application of atomic force spectroscopy (afs) to studies · abstract this review article describes...

J. Adhesion Sci. Technol., Vol. 19, No. 3–5, pp. 365–405 (2005) VSP 2005.Also available online - www.vsppub.com

Application of atomic force spectroscopy (AFS) to studiesof adhesion phenomena: a review

F. L. LEITE 1,2 and P. S. P. HERRMANN 1,∗1 Embrapa Agricultural Instrumentation, Rua XV de Novembro 1452, CEP 13560-970, São Carlos,

São Paulo, Brazil2 Institute of Physics of São Carlos, University of São Paulo (USP), CEP 13560-970, São Carlos,

São Paulo, Brazil

Received in final form 22 February 2005

Abstract—This review article describes the fundamental principles of atomic force spectroscopy(AFS) and how this technique became a useful tool to investigate adhesion forces. AFS is a techniquederived from atomic force microscopy (AFM) and can determine, at every location of the samplesurface, the dependence of the interaction on the probe–sample distance. AFS provides valuableinformation, at the nano-scale, such as, for example: (i) how the magnitude of the adhesion forcedepends on long- and short-range interactions and (ii) the tip–sample contact area. An overviewabout the theory and experiments with local force spectroscopy, force imaging spectroscopy, chemicalforce microscopy and colloidal probe technique is presented. The many applications of the AFStechnique for probing surface interactions open up new possibilities to evaluate adhesion, an importantcharacteristic of materials.

Keywords: Atomic force spectroscopy; adhesion phenomena; surface properties; atomic forcemicroscopy; interfacial phenomena.

1. INTRODUCTION

In 1980–1981 Binnig and co-workers at the IBM Zürich Research Laboratorydeveloped a new type of microscope which they called the scanning tunnelingmicroscope (STM) [1], being the first one in the scanning probe microscopy (SPM)family, that allowed visualization of surfaces on an atomic scale. Although the STMtechnique is limited to electrically conducting samples, it led to the development ofnumerous devices that utilize a range of physico-chemical interactions between atip and sample surface. Equally important, this family of techniques includes one

∗To whom correspondence should be addressed. Tel.: (55-16) 3374-2477. Fax: (55-16) 3372-5958.E-mail: [email protected]

366 F. L. Leite and P. S. P. Herrmann

of the most commonly used SPM systems, the atomic force microscope (AFM) [2],which can image surface topography of both insulating and conductive samples.

In general, the AFM studies can be divided into topographical applications(imaging mode) and force spectroscopy or so-called atomic force spectroscopy(AFS), i.e., measuring forces as a function of distance [3–6]. The former groupgenerates an image of the sample surface to observe its structural or dynamicfeatures and it has been employed very effectively on a wide variety of surfaces,including semiconductors [7], biological systems [8–11] and polymers [12–15],with resolution in the micrometer to subnanometer range, thus facilitating imagingat the submolecular level. The second group (AFS) is one of the most promisingand interesting research areas related to SPM [16], allowing the study of inter-and intra-molecular forces. AFS has already been successfully applied to studiesof biological systems [17–19], polymers (Refs [20–23] and data not shown) andinterfacial phenomena [3, 24–28]. The aim of this review is to provide a glimpseof the potential and limitations of the application of AFS to studies of adhesionphenomena.

2. ATOMIC FORCE MICROSCOPY

2.1. Principle of operation

This section briefly introduces the basic elements of AFM and its principle ofoperation. The microscope scans over the sample surface with a sharp probe, ortip, situated at the apex of a flexible cantilever that is often diving board-shaped orV-shaped and normally made of silicon. AFM utilizes a piezoelectric scanner thatmoves the sample with a sub-nanometer displacement when a voltage is applied.This piezoelectric system is employed to move the sample in three dimensionsrelative to the tip (Fig. 1). To form an image, the tip is brought into contact withor close to the sample and raster-scanned over the surface, causing the cantileverto deflect because of a change in surface topography or in probe–sample forces.A line-by-line image of the sample is formed as a result of this deflection, whichis detected using laser light reflected off the back surface of the cantilever onto aposition-sensitive photodiode detector [29, 30].

Forces acting between the sharp probe (tip) placed in close contact with the sampleresult in a measurable deformation of the cantilever (console) to which the probeis attached. The cantilever bends vertically upwards or downwards because of arepulsive or attractive interaction. The forces acting on the tip vary, dependingon the operating mode and the conditions used for imaging. A number of AFMimaging modes are available. The most widely used is the contact mode (C–AFM)[2, 31]; in this regime, the AFM tip is in intimate repulsive contact with a surface.Scanning can be done in two different ways: (1) in the ‘constant-force mode’ thecantilever deflection is kept constant by the extending and retracting piezoelectricscanner; in this method, a feedback loop adjusts the height of the sample (to

Studies of adhesion phenomena by AFS: a review 367

Figure 1. A schematic drawing of an atomic force microscope. A detector consisting of fourphotodiodes is shown. Scanning perpendicularly to the long cantilever axis, the (A + B) − (C + D)signal gives topographical data, while the (A + C) − (B + D) signal responds to friction due to torsionof the cantilever, providing lateral force information.

maintain constant deflection) by varying the voltage applied to the z portion ofthe xyz piezoelectric scanner. (2) In the ‘variable-deflection mode’ or ‘constantheight mode’ the piezotube extension is constant and the cantilever deflection isrecorded; in this method, the feedback loop is open, so that the cantilever undergoesa deflection proportional to the change in the tip–sample interaction.

‘Friction force microscopy (FFM)’ [32] is a variant of the contact mode, inwhich the laser beam detector is arranged so as to allow monitoring not onlyof the vertical component of the tip deflection (topography), but also the torsiondeformation exerted by the lateral forces acting on the tip end. Yuan and Lenhoff[33] demonstrated clearly the versatility of the FFM technique. The authorsmeasured surface mobility of colloidal latex particles adsorbed onto mica by movingthe particles with an AFM tip in the lateral force microscopy mode. Their datashowed that the mean lateral force was proportional to the particle diameter, whilethe effect of electrostatic interactions on the mobility of adsorbed particles wasseen to be weak. The results were consistent with classical theories of frictionin macroscopic systems. Recently Zamora et al. [34] showed that a water layer,adsorbed on the sample surface, affected both the normal force at the nanoasperitycontacts by the effect of a meniscus loading force and the friction force. Theinfluence of the water condensed at the tip–surface contact on the friction force wasstudied for hydrophilic, partially hydrophilic and hydrophobic surfaces. The resultsshowed that surface wettability affected significantly the dependence of friction onthe normal force and scan velocity.


The contact mode allows tracking of surface topography with a high precision andalso provides a high lateral resolution of 0.2–0.3 nm (down to true atomic resolutionunder appropriate conditions [35]), but imposes a high local pressure as well asshear stresses on the surface. In contact-mode imaging, the deflection of the tipis mainly caused by the repulsive forces between the overlapping electron orbitalsbetween the tip atoms and the sample atoms. The dominant attractive force is avan der Waals force arising primarily from the induced dipole interactions amongatoms of the tip and specimen [36]. When the image is obtained in air, layers ofwater are adsorbed, producing an additional strong attractive force due to the liquid–air interfacial tension. While in liquids, contributions from electrostatic Coulombinteractions between charges on the specimen and tip (either occurring naturally orinduced because of polarization), structural forces, such as hydration and solvationforces, and adhesion forces should be considered. However, in a fluid environment,the surface tension forces are abolished and van der Waals forces are typically alsoreduced due to screening of these forces by the intervening dielectric, resulting in areduced imaging force.

Another way of avoiding the problems caused by the capillary layer is to usethe longer-range attractive forces to monitor the tip–sample interaction. Theseattractive forces are weaker than the repulsive force detected in contact mode and,consequently, different techniques are required to utilize them. There are two maintypes of dynamic mode: the first is often known as the tapping or intermittentcontact mode (IC–AFM) [37–39], whilst the second is usually called the non-contact mode (NC–AFM) [40–42]; the new techniques developed for the use ofnoncontact mode are achieving high lateral resolution (atomic resolution), and areshowing new opportunities in sample analysis [43–45]. In the tapping mode, thecantilever is deliberately excited by an electrical oscillator to amplitudes of up toapproximately 100 nm, so that it effectively bounces up and down (or taps) as ittravels over the sample. The oscillation amplitude is measured as an RMS value ofthe deflection detector signal. The feedback system is set to detect the perturbationon the oscillation amplitude caused by intermittent contact with the surface [46, 47].When the tapping mode is carried out in liquids, the tip of the cantilever taps thesample gently during part of the force curve; this mode is similar to the tappingmode operating in air, except that the sample is tapped against the tip instead of thecantilever being driven at resonance to tap the sample [48].

In the NC–AFM, the oscillating cantilever never actually touches the surface ofthe sample, the spacing between the tip and the sample for NC–AFM is on the orderof tens to hundreds of Ångstroms, with an oscillation amplitude of only about 5 nm.Non-contact mode usually involves a sinusoidal excitation of the cantilever with afrequency close to its main resonant frequency. In order to excite the vibration of theprobe, in some applications, it is convenient to externally modulate the long-rangeprobe–sample interactions. Therefore, the relatively long-range attractive forcesinduce changes in the amplitude, frequency and phase of the cantilever and maintaina constant distance during scanning [49]. These changes in amplitude or in phase


can be detected and used by the feedback loop to produce topographic data. Otherforms will be to attach a bimorph piezoelectric to the cantilever, or if the sample canbe excited by a suitable piezoelectric actuator.

The force modulation mode [50, 51] is an extension of the dynamic mode thatuses very large vertical oscillations in which the AFM tip is actually pressed againstthe surface and the z feedback loop maintains a constant cantilever deflection (as forconstant-force mode AFM). The tip moves laterally, point-by-point, over the surfaceand a complete distribution of the surface elastic properties (amplitude signal)and/or energy dissipation characteristics (phase signal) is collected concurrentlywith the topographical image [52]. The amplitude damping is determined by theelastic surface deformation against a hard tip. Usually, the elastic constant of thecantilever should be large to achieve reasonable contrast in the force modulationmode. In this mode experiments are typically conducted at the resonant frequencyof the driving bimorph element (8–10 kHz) and oscillation amplitudes of 1 to5 nm [53].

Figure 2 represents the tip–sample interaction force (F (D)) with different AFMoperation modes. At short distances, the cantilever mainly senses interatomicforces: the very short range (≈0.1 nm) Born repulsive forces and the longer-range(up to 10 nm) van der Waals forces. At very small tip–sample distances, a strongrepulsive force appears between the atoms of the tip and those of the sample. Thisrepulsive force occurs between any two atoms or molecules that approach so closely

Figure 2. Empirical force vs distance curve that reflects the type of interaction between the scanningtip and sample during AFM measurements using specific imaging modes (adapted from Ref. [55]).


that their electron orbitals begin to overlap. It is thus a result of the so-called PauliExclusion Principle [54]. When this repulsive force is predominant in an AFMset-up, tip and sample are considered to be in ‘contact’ (regime of contact mode).

The total intermolecular pair potential is obtained by assuming an attractivepotential, (−C1/z

6) and a repulsive potential, (C2/z12). Superimposing the two

gives an expression for the well-known Lennard–Jones potential: U = C2/z12 −

C1/z6, where C1 and C2 are the corresponding coefficients for the attractive and

repulsive interactions, respectively, and z is the distance between the sample surfaceand rest position of the cantilever.

To describe the AFM tip and sample interactions, one needs to sum the attractiveand repulsive potential pairs over all interacting atoms. A simple summation for allthe atoms of the tip and sample is a good approximation for repulsive force (the firstterm of equation above). However, the van der Waals interaction (second term) isnon-additive, i.e., the interaction of two bodies is affected by the presence of otherbodies nearby, and a simple sum of the pair-wise interactions is usually greaterthan the actual force between the macro bodies of interest [55, 56]. To take intoaccount non-additivity of the van der Waals part of the interaction, some methodscan be used [57, 58]. Nevertheless, an additive approximation is used in manypractical applications, including atomistic simulation of AFM [59]. In particular,the van der Waals interaction between the atoms at the end of the tip and in thesurface is taken into account explicitly by summing the interactions of all pairsof atoms. However, a full tip contains billions of atoms and it is impossible tosum all the interactions; therefore, an approximation must be made based on thelocal geometry, material properties and structure of the tip [60, 61]. Hamaker [62]performed the integration of the interaction potential to calculate the total interactionbetween two macroscopic bodies using the following approximations: (1) the totalinteraction is obtained by the pair-wise summation of the individual contributions(additivity); (2) the summation can be replaced by an integration over the volumesof the interacting bodies assuming that each atom occupied a specific volume, witha density ρ (continuous medium); (3) ρ and C (interaction constant defined byLondon [63] and is specific to the identity of the interacting atoms) should beuniform over the volume of the bodies (uniform material properties).

However, for van der Waals interaction derived from second-order quantum per-turbation theory [64] is only an approximation to reality, since the internal states ofmolecules, i and j will be modified by the presence of all other molecules of thesystem, which means that the assumption of pair-wise additivity is not completelycorrect, especially in condensed phases, where the mean distance between atomsis small and many-body effects cannot be ignored. This problem can be solvedby a different approach, proposed by Lifshitz in 1956 [65]. Basically, the Lifshitzor macroscopic approach considers the interactions between electromagnetic wavesemanating from macroscopic bodies. The detailed original treatment is very com-plicated [66] and requires sophisticated mathematics, but several more accessibleaccounts have subsequently been published [67, 68]. The Lifshitz approach has


the great advantage of automatically incorporating many-body effects and of beingreadily applicable to interactions in a third medium [69–71].

2.2. Atomic force spectroscopy

Atomic force microscopy (AFM) can be used to determine the dependence of theinteraction on the probe–sample distance at every location [72]. To determine thespatial variation of the tip–sample interaction, force curves can be recorded at alarge number of sample surface locations, using the technique of atomic forcespectroscopy (AFS). With AFS it is possible to obtain the following information:(i) the magnitude of the force which depends on long-range attractive and adhesionforces, (ii) estimation of the point of tip–sample contact, (iii) the tip–sample contactarea and (iv) the elastic modulus and plasticity of thin and thick films [73, 74].

The point of contact is defined as the intersection of the contact region of theforce curve and the non-contact region of the force curve, i.e. the point of contact isthat height where the tip would have touched the sample, if there was no attractiveforce resulting in a mechanical instability so that the tip jumps to the sample [75].The contact area can be described and expressed by several continuum contactmechanics theories [74], besides modern molecular dynamics calculations that havebeen the source of many important insights into nano-scale mechanics [76]. Thechoice of the appropriate theory depends on the relative magnitudes of the materialsproperties and surface forces. Mechanical properties such as elastic modulus andhardness can be obtained from the corrected slope of the force curve after contact[77]; for more details, see Refs [78, 79]. One must choose the proper mechanicalrelationships with which to evaluate the data in order to determine the materialsproperties of the sample as well as the tip–sample contact area [80].

2.2.1. Local force spectroscopy. With commercially available cantilevers, AFMmay be used to measure forces accurately down to approx. 10 pN [81]. It is possibleto investigate the complex inter- and intra-molecular interactions, the ranges,magnitudes and time-dependence of rupture forces, the mechanical propertiesof molecules and the strength of individual bonds [82, 83]. There are severalfeatures of AFM that make it ideal for force sensing, such as the sensitivity of thedisplacement (around 0.01 nm), a small tip–sample contact area (about 10 nm2) andthe ability to operate under physiological conditions [84]. In order to evaluate howthe force mapping experiments are conducted, it is necessary to understand howsingle-point force–distance curves are obtained and what information they provideabout tip–sample interaction.

In local force spectroscopy (LFS) (Fig. 3a), the force curve is determined at aparticular location on the sample surface. At the start of the cycle, a large distanceseparates the tip and sample, there is no interaction between the tip and sampleand the cantilever remains in a non-interacting equilibrium state (point (a)). Asseparation decreases, the tip is brought into contact with the sample at a constantvelocity until it reaches a point close to the sample surface. As the sample moves


Figure 3. When performing force measurements, the AFM tip is brought into and out of contact withthe sample at a fixed point. The effect that the sample has upon the deflection of the tip is plottedagainst the displacement of the sample in the z-direction. (a) Local force spectroscopy and (b) forceimaging spectroscopy.

towards the tip various attractive forces pull on the tip (long- and short-rangeforces). Once the total force gradient acting on the tip exceeds the stiffness ofthe cantilever, the tip jumps into contact with the sample surface (jump-to-contact)((b)→(c)). At point (d), the tip and sample are in contact and deflections aredominated by mutual electronic repulsions between overlapping molecular orbitalsof the tip and sample atoms ((a)→(d)) is the approach curve. The shape of segment(c)→(d) indicates whether the sample is deforming in response to the force fromthe cantilever. The slope of the curve in contact region is a function of the elasticmodulus and geometries of the tip and sample and will only approach unity for rigidsystems [85–87]. This slope can be used to derive information about the hardnessof the sample or to indicate differing sample responses at different loadings. Thesegment (d)→(e) is showing the opposite direction of the segment (c)→(d). Thepiezoscanner is travelling in the backward direction. If both segments are straightand parallel to each other, there is no additional information content. If theyare not parallel, the hysteresis gives information on plastic deformation of thesample [88, 89].

During withdrawal curve (d)→(h), as the tip–sample surface distance decreases((e)→(f)), adhesion or bonds formed during contact with the surface cause the tipto adhere to the sample up to some distance beyond the initial contact point onthe approach curve. As the piezotube continues retracting, the spring force of the


bent cantilever overcomes the adhesion forces and the cantilever pulls off sharply,springing upwards to its undeflected or noncontact position ((f)→(g)). Finally,the tip–sample surface distance continues to decrease and the tip completely losescontact with the surface and returns to its starting equilibrium position ((g)→(h)).Figure 3b shows a force–volume data set, that contains an array of force curvesand a so-called height image. Force–volume imaging is based on collecting arraysof force curves. Individual curves are transformed into force–distance curves andall the curves are assembled into a three-dimensional force–volume [3] (for moredetails, see Section 2.2.2).

Approach and withdrawal curves can be divided roughly into three regions: thecontact line, the non-contact region and the zero line (Fig. 4). The zero line isobtained when the tip is far from the sample and the cantilever deflection is closeto zero (when working in liquid, this line gives information on the viscosity ofthe liquid [74]). When the sample is pressed against the tip, the correspondingcantilever deflection plot is called the contact line and this line can provideinformation on sample stiffness. The most interesting regions of the force curve aretwo non-contact regions, containing the jump-to-contact and the jump-off-contact.The non-contact region in the approach curve gives information about attractive(van der Waals or Coulomb force) or repulsive forces (van der Waals in someliquids, double-layer, hydration and steric force) before contact; this discontinuityoccurs when the gradient of the tip–sample force exceeds the spring constant ofthe cantilever (pull-on force). The non-contact region in the withdrawal curvecontains the jump-off-contact, a discontinuity that occurs when the cantilever’sspring constant is greater than the gradient of the tip–sample adhesion forces (pull-off force). A convenient way to measure forces with precision is to convert theminto deflections of a spring, according to Hooke’s law:

F = −kcδc, (1)

where the cantilever deflection δc is determined by the acting force F and the springconstant of the cantilever, kc.

Although the manufacturer describes spring constants for the cantilevers, theactual spring constant may deviate from this value by an order of magnitude. Itis, therefore, necessary to determine the spring constant experimentally. This mayinvolve determining: (i) the resonant frequency of the cantilever before and afteradding a small mass to the tip [90], (ii) ascertaining the unloaded resonant frequencywith knowledge of the cantilever’s density and dimensions [91], or (iii) thermalfluctuation of the cantilever [92, 93]. In equation (1), the acting force leads to atotal bending �z of the cantilever due interaction with the surface. The real probe-sample distance is then given by:

D = z − �z, (2)

where z is the distance between the sample surface and rest position of the cantileverand �z is the sum of the cantilever deflection, δc, and sample deformation,


(a)

(b)

Figure 4. (a) Force curve on sisal fibers illustrating the points where jump-to-contact (approach) andjump-off-contact (withdrawal) occur and the maximum values of the attractive force (pull-on forceand pull-off force); (b) contact mode topography image of sisal fiber.

δs [74]. Since we do not know in advance the cantilever deflection and thesample deformation, the distance that can be controlled is the displacement of thepiezotube. Therefore, the raw curve obtained by AFM should be called ‘deflection–


displacement curve’ rather than ‘force–distance curve’ [74]. This latter term shouldbe employed only for curves in which the force is plotted vs. the true tip–sampledistance (Fig. 2).

A complete force curve consists of two portions amounting to the movement of theprobe towards the sample (approach) and its retraction back to its starting position(withdrawal). Figure 4a illustrates these two portions of the force curve for the caseof measurements performed on a sisal fiber surface. The authors studied the surfacechemistry by force spectroscopy and investigated the morphological changes causedby chemical treatments of sisal fibers. By AFM, it was possible to observe that theuntreated sisal fiber (Fig. 4b) consisted of lengthwise macrofibrils oriented in thesame direction. The adhesion force between the AFM tip and the surface of thefibers was found to increase after benzylation of the fibers, indicating a rise in theirsurface energy. The distribution of the measured adhesion force over an area of1 µm2 was very nonuniform in all samples, but the low adhesion sites disappearedafter benzylation. These results illustrate how the AFM can be used to detectheterogeneity in the wettability of fibers, such as sisal, with nanometer resolutionand can be applied in the study of fiber-matrix adhesion in polymer composites.

The hysteresis apparent in Fig. 4a is due to the adhesion force between the probeand sample. For clean surfaces of probe and sample, adhesion can result from vander Waals interactions [94] or from covalent or metallic bonding between the probeand sample [95]. However, since the experiment was realized in ambient conditions,the pronounced hysteresis is due also to capillary forces [4, 96], as we will see inmore detail in Section 3.3.

2.2.2. Force imaging spectroscopy. In the mid-1990s, the idea of collectingdata from force–distance curves obtained from many points on a sample wasintroduced, effectively to produce a map of the tip–surface interactions [97, 98].Layered imaging is an SPM technique in which several measurements of cantileverdeflection are made at each image pixel. Each measurement of a deflection at agiven displacement is recorded. When all measurements for the current pixel arecompleted, the process is repeated at the next pixel and so on through the scanarea. The resulting spatial maps represent the lateral variation of adhesion forcedue to material inhomogeneities and the surface topography [22]. The resultingthree-dimensional data set can be thought of as a stack of ‘layers’ of images (seeFig. 5b). Each horizontal layer is an image which represents measurements takenthroughout the scan area at a specified height z. Since several measurements aremade at each pixel, the data set can also be processed vertically to yield the force–distance curve at each pixel. This force imaging spectroscopy (FIS) mode of AFMcan thus be used to measure adhesion [99], hardness, or deformability of samples.Many probe–sample interaction mechanisms can be studied.

For example, the spatial adhesion map for a 5×5 µm2 mica surface contaminatedby organic compounds is shown in Fig. 5a. The outward movement (withdrawal)of the cantilever (sections d–e, e–f and f–g of the force–distance curve shown in


Fig. 3a) was monitored and plotted. The pull-off force contrast in adhesion mapimages was adjusted to range between 0 nN (white pixel in the upper left cornerof each image) and 20 nN (black pixel in the upper left corner of each image).For the cleaved mica surface, a mean pull-off force of 19 nN and a variance (i.e.,squared standard deviation) of 3 nN2 were calculated from the best fit of a normaldistribution to the pull-off force histogram.

Adhesion maps can be constructed by measuring the vertical displacement ofthe sample, driven by the piezoscanner, with respect to its displacement when thecantilever is at rest position. Force curves can be digitally acquired at 100 or morepoints equally spaced from each other over the scanned area of the surface. Eachforce curve is comprised of a row of a maximum of 250 data points acquired duringthe vertical movements of approach and withdrawal of the cantilever; software isused to create the adhesion maps (Fig. 5b).

(a)

(b)

Figure 5. (a) A 5 × 5 µm map of the pull-off force recorded with a Si3N4 AFM tip on a contaminatedmica surface; (b) adhesion map plot illustrating the variability of the adhesion force on mica in air.


Tapping mode AFM (IC–AFM) has also been used to map tip–surface interactions[100, 101]. In this mode, the cantilever oscillates at its resonant frequency ata position just above the surface, so that the tip is in contact with the surfacefor only a very short time. A feedback loop ensures that the amplitude of thecantilever oscillation remains almost constant. It is possible to measure the phasedifference between the driving oscillation and the detected cantilever oscillation,generating a phase difference map. An increase in the phase difference arisesfrom a stronger tip–sample interaction, creating contrast in the phase map [102].However, there are still problems associated with many of the alternative methodsfor determining tip–sample interactions. Although, the image contrast is very muchunder discussion [103].

Another possibility is to use the so-called dynamic mode AFM operated in thefrequency modulation mode (FM–AFM). Schirmeisen et al. [104] measured metal–polymer adhesion properties by dynamic force spectroscopy with functionalisationof the tip by a thin layer of aluminum, while the polymer was plasma-etched. Theyfound that plasma etching of the polymer resulted in strongly enhanced interactions,indicating a chemical activation of the polymer surface. Sokolov et al. [105]analyzed the possibility of using noncontact atomic force microscopy to detectvariations in surface composition, i.e., to obtain a ‘spectroscopic image’ of thesample. The authors concluded that long-range forces acting between the AFM tipand the sample depended on the composition of both tip and sample. They showedtheoretically how van der Waals forces could be utilized for force spectroscopy.Various results have been achieved in detecting the van der Waals interactions byuse of molecular dynamics (MD) simulations and AFM measurements [106–108].

2.3. Chemical force microscopy

Adhesion is governed by short-range intermolecular forces which in many cases canbe controlled by appropriate surface modification. This provides a specific chemicalfunctionality on the probe surface. This technique is known as chemical forcemicroscopy (CFM) [109–113] and it can be used to evaluate the strengths of specificforces of attraction directly and adds chemical interaction to a mechanical surfaceprobe [114]. The AFM tip is first covered with an ordered monolayer of organicmolecules (a self-assembled monolayer) to give it a specific chemical functionality.The force of interaction can be estimated from the excess force required to pullthe tip free from the surface. The functionalization of the cantilever surface is amethodology that has been applied to biosensors [115].

Development of CFM has enabled investigation of the adhesion [116–118]and friction [119–121] between surfaces in close, molecular contact and themeasurement of nanometer-scale tribological phenomena [122]. Starting around1993, several papers have been published on the topic of CFM. The pull-offforce, friction force measurements [123–125] and also simulations using moleculardynamics (MD) have been used to investigate the indentation and friction propertiesof SAMs and the rupture of films bonded to solid substrates [126–128]. CFM


is a newly emerging method introduced recently for probing surface chemicalcomposition with high resolution [110, 129].

One of earliest examples used tungsten tips to perform force measurements ontwo chemical monolayers [85], demonstrating that it was possible to distinguishbetween two self-assembled monolayers (SAMs), one terminating in CH3 groupsand the other in CF3, simply by comparing the force–distance curves obtained fromeach surface. The investigation of force sensing has made rapid progress withthe incorporation of surface chemistry techniques to bind specific chemical groupsto the AFM tip [130]. An approach often employed is to produce gold-coatedtips, which are modified with SAMs of thiol compounds terminated in a chosenfunctional group (Fig. 6). There is an extensive literature on the subject whichshould be referred for more detailed information on the formation and properties ofself-assembled monolayers [131–133].

The functionalized tips can then be used in force–distance curve measurements.The general idea, in this case, is to probe the adhesion forces between the tip andthe surface, both with well-defined chemical composition. This type of chemicalfunctionalization is used in some research laboratories because of the well-definedsurface properties of monolayers studied [134–137]. The most consistent pull-off force studies involving CH3-terminated monolayers have been done in liquidenvironments [138–144].

It is important to understand and characterize the fundamental interactions be-tween different tips and sample surfaces under different environmental conditions.Eastman and Zhu [145] measured the adhesion force between modified AFM tipsand a mica substrate by atomic force spectroscopy. The results show that the ad-

Figure 6. Scheme for chemical modification of tips and sample substrates. Tips and substrates arefirst coated with a thin layer of Au (50–100 nm) and then, upon immersion in a solution of organicthiol, a dense SAM is formed on the Au surface. Similarly, cleaned Si or Si3N4 tips can be derivatizedwith reactive silanes. The functional groups comprise the outermost surface of the crystalline SAM,and the tip–sample interaction can be fine-tuned by varying the chemistry at the free SAM surfaces.The R in RSH and RSiCl3 represents an organic alkyl chain that ends with a functional group X (X =CH3, COOH, CH2OH, NH2, etc.) (reprinted with permission from Ref. [132]).


hesion force is sensitive to the surface energies of the materials coated on the tips,e.g., the adhesion force between a gold-coated tip and a mica surface is much largerthan that between a paraffin-coated tip and a mica surface. The authors also showthat both the van der Waals and capillary forces between the AFM tip and the sub-strate can account for this behavior of the adhesion forces. There have been only alimited number of attempts to correlate the measured adhesion forces and energiespredicted by interfacial energy theories [123, 146, 147]. This is due to the dif-ficulty in calculating the interfacial energy from the directly-measurable adhesionforce, mainly because of the continuing uncertainty whether the Johnson–Kendall–Roberts (JKR) [148] or the Derjaguin–Muller–Toporov (DMT) [149] theory of theadhesion contact should be applied to analyze the adhesion forces between the tipand the substrate.

Beach et al. [150] measured pull-off forces between hexadecanethiol monolayers,self-assembled on gold-coated silicon nitride cantilever tip and silicon wafer, usingAFM. The authors concluded that the AFM technique appeared to be a very usefultool in the examination of surface free energy of engineered materials. The surfaceenergy of the self-assembled monolayer of hexadecanethiol was calculated to bein the range 24.28 ± 6.61 to 26.93 ± 9.57 mJ/m2 using the measured pull-offforce values. These values are between the values reported in the literature fromcontact angle and force curve measurements. Duwez and Nysten [136] used tipsmodified with methyl- and hydroxyl-terminated alkanethiols and showed that AFMtips functionalized with alkanethiol SAMs could be utilized to map the distributionof adhesion forces on polypropylene (PP) surfaces (Fig. 7). The image in Fig. 7shows the lateral distribution of pull-off forces. The authors also found evidencefor additives migrating toward the surface and modification of additive distributionon the surface due to material aging, utilizing laterally resolved adhesion forcemaps [151].

Recently, a study of the effect of topography on chemical force microscopywas carried out using adhesion force mapping [152]. The authors determined thedistribution of adhesion forces measured in water by pulsed-force-mode atomicforce microscopy (PFM–AFM). The peaks with the higher adhesion forces wereattributed to the hydrophobic interactions between the CH3-terminated surfaces ofthe tip and the patterned sample in water. The results showed that variation in thegrain sizes and in the multiplicity of contacts between the tip and convexities ofthe grains resulted in differences in the width of the distribution of the observedadhesion forces.

2.4. AFM colloidal probe technique

A fundamental understanding of the factors controlling adhesion and the possibledevelopment of adhesion-free surfaces can potentially benefit greatly from directmeasurements of the strength of adhesion interactions. A number of studies havebeen carried out using the surface force apparatus technique (SFA) [153]. However,SFA requires molecularly smooth crossed cylindrical samples with a radius of


(a) (b)

Figure 7. Typical adhesion map obtained on a few regions of the polypropylene surface with a CH3-terminated tip in water (a); histogram of adhesion force distribution corresponding to the adhesionmap (b) (reprinted with permission from Ref. [151]; copyright 2001 American Chemical Society).

the order of 1 cm. Thus, the development of the AFM has provided anotherexperimental option for the measurement of surface forces which does not require alarge smooth cross-section. Of special note is the use of colloidal probes, formed byattaching a single particle in the size range 1–20 µm to the cantilever [154–158].Examples of the cantilever with attached particle are shown in Fig. 8.

Bowen et al. [156] used AFM to quantify the adhesion interaction between asilica sphere and a planar silica surface. The authors found that the experimentallymeasured adhesion forces depended on sample preparation and solution pH andthat the adhesion of such surfaces was a complex phenomenon in which non-DLVO(Derjaguin–Landau–Verwey–Overbeek) interactions probably played a substantialoverall role. AFM tips with a well-defined silica colloidal particle have also beenused to measure the adhesion of lactose carriers [159]. With this method, mapsof adhesion between an individual lactose particle and gelatin capsules have beenobtained [160].

Cho and Sigmund [161] suggested using a multi-walled carbon nanotube (MWNT)as a micrometer-length spacer and as a nanosized probe. This small-size probe isgenerally used for high-resolution imaging of topography of the sample. They pro-posed a systematic approach for data collection with a nanosize colloidal probe andan example of a directly measured surface force curve obtained with the MWNTprobe was presented. Finally, the use of MWNT in the conventional liquid mode


Figure 8. (a) Scanning electron micrograph of an 18 µm polyethylene (PE) particle at the endof an AFM cantilever (2000 ×). (Reprinted with permission from Ref. [165]; Copyright 2003American Chemical Society.) The particle was glued to the AFM cantilever with a small amount ofepoxy resin using a procedure described in Ref. [158]. (b) Epoxy-based modification of cantilevers.Using commercially-available AFM cantilevers with integral tips, the free terminus of cantilever wascoated with an epoxy resin. This epoxy-laden cantilever was then placed in direct contact with thesample. When the epoxy hardened, a portion of the sample was mechanically torn from the substrateto produce a cantilever-supported sample (reprinted with permission from Ref. [166]; copyrightElsevier).

of AFM opens the possibility of directly measuring the interaction force. Otherauthors have used a carbon nanotube as an STM or AFM probe [162–166].

3. APPLICATION OF ATOMIC FORCE SPECTROSCOPY TO THE STUDYOF ADHESION FORCES

3.1. Adhesion mechanics

In general, the total adhesion force (pull-off force) between an AFM tip and asample surface should include the capillary force (Fcap), as well as the solid–solidinteractions, which consist of van der Waals forces (FvdW), electrostatic forces (Fe)and the chemical bonding forces (Fchem).

If the measurement of the pull-off force is made in the presence of a ‘dry’atmosphere, like nitrogen or vacuum, the adhesion force, Fadh, is due mainlyto dispersion forces. Much of the present understanding of elastic adhesionmechanics (adhesion and deformation) of spheres on planar substrates is based onthe theoretical work of Johnson, Kendall and Roberts (JKR) [148] and of Derjaguin,Muller and Toporov (DMT) [149]. Thus, studies of adhesion require applicationof either the JKR or the DMT theory. For a dissimilar sphere/flat system, in the


Derjaguin approximation, one can write:

F DMTadh = 2πRt�ikj, (3)

where �ikj is the work of adhesion between two surfaces i and j in a medium k andRt is the tip radius.

In the JKR theory, separation will occur when the contact area between thesurfaces is aadh = 0.63a0, where a0 is the contact area at zero applied load. Thisseparation will occur when the pull-off force is:

F JKRadh = −3

2πRt�ikj. (4)

When plastic or elasto-plastic deformation occurs, both the DMT and JKRanalyses do not hold. Instead, the Maugis and Pollock (MP) analysis [167] canbe used, at least when full plasticity occurs. The MP analysis gives the pull-offforce as [168]:

F MPadh = 3π�ikjK

2(πH)3/2P 1/2, (5)

where H is the hardness of the yielding material, K is reduced Young’s modulus andP is applied load. Generally, for ideally smooth surfaces the theoretically predictedF DMT

adh and F JKRadh represent the lower and the upper limits of the experimentally

measured Fadh, respectively. Hence, one can write [169]:

Fadh = −αaRt�ikj, (6)

where αa is a constant with values between (3/2)π (for soft materials) and 2π

(for hard surfaces). The JKR model should appropriately describe the adhesion forlarge spheres with high surface energies and low Young’s moduli, while the DMTmodel should be appropriate for describing adhesion of small spheres of low surfaceenergies and high Young’s moduli.

To decide on which model to use, the parameter µ is used, as suggested by Tabor[170]:

µ = 2.92

(� 2

ikjRt

K2z30

)1/3

,

where z0 is the equilibrium size of the atoms at contact. Tabor suggested that whenµ exceeds unity, the JKR theory was applicable (µ > 1), otherwise the DMT modelshould be used (µ < 1).

Descriptions of the transition between these limits (µ ≈ 1) are provided by Mülleret al. [171], Maugis [172] and Johnson and Greenwood [173]. Contact area vs. loadcurves for each of the cases are shown in Fig. 9a [174]. The Maugis–Dugdale (M-D)theory can be expressed mainly in terms of a single non-dimensional parameter, the


(a)

(b)

Figure 9. JKR–DMT transition. (a) The relationship between contact area and load for an elasticsphere contacting a plane depends upon the range of attractive surface forces. Area–load curves forthe JKR limit (short-range adhesion), DMT limit (long–range adhesion), and an intermediate caseare shown. All of these approach the Hertz curve in limit γ → 0 (no adhesion). Load and area areplotted in nondimensional units as indicated (reprinted with permission from Ref. [174]; copyright1997 American Chemical Society). (b) Map of the elastic behavior of bodies. When the adhesion isnegligible, deformations fall in the Hertz limit (approximately F > 103π�R); when the adhesion issmall the behavior of materials is described by the DMT theory (approximately 10−2 < λ < 10−1),whilst JKR theory predicts the behavior of bodies with high adhesion (approximately λ > 101).The Maugis theory suits the intermediate region (approximately 10−1 < λ < 101) (adapted fromRef. [175]).


so-called elasticity parameter, λ, related to µ and defined by:

λ = 2.06

z0

(Rt�

2ikj

πK2

)1/3

= 1.16 µ. (7)

Using this theory, Johnson and Greenwood [173, 175] constructed an adhesionmap with co-ordinates µ and F (see Fig. 9b), where F is the reduced load and isgiven by:

F = Fadh

π�Rt. (8)

More recently, significant adhesion has been encountered in the area of nano-tribology where the contact size is measured in nanometers. Most practicalapplications fall in the JKR zone of the map, but the small radius of an AFMtip, for example, leads to operating values of the parameter λ which are in the M-D transition zone. Such values for AFM systems were encountered by Carpicket al. (λ ∼= 0.8) [176] and Lantz et al. (λ ∼= 0.2 → 0.3) [177]. Thus,by inserting appropriate estimates for �, K and Rt in (7), an appropriate choicebetween equations (3) and (4) can be made. The approximate values of the F canbe determined by an empirical equation given by Carpick et al. [178]:

F = −7

4+ 1

4

(4.04λ1.4 − 1

4.04λ1.4 + 1

), (9)

where λ → 0 (DMT) and λ → ∞ (JKR).Substituting the values of F in equation (9) into equation (8), one can obtain the

empirical values of the adhesion force. For values of λ encountered in the literature,the expression for the adhesion force is approximately:

F M-Dadh ≈ (1.9

aa←→ 1.6)πR�ikj, (10)

where the values of the work of adhesion �ikj are calculated as described inSection 3.2.

Recently, Shi and Zhao [179] made a comparative study of the three models, JKR,DMT and M-D, and the influence of the dimensionless load parameter. It was shownthat both the dimensionless load parameter, F , and the transition parameter hadsignificant influences on the contact area at the micro/nano-scale and, thus, shouldnot be ignored in the nano-indentation tests. Finally, all the theories reviewed in thissection, except the MP model, are continuum elastic theories and, hence, assumesmooth surfaces with no plastic deformation and no viscoelastic behavior [74].

3.2. Work of adhesion

The work of adhesion, �ikj, between surfaces of two equal solids (ii) can beexpressed in terms of their surface tension (surface energy), γik, when interacting


through a medium, k.

�ikj = 2γik (same surfaces, i, in a medium k).

Similarly, for two dissimilar surfaces (i and j), the work of adhesion is defined as:

�ikj = γik + γjk − γij. (11)

A commonly used approach to treating solid surface energies is to express surfacetension or surface energy (usually against air) as the sum of components due todispersion forces (γ d) and polar (e.g., hydrogen bonding) forces (γ p) [180]. Thus,the interfacial tension between two phases α and β is expressed in terms of the twocomponents for each phase (the cross-term is described by the geometric mean):

γαβ = γα + γβ − 2√

γ dα γ d

β − 2√

γpα γ

pβ . (12)

Four cases arise in describing the work of adhesion:(A): dissimilar surfaces i and j in contact with vapor (V)

�iVj = 2(√

γ di γ d

j +√

γpi γ

pj

). (13)

(B): identical surfaces i and i in contact with vapor (V)

�iVi = 2(γ d

iV + γpiV

). (14)

(C): dissimilar surfaces i and j in contact with liquid (L)

�iLj = 2

{γL −

[√γ d

i γ dL +

√γ

pi γ

pL

]−

[√γ d

j γ dL +

√γ

pj γ

pL

]

+[√

γ di γ d

j +√

γpi γ

pj

]}. (15)

(D): identical surfaces i and i in contact with liquid

�iLi = 2

{γL − 2

[√γ d

i γ dL +

√γ

pi γ

pL

]+ γ d

i + γpi

}. (16)

In an attempt to relate components more clearly to the chemical nature of thephase, van Oss et al. [181] suggested that the polar component could be betterdescribed in terms of acid–base interactions. Thus, surface energy can be expressedas γαβ = γ LW

α + γ ABβ . Unlike γ LW, the London–van der Waals component, the

acid–base component γ AB comprises two non-additive parameters. These acid–base interactions are complementary in nature and are the electron-acceptor surfacetension parameter (γ +) and the electron-donor surface tension parameter (γ −). The


total interfacial energy between two phases is [182]:

γαβ =(√

γ LWα −

√γ LW

β

)2

+ 2

(√γ +

α γ −α +

√γ +

β γ −β −

√γ +

α γ −β −

√γ −

α γ +β

). (17)

Several papers in the literature have provided different methodologies and theoriesfor estimation of surface tension components from contact angle data; this subjectstill is under debate [184–188].

3.3. Capillary force

If a liquid vapor is introduced, the surface energy of the solids is modified byadsorption. At a certain relative vapor pressure, capillary condensation will occur atthe point of contact between the tip and sample. An annulus of capillary condensatewill form around the tip and, consequently, a capillary force arises as a maincontribution in the measured pull-off force. To study how this adsorbed wateraffects the AFS experiments under ambient conditions it is necessary to understandwhy this layer is present, and on which conditions and parameters it depends. Whenworking in ambient conditions it is important to focus on the nanometer scale, wheretwo main effects have to be considered in the adsorption process: the disjoiningpressure, , experienced by thin films, and in the case of non-flat interfaces theLaplace pressure (L), which determines the curvature of the adsorbed layer. Thedisjoining pressure is the interaction force per unit area between gas and liquidinterfaces, and is induced by long-range interactions. For films of micrometerthickness, the disjoining pressure is negligible, but for thin films of thickness in therange 2–100 nm it has to be taken into account in the analysis of the free energy ofthe system. In general, several forces are responsible for the disjoining pressure. Forsome systems, the van der Waals interaction dominates and the disjoining pressurefor a film of thickness, t , can then be written as:

(t) = −Aslv

6π

1

t3. (18)

Depending on the sign of the Hamaker constant, Aslv, i.e., on the dielectricproperties of the three media (s, solid; l, liquid; v, vapor), the force responsible forthe disjoining pressure can be attractive, repulsive or a mixture of both, as shownin Fig. 10. Curve A is typical of a stable film (wetting), curve C corresponds to anunstable film (non-wetting) and curve B corresponds to a metastable film [189, 190].

Another possible origin for the disjoining pressure is the so-called repulsivedouble layer force, which can be very important in the case of charged surfacesor ionic solutions [61]. For an electrolyte solution, the disjoining pressure can bedescribed by:

(t) = Ks exp(−2χt), (19)

where χ is the Debye screening length of ions in the solution and Ks is a constantfactor related to the surface charge. In the case of pure water, the ions come mainly


from the solid surface, their concentration being very low. The DLVO theoryincludes the effects of both long-range forces, namely, the van der Waals and thedouble layer, when calculating the disjoining pressure, so that the (t) plot can takecomplicated shapes, due to superposition of the two contributions (Fig. 10). One canthen say that the disjoining pressure displaces the gas–liquid interface away from ortowards the solid–liquid interface. This implies a change in the internal energy ofthe system and, as a consequence, a change in the chemical potential of the liquid,which will change from zero to µliq = −(t). In order to keep the equilibriumbetween vapor and liquid phases, both chemical potentials must be equal. Fromthese considerations, it is possible to obtain the thickness of the film for a giventemperature and vapor density.

Considering only the van der Waals contribution to the disjoining pressure anda hydrophilic substrate, the thickness of the water film can be approximatelydescribed by:

t =(

Aslvvm

6πkT ln(nv/nsat)

)1/3

, (20)

where nv is particle number density for vapor phase (n = N/V , where N is thenumber of particles and V is the volume), nsat is a saturation density for whichliquid–vapor equilibrium is reached [190], kB is the Boltzmann constant and T isthe temperature; the value nv/nsat is the relative humidity [61].

Figure 10. Dependence of disjoining pressure on film thickness and type of force involved. Curve(A) corresponds to a repulsive force and is a wetting case. Curve (C) is an attractive force and anon-wetting situation and curve (B) corresponds to a metastable film (adapted from Ref. [189]).


As an AFM tip approaches the substrate, the capillary force on the tip is initiallynear zero until the tip contacts the surface of the water film. When contact is made,water wicks up around the tip to form a meniscus bridge between the tip and thesubstrate. The behavior of the force curve (pull-off force) depends directly on theheight of the water film adsorbed on the substrate. The minimum required thicknessof water film precursor for spreading [191, 192] is given by:

sf = am

(γsv

ς

)1/2

, (21)

where am is the molecular length given by am = A/6πγsv [193], ζ is the spreadingcoefficient given by ς = γs −γsl −γsv and γs is the solid–vacuum interfacial energy.The formation of a capillary neck requires a certain minimum height of the waterfilm. No capillary neck forms between two surfaces until the water film thicknessreaches the minimum thickness, sf.

Various techniques have been used extensively for the analysis of water filmson surfaces, such as ellipsometry [194], surface force apparatus [195] and AFM[196–199], among others. Miranda et al. [200] used a combination of vibrationalsum frequency generation and scanning polarization force microscopy [201] andconcluded that above the transition point (relative humidity where capillary conden-sation occurs) the AFM tip induces water nucleation and, therefore, formation of acapillary bridge. Forcada et al. [202] measured the thicknesses of solid-supportedthin lubricant films using AFM, and the differences observed between the thick-nesses measured with the force microscope and by ellipsometry were explained byappearance of instability in the liquid film. The theoretical description also predictsthe dependence of these differences on the thicknesses of the film.

In our group, measurements of water layer thickness have been realized on mica,quartz and silicon substrates. Figure 11a shows the thickness of the liquid filmdetermined by AFM and the influence of the type of substrate used. Figure 11bshows a force curve enlarged in the attractive region (approach curve) to identify thejump-to-contact distance (Djtc). The thickness of the liquid film is determined byDjtc values in the force curve (RH ≈ 70%), since in ‘drier’ conditions (RH ≈ 36%)this distance drops to values equivalent to DvdW

jtc , which is directly related to vander Waals forces (DvdW

jtc = 2.1 nm). The theoretical values for mica surface, usingequation (20), are 1.4 and 3.0 for dry and wet conditions, respectively, which agreewith values from force curve (Fig. 11a).

Luna et al. [203] used non-contact AFM to study water adsorption on graphite,gold and mica. Graphite surface is rather hydrophobic compared to gold andmica. They also showed that water adsorbed on graphite only under the influenceof the scanning tip at 90% RH or more, while in the case of gold and mica,water adsorbed on the surface spontaneously at low RH values (30%). However,it is evident that for many processes in air, understanding the behavior of wateron surfaces is fundamental to AFM studies. In fact, effects of water have beenobserved on adhesion by AFS [3, 204]. Ata et al. [205] studied the role of surface


(a)

(b)

Figure 11. (a) Histogram illustrating the values of jump-to-contact distance in air (RH ≈ 70%) forvarious sample surfaces (mica, quartz and silicon). (b) Typical force curve enlarged in the attractiveregion to show thickness of liquid film determined by AFS (kc ≈ 0.13 N/m) on muscovite mica. Theexperimental value of the jump-to-contact distance, Djtc, is about 3.4 nm.


Figure 12. Shape of the capillary neck formed between spherical and flat surfaces.

roughness in capillary adhesion. The force curves were measured with AFM underdifferent humidity conditions using a smooth particle and flat surfaces of alumina,silver and titanium-coated Si wafers. The authors concluded that both the relativehumidity of the surrounding atmosphere and the surface roughness profiles of thecontacting surface caused a discrepancy between the experimentally observed andthe theoretically predicted values of adhesion forces.

The tip becomes more sensitive to capillary forces in the presence of watervapor [206]. The contribution of capillary forces to the total interaction betweenan AFM tip and sample increases above a certain critical humidity [205]. Severalrecent studies have investigated the adhesion force between an AFM tip and varioussubstrates as a function of humidity [207, 208]. The results of these studies showthat the adhesion force depends strongly on whether the substrate is hydrophilic orhydrophobic. Hartholt et al. [209] reported that as the humidity increased from 45%to about 65%, the mobility of glass particles decreased. When the humidity roseabove 65%, the particles became immobile, indicating increased capillary forces.Xu et al. [210] obtained a flat response in force at relative humidities less than 20%.The reason for adhesion after reaching the critical humidity is the capillary forcedue to the liquid meniscus formed near the contact area (see Fig. 12).

When a sphere (tip) of radius Rt is in contact with a flat surface, a capillaryannulus of condensed water is formed around the contact surface. Its radius rc inthis instance is calculated geometrically, assuming Rt � rm, as follows [211]:

rc = √2Rtrm(cos θ1 + cos θ2), (22)

where θ1 and θ2 are the contact angles of water on the two materials in contact,respectively, and rm is the radius of curvature of the meniscus. Laplace pressureis generated within the water and the pressure in the capillary is lower thanatmospheric pressure by γlv/rm, where the surface tension of water is γlv. Whenthe Laplace pressure acts on the area of πr2

c , then it creates an adhesion force that


can be expressed as:

F CAd = 2πRtγlv(cos θ1 + cos θ2). (23)

For two identical materials, θ1 = θ2, thus:

F CAd = 4πRtγlv cos θ. (24)

Equation (23) is useful for estimating the capillary force of a micro-contact; notethat it is described as dependent only on the surface tension of bulk water and thecontact angle, θ , but is independent of the solid–solid and solid–liquid interactionparameters. This equation does not explain the force transition experimentallyobserved in several papers as a function of the relative humidity. Miranda et al.[200] discovered by scanning polarization microscopy that the force instability wascaused by a low coverage of water at the solid surface. The authors suggested thatwater, condensed from water vapor at room temperature on mica, forms a partiallydeveloped monolayer of an ice-like phase. They concluded that with decreasinghumidity the ice-like water monolayer, which is formed around 90% RH, breaksinto islands, until the water coverage is too low (20% RH).

Xu et al. [210] employed AFM adhesion measurements on mica surfaces as afunction of the relative humidity and noticed that there were three distinct forceregimes as illustrated in Fig. 13a (I, II and III). Other authors have confirmed thequalitative force behavior of regimes I and II with hydrophilic AFM tips on mica[208, 212]. Pull-off force measurements with hydrophilic tips and hydrophobicsubstrates (coated silicon), or hydrophobic tip and hydrophilic substrates, areindependent of RH [213, 214], as shown in Fig. 13b. However, the force instabilityoriginates from the ability or inability of the water film to form a liquid joining neckbetween the adjacent surfaces at high and low RH, respectively.

The decrease of the pull-off forces in regime III (high RH) with increasing RHfor a hydrophilic tip was discussed by Binggeli and Mate [207]. The adhesionforce on the tip is the sum of the capillary force and the interaction force betweenthe two solid surfaces mediated by the water in the gaps between the contactingasperities. For a spherically shaped tip in contact with a flat surface at high relativehumidities, the capillary force is independent of RH (equation (23)). The solid–solidinteraction is more complicated than the capillary forces. The presence of water inthe gap can greatly alter the nature of interaction [207]. The authors suggestedthat the decreasing adhesion force with rising RH was due to the interplay betweencapillary forces and the forces related to chemical bonding, Fchem, of the liquid inthe gap, given by:

Fchem = −∂G

∂z= −a

vµw, (25)

where Fchem is related to the chemical bonding and G is the Gibbs free energy, a

the area of the liquid film, v the molar volume and µw the chemical potential ofthe water molecules. Since the liquid water is at equilibrium with the water vapor,


(a)

(b)

Figure 13. Pull-off force measurements as a function of the relative humidity (RH) at roomtemperature. (a) Pull-off force between a hydrophilic Si3N4 tip and the mica surface, where opencircles are data acquired during increasing humidity and closed circles during decreasing humidity(adapted from Ref. [210]; copyright 1998 American Chemical Society); (b) Pull-off force vs. RHmeasured between a sharp AFM tip coated with octadecyltrichlorosilane (OTS) and a flat siliconsample (reprinted with permission from Ref. [213]; copyright 2001 American Institute of Physics).


the chemical potential of the water in the gaps around the contacting asperities isµw = kBT ln(nv/nsat). The chemical force is given by:

Fchem = −a

vkBT ln

(nv

nsat

). (26)

Thus, the force from water in the gap becomes less attractive, i.e., more repulsive,and tends to zero at higher RH, consistent with the reduction in adhesion forceobserved previously [215]. This result is also consistent with the results ofChristenson [216] who studied the effect of capillary condensation on adhesionforce between mica surfaces and observed that adhesion forces at high partialpressures were dominated by Laplace pressure rather than by solid–solid adhesion.

When relative humidity is less than 90%, both the water film thickness and theradius of the meniscus bridge are less than 10 nm [217], which is much smallerthan the radius of the AFM tips used in many studies using AFM. In this case, thecapillary force can be well described by [61]:

Fcap = 4πRtγlv cos θ(1 + D

d

) , (27)

or for different contact angles:

Fcap = 2πRtγlv(cos θ1 + cos θ2)(1 + D

d

) , (28)

where d is the distance the tip extends into the water bridge and can be calculatedby d = −1.08 cos θ/ ln RH [218], where RH is the relative humidity. Generally, itis assumed that D/d is small and equation (28) is reduced to equation (23).

He et al. [213] derived an equation for a nano-contact without restricting it toa large sphere radius, or Rt � rm. The authors deduced capillary force for nano-contacts from the sphere–plane approximation, with the distinction that they did notrequire a large contact area and, thus, did not restrict the capillary force equation tolarge sphere radius. The equation applicable to small contacts is given by:

Fcap = πRtγlv cos θ(1 + cos φ)2

cos φ

(1 + D

d

) , (29)

which is important for small asperity contacts, i.e., large φ values (Fig. 12); forsmall φ, equation (29) is reduced to equation (27). Note that equation (29) is basedon a much simplified cylindrically shaped geometry. Geometries for nanocontactsthat are more sophisticated can also be found in the literature [219].


3.4. Electrostatic forces

Hao et al. [220] have studied long-range Coulomb forces by modeling the tip–sample system as a sphere on a flat surface and as a sphere-ended conical tip on aflat sample. In the first case, the force is given by:

F = πε0V2

t−s

Rt

D(Rt/D � 1), (30)

F = πε0V2

t−s

(Rt

D

)2

(Rt/D � 1), (31)

where ε0 is the vacuum dielectric constant, Vt−s is the voltage difference betweenthe tip and sample and D is the tip–sample distance. In the case of a sphere-endedcone on a flat surface, the force can be calculated by replacing the equipotentialconducting surfaces with their equivalent image charges. Burnham et al. [221] havestudied another kind of Coulomb-like force which arises from regions of differentsurface charge densities interacting via a long-range force law, i.e., surface patchcharges. Surface patch charges arise due to different values of the workfunction ona material’s inequivalent surface regions [222]. Burnham et al. [73] used the methodof images to model a spherical tip and a flat sample, each with its own initial surfacecharge, and each with an image charge due to the presence of the other charged body[223]. Burnham and collaborators proposed the following model:

Felec = 1

4πε0ε3

[− Qt

4(D + B)2

(ε2 − ε3

ε2 + ε3

)

+ rcQtQs

Z(2D + B + rc)2

(ε1 − ε3

ε1 + ε3

)(ε2 − ε3

ε2 + ε3

)], (32)

in which Qt represents an image charge associated with the tip, D is the tip–sampledistance, B represents the position of Qt within the tip, Qs represents an imagecharge on the surface of the sample, rc is the effective radius of curvature of the tipand Z is the position of Qs. The relative permittivities ε1, ε2 and ε3 correspond tothe tip, sample and intervening medium, respectively.

When one studies the force between surfaces of low curvature, a parallel platemodel for the surface charge interaction is appropriate [222]. The force is thenindependent of D, so that the patch charge effect is not noticed and van der Waalsforces dominate. An AFM, with a highly curved tip, retains the sensitivity to D.Recent adaptations of the AFM [224–230] have been successfully used to studysurface-electrical variables: Kelvin force probe microscopy [224, 225] was usedto measure the workfunction and its distribution for a dielectric material over itssurface; scanning capacitance microscopy [226, 227] was used to measure dielectricproperties and impurity dopant distribution; charge detection microscopy [228] wasused to look at charge distribution and to measure amounts of charge as small astwo or three electron charges [229, 230].


When the tip and sample are exposed to air for relatively long time, no netcharges are expected to remain [231] and electrostatic force is zero; however,capillary forces are present. By controlling the cleanliness of the surfaces (UHVenvironment), the adhesion force due to van der Waals forces should become thedominant attractive force between uncharged, non-magnetic surfaces. In a solution,other forces associated with double-layer, hydration and hydrophobicity need to beconsidered too.

3.5. Other types of adhesion forces

The adhesion (pull-off force) obtained by force spectroscopy can vary with thesample and the environment in which the measurements are made. In the previoussections, only components of the adhesion force in flat and rough inorganicsurfaces under ambient conditions were considered. In this section, other possibleinteractions measured by force spectroscopy on polymer, macromolecules andbiological surfaces will be reviewed.

The first interaction considered here is “specific forces”. Specific forces arenon-covalent forces that generate very strong adhesion between specific pairs ofmolecular groups; most of the interactions between biological molecules are dueto these forces. In order to measure specific forces with AFS, it is necessaryto functionalize the tips by covering them with one of the two molecules understudy. Several researchers have used AFS to measure specific forces (biotin–biotin, biotin–streptavidin, adenine–thymine, biotin–antibiotin, antigen–antibody,etc.) [232–236].

The second interaction is called depletion force (polymer-mediated interactions)and arises when the measurements are made in solution [237, 238]. When thesurfaces are closer than the root-mean-square radius of a polymer coil Rg(Rg =l√

nm/√

6), where nm is the number of monomers and l is the length of amonomer [239], the coil is pushed out of the gap, resulting in a reduced polymerconcentration between the surfaces, giving rise to the depletion forces. Fleer et al.[240] have deduced the depletion force to be of the form:

Fdep = πµ

vm(D + 2Rt)(D − 2TL), (33)

in which D is the distance between the surfaces, µ is the chemical potential of thesolvent, vm is the solvent molecular volume and TL is the thickness of polymer layer.

The net interaction between two polymer-covered surfaces also depends on thepolymer–surface interactions and on the availability of free binding sites on theopposite surface [74]. If there are free binding sites on the opposite surface, somepolymer coils will form bridges between the two surfaces and give rise to a thirdinteraction called bridging force [241–244]. Any polymer that naturally adsorbsonto a surface from solution has the potential to form bridges between two suchsurfaces; however, if the coverage is too high, as in the case of a brush, there will be


only a few free binding sites for bridges to form, whereas if it is too low the densityof bridges will also be low [61].

In this section the forces involving biological systems and polymeric films werebriefly reviewed, but other reviews can be consulted for a more complete account[245, 246].

3.6. Total pull-off force

The total pull-off force measured by force spectroscopy or adhesion force betweenthe AFM tip and flat inorganic surfaces is then given by the sum of equations (6),(26), (29) and (32):

F airpull = Fcap + FvdW + Fchem + Felec, (34)

or in the absence of electrostatic charges:

F airpull =

πRγ cos θ

(1 + cos φ)2

cos φ

(1 + D

d

)

cap

+ [αR�ikj]vdW +[−a

vkT ln

(p

ps

)]chem

,

(35)assuming two identical surfaces (θ1 = θ2 = θ ).

An alternative expression was proposed by Sendin and Rowlen [247], whomeasured adhesion forces with AFM under ambient conditions. The authors studiedthe nature of the pull-off force on a variety of surfaces as a function of relativehumidity. A mathematical model of pull-off force as a function of relative humiditywas proposed in which the chemical specificity was explained. The proposed formof the relationship between measured pull-off force and relative humidity is

F airpull = Fstv + Fstw + Fcap

1 + e−[((p/ps)−(p′/p′s))/m] , (36)

where Fstv is the surface–tip adhesion force in the presence of water vapor, Fstw isthe surface–tip adhesion force in the presence of liquid water, Fcap is the adhesionforce due to capillary condensation, p′/p′

s is the relative humidity at the transitionpoint between the two regimes and m is the slope of the transition. The capillaryforce may be calculated as the sum of force due to surface tension (Ft) and the forcedue to a pressure difference across a sphere’s surface (Fp) [248].

The equations cited previously do not describe the effect of surface topography onthe adhesion force, although adhesion force is greatly affected by small roughnessof the solid surfaces in contact [3, 211, 249]. Microparticle adhesion studies byAFM have shown the effect of roughness on adhesion. Segeren et al. [250]studied this phenomenon and showed that the interactions between smooth silicaparticles, or rough toner particles, and silicon substrates were influenced by thetrue area of contact, which reflects both the roughness of the probe and that of the


substrate. Rabinovich et al. [251] proposed an expression that takes into accountthis dependence (equation (37)):

Fpull = 3π�Rtr2

2(r2 + Rt)+ (ARt/6H 2

0 )(1 + 58RMS1

λ21

)(1 + 1.82RMS2

H0

)2 , (37)

that Rabinovich et al. [251] used to describe a rough surface with two asperities,one with a short-range roughness λ2 and a small asperity radius r2 superimposedover another surface with a long-range roughness λ1 and a large asperity radius r1.A and H0 are the Hamaker constant and the distance of closest approach betweenthe two surfaces, respectively. The authors model roughness as a distribution ofclosely packed hemispheres with equal radius r = λ2/58RMS. RMS and λ are theroot-mean-square roughness and the mean peak-to-peak distance, respectively (seemore details in Ref. [252]).

Several other studies have attempted to incorporate roughness into adhesiontheories [252–257]. Studies of adhesion force have been carried out on liquidsystems where the interactions involved are affected and modified by the type ofsolution used and interactions forces [258, 259]. Jacquot and Takadoum [258]studied interactions between various materials in four different liquid media (water,ethanol, ethylene glycol and formamide) and concluded that the calculated adhesionforce closely correlated with AFM measurements, except in water. This differenceobserved for water was discussed in terms of chemical interactions between theSi3N4 tip and water. Hoh et al. [260] studied the adhesion interaction between asilicon nitride AFM tip and glass substrate in water. The adhesion measured was inthe range 5–40 nN, of which a large component was likely to be due to hydrogenbonding between the silanol groups on both surfaces. The results demonstrate thatthe chemical interactions between the tip and sample can be modulated and providea basis for designing conditions for imaging and manipulating biological moleculesand structures.

When pull-off force measurements on inorganic surfaces are performed in solu-tion, other interactions arise, such as solvation, hydration and hydrophobic forces.The adhesion force studies in solution are still much debated and more complexthan measurements of the pull-off force in air, since additional forces arise whenan AFM tip is immersed in solution. Repulsive forces may arise from solvation orhydration forces since the water near hydrophilic surfaces is structured. In aqueoussolutions, electrical double-layer forces also arise, which may be either attractive orrepulsive, and may be present between the surface of the tip and sample [261, 262].

4. CONCLUDING REMARKS

The potential of atomic force spectroscopy (AFS) as a tool to evaluate adhesionphenomenon was presented. The measurements of surface–surface interactions


at the nano-scale are considered vital, because in this range new properties ofthe materials can be evaluated. The future of the AFS technique is relatedbasically to the investigation of basic concepts coupled with theoretical models andexperimental results, and applications to solve practical problems as, for example,in nanotribology, nanobiotechnolgy and physical chemistry of surfaces. Theprogress is expected to occur in the research on nanosensors, using chemical forcemicroscopy as electronic nose and electronic tongue; the investigation of lubricatingfilms, and contamination using colloidal particle attached to the cantilevers, with theknown geometry, atomic structure, and chemical composition; the investigationsof adhesion force to characterize dynamics of aggregates in soil particles, as wellas elucidating the effects of sorption mechanisms (interfacial phenomena betweenpesticides, organic matter, mineral particles).

The discussions presented in this review article demonstrate the range and thecomplexity of the subject and they bring out the importance for investigations inthe field of nanoscience and nanotechnology, due to the challenges as well as thewealth of information which can be derived from the experiments, as well as fromtheoretical models.

Acknowledgements

The authors are grateful to Embrapa for the facilities support, and the nanobiotech-nology network (CNPq/MCT) for the financial support. F. L. L. acknowledgesa grant from the National Council for Scientific and Technological Development(CNPq-CT-Hidro), a foundation linked to the Ministry of Science and Technology(MCT-BRAZIL).

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