39
𝐸′′(𝑓) =
1
2
𝐹
0
ℎ
0
sin(𝛿)
(1 − 𝜈
2
)
√ℎ𝑅
where
δ
is the phase lag between oscillations of indentation and load (see right side of
. tan(
δ
)
is the dissipation (damping) factor which is the ratio between loss and storage modulus. Materials with a
higher damping ratio than 1 are considered to be viscoelastic fluids and below 1, viscoelastic solids. Also,
viscoelastic solids have a higher storage modulus than loss modulus at low frequencies which switches at
higher frequencies while it is the other way around for viscoelastic fluids. Complex modulus can be
calculated according to this formula:
𝐸
∗
= √𝐸’
2
+ 𝐸
′′2
If the amplitude of the input oscillation is small enough, the measurements can be considered within the
material linear viscoelastic region (LVR). Within the LVR, the response is assumed to be independent of
the input amplitude and sinusoidal. Furthermore, when selecting the amplitude of oscillations, the depth
should be considered due to the curvature of the sphere, as it is assumed that the contact area does not
change during oscillations, so that
ℎ
0
ℎ
≪ 0.25.
The performance of the DMA can be evaluated in the
DataViewer by comparing the amplitude which was measured with the amplitude which was set in the
experiment and by looking at the R-squared values of cosine fits.
Figure 31:
DMA data analysis in DataViewer.
3.4.7 Matrix scan
Instead of performing a single indentation, an automated grid scan can be configured to obtain the map
of mechanical properties. Parameters that can be selected are these:
-
the number of points in the X and Y directions (
“
# X
”
,
“
# Y
”
);
-
distance between indentation points in the X and Y directions (
“
dX
”
,
“
dY
”
);
-
distance by which the probe is lifted up between indentations “Z at XY move (
µ
m)”;
-
automatic find
surface before each indentation “Auto find surface”;
-
“
Coarse within safe zone while maintaining the number of points
” –
if checked, it will decrease
the distance between indentation locations to keep the number of points and if unchecked,
