coagulate, a new particle with volume i þ j is formed. Therefore, the following
equations are valid:
Nðt; i þ jÞ ¼ Nðt À 1; i þ jÞ þ f ij
Nðt À 1; iÞ
N tot
Á
Nðt À 1; jÞ
N tot
Nðt; iÞ
¼ Nðt À 1; iÞ À f ij
Nðt À 1; iÞ
N tot
Á
Nðt À 1; jÞ
N
Nðt; jÞ
¼ Nðt À 1; jÞ À f ij
Nðt À 1; iÞ
N tot
Á
Nðt À 1; jÞ
N tot
i; j 2 N
ð4:10Þ
0
5
10
15
20
particle diameter [a.u.]
0
1
2
3
collision
parameter
Size of collision partner
1
3
5
10
20
0
5
10
15
20
particle diameter [a.u.]
0
0.2
0.4
0.6
0.8
1
collision
parameter (d 1
d 2
)
-0.5
Size of collision partner
1
5
10
20
(a)
(b)
Figure 4.4 Influence of electrical charge on the
collision parameter. The collision parameter is
plotted against particle size (as in Figure 4.3).
The parameter for the curves is the size of the
collision partner. The decreasing collision
parameter with increasing particle size limits
particle growth during synthesis. (a) Collision
parameter for electrically charged particles,
where the charge Q is proportional to the
particle diameter d, Q / d. (b) Collision
parameter for particles, where the electrical
charge Q follows the relationship: d d 0 )
Q ¼ 1 and d > d 0 ) Q ¼ 1 þ k 3 ðd À d 0 Þ;
d 0 ¼ 3.
4.1 Fundamental Considerations j51