Environmental Engineering Reference
In-Depth Information
Figure 5.13
Electronic states which determine the electron attachment process involving vibra-
tionally excited molecular states.
Here (
AB
)
denotes an autodetaching state of the negative ion and
AB
denotes
a vibrational excited state of the molecule. The probability of attachment after for-
mation of the autodetaching state (
AB
)
is proportional to
exp
"
#
,
R
R
c
Γ
(
R
)
dR
„
v
(5.148)
where
(
R
) is the width of the autodetachment level,
v
is the relative velocity of
the nuclei,
R
is the distance of the electron captured into the autodetachment level,
and
R
c
is the distance at which the states intersect. The exponential factor is the
survival probability of the autodetaching state, and it is usually quite small. Hence,
the greater the distance at which the electron is captured, the higher the probability
for formation of the negative ion. Because the capture distance increases with an
increase of the molecular vibrational temperature, the attachment rate constant
also increases with an increase of the vibrational temperature.
We can apply these features to the analysis of the balance equations for the elec-
tron number density and vibrational temperature
T
v
, which have the form
@
Γ
N
e
@
@
T
v
@
D
ν
at
N
e
C
ν
ion
N
e
,
D
N
e
k
ex
„
ω
M
rel
.
t
t
Here
Nk
at
is the electron attachment frequency, (
k
at
is the rate constant for
this process,
N
is the number density of molecules),
ν
D
at
ion
is the ionization frequen-
cy,
k
ex
is the rate constant for the vibrational excitation of molecules by electron
impact,
ν
is the vibrational energy of the molecule, and
M
rel
is the vibrational re-
laxation rate. Linearizing these equations, assuming that perturbations of
N
e
and
T
v
vary with time as exp(
„
ω
ion
for an unperturbed state,
we find that the process being studied is oscillatory in nature if
d
i
ω
t
), and taking
ν
D
ν
at
ν
at
/
dT
v
>
0. The
frequency is
d
ν
at
dT
v
2
E
ω
D
k
ex
N
e
„
ω
,
(5.149)
and the oscillations are known as Eletskii oscillations [77].
