Chemistry Reference
In-Depth Information
moreover shows that the capture cross section increases faster with temperature than
the survival probability decreases. Thus, the attachment cross section increases with
temperature. It is, however, always one or two orders of magnitude smaller than the
cross section for the corresponding elastic electron-molecule scattering.
9.2.2.2 Destruction of Ions
Whereas in an electronegative gas discharge only two processes are primarily respon-
sible for the production of ions and electrons—electron impact ionization and
dissociative attachment—a large number of processes may lead to the destruction
of ions and electrons (see Table 9.1). Depending on the parameters of the discharge,
the loss of ions may be due primarily to recombination or detachment. Recombination
may furthermore occur between positive ions and electrons or between positive and
negative ions (annihilation). For molecular positive ions, the former process is usually
accompanied by dissociation and is thus called dissociative recombination. Ion-ion
annihilation, on the other hand, is in most cases only a charge transfer, which does
not lead to a rearrangement of the nuclei. Finally, detachment of negative ions can
either be initiated by electrons or by neutrals. Electron-induced detachment is similar
to electron impact ionization whereas detachment due to (molecular) neutrals may
lead to dissociation, as well as association, given that the neutral is in a metastable
state.
Dissociative recombination
is triggered by slow electrons. It is thus a resonant
process, similar to dissociative attachment. Very often, it is the dominant loss process
for positive ions and electrons with relatively large cross sections because at least one
of the atomic fragments in the exit channel is usually in an excited state, implying
that the energy in the exit channel can be distributed in many different ways [78].
The resonance model for dissociative recombination, originally proposed by
Bardsley [63,64], is based on the potential energy surface diagram shown in
Figure 9.13. The most favorable situation for the process to take place is when
an antibonding potential energy surface of the molecule
AB
, which is the collision
compound for this reaction, crosses the potential energy surface of the positive ion
and is below the vibrational ground state of the ion for large internuclear distances.
This is the case for
H
2
,
N
2
, and
O
2
, for instance.
The cross section for dissociative recombination can then be cast into the form
(9.91), with
M
and
K
as the reduced mass and the relative momentum of the
(
A
,
B
)
system, respectively,
m
and
k
as the corresponding quantities of the
(
e
−
,
AB
+
)
system,
(
−
)
dE
χ
ν
i
(
R
)
as the initial vibrational state of
AB
+
, and
(
R
)
as the solution of the
complex conjugate to (9.79) with
V
d
(
R
)
=
V
AB
(
R
)
,
V
0
(
R
)
=
V
AB
+
(
R
)
, and
V
dk
(
R
)
as
the interaction between the
AB
state and the
e
−
−
AB
+
scattering continuum. The
inhomogeneity representing the boundary condition,
J
(
R
)
=[
V
d
(
∞
)
−
V
d
(
R
)
]
C
K
(
R
)
,
now contains a Coulomb wave
because the scattering continuum is for two
charged particles: an electron and a positive ion. More sophisticated approaches use
quantum defects to characterize the scattering states [89,90].
In electronegative gas discharges, there is an additional recombination channel:
ion-ion annihilation
. The potential energy surface diagram relevant for this pro-
cess is shown in Figure 9.14. The essential point is the crossing of the potential
C
K
(
R
)
