JPK instruments nanowizard afm User manual

NanoWizard®AFM
Handbook
Version 2.2a
05 / 2012
© 2004-2012 JPK Instruments AG
all rights reserved

JPK Instruments NanoWizard®Handbook Version 2.2a 1
Contents
1. Introduction...........................................................................................................................................1
1.1 About this handbook........................................................................................................................................ 1
1.2 What is an Atomic Force Microscope? ............................................................................................................ 1
1.3 Scanning Probe Microscopy............................................................................................................................ 2
1.4 Atomic Force Microscopy ................................................................................................................................ 3
1.5 AFM cantilevers............................................................................................................................................... 4
2. Imaging modes.....................................................................................................................................5
2.1 Feedback and imaging control......................................................................................................................... 5
2.2 Amplitude feedback in dynamic modes ........................................................................................................... 5
2.3 Another way of thinking about imaging modes ................................................................................................ 6
2.4 Operation......................................................................................................................................................... 8
2.5 Phase imaging................................................................................................................................................. 9
2.6 Force adjustment in imaging modes.............................................................................................................. 10
2.7 Applications ................................................................................................................................................... 11
3. Force spectroscopy ............................................................................................................................12
3.1 Introduction.................................................................................................................................................... 12
3.2 Data processing for analysis.......................................................................................................................... 13
3.3 Applications ................................................................................................................................................... 16
4. More about cantilevers .......................................................................................................................18
4.1 General points ............................................................................................................................................... 18
4.2 Handling information...................................................................................................................................... 18
4.3 Cantilever types for different imaging modes................................................................................................. 19
4.4 Tip modification ............................................................................................................................................. 20
4.5 Spring constant.............................................................................................................................................. 21
5. Cell imaging........................................................................................................................................24
5.1 AFM in relation to other cell imaging techniques ........................................................................................... 24
5.2Sample preparation ....................................................................................................................................... 25
5.3 Imaging modes.............................................................................................................................................. 27
5.4 Critical imaging parameters........................................................................................................................... 28
5.5 Using the oscilloscope to optimize the imaging parameters.......................................................................... 28
5.6 Artifacts.......................................................................................................................................................... 30
6. Single molecule imaging.....................................................................................................................31
6.1 Preparation is key.......................................................................................................................................... 31
6.2 Imaging hints – intermittent contact mode in liquid........................................................................................ 33
6.3 Imaging hints - contact mode in liquid............................................................................................................ 34
6.4 Imaging hints – imaging in air........................................................................................................................ 35
6.5 Simple DNA protocol for imaging tests.......................................................................................................... 35
7. Artifacts...............................................................................................................................................37
7.1 Tip shape issues............................................................................................................................................ 37
7.2Artifacts from damaged tips........................................................................................................................... 38
7.3 Contamination ............................................................................................................................................... 39

JPK Instruments NanoWizard®Handbook Version 2.2
2
7.4 Other imaging considerations........................................................................................................................ 39
8. Useful physics for SPM...................................................................................................................... 41
8.1 The cantilever resonance .............................................................................................................................. 41
8.2 Thermal noise spring constant calibration ..................................................................................................... 41
8.3 Young’s Modulus of materials........................................................................................................................ 45
9. Useful chemistry and sample/tip preparations................................................................................... 47
9.1 Cleaning cantilevers and tips......................................................................................................................... 47
9.2 Silanization and APTES treatment ................................................................................................................ 48
9.3 Home made gel packs for cantilever storage................................................................................................. 49
9.4 Suppliers of AFM accessories....................................................................................................................... 49
10. References......................................................................................................................................... 51
10.1 General AFM Papers..................................................................................................................................... 51
10.2 Spring constant calibration references .......................................................................................................... 53
10.3 Books ............................................................................................................................................................ 54

JPK Instruments NanoWizard®Handbook Version 2.2a 1
1. Introduction
1.1 About this handbook
Here you can find information about the principles and methods of scanning probe
microscopy. The focus is on applications in biotechnology and life science.
The particular details of the JPK NanoWizard®
AFM system, for both the software
and hardware, can be found separately in the NanoWizard®
User Manual. The aim
of this document is to introduce AFM for those who are not familiar with the
technique, and to provide background information and resources to
aid those who
are familiar with the technique to extend their knowledge of particular applications.
The first sections of this handbook introduce the AFM technique, starting w
ith the
general ideas behind scanning probe microscopy. Later sections of this handbook
provide more detailed information and background for more experienced users.
1.2 What is an Atomic Force Microscope?
AFM is very different from optical microscopy.
Ther
e are no lenses, there is no requirement for a light source to illuminate the
sample, there is no eyepiece to look through; the microscope itself does not even
look like a typical optical microscope. The imaging technique consists of a
mechanical device, w
hich is able to measure very small forces when atoms or
molecules come close together, so it was named atomic force microscopy.
Cantilevers are at the heart of an atomic force microscope.
A critical part of the device called the cantilever is a plate sp
ring, which is fixed at
one end. At the other end it supports a pointed tip.
The tip can be moved across a
sample surface line by line, just like a lawn mower in the garden.
The pointed tip is brought into contact with the sample and moved across the
su
rface. The instrument measures the deflection of the cantilever as it scans, and
from this information about the tip movement a three-
dimensional image of the
sample is built up.

2 JPK Instruments NanoWizard®Handbook Version 2.2
1.3 Scanning Probe Microscopy
As the name suggests, the heart of an SPM is
a probe that is scanned over the
sample surface to build up some form of image. The type of image you get
depends on the interaction that is measured by the probe. Images can be
produced that reflect many different properties of the sample. The sample h
eight
information (topography), usually forms one aspect of the image, but images can
also be collected that show other properties, including mechanical, electrostatic,
optical, or magnetic information about the sample surface.
Different probes and meas
urement systems are often used for the different
properties, but one requirement is that
the interaction between the probe and the
sample is localized
in some way. This is so that the measured signal is dominated
by some small region of the sample closest
to the tip, so that an image of the
sample can be formed as the tip is scanned over the surface. This implies that the
interaction must have a strong distance dependence, so that only the nearest parts
of the sample contribute to the interaction felt by
the tip. The range of the
interaction will be one factor in the final resolution of the instrument. When the
interaction has a very strong distance dependence, such as the electron tunneling
current used in STM, the resolution can be good enough to “see” individual atoms.
Since the measured signal should be dominated by the small region of probe and
sample that are closest together, the actual probe does not need to be an isolated
point. The probe can be part of some larger structure that is more
convenient to
mount and scan. The size of the probe can be relatively large, perhaps hundreds
of microns or more, but if the interaction has a short enough range then the signal
will be dominated by the very tip region of the probe, so that resolutions c
an still be
achieved in the range from atomic distances to microns.
The idea of a probe measuring a local interaction and building up an image is
relatively straightforward, but the actual implementation of a system with a
resolution in this range is te
chnically challenging. Many factors came together in
the development of scanning probe microscopy, including the development of
piezoelectric materials that made it possible to reproducibly position and scan
components with a sub-nanometer precision.
Th
e following diagram shows some of the different forms of scanning probe
microscopy that have been developed. The techniques are usually named after
the interaction that they measure. The list is not complete, as there are many
different forms of scanning
probe microscopy, and new techniques are still being
developed. The information in this handbook is mainly concerned with Atomic
Force Microscopy.

JPK Instruments NanoWizard®Handbook Version 2.2a 3
Scanning Tunneling Microscope –STM
H. Rohrer, G. Binnig (1981)
The family of Scanning Probe Microscopes -SPMs
Scanning Near-field
Optical Microscope
–SNOM
Photon Scanning
Tunnelling Microscope
-PSTM
Atomic Force Microscope
–AFM
G. Binning, C. Quate, C
Gerber (1986)
Magnetic Force Microscope
-MFM
Electrostatic Force Microscope
-EFM
Shear Force Microscope
-ShFM
Scanning Ion Conductance
Microscope
-SICM
Scanning Capacitance
Microscope
-SCM
Scanning Chemical Potential
Microscope
-SCPM
Scanning Thermal Microscope
-SThM
1.4 Atomic Force Microscopy
The atomic force microscope (AFM) is one of the fam
ily of scanning probe
microscopes, and is widely used in biological applications. The AFM uses a
flexible cantilever as a type of spring to measure the force between the tip and the
sample. The basic idea of an AFM is that the local attractive or repulsiv
e force
between the tip and the sample is converted into a bending, or deflection, of the
cantilever. The cantilever is attached to some form of rigid substrate that can be
held fixed, and depending whether the interaction at the tip is attractive or
repulsive, the cantilever will deflect towards or away from the surface.
This cantilever deflection must be detected in some way and converted into an
electrical signal to produce the images. The detection system that has become
the standard method for A
FM uses a laser beam that is reflected from the back of
the cantilever onto a detector. The optical lever
principle is used, which means
that a small change in the bending angle of the cantilever is converted to a
measurably large deflection in the position of the reflected spot.
The attractive or repulsive force between the tip and the sample causes a
deflection of the cantilever towards or away from the sample. As the cantilever
deflects, the angle of the reflected laser beam changes, and the spot f
alls on a
different part of the photodetector. The signals from the four quadrants of the
detector are compared to calculate the deflection signal.
Most AFMs use a photodiode that is made of four quadrants, so that the laser spot
position can be calcula
ted in two directions. The vertical deflection (measuring the
interaction force) can be calculated by comparing the amount of signal from the
“top” and “bottom” halves of the detector. The lateral twisting of the cantilever can
also be calculated by comparing the “left” and “right” halves of the detector.
AFM is particularly suited for biological applications, because the samples can be

4 JPK Instruments NanoWizard®Handbook Version 2.2
imaged in physiological conditions. There is no need for staining or coating, and
no requirement that the sample sh
ould conduct electrons. Therefore high
resolution imaging is possible in physiological buffer or medium, and over a range
of temperatures. Living cells can be imaged, as well as single molecules such as
proteins or DNA. The force contrast gives 3-dimens
ional topography information,
as well as the possibility to access other information such as the mechanical
properties or adhesion.
1.5 AFM cantilevers
Cantilevers are fabricated on chips
What you get when you order cantilevers is a small micro-precision-
machined
rectangular or triangular piece of silicon or silicon nitride with a shiny surface. The
minute cuboid you can see is not the cantilever itself, but the chip that holds the
cantilever. Generally you need a magnifying glass to see the cantilever at
the
narrow side of the chip. Sometimes there are two or more cantilevers attached to
the narrow edges of the chip.
What you are unable to see without a good optical microscope is the tip at the end
of the cantilever. Typically the tip is a few microns
long, and shaped like a pyramid
or a cone. The radius and angle of the end of the tip determines the imaging
quality.
Cantilevers can be thought of as springs.
From physics lessons in school, you may recall that the extension of springs can be
described by Hooke's Law F = - k * s.
This means: The force F
you need to extend the spring depends in a linear way on
the distance sthat you extend it. This linear behavior
just means that if you double
the deflection of the spring, the force is also doubled.
The four damping springs of a car's wheels have a higher spring constant than the
spring in your ball pen. The spring constants of the commercially available
cantilevers vary over four orders of magnitude; cantilevers with spring constants
between 0.
005 N/m and 40 N/m are commercially available. You can deduce the
properties of a cantilever from its outer shape. Thicker and shorter ones tend to be
stiffer and have higher resonant frequencies.
chip
cantilever

JPK Instruments NanoWizard®Handbook Version 2.2a 5
2. Imaging modes
2.1 Feedback and imaging control
The detection system measures the cantilever deflection as the tip is moved over
the surface by the scanning system. It is possible to scan laterally over the surface
without c
hanging the height of the cantilever and just measure this deflection
signal. This is known as “constant height” imaging, but is not the most common
solution. The force applied by the cantilever depends on the deflection, so higher
parts of the sample will experience higher forces in this mode.
It is much more common to use some form of feedback loop to monitor the
cantilever response, and adjust the height of the cantilever accordingly to take
account of the changes in surface height. In this case, th
e base of the cantilever is
moved up and down over higher and lower parts of the sample. All parts of the
sample should now experience the same force, if the system is well set up, and the
maximum force can be controlled.
A “PI” controller is often used
to control the imaging, which means that
proportional-
integral feedback is used. The difference between the setpoint and
actual values is used to change the height position of the cantilever. There are two
values to set how the height position is update
d; a time constant for the integrator
and a value for the proportional gain. These two values control how quickly the
feedback responds to a change in sample height. The actual values need to be
optimized for different imaging conditions, depending on th
e sample topography
and scan speed for example.
If a value of the cantilever deflection is selected then the feedback system adjusts
the height of the cantilever to keep this deflection constant as the tip moves over
the surface. Thus the microscope ima
ges using “constant force” rather than
constant height. When the deflection of the cantilever is used as the feedback
signal, this is usually known as contact mode imaging.
2.2 Amplitude feedback in dynamic modes
There are other ways of operating the syst
em, using dynamic modes where the
cantilever vibrates, and this oscillation of the cantilever is measured rather than the
static deflection of the tip. There are different ways to excite the oscillations -
the
cantilever substrate can be shaken directly,
or a magnetic field can be used to
drive the cantilever itself if it is coated with a ferromagnetic layer. In aqueous
conditions, the most common technique is to drive the cantilever acoustically
through the liquid. In all these cases, however, the measu
rement of the cantilever
oscillation and control systems are similar, and the cantilever is usually driven
close to resonance.
In these dynamic modes, a setpoint amplitude is chosen, and the height adjusted
to match this amplitude through the feedback system. In addition to the height and
error signal information from this constant amplitude mode, the phase between the

6 JPK Instruments NanoWizard®Handbook Version 2.2
drive signal and the cantilever can also be measured. There are several different
dynamic modes, depending on how much of the oscillation
cycle the tip actually
makes contact with the surface.
Intermittent contact mode is widely used, and can give a combination of the
benefits of the other modes. The cantilever oscillates and the tip makes repulsive
contact with the surface of the sample
at the lowest point of the oscillation. The
lateral forces can be much lower than contact mode, since the proportion of the
time where the tip and sample are in contact is quite low. There may be a higher
normal force between the tip and sample when they are in contact, however.
In non-
contact mode the cantilever oscillates close to the sample surface, but
without making contact with the surface. This mode is not so widely used, since
the attractive force means that there is a possibility of the tip ju
mping into contact
with the surface. The capillary force makes this particularly difficult to control in
ambient conditions. Very stiff cantilevers are needed so that the attraction does not
overcome the spring constant of the cantilever, but the lack of
contact with the
sample means that this mode should cause the least disruption.
Another mode is possible, where the tip does not leave the surface at all during the
oscillation cycle. This is something like a dynamic form of contact mode, and is
usually called force modulation mode.
2.3 Another way of thinking about imaging modes
The imaging modes can also be thought of in terms of the forces between the tip
and surface. Generally, when two objects are brought together, the long range
forces are attra
ctive, and the force becomes repulsive when the objects are close
together. The longer-
range attractive forces are usually van der Waals forces and
capillary forces, and then the repulsive interaction takes over at short ranges, when
the objects are in “c
ontact” and the electron orbitals begin to overlap. The situation
may be a lot more complex, however, when electrostatics and other interactions
from soft samples in liquid are taken into account.
Broadly, though, a general curve can be drawn of the tip-
sample force against
distance, and the different operating modes can be matched with different parts of
the curve. An example is shown, which demonstrates the main features. The
curve is a general approximation, however, and different samples will have
very
different curves in practice. Negative force (below the axis) is attractive in this
diagram, and positive force (above the axis) is repulsive. As the tip and sample
approach from a long distance, the attractive force increases to some minimum in
th
e curve. Approaching beyond this minimum reaches a relatively sharp upwards
part of the curve into the repulsive regime.

JPK Instruments NanoWizard®Handbook Version 2.2a 7
Contact and Force modulation modes both stay entirely in the repulsive part of the
curve. In this kind of model of two objects a
pproaching one another, there is no
one point where the objects go from being “not in contact” to being “in contact”,
since they interact in some way over the whole range of distances that separate
them. So “contact mode” is just a shorthand for choosing
a particular value of
repulsive force for the feedback to use to control the height. In contact mode a
single value of the force is chosen and in force modulation mode the force is
varied.
Intermittent contact mode moves between the attractive and repu
lsive parts of the
curve. The maximum force perpendicular to the sample may be higher or lower
than in contact mode, but this is only applied for a short part of the cantilever cycle.
Therefore the sample damage and lateral drag can both be reduced compar
ed with
contact mode for some samples.
Non-
contact mode is the only one that stays in the attractive part of the curve, but
this makes it difficult to control, so it is not often used. In liquid, the attractive part
of the curve may not be so obvious, an
d the oscillation is heavily damped, so it is
not usually possible to use it on biological samples in liquid.
The ranges for the operation of the different modes also vary a lot, so the force
values can overlap for different modes, but this overview
shows the general
operating regimes for the different imaging modes.

8 JPK Instruments NanoWizard®Handbook Version 2.2
2.4 Operation
Contact mode
In contact mode, the tip never leaves the surface, so this mode can be used for
very high resolution imaging, such as atomic resolution of inorganic crystals or
the
images of protein crystals showing the subunits of the proteins. The maximum
vertical force is also controlled, so the compression of the sample can be limited.
The lateral forces as the tip moves over the surface can be a problem in some
situations
, but can actually be an advantage in other situations. The lateral
deflection can give information about the friction force between the tip and the
sample, and can show up areas that may have the same height, but different
chemical properties.
In contac
t mode, the setpoint value is the deflection of the cantilever, so a lower
value of the setpoint gives a lower imaging force.
Intermittent contact mode
In intermittent contact mode, the tip is not in contact with the surface for most of the
oscillation
cycle. The lateral forces can therefore be much lower, and this mode
can be used for imaging samples such as molecules that are not firmly stuck down
on the surface, without moving them around.
The cantilever is usually driven close to a resonance of
the system, to give a
reasonable amplitude for the oscillation and also to provide phase information. The
phase of the cantilever oscillation can give information about the sample properties,
such as stiffness and mechanical information or adhesion. The
resonant frequency
of the cantilever depends on its mass and spring constant; stiffer cantilevers have
higher resonant frequencies.
In intermittent contact mode, the setpoint value is the amplitude of the oscillation,
so a higher setpoint value means less
damping by the sample and hence a lower
imaging forces.
Cantilevers and spring constants
Different imaging modes tend to use cantilevers with different properties. In contact
mode, the deflection of the cantilever is controlled as the tip is scann
ed over the
surface. A softer cantilever means that a lower force can be used to give the same
deflection. Often lower forces give better imaging, so the softest cantilevers are
generally used for contact mode imaging. Many cantilevers are available wit
h
spring constants (k) below 0.5 N/m.
Stiffer cantilevers are usually used for intermittent contact mode, particularly in air.
These generally have a resonant frequency of 200 –
400 kHz, and spring constants
of more than 10 N/m. These stiffer cantilever
s give more stable imaging in air,
since the cantilever is able to break free of the capillary forces when the tip touches
the sample. As there can be very low average deflection values during careful
imaging, the stiffer cantilevers do not necessarily damage the surface.

JPK Instruments NanoWizard®Handbook Version 2.2a 9
The mass of a cantilever strongly influences its resonant frequency and spring
constant. A light cantilever with a high spring constant will have high resonant
frequency. The higher the resonance frequency, the better the high spee
d
response of the cantilever in air.
m
k
π
s2
1
Freq.Re =f.
For intermittent contact mode in liquid, the capillary force is not a problem, and
softer cantilevers are often used. “Contact mode” cantilevers are often used for
intermittent contact mode in
liquid conditions. The resonant frequencies are much
lower, and the damping of the liquid around the cantilever has a strong effect on
the resonance. The resonance of typical soft cantilevers in liquid is usually a few
kilohertz, but in fact the cantilev
er is often driven at a resonance of the liquid cell or
acoustic cavity in this frequency range rather than the actual cantilever resonance.
The spring constant of a cantilever can be estimated from its geometry and the
properties of the material it is m
ade from. The spring constant depends very
strongly on the thickness of the cantilever, however, and this can be difficult to
measure accurately. If a calibrated reference cantilever is available, then the
cantilevers can be pushed against one another to
compare the deflection of one
cantilever by the other. For soft cantilevers another option is to measure the
thermal noise and calculate the spring constant. This is an attractive option, since
the cantilever is not damaged by the measurement, and no ex
tra equipment is
required. These methods are discussed further in Section 4.5
2.5 Phase imaging
During an AFM experiment in intermittent contact mode the cantilever is driven at
some frequency in the kilohertz ra
nge (a few kHz in liquid, or a few hundred kHz in
air typically). The whole cantilever vibrates with the same frequency, but depending
on the condi
tions of the tip and sample there will be some phase shift between the
drive signal and the cantilever movement measured by the lock-in-
amplifier. This
phase shift can be measured and displayed in a phase image.
The phase signal is sensitive to properties of the tip-
sample interaction, and may
show up mechanical information about the sample. Adhesion between th
e tip and
sample or other dissipation of the cantilever energy by a viscoelastic response of
the sample are two mechanisms that may cause a large phase shift of the
resonance. This means that sometimes in phase images two different components
embedded on
a topographically flat sample can be distinguished, as in the example
shown here.
Height and phase images of the same area are shown, with the scale bar of 1
micron in each case. In the height image, there is an area in the lower right hand
corner where
the texture is different. The height changes smoothly, however, and
different regions can not be distinguished within it. In the phase image, there is a
sharp change of phase shift at the edge of the textured area, and there is a sharply
contrasting regi
on within it. This feature is marked with an arrow in the phase
image. This is typical of the case where material property differences show up in
the phase, independently of the height.

10 JPK Instruments NanoWizard®Handbook Version 2.2
The qualit
y of a phase image can be strongly influenced by varying the setpoint in
intermittent contact mode. The phase should also be corrected when the cantilever
is tuned at the start of intermittent contact mode imaging. There are always some
offsets due to th
e system, which do not depend on the sample interaction. The
phase should be set so that it goes through the centre of the resonance, when the
tip is not interacting with the sample. Then when the tip and sample are brought
together, the phase shift due
to the sample can be distinguished. This operation is
described for the JPK AFM and software system in the NanoWizard® User manual.
2.6 Force adjustment in imaging modes
The force applied to the sample can strongly influence the quality of the image,
particularly on soft sam
ples. It is therefore essential to be informed about the
current force.
Contact mode
If the spring constant of the contact mode cantilever is known it is easy to get
information about the force applied to a sample during imaging. In
the JPK
NanoWizard software, the setpoint can be displayed in units of force if the
cantilever has been calibrated. With this value it is possible to adjust the current
force applied to the sample exactly.
Le Grimellec, C. et al.
Biophys. J.
75:695-703
(1998). "Imaging of the
surface of living cells by low-
force
contact-
mode atomic force
microscopy”
Intermittent contact mode
In intermittent contact mode it is also possible to determine the average force
applied to the sample during imaging, using the
vertical deflection signal. A useful
reference for this can be found in:
Vié, V. et al.
Ultramicroscopy
82:279-
288 (2000).
"Imaging of the surface of living cells
by low-force contact-
mode atomic
force microscopy”
The typical forces applied to a samp
le strongly depend on the particular application
and the type of sample:
Scanning of living cells
100 pN
le Grimellec, 1998
1-30 nN Fritz 1994,
Radmacher 1997
Nano-scribing
~ 5 nN, depending on the material
Nano-manipulation < 1 nN in any case
< 50
0 pN to move molecules in
case of H-bonds
~ 100 pN to move molecules

JPK Instruments NanoWizard®Handbook Version 2.2a 11
2.7 Applications
Molecules and membrane surfaces
The highest resolution images are usually obtained on single molecules
immobilized on a surface such as glass or mica. It is possibl
e to study protein
sub-structure and organization, particularly in 2-
dimensional protein crystals. This
can also be successful with membrane proteins, in conditions that would not allow
3-dimensional crystallization for standard structural investigations.
Long
molecules such as DNA or glycoproteins can be studied to measure intrinsic
properties such as the persistence length, or interactions with bound proteins. The
molecules do not need coating or staining and can be imaged in air or liquid.
Molecules
can be studied in action, for example enzymes such as collagenase or
amylase digesting their substrate.
One of the most important factors in high resolution imaging is the sample
preparation, that the sample should be very clean and firmly adsorbed to the
substrate.
DNA
Protein crystal
Cell imaging
AFM has many advantages for cell imaging, since the cells can be imaged at high
resolution in physiological conditions, in buffer or medium. Living cells can be
imaged, and this has led to studies of the e
ffects of different drugs or conditions on
the cell morphology and behavior
. Cells infected with parasites or viruses have
also been studied. The details of the cytoskeleton are usually visible in the images
of live cells, while fixed cells show the high
est resolution features of the membrane
surface. Many possibilities open up if the AFM can be mounted on an inverted
optical microscope, so that DIC or fluorescence images can be compared with the
3-dimensional topographic information, or the maps of the
mechanical properties
of the cell surface.
AFM and optical
Other modes and interactions
Apart from simply imaging, AFM cantilevers can be used in many other modes of
interaction with the surface. The tip can be used to pattern the surface, move and
m
anipulate molecules or parts of the sample, or even to dissect the sample on a
nanometer scale.
Nanolithography is possible, for example by applying a bias voltage and using the
natural water capillary that forms between the tip and sample in air to oxidize
patterns on the surface. With modified cantilever tip surfaces, molecules on the tip
can be patterned onto the surface, or molecules on the surface can be picked up
and moved around. The tip can be used to image normally, and then higher
forces applied to cut through parts of the sample, for example to dissect a labeled
part from a chromosome.
There are as many applications for AFM as there are biological samples, so it is
beyond the scope of this introduction to give a full picture here. The applic
ations
page for the NanoWizard®AFM and the NanoWizard®
image gallery on the JPK
website contain more examples of the range of AFM applications and experiments
that are possible.
www.jpk.com

12 JPK Instruments NanoWizard®Handbook Version 2.2
3. Force spectroscopy
3.1 Introduction
The AFM is best known for its high-
resolution imaging capabilities, but it is also
a powerful tool for sensitive force measurements.
Information about the
sample is also available from measuring the changes while the separation from
the surface is
varied at a single point, rather than by scanning the lateral
position of the tip. In this mode the base of the cantilever is moved in the
vertical direction towards the surface using the piezo and then retracted again.
During the motion, the deflection
of the cantilever and other signals, such as
the amplitude or phase in dynamic AFM modes, can be measured. This is
usually called force spectroscopy.
The AFM tip is able to probe an extremely small interaction area (using a tip
radius in the range of 5-
50 nanometers), and this gives it a high sensitivity to
small forces. The study of interaction forces with the AFM has led to deeper
understanding of many biological and physical processes down to the single
molecule level.
Simple force curves
The data from an experiment is often displayed as a simple x-
y plot. The height
positions for the approach or retract of the cantilever are usually chosen as the x-
axis, and the cantilever property that is being measured is the y-axis.
This is
usually the vertical deflection of the cantilever, which can give a direct measure of
the interaction force. These "force-
distance" plots are often referred to as force
curves.
The basic force spectroscopy curves can be understood by thinking ab
out the
example of a cantilever in air approaching a hard, incompressible surface such as
glass or mica. As the cantilever approaches the surface, initially the forces are too
small to give a measurable deflection of the cantilever, and the cantilever rem
ains
in its undisturbed position. At some point, the attractive forces (usually Van der
Waals and capillary forces) overcome the cantilever spring constant and the tip
jumps into contact with the surface.

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Once the tip is in contact with the sample, it
remains on the surface as the
separation between the base and the sample decreases further, causing a
deflection of the tip and an increase in the repulsive contact force. As the cantilever
is retracted from the surface, often the tip remains in contact w
ith the surface due to
some adhesion and the cantilever is deflected downwards. At some point the force
from the cantilever will be enough to overcome the adhesion, and the tip will break
free.
More complex interactions
Many interesting samples are not
hard and incompressible, and a more general pair
of approach and retract curves will include sample compression, hysteresis and
more complex adhesion between the tip and surface. In liquid, there may not be an
obvious snap to contact in the approach curv
es even over a hard surface such as
mica. Over a soft, compressible sample in liquid, the force curve often shows a
gradual increase in force, without the sharp onset of the interactions seen in air. It
is often difficult to define a single point where t
he tip and sample come into
“contact”, since the initial compression of the surface causes very little deflection of
the cantilever.
The gradient of the repulsive contact region changes as the sample is indented and
the apparent stiffness may change a
s the structure is compressed. For thin
samples on a hard surface, the linear repulsive contact regime may be seen at
large deflections, as the tip may indent the sample enough to feel the supporting
surface below. The contact area will change as the tip
indents a soft surface, so
the actual interactions involved in compression can be hard to quantify, and
different points within the region will experience different levels of compression.
When the tip is retracted from the surface, there is often a hyst
eresis seen, if the
sample is not perfectly elastic, and many different adhesion responses can be
observed. In some cases, the cantilever pulls the tip free in stages, such as when
there are long molecules in the sample or on the tip. Extendable contacts
are made
between the tip and sample, so that as the base of the cantilever retracts, the tip is
deflected down towards the sample until the force is strong enough to break the
contacts. Different molecules or parts of the sample may adhere and each part
may be broken separately, or together. These situations produce a variety of
adhesion events, and successive force curves can show very different responses.
The force curves are often repeated at different locations to build up a map of the
tip-surface i
nteraction, or repeated many times at the same point to give a full
statistical understanding of the interaction.
3.2 Data processing for analysis
The most direct way to plot the data shows the movement of the piezo during the
force curve (as a distance)
against the deflection of the cantilever. The deflection is
measured by an optical beam deflection setup which delivers an electrical signal (in
Volts, as the signal from the photodiode) that is proportional to the cantilever
deflection. In the example below,
Approach (red) and retract (blue) curves are both
plotted on the same axes.

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Typical interaction for
an uncoated
hydrophilic cantilever in air
approaching a hard incompressible
hydrophilic surface (e.g. glass or
mica). Hy
drophilic surfaces are
covered with a thin water layer in
ambient conditions. These layers
join when the tip and sample are
close together, forming a capillary
neck between them and hence a
strong adhesion.
Calibration of the cantilever deflection
The deflection of the cantilever spring is directly proportional to the tip-
sample
interaction force, but there are two measurements required to convert the
photodetector signal into a quantitative value of force. The first stage is to calibrate
the distance tha
t the cantilever actually deflects for a certain measured change in
photodetector voltage. This value depends on type of cantilever, but also on the
optical path of the AFM detection laser, and will be slightly different each time the
cantilever is mounte
d in the instrument. Once the deflection of the cantilever is
known as a distance, the spring constant is then needed to convert this value into a
force, using the well-known Hooke's law.
F = - k * x
x = cantilever deflection
(units of distance)
k = spring constant
F = deflection force
A force curve between a plain cantilever tip and a bare hard substrate is used to
determine the sensitivity of the experimental setup. This is a measurement of the
deflection of the tip in nanometers for a given moveme
nt of the detection laser on
the photodetector. The repulsive contact region, where the deflection rises steeply
upwards, is linear for a hard surface and tip. Therefore the software can easily
determine the factor for converting Volts into nanometers.
This measurement can
then be used for calibrating the applied forces when the samples of interest are
investigated. The sensitivity can then also be used to set the oscillation amplitude
in intermittent contact mode as actual nanometers of oscillation.
The gradient chosen for sensitivity
measurements and the baseline
offset for the deflection are both
marked on this plot.
Since the hard repulsive interaction
regime is used for the sensitivity
measurement, the force curves ar
e
often actually done at the end of the
experiment to avoid damaging the
tip.
The example above shows the two regimes useful for calibrating the deflection.
When the cantilever is far from the surface, the interaction forces are virtually zero
(the flat
part of the curve on the right hand side). This offset , which may be due to
the initial settings of the equipment, or to thermal drift, should be subtracted from all
the deflection data in order to calculate the true interaction force.
On a hard surface:
Change in cantilever deflection =
change in piezo height

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The other linear region, on the left hand side of the plot, is where the tip is resting
on the surface. If the surface is not compressed by the cantilever forces, then the
change in the piezo he
ight (known from the height calibration in nm) is equal to the
cantilever deflection (measured from the photodiode in Volts).
The sensitivity is the conversion
factor (nm true deflection per Volt
measured deflection) needed to
convert the photodiode deflec
tion
into units of length.
The example from above has been
shifted here to give a zero baseline.
The sensitivity (measured from the
curve above as 22 nm/V) has been
used to convert the deflection into
units of length (nm).
The deflection values here a
re now
ready to be converted to units of
Force (N).
Correction of the height for the cantilever deflection
The plot so far has used an x-
axis of the cantilever height directly
measured from the piezo position. For quantitative analysis of indentation
or
stretching, however, the cantilever is obviously deflected from its
equilibrium position. The deflection should be taken into account to extract
the true tip position relative to the surface. The deflection can then be
plotted against the tip-sample sepa
ration, rather than the piezo height.
Now that the deflection is in units of length, it can be subtracted from the
piezo height at each point to correct for the tip position.
After the sensitivity conversion, the straight line part of the repulsive
int
eraction (left hand side of the curve above) has a gradient of 1, since this
is the basis of the sensitivity calculation. Once the height scale is
corrected, this becomes a vertical line (as seen in the curve below). This is
because the tip-sample separa
tion remains constant at zero, and the action
of the piezo movement merely increases or decreases the force.
The example from above has had
the x-
axis corrected for the tip
deflection. The x-
axis is now the
true tip-sample se
paration, rather
than the piezo height measured
directly.
For quantitative force measurement, the spring constant of the cantilever must be
calibrated, so that the nanometers deflection of the cantilever can be converted into
actual force values. There ar
e various different ways of calibrating spring constants
of cantilevers, depending on the equipment that is available. See Section 4.5
for
more details. The example above has had the deflection multiplied by
the spring
constant to express the deflection as a force and would now be ready for analysis.
Retract
Approach

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3.3 Applications
There are a huge number of potential applications of force spectroscopy, ranging
from nano-mechanical investigations of elastic properties to pro
tein unfolding and
investigations of single chemical bonds, so only a brief overview is possible here.
Virtually any sample can be studied using force spectroscopy, and different
interactions or tip coatings and shapes will all give complementary informat
ion
about the sample.
Molecular interactions
When molecules are attached to the tip and/or the sample, the stretching, unfolding
or adhesion of single molecules can be studied. Long chain molecules, such as
DNA or dextran can be stretched between the ti
p and the sample. The stiffness,
persistence length and internal molecular transitions can be studied. The melting
transition in DNA can be seen as the backbone rearranges under raised tension.
Molecules with complex 3-dimensional structure, such as m
any proteins, can be
unfolded in a controlled way so that the structural units can be investigated. Titin
and bacteriorhodopsin are examples of proteins that have been intensively studied.
Membrane proteins can be pulled out of the membrane, and the “pop
ping” out of
individual alpha-helices has been seen.
The adhesion can be measured between molecules attached to the tip and to the
sample. These can be antibodies and antigens or other receptor-
ligand pairs. The
adhesive forces can be measured and mapp
ed over the surface, and information
extracted about the energy and kinetics of the binding. These techniques have
also been applied to the binding between complementary and mismatched DNA
strands.
Cellular mechanics and interactions
The viscoelastic r
esponse of cells can be studied by using the cantilever to indent
the cell. On living cells, the changes in mechanical properties can be seen as the
cell divides, or when drugs such as cytochalasin, which disrupts the cytoskeleton,
are added. Mechanosensi
tive cells such as osteoblasts or ear cells can be
stimulated with the cantilever, and the response monitored. Adhesion maps over
the surface are also possible to investigate the distribution of receptors.
The following table gives an overview of some i
nteractions, and the part of the
force curves that they are measured in.