Biomedical Engineering Reference
In-Depth Information
P
=
kk
T
(3-2)
B
and is approximately 5 pN for a cantilever of
k
~ 0.01 N/m. However, in
practice, the bandwidth of signal acquisition can further decrease load
resolution of such compliant cantilevers to ~10 pN; this is because the
cantilever resonant frequency is within the measurement bandwidth.
The standard equations of elastic contact analysis assume negligible
adhesion, whereas JKR-type theories of elastic contact exploit probe-
surface adhesion. In practice, with biological samples there is typically a
measureable degree of adhesion when the charged, proteinaceous sample
surface is displaced from the charged, synthetic cantilevered probe. For
experimental analyses that assume negligible adhesion, probe
interactions can be minimized by conducting experiments in ionic
buffers such as 150 mN phosphate buffered saline.
As noted, the mechanical stiffness of AFM cantilevers can adversely
affect the inferred mechanical properties of the indented material,
including the
apparent
elastic modulus of the biomaterial surface
E
a
. For
example, when the stiffness of a μm-scale bundle of actin protein
filaments is analyzed with sharp (
R
~ 25 nm) probe cantilevers of
k
1
=
0.01 N/m and
k
2
= 0.5 N/m to the same depth
h
~ 15 nm, the inferred
E
a
differ by an order of magnitude (
E
a1
= 2.4 ± 1.0 MPa; and
E
a2
=19.6 ± 4.2
MPa, reporting one standard deviation of the average value). Unless this
filamentous bundle were also characterized by independent mechanical
experiments, it would not be possible to rule out either data set. Instead,
one could analyze other synthetic materials for which
E
is established by
that
E
a
of polydimethylsiloxane elastomer (
E
~ 1.8 MPa), amorphous
polystyrene (
E
~ 2.7 GPa), and glass (
E
~ 70 GPa) also depend on AFM
cantilever stiffness. As in the case of a biological material,
E
a
of these
synthetic materials increased with increasinig
k
, and the compliant
cantilevers typically employed for high-resolution imaging of biological
samples failed to accurately measure
E
a
of materials of ~2 GPa and
higher. This indicates that AFM cantilevers used to obtain spatial
information and sample topography on hydrated biomaterials may in fact
be too compliant to accurately infer mechanical properties of these
imaged regions. Further, the reasonable supposition that one should aim
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