Solvation Forces Using Sample-Modulation Atomic Force Microscopy

Oscillatory solvation forces in liquid were studied using off-resonance, low-amplitude, sample-modulation atomic force microscopy (AFM). Experiments w...
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Solvation Forces Using Sample-Modulation Atomic Force Microscopy Roderick Lim,† Sam F. Y. Li,‡ and Sean J. O’Shea*,† Institute of Materials Research and Engineering, 3 Research Link, Singapore 117602, and Department of Chemistry, National University of Singapore, Lower Kent Ridge Road, Singapore 119260 Received December 10, 2001. In Final Form: April 1, 2002 Oscillatory solvation forces in liquid were studied using off-resonance, low-amplitude, sample-modulation atomic force microscopy (AFM). Experiments were carried out with as-purchased tips and with tips modified by the attachment of 10-µm-sized glass beads on a highly oriented pyrolytic graphite (HOPG) substrate submerged in octamethylcyclotetrasiloxane (OMCTS). The sample-modulation response curves allow us to make a direct measurement of the interaction stiffness (force gradient) as a function of tip-sample distance, and we show how this technique is capable of measuring both repulsive and attractive solvation potentials in a single approach with the correct selection of cantilever stiffness. We calculate the solvation force by integrating the stiffness over the tip-sample distance, from which we see clear oscillatory behavior. Normalizing the force with the tip radius allows comparisons to be made between these results and previous surface force apparatus (SFA) data, which sometimes agree with SFA data and sometimes differ markedly. We attribute this to variations in tip roughness and geometry. Our results suggest that nanoscopic roughness can indeed significantly affect force measurements in AFM. Characterization of the bead surface revealed that the beads always contain asperities, and we conclude that these asperities give rise to significant variability in oscillatory force curves, as oscillatory forces occur only near the asperities.

I. Introduction The molecular ordering of liquids, as induced by confinement between two solid surfaces, has been well studied because of its influence on surface-surface interactions.1 Examples of liquid-mediated surfacesurface interactions can be found in areas such as tribology, adhesion, and the structuring of biological molecules. This ordering can lead to oscillatory solvation forces and has been studied extensively both theoretically2-5 and experimentally using the surface force apparatus (SFA).6-8 The force oscillations are reflections of the geometric packing experienced by the liquid due to the confinement imposed by the surfaces, with the period of oscillation approximately equal to the molecular diameter of the liquid.1 More recently, atomic force microscopy (AFM)9-12 has shown that oscillatory solvation forces can be present in a liquid confined between a smooth surface and a tip only nanometers in size. Subsequent theoretical work has shown that solvation forces can indeed occur in small confinement volumes such as in AFM.13-16 The main * To whom correspondence should be addressed. Phone: (65) 874-4314. Fax: (65) 872-0785. E-mail: [email protected]. † Institute of Materials Research and Engineering. ‡ National University of Singapore. (1) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: New York, 1992. (2) Mitchell, D. J.; Ninham, B. W.; Pailthorpe, B. A. J. Chem. Soc., Faraday Trans. 2 1977, 74, 1096. (3) Chan, D. Y. C.; Mitchell, D. J.; Ninham, B. W.; Pailthorpe, B. A. J. Chem. Soc., Faraday Trans. 2 1979, 75, 556. (4) van Megen, W.; Snook, I. J. Chem. Soc., Faraday Trans. 2 1979, 75, 1095. (5) Chan, D. Y. C.; Mitchell, D. J.; Ninham, B. W.; Pailthorpe, B. A. J. Chem. Soc., Faraday Trans. 2 1980, 76, 776. (6) Horn, R. G.; Israelachvili, J. N. J. Chem. Phys. 1981, 75, 1400. (7) Christenson, H. K. J. Chem. Phys. 1983, 78, 6906. (8) Klein, J.; Kumacheva, E. Science 1995, 269, 816. (9) O’Shea, S. J.; Welland, M. E.; Rayment, T. Appl. Phys. Lett. 1992, 60, 2356. (10) O’Shea, S. J.; Welland, M. E.; Pethica, J. B. Chem. Phys. Lett. 1994, 223, 336. (11) O’Shea, S. J.; Welland, M. E. Langmuir 1998, 14, 4186. (12) Han, W. H.; Lindsay, S. M. Appl. Phys. Lett. 1998, 72, 1656.

difficulties associated with AFM-type measurements are the characterization of the underlying AFM tip chemistry where contamination can occur17,18 and characterization of the geometry of the tip at the nanometer scale.11 It has been shown from SFA data that oscillatory behavior does not occur if the surfaces are rough, because asymmetry and roughness break up the ordering of the liquid.1 The oscillatory behavior of the solvation (layering effect) is lost and replaced by a purely monotonic solvation force when the two opposing surfaces are randomly rough.19 Theoretical investigations also show that oscillatory behavior is significantly reduced for a liquid confined between two rough surfaces.20,21 Unfortunately, it is inherently difficult to replicate experiments with the matching theoretical conditions because difficulties arise when one tries to isolate surface roughness as an effect and when one tries to vary the surface roughness quantitatively. AFM has further raised the issue of nanoscale roughness and asperities in AFM solvation measurements.11 The purpose of this paper is to (a) study the effects of tip roughness and geometry in the AFM measurements of the solvation force and (b) demonstrate the utility of sample-modulation stiffness measurements for solvation forces. We have previously shown that measuring the tipsample force gradient (i.e., the force derivative with respect to the separation, which is also called stiffness or compliance) is considerably more sensitive in the AFM measurement of solvation forces than measuring the normal force directly from the static cantilever deflection.10 In (13) Gelb, L. D.; Lynden-Bell, R. M. Phys. Rev. B 1994, 49, 2058. (14) Gao, J. P.; Luedtke, W. D.; Landman, U. J. Phys. Chem. B 1997, 101, 4013. (15) Patrick, D. L.; Lynden-Bell, R. M. Surf. Sci. 1997, 380, 224. (16) Iwamatsu, M. J. Colloid Interface Sci. 1998, 204, 374. (17) Lo, Y.; Huefner, N. D.; Chan, W. S.; Dryden, P.; Hagenhoff, B.; Beebe, T. P., r. Langmuir 1999, 15, 6522. (18) Bowen, W. R.; Hilal, N.; Lovitt, R. W.; Wright, C. J. Colloids Surf. A 1999, 157, 117. (19) Christenson, H. K. J. Phys. Chem. 1986, 90, 4. (20) Frink, L. J. D.; van Swol, F. J. Chem. Phys. 1998, 108, 5588. (21) Gao, J. P.; Luedtke, W. D.; Landman, U. Tribol. Lett. 2000, 9, 3.

10.1021/la011789+ CCC: $22.00 © 2002 American Chemical Society Published on Web 06/28/2002

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this work, we demonstrate the use of the compliance method by carrying out sample-modulation force spectroscopy. Although sample-modulation force curves are slightly noisier in liquid environments than the curves obtained with the corresponding force-modulation technique,11 the technique allows for very stiff systems to be studied more readily. If tip instabilities are avoided by choosing the appropriate cantilever stiffness (kc), forcedistance curves for both the attractive and repulsive parts of the oscillatory potential can be obtained in a single measurement. Experiments were performed with either as-purchased tips or tips consisting of 10-µm glass beads glued to the free end of the cantilever. The attachment of colloidal beads as AFM tips22 has been shown to be a very useful technique in the controlled modification of probe size and geometry for many different interactions.22-28 We employ this technique to increase the interaction area of the confining surface and to introduce random roughness into our experiments. By comparing results from this present work, using as-purchased tips, to previous SFA6 and AFM11 data, we show that AFM solvation force measurements can vary markedly for different tip geometries. Roughness is more difficult to quantify. Oscillatory behavior is observed using bead-modified tips, which have randomly rough surfaces. However, roughness as defined from AFM or SEM imaging is not sufficient for solvation force measurements as the interacting surfaces are frequently dominated by a few protruding asperities. Finally, we suggest and discuss possibilities that can explain some discrepancies between the solvation force measurements of this work and previous AFM work. II. Experimental Section Figure 1 illustrates the schematics of our experimental setup. We have carried out sample-modulation force spectroscopy experiments with a modified commercial AFM system (Molecular Imaging Co.). The liquid cell, which encloses the entire sample surface and cantilever, is filled with octamethylcyclotetrasiloxane (OMCTS). A piezostack is used to oscillate the sample at typical peak-to-peak amplitudes of 2 Å. The amplitude of induced cantilever oscillations is measured using an EG&G 7265 lock-in amplifier. Experiments were performed in an enclosed chamber purged with N2 without any prior treatment to the OMCTS (Aldrich Chemical Co.). Freshly cleaved HOPG, which is atomically smooth, was the surface used. In a typical force-distance experiment, the piezoelectric displacement (Z) is varied in a known manner while the static cantilever deflection and oscillation amplitude are measured simultaneously. Figure 2a shows a typical force curve taken in OMCTS. The periodic-like behavior in both the amplitude and static deflection curves results from solvation forces. The piezoelectric displacement is converted to the tip-sample distance (D) by

D ) (Z - Z0) -

(V - V0) , Ω

(1)

where V is the photodiode output signal, V0 is the photodiode output signal at large separation (i.e., no deflection), Z0 is the (22) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991, 353, 239. (23) Gady, B.; Reifenberger, R.; Rimai, D. S.; Demejo, L. P. Langmuir 1997, 13, 2533. (24) Toikka, G.; Hayes, R. A.; Ralston, J. Langmuir 1996, 12, 3783. (25) Considine, R. F.; Hayes, R. A. ; Horn R. G. Langmuir 1999, 15, 1657. (26) Kohonen, M. M.; Karaman, M. E.; Pashley, R. M. Langmuir 2000, 16, 5749. (27) Heim, L.; Blum, J.; Preuss, M.; Butt, H. J. Phys. Rev. Lett. 1999, 83, 3328. (28) Mohideen, U.; Anushree, R. Phys. Rev. Lett. 1998, 81, 4549.

Figure 1. Schematic of the experimental setup for the samplemodulation technique. value of Z at V ) V0 after tip-sample contact has occurred, and Ω is the photodiode sensitivity (i.e., output signal per unit deflection of the cantilever). The value of Ω is found from the slope of the static deflection curve in the hard-wall repulsive regime (see Figure 2a). The force F is found from the deflection data by

F ) kc

(

)

V - V0 Ω

(2)

where kc is the cantilever spring constant. Figure 2b shows the converted data of Figure 2a. Tip instabilities are clearly seen as discontinuous jumps in the tip-sample separation. In the interpretation of our data, we assign the D ) 0 separation to occur at hard-wall repulsion. The error in the D ) 0 position is estimated to be (2 Å. The amplitude signal can be used to find the tip-sample interaction stiffness as follows. The dynamic solution of the equation of motion of a sample driven system can be written29

d ) A0

ki[1 + (2m*ωβi/ki)2]1/2

x(ki + kc - m*ω2)2 + [2m*ω(βi + βc)]2

(3)

where d is the tip displacement, A0 is the driving amplitude, ω is the driving frequency, ki is the tip-sample interaction stiffness (the desired quantity), βi is the interaction damping constant, βc is the cantilever damping constant, and m* is the effective mass. In the low-frequency limit (ω f 0), eq 3 reduces to

ki d )( A0 ki + kc

(4)

Equation 4 represents all of the data presented in this work because the working frequency (∼400 Hz) is always much smaller than the fundamental cantilever resonance. Hence, by estimating (29) Burnham, N. A.; Kulik, A. J.; Gremaud, G.; Gallo, P. J.; Oulevey F. J. Vac. Sci. Technol. B 1996, 14, 794.

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Lim et al. width of each cantilever are measured with a scanning electron microscope (SEM). Lever thicknesses are calculated by using the measured fundamental frequency and eliminating kc from eqs 5 and 6. As-purchased AFM cantilevers are modified by gluing 10-µm glass beads (Duke Scientific Co.) to preflattened tips. Flattened tips are made by scratching a tip against a clean Si substrate. The beads are cleaned by repeated ultrasonication in toluene. Great care is taken not to coat the lower surface of the bead with glue during bead attachment. SEM characterization of the bead geometry and surface condition is carried out after experimentation to avoid contamination. Measurements of bead surface roughness are carried out by reverse AFM imaging in contact mode31 on a sample set of 10 beads randomly chosen from the same batch of cleaned beads. Roughness measurements calculated from AFM images are reported as root-mean-square roughness values

x

N

∑(z - zj)

Rrms )

Figure 2. (a) Raw data of deflection (dashed line) and normalized amplitude (solid line) curves for a Si AFM cantilever with kc ) 1.79 N/m and Rtip ) 50 nm immersed in OMCTS. The thick dashed line indicates the slope used to calculate the sensitivity Ω and the definitions of Z0 and V0. The dashed lines indicate the positions of amplitude maxima that correspond to applied force maxima and minima. (b) Applied force (filled circles) and normalized amplitude (open circles) plot as a function of tip-sample distance D after conversion of the data of Figure 2a using eqs 1 and 2. A periodicity in the amplitude data of ∼9 Å is observed at separations of D ) 0-40 Å. Tip instability (jumps) also occur at these distances. At separations greater than 40 Å, no instabilities occur, and the apparent periodicity is 4-5 Å. the cantilever stiffness kc (see below), we can extract the tipsample interaction stiffness ki by measuring the normalized change in amplitude (d/A0). Furthermore, ki can be related to the interaction force law F(D) by ki ) -dF/dD. Cantilever spring constants are calculated by measuring the fundamental resonance frequency (ω0) of each lever in a vacuum chamber prior to experimentation and relating ω0 to the physical dimensions of the cantilever using30

ω02 )

kc kc ) m* nmc + mtip

(5)

and

kc )

Ebt3 4L3

(6)

where mtip is the tip mass; mc is the cantilever mass; n is a geometric correction factor; E is the Young’s modulus; and L, b, and t are the lever length, width, and thickness, respectively. Rectangular Si AFM cantilevers (Nanosensors) are used in these experiments, for which E ) 179 GPa; n ) 0.24; and mc ) FcLbt, where Fc is the lever density (2330 kg/m3 for Si). The length and (30) Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. Rev. Sci. Instrum. 1993, 64, 403.

2

i

i)1

N

(7)

where N is the number of height positions along a line profile, zi is the height at position i, and zj is the average height. In reverse AFM imaging, the beads are attached to Si3N4 cantilevers (kc ) 0.2 N/m) and scanned over a calibration grid (NT-MDT TGT01), consisting of a periodic array of sharp asperities. In this way, the image is equivalent to an AFM image of the bead surface. Cantilevers having stiffness values of kc ≈ 2-4 N/m were used in as-purchased tip experiments, and cantilevers of kc ≈ 60 N/m were chosen for bead-modified experiments. We discuss in detail below the reason behind the choice of cantilever stiffness.

III. Results and Discussion I. Sample-Modulation Force Spectroscopy. Figure 2a is an example of raw data obtained for an as-purchased Si cantilever (kc ) 1.8 N/m, Rtip ≈ 50 nm) immersed in OMCTS. The piezostack was driven at a peak-to-peak amplitude of 2 Å at low modulation frequency (ω/ω0 ) 0.006). The vertical dotted lines indicate corresponding features between the deflection and amplitude curves. Solvation effects can be seen with characteristic “jumps” in the deflection curve and corresponding periodic changes in the amplitude curve. In this particular experiment, instabilities occur at separations smaller than ∼40 Å (see Figure 2b). In this region (D ) 0-40 Å), the periodicity of the amplitude signal is ∼9 Å, which is approximately equal to the diameter of an OMCTS molecule. At separations greater than ∼40 Å, the amplitude periodicity is halved to 4-5 Å. Experiments done with cantilevers of different spring constants show that these half-period oscillations are consistently observed provided that kc > |ki|, i.e., no instabilities occur. Further understanding is obtained by comparing the amplitude with the simultaneously measured applied force, i.e., the static cantilever deflection. Between D ) 0 and 40 Å, the 9 Å periodicity observed in the amplitude corresponds to discontinuous jumps in the applied force curve. These jumps occur only on the attractive part of the force curve. In contrast, for separations greater than 40 Å, no discontinuous jumps in the applied force curve are seen. Careful comparisons made between applied force curves and amplitude curves show that the amplitude maxima of the half-period oscillation are features that correspond directly to alternating maxima and minima in the applied force (as indicated by the dotted lines in Figure 2a). The above amplitude response curve arises from the sample modulation technique. Because the measured (31) Neto, C.; Craig, V. S. J. Langmuir 2001, 17, 2097.

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amplitude d/A0 can never be negative, the solutions to eq 4 are restricted to

ki )

kc

( )

A0 -1 d

for ki g 0

(8)

for -kc < ki e 0.

(9)

and

ki )

-kc A0 +1 d

( )

A discontinuity occurs at ki f -kc, which corresponds to tip instability. Note that the value of ki is positive when the sample and tip are in repulsive contact and negative when the interactions are in the attractive regime. Figure 3a shows the solution graphically, and we note that, for a given amplitude d/A0, there are two possible solutions of ki. Therefore, for a force curve showing oscillatory behavior about ki, as in these experiments, the amplitude response d/A0 appears rectified, i.e., period-halved. When tip instabilities occur, the apparent periodicity returns to ∼9 Å because the experiment does not sample the attractive minima, i.e., the strong attractive component of the data is not observed. The phase response acquired during force curve measurements supports the above interpretation that the period halving in the amplitude is the sample-modulation response to the attractive and repulsive regimes of the force curve. The phase response should not show any rectified behavior, i.e., the oscillation in the phase measurement should be ∼9 Å even in regions where the amplitude oscillation is ∼4-5 Å. This is indeed observed (data not shown). Note that we do not generally use phase data in this study because various instrument restrictions do not allow for an accurate quantitative analysis. Interestingly, the graph of Figure 3a indicates that, in the attractive regime where -kc < ki < -kc/2, the value of d/A0 is greater than unity. We find evidence of this phenomenon particularly in the solvation shell immediately preceding the first tip instability in approach curves and immediately following the last tip instability in retraction force curves. We show in Figure 3b an approach curve where such a measurement has been made. The value of kc in this particular experiment is 1.9 N/m and the probe used is an AFM tip modified with a glass bead (Rtip ≈ 2.5 µm). As in Figure 2a, we observe oscillations of ∼5 Å in the amplitude curve between Z ) 46 nm and Z ) 49 nm, with no tip instabilities in the corresponding deflection curve. At displacements of less than Z ) 46 nm, discontinuities are seen in the deflection curve that are a result of tip instability. The arrow indicates the force minimum that precedes the first tip instability, and at this distance, the normalized amplitude peak is greater than unity. Using eq 9, we find that this attractive peak has an interaction stiffness of ki ) -1.02 N/m, which lies in the range of -kc < ki < -kc/2. Data where d/A0 is greater than unity are sparse because of the exponential dependence of the solvation force on the tipsample distance, which demands that all conditions have to be precise such that ki falls in the window of -kc < ki < -kc/2. The attractive minimum indicated by the arrow in Figure 3b is the fourth minimum observed from the sample surface. The three solvation minima nearer the surface can be measured by using a stiffer cantilever, and an

Figure 3. (a) Solution to eq 4 (normalized amplitude d/A0 vs interaction stiffness ki) shown graphically. Note that tip instability occurs when ki < kc. The value of d/A0 is greater than unity in the region -kc < ki < -kc/2. (b) Plot showing the approach force curves for an experiment where kc ) 1.9 N/m and the probe used is an AFM tip modified with a glass bead (Rtip ≈ 2.5 µm). The amplitude maximum at Z ) 46.5 nm (position of arrow) corresponds to a force minimum for which the normalized amplitude is greater than unity.

estimate of the values of ki that can occur can be found using an approximate expression for the oscillatory forces10

e (2πD σ )

ki ) kBTFn(2πRtip) cos

-D/τ

(10)

for a parabolic tip of radius Rtip, where kB is the Boltzmann constant, T is the temperature, Fn is the number density of molecules in the bulk liquid, τ is a decay length, and σ is the diameter of the liquid molecules. Using eq 10 and Rtip ≈ 2.5 µm, we estimate ki for the first three force minima to be -24, -9, and -3 N/m, respectively, for the experiment of Figure 3b. These values fall in the range where ki < -kc and are indeed observed as tip instabilities. A corollary of the above analysis is that, if sample modulation is to be used to map the force curve, then (i) the applied force must be measured simultaneously to provide an indication of the sign of the force interaction, i.e., repulsive or attractive, and (ii) discontinuities in the force curve must be avoided by using a cantilever of sufficiently high stiffness (kc) for a given tip radius.

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ized amplitude and applied force plotted against the tipsample distance (D). The dotted lines show that the amplitude maxima correspond to alternating applied force maxima and minima. Figure 4b is a plot of stiffness as calculated from the normalized amplitude data. The peakto-peak stiffness values are measured from the stiffness minimum to stiffness maximum as indicated by the arrows and vary from 3 to 1.5 to 0.7 to 0.3 N/m for the first, second, third, and fourth solvation layers, respectively. Upon integration of the stiffness with respect to the tip-sample distance, the force can be calculated and normalized by the tip radius (Figure 4c). Normalization allows for a comparison between this present work and similar AFM or SFA data. The normalized forces corresponding to the first, second, third, and fourth solvation layers are measured to be 24, 13, 5, and 2.5 mN/m, respectively. To compare the relative strength of the solvation force to the van der Waals contribution of the measured force, we calculate the theoretically expected nonretarded van der Waals force as given by the continuum Lifshitz theory.32 The attractive van der Waals force between a sphere and a plane is given by

Fsp-pl vdw ) -

AR 6D2

(11)

where R is the sphere radius and A is the Hamaker constant. This force is expected if the intervening liquid is a structureless continuum, defined solely in terms of the bulk dielectric permittivity. The Hamaker constant is not known for the SiO2-OMCTS-HOPG system, and we approximate the value using eq 11.13 of ref 1 as

(

)(

)

3hve 1 - 3 2 - 3 3 Atot ≈ kBT + 4 1 + 3 2 + 3 8x2 (n12 - n32)(n22 - n32) (n12 + n32)1/2(n22 + n32)1/2[(n12 + n32)1/2 + (n22 + n32)1/2] (12)

Figure 4. Representative force curves from a single approach measured in OMCTS (kc ) 2.5 N/m, ω/ω0 ) 0.006, Rtip ) 26 nm). (a) Applied force ([) and normalized amplitude (b) plotted as a function of separation (D). The dotted lines indicate that each amplitude maximum corresponds (alternatively) to either an applied force maximum or an applied force minimum. No tip instabilities are present. (b) Amplitude data, converted into stiffness (ki), as a function of separation (D). The peak-to-peak stiffness values for the first, second, third, and fourth solvation (4) layers (k(1) i -ki ) are measured to be 3, 1.5, 0.7, and 0.3 N/m, respectively. (c) Normalized force (F/Rtip) as a function of separation D (b), as calculated by integration of the stiffness data of Figure 4b. F/Rtip values for the first, second, third, and fourth solvation layers (F(1)/Rtip-F(4)/Rtip) are measured to be 24, 13, 5, and 2.5 mN/m, respectively. Also shown is the estimated van der Waals force (O) for the SiO2-OMCTS-HOPG system.

II. Solvation Forces Measured with As-Purchased AFM Tips. The force curves of Figure 4 are representative of data typically measured with an as-purchased bare AFM tip. Scanning electron microscopy (SEM) revealed the (post-experiment) tip radius to be 26.2 ( 5.8 nm, and kcwas measured to be 2.5 N/m. With this choice of kc, no tip instabilities were observed. Figure 4a shows the normal-

where h is Planck’s constant, ve is the electronic absorption frequency, n is the index of refraction, and  is the dielectric constant. The subscripts 1, 2, and 3 on  and n are indices representing SiO2, HOPG, and OMCTS, respectively. The respective dielectric constants and index of refraction values used here are 1 ) 3.82 and n1 ) 1.448,33 2 ) 2.61 and n2 ) 2.15,34 and 3 ) 2.318 and n3 ) 1.3977 for each respective material, giving Atot ≈ 0.9 × 10-20 J. The theoretical van der Waals force curve is shown in Figure 4c. The van der Waals force is not discernible in the applied force data of Figure 4a as it is below the noise level. The normalized force measurements reported in this paper for as-purchased tips differ from our results reported previously11 but are in good agreement with SFA6 data. As listed in Table 1, the oscillatory forces measured here are 3-4 times greater than those reported in ref 11. It is important to note that tip instabilities were also not present at the second, third, and fourth solvation layers in ref 11. As discussed by Israelachvili,1 there are several factors that can influence oscillatory force measurements. These include (i) contamination, i.e., the presence of both miscible and immiscible components in the liquid under (32) Mahanty, J.; Ninham, B. W. Dispersion Forces; Academic Press: New York, 1976. (33) Bergstrom, L. Adv. Colloid Interface Sci. 1997, 70, 125. (34) Kelly, B. T. Physics of Graphite; Applied Science Publishers: London, New York, 1981.

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Table 1. Comparison of Selected Experimental Data Showing the Variation in F/Rtip between Different Experimentsa F/Rtip (mN/m) instrument/reference al.6

SFA/Horn et AFM/O’Shea et al.11 AFM/this work AFM/this work AFM/this work

Rtip

2nd layer

3rd layer

4th layer

1 cm 14 nm 26 nm 19 nm 10-µm bead

14 3.4 13 10.5 1.6

4.5 1.0 5 6.2 0.6

1.9 1.1 2.5 1.1 0.2

a F/R is shown for the second, third, and fourth solvation layers. tip See text for details.

study; (ii) the shape of the liquid molecules; and (iii) surface geometry, structure, and roughness. In general, these three factors can affect the geometrical layering of the liquid molecules in the tip-substrate cavity. It is important to understand how these factors can affect AFM measurements of solvation forces and how these factors can bring about differences in AFM solvation force measurements. (i) Contamination. Experiments were performed with as-purchased OMCTS in a N2-purged environment. No further attempts were made to purify the OMCTS. OMCTS is hydroscopic, and the possibility of water or organic contamination of the tip/liquid/sample cannot be excluded and is a general problem for AFM studies in liquids. Horn et al.6 reported that the presence of water in SFA experiments (mica-OMCTS-mica) resulted in behavior very much like that of a purely attractive van der Waals force where the oscillation amplitudes were lowered to the point where the forces became attractive at all distances. Our results, however, show no evidence of such behavior. Furthermore, no significant capillary effects can be seen in the AFM force curves. We also note that the magnitudes of the measured AFM force oscillations are close to those measured using the SFA with purified and dry OMCTS (see Table 1). Hence we discount water and other sources of contamination as being significant in our experiments. Note that we do not preclude the presence of water contamination within the OMCTS bulk liquid but merely observe that such contamination does not appear to influence the forces at tip-sample contact. This behavior might be the result of the small radius of curvature of the system, which allows contaminants to disperse rapidly from the contact zone, or the use of a hydrophobic substrate (HOPG). (ii) Molecular Shape. The geometry of the liquid molecules is significant because it also influences the packing structure of molecular layers. Many SFA measurements have shown that OMCTS exhibits strong, readily observable oscillatory forces because the packing geometry approximates that of confined hard spheres. OMCTS is an inert, rigid molecule that is approximately spherical in shape, having a major diameter of 1.0-1.1 nm and a minor diameter of 0.7-0.8 nm.35 In Figure 4c, the force oscillations have a mean periodicity of 10.7 ( 1.2 Å. Similarly to other studies,9,10 we usually observe up to seven or eight solvation layers of OMCTS with weaker cantilevers (Figure 2a). (iii) Surface Curvature and Geometry. We now consider the possible effects of the tip on our measurements. Monte Carlo simulations15 carried out for confined spherical molecules indicate that solvation forces can be present between a flat surface and extremely sharp tips (Rtip ) 1-10σ). Importantly, eq 10 and computer simulations13 (35) Scott, D. W. J. Am. Chem. Soc. 1946, 68, 2294.

Figure 5. Plot of ki (b) and calculated values of F/Rtip (O) as a function of separation D. For this tip (Rtip ) 19 nm), the F/Rtip values for the second, third, and fourth solvation layers are 10.5, 6.2, and 1.1 mN/m, respectively.

show that solvation forces scale with the tip radius. This result implies that smooth tips with different tip sizes should measure the same normalized force F/Rtip. However, this is not found for our AFM experiments. A possible explanation of the differences between AFM experiments is that the surface roughness or the tip symmetry differs. Repeating our experiments with differently sized tips (Rtip ≈ 20-50 nm) gave varying oscillatory force magnitudes, whereas repeated measurements using the same tip gave reproducible data. The data shown in Figure 4, which was collected using a tip of radius 26 nm, resulted in large oscillatory forces. These particular data are in close agreement with SFA results,6 although the AFM tip radius is 6 orders of magnitude smaller than the radius of curvature of the SFA. Because the SFA data were taken using atomically smooth mica surfaces, the similarity in the data of Figure 4 and the SFA experiments suggests that the tip used is molecularly smooth (on the length scale of the OMCTS molecule, ∼1 nm) and geometrically symmetric. In contrast, the data from ref 11 show considerably smaller oscillatory forces (see Table 1) for a similarly sized tip (Rtip ) 14 nm). In this way, measurements of known oscillatory forces in simple liquids (OMCTS) provide a qualitative indication of the surface roughness and symmetry of the interacting surfaces. The smaller solvation forces measured in our previous work could also be attributed to a faster relaxation time of the confined liquid molecules. A smaller tip size implies a smaller confinement volume for the liquid, and hence the confined molecules might relax more quickly, i.e., the collective motion of the confined molecules is less “solidlike” for a smaller confinement volume.36 It is difficult to comment further on this conjecture, as the AFM data are too sparse to allow any quantitative statements on the effect of relaxation times. In this respect, Figure 5 shows force curves measured using a small tip (Rtip ) 19.1 ( 3.4 nm). F/Rtip values for the second, third, and fourth solvation layers were measured to be 10.5, 6.2, and 1.1 mN/m respectively (see Table 1). These values are similar in magnitude to the measurements made in Figure 4 (using Rtip ) 26 nm) but do not show a distinct exponential variation with distance. Whether such differences arise from possible relaxation effects or tip roughness or both is not known at present. The variations in the force measurements underlie the importance and difficulty of characterizing the tip (rough(36) O’Shea, S. J. Jpn. J. Appl. Phys. 2001, 40, 4309.

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Figure 6. (a) High-resolution SEM image (side view) of the surface of a bead attached to an AFM tip showing asperities protruding from the surface. The asperities are typically 10-20 nm in radius and ∼30 nm in height. This bead was used in the force measurements presented in Figure 7. (b) Top: 200 nm × 200 nm reverse AFM image of a 10-µm bead surface. The average height and rootmean-square roughness values are 15.8 and 4.9 Å, respectively. Bottom: Cross-sectional image of the surface taken along the solid line shown in the image. The average height and root-mean-square roughness for 50 points picked randomly along this line scan are 14.9 and 5.6 Å, respectively. These heights are indicated by the dashed lines in the cross section. (c) Top: Larger-area reverse AFM image (1 µm × 1 µm) of the 10-µm bead that includes the area scanned in Figure 6b. The bright spots in this image are either contaminants on the surface or asperities protruding from the surface. The average height and rms roughness are 44.8 and 19.1 Å, respectively. Bottom: Cross-sectional image of the surface taken along the solid line shown in the image. The average height and root-mean-square roughness for 50 points picked randomly along this line scan are 41.1 and 19.8 Å, respectively. These heights are indicated by the dashed lines in the cross section. The features marked 1, 2, and 3 correspond to large asperities that dominate the short-range force interactions.

ness, size, and symmetry) at the molecular level for solvation force measurements. It is doubtful if the peakto-peak oscillation can be used to estimate the tip radius, and one cannot assume a priori that a nanoscale tip has low surface roughness. III. Solvation Forces Measured with Bead-Modified Tips. Oscillatory behavior in the solvation force was observed for bead-modified tips (Rtip ) 10 µm) approaching an HOPG surface immersed in OMCTS. However, the forces were variable and significantly smaller than expected for a smooth sphere approaching a flat. The beads

are clearly not “molecularly smooth”, and we have carried out experiments to analyze the morphology of the bead surface to provide insight into how surface roughness influences the force measurements. (i) Roughness Measurements. Figure 6a shows an SEM image of the surface of a 10-µm bead used for the experimental results of Figure 7. Although we cannot be certain that Figure 6a shows the exact “interacting” surface, clearly, asperities 10-20 nm in radius and ∼30 nm in height can be seen protruding from the bead surface. Reverse AFM imaging of the bead surfaces is shown in

Solvation Forces Using Sample-Modulation AFM

Figure 7. Plot of stiffness (b) and F/Rtip (O) as a function of D for the bead-modified tip shown in Figure 6. The F/Rtip values for the second, third, and fourth solvation layers are 1.6, 0.6, and 0.2 mN/m, respectively.

Figure 6b and c. The scan range of 200 nm × 200 nm in Figure 6b was chosen to be of the same order as the force interaction area of a 10-µm bead, i.e., the interaction area1 is 2πRtipσ ≈ 31 400 nm2, which corresponds to a scan range of about 150 nm × 150 nm. The scan size was increased to 1 µm × 1 µm to determine whether the surface roughness was homogeneously distributed on the bead surface. The resulting image (Figure 6c) reveals that the bead surface is not smooth on this length scale. The bright spots are either contaminants or asperities protruding from the surface. The average height (zj) and rms roughness values are 15.8 and 4.9 Å, respectively, for Figure 6b and 44.8 and 19.1 Å, respectively, for Figure 6c. We have included cross-sectional line scans in both Figure 6b and c. The black lines in each topographical image indicate where the cross section was taken. We analyze the cross sections by measuring height (z) values at 50 random locations on each curve and calculate the average height (zj) and the rms roughness. For Figure 6b, we find zj ) 14.9 Å and Rrms ) 5.6 Å. Similarly, for Figure 6c, we measure zj ) 41.1 Å and Rrms ) 19.8 Å. The dotted lines in the cross section represent these distances, and we observe that, even though most of the undulating features are in the subnanometer regime, peaks and troughs lie above and below the measured roughness level. For example, in Figure 6c, the heights of the asperities labeled 1, 2, and 3 are measured to be 90, 80, and 107 Å, respectively. The three asperities have radii of curvature that we estimate to be between 5 and 10 nm. Clearly, characterizing the surface using a single rms roughness value is not sufficient in providing a quantitative description of surfaces. In our experiments, for example, we find that asperities are present on all of the glass beads used, and such protrusions will necessarily dominate in the measurement of short range force interactions. The existence of large surface roughness on nominally “spherical” beads is also critical in the measurement of certain long-range forces such as Casimir forces28 and is clearly significant in any measurement of adhesion forces for “chemical” AFM applications. (ii) Force Measurements. Measurements of oscillatory forces in OMCTS with bead-modified tips are variable. Differences in the force curve can occur in repeated force measurements either using the same tip or between different tips. In some cases, oscillatory behavior is completely eliminated from the force curves and replaced by a monotonic attractive force. Figure 7 shows data of a force measurement where oscillatory behavior is observed. The periodicity of the force oscillations is 10.2 ( 0.8 Å. The cantilevers we use in bead-modified experiments have

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kc values of ∼60 N/m, and tip instability occurs only at the solvation layer closest to the surface. The peak-to-peak stiffness values corresponding to the second, third, and fourth solvation layers are measured to be 60, 25, and 20 N/m (Figure 7a) and the corresponding normalized force values are 1.6, 0.6, and 0.2 mN/m, respectively (see Table 1). Table 1 shows that the bead-modified tips have significantly smaller peak-to-peak force amplitudes compared with the SFA data and the AFM tips used in this work. This observation and the strong variability in the data are indicative of a rough surface.20 However, the observation of oscillatory forces is, in itself, of interest because the current understanding is that a randomly rough surface of only a few angstroms is sufficient to eliminate oscillatory forces.1 The observation of oscillatory forces indicate that liquid molecules in the bead-substrate gap can behave cooperatively over localized regions, i.e., around the asperities. The random surface roughness suggests that the variation in force curve measurement arises from the specific morphology of the bead surface that faces the sample surface. The morphology can even change during experimentation, for example, if the surfaces come into mechanical contact and the contacting asperities deform plastically. From this study, we conclude that the oscillatory behavior of the solvation force need not entirely vanish for randomly rough surfaces that have surface features larger than the molecular size of the mediating liquid. Instead, for small interaction areas, the observed oscillatory behavior can be taken as an “averaging” of the oscillatory forces over individual asperities. IV. Conclusion We have shown that solvation forces in liquids can be studied using sample-modulation AFM. Although sample modulation is comparatively noisier than the forcemodulation technique, it allows for stiffer systems to be studied. By avoiding tip instability jumps (i.e., using a stiff cantilever), one is able to measure both repulsive and attractive solvation potentials in a single approach. The use of stiffer cantilevers in force measurements reduces the experimental sensitivity. We have also discussed the factors and difficulties that can affect solvation force measurements using samplemodulation AFM. The solvation forces measured using AFM probes can be comparable to those measured by the SFA, although the two techniques have contact areas differing by 6 orders of magnitude. However, surface roughness and the asymmetric shape of the AFM tip usually result in a decrease in the magnitude of the oscillatory force and variability between measurements using different tips. By scaling the force measurements with the tip radius, we can compare our results to SFA data and make a qualitative inference on the roughness of the AFM tip used. The precise role of tip shape in the AFM measurement of solvation forces is as yet unclear,11 because it is difficult to independently characterize the geometric shape of the tip at the molecular level. Frink et al. theoretically investigated the role of surface roughness in solvation forces by simulating three categories of roughness: (1) random roughness in discrete distributions, (2) random roughness in continuous distributions, and (3) patterned roughness.20 Unfortunately, it is not possible to verify these theoretical predictions experimentally because of difficulties associated with

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preparing and characterizing the specific surfaces required. Nevertheless, by attaching glass beads to AFM tips, the effect of asperities on solvation force measurements can be examined. Reverse AFM imaging shows that the surface of the beads are not entirely “smooth”, as is often assumed, but can have large asperities which clearly affect force curve measurements. It is not sufficient to measure the average rms roughness because the presence of large asperities might be “averaged out”, whereas such asperities might dominate the short-range force interactions. Interestingly, it has been suggested by groups using similar bead-modified AFM techniques that DLVO (Derjaguin-Landau-Verwey-Overbeek) theory does not accurately describe the double layer repulsion25 and van

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der Waals force24 because surface roughness is not taken into account. We have observed oscillatory forces in several force curve experiments using bead-modified tips of known roughness, thus demonstrating directly that oscillatory forces can occur even for randomly rough surfaces. The most plausible explanation for this observation is that only the foremost asperities on the bead surface interact with the sample surface, giving rise to a weaker, “averaged” oscillatory force and also resulting in considerable variation in the force curve measurements for different bead morphologies. LA011789+