Environmental Engineering Reference
In-Depth Information
size. Then the ionization equilibrium for a dielectric cluster results from the pro-
cesses [66]
A
(
Z
C
1)
,
A
(
Z
C
1)
A
(
Z
C
1)
A
Z
n
e
C
!
C
A
!
C
A
,
n
n
n
A
(
Z
C
1)
B
C
C
A
Z
n
!
B
C
,
(6.23)
n
so an autodetaching state (
A
(
Z
C
1
n
)
is quenched by collisions with surround-
ing atoms. Because the rate constant for electron attachment to a dielectric cluster
greatly exceeds the cluster ionization rate constant for ionization by electron im-
pact, these particles are negatively charged.
In contrast to metal particles, the binding energies for active centers do not de-
pend on particle size, because the action of each center is concentrated in a small
region of space. Evidently, the number of such centers is proportional to the area of
the particle's surface, and for particles of micrometer size this value is large com-
pared with that occupied by the charges. Hence, we consider the regime of charging
of a small dielectric particle far from the saturation of active centers. Then positive
and negative charges can exist simultaneously on the particle's surface. They move
over the surface and can recombine there. Usually, the binding energy of electrons
in negative active centers is in the range EA
D
2
4 eV, and the ionization potential
for positive active centers is about
J
0
10 eV. Hence, attachment of electrons is
more profitable for electrons of a glow discharge, and a small dielectric particle has
a negative charge in a glow gas discharge.
The electric potential on the cluster surface is
Ze
/
r
0
,where
Z
and
r
0
are the
cluster charge and cluster radius, respectively. The electron state is stable,
e
' D
EA,
and from this we have the critical cluster charge
Z
where the electron state on the
cluster surface is stable [66]:
'<
EA
e
2
.
Z
D
r
0
(6.24)
In particular, for
r
0
D
1
μ
m and EA
D
3eV for a dielectric cluster, we have
10
3
, and the cluster electric potential is 3 V. Under these parameters,
a typical distance between neighboring occupied active centers is about 0.3
Z
D
2
m,
which is one or two orders of magnitude larger than a typical distance between
neighboring active centers. If the particle charge exceeds the critical charge
Z
ac-
cording to (6.24), the bound electron state becomes an autodetaching state, but in
this case the barrier size is
R
μ
e
2
/EA, where
Z
is the cluster charge. From this
it follows that because this distance exceeds a typical atomic size, the lifetime of
the autodetaching state is long enough. Therefore, the cluster charge may exceed
greatly the critical value given by (6.24).
Dj
Z
j
