Biomedical Engineering Reference
In-Depth Information
cantilever and sample. The spring constants
k
cant
of the cantilever can be determined
via the resonant frequency
f
0
of the freely oscillating cantilever (Sader et al., 1995),
while their quality factors
Q
can be obtained from resonance curves (Ebeling et al.,
2006b).
To illustrate the main differences between the “conventional” AM-mode and the
presently much less used FM-mode in air, we present two spectroscopy experiments
in Figure 2.13, where the oscillating cantilever was approached to and retracted from
a mica surface in both modes. The corresponding spectroscopy curves are presented
in Figures 2.13a and 2.13b. The measured quantities in the AM-mode are amplitude
and phase, whereas amplitude and frequency shift are recorded in FM-mode.
As already discussed by others (Anczykowski et al., 1996; San Paulo & Garcıa,
2002; Holscher & Schwarz, 2007), the amplitude and phase shift curves recorded in
AM-mode sometimes show a significant hysteresis during approach and retraction.
At specific positions (marked by arrows in Figure 2.13a), the oscillation becomes
(a)
(b)
22
(c)
22
6
4
2
0
-2
-4
-6
-8
8.5 N/m
20
20
18
18
16
16
Approach
Retraction
Approach
Retraction
14
14
7 nN
12
0
12
30
20
10
120
100
80
60
40
20
0
45 eV/nm
-50
0
Approach
Retraction
-100
-10
-20
-30
-150
-200
-40
02468 0 2 4
Piezo movement (nm)
02468 0 2 4
Piezo movement (nm)
0
2
4
6
8
Rel. distance (nm)
FIGURE 2.13
Examples of “spectroscopy measurements” obtained on mica in ambient con-
ditions. (a) Amplitude and phase versus distance curves in the tapping mode. The instabil-
ities during approach and retraction cause a hysteresis. (b) Such a behavior is not observed
in the constant-excitation mode where the approach and retraction curves of the amplitude
and frequency shift are identical within the noise limit. The parameters of the cantilever
were
f
0
=
465. (c) Using the algorithm described
in the text, we reconstruct the tip-sample potential and force from the data sets shown in
(b). The interaction force decreases until it reaches a minimum of
167 224 Hz,
k
cant
=
37
.
5N/m, and
Q
=
7 nN and increases
again with a slope of 8.5 N/m. The origin of all x-axes has been arbitrarily set to the left of
the graphs.
−
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