Reprinted from

REVIEW PAPER

Liquid Atomic Force Microscopy: Solvation Forces, Molecular Order, and Squeeze-Out

Sean J. O’Shea, Nitya N. Gosvami, Leonard T. W. Lim, and Wulf Hofbauer

Jpn. J. Appl. Phys. 49 (2010) 08LA01

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Liquid Atomic Force Microscopy: Solvation Forces, Molecular Order, and Squeeze-Out

Sean J. O’Shea, Nitya N. Gosvami1, Leonard T. W. Lim, and Wulf Hofbauer

Institute of Materials Research and Engineering, 3 Research Link, Singapore 1176021Leibniz-Institut fur Neue Materialien, D-66123 Saarbrucken, Germany

Received February 11, 2010; accepted April 9, 2010; published online August 20, 2010

We review the use of atomic force microscopy (AFM) in liquids to measure oscillatory solvation forces. We find solvation layering can occur for all

the liquids studied (linear and branched alkanes) but marked variations in the force and dissipation may arise dependent on: a) the temperature, b)

the tip shape/radius of curvature, and c) the degree of molecular branching. Several findings (e.g., the strong temperature dependence in

measured solvation forces, solvation oscillations using branched molecules) differ from those observed using the Surface Force Apparatus,

because of the nanoscale area probed by AFM. Conduction AFM is used to explore how liquid is squeezed out of the tip–sample gap, and enables

the change in contact area of the tip–sample junction to be monitored and compared to mechanical models. We find elastic models provide a good

description of the deformation of ordered, solid-like solvation layers but not disordered, liquid-like layers.

# 2010 The Japan Society of Applied Physics

DOI: 10.1143/JJAP.49.08LA01

1. Introduction

Using atomic force microscopy (AFM) in liquid environ-ments requires an understanding of the liquid mediatedforces acting between two surfaces, i.e., the AFM tip andthe sample. Liquids confined at small separations (�nm)between two surfaces behave differently from the bulkliquid. In addition to van der Waals and electrostatic forcesacting, the liquid molecules between the surfaces may pack(or order) into well defined solvation layers.1) The liquidordering results in solvation forces curves which oscillateperiodically as successive, discrete layers of liquid mole-cules are displaced from the gap between the surfaces. Theoscillation period is approximately equal to the diameter ofthe liquid molecules.

In a previous report2) we discussed early measurementsof solvation forces using AFM, with an emphasis on howoscillatory forces could influence AFM imaging in liquids.Here we summarise more recent results and are primarilyconcerned with studying the material state of the confinedliquid, e.g., does the confined material behave as a solidor liquid, etc. Under certain circumstances we can also tietogether imaging and material property measurementsbecause high-resolution frequency modulation AFM (FM-AFM) imaging can show in-plane ordering of a solvationlayer, which is a clear indication the confined liquid hassolid-like properties.

A major issue to consider is that much of our presentunderstanding of the material properties of confined liquidscomes from experiments using the surface force apparatus(SFA), in which two macroscopic mica surfaces are broughttogether. The radius of curvature (R) of the surfaces usedin SFA (R � 10 mm) is orders of magnitude larger than thetip in AFM (Rtip � 10 nm), and a particular interest is howAFM solvation force measurements differ from SFA results.The conditions necessary to observe oscillatory forces inSFA were summarized by Israelachvili.3) Oscillatory forcesare not seen if the surfaces are rough, the molecules areirregularly shaped or mixtures of dissimilar molecules arepresent. Asymmetry and roughness break up the ordering ofthe liquid and force oscillations ‘‘average out’’ in the SFAforce curve. In the SFA, both the liquid molecules and thesurfaces need a high degree of order or symmetry. We findthis is not necessarily the case in AFM where oscillatory

forces can still be observed for blunt tips, branchedmolecules and liquid mixtures (see §2). Clearly the radiusof curvature (R) of the surfaces is significant. In AFM,where R is always small, a significant proportion of theconfined liquid molecules can still behave co-operativelyover nanoscale regions, irrespective of the tip or moleculargeometry.

We have also found another important consequence ofthe small confinement area in AFM and this concerns howliquid moves in and out of the gap between tip and sample,i.e., the squeeze out behaviour of the liquid (see §3). InSFA experiments, confined liquid molecules must travelmany microns to exit the contact zone between the twosurfaces, and the resultant fluid flow can be describedhydro-dynamically.4) In contrast, AFM experiments moreresemble molecular dynamic computer simulations,5)

with confined molecules exiting the contact zone and intothe liquid bulk over nanometer distances, comparableto diffusion lengths. As described in §3, some remarkableconsequences of the squeeze out occurring at nanometerlength scales are a strong temperature dependence of themeasured solvation forces, and the possible trapping ofliquid even within a nanoscale contact zone. An importantcorollary of the latter result is that one cannot use con-tinuum mechanics models of the tip–sample contact inAFM if liquid remains trapped between the surfaces. Theimportance of length scales and temperature in the squeezeout process naturally leads to consideration of the changein viscosity (i.e., dissipation) in solvation force measure-ments and this aspect is discussed in §4. In §5 we concludewith a brief summary and outline some major unresolvedproblems.

In all experiments discussed below, the AFM canti-lever and sample are completely immersed in the liquid,i.e., there are no capillary forces acting. The molecularstructures of the liquids commonly used are shownschematically in Fig. 1. The substrate most often usedis highly orientated pyrolytic graphite (HOPG). In thetemperature dependent measurements, all the liquid withinthe cell is essentially at the same temperature. Finally,we can generally verify the true contact between thetip and a HOPG sample (i.e., where the tip–sampleseparation is zero) by directly imaging the HOPGlattice.

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2. Effect of Molecule Scale Roughness

AFM solvation force measurements using highly branched,asymmetric molecules can reveal force oscillations,6) whichagree with computer simulations7–12) but can differ markedlyfrom SFA observations.13,14) Similarly, if rough surfaces areused in SFA no force oscillations are typically seen,3)

in contrast to AFM data.15) Below we outline our presentunderstanding of the effect of molecular scale roughness(either surface roughness or inherent molecular asymmetryof the liquid molecules) in AFM force measurement.

2.1 Influence of molecular structure of the confined liquid

What is the effect of molecular geometry on solvationforces? Early SFA results did not reveal any oscillatorysolvation force for branched alkanes and other highlyasymmetric molecules, leading to the conclusion that theliquid molecules must exhibit a symmetric structure toexhibit oscillatory forces.3) Put simply, asymmetric mole-cules cannot pack suitably over the large geometric area ofthe SFA contact zone, implying that any force oscillationsbecome ‘‘smeared out’’ or ‘‘averaged’’. An example weconsider extensively in this review is squalane; an atypicalbranched molecule used in many studies of boundarylubrication. The initial SFA experiments using squalaneshowed no oscillatory solvation force.13,14) Later, Granicket al. revisited the problem and showed oscillatory forces forsqualane using SFA, and suggested the method of cleavingthe mica for SFA measurements could have dramatic effectson the force measurements.16) More recent experimentsby Israelachvili et al. on squalane again showed only amonotonic force variation with no oscillations.17) Thusexperiments performed on branched molecules using SFAremain controversial.18)

In contrast, AFM shows oscillatory type force curvesusing several highly branched molecular liquids near aHOPG surface. The first results6) demonstrated clearsolvation oscillations in squalane using sample modulationAFM. The layering can also be observed using staticdeflection AFM, as shown in Fig. 2(a), in which fivesolvation jumps are seen as indicated by the labels n ¼1{5, where n ¼ 0 corresponds to the tip in direct contactwith the HOPG substrate and n ¼ 1 is the squalanemonolayer. The squalane monolayer can also be imaged,as shown in Fig. 2(b);19) an important result because notonly does it confirm the ‘‘non-liquid’’ nature of the solvationlayer, but it is the first direct evidence (as distinct fromdiffraction experiments20,21)) that branched liquid moleculescan form crystalline structures near a surface.22) Subse-quently, we also measured oscillatory liquid forces in phenyloctane,23) heptamethylnonane (HMN),19) and binary liquidmixtures.24) Force measurements in liquid mixtures showthat discrete co-existent molecular layers can form, with

Spherical : OMCTS

Branched : Squalane

Heavily branched : HMN

Mixed : Phenyloctane

Linear : Hexadecane

C C C C C C C C

C C C C C C C C

Fig. 1. Schematic diagrams which highlight the molecular ‘‘shape’’

of the liquids. The spherical molecule octamethylcyclotetrasiloxane

(OMCTS) [SiO(CH3)2]4; linear alkane hexadecane (C16H34); branched

alkane 2,6,10,15,19,23-hexamethyltetracosane (squalane, C30H62);

branched alkane 2,2,4,4,6,8,8-heptamethylnonane (HMN, C16H32); linear

with ring phenylocatane (C14H22). The end of each straight line indicates

the position of a carbon atom.

(a)

Tip-Sample distance (nm)

For

ce (

nN)

(b)

Fig. 2. (Color online) (a) Contact mode (static) data showing force as

a function of the tip–sample separation for squalane on HOPG. Clear

solvation jumps are observed (indicated by n ¼ 1{5) where n ¼ 0 is the

graphite surface and n ¼ 5 is the solvation layer farthest from the surface.

A solvation ‘‘jump’’ occurs when the force is high enough to squeeze out

the molecules in layer n and the tip ‘‘jumps’’ to layer n � 1. The data is

taken at room temperature with a gold coated cantilever of spring

constant 0.76 N/m and tip radius �36 nm. (b) STM topographic image

(13� 13 nm2) of squalane molecules adsorbed on HOPG at room

temperature, revealing molecular resolution. STM conditions: 1 V (sample

positive), 12 pA.

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one molecular species being preferentially adsorbed closestto the surface.

Clearly, the smaller contact area in the AFM experimentscompared to SFA means that AFM can probe liquidinteractions which occur over much smaller length scales.Our general conclusion thus far is that in principleoscillatory forces may be observed for all liquids at thenanoscale using AFM, irrespective of molecular symmetry.This conclusion is strongly supported by molecular simu-lations over nanoscale contact areas revealing ordered liquidstructures of asymmetric molecules7–10) and liquid mix-tures25) on various surfaces. Neutron and helium atomscattering20) and X-ray reflectivity measurements21) havealso indicated strong layering of branched molecules close toa solid surface. The phrasing in principle and may emphasisewe must exercise caution in any generalisation. Very fewliquids and surfaces have been tested; the surfaces mustbe locally smooth (see §2.2); and the time scale of themeasurement must be rapid enough to sample any localizedordering (see §4). Depending on specific experimentalconditions (tip, surface, liquid, temperature, approach speed)solvation layers may not be observed at all or the layering isweak with no sharp ‘‘jumps’’ between layers. For example, in§3.3 we discuss the indistinct solvation layering that resultswhen measurements are undertaken at 65 �C in squalane.

2.2 Influence of tip size and surface roughness

It has been shown using AFM that solvation forces may stillbe observed on nominally rough surfaces15,26) because the tipis of the same length scale as the roughness, whereas roughsurfaces in SFA experiments will ‘‘average out’’ oscillatoryforce behaviour. An example is shown in Fig. 3 for solvationlayers in octamethylcyclotetrasiloxane (OMCTS) near analkane-thiol self-assembled monolayer (SAM) on Au(111).The SAM surface is rough at the molecular scale yet stronglayering is observed. Obviously, the degree of layeringdepends on the size of the molecule compared to the localroughness and OMCTS is rather large (�0:9 nm) comparedto the local SAM corrugation (�0:07 nm27)). Nevertheless,we also observe layering of the smaller, linear alkanes onSAM.28)

A related observation is that very blunt AFM tips(Rtip � 350 nm) can measure the same magnitude of sol-vation forces as ultrasharp tips (Rtip � 14 nm).26) The under-lying reason is that micro-asperities on the tip dominate theshort range interaction. We made similar observations usingcolloid spheres of known radius (Rtip ¼ 10 mm) as tips.15)

Despite using various cleaning methods the colloid tips werealways rough at the molecular level, as revealed by inverseAFM imaging. Solvation oscillations could arise even withthese molecularly rough colloid tips.

We have explicitly studied the magnitude of the oscil-latory solvation force (F) as a function of the AFM tip radius(Rtip ¼ 15 to 100 nm as measured by scanning electronmicroscopy) in the liquids OMCTS, hexadecane anddodecanol.29) We find a clear trend, namely the normalizedforce (F=Rtip) decreases with increasing tip radius. Thedecrease in F=Rtip was found in all three liquids and in eachsolvation layer. Figure 4 shows the n ¼ 1 solvation layerresults taken in hexadecane. We hypothesise that the majorcause for the non-constant value of F=Rtip is the variation in

nanoscale roughness or geometry at the tip apex. Increasingroughness leads to an ‘‘averaging’’ of the oscillatory forcesover the tip area, giving smaller magnitude oscillations inthe force curve.

This observation has important consequences for obtain-ing quantitative results of surface force interactions usingAFM. The Derjaguin approximation is widely used as amethod of scaling the measured forces obtained by AFM andSFA to enable comparisons between different experiments tobe made.3) For the surface geometry used in AFM andSFA, the Derjaguin approximation turns out simply to bea normalisation of the force with the radius of curvature,i.e., experiments need to compare F=Rtip. The systematicvariation we observe in F=Rtip for a given liquid-surfacesystem strongly suggests a need for caution in normalisingAFM data for comparison between experiments and also inusing AFM to obtain the surface adhesion.30) Unfortunatelyit is very difficult to calibrate the exact tip shape on a sub-nanometer scale31) and at present we must undertake manyidentical experiments combined with a statistical analysis toobtain meaningful conclusions. A useful empirical observa-tion is that using very sharp tips (�30 nm) gives the most

Pull off minima

Tip-Sample distance (nm)

For

ce (

nN)

Fig. 3. (Color online) Solvation layering of OMCTS near a decane-thiol

self-assembled monolayer (SAM) surface formed on gold. Solvation jump

distances of �0:9 nm were observed corresponding to the diameter of the

OMCTS molecule. The tip contacts the SAM surface at tip–sample

distance D ¼ 0 nm. The solvation layers are labelled n ¼ 1 (OMCTS layer

closest to SAM surface) to n ¼ 5 (layer farthest from the surface).

Rtip (nm)

F/ R

tip

(mN

/m)

20 40 60 80 1000

100

200

300

Fig. 4. Data taken with different sized tips (Rtip) showing the normal-

ised magnitude of the first (n ¼ 1) solvation layer force for dodecanol on

HOPG. If the force is normalised (F=Rtip) there is a clear trend of

decreasing F=Rtip as the tip becomes larger.

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consistent measurements of the forces, presumable becauselarge differences in tip shape cannot occur if Rtip isextremely small.

In summary, the main point to note is that in AFM theconditions required for observing solvation oscillationsappear more relaxed compared to the SFA, i.e., in AFMthe effect of roughness or asymmetric liquid molecules donot ‘‘average out’’ the force oscillation over the nanometerscale contact area.

3. Importance of Liquid Squeeze-Out in Solvation

Force Measurement

Pressure must be applied to squeeze-out solvation layers andbring the AFM tip and substrate surface together. It turns outthat the squeeze-out process has a significant bearing on themeasured force curves because the liquid flow from the tip–sample junction is dependant on the state of the confinedliquid material, which in turn is dependent on parameterssuch as temperature and molecular order in the confinedliquid layers. Again, we find differences in AFM comparedwith SFA data arising from the nanoscale volume of theconfined material in AFM, most notably in the temperaturedependence.

3.1 Strong temperature dependence in AFM

measurements of solvation

We have used AFM to measure solvation forces in theliquids OMCTS, n-hexadecane, and n-dodecanol over thetemperature range from 25 to 75 �C.32) Some experimentalpoints to note are, only data with the smallest Rtip areanalysed (for reasons given in §2.2), and the approach andretract speed was kept approximately constant at �5 nm/sbecause the force required to remove a solvation layer varieslogarithmically with the approach velocity.33)

Discrete solvation layers were observed for all threeliquids at every temperature. However, there is a largedecrease in the magnitude of the measured solvation forceswith the modest (50 �C) increase in temperature (Fig. 5).This surprising temperature decrease was seen for all threeliquids and for each solvation layer. The result is surprisingbecause experimentally34) and theoretically35) it is knownthat oscillatory solvation forces should not be stronglytemperature dependent because the change in liquid densitywith temperature is weak. The AFM experiments show thesolvation force changes by �30% for OMCTS and �60%for hexadecane and dodecanol over 50 �C. Theoreticallysuch large changes in solvation force require a temperaturevariation of hundreds of degrees.36,37)

Why are the AFM forces so strongly temperature depend-ent? Again, the small length scale in AFM introducesanother mechanism into the measurement; in this caserelated to how the liquid squeezes out of the tip–sample gapwhen pressure is applied. The squeeze out process isthermally activated, giving rise to the large change in themagnitude of the squeeze out pressure with temperature.Essentially, a higher temperature lowers the energy barrierfor a hole (i.e., a region free of liquid) to nucleate in thecontact zone, prior to the removal of the liquid molecules.4,5)

An analytical description of the mechanism was presentedby Persson and Tosatti4) and subsequently several computersimulations38,39) of liquid confined between two surfaces

have explicitly shown temperature dependent results whichmatch the trends observed in our AFM data. A simple modelcan be given based on transition rate theory to describethe kinetics and associated energy barriers for the tip to‘‘jump’’ between the solvation layers.40) Similar models areused in chemical force microscopy analysis of adhesionforces41,42) and we simply modify to show the temperature(rather than velocity) dependence of the forces.32) The modelshows40,43) that at constant loading rate, the force required torupture the nth solvation layer (Fn) decreases approximatelylinearly with increasing temperature, and this is the majorvariation we observe in the AFM solvation force (Fig. 5).Transition rate theory also shows how temperature depend-ent data can be used to monitor changes in the free energyduring squeeze-out,32,41) giving a powerful technique tofurther our understanding of the material state of confinedliquid.

The key point of our results is that since solvation forcesare only weakly temperature dependent, the strong temper-ature effect we observe is not related to the fundamentalbehaviour of the solvation force, but indicates we aremeasuring how the layers are squeezed from the tip–samplegap. This contrasts with experiments using the SFA in whichno temperature variation is expected. The large changesobserved in solvation force with temperature has implica-tions for the measurement of localised forces using AFM,e.g., biological force interactions should be measured atphysiological temperatures; in measuring single asperityfriction at realistic (i.e., elevated) temperatures.

(a)

Temperature (oC)

F/ R

tip

(mN

/m)

25 30 35 40 45 50 5510

30

50

70

(b)

Temperature (oC)

F/ R

tip

(mN

/m)

20 30 40 50 60 70 800

20

40

60

80

100

Fig. 5. Temperature dependence of the normalized peak–peak solva-

tion force (F=Rtip) near HOPG for, (a) solvation layer n ¼ 1 in OMCTS,

and (b) solvation layer n ¼ 2 in hexadecane. F=Rtip decreases signifi-

cantly with increasing temperature. Data is only presented for the

smallest radius tips used (Rtip < 30 nm for hexadecane; Rtip < 40 nm for

OMCTS with the circle and square symbols showing different tips).

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3.2 Using conduction AFM to monitor mechanical

deformation

It remains experimentally challenging to study the detailedmechanics of a single AFM contact. Conducting-AFM (C-AFM) can assist in this respect by revealing subtle changesin the contact junction which are not observed in standardforce measurements. In C-AFM the current flow between aconducting substrate (e.g., HOPG) and a metal coated AFMtip is simultaneously measured as a force curve is taken,as shown in Fig. 6(a). A constant bias is applied, which istypically <1 V in liquids to ensure no electrochemicalreactions occur. It is also important to ensure that themetal coating on the tip apex does not wear away duringmeasurements. Below we summarise some findings on theuse of C-AFM to investigate the squeeze-out of solvationlayers.

In our liquid-HOPG experiments the measured current (i)is proportional to the tip–sample contact area (�a2 where a isthe contact radius). Thus a plot of current versus force shows

the relative change in area with applied force, which in turncan be compared with the contact area calculated from amechanical model of the tip–sample point contact.44,45) Notethat the absolute (as distinct to relative) value of the contactarea can be estimated from either fitting the force to amechanical model or relating the current flow to electronictransport across the junction. A consideration of the errorsinvolved leads to the conclusion that the mechanical modelis best,46) because there are very large uncertainties inelectrical properties at the nanoscale.

A suitable, mechanical description of the elastic defor-mation of a contact is the Maugis–Dugdale (MD) model,45)

which incorporates all previous models as special cases.For example, one limiting case is the Derjaguin–Muller–Toporov (DMT) model,47)

a ¼3Rtip

4KðFa þ FcÞ

� �1=3

ð1Þ

where K is the effective elastic modulus, Fa is the appliednormal force and Fc is the pull-off force. We find that theDMT model provides a good fit to the force-current data formany of the liquids we have investigated on HOPG.

Both the current and the force data may reveal discretesolvation layering near a surface. Figure 6(a) shows raw dataas the tip approaches the substrate taken in squalane as afunction of piezoelectric displacement (Z). Jumps betweensolvation layers (labelled n ¼ 1 to 4) are observed as thetip approaches the HOPG substrate (labelled n ¼ 0). Thisexample shows a sharp increase in current at Z � 11 nm asthe tip pushes away the n ¼ 2 solvation layer and jumps intocontact with the n ¼ 1 layer. These very sharp current jumpsare typical of a solid-like material being squeezed from thegap (see below). Similarly, near Z � 2 nm the monolayer(n ¼ 1) is squeezed out and the tip contacts the HOPG(n ¼ 0). The exceptionally large increase in current nearZ � 2 nm has been studied in detail46) and we infer that justbefore the squeeze-out of the monolayer there is a character-istic rearrangement of the molecular packing under the tipapex which brings the tip slightly closer to the substrate.This interpretation is based on computer simulations of thephenomena.5,48)

How can we say a material shows solid like behaviour?For linear molecules on HOPG, a crystalline image can oftenbe observed, for example Fig. 2(b). However, imaging is nota necessary condition, particularly since imaging may beproblematic if the confined material does not have long rangecrystalline order. A more general approach is to find if the C-AFM data can be fitted to a point contact model. We begin byre-plotting the data to show current as a function of force, asin Fig. 6(b) for squalane at 25 �C with the tip in contact withthe HOPG substrate (n ¼ 0). In this example the force curvesare reversible in loading and unloading cycles, demonstratingthe contact is elastic. Since the current is proportional tocontact area we can compare the changes in current as the tipis pulled away from the surface with the MD model and testif a good fit can be obtained. Note that using pull-off datais preferred as this ensures that the adhesion minima issampled.49) For Fig. 6(b), we find the DMT model providesa good fit to the data, i.e., the relative change in the current(I) is well described by I / �a2 / ðFa þ FcÞ2=3 as expectedfrom eq. (1). Similarly, data obtained on the monolayer

(a)

Piezo displacement (nm)

For

ce (

nN)

Cur

rent

(nA

)

(b)

Force (nN)

Cur

rent

(nA

)

Con

tact

are

a (n

m2 )

Fig. 6. Conduction AFM data for squalane at 25 �C taken near HOPG,

using a gold coated cantilever of spring constant 0.76 N/m and tip radius

�36 nm. The approach speed is 10 nm/s. (a) Typical raw data showing

simultaneous force (solid line) and current (circle) measurements as a

function of displacement of the piezoelectric actuator in the surface

normal direction (Z ). Solvation ‘‘jumps’’ are observed in both the force

and current curves and are labelled n ¼ 0 to 4, with n ¼ 1 showing the

displacement where the tip jumps from layer n ¼ 1 to the HOPG substrate

n ¼ 0. (b) Data re-plotted as current vs force for the tip in contact with the

HOPG (n ¼ 0 region). The variation in current while pulling the tip back off

the surface (triangles) is fitted with the Maugis–Dugdale model (solid line)

from which the contact area can be estimated, as shown.

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(n ¼ 1) show similar variation with load and are well fittedwith a DMT model.19,46) This strongly indicates that thesqualane monolayer also behaves as an elastic, solid-likelayer at 25 �C, as confirmed by scanning tunnelling mi-croscopy (STM) imaging as shown in Fig. 2(b). Further, wehave tested a series of n-alkanes50) and found that if anordered monolayer can be imaged (e.g., hexadecane andtetradecane form ordered lamellar monolayers at 25 �C,whereas octane does not) then the force-current curves forboth the tip–HOPG (n ¼ 0) and tip–monolayer (n ¼ 1)contact are well described by the DMT model.

Thus, there is strong evidence that the squeeze-out anddeformation of confined solvation layers behave as an elasticsolid, provided the C-AFM data shows that the change inrelative area with load can be fitted to a continuum model ofthe point contact.

3.3 Liquid molecules can be trapped in the tip–sample

contact zone

In general a sudden, discontinuous jump in the currentoccurs as the tip traverses a solvation layer [e.g., the n ¼ 1

layer highlighted in Fig. 6(a)], provided the layer is solid-like, as described above. What is the behaviour of confinedmaterials which do not form crystalline layers on HOPG?

Figure 7(a) shows a current vs force curve for squalane onHOPG at 65 �C and 10 nm/s approach speed. At highertemperature the solvation jumps become smaller (see §3.1)and importantly the transition between solvation layersmay become blurred. For example, in Fig. 7(a) as the tipapproaches the substrate there is no clear transition from themonolayer (n ¼ 1) measured at low load to hard contact onthe graphite (n ¼ 0) at high load. Also, significant hysteresisis observed between the approach and retraction cycles,indicating non-elastic response. Finally, the relative changein current (i.e., area) with load cannot be fitted to any elasticcontact model, even if the tip is in mechanical contact withthe HOPG substrate [see the pull-off curve in Fig. 7(a)]. Thisis a very surprising result because it states that the junctioncannot be modelled as a simple elastic asperity, even thoughthere is solid-solid contact!

We hypothesise the above observations (large hysteresisin the force curve, non-uniform current variation with force)arise because the confined molecules are in a liquid-likestate, which leads to some molecules becoming trapped inthe contact zone [Fig. 7(b)].19) Recent simulations of thesqueeze-out of butane and its branched isomer, iso-butane,48)

show the linear butane molecules form an ordered mono-layer and are completely removed from the contact zoneunder applied pressure, as described in §3.2. In contrast,iso-butane remains liquid-like in the contact zone and showsa higher resistance to displacement, leading to the trappingof a few molecules, even at very high pressure. The confinediso-butane exhibits visco-elastic behaviour and is onlyslowly removed from the gap. If the pressure becomessufficiently high before the molecules can be displaced, thenthe confining surfaces will deform enabling hollows filledwith molecules to be created, as shown schematically inFig. 7(b).

The experimental condition which has changed is thatthe temperature has increased from 25 �C (Fig. 6) to 65 �C(Fig. 7). Despite repeated attempts, no image of the squalane

monolayer could be obtained at 65 �C, strongly suggesting themonolayer structure seen at 25 �C [Fig. 2(b)] has disappearedat 65 �C. A recent simulation22) shows that the solid-phase ofthe squalane monolayer on graphite melts at�52 �C. Thus thestate of the confined material has changed from solid-liketo liquid-like, and this is the underlying cause of the verydifferent force curves obtained in Figs. 6(b) and 7(a).

We have observed similar behaviour for a range of highlybranched (e.g., squalane, heptamethylnonane19)) and linearmolecules (alkanes, alcohols46,50)). Studies of alkanes areespecially revealing because their adsorption on graphite hasbeen extensively studied. Differential scanning calorimetry(DSC) and neutron scattering of alkanes adsorbed onpowdered graphite51–54) can reveal the phase of the adsorbedmaterial. For example, at 25 �C hexadecane forms a twodimensional solid monolayer co-existing with the bulkliquid. The solid nature is confirmed in many STM studiesshowing ordered hexadecane layers on HOPG.55) On heat-ing, the hexadecane monolayer undergoes an order–disorderphase transition from the ordered, solid layer to an adsorbedlayer showing no order, i.e., liquid-like. This transitionis termed monolayer melting and the DSC data gives themonolayer melting temperature (Tm), which is typically 10%higher than the bulk liquid melting temperature,56) e.g., forhexadecane bulk liquid melting occurs at 16 �C whereas

(a)

approach

pull off

Force (nN)

Cur

rent

(nA

)

(b)

SUBSTRATE

TIP

Fig. 7. (Color online) (a) Conduction AFM curve for squalane at 65 �C

taken near HOPG using a gold coated cantilever of spring constant

0.76 N/m and tip radius �36 nm. The approach speed is 10 nm/s. The

variation in current is shown for both tip approach and tip pull off. The

approach curve between 0 to 5 nN is sampling the squalane monolayer

(n ¼ 1) and at high forces (�11 nN) the HOPG substrate, but the position

of the transition between the two layers (i.e., n ¼ 1! 0) is not well

defined. (b) Schematic of the proposed trapping of liquid under the tip,

leading to current vs force curves as shown in (a). The dots represent

liquid molecules.

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Tm � 57 �C. Our AFM and STM images show the hexade-cane monolayer on graphite is well ordered at 25 �C and hassolid-like squeeze out curves similar to Fig. 6(b), whereas at65 �C the monolayer cannot be imaged and shows forcecurves similar to Fig. 7(a). Similar behaviour is observed foroctane, decane, dodecane, and tetradecane; the current vsforce curves indicate solid like behaviour below Tm anddisordered (liquid-like) behaviour above Tm.

The liquid-trapping interpretation is further supported bymeasurements at different tip–surface approach speeds.For example, for the case shown in Fig. 7(a), experimentsperformed at much slower approach speed (1 nm/s comparedto typical speeds of �10 nm/s) give the elastic responseexpected for the tip in contact with the HOPG, i.e., the changein current with force can again be fitted to the MD modelwhen the tip is pulled off the surface. Put simply, at slowenough approach speed, confined liquid has time to move outof the contact zone, but at fast speeds may become trapped.

To summarise the C-AFM results, continuum elasticmodels are well suited to describe ordered, solid-likematerials (§3.2). However, when the confined moleculesare disordered simple elastic models cannot be appliedbecause the viscoelastic/liquid-like properties of the con-fined material may lead to liquid trapping within the junction(§3.3). It is the disorder/order distinction in the state ofthe confined liquid which leads to striking differences inthe solvation layering and squeeze-out behaviour, with thedegree of molecular branching playing a secondary role.

4. Dissipation Measurements of Dodecanol Solvation

Layers

Given the influence of temperature and approach speeds onboth the observation of solvation forces and the squeeze-outbehaviour, it is natural to consider the temporal response ofthe confined material to an applied load. Specifically, whatcan we learn from the viscosity (i.e., dissipation) changeduring a force curve measurement of solvation forces? Themeasurement of viscosity in the flow of confined liquids hasbeen extensively studied using the SFA.57) In contrast, wehave little understanding of dissipation in similar liquidAFM experiments. Below we summarise some AFMfindings to date.

4.1 AFM measurement of dissipation in solvation layers

Early studies of OMCTS near HOPG found the effectiveviscosity increases over four orders of magnitude above thebulk value for the solvation layers closest to the surface,even for very small tip radii (Rtip � 10 nm).26,58) Subse-quently there have been several reports of the strong increasein damping for confined liquids on various substrates, andusing a variety of methods to obtain the dissipation signalsuch as off resonance interferometry,59) FM-AFM,60,61)

lateral tip oscillation,62) and tuning fork.63)

FM-AFM offers not only dissipation data but also thepossibility of obtaining atomic resolution imaging (notehowever, the increasingly high damping from solvationlayering may negate this attribute for non-contact imag-ing2)). Figure 8 shows representative data for dodecanol onHOPG using FM-AFM.64) The dissipation force curves[Fig. 8(b)] show the characteristic strong increase in damp-ing as the surface is approached. The increase in dissipation

is largest as the temperature nears the bulk melting temper-ature (23 �C) yet remains very clear at 39.5 �C, well abovethe bulk melting.

One reason for the strong increase in dissipation abovethe bulk liquid is that the dodecanol liquid layers have acrystalline order, i.e., are solid like. This is shown by directimaging of the solvation layers up to several nanometersaway from the solid surface [Fig. 8(a)]. The use of the word‘‘crystalline’’ reflects the fact that we can image a solidordered structure, i.e., the solvation layers appear ordered inboth lateral and surface normal directions. The ability toimage long-range crystalline order is one simple definitionof a solid65) and thus in this case we can unequivocally statethat at 25 �C the confined dodecanol is solid-like withinmany solvation layers. The question on whether a confinedmaterial is solid or liquid is usually answered using solelyforce curve data (see §3.3). Thus, directly imaging orderedstructure within a solvation layer can be regarded as furtherevidence that the particular layer is indeed a solid. In future,we anticipate images can be correlated with force curvemeasurement to better understand whether a confinedmaterial is a solid or liquid.59)

(a)

Piezoelectric Z displacement (nm)-1 0 2 4

Dis

sipa

tion

(ar

b. u

nits

)

4

3

2

1

(b)

Fig. 8. (Color online) Dissipation data taken for dodecanol solvation

layers on HOPG. The vibration amplitude is 0.25 nm peak–peak. (a) A

FM-AFM dissipation image (7:5� 7:5 nm2) at 25 �C under constant

frequency scanning, showing molecular order in the solvation layer.

(b) Force curves showing the dissipation as a function of relative tip–

sample separation (Z ), using the same tip at different temperatures (25 to

39.5 �C). Negative Z is closer to the surface. Far from the surface (at

Z � 5 nm) each curve is normalised to 1 and progressively offset by +0.5

for clarity.

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4.2 Hypothesis linking tip shape and dissipation

A distinct feature of Fig. 8(b) is the appearance of peaks inthe energy dissipation just as a solvation layer is squeezedout of the junction. The peaks are typically �0:1 to �0:6 eV(per cantilever oscillation cycle) above the backgrounddissipation signal. A plausible model explaining the dis-sipation peaks64) assumes that at the point where the tipbegins to penetrate the solvation layer, the vibrating tiprepeatedly expels and reincorporates molecules under the tipapex in the oscillation cycle, resulting in increased dissipa-tion, e.g., from viscous flow of the displaced molecules.

Section 2.2 highlighted the significance of the tip shapein oscillatory force measurement. We hypothesize that tipshape is also critical in dissipation measurements. We findthat the presence of the peaks depends to a large extent onthe particular tip used. For many tips the peaks appearedsmooth or were not visible at all. We also found dissipationpeaks could be ‘‘induced’’ by deliberately blunting a tip.Some dissipation curves with two peaks near the squeeze outpoint were also observed. As in §2.2, it is difficult to directlytest the hypothesis because the nanoscale shape of the tipapex must be known. Nevertheless, our subjective observa-tions of many force measurements indicate that tip shapedoes significantly alter the dissipation curve in the squeezeout of solvation layers. If true, then one can postulate that tipgeometry may be the underlying cause of the high variabilityand different ‘‘features’’ reported in AFM dissipationmeasurements. For example, oscillations in the dissipationsignal corresponding to solvation layering have beenreported for OMCTS using gold coated tips59) but not withultrasharp silicon tips26) or carbon nanotube tips.61)

5. Conclusions

We have outlined our recent research in AFM forcemeasurement of oscillatory solvation forces. We concludewith some general observations of interest. Firstly, we arebeginning to find significant differences between AFM andSFA measurement because of the nanoscale volume probedby the AFM tip. The observation of solvation oscillationsusing branched molecules and rough surfaces suggests thatAFM can detect even highly local packing of liquids near asurface. Secondly, liquid is squeezed out from the tip–substrate gap on a much smaller length scale than in SFAresulting in entirely new phenomena, such as a strongtemperature dependence of the measured solvation forcesand nanoscale liquid trapping. The latter leads to thesignificant observation that continuum elastic models appearto provide a good description of the deformation of ordered,solid-like solvation layers but cannot be used if the confinedmolecules have disordered, liquid-like layers. Lastly, AFMprovides the ability to tie in molecular scale imaging withthe measured force curves, providing a direct indication ofthe material state of the confined liquid. We highlighted thisaspect using alkanes adsorbed on HOPG and find a stronginterconnection between crystalline order in the layers, theshape of molecules and how this effects ordering andmobility (i.e., branched versus linear chains), and thetemperature of the system (i.e., above or below the meltingtemperature of the confined liquid).

Not surprisingly, there remain many problems. Oneobvious question is how general are the results. Very few

systems (surfaces and liquids) have been studied and waterin particular requires extensive research. The shape of thetip apex also remains unknown and is a major cause ofuncertainty. We have shown large tip size gives rise to asystematic error in F=Rtip and speculate that variable tipshape is also critical in dissipation phenomena. Furthercomputer simulations of liquid confinement and dissipationare desirable. Finally, measuring the effect of molecularshape, temperature and speed of approach on dissipationwith dynamic mode AFM will provide critical informationon the timescales of the molecular motion and lead to abetter quantification of the terms ‘‘solid-like’’ and ‘‘liquid-like’’. In this regard, simple rate theory can also be usedto disentangle enthalpy and entropy contributions to themeasured free energy.41)

It is encouraging that two major experimental problems ofAFM, namely atomic resolution and faster AFM in liquid,were identified in the Japan AFM Road Map66) as criticalresearch directions. Many of the problems mentioned abovecould be addressed by high speed, molecular resolutionAFM.

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