4.1 Fundamental Considerations 45
To obtain a narrower particle-size distribution and, what is more important, to
avoid the formation of a few large particles, it is necessary to influence the process
of particle formation in a way that the simple collision parameter, which increases
with increasing particle size is altered. In contrast, one would prefer a system in
which the collision parameter decreases with increasing particle size. Two of the
technical possibilities to influence particle coagulation and obtain this goal were
already mentioned: (i) Decreasing the temperature, a measure that reduces the
collision probability in general; however, it is not size sensitive. (ii) Quenching
immediately after the first particles were formed with a cold gas; indeed, this
process step reduces the number of large particles, and (iii) electrical charging of
the particles. The effect of this latter measure will now be discussed.
To reduce the probability of coagulation, one can think of loading the particles
with electric charges of equal sign, as electrical charges of equal sign repel each
other. Electrical charges of spherical particles are proportional to the particle
diameter. This is an experimentally and theoretically well-proven fact. The repelling force between two particles carrying electric charges of equal sign is directly
proportional to the product of the electrical charges. Lastly, this leads to a modification of the collision parameter, which is for charged particles the inverse to that
of neutral particles, it is indirectly proportional to the square root of the product
of the particle diameters. The temperature dependence remains unchanged as
linear. Figure 4.6 displays the collision parameter as a function of the particle
diameter for three different particle sizes.
The consequence of particle charging on the “collision parameter” is visible in
Figure 4.6, where the collision parameter is plotted versus particle diameter for
collision partners with different sizes. In contrast to neutral particles (Figure 4.3),
Figure 4.6 Collision parameter of particles
carrying electrical charges of equal sign. The
collision parameter is plotted versus the
particle size. The size of the collision partner
is the parameter for the curves. The
decreasing collision parameter with
increasing particle size limits particle growth
during synthesis. The electrical charge of the
particles is proportional to the particle
diameter.
0
5
10
15
20
particle diameter [a.u.]
0
0.25
0.5
0.75
1
collision
parameter
(d 1
d 2
)
–0.5
Collision partner diameter
10
5
1
To obtain a narrower particle-size distribution and, what is more important, to
avoid the formation of a few large particles, it is necessary to influence the process
of particle formation in a way that the simple collision parameter, which increases
with increasing particle size is altered. In contrast, one would prefer a system in
which the collision parameter decreases with increasing particle size. Two of the
technical possibilities to influence particle coagulation and obtain this goal were
already mentioned: (i) Decreasing the temperature, a measure that reduces the
collision probability in general; however, it is not size sensitive. (ii) Quenching
immediately after the first particles were formed with a cold gas; indeed, this
process step reduces the number of large particles, and (iii) electrical charging of
the particles. The effect of this latter measure will now be discussed.
To reduce the probability of coagulation, one can think of loading the particles
with electric charges of equal sign, as electrical charges of equal sign repel each
other. Electrical charges of spherical particles are proportional to the particle
diameter. This is an experimentally and theoretically well-proven fact. The repelling force between two particles carrying electric charges of equal sign is directly
proportional to the product of the electrical charges. Lastly, this leads to a modification of the collision parameter, which is for charged particles the inverse to that
of neutral particles, it is indirectly proportional to the square root of the product
of the particle diameters. The temperature dependence remains unchanged as
linear. Figure 4.6 displays the collision parameter as a function of the particle
diameter for three different particle sizes.
The consequence of particle charging on the “collision parameter” is visible in
Figure 4.6, where the collision parameter is plotted versus particle diameter for
collision partners with different sizes. In contrast to neutral particles (Figure 4.3),
Figure 4.6 Collision parameter of particles
carrying electrical charges of equal sign. The
collision parameter is plotted versus the
particle size. The size of the collision partner
is the parameter for the curves. The
decreasing collision parameter with
increasing particle size limits particle growth
during synthesis. The electrical charge of the
particles is proportional to the particle
diameter.
0
5
10
15
20
particle diameter [a.u.]
0
0.25
0.5
0.75
1
collision
parameter
(d 1
d 2
)
–0.5
Collision partner diameter
10
5
1