web 06/18/1998
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chanics, and to compare the data with that found using the SFA. Experimental Section The AFM used is a standard optical deflection type. The cantilever and sample are completely immersed in a stainless steel liquid cell, which is thoroughly cleaned before experimentation. A digital AFM control system10 is used to enable multiple signal inputs to be measured simultaneously. In this study the applied force and force gradient (both magnitude and phase) are measured as the tip-sample separation distance is varied. Such data are called a force curve. The digital implementation of the feedback loop facilitates the acquisition of the force curve because of the ease of control of the tip-sample approach speed and the separation distances. This is important when using modulation techniques because one must ramp slow enough to sample sufficient modulation cycles within a given distance but fast enough to minimize thermal drift problems. Errors in the tipsample distance can arise from hysteresis effects in the piezoelectric tubescanner and a few force curves prior to the data collection are required to ensure that this problem is minimized. It is also important, particularly for the phase information, to characterize the frequency response of the system electronics and detection photodiode and to correct the data if necessary by the appropriate transfer function. In AFM the detection of the force gradient between the tip and sample is generally more sensitive than the measurement of the applied (static) force, although it is still desirable to measure both simultaneously.11 However, a difficulty for force gradient detection in liquids is the high damping of the AFM cantilever; i.e., the quality (Q) factor is typically j5 for soft levers, so that operating at the cantilever resonance to enhance the signal/noise ratio is not a useful technique. This also makes noncontact imaging modes difficult to implement in liquids. Notwithstanding this difficulty, the force gradient can be measured by modulating the tip-sample separation and measuring the corresponding response of the cantilever. The modulation method we adopt is to drive the AFM cantilever by the direct application of a force to the tip,9,12 and it is useful to note the direct similarity between this AFM modulation technique and the method of Pethica and co-workers for indentation on solid surfaces.13 Alternative means can be used to vary the tip-sample separation,14 for example, by displacement of the sample. While the latter methods can provide data, we have found that when working in liquid environments, the force modulation technique is considerably less noisy; i.e., hydrodynamic effects are minimized. The force modulation technique is implemented by coating the cantilever with a magnetic material (a ∼20 nm Co thin film evaporated on the non-tip side) and applying a sinusoidal magnetic field normal to the cantilever surface. The resulting oscillatory components of the lever deflection signal are measured using a lockin amplifier. The Co film magnetization is orientated such that the applied magnetic field results in a torque that bends the lever. This is achieved by placing a CoSm magnet beneath the cantilever during evaporation. If the film magnetization is across the width of the lever, the lever will twist rather than bend. To minimize unwanted deflection signals arising from the flexing of the whole lever in the applied magnetic field, the lever is masked during evaporation so that only the region at the very end of the lever is coated with Co. In our experiments a coil is wound around the liquid cell to produce a magnetic field that is approximately normal to the sample surface. The maximum field strength is ∼10-3 T, and the resulting maximum force applied to the tip is ∼2 nN. Note that the oscillatory driving force on the tip cannot be too large, because any structure in the force curve may become “smeared out” because the tip is moving too far, or too small such that the signal/noise ratio is compromised. (10) Wong, T. M. H.; Welland, M. E. Meas. Sci. Technol. 1993, 4, 270. (11) Durig, U.; Zuger, O.; Pohl, D. W. Phys. Rev. Lett. 1990, 65, 349. (12) Florin, E. L.; Radmacher, M.; Fleck, B.; Gaub, H. E. Rev. Sci. Instrum. 1994, 65, 639. (13) Pethica, J. B.; Oliver, W.C. Phys. Scripta 1987, T19, 61. (14) Burnham, N. A.; Gremaud, G.; Kulik, A. J.; Gallo, P.-J.; Oulevey, F. J. Vac. Sci. Technol. B 1996, 14, 1308.
Figure 1. Schematic diagram of the model used for the lever. The tip apex is a sphere (Rtip) rigidly attached to a rectangular cantilever. The lever and sphere are totally immersed in liquid. Two liquids are used, namely octamethylcyclotetrasiloxane (OMCTS), a large almost spherical molecule, and n-dodecanol (C11H23CH2OH), a linear molecule with a polar headgroup. A freshly cleaved graphite surface (HOPG) is used as the sample. Silicon AFM cantilevers are used with nominal spring constants of either 0.5 or 1.0 N/m. The cantilevers are imaged after use in a 400 keV JEOL scanning transmission electron microscope (STEM). The radius of curvature of a tip apex can be estimated to within ∼(3 nm from the STEM micrograph, provided the tip is sharp and has a well-defined geometry.
Analysis To interpret the data, we begin by outlining the dynamic response of a micofabricated cantilever beam in a fluid. There is much current interest in this type of problem both in order to understand AFM imaging in liquids and for MEMS sensor applications.15 Previous studies have shown that the simple harmonic oscillator model provides an adequate description of the cantilever motion for small amplitudes, and consequently, the response of an AFM cantilever can be readily evaluated for a variety of driving methods (e.g., modulating the sample, modulating the lever base, etc.).14 For our experiments, in which the tip is driven by a sinusoidal force at frequency ω, the appropriate equation of motion is
m*
d2y + Fdrag + (ki + kc)y ) Fa dt2
(1)
with
y ) yreference + y1 cos(ωt - δ) Fa ) Fo + F1 cos(ωt)
dy dt γ ) γ c + γs + γi
Fdrag ) γ
where Fa is the applied magnetic force (static component Fo, dynamic component F1), Fdrag is the damping force acting on the lever, y is the position of the tip, δ is the phase difference between the driving force and the lever response, m* is the effective mass, and kc is the spring constant of the lever. The term γ is separated into γi, γC, and γs, which are respectively the damping terms for the tip-surface interaction, the free cantilever beam, and the hydrodynamic squeezing between the cantilever and the surface. The tip-sample stiffness is ki ) dF/dD in the surface normal direction, where F represents the surface forces acting on the tip and D is the tip-sample separation. Figure 1 is a schematic diagram showing some of the (15) Hosaka, H.; Itao, K.; Kuroda, S. Sens. Actuators A 1995, 49, 87.
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Table 1. Calculated and Experimental Values for a Freely Oscillating Si Cantilever in Air and in OMCTSa parameter
value
L, µm b, µm t, µm Ltip, µm
247 58 1.92 214
m*air × 10-12, kg fo, kHz (expt) Q (expt)
17.7 40.6 102
m*liquid × 10-12, fo, kHz (expt)
253.7 10.5 10.7
kg
fo, kHz (calc)
parameter
value
htip, µm Rtip, nm OEL kc, N/m (calc)
13 14 1.54 1.1
In Air Q (calc) γc ×10-6, kg Hz (calc) In OMCTS Q (expt) Q (calc) γc × 10-6, kg Hz (calc)
125 0.036
2.5 3.0 5.6
a
This lever was used for most of the data presented in this paper but is representative of other cantilevers used. We used estimated valus of mtip ≈ 1.3 × 10-12 kg and effective mass of the evaporated cobalt ≈ 1.0 × 10-12 kg. For OMCTS FL ) 956 kg/m3 and η ) 0.002 35 Pa s. For air FL ) 1.2 kg/m3 and η ) 1.8 × 10-5 Pa s.
definitions. The relevant solutions for the amplitude and phase response are
y1 ) F1
1
x(ki + kc - m*ω )
2 2
(2) 2
(3)
m*air
)
kc )
kc nmc + mtip
Ebt3 4L3
(4)
(5)
where mtip is the tip mass, mc is the cantilever mass, E is Youngs modulus (179 GPa for Si cantilevers), and L, b, and t are the lever length, width, and thickness, respectively. For rectangular levers n ) 0.24 and mc ) FCLbt, where Fc is the lever density (2330 kg/m3 for Si). Table 1 illustrates the typical magnitudes of the parameters involved with data for a Si lever used in this study. The cantilever lengths are measured from scanning electron micrographs. The lever thickness is calculated using the measured fundamental frequency in air and eliminating kc from eqs 4 and 5.16 The Q factor is measured from the FWHM of the resonance peak17 or, if Q is low, from the best fit of eq 2 to the experimental response curve. Since (16) Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. Rev. Sci. Instrum. 1993, 64, 403. (17) Chen, G. Y.; Warmack, R. J.; Thundat, T.; Allison, D. P.; Huang, A. Rev. Sci. Instrum. 1994, 65, 2532.
FLω 2 X η
(6)
where η is the fluid viscosity, FL is the liquid density, and X is a characteristic length (in our case the lever width). Typically, Re lies between ∼1 and ∼100 for the frequencies (∼200 Hz to ∼20 kHz) and levers we have used. This implies that the flow is usually in the inertial regime and some additional mass of fluid surrounding the cantilever will be accelerated by the lever motion. To account for this we write the drag force in the equation of motion as20
Fdrag ) γ
2
The fundamental resonance frequency of the cantilever is ωo ) xk/m* and the quality factor is defined as Q ) m*ωo/γ. In this study we measure y1 and δ and wish to find the material properties ki and γi. To proceed, we first evaluate the cantilever parameters kc and γc. This can be done by measuring the frequency response of the cantilever far from any surface, i.e., where ki ) γi ) γs ) 0. The use of rectangular AFM levers, in contrast to triangular levers, simplifies the analytical modeling of the two parameters ωo and γc (or Q), which define the frequency response curve of the free lever. Specifically, for data taken in air, we can write for the fundamental mode,
kc
Re )
+ (γ) ω
γω tan δ ) ki + kc - m*ω2
ωo2 )
the purpose of this work is to understand the behavior under liquids, we ignore the relatively small effects of inertial drag and damping in air in the calculation of ωo. These effects have been studied in detail elsewhere.18 When a cantilever is immersed in a liquid, the increased viscosity and density change the response appreciably from that in air. The resonance frequency and the quality factor decrease markedly. For microfabricated cantilevers oscillating at a small amplitude the relevant Reynolds number for the fluid flow is,15,19
dy d2y + mL 2 dt dt
(7)
where mL represents the additional fluid mass being accelerated. The equations retain the same form except * ) that the effective mass in liquid now becomes mliquid nmc + mL + mtip.17 To evaluate mL, we use the simplified theory of Greenspon21 for the vibration of plates in water, from which
mL m*air
)
FL L A2 f(b/L) FC t B
(8)
Equation 8 differs by a factor of 2 from that of Greenspon to account for liquid being on both sides of the plate.22 For the lowest vibrational mode of a rectangular cantilever structure the beam function is A2/B ≈ 0.6. The function f(b/L) is evaluated by Greespon21 but can be approximated as f(b/L) ) xb/L for b/L > 0.1. For the fundamental mode of an AFM cantilever in liquid we therefore use * ) nmc + mtip + 0.6nFL(Lb)3/2 mliquid
(9)
in the equations of motion, which results in reasonable values of ωo (within 20%) for our data taken in OMCTS using four different cantilevers (e.g., see Table 1). We also find a good fit ((∼12% in ωo) to the recent data of Walters et al.23 for microfabricated cantilevers of different dimensions immersed in water and to the data of Inaba et al.22 for millimeter-sized metal cantilevers immersed in water and water mixtures. These latter two studies allow a better test of eq 9 because the driving force is thermal excitation, which provides a white noise source, (18) Blom, F. R.; Bouwstra, S.; Elwenspoek, M.; Fluitman, J. H. J. J. Vac. Sci. Technol. B 1992, 10, 19. (19) Sader, J. E.; Larson, I.; Mulvaney, P.; White, L. R. Rev. Sci. Instrum. 1995, 66, 3789. (20) Landau, L. D.; Lifshitz, E. M. Fluid Mechanics; Pergamon: London, New York, Paris, 1959. (21) Greenspon, J. E. J. Acoust. Soc. Am. 1961, 33, 1485. (22) Inaba, S.; Akaishi, K.; Mori, T.; Hane, K. J. Appl. Phys. 1993, 73, 2654. (23) Walters, D. A.; Cleveland, J. P.; Thomson, N. H.; Hansma, P. K.; Wendman, M. A.; Gurley, G.; Elings, V. Rev. Sci. Instrum. 1996, 67, 3583.
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allowing a simple interpretation of the response over a wide frequency range. The lever response in n-dodecanol, which is very heavily damped (Q ∼ 1.25), gave estimates of ωo that were much poorer (up to 50% error). We note that eq 9 may prove useful for estimating the operating frequency in tapping mode AFM in liquids, in which it is sometimes difficult to distinguish the lever resonance from the “forest” of peaks caused by the motion of the disturbed fluid.24 For the tapping mode in a liquid the lever is driven by the modulation of the sample surface. In this case, the amplitude response of the cantilever has a form similar to eq 2 if we assume the interaction damping is negligible (γi ≈ 0).14 Ignoring the tip mass the resonance frequency in liquid is approximately
ωo air2 ωo liquid2
FL xLb ≈ 1 + 0.6 FC t
(10)
where use has been made of eqs 4 and 9. The situation is less satisfactory if an analytical expression is required for the cantilever damping term γc (or Q) as a function of the lever dimensions. Here closedform solutions for oscillatory motion in a fluid are available only for a few simple structures, such as rods and spheres. For a sphere of radius R oscillating freely in a fluid the damping term is,20
R4 γc ) 6πηR + 3πR2 x2FLηω + 16η 3 h
(11)
The first term is the usual Stokes expression for viscous (i.e., low Re number) flow and the second term is the high Re number limit of the dissipative forces.20 As noted above, high Re terms are significant for AFM experiments in liquids. To model the damping of a rectangular structure, we follow a method used in micromachining applications in which an arbitrary beam shape is modeled as a “string” of spheres of diameter equal to the beam width, as discussed by Hosaka et al.15 (note that their definition of Q differs from ours by a factor of 2). Using the string of spheres model with R ) b/2, we can rewrite eq 11 for the free cantilever as
(
γC ) n 3πηL +
3 πbLx2FLηω 4
)
(12)
since the number of spheres per unit length is 1/b. Equation 12 is conveniently evaluated at ω ≈ ωo. The experimental and theoretical values of Q found using eq 12 agree within ∼40% for our data taken in OMCTS (e.g., see Table 1). If eq 12 is tested against the more extensive data of Walters et al. taken in water (using FL ) 1000 kg/m3, η ) 10-3 Pa s)23 and Blom et al. taken in air (using FL ) 1.2 kg/m3, η ) 1.8 × 10-5 Pa s),18,25 we find the calculated and measured Q can differ by up to 60%. A difficulty, as shown experimentally,23 is that γc cannot depend solely on a single dimensional parameter (R) for rectangular structures as in eq 11. The damping depends on L, b, and t, and our use of R ) b/2 is simply a reasonable approximation. We therefore concur with Walters et al. that eqs 11 and 12 provide only a rough estimate of the damping. Nevertheless, for AFM experiments in liquids one invariably finds that Q is very low, so it is arguable whether a more accurate expression is (24) Schaffer, T. E.; Cleveland, J. P.; Ohnesorge, F.; Walters, D. A.; Hansma, P. K. J. Appl. Phys. 1996, 80, 3622. (25) CRC Handbook of Chemistry and Physics; Weast, R.C., Ed.; CRC Press: Boca Raton, FL, 1982.
required for most applications. In particular, it is possible to model changes in liquid damping for a given lever using simple analytical models as given above.17,22 Results and Discussion (i) Stiffness ki. Using the above analysis for the free lever, we can now measure ki and γi as the tip approaches and interacts with a surface. The compliance ki can be found from eqs 2 and 3 as
[
ki ) (OEL) kc
]
yo cos δ - kc + m*ω2 y1
(13)
where yo is the amplitude of the lever oscillation at ω ≈ 0 and far from the surface, i.e., yo ) F1/kc. Thus, by measuring y1, we can obtain ki. It is convenient to put yo/y1 ) (yo/yfar)(yfar/y1) where yfar is the value of y1 farthest from the surface in a given force curve. Hence at a given frequency the amplitude data are normalized to unity far from the surface and the amplitude multiplied by the spectral response yfar/yo. The maximum stiffness that can be measured is set by (a) the large error arising from the flexing of the lever in repulsive contact because the magnetic coating extends along some length of the cantilever, (b) the signal/noise level in the amplitude ratio yo/y1, and (c) the lever spring constant kC. In this study the maximum reliable stiffness measured is ∼5 N/m. The term OEL is the “off-end loading” correction, which arises because the tip is not at the end of the cantilever. This correction can be large and we use the expression OEL (L/Lt)3,26 where Lt is the length of the lever measured up to the tip. Figure 2a gives an example of the raw data obtained at the OMCTS/graphite interface at low modulation frequency (ω/ωο ) 0.035). Off the surface periodic changes in the amplitude of the lever oscillation due to solvation forces can be seen. It is worth recalling that the solvation layers surround both surfaces,1 i.e., the tip apex as well as the graphite surface. At the (arbitrary) sample displacement of 0 Å the tip experiences a strong repulsive force and the lever oscillation is heavily damped. In this example the amplitude falls abruptly rather than smoothly at the positions marked 1 and 2. These positions are also associated with distinct instabilities in the applied force, which we have previously found to correspond to strongly bound liquid at the surface.27 The stiffness data also strongly suggest that this region is a solvation layer of OMCTS, and Figure 2b shows the amplitude data plotted as interaction stiffness (ki). Off the surface the solvation oscillations are of order 0.1 N/m peak-peak, as shown more clearly in Figure 3a. Between positions 1 and 2 the stiffness is approximately constant at 3.8 N/m. At position 2 the stiffness jumps to ∼7 N/m, but it must be emphasized that this value of ki should be regarded in qualitative terms only. At high loads the experimental uncertainties, principally the flexing of the cantilever, imply that ki may be .20 N/m and the only meaningful comment one can make is that ki is large. The low stiffness between positions 1 and 2 suggests that a compliant substance is present between the tip and substrate. The most likely material is obviously an OMCTS solvation layer and this is the assumption we adopt. However, the possibility of organic contamination of the tip or sample cannot be excluded and is a general problem for AFM in liquids. Another possibility, that the (26) Sader, J. E.; White, L. R. J. Appl. Phys. 1993, 74, 1. (27) O’Shea, S. J.; Welland, M. E.; Rayment, T. Appl. Phys. Lett. 1992, 61, 2240.
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Figure 2. Force curves for a 14 nm radius tip approaching a HOPG surface in OMCTS. The distance is the displacement of the sample toward the tip, and zero is arbitrarily set where the applied force becomes repulsive. Large positive distances correspond to the tip being far from the surface. The region between positions 1 and 2 is a strongly bound solvation layer. (a) The normalized amplitude of the force driven cantilever oscillation as a function of distance. The dark curve is the applied force. (b) The amplitude data of (a) plotted as interaction stiffness ki. The dark curve is the applied force.
region corresponds to the tip in repulsive contact with the HOPG substrate, is not plausible if we consider a simple continuum model of the contact, namely13
ki ) 2E*a
(14)
where E* is the effective Youngs modulus and a is the radius of the (circular) contact area. If the contact were to the HOPG substrate, then E* ∼ 40GPa28 and eq 14 yields a ∼ 0.5 Å. This is clearly too small for a tip with a measured radius of curvature of 14 nm. Alternatively, if the region is an OMCTS solvation layer, we can expect E* to be much lower. In this case, since the adhesive force is very low (
