Biomedical Engineering Reference
In-Depth Information
des
value can be determined [26, 54, 61-64, 70] from the
linear dependence of ln(
The
E
a
2
, the so-called Kissinger
coordinates (see Fig. 2.9c and the inset in Fig. 2.10). The resulting
transport
T
/
β
) on 1/
T
m
m
des
has been identified [63, 70]
as corresponding to the thermodynamic characteristic ∆
characteristic
−
E
a
ads
,
H
representing the enthalpy heat of hydrogen adsorption by the
material.
In such a context, it seems appropriate to examine in some
detail and substantiate the method used to determine, starting from
TPD spectra, the diffusion) characteristics of hydrogen sorption by
carbon materials, in case of the different chemisorption processes
(I-IV, see Table 2.1).
If the limiting stage for thermal desorption process is the removal
by diffusion of hydrogen from the material heated in a vacuum at
the constant rate
the process may be formally regarded
as a first-order reaction and the hydrogen desorption rate can be
described [68, 71] by the equation:
β
= ∂
T/
∂
t,
X t
( )
u
( )
t
K T t
(
( ))
X t
( ),
(2.20)
t
where
) is the average concentration of diffusant adsorbate
remaining in the material subjected to heating,
X
(
t
K
(
T
(
t
)) is the
rate constant of desorption at the material temperature
T
(
t
), and
t
is
the time during which 63% of the adsorbate leaves the material.
Considering the following equations:
the heating time
.
The relaxation time of the process (
τ =
1/
K
)
Q
K T t
(
( ))
K
exp
,
(2.21)
0
RT t
( )
1
D
0
K
,
(2.22)
0
2
L
0
where
are the pre-exponential factors of the rate constant
and the relaxation time of the diffusion process of hydrogen desorption
from the material [68, 71],
K
and
τ
0
0
are the effective diffusion-activation
energy and the pre-exponential factor of hydrogen diffusivity in the
material (Table 2.1), and
Q
and
D
0
is the characteristic diffusion length for
hydrogen removal process [68, 71]. The condition for the maximum
desorption rate at
L
T
,
∂
u
/∂
T
= 0, yields
m
2
T
Q
QL
2
(2.23)
,
m
b
RT T
(
)
RT T
(
)
m
m
