Environmental Engineering Reference
In-Depth Information
Correspondingly, the rate constants for neutralization of a singly negatively charged
cluster in collisions with ions
k
1,0
and the rate constants for neutralization of a
singly positively charged cluster in collisions with electrons
k
C
1,0
are given by
k
i
1
,
k
e
1
.
e
2
r
0
T
i
e
2
r
0
T
e
k
1,0
D
C
k
C
1,0
D
C
The rate constant for electron attachment to a negatively charged cluster contains
an additional factor, exp(
e
2
/(
r
0
T
e
)), and the rate constant for ion attachment to a
positively charged cluster contains the factor exp(
e
2
/(
r
0
T
)), and therefore these
processes are weak. Next, the ratios of the number densities of neutral
N
0
,nega-
tively charged
N
and positively charged
N
C
clusters are equal depending on the
plasma parameters:
N
N
0
D
k
e
N
e
k
i
N
i
1
N
N
0
D
k
i
N
i
k
e
N
e
1
r
0
T
i
r
0
T
e
,
,
e
2
e
2
C
C
2
1
r
0
T
e
k
e
N
e
k
i
N
i
e
2
C
N
N
D
1
r
0
T
i
.
e
2
C
6.1.6
Ionization Equilibrium for Large Dielectric Clusters
The character of the ionization equilibrium for a dielectric cluster in an ionized
gas is determined by the properties of the cluster surface. Each dielectric particle
or cluster has on its surface traps for electrons that we call active centers. Electrons
are captured by these centers, and this leads to the formation of negative ions at cer-
tain points on the cluster surface. The ionization equilibrium of a dielectric cluster
in a plasma corresponds to the equilibrium of these bound negative ions and free
plasma electrons. Although bound electrons can transfer between neighboring ac-
tive centers, this process proceeds slowly. The ionization equilibrium in this case
results from detachment of bound negative ions on the cluster surface by electron
impact and the capture of electrons by active centers of the cluster surface.
Thus, metal and dielectric clusters are characterized by different charging pro-
cesses in ionized gases. In the case of a metal cluster, valence electrons are located
over the entire cluster volume, whereas they form negative ions on the surface of
dielectric clusters. Ionization of metal clusters at high temperatures results from
collision of internal electrons that leads to the formation of fast electrons which
are capable of leaving the cluster surface. This thermoemission process and attach-
ment of plasma electrons to the cluster surface determine the ionization balance for
clusters which have a positive charge at high temperatures and a negative charge
at low temperatures. The electron binding energy for a large metal cluster tends to
the work function of a bulk metal. Dielectric clusters are negatively charged since
their ionization potential greatly exceeds their electron affinity.
Let us consider the diffusion regime of charging of dielectric clusters if the mean
free path of ions and electrons in a buffer gas is small compared with the cluster
