Lecture 7: Measurement of
Forces on the Nanoscale
What did we cover in the last
lecture?
Interactions between macroscopic
bodies.The effects of geometry on
dispersion interactions
Determining the energy scale of
dispersion interactions (Hamaker
constant, A~ 10-20 J)
Range of interactions between
macroscopic bodies can be up to
100nm
Magnitude of forces between
macroscopic bodies (pN to nN )
In this lecture…
How do we measure nanoscale forces?
Atomic Force Microscopy
Cantilever deflection method
Detection technique
Useful references
Intermolecular and surface forces,
J Israelachvili (Academic Press)
The Feynman Lectures on Physics,
Feynman, Leighton and Sands
(Addison Wesley)
Scanning Force Microscopy,
D. Sarid (Oxford Series in optical and
imaging sciences)
Scanning Probe Microscopy and
Spectroscopy: Methods and
applications
R. Wiesendanger (Cambridge
University Press)
Forces at the nanoscale
Forces between nanoscale objects typically occur in the
range 1pN-1nN and can be difficult to measure.
Ideally we need a measurement system where the change in
applied force gives a linear response in the measurement
device (although this is not necessary)
Recall
z
-Fspring
Fspring  kz
Atomic force microscopy
In the first year, you considered how atomic force
microscopy can be used to image the surface of a sample
20mm x20mm
Contact
mode
Non-contact
(tapping) mode
AFM can also be used to measure
forces…
The AFM cantilever bends/deflects in response to an
applied force
l
The force, F, on
the cantilever is
z
F  kz
F
where
3EI
k 3
l
E= Youngs Modulus of cantilever (Pa)
I= Geometric moment of inertia (m4)
(See OHP)
Problem I
Calculate the spring constant of a 200 mm
long, 10 mm wide and 1 mm thick AFM
cantilever having a rectangular cross section
and a Young’s modulus of E=150 GPa.
Hence determine the displacement of the
cantilever when a force of
a) 1picoNewton
b) 1nanoNewton
is applied to it.
How do we detect the deflection of
the cantilever?
The deflection is
detected by reflecting a
laser beam off the back
of the cantilever.
Laser light
(633nm)
The light is collected on a split
photodiode detector
Photodiode
current
Interpreting the photodiode signal
The photodiodes are connected to a differential current
amplifier which produces a signal that is proportional to the
difference in photocurrents generated by the two diodes
isignal  i1  i2
If isignal > 0 force acts upwards
If isignal < 0 force acts downwards
Can measure 0.1nm cantilever displacements
Calibrating the cantilever spring
constant I: hang weights off the end
In practice, it is often difficult to calculate the spring constant
of a cantilever, so it has to be measured!
One way to do this is to place
objects of known mass on the
cantilever and measure the
deflection z (or current signal
isignal)
However, this is tricky and can result in contamination of
the cantilevers!
Calibrating the cantilever spring
constant II: Thermal tuning
A more elegant method involves measuring the natural
response of the cantilever in response to thermal motion
z
The mean square displacement of the cantilever <z2>
is obtained from the noise signal and used in
combination with equi-partition theory (more on this in
Thermal Physics ) to give;
k BT
k 2
z
How small a force can we detect?
Typical cantilever spring constant: 0.01-50 Nm-1
We can routinely measure cantilever displacements of ~
0.1nm
We can therefore measure forces > 10 pN with
relative ease using AFM
Example 1: Force-distance curves
AFM can be used to map out the dispersion
(and other) forces as a function of the distance
between sample and tip
Surface
http://www.nanoscience.com/
Example II:Protein (un-)folding
AFM is routinely used to map out the forces associated
with the folding and unfolding of individual protein
molecules
blenderartists.org/forum/s
howthread.php?t=109254
G. Bao & S. Suresh
Nature Materials 2, 715 - 725 (2003)
Summary of key concepts
Atomic force microscopes can be
used to measure forces
F
The spring constant of an AFM
cantilever is determined by its
material properties and its physical
dimensions
A split photodiode arrangement is
used to detect deflections and to
measure forces with >10pN
precision
F  kz
3EI
k 3
l