Biomedical Engineering Reference
In-Depth Information
2
m
T
Q
Q
(2.24)
,
ln
ln
b
RT
RK
m
0
where
K
(
T
) and
D
(
T
) are the rate constant and diffusivity at
T
.
We note that Eq. (2.23) in the general kinetic setting, i.e.,
without Eq. (2.22) substituted in it, is similar to Eq. (2.1) in Ref.
[63], containing a misprint, the “inverted” factor
m
m
m
R/
E
des
in the right-
hand side. Equations (2.23) and (2.24) can be used for TPD spectra
analysis, for defining the diffusion characteristics of sorption
processes, including processes I-IV.
It is also possible to estimate
a
L
using the formula [10]
1 / 2
D T
(
)
D
T
L
m
,
(2.25)
b
where ∆
T
is the full width at half maximum (FWHM) of the TPD
peak.
The diffusion nature of the limiting stage of the process can be
confirmed by studying the dependence of temperature
T
of the TPD
m
peak maximum on
L,
for a given material heating rate (
β
). In other
words, this requires the evaluation of the intercept ln(T
) on
the vertical Kissinger axis (see Fig. 2.9c and the inset in Fig. 2.10) as
a function of
QL/RD
0
L
on the diagram representing a linear dependence of
T
2
ln(T
, (see Eq. (2.24)).
In particular, studying chemisorption processes I or II, it is
advisable to carry out TPD experiments with samples of various
thicknesses, because diffusion removal of the adsorbate from the
samples free surface can be a limiting factor, i.e., the thickness of
sample may be evaluated by considering the characteristic diffusion
path
/
β
) on 1/
T
m
m
If hydrogen desorption is limited not by the stage of adsorbate
removal by diffusion but by the “chemical” kinetic stage, a rate
constant
L
.
K
(
T
(
t
)) in Eqs. (2.20)-(2.24) and the pre-exponential factor
K
are described by the Polanyi-Wigner transport equation [70]; it
is then advisable to use the kinetic characteristic
0
E
des
instead of
Q
. In
a
most cases, the typical
K
values for different chemical reactions are
0
9
−1
not lower than 10
[68, 70], and such a circumstance simplifies
the identification of the process nature.
The difference in the adsorption and desorption activation
energies (
s
E
E
des
des
and
, respectively) is the enthalpy of the sorption
a
a
process [68],
