2 Chapter 1
Sample imaging at sub-optical resolution is not the only function of Atomic Force
Microscopy. Interaction forces on the nanoNewton scale can be measured with ease of
operation and of sample preparation. AFM allowed for the first time the direct
measurement of molecular and surface forces between nanometer sized surfaces (the
interaction area can be as small as 10×10 nm
2
). Soon after the invention of AFM, forces
were measured in air [19] and in water [20,21]. Recent developments in technology
enable the measurements of forces at the colloidal (micrometer) and macromolecular
(nanometer) level. Measuring interactions occurring at the surface of colloidal particles
can solve many phenomena of scientific and industrial interest. For example the
wettability of the surface of finely divided solid particles is of fundamental importance
in determining complex processes, such as dispersion stability, froth flotation and laying
of dust.
1.2 Thesis Outline
This Thesis describes a number of applications of the Atomic Force Microscope to the
study of problems of relevance in colloid and surface science. Both aspects of AFM
have been exploited, the imaging mode and the force measurement mode. Section 1.3
introduces the functional principles and main components of an Atomic Force
Microscope. Section 1.4 describes from a theoretical point of view the interaction forces
that are important in our studies. Section 1.5 and 1.6 present a review of previous results
obtained with AFM used in imaging and in force measurement mode respectively.
Chapter 2 describes the experimental approach used in this Thesis work, especially
regarding the direct measurement of forces. The colloid probe technique, whereby the
forces between a model colloidal particle and a flat surface are measured, is described in
detail. A new method for the characterisation of surface roughness and cleanliness of
colloid probes is proposed.
The two main applications of the AFM, imaging and force measurement, rely on the
same measuring principle, that of detecting the deflection of a microscopic cantilever in
consequence of the interaction of a mounted tip with the sample surface. However the
type of information obtainable in the two modes is distinct, therefore the results obtained
with the two modes are presented separately. Chapter 3 is the account of the applications
Chapter 1 3
of AFM as an imaging instrument to four diverse samples of interest in the field of
colloid and interface science. The studied systems were: Langmuir-Blodgett films of a
complex dye molecule with interesting optical applications; dispersions of Ca(OH)
2
nanoparticles of relevance for wall paintings (frescos) restoration; gold nanostructured
surfaces, prepared with the innovative technique of flame spraying of water in oil
emulsions; a synthetic system that conjugates properties of self-assembling and of
specific molecular recognition.
The remaining Chapters present the results of the direct measurement of forces obtained
with AFM used in the colloid probe configuration. Chapter 4 describes direct
measurement of hydrodynamic forces acting on a sphere in viscous Newtonian liquids.
Strikingly these results can be fitted only with a solution of the Navier-Stokes equations
obtained under slip boundary conditions.
The quantitative measurement of forces with an AFM depends on the accurate
evaluation of the spring constant of the force-sensing device, the cantilever. Many
methods exist in the literature for the estimation of the spring constant of bare AFM
cantilevers but none is directly applicable to the colloid probe. Chapter 5 presents a new
method for the determination of the spring constant of AFM cantilevers bearing a colloid
probe. The proposed method is based on hydrodynamic force measurements.
Chapter 6 describes preliminary results of direct measurements of equilibrium forces
acting in aqueous solutions of different pH between surfaces constituted by mixed Self-
Assembled Monolayers (SAM) of thiols on gold.
A summary of the conclusions reached in these studies is provided in Chapter 7, together
with suggestions for further studies on the addressed problems.
1.3 The Atomic Force Microscope
A number of acronyms have been invented in connection with the birth of the Scanning
Tunneling Microscope (STM). The family of techniques that make use of a microscopic
tip of different nature to probe the local properties of surfaces is known under the name
of Scanning Probe Microscopies (SPM). The Atomic Force Microscope (AFM) is also
4 Chapter 1
often referred to in the literature as Scanning Force Microscope (SFM), but throughout
this Thesis the denomination AFM is maintained. Other used acronyms are always
specified the first time they appear.
1.3.1 Functional Principles
The heart of the Atomic Force Microscope is a flexible cantilever, with a mounted
microfabricated tip, that deflects when the tip interacts with the surface of the sample.
The sample is mounted on top of a ceramic piezoelectric crystal and is raster scanned
under the tip (or vice versa the tip is scanned above an immobile sample, depending on
the design of the instrument, see Sections 2.1.1 and 2.1.2), and the cantilever deflection
is measured in order to reproduce the sample topography. A controller collects and
processes the data, and drives the piezo scanner. As shown in Figure 1.1 a pyramidal
probe tip is mounted on a sensitive cantilever spring and positioned very close (or in
contact) to the sample surface. Interaction forces between the sample and the tip cause
the cantilever to deflect according to Hooke’s Law:
F=k x (1.1)
where k is the spring constant (N/m), characteristic of each cantilever and x is the
cantilever vertical deflection (nm).
Figure 1.1 Schematic illustration of the main components of an AFM.
AFM cantilevers and tips are described in detail in Section 1.3.3. The cantilever
deflection is normally measured with sub-Angstrom sensitivity with the optical lever
Chapter 1 5
method [22,23]. The method consists in focusing a laser beam on the rear side of the
cantilever and in collecting the deflected beam with a position sensitive detector,
normally a quartered photodiode (see Section 1.3.5). In this arrangement a small
deflection of the cantilever tilts the reflected beam and changes the position of the beam
on the photodetector. Using this method both the vertical deflection and the torsion of
the cantilever can be monitored.
The sensitivity of the Atomic Force Microscope to forces at the microscopic level has
been initially used to obtain topographic maps of a sample surface at very high
resolution. Different imaging modes are discussed in Section 1.3.2. The same principle
can be applied to the direct measurement of forces and thus provide information on other
surface properties of the sample (see Section 1.6).
1.3.2 Imaging Modes
The monitored property in AFM, the interaction force with the sample, can be kept
constant (equiforce mode) or varied (variable deflection mode) during the scanning
motion. In the equiforce mode, during the scan process the force is controlled by
keeping the deflection of the cantilever constant by means of a feedback loop. The
feedback loop controls the movements of the piezo in the direction normal to the sample
surface (z). The parameters of the feedback, the so-called PID settings (acronym for
proportional, integral and derivative of the error signal), must be optimised for each
sample and scanning conditions. The voltage reading coming from the z piezo feedback
signal is digitised and thus yields an accurate measure of the motion of the z piezo; the
resulting image is called ‘topography’ image. In the variable deflection mode, during the
scan process the feedback control is turned off and deflections of the cantilever are
measured from the current of the photodetector. This mode is normally applied to
samples with limited range in the vertical direction. The resulting image is called
‘deflection’ or ‘internal sensor’ or ‘error’ image. Atomic resolution on crystalline
samples can be achieved in this mode, keeping the scanning rates high (> 10 Hz) and the
applied pressure elevated.
The AFM can operate both in contact and non-contact regime. In the former regime, the
tip is in Born contact with the sample and traces the sample features like a surface
profilometer [24]. Contact imaging normally achieves the higher resolution, but often
6 Chapter 1
implies a greater damage to soft samples. In particular when operating in air, the
ambient humidity is sufficient to create a meniscus of water between the tip and the
sample, which creates capillary attractive forces between tip and sample surface.
Because of this effect the control on applied pressures in AFM imaging performed in
contact and in air is limited, which is a problem especially with soft biological or
colloidal samples. Imaging in aqueous electrolyte solutions has become very popular
because it is potentially less destructive to soft samples; Weisenhorn e al. [20] f und
that imaging forces between tip and sample in water were at least one order of
magnitude smaller than in air. Besides, there is of course a great interest in imaging
biological and chemical samples in aqueous environments. A different imaging mode
that further reduces tip-sample direct contact is the non-contact imaging mode. Digital
Instrument has patented the non-contact mode with the name Tapping Mode, and the
two expressions are nowadays used without distinction. In the non-contact mode the
cantilever is kept vibrating, by means of the piezoelectric elements, above and close to
the sample (within 10 nm to the sample), at a modulation frequency close to the
resonance frequency of the cantilever. The signal of the detector is measured by lock-in
techniques and variations in phase or amplitude of the vibration are converted into
information on the surface properties and morphology. Gradients in force in direction
normal to the sample surface (F’=δF/δz) ca se a change in the cantilever spring constant
k:
k
eff
= k-F’ (1.2)
where k is the spring constant in absence of tip-sample interactions. The variation in
spring constant produces a variation in the resonance frequency ω
0
of the cantilever:
ωω∝
=
−
′
≈−
′
k
m
eff
1
2
1
2
1
2
0
1
2
k
m
F
k
F
k
(1.3)
where the last equation is true in case of F’<k. Therefore:
∆ω/ω
0
=(ω-ω
0
)/ω
0
=-F’/2k (1.4)
so force with a positive gradient (F’>0) yields a decrease in resonance frequency of the
cantilever.
Chapter 1 7
1.3.3 Probes
An AFM probe is constituted by a tip, the part that interacts directly with the sample,
mounted at the end of a flexible support, the cantilever. The cantilever, oriented at an
angle of about 12 degrees with the surface, provides support for the tip and is deflected
by the pressure on the tip. By monitoring the deflection of the cantilever, the position of
the tip over the sample features is traced and then converted into an electronic image.
The first AFM tip-cantilever assembly, constructed by Binnig et al. in 1986 [2], was
made by meticulously gluing a tiny shard of diamond at the end of a rectangular strip of
gold foil. This cumbersome construction allowed to resolve lateral features as small as
300 Å. However without the breakthrough in tip manufacture, the AFM would have
probably remained a curiosity in a few research groups. Not long afterwards the first
silicon microcantilevers were fabricated. Today the typical tip-cantilever assembly is
microfabricated industrially from Silicon or Silicon Nitride (Si
3
N
4
); cantilevers are
mainly of two shapes: rectangular and V-shaped [25], as depicted in Figure 1.2. Factors
determining the mechanic properties of cantilevers are the width (w), the thickn ss (t)
and the length (l) of e legs, and the elastic (or Young) modulus (see Section 5.1).
(a) (b)
Figure 1.2 AFM cantilevers (a) V-shaped and (b) rectangular. The dimensions of the
cantilevers (w, t and l) are defined.
The rear side of the cantilever (the one not in closest proximity with the sample) is
usually coated with a thin layer of gold to enhance its reflectivity. The cantilever stylus
used in AFM experiments should meet the following criteria [25]:
8 Chapter 1
1) In order to register a measurable deflection due to a small force, the cantilever must
have a relatively low spring constant, typically between 0.1 and 1 N/m.
2) A high resonance frequency reduces the sensitivity of the cantilever to mechanic
vibrations of low frequency, and allows higher imaging rates. Therefore cantilevers with
resonance frequencies around 10-100 KHz are ideal. The cantilever resonance frequency
ω
0
is given by:
ω
pi
0
1
1
2
k
m
=
/2
(1.5)
where k is the spring constant and m the mass of the cantilever. In order to keep k small
and ω
0
big, m must be very small. Modern microfabrication techniques allow the
construction of cantilevers with very small masses (typical length 100 µm and thickness
< 1 µm).
3) In order to reduce the effect of lateral forces in AFM, high lateral stiffness of the
cantilever is desirable. When operating in contact imaging or in force mode, frictional
forces can cause appreciable lateral bending of the cantilever, leading to stick-slip
motion of the lever [17]. A V-shaped cantilever is preferable to exploit a substantial
lateral stiffness.
4) To obtain a good imaging resolution, the tip must have a small effective radius of
curvature (ca. 300 Å) and a small aperture angle, a pyramidal or conical geometry which
makes the terminal point of the tip very sharp, and a high aspect ratio (ratio between
height and width of the tip) in order to be able to penetrate in small pits of the surface
(see next section).
Many nanotechnology companies sell cantilevers and tips of many types and
dimensions, and cost is usually the only limitation to choice. The choice of tip type and
spring constant of the cantilever depends on the application: probes with a lower spring
constant are more sensitive, but at the same time are more easily trapped by capillary
forces on the surface of humid samples. Stiffer probes are less sensitive but can be
pulled free from the surface more easily. The tips and cantilevers employed in this
Thesis work were mainly sourced from two companies, Topometrix (now
Chapter 1 9
Thermomicroscopes) and Digital Instruments. The imaging work presented in Chapter 3
was obtained with the cantilevers and tips listed in Table 1.1 and 1.2.
The cantilevers employed for force measurements were sources from Digital
Instruments. The technical details on the employed cantilevers are listed in Table 1.3.
For imaging purposes the exact shape of the tip is of great importance. Several existing
techniques for the determination of the shape and size of the scanning tip are reviewed in
Section 1.3.6. The control over tip geometry in the force measurements presented in this
Thesis was obtained by using a colloid probe instead of the bear pyramidal tip (see
Section 2.2).
Table 1.1 Physical Properties of Topometrix AFM Cantilevers.
Cantilever Contact AFM
#1520
Contact AFM
#1530
Non-Contact AFM
#1660
GeometryV-Shaped V-shaped Rectangular
Material Si
3
N
4
Si
3
N
4
Si
Leg Length l (µm) 200 100 225
Leg Width w (µm) 36 22 30-45
Thickness t (µm) 0.6 0.6 6-8
Spring Constant k
(N/m)
0.064 0.37 24-85
Nominal Resonance
Frequency (KHz)
17 66 160-220
Table 1.2 Physical properties of Topometrix AFM Tips.
Cantilever#1530-#1520 #1660
Material Si
3
N
4
Si
Tip GeometryPyramidal, base 4 µm,
height 4µm
Triangular Pyramidal, base
3-6 µm, height 10-20 µm
Aspect Ratio~ 1:1 ~ 3:1
Tip radius < 50 nm < 20 nm
10 Chapter 1
Table 1.3 Physical properties of Digi al Instruments cantilevers type NP.
GeometryMaterial
Leg
Length
l (µm)
Leg
width
w
(µm)
Thickness
t (µm)
Spring
Constant k
(N/m)
Resonant
Frequency
Range
(KHz)
V-Shaped Si
3
N
4
200 40 0.4-0.6 0.01-0.6 5-50
1.3.4 Scanners
The motion of SPM probes is controlled over microscopic distances by ceramic
piezoelectric elements. Piezoelectric materials can be made to contract or to expand
proportionally to an applied voltage. The occurrence of expansion or elongation depends
on the polarity of the applied voltage. SPM techniques make use of piezoelectric
elements with very low expansion coefficients, of the order of 1 µm f r 100 V applied
voltage, which allow very fine positioning of the probe (1 Å with an applied voltage of
100 mV). Scanners normally consist of a hollow tube made of piezoelectric material
such as PZT (lead zirconium titanate). All piezoelectric materials are affected by
phenomena like nonlinearity and hysteresis, which are undesirable, but can be corrected
for by conditioning the voltage applied to them. Calibration of a scanner consists in
scanning a standard grid of known dimensions and correcting the scanner's piezo control
electronics to compensate for nonlinearities. Longer scanner tubes contain longer piezo
elements and allow scans over larger areas, but are more sensitive to ambient noise
because of a lower resonant frequency. On the other hand shorter scanner tubes contain
shorter piezo elements and can scan smaller areas, but are more precisely controlled and
can achieve higher resolutions. The scanners employed in this Thesis work were sourced
from Topometrix and from Digital Instruments. Three types of Topometrix scanners
were used with the AFM Explorer 2000 (see Section 2.1.1): a liquid scanner and an air
scanner, both with maximum scan area of 130 µ in pl e and 8 µm in the vertical
direction, and a liquid scanner with maximum scan area of 2 µm in pl ne and 0.8 µ in
the vertical direction. For force measurements a Digital Instruments scanner (called "J"
scanner) with maximum scan area of 100 µm in plane and 5 µm i the vertical direction
was used.
Chapter 1 11
1.3.5 Optical Detection Method
Historically a few methods have been used to detect cantilever deflections: the electronic
tunneling method, the interferometric method and the optical lever method [24]. The
first AFM ever built [2] had an electronic tunneling detection method: the tunneling
current between a metallic tip and the rear side of the conductive cantilever was
collected and revealed the cantilever position. This method had several drawbacks,
principally that the interaction forces of the AFM tip with the metallic tip was
comparable to that with the sample, the method could not operate in liquid and even in
air the tunneling was not stable. In the interferometric method a laser beam focused on
the cantilever interfered with a reference beam and the deflections of the cantilever were
detected by the variation of the interfering beam intensity.
Most modern AFMs designs employ optical detection methods to sense the small
cantilever deflections. The laser beam deflection method, also called optical lever, was
first introduced by Meyer and Amer [23] and Alexander et al. [22]. The cantilever
displacement is measured by detecting the deflection of the laser beam, which is
reflected off the rear side of the cantilever and then reflected off a rotating mirror and
into a position-sensitive detector (PSD, see Figure 1.1). The direction of the reflected
laser beam is sensed by the PSD, which is typically divided in four quadrants, as
illustrated in Figure 1.3.
Figure 1.3 Position Sensitive Detector divided in four quadrants A, B, C and D,
employed in the optical detection method used in AFM.
12 Chapter 1
When the cantilever is in rest position, the laser beam must be centred on the PSD (red
spot in Figure 1.3). In case of vertical deflections of the cantilever, i.e. due to attractive
or repulsive interactions of the tip with the surface, the beam spot moves vertically on
the PSD (occupying the position indicated in blue in Figure 1.3). The optical detection
method also allows measuring frictional forces acting on the tip [26]: these are
manifested in a lateral shift of the laser beam spot (green spots in Figure 1.3). The
vertical or lateral movements of the laser spot are detected by calculating the differences
of the signal due to the different quadrants of the PSD. The difference in signal in the
vertical direction, i.e. the difference between the signal coming from the quadrants
(A+B) minus that from (C+D), is proportional to the vertical deflection of the cantilever,
with a proportionality constant given by the optical sensitivity. The difference in signal
in the horizontal direction, i.e. the difference between the signal coming from the
quadrants (A+C) minus that falling in (B+D), are proportional to the torsional deflection
of the cantilever. The vertical sensitivity of the light lever is determined from the change
in signal at the diode due to the deflection of the cantilever when the substrate and the
tip are in contact (compliance region, see Section 2.3). Sub-Angstrom sensitivity in the
vertical direction can be achieved with the optical method. In contrast to the tunneling
detection method the laser beam exerts only negligible forces on the cantilever. However
the method requires a mirror-like surface of dimensions of several µm at the rear side of
the cantilever.
Cantilever deflection in typical force measurements involves strains of less than 0.05%,
well within the linear deflection region for most ceramic materials. Deflections larger
than 250 nm are not commonly encountered in AFM force measurements and are
beyond the typical linear range of cantilever oscillators in non-contact [27]. However it
should be considered that under load the tip might describe an arc rather than a simple
vertical translation. This would lead to shearing at the surface, which in turn reduces
accuracy in adhesion measurements [28,29].
1.3.6 Resolution
The resolution of optical microscopes is normally quantified in terms of magnification;
this term is somewhat ambiguous with respect to SPM. While optical microscopes utilise
optical components to extend the capabilities of the human eye, SPMs derive an image
entirely from electronic means. SPMs render an image from an electro-mechanical
Chapter 1 13
interaction with the sample, which is then translated electronically onto a computer
screen. An SPM must be calibrated with a known standard, such as an etched silicon
grid. If a certain voltage V is required to scan a distance of 1 µm, and a f ature in the
scanned area requires one quarter of this voltage to be scanned, then the object measures
one quarter of 1 µm. This is true if the scanners have a linear response or if their non-
linearity can be compensated for.
One of the main factors limiting resolution when imaging relatively rough surface with
an AFM is the finite dimension of the probe tip. Each AFM image of rough surfaces
contains a component of ‘self-imaging’ of the tip [30,31]. At each pixel the image
contains information on the tip as well as on the sample surface. The protrusions present
on the image can be regarded as surface features broadened by the shape of the tip. This
convolution affects the whole image uniformly (unless tip damage or modification
occurs during the scanning motion). Absolute measurements of the size of the features
are therefore affected by an error, which is normally an overestimation of the width of
peaks and bumps, and an underestimation of holes and pits. To minimise the effect of tip
convolution, tips should have a very high aspect ratio (ratio height/width) and a small tip
radius.
Tip geometry and size of the tips therefore influence also the depth of field, i.e. the
possibility to reach a recess of the surface. Another factor limiting the depth of field in
SPM is the travel limits of the scanners, normally around 10 µm. For both these reasons
SPM is in general more suited to studying relatively flat samples. When trying to
achieve atomic resolution on very flat surfaces (e.g. crystals) the macroscopic tip
structure is not critical. In this case very few atoms of the tip apex are in contact with the
sample surface and other factors can become determining for obtaining a high quality
image. For example instrumental artefacts may be due to noise due to environmental
vibrations, scanner nonlinearity, piezo hysteresis and creep. Vibrations are minimised by
placing the microscope on a vibration isolation platform. During the imaging
experiments described in Chapter 3 the Topometrix microscope was placed on an air
inflated table (TMC).
In some cases an absolute and accurate distance measurement is required, for example in
width and roughness measurements on industrial surfaces like patterns of integrated
circuits, optical surfaces and data storage samples. As device dimensions continue to
14 Chapter 1
shrink, the requirements for accuracy, reproducibility, high-resolution positioning,
reliable calibration become more compelling. In these cases a reliable method to
characterise the tip geometry is required. Existing methods belong to two distinct
categories: in the first category the unknown geometry of the tip is determined by
imaging a calibration grid of known shape [30,32-35]. The geometry of the tip
characteriser must be stable and independently measured with small uncertainties
compared to the size of the tip. An AFM tip characteriser was used in this Thesis work
to characterise a colloid probe sphere (see Section 2.2). In the second category a ‘blind’
numerical calculation obtains the shape of the tip without independent knowledge of the
characteriser geometry [31].
A great limit to resolution of specimens adsorbed on substrates in liquids, as is the case
of Ca(OH)
2
particles illustrated in Section 3.4, is the stable immobilisation of the sample
on the solid substrate. If the specimen is loosely bound to the substrate, the scanning tip
sweeps it away and the image reports blurry and indistinguishable objects. The adhesion
is normally strong enough for imaging when the sample adheres via electrostatic
attraction to the substrate surface.
1.4 Theory on Surface Forces
Colloidal systems consist of a discontinuous phase formed by small particles distributed
homogeneously throughout a continuous phase. The small particles have at least one
dimension between 1 and 1000 nm, and their behaviour strongly depends on the very
high ratio of surface area to volume. Some natural and synthetic colloidal systems are
constituted by solid or liquid particles dispersed in a gas (aerosols) or more rarely in a
solid (alloys), but the systems of greater interest to this Thesis are those in which the
continuous phase is liquid. Inside this category, our attention is further concentrated on
lyophobic colloids, i.e. systems that can be dispersed by mechanical agitation or by
application of an external source of energy. Most materials of interest in technological
applications have a lyophobic nature, so great attention is dedicated to lyophobic
colloids, not only in basic research [36-40],but also in productive and applicative
perspectives. At the interfaces between colloidal particles and the dispersion medium
characteristic surface phenomena, such as surfactant adsorption or charging, take place
and determine the overall physical properties of the system. Therefore studying colloidal
Chapter 1 15
systems implies studying surfaces properties, like surface interactions and surface
structure and morphology. Encounters between particles in a colloidal system are
frequent and the stability of the dispersed phase depends on the interactions between the
particles. The main contribution to aggregation comes from the van der Waals attractive
force, while stability is a consequence of repulsive interactions between similarly
charged particles or favourable interactions between a particle and the surrounding
dispersion medium. In the 1940s Derjaguin and Landau [41] in Russia and Verwey and
Overbeek [42] in the Netherlands separately developed a quantitative theory that
explains most aspects of colloidal stability. In honour of its inventors, this theory goes
under the acronym of DLVO. The main point of DLVO theory states that the stability of
a colloidal system depends on the balance between attractive van der Waals forces and
repulsive electrostatic forces.
The DLVO theory constitutes the foundation of modern understanding of the
interactions in colloidal systems and has been proven to be adequate for many systems
[43], particularly in cases of symmetric electrolytes at moderate potentials and
concentrations. However the understanding of surface forces has improved since the first
formulation of the DLVO theory, and nowadays several other theories complete the
description provided fifty years ago. More complicated calculations, called primitive
models, have been developed that incorporate ion size, ion correlation and the
dependence of the dielectric constant of the solvent on ion concentration [44,45].
Especially in the case of asymmetric electrolytes deviations from DLVO predictions
have been calculated [46].
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