Biomedical Engineering Reference
In-Depth Information
bonding and thus also lead to significant adhesive effects at small
contacts; for the case above such secondary bonding influences would
lead to
N , still comparable to the deformation forces.
Consideration of other interactions between the tip and the surface, such
as those arising from electrostatic effects or capillary meniscus effects,
lead to the same conclusion: Contact measurements using AFMs will be
significantly influenced, if not dominated, by surface force effects and
such contacts will be more adhesion like than indentation like.
A key feature of surface forces is that their influence can extend
beyond the surface and hence they can deform the probe spring prior to
contact (as opposed to the forces associated with material deformation,
which can only affect the spring once contact has been made). For the
very stiff nanoindentation probe springs, this effect is negligible, but for
the much more compliant AFM cantilever probe springs this effect, as
noted above, can be significant. Hence, just as in a predominantly
indentation-like contact formed by a nanoindenter, the force imposed by
the indenter is balanced against those associated with deformation of the
body, in a predominantly adhesion-like contact formed by an AFM the
surface forces are balanced against those associated with deformation of
the cantilever.
F
a, surface
10
μ
4. Dynamic Behavior
The difference in the stiffness values of the probe springs for
nanoindentation and AFM contact instrumentation is also reflected in the
dynamic properties of the spring. In the absence of other influences (such
as contact forces) the tip behaves as a simple harmonic oscillator with
motion about the imposed equilibrium position given by
ω
S
t
) (2-17)
where
a
S
is the free amplitude of vibration,
t
is time, and ω
S
is the
characteristic free resonant frequency of oscillation. The resonant
frequency is related to the probe stiffness by
w
=
s
+
a
S
sin(
ω
2
=
k
S
/
m
∗
(2-18)
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