Biomedical Engineering Reference
In-Depth Information
k
/
m
(3-1)
where
f
o
is the cantilever first mode of resonance and
m
is the effective
cantilever mass. As the amplitude of oscillation is also directly related to
k
, the cantilever mass value can be obviated. Note that this is an estimate,
in that AFM cantilevers are not simple harmonic oscillators, but in fact
have several other modes of deformation including torsion. Signal drift
rate is measured simply as the change in cantilever deflection with time,
at least over times that are comparable to the experiment duration. The
inherent sensitivity of AFM cantilevers requires thermal stability to
minimize deflection fluctuations.
2
π
f
o
=
3.4.2
. Effects of cantilever stiffness on inferred mechanical properties
The choice of cantilever has a significant effect on inferred mechanical
properties of the biomaterial sample, due to the fact that cantilever
deflection represents an additional mode of mechanical energy
dissipation. Simply put, if the cantilever is much stiffer than the sample,
it will penetrate the sample without deflecting at the free end, and thus no
indentation force or depth will be registered. Conversely, if the cantilever
is much more compliant than the sample, it will deflect through its full
range without penetrating the sample, and thus no indentation depth will
be attained as required for calculation of properties. The obvious
recommendation is to choose a cantilever of “correct” stiffness, one that
is neither too stiff nor too compliant. However, if the biomaterial sample
is in fact a material of study that is not yet well characterized, this
selection becomes iterative. At best, a range of cantilever stiffnesses may
be employed to assay the range of mechanical properties. At worst, a
single cantilever stiffness is chosen and the reported properties of the
sample in fact reflect the stiffness of the sample and the cantilever.
When the AFM cantilever is in contact with a compliant surface (as
compared to the rigid surface on which OLS was calibrated), the
cantilever oscillation energy is dominated by thermal fluctuations on the
order of
k
B
T
, where
T
is temperature and
k
B
is the Boltzmann constant. It
is this so-called “thermal noise” that limits the resolution of AFM
cantilevers. Thus, the root-mean-square variation <
P
> or load signal
resolution depends on both temperature and cantilever spring constant
k
:
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