REVIEW OF SCIENTIFIC INSTRUMENTS 76, 103705 共2005兲

A highly sensitive atomic force microscope for linear measurements
of molecular forces in liquids
Shivprasad Patil, George Matei, Hang Dong, and Peter M. Hoffmanna兲
Department of Physics, Wayne State University, 666 West Hancock, Detroit, Michigan 48201

Mustafa Karaköse and Ahmet Oral
Department of Physics, Bilkent University, Ankara, Turkey

共Received 26 July 2005; accepted 29 August 2005; published online 24 October 2005兲
We describe a highly improved atomic force microscope for quantitative nanomechanicalmeasurements in liquids. The main feature of this microscope is a modified fiber interferometer
mounted on a five axis inertial slider which provides a deflection sensitivity that is significantly
better than conventional laser deflection based systems. The measured low noise floor of
572.0 fm/ 冑Hz provides excellent cantilever amplitude resolution. This allows us to operate theinstrument far below resonance at extremely small cantilever amplitudes of less than 1 Å. Thus
linear measurements of nanomechanical properties of liquid systems can be performed. In
particular, we present measurements of solvation forces in confined octamethylcyclotetrasiloxane
and water with amplitudes smaller than the size of the respective molecules. In general, thedevelopment of the instrument is important in the context of quantitative nanomechanicalmeasurements in liquid environments. © 2005 American Institute of Physics.
关DOI: 10.1063/1.2083147兴

I. INTRODUCTION

Since the invention of scanning tunneling microscopy
共STM兲 and atomic force microscopy 共AFM兲, probe-based
techniques have been able to address many long-standing
issues in surface science, biology, tribology, semiconductor
physics, magnetism, and nanoscience.1–6 In addition to imaging, scanning probe techniques have the ability to measurevarious quantities as a function of tip-surface separation with
unprecedented spatial resolution. AFM, in particular, hasbeen used to measure forces between single molecules,
bonding forces between atoms, adhesion, and friction at thenanoscale,7–12 as well as structural or hydration forces inliquids.13–17 O’Shea et al.13 used AFM for the first time tomeasure oscillatory solvation forces in a nonpolar liquid, octamethylcyclotetrasiloxane 共OMCTS兲, confined between two
solid surfaces. These forces and the layering of the liquid atinterfaces with molecular separation are important fortribology.18 Interfacial water confined between surfaces isalso a topic of immense interest, especially in the context ofcell biology, interactions between macromolecules or colloids in water, and protein folding.19 There is clearly a needfor instruments that can quantify the nanomechanical properties of liquids. One of these instruments is the surface force
apparatus 共SFA兲. In SFA cylindrical rods wrapped with mica
sheets are brought together in liquid.20 One of the surfaces isheld fixed and the other is mounted on a spring to measure
the force between the surfaces. The separation between thesurfaces is measured independently by interferometry. Oscillatory forces due to solvation shells in confined water werefirst observed in 1983 by Israelachvili and Pashley usinga兲Electronic mail: hoffmann@physics.wayne.edu

0034-6748/2005/76共10兲/103705/7/$22.50

SFA.21 Despite much work since there is still a lack of sufficient data to draw clear conclusions about the collective
behavior of liquid molecules under confinement. The maindrawbacks of SFA are lack of spatial resolution, the restriction to mica surfaces, and the jump-to-contact instability inthe force measurement due to large interacting surface areas.
These disadvantages have prompted researchers to measureforces in liquids using AFM. However, in AFM the signal
strength is extremely small due to small contact areas. In
addition, the tip-surface separation and tip geometry are typically unknown. Thus the two techniques have strengths aswell as disadvantages and can be seen as complementary
techniques.
For better signal-to-noise ratio AFM is usually operated
at the resonance frequency of the cantilever and changes in
the amplitude or frequency are measured as the tip approaches the surface.22,23 Typically amplitudes of the orderof 1 – 10 nm are used for measurement of surface forces using this dynamic technique. In the context of measurementsof solvation forces, this presents two problems: 共1兲 the possibility of disrupting the molecular layers and 共2兲 difficulties
in relating the measured quantities to the stiffness and damping of these layers in a straightforward manner. The former
problem makes the measured damping and forces a functionof very complicated processes associated with disturbing alarge number of layers during the travel of the tip. The latterproblem stems mainly from the fact that the force field is not
linear over the cantilever oscillation amplitude. The amplitude should be at least smaller than the molecule size forlinear measurement of the stiffness of layers in confined liquids. Thus there is a need to enhance the sensitivity of AFM
techniques in order to avoid complicated ways of interpret-

76, 103705-1© 2005 American Institute of Physics

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103705-2

Patil et al.

ing the data resulting from large amplitude measurement
techniques. This can be achieved by using more sensitive
deflection sensors, such as a fiber based interferometer.24 A
high-sensitivity deflection sensor allows the use of smallamplitude, off-resonance techniques which have been used inultrahigh vacuum 共UHV兲 to linearly measure the stiffness of
atomic bonds.10,25,26 This method employs extremely small
共sub-兲angstrom amplitudes for force measurements.
In this article we describe the development of smallamplitude, off-resonance AFM using a fiber-based interferometer for measuring forces in liquids. This instrument has
been used for measurement of solvation forces in OMCTS
and water confined between atomically flat surfaces and asilicon tip. We discuss the results obtained in terms of instrument performance.

II. INSTRUMENT DESIGN

To use the small-amplitude technique in liquid environments with a fiber-based interferometer involves certain issues. Compared to UHV operation, the design for sliders andcoarse approach mechanisms changes considerably owing to
the fact that sample, tip, and fiber end have to be immersed
in liquid while performing measurements. Second, the contribution of thermal noise differs significantly due to thechange in quality factor and cantilever stiffness values usedin liquids. The quality factor in liquid is of order 1 whereas
in UHV it can well exceed 1000. Also the stiffness of thecantilever is typically 1 N / m and in UHV stiffnesses ofabout 100 N / m have to be used to avoid snap-to-contact.
Third, the refractive index of the liquid environments has asignificant impact on sensitivity for the fiber based interferometer detection system. The most obvious difference between a previous UHV-based fiber interferometric AFM26
and the present liquid-based AFM is the completely different
geometry. While in UHV, the sample was vertical and coarse
motions of both sample and fiber were primarily horizontal,
in liquids the sample has to be horizontal and the coarse
motions have to be 共at least partially兲 vertical. This posessignificant challenges, since piezobased coarse positioners
are difficult to design for operation against gravity.27–30
The liquid AFM is built on a heavy base with a diameterof 6 in. and a height of 3.5 in.. The central part of the block
is hollowed out to accommodate the vertical sample coarse
approach and the sample scanner. As shown in Fig. 1, thesample coarse approach relies on the inertial slider
principle.27,30 In particular, a heavy steel piece 共“hammer”兲 isglued to the lower end of a tube piezo 共the “hammer
piezo”兲.31 On the upper part of the tube piezo a quartz tube is
attached, which fits into an opening of the XY positioner
共described in the following兲 and is held by a leaf spring.
Inside the glass tube is the scan piezo tube32 with the outerelectrode sectioned into quadrants to allow for x and y motion. The sample holder is attached to the scan piezo. For
coarse motion, pulses are given to the hammer piezo whichhave a “slow” rising edge and a fast drop off. During theslow, rising part of the pulse, the tube piezo contracts or
expands, moving the hammer up 共or down兲. The upper end

Rev. Sci. Instrum. 76, 103705 共2005兲

FIG. 1. Photograph showing the AFM base with the sample coarse positioning system.

remains clamped. When the pulse suddenly switches off, theinertia of the hammer keeps it in place forcing the glass tube
to slide past the leaf spring.
The XY 共horizontal兲 sample positioner also uses the inertial slider principle. In this case shear piezos are mounted
to heavy steel plates. Overall, the XY sample positioner consists of grooves cut into the AFM base, a middle plate with aset of three shear piezos on each side and a top plate withgrooves perpendicular to the grooves in the AFM base. On
top of each shear piezo mounted on the middle plate is amacor piece, which serves as a seat for a 2 mm sapphire ball.
The sapphire ball can slide on a sapphire plate that is glued
inside one of the grooves. Since the grooves on the base andthe top plate are perpendicular to each other 共matching theshear direction of the respective shear piezos兲, X and Y motion can be generated providing a total travel of 5 mm and astep size as small as 50 nm. In the middle of each plate is ahole to accommodate the z coarse approach assembly described previously, as well as the scan piezo and sample
holder. The sample holder consists of an aluminum plate
which has three magnets glued into recessed holes which
serve as holders for the actual sample or liquid cell. The
liquid cell consists of a Viton O-ring 共2 in. diameter and0.063 in. thickness兲 compressed between two circular Kel-F
sheets. A nickel plate is attached to the base of the cell inorder to mount the cell to the three magnets on the sample
holder providing a stiff contact between the scanner piezo
and the liquid cell and at the same time allowing easy sample
exchange. The top Kel-F sheet has a hole in the center for thecantilever and fiber to be brought close to the surface. The
two Kel-F sheets and the nickel plate are held together withfour screws. The substrate is held in position between thebottom Kel-F sheet and the pressed-down O-ring. A glass
syringe with a fine needle is used to fill or remove liquid.
Once the coarse positioners are put into place, a coverplate is mounted on top of the AFM base, which has a holefor the sample holder and tapped screw holes for the cantilever mount and the fiber coarse positioner. Once this plate ismounted, only the sample holder is visible. This can be seenin the schematic in Fig. 2 and the photograph of the assembled AFM in Fig. 3.
On top of the cover plate the cantilever mount is

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103705-3

Small-amplitude atomic force microscope

FIG. 2. Cross-sectional schematic of liquid AFM.

mounted using three screws. A 12° angle is introduced at thefree end of this mount where a dither piezo, a shear piezo, amacor spacer, and the actual cantilever holder are glued. The
angle allows the tip to reach the surface first. The cantilever
holder is made of steel and the cantilevers are held by a leaf
spring made of copper-beryllium fastened by two screws.
The cantilever holder is glued to the shear and dither piezos
to allow for cantilever oscillations normal and lateral to thesurface. The cantilever motion is detected using a fiber interferometer 共see the following兲. A fiber slider is required for
precisely positioning the fiber with respect to the cantilever
and adjusting the angle between fiber and cantilever in orderto achieve high sensitivity. The fiber slider is mounted to thecover plate so that the fiber is located right above the cantilever as shown in Fig. 3.
The AFM is placed on a tabletop vibration isolation system with natural frequency below 2 Hz.33 The tip sample
approach is monitored using a charge coupled device camera. The AFM is kept inside an aluminum acoustic shielding
box which is lined with sound/temperature insulating material. The humidity is controlled by using suitable desiccantswithin the AFM enclosure.
III. FIBER SLIDERFor measurements at cantilever amplitudes down to lessthan 1 Å we need a deflection sensor with very high sensitivity. We are using a fiber-based interferometer. In order to

FIG. 3. Photograph of completely assembled AFM system, showing cantilever mount, fiber positioner, and liquid cell.

Rev. Sci. Instrum. 76, 103705 共2005兲

FIG. 4. Schematic view of fiber coarse positioner. The positioner consists of
two perpendicularly mounted sliders: The yz␾ slider on the left and the xz␪
slider on the right. The fiber is mounted to the end of the fiber piezo.

achieve maximum sensitivity the fiber needs to be aligned
exactly perpendicularly and at a suitable distance with respect to the cantilever. This is achieved through a fiber positioner or “slider” 共Fig. 4兲 which can rotate in two directions,␪ and ␾ and move in x, y, and z directions. The fiber positioner in our instrument works on the inertial principle similar to the one described in Ref. 26 for UHV environments.
However, as mentioned previously, the overall geometry of
the fiber positioner is very different owing to the vertical axisof the liquid AFM as opposed to the horizontal orientation of
the UHV-based AFM. Successful operation of any inertial
slider in five directions depends on the friction between sliding parts. Compared to the UHV system, there are two maindifferences: One is the vertical orientation of the slider, theother is the presence of liquid layers on the sliding surfaces
due to the operation in the ambient. The static friction has tobe sufficient to overcome gravity, whereas the kinetic frictionneeds to be low enough to allow sliding. This requires optimal adjustment of the contact force between the sliding partsof the positioner. In our design we are able to adjust thecontact force with the help of screw-mounted magnets.
The fiber slider consists of two parts: a yz␾ and a xz␪
slider, which are oriented perpendicularly to each other. Eachslider has a set of three piezo stacks with each consisting of
three shear piezos.34 The stacks are arranged in the shape ofa equilateral triangle. High voltage, slow-on, fast-off pulses
共200– 300 V兲 are applied selectively to the stacks of piezos
to initiate the inertial motion.27 The number of pulses, thepulse height and width can be adjusted in the driver software.
The two shear piezos at the bottom of each stack have polarization direction opposite to each other. The top piezo has
its polarization direction orthogonal to the two bottom piezos. For vertical motion pulses are given to the two bottom
piezos, whereas for lateral motion the top piezo is used. For
rotation pulses with opposite sign are applied to the top piezo
on one stack with respect to the top piezos of the other two
stacks.
1 mm sapphire balls are glued to the top of the piezo
stacks. The xz␪ slider has sapphire plates which can slidewith respect to the sapphire balls glued to the piezo stacks on
the yz␾ slider. The xz␪ slider in turn has piezo stacks whichmove a plate holding a fine approach fiber piezo and the fiber
itself. The two sliders are held in place by magnets glued toflat ended screws as shown in Fig. 4. The magnets exerts an

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Patil et al.

attractive force on a magnetic steel plate attached to the backof the slider plate. The strength of the force can be judiciously chosen for the vertical sliding motion by adjusting
the magnet-to-steel-plate separation with the screw, for reasons discussed previously. There are stoppers for both thesliders to limit the motion and prevent the sliders to slide off
the sapphire plates.
The optical fiber itself is passed through a glass ferrule
which is glued to the fine approach tube piezo 共“fiber
piezo”兲.35 The fiber piezo is glued to the plate that slides withrespect to the xz␪ slider, as shown in the Fig. 3. During
alignment, the fiber piezo moves the fiber back and forthallowing us to find the quadrature point where the slope of
the interference pattern is maximized. While collecting data,
the fiber piezo is controlled via a feedback loop to keep thefiber position at the quadrature point at all times.
IV. FIBER INTERFEROMETER

Our fiber interferometer is similar to the one reported
earlier for the UHV system26 and is ultimately based on thedesign of Rugar et al.24 If the fiber is held close and perpendicular to the cantilever, the multiple reflections of the lightbetween the end of the fiber and the cantilever enhance thesignal sensitivity considerably.26 The five-axis fiber slider described previously is used to align the fiber with respect tothe cantilever to achieve the required sensitivity. The generalscheme of the interferometer is as follows. A laser diode with2 – 3 mW power and 1310 nm wavelength is coupled into a2 ⫻ 2, single mode, 50% fiber splitter. One of the outputs ofthe splitter is connected to the fiber positioned over the cantilever. The other output is connected to the reference photodiode. The reference photodiode signal measures the powerof the laser and, multiplied by a suitable factor, is subtracted
from the interference pattern recorded by the signal photodiode. This helps to subtract out any laser noise.
Of the light that exits the splitter toward the cantilever, aportion reflects back from the end of the fiber while the remaining intensity exits to reach the cantilever, where it isreflected and can couple back into the fiber. Multiple reflections can occur between the fiber end and the cantilever. The
light that returns from the cantilever again passes through the2 ⫻ 2 splitter and 50% of it is directed toward the signal
photodiode, while the rest is lost. At the cantilever, the interference of the primary with the multiply reflected beams generates a current at the signal photodiode 共Fig. 5兲, which isextremely sensitive with respect to fiber-cantilever distance.
To improve sensitivity, the end of the fiber is cleavedwith a precision fiber cleaver36 to give 3%–4% reflectivity. It
is then coated with Si and a protecting layer of gold to help
prevent the oxidation of Si. Typically we obtain reflectivityof order of 25%–30% using a thermal evaporator.

FIG. 5. Schematic view of fiber interferometer.

amplifier circuits. Giessibl37 and Hembacher et al.38 haveprovided a method to measure the real sensitivity and thetotal integrated noise figure of AFM instruments. The noise
figure ultimately determines the deflection resolution of the
instrument.38
The AFM sensor sensitivity is defined by the voltage
generated by a certain deflection above the noise floor of the
instrument. This value can be determined from a spectral
density graph of the thermally activated cantilever motion in
the vicinity of the cantilever resonance. Figure 6 shows atypical power spectral density 共␮V / 冑Hz兲 of a cantilever withstiffness 1.67 N / m measured in air in our instrument. This
spectrum is fitted to a simple harmonic oscillator model withwhite noise and 1 / f background:
V共f兲 =

冑C
2+ Unoise+fp

2
Vsensor冉 冊 冉 冊f 2
f2 2
1− 2 +
Qf 0
f0

.

共1兲

Here C is a constant and p is a power close to 1 共1.3 inour case兲 describing the “1 / f” noise. The fit yields values forthe quality factor Q, resonance frequency f 0, and white floor
noise Unoise. In the data presented by Hembacher et al.38 for

V. AFM NOISE AND SENSITIVITY

The performance of an AFM is due to its ability to measure small deflections or changes in amplitude above thenoise floor of the instrument. Noise is mainly due to thethermal motion of the cantilever, vibrational, and acoustic
noise from the environment, as well as electronic noise in the

FIG. 6. Voltage noise density vs frequency in the vicinity of the resonancepeak. Fitting this graph to a harmonic oscillator with noise floor, Unoise, asensitivity of 409.1 ␮V / pm and an integrated noise density of
572.0 fm/ 冑Hz was determined, which is highly improved over conventionallaser deflection systems.

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103705-5

Rev. Sci. Instrum. 76, 103705 共2005兲

Small-amplitude atomic force microscope

their qPlus sensor no 1 / f noise seemed to be present. In ourcase we had to add this term to reflect the observed slope ofthe noise background versus frequency.
The signal generated in terms of voltage due to thermal
activation, Vthermal, is obtained by subtraction of the noise
floor 共1 / f and thermal noise Unoise兲 from the fitted curve andintegration over the measured bandwidth. The thermal fluctuation of the cantilever deflection 具zthermal典 is calculated byusing the equipartition theorem which equates kBT / 2 to every quadratic degree of freedom. Hence zthermal = 冑kBT / kL,
where kB is Boltzmann’s constant, T is temperature, and kL iscantilever stiffness. The sensitivity then becomes
S=

Vthermal.
具zthermal典

共2兲

For comparison of different force sensors the spectral
amplitude noise density is calculated by dividing the noise
floor by the sensitivityz̃ =Unoise + 冑C/f p
.
S

共3兲

This formula was modified from Ref. 38 to include the
1 / f noise. As quoted in Ref. 38 a conventional beam deflection system provides a sensitivity, S, of the order of
1.6 ␮V / pm and a noise figure z̃ of 2400 fm/ 冑Hz. Our measurement yielded a sensitivity above the noise floor of
409.1 ␮V / pm, i.e., an improvement of 255⫻ and a noise
figure of 572.0 fm/ 冑Hz, i.e., more than 4⫻ lower comparedto the quoted beam deflection system, even though a lever ofcomparable stiffness was used. Compared to the qPlus sensor
of Hembacher et al.,38 which has much lower thermal noisedue to the large cantilever stiffness of 1800 N / m, our systemprovided a 23-fold improvement of sensitivity. On the other
hand, the noise in our system was higher by a factor of 3.6.
However, considering that the thermal noise is proportional
to the square root of the lever stiffness, we should have expected an increase in the noise of the order of 冑1800/ 1.67
= 32.8. This shows that the noise floor of our instrument isvery low and should allow for measurements of very smallchanges in amplitude. This is evident in the fact that we areable to directly measure density fluctuations in confined water layers 共see the following兲 at angstrom level amplitudes.
The theoretical limit of the drive amplitude of the thermal noise 共as opposed to the actual, resonance enhanced amplitude of the lever at resonance, 具zthermal典兲 is given by37
Athermal =

冑

4KBT
.
KLQ␻

共4兲

Using the parameter values obtained from our fit this gives
24.3 fm/ 冑Hz at the lever resonance. The measured value ofthe amplitude noise floor at resonance, z̃, contains all sourcesof noise in the system. Consequently it is higher than thetheoretical thermal noise limit.
Our experiments are performed far below the resonancein order to simplify data interpretation and to keep amplitudes low 共i.e. avoiding resonance enhancement of the amplitude兲. This puts even more stringent requirements on the
AFM than on-resonance measurement methods. This is be-cause the thermal and 1 / f noise density will be higher atlower frequencies. Therefore, it is difficult for conventional
AFM to measure at low frequencies. In our experiments 共described below兲, the amplitude noise density was measured to
be 650 fm/ 冑Hz at 400 Hz far below the resonance of
59.6 kHz. This noise figure, although slightly higher than z̃,is still very low and allows measurements of molecular waterlayers.
VI. OPERATION OF THE AFM

The prime aim of developing this instrument was tomake linear force measurement in liquids using offresonance frequencies and small amplitudes. Sufficiently
stiff levers are used to avoid mechanical instabilities. The
cantilevers used in the experiments presented below had
stiffness values of 0.65 N / m. Typically, cantilevers have a
50 Å thick aluminum or gold reflective coating when purchased from the manufacturer. We coat the backside of theselevers with an additional 100 nm of gold to further improvereflectivity of the infrared light we use. After mounting theliquid cell on the scanner piezo, the cantilever is put in place
and the five axis fiber slider is used to align the fiber on the
cantilever. The fine positioning is done with help of a joystick. Once the alignment is completed, the fiber is locked toa position of highest sensitivity 共quadrature point兲 using a
feedback loop. The cantilever is then oscillated at a few hundred Hz, which is well below the resonance frequency. Initially the sample approach is done using hammer piezocoarse approach. The liquid to be investigated is filled in theliquid cell using a glass syringe.
Unlike in UHV or air environments with similar detection mechanism, care has to be taken not to disturb the alignment while filling the cell with liquid. We use both nonpolarorganic as well as polar liquids like water. These liquids havevery different refractive indices compared to air 共wherealignment for optimum signal is done兲. This induces either
reduction or enhancement in the signal after introducing theliquid in the gap between the cantilever and fiber end. We
observed that for water the signal sensitivity typically increases by about 30%. On the other hand for organic liquid
like OMCTS it decreases by about 25%. Sometimes the capillary forces disturb the alignment while filling the cell withliquid. The quadrature lock is kept on while filling in theliquid so that such drifts do not disturb the alignment too
significantly causing the signal to be lost altogether. A minor
alignment procedure is required afterwards to regain thesame sensitivity.
When the cantilever is close to the surface the approachis done using computer-controlled auto approach. The auto
approach works by sending a pulse to the hammer piezo andthen performing a z scan with the scanner piezo. Once the tip
is engaged with the surface the feedback is suspended andthe software is used for obtaining force distance curves. The
software and electronics for the operation were purchasedfrom Nanomagnetics Instruments39 and have been describedin Ref. 26. The amplitude and phase of the cantilever oscillations are measured with a lock-in amplifier. For repeating
the measurements on the same liquid or starting a set of

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Patil et al.

experiments the fiber slider can be lifted and taken out. Then
we remove the cantilever mount from the setup. Finally theliquid cell can be detached from the magnets holding it to thescanning piezo.
Owing to the small amplitudes and off-resonance operation, our measurements are performed in the linear regime.
Thus, the changes in amplitude and phase upon approach canbe related to interaction stiffness and damping coefficientthrough these simple equations:40
k = kL冉A0cos ␸ − 1
A

冊

共5兲

and

␥=−

k LA 0sin ␸ ,A␻

共6兲

where k is interaction stiffness, kL is cantilever stiffness, A0
is free amplitude, A is the amplitude of the cantilever, ␸ isthe phase difference between the cantilever end and the piezo
actuator, and ␥ is the damping coefficient.

VII. EXPERIMENT

We have previously reported measurements of molecularordering of water.17 These measurements were performed
with a previous 共unpublished兲 version of a similar instrument, which was very cumbersome to use. The version reported on here is much easier to use and has yielded resultsof similar quality in much shorter time. With this and improved AFM, we carried out initial benchmark experiments
to measure solvation forces in OMCTS and water. Future
experiments with this instrument will explore the dynamic
behavior of these layered liquid systems in more detail as
was previously possible.
OMCTS is often chosen for liquid ordering experiments
because of its globular shape with a mean diameter of about
9 Å and its nonpolar nature. There are many other reports inthe literature on measurement of solvation forces in OMCTS
confined between two surfaces using SFA and AFM.13,14,20,41
OMCTS was purchased from Sigma-Aldrich.42 Before every
experiment, we filtered the liquid to ensure that it is freefrom any contaminants. The filtration process involves putting molecular sieves in OMCTS overnight which absorb
water from the OMCTS and then passing it through a syringe
filter with 0.02 ␮m pore size. In the present experiment themeasurements were performed with 0.65 N / m silicon cantilevers purchased from MicroMasch.43 We used a measurement frequency of 400 Hz which is well below the resonancefrequency in the liquid of 10.3 kHz. The sample was siliconcovered with a thin and smooth oxide layer prepared by thefollowing treatment: A 1⬙ ⫻ 1⬙ piece of Si共100兲 wafer was
put in a hydrogen peroxide and sulfuric acid bath 共1:3 proportion兲 and heated to 100 ° C for 20 min. The wafer wasrinsed with deionized water and kept in an oven at 120 ° C
overnight to remove any water remaining on the surface. For
experiments in water we used mechanically cleaved, atomically flat mica as substrate.

FIG. 7. Junction stiffness and damping coefficient vs separation for a siliconoxide substrate immersed in OMCTS. The free amplitude of the cantilever
was 4.4 Å. The stiffness was calculated from Eq. 共5兲 and the damping fromequation 共6兲. Clear stiffness and damping coefficient oscillations can be seen
with an average separation of 10.2 Å, consistent with the size of the OMCTS molecule. The stiffness and damping coefficient are out of phase.

VIII. RESULTS AND DISCUSSION

Figure 7 shows the stiffness as well as damping coefficient versus separation data measured with a 4.4 Å free amplitude which is smaller than the size of OMCTS molecules.
The speed of approach-retract was 9 Å / s. As can be seen in
Fig. 7, the average separation between peaks is 10.2 Å. An
attractive background is seen in the stiffness curve. The
damping coefficient and stiffness are out of phase in thisexperiment. The sample used is silicon oxide prepared by themethod described in previous section.
In the field of confined liquids there is a general disagreement regarding the state of confined liquid 共solid, liquid, or viscoelastic兲44,45 and its mechanical properties. Using
this instrument we can make continuous, simultaneous, anddirect measurement of damping coefficient and stiffness
which, through a suitable model, will lead to useful information about the dynamics of the confined liquids.
The other liquid under investigation was water. As
shown in Fig. 8 we observed four peaks in the stiffnessseparation curve measured on a confined water film. The

FIG. 8. Junction stiffness versus separation graph for a mica substrate immersed in de-ionized water. The free amplitude of the cantilever was 0.92 Å.
Clear stiffness oscillations due to solvation forces can be seen with an average separation of 2.9 Å, consistent with the hydrogen bonding length ofwater.

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103705-7

amplitude used for these measurements was 0.92 Å. A stronghydrophilic repulsive background was observed due to themica surface. The average separation between peaks wasobserved to be 2.9 Å, which is consistent with earlier
reports.15,17,21 The successful operation in water is promisingfor further understanding of short range hydrophobic andhydrophilic interactions. A quantitative force measurement ofstiffness of water confined within biological membranes suchas lipid bilayers is another area where this instrument canmake meaningful contributions.
The smallest measurable stiffness, ␦k, in these experiments was found to be about 0.05 N / m using a 0.65 N / mcantilever at 0.92 Å amplitude and 400 Hz oscillation amplitude. The lock-in time constant was set to 100 ms. Longer
time constants could not be used because of thermal drift inthe system. In the presence of water the Q of the lever will
be reduced significantly. If we assume a reduction of Q by afactor of about 20 共Ref. 46兲 we find a thermal noise densityof 2000 fm/ 冑Hz at 400 Hz 关Eq. 共4兲 and Ref. 40兴. Thus, under these conditions thermal lever noise will overwhelm allother noise sources in our instrument. At a measurement
bandwidth of 10 Hz 共100 ms time constant on lock-in兲 thiscauses a 0.067 Å noise in the amplitude signal, which corresponds to a smallest measurable stiffness of 0.05 N / m underthese conditions—agreeing with the experimentally observed
value. Thus we seem to be limited only by thermal noise in
our liquid measurements.
In conclusion, an atomic force microscope with highsensitivity was developed that allows the use of ultrasmall
amplitudes of the order of angstroms in liquid environments.
The instrument has been employed to measure oscillatory
solvation forces in confined liquids such as OMCTS andwater. Extremely small amplitudes and off-resonance operation are key features of this instrument which allows us toperform linear measurements, eliminate potential problems
associated with disrupting the liquid layers during measurement and avoids extensive de-convolution processes, which
would otherwise be necessary to interpret the measured data.
The development of this instrument promises to have significant importance for quantitative measurement of interaction
between biological macromolecules and for probing hydrophobic, hydrophilic interactions in water. The study of confined liquids and the interaction between confining surfaces
is also important in the field of tribology.
ACKNOWLEDGEMENTS

One of the authors 共P.M.H.兲 would like to acknowledge
funding by NSF 共MRI Grant No. DBI-0321011, ANESA
Grant No. INT-0217789, and CAREER Grant No. DMR0238943兲. A.O. and P.M.H. would like to acknowledge support through the Turkish Government 关TUBITAK Grant No.
TBAG-U/50 共102T117兲兴 and the National Science Foundation for international collaborative research.
1
2
3

Rev. Sci. Instrum. 76, 103705 共2005兲

Small-amplitude atomic force microscope

E. Meyer, Prog. Surf. Sci. 41, 3 共1992兲.
U. Hartmann, Annu. Rev. Mater. Sci. 29, 53 共1999兲.
R. Garcia and R. Perez, Surf. Sci. Rep. 47, 197 共2002兲.

J. L. Alonso and W. H. Goldmann, Life Sci. 72, 2553 共2003兲.
F. J. Giessibl, Rev. Mod. Phys. 75, 949 共2003兲.
6
N. C. Sanotos and M. A. R. B. Castanho, Biophys. Chem. 107, 133
共2004兲.
7
B. Cappella and G. Dietler, Surf. Sci. Rep. 34, 1 共1999兲.
8
R. W. Carpick and M. Salmeron, Chem. Rev. 共Washington, D.C.兲 97,
1163 共1997兲.
9
M. Guggisberg, M. Bammerlin, C. Loppacher, O. Pfeiffer, A. Abdurixit,
V. Barvich, R. Bennewitz, A. Baratoff, E. Meyer, and H. J. Güntherodt,
Phys. Rev. B 61, 11151 共2000兲.
10Peter M. Hoffmann, Steve Jeffery, John Pethica, H. Ö. Özer, and A. Oral,
Phys. Rev. Lett. 87, 265502 共2001兲.
11
N. A. Burnham and R. J. Colton, J. Vac. Sci. Technol. A 7, 2904 共1989兲.
12
C. M. Mate, G. M. Macclelland, R. Erlandsson, and S. Chaing, Phys. Rev.
Lett. 59, 1942 共1987兲.
13
S. J. O’Shea, M. E. Welland, and T. Rayment, Appl. Phys. Lett. 60, 2356
共1992兲.
14
S. J. O’Shea and M. E. Welland, Langmuir 14, 4186 共1998兲.
15
S. P. Jarvis, T. Uchihashi, T. Ishida, H. Tokumoto, and Y. Nakayamam, J.
Phys. Chem. B 104, 6091 共2000兲.
16
Wenhai Han and S. M. Lindsay, Appl. Phys. Lett. 72, 1656 共1998兲.
17
S. Jeffery, P. M. Hoffmann, J. B. Pethica, C. Ramanujan, H. Ö. Özer, andA. Oral, Phys. Rev. B 70, 054114 共2004兲.
18
J. Van Alsten and S. Granick, STLE Tribol. Trans. 33, 456 共1990兲.
19
J. L. Finney, Faraday Discuss. 103, 1 共1996兲.
20
J. N. Israelachvili, Intermolecular and Surface Forces 共Academic, London, 1992兲.
21
J. N. Israelachivili and R. M. Pashley, Nature 共London兲 306, 249 共1983兲.
22
Y. Martin, C. C. Williams, and H. K. Wickramasinghe, J. Appl. Phys. 61,
4723 共1987兲.
23
T. R. Albrecht, P. Grütter, D. Horne, and D. Rugar, J. Appl. Phys. 69, 668
共1991兲.
24
D. Rugar, H. J. Mamin, and P. Guethner, Appl. Phys. Lett. 55, 2588
共1989兲.
25
P. M. Hoffmann, A. Oral, R. A. Grimble, H. Ö. Özer, S. Jeffery, and J. B.
Pethica, Proc. R. Soc. London 457, 1161 共2001兲.
26
A. Oral, R. A. Grimble, H. Ö. Ozer, and J. B. Pethica, Rev. Sci. Instrum.
74, 8, 3656 共2003兲.
27
D. W. Pohl, Rev. Sci. Instrum. 58, 54 共1987兲.
28
Ch. Renner, Ph. Niedermann, A. D. Kent, and Ø. Fisher, Rev. Sci.
Instrum. 61, 965 共1990兲.
29
C. N. Woodburn, A. W. McKinnon, D. A. Roberts, M. E. Taylor, and M.
E. Welland, Meas. Sci. Technol. 4, 535 共1993兲.
30
B. L. Blackford and M. H. Jericho, Rev. Sci. Instrum. 68, 133 共1997兲.
31
EBL No 2 piezotube, 12.7 mm o.d.⫻ 1 mm wall thickness 25.4 mm long
Staveley Sensors Inc., 91 Prestige Circle, East Harford, CT.
32
EBL No. 2 piezotube, 6.3 mm o.d.⫻ 1 mm wall thickness, 25.4 mm long
Staveley Sensors Inc., 91 Prestige Circle, East Harford, CT.
33
Vibration Isolation from minus-K Technologies, 420 S Hindry Ave., Unit
E Englewood, CA 90301.
34
EBL no 2 shear plates, Staveley Sensors Inc., 91 Prestige Circle, East
Hartford, CT.
35
EBL No.1 piezotube 3.18 mm o.d.⫻ 0.38 mm wall thickness, 12.7 mm
long, Staveley Sensors, Inc., 91 Prestige Circle, East Hartford, CT.
36
Metrotek, 6880, 46th Ave. North Suite 100, St, Petesburg, FL.
37
F. J. Giessibl, thesis, University of Augsburg, Germany 共2000兲.
38
S. Hembacher, F. J. Giesibl, and J. Mannhart, Appl. Surf. Sci. 188, 445
共2002兲.
39
Nanomagnetics Instruments Ltd., 17 Croft Road, Oxford OX3 0JZ, UK,
http://www.nanomagnetics-inst.com.
40
P. M. Hoffmann, Small-Amplitude Atomic Force Microscopy in Dekker
Encyclopedia of Nanotechnology 共Dekker, New York, 2004兲, p. 3641.
41
S. J. O’Shea, M. E. Welland, and J. B. Pethica, Chem. Phys. Lett. 223,
336 共1994兲.
42
Sigma-Aldrich Corp. St. Louis, MO.
43
Cantilevers from µmasch, 7086 SW Beveland Road, Portland, OR.
44
J. Klein and E. Kumacheva, J. Chem. Phys. 108, 6996 共1998兲.
45
A. L. Demirel and S. Granick, J. Chem. Phys. 115, 1498 共2001兲.
46
D. A. Walters, J. P. Cleveland, N. H. Thompson, P. K. Hansma, M. A.
Wendman, G. Gurley, and V. Elings, Rev. Sci. Instrum. 67, 3583 共1996兲.
4
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