Biology Reference
In-Depth Information
of the AFM to an inverted optical microscope facilitates this task. Transmitted
light microscopy, specially phase contrast or Normarsky microscopies, allows
us to visualize cells and even organelles within cells and to easily position
the AFM tip on the desired location. In addition, luorescence microscopy is
also suitable for visualization of luorescently tagged molecules immobilized
on the substrate or expressed on cells.
Figure 11.2b
shows an optical
micrograph showing an AFM cantilever and a monocytic cell immobilized on
the substrate.
Contact mode imaging consists of scanning the sample with the tip in the
horizontal plane by applying a constant compressing force. The vertical piezo
continuously corrects its position to account for the changes in topography
of the sample and then keep the applied force constant. This continuous
correction leads to the topographic image of the sample surface.
11.2.2 Force Spectroscopy
In the force spectroscopy mode or, simply, force mode, the cantilever is moved
in the vertical direction in approaching and withdrawing cycles
(
Fig. 11.2b
).
The cantilever starts away from the sample and the piezo approaches the
tip making contact until a set force is reached, then it withdraws away to the
initial position. During approach and retraction, the vertical displacement
(
) and the cantilever delection is monitored generating what is known
as a force-distance (
z
) curve, or just a force curve
(
Fig. 11.2b
)
. Force
measurements require routinely calibrating the sensitivity of the optical
detection system (optical lever sensitivity, OLS) and the spring constant of
the cantilever before each session. The OLS is calculated from the slope in
a force-distance curve obtained on a hard substrate (such as glass). When
pressing on a hard substrate the delection of the cantilever is the same as the
displacement of the piezo, thus we can transform the voltage signal detected
by the photodiode into delection of the cantilever. To calibrate the spring
constant of the cantilever, different methods exist. The most widely used
is probably the thermal luctuations method.
F-z
17
It consists of measuring the
mean square displacement <
> of the cantilever due to thermal luctuations.
Assuming the cantilever response to be linear and with a single degree of
freedom, the equipartition theorem can be applied to equate the average
elastic potential energy <
d
2
E
> =
k
<
d
2
>/2 to the thermal energy
k
B
T
/2,
k
B
being
the Boltzmann constant and
, the absolute temperature. Doing so, we can
estimate the spring constant as
T
>. Another common calibration
method is the Sader method, which takes into account the geometry and
material properties of the cantilever.
k
=
k
B
T
/<
d
2
The uncertainty in force due to
systematic errors in the calibration of the system has been estimated to be
18
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