Environmental Engineering Reference
In-Depth Information
Ta b l e 2 . 10
The rate constant for dissociative recombination
α
given at room temperature and
expressed in units of 10
7
cm
3
/s [11, 86].
Ion
Ion
Ion
α
α
α
Ne
2
1.8 H
3
NH
4
2.3
16
Ar
2
CO
2
CH
5
6.9
3.6
11
Kr
2
NH
4
H
C
10
CO
1.1
NH
3
28
Xe
2
N
4
NH
4
20
20
(NH
3
)
2
27
N
2
O
4
H
3
O
C
2.2
14
H
2
O24
O
2
2.0 H
3
O
C
H
3
O
C
17
(H
2
O)
2
34
NO
C
CO
C
H
3
O
C
3.5
CO
14
(H
2
O)
3
44
CO
C
CO
C
H
3
O
C
6.8
(CO)
2
19
(H
2
O)
4
50
simple model [52] for the analysis of this process with introduction of the ion ra-
dius
R
0
, so penetration of an electron inside a sphere of a radius
R
0
leads to the
recombination process (2.76) because of the strong interaction between the elec-
tron and ion in this region. On the basis of (2.6), we have that the cross section of
dissociative recombination or electron penetration in the region with distances
r
from the ion
r
<
R
0
with positive charge
e
is [119]
R
0
R
0
.
e
2
ε
σ
D
π
C
c
In the limit of low electron energies
we obtain from this the following expression
for the rate constant for this process averaged over the Maxwell energy distribution
for electrons:
ε
*
s
2
+
2
p
2
R
0
e
2
p
m
e
T
e
m
e
σ
π
α
D
D
.
(2.78)
c
R
0
is several atomic units (
a
0
) for complex ions and is equal to the ion radius
for cluster ions. Therefore, at room temperature the coefficient for dissociative re-
combination of an electron and a complex ion according to (2.77) is of the order
of 10
6
cm
3
/s. It is sufficiently large value if we compare it with the atomic rate
constant (
k
0
10
9
cm
3
/s) or with the coefficient for dissociative
recombination for simple molecules (Table 2.10). Note that the above model, which
describes the case of a strong interaction of the colliding electron and ion, gives an
upper limit for the value of the dissociative recombination coefficient involving
complex ions, and the radius of the sphere of strong electron-ion interaction
R
0
is
usually equal to several Bohr radii. Note that for large cluster ions,
R
0
in (2.78) is
the cluster radius.
D
a
0
e
2
/
„D
6.13
