2.2 Elementary Consequences of Small Particle Size 15
Figure 2.10 Theoretical dependency of the specific surface area of the particle diameter. Due
to the agglomeration of the particles, experimentally these values are not realized.
0
20
40
60
80
100
particle diameter [nm]
10
1
10
2
10
3
10
4
specific
surface
[m
2
¥ g
–1
]
To get an idea about the magnitudes of surfaces that may be expected in case
of nanoparticles, Figure 2.10 displays the theoretical surface of one gram of a
powder consisting of spherical particles with a density of 3.5 × 10
3 kg m
−3 (alumina).
In Figure 2.10, the surface is given in the non-SI unit m
2 g
−1 . This unit is applied
because this is the only unit that is generally accepted for the specific surface area.
In general, the specific areas visible in Figure 2.10 are never realized experimentally. The reason for this discrepancy is found in the agglomeration of the particles.
The influence of this phenomenon increases with decreasing particle diameter, as
the influence of the van der Waals forces increases too. (Van der Waals forces are
weak interactions between molecules or small particles having their origin in
quantum dynamics. These forces are neither covalent nor based on electrostatic
or dipolar interaction.) Experimentally, the largest values are measured with activated charcoal in the range of 2000 m
2 g
−1 and finely dispersed amorphous silica
with values up to 600 m
2 g
−1
.
The surface is such an important topic for nanoparticles that there is a full
chapter devoted to surface and surface-related problems (see Chapter 3).
2.2.2
Thermal Phenomena
Each isolated object, in this case a nanoparticle, has a thermal energy, which is
directly proportional to the temperature. Furthermore, each object tries to be in
a state where the energy is a minimum. Generally, this is a stable state. Certainly,
energetically speaking, there are other states with higher energy possible. The
energy difference between the state of lowest energy and the next one may depend
for example, on the mass of the particle. As the mass of the particle decreases
with particle diameter, there is the possibility that, starting at a sufficiently high
temperature, the thermal energy gets larger than the difference between the
Figure 2.10 Theoretical dependency of the specific surface area of the particle diameter. Due
to the agglomeration of the particles, experimentally these values are not realized.
0
20
40
60
80
100
particle diameter [nm]
10
1
10
2
10
3
10
4
specific
surface
[m
2
¥ g
–1
]
To get an idea about the magnitudes of surfaces that may be expected in case
of nanoparticles, Figure 2.10 displays the theoretical surface of one gram of a
powder consisting of spherical particles with a density of 3.5 × 10
3 kg m
−3 (alumina).
In Figure 2.10, the surface is given in the non-SI unit m
2 g
−1 . This unit is applied
because this is the only unit that is generally accepted for the specific surface area.
In general, the specific areas visible in Figure 2.10 are never realized experimentally. The reason for this discrepancy is found in the agglomeration of the particles.
The influence of this phenomenon increases with decreasing particle diameter, as
the influence of the van der Waals forces increases too. (Van der Waals forces are
weak interactions between molecules or small particles having their origin in
quantum dynamics. These forces are neither covalent nor based on electrostatic
or dipolar interaction.) Experimentally, the largest values are measured with activated charcoal in the range of 2000 m
2 g
−1 and finely dispersed amorphous silica
with values up to 600 m
2 g
−1
.
The surface is such an important topic for nanoparticles that there is a full
chapter devoted to surface and surface-related problems (see Chapter 3).
2.2.2
Thermal Phenomena
Each isolated object, in this case a nanoparticle, has a thermal energy, which is
directly proportional to the temperature. Furthermore, each object tries to be in
a state where the energy is a minimum. Generally, this is a stable state. Certainly,
energetically speaking, there are other states with higher energy possible. The
energy difference between the state of lowest energy and the next one may depend
for example, on the mass of the particle. As the mass of the particle decreases
with particle diameter, there is the possibility that, starting at a sufficiently high
temperature, the thermal energy gets larger than the difference between the