46 4 Gas-Phase Synthesis of Nanoparticles
where the collision parameter increases with increasing particle size, calculated
values for electrically charged particles (Figure 4.6) show a continuous decrease
of the collision parameter with increasing size of the collision partners. Figure 4.6
demonstrates that charging the particles limits the size of the particles. The long
tail on the side of the large particles in the size distribution may be avoided, as
the collision probability of large particles is significantly reduced. The experimental results confirm these considerations.
How is it possible to exploit the advantages of a synthesis process with charged
particles? As will be demonstrated later, the best possibilities are found using
plasma processes. As the next possibility, one may think of charging by thermal
electron emission. This seems to be promising, as the radius of nanoparticles is
small and the processing temperature high. However, such a thermal charging
process does not give a high percentage of electrically charged particles. It can be
shown theoretically that a partial ionization of the particles does not lead to the
intended effect. Therefore, it is not surprising that this phenomenon was never
observed experimentally.
Box 4.4 Electrical Charges of Small Particles
To analyze the coagulation behavior of charged particles, first it is necessary
to calculate the electrical charges of the particles. To do this, electrically
charged particles are treated as spherical capacitors. The capacitance C of a
sphere is equal to the diameter, C = d, carrying the electrical charge Q = VC.
(V . . . electric potential) The assumption that all particles are charged to
the same potential, V
Q
C
Q
d
= = = const leads to the important relationship
describing the dependency of the electrical charge of the diameter:
Q VC Vd
=
= .
(4.8)
Small particles carry fewer electric charges than larger ones. This relationship
is experimentally well proven in aerosol physics [2]. Taking the quantized
nature of electrical charges into account, one has, according to Zieman et al.
[2], to rewrite Eq. (4.8)
d d
Q Q
d d
Q Q
d d
≤ ⇒ =
> ⇒ =
+
−
(
)
0
0
0
0
0
κ
(4.9)
(d 0 is the limiting diameter, Q 0 is the electrical charge of the smallest particles,
κ is the constant factor, which is not necessarily an integer number, as only
mean values over many particles are considered. This smears the quantization
of the electric charge).
where the collision parameter increases with increasing particle size, calculated
values for electrically charged particles (Figure 4.6) show a continuous decrease
of the collision parameter with increasing size of the collision partners. Figure 4.6
demonstrates that charging the particles limits the size of the particles. The long
tail on the side of the large particles in the size distribution may be avoided, as
the collision probability of large particles is significantly reduced. The experimental results confirm these considerations.
How is it possible to exploit the advantages of a synthesis process with charged
particles? As will be demonstrated later, the best possibilities are found using
plasma processes. As the next possibility, one may think of charging by thermal
electron emission. This seems to be promising, as the radius of nanoparticles is
small and the processing temperature high. However, such a thermal charging
process does not give a high percentage of electrically charged particles. It can be
shown theoretically that a partial ionization of the particles does not lead to the
intended effect. Therefore, it is not surprising that this phenomenon was never
observed experimentally.
Box 4.4 Electrical Charges of Small Particles
To analyze the coagulation behavior of charged particles, first it is necessary
to calculate the electrical charges of the particles. To do this, electrically
charged particles are treated as spherical capacitors. The capacitance C of a
sphere is equal to the diameter, C = d, carrying the electrical charge Q = VC.
(V . . . electric potential) The assumption that all particles are charged to
the same potential, V
Q
C
Q
d
= = = const leads to the important relationship
describing the dependency of the electrical charge of the diameter:
Q VC Vd
=
= .
(4.8)
Small particles carry fewer electric charges than larger ones. This relationship
is experimentally well proven in aerosol physics [2]. Taking the quantized
nature of electrical charges into account, one has, according to Zieman et al.
[2], to rewrite Eq. (4.8)
d d
Q Q
d d
Q Q
d d
≤ ⇒ =
> ⇒ =
+
−
(
)
0
0
0
0
0
κ
(4.9)
(d 0 is the limiting diameter, Q 0 is the electrical charge of the smallest particles,
κ is the constant factor, which is not necessarily an integer number, as only
mean values over many particles are considered. This smears the quantization
of the electric charge).