Biomedical Engineering Reference
In-Depth Information
to match cantilever stiffness [N/m] to sample stiffness [N/m
2
] to measure
mechanical properties accurately is not straightforward to obtain:
E
a
of
polystyrene did not approximate the known stiffness of this material
except for the stiffest cantilever, and
E
a
of polydimethylsiloxane
fluctuated within an order of magnitude of known stiffness for all
cantilevers considered.
Table 3-2. Apparent elastic moduli of three materials inferred from AFM-enabled
indentation with cantilevers of varying stiffness
k
: glass (
E
~ 70 GPa); polystyrene or
PS (
E
~ 2.7 GPa); and polydimethylsiloxane or PDMS (
E
~ 1.8 MPa). Courtesy of
D. Nikova and K. J. Van Vliet. All values in MPa.
k
:
0.01 N/m
0.03 N/m
0.1 N/m
0.5 N/m
2 N/m
42 N/m
Glass
19.20 ± 8.44 53.03 ± 10.13 840.71 ± 90.06 1850 ± 670
2220 ± 950
57880 ± 6200
PS
3.19 ± 2.60
18.95 ± 7.60
172 ± 4.06
244.6 ± 79
338.96 ± 83
2400 ± 370
PDMS
5.42 ± 4.06
2.40 ± 1.95
—
8.54 ± 2.42 11.13 ± 2.07
14.96 ± 1.66
3.4.3.
Objective identification of mechanical contact point
Another key difference between instrumented indentation and AFM-
enabled indentation is the inherent challenge of identifying the initiation
of mechanical contact in the latter approach. As the force transducer
(cantilever) is mechanically compliant, the probe deflects away from
the surface prior to the establishment of firm contact that deforms the
sample surface. Post-processing methods to identify this point include
graphing log(
P
) vs. log(
h
) to determine the point at which large load
fluctuations cease and actual loading commences.
10
This method still
requires subjective choice of the threshold fluctuations, and the
calculated mechanical properties are sensitive to this choice.
An alternative approach, for the specific case of spherical elastic
contact, expresses the Hertzian contact equation (see
Chapter 5
) to be
linear not in applied load
P
but in resulting indentation depth
h
11
:
2/3
4
ER
31− ν
P
2/3
=
a
−
h
(3-3)
()
2
In this way, the slope of
P
2/3
vs. h provides an estimate for
E
that
is independent of contact point determination
a
, though still requires
accurate estimate of probe radius
R
and Poisson's ratio
ν
.
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