26 3 Surfaces in Nanomaterials
Even when the situation at the surface can be described by quite plausible physical and exact mathematical models, the experimental situation is very poor.
Usually, it is impossible to discriminate between the total surface energy and the
surface stress. Therefore, it is necessary to use the values published for the surface
energy for all applications. From the considerations above it is clear that the determination of the surface energy by measuring the interface stress is not sufficient.
These methods deliver only the surface stress, whereas calorimetric measurements, e.g. connected to grain growth, result in a value for the surface energy.
Lastly, only these values are useful for thermodynamic considerations.
In the case of anisotropic lattices, the relations are more complex since there
are directional bonds. The surface energy of these materials depends on the direction; hence, to minimize surface energy, these materials crystallize in rods or
platelets. Furthermore, surface-active substances can influence the surface energy.
Technically, this fact is used for the production of one- or two-dimensional particles such as needles or plates.
In the case of small particles, the surface energy dominates the behavior. Whenever possible, particles that are touching each other will coagulate with a temperature flash. Figure 3.5 displays a graph showing the temperature flash occurring
as a consequence of the coagulation of two spherical particles of equal size. For
reasons of simplicity, it is assumed the resulting particle is spherical too. Furthermore, as material, zirconia particles with a density ρ = 5.6 × 10
3 kg m
−3
, a surface
energy γ = 1 J mol
−1
, and a heat capacity C p = 56.2 J mol
−1 K
−1
≙ 781 J kg
−1 was
selected. (For reasons of simplicity, the materials data are those of conventional
materials; the value for the surface energy is a rough approximation. According
to more recent results, this value may be too low.) From Figure 3.5 one learns
that, in the case of small particles, the temperature flash may be in the range of
a few hundred Kelvin. Considering more recent values of the surface energy,
which are a few times higher, the temperature flash may further increase by a few
hundred Kelvin.
Figure 3.5 Temperature flash occurring as a consequence of the adiabatic coagulation of two
spherical zirconia particles of equal size.
0
2
4
6
8
10
particle diameter [nm]
0
400
800
1200
1600
2000
temperature
flash
[K]
Even when the situation at the surface can be described by quite plausible physical and exact mathematical models, the experimental situation is very poor.
Usually, it is impossible to discriminate between the total surface energy and the
surface stress. Therefore, it is necessary to use the values published for the surface
energy for all applications. From the considerations above it is clear that the determination of the surface energy by measuring the interface stress is not sufficient.
These methods deliver only the surface stress, whereas calorimetric measurements, e.g. connected to grain growth, result in a value for the surface energy.
Lastly, only these values are useful for thermodynamic considerations.
In the case of anisotropic lattices, the relations are more complex since there
are directional bonds. The surface energy of these materials depends on the direction; hence, to minimize surface energy, these materials crystallize in rods or
platelets. Furthermore, surface-active substances can influence the surface energy.
Technically, this fact is used for the production of one- or two-dimensional particles such as needles or plates.
In the case of small particles, the surface energy dominates the behavior. Whenever possible, particles that are touching each other will coagulate with a temperature flash. Figure 3.5 displays a graph showing the temperature flash occurring
as a consequence of the coagulation of two spherical particles of equal size. For
reasons of simplicity, it is assumed the resulting particle is spherical too. Furthermore, as material, zirconia particles with a density ρ = 5.6 × 10
3 kg m
−3
, a surface
energy γ = 1 J mol
−1
, and a heat capacity C p = 56.2 J mol
−1 K
−1
≙ 781 J kg
−1 was
selected. (For reasons of simplicity, the materials data are those of conventional
materials; the value for the surface energy is a rough approximation. According
to more recent results, this value may be too low.) From Figure 3.5 one learns
that, in the case of small particles, the temperature flash may be in the range of
a few hundred Kelvin. Considering more recent values of the surface energy,
which are a few times higher, the temperature flash may further increase by a few
hundred Kelvin.
Figure 3.5 Temperature flash occurring as a consequence of the adiabatic coagulation of two
spherical zirconia particles of equal size.
0
2
4
6
8
10
particle diameter [nm]
0
400
800
1200
1600
2000
temperature
flash
[K]