Application of atomic force spectroscopy (afs) to studies of adhesion phenomena

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 studies
of 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, Brazil
2 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 technique
derived from atomic force microscopy (AFM) and can determine, at every location of the sample
surface, the dependence of the interaction on the probe–sample distance. AFS provides valuable
information, at the nano-scale, such as, for example: (i) how the magnitude of the adhesion force
depends on long- and short-range interactions and (ii) the tip–sample contact area. An overview
about the theory and experiments with local force spectroscopy, force imaging spectroscopy, chemical
force microscopy and colloidal probe technique is presented. The many applications of the AFS
technique for probing surface interactions open up new possibilities to evaluate adhesion, an important
characteristic of materials.
Keywords: Atomic force spectroscopy; adhesion phenomena; surface properties; atomic force
microscopy; interfacial phenomena.
1. INTRODUCTION
In 1980–1981 Binnig and co-workers at the IBM Zürich Research Laboratory
developed a new type of microscope which they called the scanning tunneling
microscope (STM) [1], being the ﬁrst one in the scanning probe microscopy (SPM)
family, that allowed visualization of surfaces on an atomic scale. Although the STM
technique is limited to electrically conducting samples, it led to the development of
numerous devices that utilize a range of physico-chemical interactions between a
tip 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: herrmann@cnpdia.embrapa.br

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 group
generates an image of the sample surface to observe its structural or dynamic
features 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 imaging
at the submolecular level. The second group (AFS) is one of the most promising
and interesting research areas related to SPM [16], allowing the study of inter-
and intra-molecular forces. AFS has already been successfully applied to studies
of biological systems [17–19], polymers (Refs [20–23] and data not shown) and
interfacial phenomena [3, 24–28]. The aim of this review is to provide a glimpse
of the potential and limitations of the application of AFS to studies of adhesion
phenomena.
2. ATOMIC FORCE MICROSCOPY
2.1. Principle of operation
This section briefly introduces the basic elements of AFM and its principle of
operation. The microscope scans over the sample surface with a sharp probe, or
tip, situated at the apex of a flexible cantilever that is often diving board-shaped or
V-shaped and normally made of silicon. AFM utilizes a piezoelectric scanner that
moves the sample with a sub-nanometer displacement when a voltage is applied.
This piezoelectric system is employed to move the sample in three dimensions
relative to the tip (Fig. 1). To form an image, the tip is brought into contact with
or close to the sample and raster-scanned over the surface, causing the cantilever
to 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, which
is detected using laser light reflected off the back surface of the cantilever onto a
position-sensitive photodiode detector [29, 30].
Forces acting between the sharp probe (tip) placed in close contact with the sample
result in a measurable deformation of the cantilever (console) to which the probe
is attached. The cantilever bends vertically upwards or downwards because of a
repulsive or attractive interaction. The forces acting on the tip vary, depending
on the operating mode and the conditions used for imaging. A number of AFM
imaging 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’ the
cantilever deflection is kept constant by the extending and retracting piezoelectric
scanner; 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 four
photodiodes 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 torsion
of the cantilever, providing lateral force information.
maintain constant deflection) by varying the voltage applied to the z portion of
the xyz piezoelectric scanner. (2) In the ‘variable-deflection mode’ or ‘constant
height mode’ the piezotube extension is constant and the cantilever deflection is
recorded; in this method, the feedback loop is open, so that the cantilever undergoes
a deflection proportional to the change in the tip–sample interaction.
‘Friction force microscopy (FFM)’ [32] is a variant of the contact mode, in
which the laser beam detector is arranged so as to allow monitoring not only
of the vertical component of the tip deflection (topography), but also the torsion
deformation exerted by the lateral forces acting on the tip end. Yuan and Lenhoff
[33] demonstrated clearly the versatility of the FFM technique. The authors
measured surface mobility of colloidal latex particles adsorbed onto mica by moving
the particles with an AFM tip in the lateral force microscopy mode. Their data
showed that the mean lateral force was proportional to the particle diameter, while
the effect of electrostatic interactions on the mobility of adsorbed particles was
seen to be weak. The results were consistent with classical theories of friction
in macroscopic systems. Recently Zamora et al. [34] showed that a water layer,
adsorbed on the sample surface, affected both the normal force at the nanoasperity
contacts by the effect of a meniscus loading force and the friction force. The
influence of the water condensed at the tip–surface contact on the friction force was
studied for hydrophilic, partially hydrophilic and hydrophobic surfaces. The results
showed that surface wettability affected significantly the dependence of friction on
the normal force and scan velocity.

The contact mode allows tracking of surface topography with a high precision and
also provides a high lateral resolution of 0.2–0.3 nm (down to true atomic resolution
under appropriate conditions [35]), but imposes a high local pressure as well as
shear stresses on the surface. In contact-mode imaging, the deflection of the tip
is mainly caused by the repulsive forces between the overlapping electron orbitals
between the tip atoms and the sample atoms. The dominant attractive force is a
van der Waals force arising primarily from the induced dipole interactions among
atoms of the tip and specimen [36]. When the image is obtained in air, layers of
water are adsorbed, producing an additional strong attractive force due to the liquid–
air interfacial tension. While in liquids, contributions from electrostatic Coulomb
interactions between charges on the specimen and tip (either occurring naturally or
induced because of polarization), structural forces, such as hydration and solvation
forces, and adhesion forces should be considered. However, in a fluid environment,
the surface tension forces are abolished and van der Waals forces are typically also
reduced due to screening of these forces by the intervening dielectric, resulting in a
reduced imaging force.
Another way of avoiding the problems caused by the capillary layer is to use
the longer-range attractive forces to monitor the tip–sample interaction. These
attractive forces are weaker than the repulsive force detected in contact mode and,
consequently, different techniques are required to utilize them. There are two main
types of dynamic mode: the first is often known as the tapping or intermittent
contact 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 of
noncontact mode are achieving high lateral resolution (atomic resolution), and are
showing new opportunities in sample analysis [43–45]. In the tapping mode, the
cantilever is deliberately excited by an electrical oscillator to amplitudes of up to
approximately 100 nm, so that it effectively bounces up and down (or taps) as it
travels over the sample. The oscillation amplitude is measured as an RMS value of
the deflection detector signal. The feedback system is set to detect the perturbation
on 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 the
sample gently during part of the force curve; this mode is similar to the tapping
mode operating in air, except that the sample is tapped against the tip instead of the
cantilever being driven at resonance to tap the sample [48].
In the NC–AFM, the oscillating cantilever never actually touches the surface of
the sample, the spacing between the tip and the sample for NC–AFM is on the order
of 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 a
frequency close to its main resonant frequency. In order to excite the vibration of the
probe, in some applications, it is convenient to externally modulate the long-range
probe–sample interactions. Therefore, the relatively long-range attractive forces
induce changes in the amplitude, frequency and phase of the cantilever and maintain
a 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. Other
forms will be to attach a bimorph piezoelectric to the cantilever, or if the sample can
be excited by a suitable piezoelectric actuator.
The force modulation mode [50, 51] is an extension of the dynamic mode that
uses very large vertical oscillations in which the AFM tip is actually pressed against
the surface and the z feedback loop maintains a constant cantilever deflection (as for
constant-force mode AFM). The tip moves laterally, point-by-point, over the surface
and a complete distribution of the surface elastic properties (amplitude signal)
and/or energy dissipation characteristics (phase signal) is collected concurrently
with the topographical image [52]. The amplitude damping is determined by the
elastic surface deformation against a hard tip. Usually, the elastic constant of the
cantilever should be large to achieve reasonable contrast in the force modulation
mode. In this mode experiments are typically conducted at the resonant frequency
of the driving bimorph element (8–10 kHz) and oscillation amplitudes of 1 to
5 nm [53].
Figure 2 represents the tip–sample interaction force (F(D)) with different AFM
operation modes. At short distances, the cantilever mainly senses interatomic
forces: 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 strong
repulsive force appears between the atoms of the tip and those of the sample. This
repulsive 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 scanning
tip 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 Pauli
Exclusion Principle [54]. When this repulsive force is predominant in an AFM
set-up, tip and sample are considered to be in ‘contact’ (regime of contact mode).
The total intermolecular pair potential is obtained by assuming an attractive
potential, (−C1/z6
) 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 surface
and rest position of the cantilever.
To describe the AFM tip and sample interactions, one needs to sum the attractive
and repulsive potential pairs over all interacting atoms. A simple summation for all
the atoms of the tip and sample is a good approximation for repulsive force (the first
term of equation above). However, the van der Waals interaction (second term) is
non-additive, i.e., the interaction of two bodies is affected by the presence of other
bodies nearby, and a simple sum of the pair-wise interactions is usually greater
than the actual force between the macro bodies of interest [55, 56]. To take into
account non-additivity of the van der Waals part of the interaction, some methods
can be used [57, 58]. Nevertheless, an additive approximation is used in many
practical 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 the
surface is taken into account explicitly by summing the interactions of all pairs
of atoms. However, a full tip contains billions of atoms and it is impossible to
sum all the interactions; therefore, an approximation must be made based on the
local geometry, material properties and structure of the tip [60, 61]. Hamaker [62]
performed the integration of the interaction potential to calculate the total interaction
between two macroscopic bodies using the following approximations: (1) the total
interaction is obtained by the pair-wise summation of the individual contributions
(additivity); (2) the summation can be replaced by an integration over the volumes
of the interacting bodies assuming that each atom occupied a specific volume, with
a density ρ (continuous medium); (3) ρ and C (interaction constant defined by
London [63] and is specific to the identity of the interacting atoms) should be
uniform 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 of
molecules, i and j will be modified by the presence of all other molecules of the
system, which means that the assumption of pair-wise additivity is not completely
correct, especially in condensed phases, where the mean distance between atoms
is small and many-body effects cannot be ignored. This problem can be solved
by a different approach, proposed by Lifshitz in 1956 [65]. Basically, the Lifshitz
or macroscopic approach considers the interactions between electromagnetic waves
emanating from macroscopic bodies. The detailed original treatment is very com-
plicated [66] and requires sophisticated mathematics, but several more accessible
accounts have subsequently been published [67, 68]. The Lifshitz approach has

the great advantage of automatically incorporating many-body effects and of being
readily 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 the
interaction on the probe–sample distance at every location [72]. To determine the
spatial variation of the tip–sample interaction, force curves can be recorded at a
large number of sample surface locations, using the technique of atomic force
spectroscopy (AFS). With AFS it is possible to obtain the following information:
(i) the magnitude of the force which depends on long-range attractive and adhesion
forces, (ii) estimation of the point of tip–sample contact, (iii) the tip–sample contact
area 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 the
force curve and the non-contact region of the force curve, i.e. the point of contact is
that height where the tip would have touched the sample, if there was no attractive
force 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 contact
mechanics theories [74], besides modern molecular dynamics calculations that have
been the source of many important insights into nano-scale mechanics [76]. The
choice of the appropriate theory depends on the relative magnitudes of the materials
properties and surface forces. Mechanical properties such as elastic modulus and
hardness 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 mechanical
relationships with which to evaluate the data in order to determine the materials
properties of the sample as well as the tip–sample contact area [80].
2.2.1. Local force spectroscopy. With commercially available cantilevers, AFM
may be used to measure forces accurately down to approx. 10 pN [81]. It is possible
to investigate the complex inter- and intra-molecular interactions, the ranges,
magnitudes and time-dependence of rupture forces, the mechanical properties
of molecules and the strength of individual bonds [82, 83]. There are several
features of AFM that make it ideal for force sensing, such as the sensitivity of the
displacement (around 0.01 nm), a small tip–sample contact area (about 10 nm2
) and
the ability to operate under physiological conditions [84]. In order to evaluate how
the force mapping experiments are conducted, it is necessary to understand how
single-point force–distance curves are obtained and what information they provide
about tip–sample interaction.
In local force spectroscopy (LFS) (Fig. 3a), the force curve is determined at a
particular location on the sample surface. At the start of the cycle, a large distance
separates the tip and sample, there is no interaction between the tip and sample
and the cantilever remains in a non-interacting equilibrium state (point (a)). As
separation decreases, the tip is brought into contact with the sample at a constant
velocity 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 with
the sample at a fixed point. The effect that the sample has upon the deflection of the tip is plotted
against the displacement of the sample in the z-direction. (a) Local force spectroscopy and (b) force
imaging spectroscopy.
towards the tip various attractive forces pull on the tip (long- and short-range
forces). Once the total force gradient acting on the tip exceeds the stiffness of
the 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 are
dominated by mutual electronic repulsions between overlapping molecular orbitals
of 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 from
the cantilever. The slope of the curve in contact region is a function of the elastic
modulus and geometries of the tip and sample and will only approach unity for rigid
systems [85–87]. This slope can be used to derive information about the hardness
of the sample or to indicate differing sample responses at different loadings. The
segment (d)→(e) is showing the opposite direction of the segment (c)→(d). The
piezoscanner is travelling in the backward direction. If both segments are straight
and parallel to each other, there is no additional information content. If they
are not parallel, the hysteresis gives information on plastic deformation of the
sample [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 tip
to adhere to the sample up to some distance beyond the initial contact point on
the 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 loses
contact 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 curves
and a so-called height image. Force–volume imaging is based on collecting arrays
of force curves. Individual curves are transformed into force–distance curves and
all the curves are assembled into a three-dimensional force–volume [3] (for more
details, see Section 2.2.2).
Approach and withdrawal curves can be divided roughly into three regions: the
contact line, the non-contact region and the zero line (Fig. 4). The zero line is
obtained when the tip is far from the sample and the cantilever deflection is close
to zero (when working in liquid, this line gives information on the viscosity of
the liquid [74]). When the sample is pressed against the tip, the corresponding
cantilever deflection plot is called the contact line and this line can provide
information on sample stiffness. The most interesting regions of the force curve are
two 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 some
liquids, double-layer, hydration and steric force) before contact; this discontinuity
occurs when the gradient of the tip–sample force exceeds the spring constant of
the cantilever (pull-on force). The non-contact region in the withdrawal curve
contains the jump-off-contact, a discontinuity that occurs when the cantilever’s
spring 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 them
into 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 spring
constant of the cantilever, kc.
Although the manufacturer describes spring constants for the cantilevers, the
actual spring constant may deviate from this value by an order of magnitude. It
is, therefore, necessary to determine the spring constant experimentally. This may
involve determining: (i) the resonant frequency of the cantilever before and after
adding a small mass to the tip [90], (ii) ascertaining the unloaded resonant frequency
with knowledge of the cantilever’s density and dimensions [91], or (iii) thermal
fluctuation of the cantilever [92, 93]. In equation (1), the acting force leads to a
total 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 cantilever
and 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) and
jump-off-contact (withdrawal) occur and the maximum values of the attractive force (pull-on force
and pull-off force); (b) contact mode topography image of sisal fiber.
δs [74]. Since we do not know in advance the cantilever deflection and the
sample deformation, the distance that can be controlled is the displacement of the
piezotube. Therefore, the raw curve obtained by AFM should be called ‘deflection–

displacement curve’ rather than ‘force–distance curve’ [74]. This latter term should
be employed only for curves in which the force is plotted vs. the true tip–sample
distance (Fig. 2).
A complete force curve consists of two portions amounting to the movement of the
probe 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 case
of measurements performed on a sisal fiber surface. The authors studied the surface
chemistry by force spectroscopy and investigated the morphological changes caused
by chemical treatments of sisal fibers. By AFM, it was possible to observe that the
untreated sisal fiber (Fig. 4b) consisted of lengthwise macrofibrils oriented in the
same direction. The adhesion force between the AFM tip and the surface of the
fibers was found to increase after benzylation of the fibers, indicating a rise in their
surface energy. The distribution of the measured adhesion force over an area of
1 µm2
was very nonuniform in all samples, but the low adhesion sites disappeared
after benzylation. These results illustrate how the AFM can be used to detect
heterogeneity in the wettability of fibers, such as sisal, with nanometer resolution
and 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 probe
and sample. For clean surfaces of probe and sample, adhesion can result from van
der Waals interactions [94] or from covalent or metallic bonding between the probe
and 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 in
more detail in Section 3.3.
2.2.2. Force imaging spectroscopy. In the mid-1990s, the idea of collecting
data from force–distance curves obtained from many points on a sample was
introduced, effectively to produce a map of the tip–surface interactions [97, 98].
Layered imaging is an SPM technique in which several measurements of cantilever
deflection are made at each image pixel. Each measurement of a deflection at a
given displacement is recorded. When all measurements for the current pixel are
completed, the process is repeated at the next pixel and so on through the scan
area. The resulting spatial maps represent the lateral variation of adhesion force
due to material inhomogeneities and the surface topography [22]. The resulting
three-dimensional data set can be thought of as a stack of ‘layers’ of images (see
Fig. 5b). Each horizontal layer is an image which represents measurements taken
throughout the scan area at a specified height z. Since several measurements are
made 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 AFM
can 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 contaminated
by 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 map
images was adjusted to range between 0 nN (white pixel in the upper left corner
of 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 normal
distribution to the pull-off force histogram.
Adhesion maps can be constructed by measuring the vertical displacement of
the sample, driven by the piezoscanner, with respect to its displacement when the
cantilever is at rest position. Force curves can be digitally acquired at 100 or more
points equally spaced from each other over the scanned area of the surface. Each
force curve is comprised of a row of a maximum of 250 data points acquired during
the vertical movements of approach and withdrawal of the cantilever; software is
used 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 contaminated
mica 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 at
a position just above the surface, so that the tip is in contact with the surface
for only a very short time. A feedback loop ensures that the amplitude of the
cantilever oscillation remains almost constant. It is possible to measure the phase
difference between the driving oscillation and the detected cantilever oscillation,
generating a phase difference map. An increase in the phase difference arises
from a stronger tip–sample interaction, creating contrast in the phase map [102].
However, there are still problems associated with many of the alternative methods
for determining tip–sample interactions. Although, the image contrast is very much
under discussion [103].
Another possibility is to use the so-called dynamic mode AFM operated in the
frequency modulation mode (FM–AFM). Schirmeisen et al. [104] measured metal–
polymer adhesion properties by dynamic force spectroscopy with functionalisation
of the tip by a thin layer of aluminum, while the polymer was plasma-etched. They
found 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 detect
variations in surface composition, i.e., to obtain a ‘spectroscopic image’ of the
sample. The authors concluded that long-range forces acting between the AFM tip
and the sample depended on the composition of both tip and sample. They showed
theoretically how van der Waals forces could be utilized for force spectroscopy.
Various results have been achieved in detecting the van der Waals interactions by
use 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 can
be controlled by appropriate surface modification. This provides a specific chemical
functionality on the probe surface. This technique is known as chemical force
microscopy (CFM) [109–113] and it can be used to evaluate the strengths of specific
forces of attraction directly and adds chemical interaction to a mechanical surface
probe [114]. The AFM tip is first covered with an ordered monolayer of organic
molecules (a self-assembled monolayer) to give it a specific chemical functionality.
The force of interaction can be estimated from the excess force required to pull
the tip free from the surface. The functionalization of the cantilever surface is a
methodology 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 the
measurement of nanometer-scale tribological phenomena [122]. Starting around
1993, several papers have been published on the topic of CFM. The pull-off
force, friction force measurements [123–125] and also simulations using molecular
dynamics (MD) have been used to investigate the indentation and friction properties
of SAMs and the rupture of films bonded to solid substrates [126–128]. CFM

is a newly emerging method introduced recently for probing surface chemical
composition with high resolution [110, 129].
One of earliest examples used tungsten tips to perform force measurements on
two chemical monolayers [85], demonstrating that it was possible to distinguish
between two self-assembled monolayers (SAMs), one terminating in CH3 groups
and the other in CF3, simply by comparing the force–distance curves obtained from
each surface. The investigation of force sensing has made rapid progress with
the incorporation of surface chemistry techniques to bind specific chemical groups
to the AFM tip [130]. An approach often employed is to produce gold-coated
tips, which are modified with SAMs of thiol compounds terminated in a chosen
functional group (Fig. 6). There is an extensive literature on the subject which
should be referred for more detailed information on the formation and properties of
self-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 and
the surface, both with well-defined chemical composition. This type of chemical
functionalization is used in some research laboratories because of the well-defined
surface properties of monolayers studied [134–137]. The most consistent pull-
off force studies involving CH3-terminated monolayers have been done in liquid
environments [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 tips
and 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 are
first coated with a thin layer of Au (50–100 nm) and then, upon immersion in a solution of organic
thiol, a dense SAM is formed on the Au surface. Similarly, cleaned Si or Si3N4 tips can be derivatized
with 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 larger
than that between a paraffin-coated tip and a mica surface. The authors also show
that 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 a
limited number of attempts to correlate the measured adhesion forces and energies
predicted by interfacial energy theories [123, 146, 147]. This is due to the dif-
ficulty in calculating the interfacial energy from the directly-measurable adhesion
force, mainly because of the continuing uncertainty whether the Johnson–Kendall–
Roberts (JKR) [148] or the Derjaguin–Muller–Toporov (DMT) [149] theory of the
adhesion contact should be applied to analyze the adhesion forces between the tip
and 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, using
AFM. The authors concluded that the AFM technique appeared to be a very useful
tool in the examination of surface free energy of engineered materials. The surface
energy of the self-assembled monolayer of hexadecanethiol was calculated to be
in the range 24.28 ± 6.61 to 26.93 ± 9.57 mJ/m2
using the measured pull-off
force values. These values are between the values reported in the literature from
contact angle and force curve measurements. Duwez and Nysten [136] used tips
modified with methyl- and hydroxyl-terminated alkanethiols and showed that AFM
tips functionalized with alkanethiol SAMs could be utilized to map the distribution
of adhesion forces on polypropylene (PP) surfaces (Fig. 7). The image in Fig. 7
shows the lateral distribution of pull-off forces. The authors also found evidence
for additives migrating toward the surface and modification of additive distribution
on the surface due to material aging, utilizing laterally resolved adhesion force
maps [151].
Recently, a study of the effect of topography on chemical force microscopy
was carried out using adhesion force mapping [152]. The authors determined the
distribution of adhesion forces measured in water by pulsed-force-mode atomic
force microscopy (PFM–AFM). The peaks with the higher adhesion forces were
attributed to the hydrophobic interactions between the CH3-terminated surfaces of
the tip and the patterned sample in water. The results showed that variation in the
grain sizes and in the multiplicity of contacts between the tip and convexities of
the grains resulted in differences in the width of the distribution of the observed
adhesion forces.
2.4. AFM colloidal probe technique
A fundamental understanding of the factors controlling adhesion and the possible
development of adhesion-free surfaces can potentially benefit greatly from direct
measurements of the strength of adhesion interactions. A number of studies have
been 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 adhesion
map (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 another
experimental option for the measurement of surface forces which does not require a
large smooth cross-section. Of special note is the use of colloidal probes, formed by
attaching 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 a
silica sphere and a planar silica surface. The authors found that the experimentally
measured adhesion forces depended on sample preparation and solution pH and
that the adhesion of such surfaces was a complex phenomenon in which non-DLVO
(Derjaguin–Landau–Verwey–Overbeek) interactions probably played a substantial
overall role. AFM tips with a well-deﬁned silica colloidal particle have also been
used to measure the adhesion of lactose carriers [159]. With this method, maps
of adhesion between an individual lactose particle and gelatin capsules have been
obtained [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 is
generally used for high-resolution imaging of topography of the sample. They pro-
posed a systematic approach for data collection with a nanosize colloidal probe and
an example of a directly measured surface force curve obtained with the MWNT
probe 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 end
of an AFM cantilever (2000 ×). (Reprinted with permission from Ref. [165]; Copyright 2003
American Chemical Society.) The particle was glued to the AFM cantilever with a small amount of
epoxy 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 was
coated with an epoxy resin. This epoxy-laden cantilever was then placed in direct contact with the
sample. When the epoxy hardened, a portion of the sample was mechanically torn from the substrate
to produce a cantilever-supported sample (reprinted with permission from Ref. [166]; copyright
Elsevier).
of AFM opens the possibility of directly measuring the interaction force. Other
authors have used a carbon nanotube as an STM or AFM probe [162–166].
3. APPLICATION OF ATOMIC FORCE SPECTROSCOPY TO THE STUDY
OF ADHESION FORCES
3.1. Adhesion mechanics
In general, the total adhesion force (pull-off force) between an AFM tip and a
sample surface should include the capillary force (Fcap), as well as the solid–solid
interactions, 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 mainly
to dispersion forces. Much of the present understanding of elastic adhesion
mechanics (adhesion and deformation) of spheres on planar substrates is based on
the theoretical work of Johnson, Kendall and Roberts (JKR) [148] and of Derjaguin,
Muller and Toporov (DMT) [149]. Thus, studies of adhesion require application
of either the JKR or the DMT theory. For a dissimilar sphere/ﬂat system, in the

Derjaguin approximation, one can write:
FDMT
adh = 2πRt ikj, (3)
where ikj is the work of adhesion between two surfaces i and j in a medium k and
Rt is the tip radius.
In the JKR theory, separation will occur when the contact area between the
surfaces is aadh = 0.63a0, where a0 is the contact area at zero applied load. This
separation will occur when the pull-off force is:
FJKR
adh = −
3
2
πRt ikj. (4)
When plastic or elasto-plastic deformation occurs, both the DMT and JKR
analyses do not hold. Instead, the Maugis and Pollock (MP) analysis [167] can
be used, at least when full plasticity occurs. The MP analysis gives the pull-off
force as [168]:
FMP
adh =
3π ikjK
2(πH)3/2
P1/2
, (5)
where H is the hardness of the yielding material, K is reduced Young’s modulus and
P is applied load. Generally, for ideally smooth surfaces the theoretically predicted
FDMT
adh and FJKR
adh 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 for
large spheres with high surface energies and low Young’s moduli, while the DMT
model should be appropriate for describing adhesion of small spheres of low surface
energies 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
K2z3
0
1/3
,
where z0 is the equilibrium size of the atoms at contact. Tabor suggested that when
µ exceeds unity, the JKR theory was applicable (µ > 1), otherwise the DMT model
should be used (µ < 1).
Descriptions of the transition between these limits (µ ≈ 1) are provided by Müller
et al. [171], Maugis [172] and Johnson and Greenwood [173]. Contact area vs. load
curves 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 elastic
sphere contacting a plane depends upon the range of attractive surface forces. Area–load curves for
the JKR limit (short-range adhesion), DMT limit (long–range adhesion), and an intermediate case
are shown. All of these approach the Hertz curve in limit γ → 0 (no adhesion). Load and area are
plotted in nondimensional units as indicated (reprinted with permission from Ref. [174]; copyright
1997 American Chemical Society). (b) Map of the elastic behavior of bodies. When the adhesion is
negligible, deformations fall in the Hertz limit (approximately F > 103π R); when the adhesion is
small 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 from
Ref. [175]).

so-called elasticity parameter, λ, related to µ and defined by:
λ =
2.06
z0
Rt
2
ikj
πK2
1/3
= 1.16 µ. (7)
Using this theory, Johnson and Greenwood [173, 175] constructed an adhesion
map with co-ordinates µ and F (see Fig. 9b), where F is the reduced load and is
given 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 practical
applications fall in the JKR zone of the map, but the small radius of an AFM
tip, 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 Carpick
et 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 choice
between equations (3) and (4) can be made. The approximate values of the F can
be 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:
FM-D
adh ≈ (1.9
aa
←→ 1.6)πR ikj, (10)
where the values of the work of adhesion ikj are calculated as described in
Section 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 shown
that both the dimensionless load parameter, F, and the transition parameter had
significant influences on the contact area at the micro/nano-scale and, thus, should
not be ignored in the nano-indentation tests. Finally, all the theories reviewed in this
section, except the MP model, are continuum elastic theories and, hence, assume
smooth 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 be
expressed 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 surface
tension or surface energy (usually against air) as the sum of components due to
dispersion 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 two
components for each phase (the cross-term is described by the geometric mean):
γαβ = γα + γβ − 2 γ d
α γ d
β − 2 γ
p
α γ
p
β . (12)
Four cases arise in describing the work of adhesion:
(A): dissimilar surfaces i and j in contact with vapor (V)
iVj = 2 γ d
i γ d
j + γ
p
i γ
p
j . (13)
(B): identical surfaces i and i in contact with vapor (V)
iVi = 2 γ d
iV + γ
p
iV . (14)
(C): dissimilar surfaces i and j in contact with liquid (L)
iLj = 2 γL − γ d
i γ d
L + γ
p
i γ
p
L − γ d
j γ d
L + γ
p
j γ
p
L
+ γ d
i γ d
j + γ
p
i γ
p
j . (15)
(D): identical surfaces i and i in contact with liquid
iLi = 2 γL − 2 γ d
i γ d
L + γ
p
i γ
p
L + γ d
i + γ
p
i . (16)
In an attempt to relate components more clearly to the chemical nature of the
phase, van Oss et al. [181] suggested that the polar component could be better
described in terms of acid–base interactions. Thus, surface energy can be expressed
as γαβ = γ LW
α + γ AB
β . 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 surface
tension parameter (γ +
) and the electron-donor surface tension parameter (γ −
). The

total interfacial energy between two phases is [182]:
γαβ = γ LW
α − 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 theories
for estimation of surface tension components from contact angle data; this subject
still is under debate [184–188].
3.3. Capillary force
If a liquid vapor is introduced, the surface energy of the solids is modified by
adsorption. At a certain relative vapor pressure, capillary condensation will occur at
the point of contact between the tip and sample. An annulus of capillary condensate
will form around the tip and, consequently, a capillary force arises as a main
contribution in the measured pull-off force. To study how this adsorbed water
affects the AFS experiments under ambient conditions it is necessary to understand
why this layer is present, and on which conditions and parameters it depends. When
working in ambient conditions it is important to focus on the nanometer scale, where
two main effects have to be considered in the adsorption process: the disjoining
pressure, , experienced by thin films, and in the case of non-flat interfaces the
Laplace pressure (L), which determines the curvature of the adsorbed layer. The
disjoining pressure is the interaction force per unit area between gas and liquid
interfaces, and is induced by long-range interactions. For films of micrometer
thickness, the disjoining pressure is negligible, but for thin films of thickness in the
range 2–100 nm it has to be taken into account in the analysis of the free energy of
the system. In general, several forces are responsible for the disjoining pressure. For
some systems, the van der Waals interaction dominates and the disjoining pressure
for 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 dielectric
properties of the three media (s, solid; l, liquid; v, vapor), the force responsible for
the disjoining pressure can be attractive, repulsive or a mixture of both, as shown
in Fig. 10. Curve A is typical of a stable film (wetting), curve C corresponds to an
unstable film (non-wetting) and curve B corresponds to a metastable film [189, 190].
Another possible origin for the disjoining pressure is the so-called repulsive
double layer force, which can be very important in the case of charged surfaces
or ionic solutions [61]. For an electrolyte solution, the disjoining pressure can be
described by:
(t) = Ks exp(−2χt), (19)
where χ is the Debye screening length of ions in the solution and Ks is a constant
factor 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 theory
includes the effects of both long-range forces, namely, the van der Waals and the
double layer, when calculating the disjoining pressure, so that the (t) plot can take
complicated shapes, due to superposition of the two contributions (Fig. 10). One can
then say that the disjoining pressure displaces the gas–liquid interface away from or
towards the solid–liquid interface. This implies a change in the internal energy of
the 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 equilibrium
between vapor and liquid phases, both chemical potentials must be equal. From
these considerations, it is possible to obtain the thickness of the film for a given
temperature and vapor density.
Considering only the van der Waals contribution to the disjoining pressure and
a hydrophilic substrate, the thickness of the water film can be approximately
described 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 the
number of particles and V is the volume), nsat is a saturation density for which
liquid–vapor equilibrium is reached [190], kB is the Boltzmann constant and T is
the 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 a
non-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 initially
near 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 the
substrate. The behavior of the force curve (pull-off force) depends directly on the
height of the water film adsorbed on the substrate. The minimum required thickness
of 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 spreading
coefficient 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 water
film. No capillary neck forms between two surfaces until the water film thickness
reaches the minimum thickness, sf.
Various techniques have been used extensively for the analysis of water films
on surfaces, such as ellipsometry [194], surface force apparatus [195] and AFM
[196–199], among others. Miranda et al. [200] used a combination of vibrational
sum frequency generation and scanning polarization force microscopy [201] and
concluded that above the transition point (relative humidity where capillary conden-
sation occurs) the AFM tip induces water nucleation and, therefore, formation of a
capillary bridge. Forcada et al. [202] measured the thicknesses of solid-supported
thin lubricant films using AFM, and the differences observed between the thick-
nesses measured with the force microscope and by ellipsometry were explained by
appearance of instability in the liquid film. The theoretical description also predicts
the 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 film
determined by AFM and the influence of the type of substrate used. Figure 11b
shows a force curve enlarged in the attractive region (approach curve) to identify the
jump-to-contact distance (Djtc). The thickness of the liquid film is determined by
Djtc 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 van
der Waals forces (DvdW
jtc = 2.1 nm). The theoretical values for mica surface, using
equation (20), are 1.4 and 3.0 for dry and wet conditions, respectively, which agree
with 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 and
mica. They also showed that water adsorbed on graphite only under the influence
of 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 water
on surfaces is fundamental to AFM studies. In fact, effects of water have been
observed 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%) for
various sample surfaces (mica, quartz and silicon). (b) Typical force curve enlarged in the attractive
region to show thickness of liquid ﬁlm determined by AFS (kc ≈ 0.13 N/m) on muscovite mica. The
experimental 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 under
different humidity conditions using a smooth particle and flat surfaces of alumina,
silver and titanium-coated Si wafers. The authors concluded that both the relative
humidity of the surrounding atmosphere and the surface roughness profiles of the
contacting surface caused a discrepancy between the experimentally observed and
the theoretically predicted values of adhesion forces.
The tip becomes more sensitive to capillary forces in the presence of water
vapor [206]. The contribution of capillary forces to the total interaction between
an AFM tip and sample increases above a certain critical humidity [205]. Several
recent studies have investigated the adhesion force between an AFM tip and various
substrates as a function of humidity [207, 208]. The results of these studies show
that the adhesion force depends strongly on whether the substrate is hydrophilic or
hydrophobic. Hartholt et al. [209] reported that as the humidity increased from 45%
to about 65%, the mobility of glass particles decreased. When the humidity rose
above 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 force
due 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 capillary
annulus of condensed water is formed around the contact surface. Its radius rc in
this 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 pressure
is generated within the water and the pressure in the capillary is lower than
atmospheric pressure by γlv/rm, where the surface tension of water is γlv. When
the Laplace pressure acts on the area of πr2
c , then it creates an adhesion force that

can be expressed as:
FC
Ad = 2πRtγlv(cos θ1 + cos θ2). (23)
For two identical materials, θ1 = θ2, thus:
FC
Ad = 4πRtγlv cos θ. (24)
Equation (23) is useful for estimating the capillary force of a micro-contact; note
that it is described as dependent only on the surface tension of bulk water and the
contact angle, θ, but is independent of the solid–solid and solid–liquid interaction
parameters. This equation does not explain the force transition experimentally
observed in several papers as a function of the relative humidity. Miranda et al.
[200] discovered by scanning polarization microscopy that the force instability was
caused by a low coverage of water at the solid surface. The authors suggested that
water, condensed from water vapor at room temperature on mica, forms a partially
developed monolayer of an ice-like phase. They concluded that with decreasing
humidity the ice-like water monolayer, which is formed around 90% RH, breaks
into islands, until the water coverage is too low (20% RH).
Xu et al. [210] employed AFM adhesion measurements on mica surfaces as a
function of the relative humidity and noticed that there were three distinct force
regimes as illustrated in Fig. 13a (I, II and III). Other authors have confirmed the
qualitative force behavior of regimes I and II with hydrophilic AFM tips on mica
[208, 212]. Pull-off force measurements with hydrophilic tips and hydrophobic
substrates (coated silicon), or hydrophobic tip and hydrophilic substrates, are
independent of RH [213, 214], as shown in Fig. 13b. However, the force instability
originates from the ability or inability of the water film to form a liquid joining neck
between the adjacent surfaces at high and low RH, respectively.
The decrease of the pull-off forces in regime III (high RH) with increasing RH
for a hydrophilic tip was discussed by Binggeli and Mate [207]. The adhesion
force on the tip is the sum of the capillary force and the interaction force between
the two solid surfaces mediated by the water in the gaps between the contacting
asperities. For a spherically shaped tip in contact with a flat surface at high relative
humidities, the capillary force is independent of RH (equation (23)). The solid–solid
interaction is more complicated than the capillary forces. The presence of water in
the gap can greatly alter the nature of interaction [207]. The authors suggested
that the decreasing adhesion force with rising RH was due to the interplay between
capillary forces and the forces related to chemical bonding, Fchem, of the liquid in
the gap, given by:
Fchem = −
∂G
∂z
= −
a
v
µw, (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 of
the 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 room
temperature. (a) Pull-off force between a hydrophilic Si3N4 tip and the mica surface, where open
circles 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. RH
measured between a sharp AFM tip coated with octadecyltrichlorosilane (OTS) and a ﬂat silicon
sample (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 is
µw = kBT ln(nv/nsat). The chemical force is given by:
Fchem = −
a
v
kBT 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 force
observed previously [215]. This result is also consistent with the results of
Christenson [216] who studied the effect of capillary condensation on adhesion
force between mica surfaces and observed that adhesion forces at high partial
pressures were dominated by Laplace pressure rather than by solid–solid adhesion.
When relative humidity is less than 90%, both the water ﬁlm thickness and the
radius of the meniscus bridge are less than 10 nm [217], which is much smaller
than the radius of the AFM tips used in many studies using AFM. In this case, the
capillary 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 calculated
by d = −1.08 cos θ/ ln RH [218], where RH is the relative humidity. Generally, it
is 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 to
a 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 not
require a large contact area and, thus, did not restrict the capillary force equation to
large 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); for
small φ, equation (29) is reduced to equation (27). Note that equation (29) is based
on a much simpliﬁed cylindrically shaped geometry. Geometries for nanocontacts
that 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 a
flat sample. In the first case, the force is given by:
F = πε0V 2
t−s
Rt
D
(Rt/D 1), (30)
F = πε0V 2
t−s
Rt
D
2
(Rt/D 1), (31)
where ε0 is the vacuum dielectric constant, Vt−s is the voltage difference between
the tip and sample and D is the tip–sample distance. In the case of a sphere-ended
cone on a flat surface, the force can be calculated by replacing the equipotential
conducting surfaces with their equivalent image charges. Burnham et al. [221] have
studied another kind of Coulomb-like force which arises from regions of different
surface charge densities interacting via a long-range force law, i.e., surface patch
charges. Surface patch charges arise due to different values of the workfunction on
a material’s inequivalent surface regions [222]. Burnham et al. [73] used the method
of images to model a spherical tip and a flat sample, each with its own initial surface
charge, 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–sample
distance, B represents the position of Qt within the tip, Qs represents an image
charge on the surface of the sample, rc is the effective radius of curvature of the tip
and Z is the position of Qs. The relative permittivities ε1, ε2 and ε3 correspond to
the tip, sample and intervening medium, respectively.
When one studies the force between surfaces of low curvature, a parallel plate
model for the surface charge interaction is appropriate [222]. The force is then
independent of D, so that the patch charge effect is not noticed and van der Waals
forces 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 study
surface-electrical variables: Kelvin force probe microscopy [224, 225] was used
to measure the workfunction and its distribution for a dielectric material over its
surface; scanning capacitance microscopy [226, 227] was used to measure dielectric
properties and impurity dopant distribution; charge detection microscopy [228] was
used to look at charge distribution and to measure amounts of charge as small as
two or three electron charges [229, 230].

When the tip and sample are exposed to air for relatively long time, no net
charges are expected to remain [231] and electrostatic force is zero; however,
capillary forces are present. By controlling the cleanliness of the surfaces (UHV
environment), the adhesion force due to van der Waals forces should become the
dominant attractive force between uncharged, non-magnetic surfaces. In a solution,
other forces associated with double-layer, hydration and hydrophobicity need to be
considered too.
3.5. Other types of adhesion forces
The adhesion (pull-off force) obtained by force spectroscopy can vary with the
sample and the environment in which the measurements are made. In the previous
sections, only components of the adhesion force in flat and rough inorganic
surfaces under ambient conditions were considered. In this section, other possible
interactions measured by force spectroscopy on polymer, macromolecules and
biological surfaces will be reviewed.
The first interaction considered here is “specific forces”. Specific forces are
non-covalent forces that generate very strong adhesion between specific pairs of
molecular groups; most of the interactions between biological molecules are due
to these forces. In order to measure specific forces with AFS, it is necessary
to functionalize the tips by covering them with one of the two molecules under
study. 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 the
surfaces 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 a
monomer [239], the coil is pushed out of the gap, resulting in a reduced polymer
concentration between the surfaces, giving rise to the depletion forces. Fleer et al.
[240] have deduced the depletion force to be of the form:
Fdep = π
µ
vm
(D + 2Rt)(D − 2TL), (33)
in which D is the distance between the surfaces, µ is the chemical potential of the
solvent, 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 the
polymer–surface interactions and on the availability of free binding sites on the
opposite surface [74]. If there are free binding sites on the opposite surface, some
polymer coils will form bridges between the two surfaces and give rise to a third
interaction called bridging force [241–244]. Any polymer that naturally adsorbs
onto a surface from solution has the potential to form bridges between two such
surfaces; 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 density
of bridges will also be low [61].
In this section the forces involving biological systems and polymeric films were
briefly 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 between
the AFM tip and flat inorganic surfaces is then given by the sum of equations (6),
(26), (29) and (32):
Fair
pull = Fcap + FvdW + Fchem + Felec, (34)
or in the absence of electrostatic charges:
Fair
pull =



πRγ cos θ
(1 + cos φ)2
cos φ 1 +
D
d




cap
+ [αR ikj]vdW + −
a
v
kT ln
p
ps chem
,
(35)
assuming two identical surfaces (θ1 = θ2 = θ).
An alternative expression was proposed by Sendin and Rowlen [247], who
measured adhesion forces with AFM under ambient conditions. The authors studied
the nature of the pull-off force on a variety of surfaces as a function of relative
humidity. A mathematical model of pull-off force as a function of relative humidity
was proposed in which the chemical specificity was explained. The proposed form
of the relationship between measured pull-off force and relative humidity is
Fair
pull = Fstv +
Fstw + Fcap
1 + e−[((p/ps)−(p /ps))/m]
, (36)
where Fstv is the surface–tip adhesion force in the presence of water vapor, Fstw is
the surface–tip adhesion force in the presence of liquid water, Fcap is the adhesion
force due to capillary condensation, p /ps is the relative humidity at the transition
point between the two regimes and m is the slope of the transition. The capillary
force may be calculated as the sum of force due to surface tension (Ft) and the force
due to a pressure difference across a sphere’s surface (Fp) [248].
The equations cited previously do not describe the effect of surface topography on
the adhesion force, although adhesion force is greatly affected by small roughness
of the solid surfaces in contact [3, 211, 249]. Microparticle adhesion studies by
AFM have shown the effect of roughness on adhesion. Segeren et al. [250]
studied this phenomenon and showed that the interactions between smooth silica
particles, or rough toner particles, and silicon substrates were influenced by the
true 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 account
this dependence (equation (37)):
Fpull =
3π Rtr2
2(r2 + Rt)
+
(ARt/6H2
0 )
1 +
58RMS1
λ2
1
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 superimposed
over 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 between
the two surfaces, respectively. The authors model roughness as a distribution of
closely packed hemispheres with equal radius r = λ2
/58RMS. RMS and λ are the
root-mean-square roughness and the mean peak-to-peak distance, respectively (see
more details in Ref. [252]).
Several other studies have attempted to incorporate roughness into adhesion
theories [252–257]. Studies of adhesion force have been carried out on liquid
systems where the interactions involved are affected and modiﬁed by the type of
solution 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 adhesion
force closely correlated with AFM measurements, except in water. This difference
observed for water was discussed in terms of chemical interactions between the
Si3N4 tip and water. Hoh et al. [260] studied the adhesion interaction between a
silicon nitride AFM tip and glass substrate in water. The adhesion measured was in
the range 5–40 nN, of which a large component was likely to be due to hydrogen
bonding between the silanol groups on both surfaces. The results demonstrate that
the chemical interactions between the tip and sample can be modulated and provide
a basis for designing conditions for imaging and manipulating biological molecules
and 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 complex
than measurements of the pull-off force in air, since additional forces arise when
an AFM tip is immersed in solution. Repulsive forces may arise from solvation or
hydration forces since the water near hydrophilic surfaces is structured. In aqueous
solutions, electrical double-layer forces also arise, which may be either attractive or
repulsive, 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 adhesion
phenomenon was presented. The measurements of surface–surface interactions

at the nano-scale are considered vital, because in this range new properties of
the materials can be evaluated. The future of the AFS technique is related
basically to the investigation of basic concepts coupled with theoretical models and
experimental results, and applications to solve practical problems as, for example,
in nanotribology, nanobiotechnolgy and physical chemistry of surfaces. The
progress is expected to occur in the research on nanosensors, using chemical force
microscopy as electronic nose and electronic tongue; the investigation of lubricating
films, and contamination using colloidal particle attached to the cantilevers, with the
known geometry, atomic structure, and chemical composition; the investigations
of adhesion force to characterize dynamics of aggregates in soil particles, as well
as elucidating the effects of sorption mechanisms (interfacial phenomena between
pesticides, organic matter, mineral particles).
The discussions presented in this review article demonstrate the range and the
complexity of the subject and they bring out the importance for investigations in
the field of nanoscience and nanotechnology, due to the challenges as well as the
wealth of information which can be derived from the experiments, as well as from
theoretical 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. acknowledges
a 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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