Biomedical Engineering Reference
In-Depth Information
is therefore useful to examine a possibility of the data interpreting
in Ref. [26], employing the characteristics of dissociative-associative
hydrogen chemisorption (process I, Table 2.1) and using the method
described in the previous section.
Using the experimental dependence [26] of
T
of the peak B
m
on
β
(Fig. 2.9c) and the formula (2.24), we can obtain a
K
value
0
approximately equal to 2 × 10
2
s
-1
, which is obviously not a typical
9
-1
value of the frequency factor (
) of the rate constant in the
Polanyi-Wigner transport equation for chemical reactions [68, 70].
Hence, we may assume that the limiting step in the process is the
diffusion, step, not the kinetic one. Using the “diffusion” expression
(2.22) for
K
≥ 10
s
0
≈ 40 µm,
which is obviously the total thickness of the single-wall nanotube
samples [26]. A value
K
and taking
D
from Table 2.1, we obtain
L
0
0I
≈ 70 µm has been obtained [10], using
Eq. (2.25). This implies that the thermal desorption (peak B) from a
single-wall nanotube samples [26] is limited by hydrogen diffusion
to their external surface, which formally manifests itself as the first-
order reaction. Then a characteristic diffusion path
L
corresponds to
the total thickness of the samples, and the diffusivity is described by
the equation and the characteristics
L
D
, Q
, and
D
for chemisorption
0I
I
I
process I (Table 2.1).
The absolute values of hydrogen concentration absorbed by
nanotubes (about 5-10 wt%, or
/C ≈ 0.3-0.7) at 133 K and
40 kPa given in Ref. [26] for the TPD peak B correspond to the
maximum (carbohydride) concentration of adsorbate (
X
= H
2
≈ 0.5,
Table 2.1) on all external and internal graphene surfaces of the single-
wall nanotube samples, where almost all carbon atoms are theoretically
[9, 29] at the surface (C ≈ C
X
Im
s
). Obviously, in the sorption monolayer
there is no place for the adsorbate corresponding to the TPD peak A,
which sorption capacity is of the same order as that for peak B, as it
follows from a comparison of the areas below the peaks in Fig. 2.9a.
In such a context, it is worth noticing that the theoretical value
of the total (inner and outer) specific surface area of individual
nanotubes or their bundles (
tot
3
2
−1
) may be considered
as upper limit for carbon-based materials only if the graphene layers
do not have a high concentration of vacancies, discontinuities, holes
or other defects [9, 29]. Eletskii [9] noted that the entire mass of
a single-wall nanotube is contained in the layers surface. In other
words [29], the percentage of the surface carbon atoms in bundles
of the single-wall nanotubes may reach about 100%, i.e.,
C ≈ C
S
≈ 2.6 × 10
m
g
th
.
This approach, however, does not take into account the difference
s
