3.2 Surface Energy 27
Box 3.4 Temperature Flash Caused by Particle Coagulation
During coagulation of two particles with the diameter d, the surface a resulting of
the new particle with the diameter d resulting is smaller than the sum of the surfaces a starting of two starting particles.
a
d
a
d
starting
resulting
resulting
and
= ( )
=
2
2
2
π
π
v
v
d
d
d
d
resulting
starting
resulting
resulting
=
⇒
=
⇒
=
2
6
2 6
2
3
3
1
3
π
π
.
This leads to an excess of surface energy
∆
∆
∆
∆
u
a
d
d
d
U N u
=
=
−
=
−
⇒
=
γ
γ π
π
γπ
(
)
.
2
2 2
2
2
2
2
3
resulting
The system contains N
M
v
= ρ start
particles per mol and the increase of the
temperature ΔT in an adiabatic system is: (ρ is the density, C p is the heat
capacity, M is the molecular weight)
∆
∆
∆
∆
T
U
C
N u
C
M
v
u
C
M
d
d
M
C
=
=
=
=
−
=
−
p
p
start
p
p
ρ
ρ π
γπ
ρ
γ
6
2 2
6 2 2
3
2
2
3
2 2
3
1
d
.
(3.8)
Lastly, one has to realize that the temperature flash makes coagulation possible
at all, as the increased temperature increases the mobility of the atoms. The significant decrease of the temperature flash with increasing particle size explains
the occurrence of odd-shaped particles in the size range above 3 or 4 nm. This is
not pure theory. The process of coagulation can be observed in the electron microscope, too. Figure 3.6 displays a series of excellent electron micrographs displaying
the process of coagulation of two gold particles. The series starts with two particles;
one is in an orientation where lattice fringes are visible. These particles are moving
around on the surface of the carbon specimen carrier. This movement changes
the relative orientation of the particle lattice to the electron beam and; therefore,
the lattice fringes. When, by chance, the particles touch each other, the particles
rotate until their orientation is equal. Now coagulation starts; the larger particle
swallows the smaller one. This process needs a significant thermal mobility of the
atoms, to some extent, the necessary thermal energy is provided from the reduction of the surface.
The temperature flash occurring due to coagulation has a severe influence on
the particle formation during synthesis. Lastly, the consequence is that, using a
random process; it is nearly impossible to obtain very small particles, provided
one does not take special measures to thwart coagulation. This will be discussed
in Chapter 4 in great detail.
Box 3.4 Temperature Flash Caused by Particle Coagulation
During coagulation of two particles with the diameter d, the surface a resulting of
the new particle with the diameter d resulting is smaller than the sum of the surfaces a starting of two starting particles.
a
d
a
d
starting
resulting
resulting
and
= ( )
=
2
2
2
π
π
v
v
d
d
d
d
resulting
starting
resulting
resulting
=
⇒
=
⇒
=
2
6
2 6
2
3
3
1
3
π
π
.
This leads to an excess of surface energy
∆
∆
∆
∆
u
a
d
d
d
U N u
=
=
−
=
−
⇒
=
γ
γ π
π
γπ
(
)
.
2
2 2
2
2
2
2
3
resulting
The system contains N
M
v
= ρ start
particles per mol and the increase of the
temperature ΔT in an adiabatic system is: (ρ is the density, C p is the heat
capacity, M is the molecular weight)
∆
∆
∆
∆
T
U
C
N u
C
M
v
u
C
M
d
d
M
C
=
=
=
=
−
=
−
p
p
start
p
p
ρ
ρ π
γπ
ρ
γ
6
2 2
6 2 2
3
2
2
3
2 2
3
1
d
.
(3.8)
Lastly, one has to realize that the temperature flash makes coagulation possible
at all, as the increased temperature increases the mobility of the atoms. The significant decrease of the temperature flash with increasing particle size explains
the occurrence of odd-shaped particles in the size range above 3 or 4 nm. This is
not pure theory. The process of coagulation can be observed in the electron microscope, too. Figure 3.6 displays a series of excellent electron micrographs displaying
the process of coagulation of two gold particles. The series starts with two particles;
one is in an orientation where lattice fringes are visible. These particles are moving
around on the surface of the carbon specimen carrier. This movement changes
the relative orientation of the particle lattice to the electron beam and; therefore,
the lattice fringes. When, by chance, the particles touch each other, the particles
rotate until their orientation is equal. Now coagulation starts; the larger particle
swallows the smaller one. This process needs a significant thermal mobility of the
atoms, to some extent, the necessary thermal energy is provided from the reduction of the surface.
The temperature flash occurring due to coagulation has a severe influence on
the particle formation during synthesis. Lastly, the consequence is that, using a
random process; it is nearly impossible to obtain very small particles, provided
one does not take special measures to thwart coagulation. This will be discussed
in Chapter 4 in great detail.