Biomedical Engineering Reference
In-Depth Information
molecules. But while heating (TD process), some blisters are broken
due to the increase of the pressure up to the tensile strength of the
graphite layers forming the blister [5]. The number of etch-pits after
TD (Fig. 2.22b) is considerably smaller than the number of previously
existing blisters (Fig. 2.21c), showing that not all the blisters are
broken leaving behind an etch-pit, and that, under TD heating, some
blisters merge and/or coagulate.
By the analysis of data from Fig. 2.21 and of other results,
an average blister radius of 25 nm and a height of 4 nm was
found [5]. Considering a blister as a semi-ellipse, a blister area
S
-11
2
-19
3
) have been
evaluated. The amount of retained hydrogen in this sample is
≈ 2.0 × 10
cm
and a volume
V
≈ 8.4 × 10
cm
b
b
Q
≈ 2.8
14
2
× 10
(Fig. 2.22a) and the number of hydrogen molecules
captured inside the blister turns out to be (
H
/cm
2
[5].
Thus, within the ideal gas approximation, the pressure for a
single blister at room temperature is
Q S
) ≈ 5.5 × 10
3
b
7
Pa, estimating an accuracy comparable with the order of magnitude.
During a TD heating at 1000 K, the pressure can reach a value
P
P
≈
k
(
Q
S
)
/V
≈ 2.5 × 10
H2
b
b
Pa, which can be enough for some blisters to get
broken, especially in the presence of defective walls. In Ref. [6],
≈ 8.5 × 10
7
H2
probably for a misprinting, estimated pressures lower by one order
of magnitude have been reported. The hypothesis of misprinted
values is confirmed by the fact that in previous similar studies [7-8],
pressure values of
P
≈ (30-50) MPa have been declared by the
H2
same authors.
It is relevant to note that values [10] of hydrogen fugacity as
a function of pressure (up to 1.9 × 10
8
Pa) and temperature ( in
the 223-1000 K range), estimated using the Abel-Noble equation
of state, show that the ideal gas approximation (used above) can
be used under the conditions of [5] within an order-of-magnitude
accuracy.
In Ref. [5] the pressure values are compared with known
experimental values of tensile and compressive strengths for
graphite, 10
Pa, respectively. But it seems more
reasonable to use recent data on elasticity, strength and toughness
of carbon nanorods and nanotubes [11-13], data on stress-strain
state of multiwall carbon nanotube under internal pressure [14],
and, for instance, data on carbon onions as nanoscopic pressure cells
for diamond formation [15]. In these studies [11-15] considerably
higher values (by several orders of magnitude, in comparison with
7
Pa and 3 × 10
7
