3.2 Surface Energy 25
Box 3.3 Origin of Surface Energy
Breaking a chunk of material into two parts forms two surfaces, with n broken
bonds. The binding energy u per atom is split to both sides. Hence, for breaking, the energy
u
n
u
break = 2
.
The specific energy to break the bonds is
γ 0
2
= N
u
*
,
(3.5)
where N
* is the number of broken bonds per square meter. Due to the uncompensated bonds at the surface, a force f perpendicular to the surface emerges.
If a is the area occupied by one atom, the resulting surface stress is
σ =
f
a
.
The stress σ leads to a surface stretch ε s , assumed constant in any direction of
the tangent plane of the particle, of the surface, (To be mathematically exact,
σ and ε s are vectors in the tangential plane of the surface. For reasons of simplicity, they are replaced by their absolute values. In the context of these considerations, this does not make any difference.) leading to the contribution γ S
to the surface energy.
γ γ γ
= +
0
s .
(3.6)
The contribution γ 0 exists only in the case of solids; for liquids γ 0 = 0 is valid.
The pressure p caused by surface stress σ is given by
p
d
= 4
σ .
(3.7)
For more details see [1].
against any intuition, this does not lead to a hydrostatic pressure in the material,
rather to a stress in the surface plane. Consequently, the surface stress deforming
the surface results in the surface stretching. In a spherical particle of limited size,
the situation is different. Caused by the curvature, in connection with the surface
stress, a hydrostatic pressure, comparable with one stemming from a gas or a
liquid at the outside, in the particle comes into action. This allows modeling of
the surfaces of particles as a skin made of elastic material. Consequently, the
rubber skin model of the surface was developed.
Box 3.3 Origin of Surface Energy
Breaking a chunk of material into two parts forms two surfaces, with n broken
bonds. The binding energy u per atom is split to both sides. Hence, for breaking, the energy
u
n
u
break = 2
.
The specific energy to break the bonds is
γ 0
2
= N
u
*
,
(3.5)
where N
* is the number of broken bonds per square meter. Due to the uncompensated bonds at the surface, a force f perpendicular to the surface emerges.
If a is the area occupied by one atom, the resulting surface stress is
σ =
f
a
.
The stress σ leads to a surface stretch ε s , assumed constant in any direction of
the tangent plane of the particle, of the surface, (To be mathematically exact,
σ and ε s are vectors in the tangential plane of the surface. For reasons of simplicity, they are replaced by their absolute values. In the context of these considerations, this does not make any difference.) leading to the contribution γ S
to the surface energy.
γ γ γ
= +
0
s .
(3.6)
The contribution γ 0 exists only in the case of solids; for liquids γ 0 = 0 is valid.
The pressure p caused by surface stress σ is given by
p
d
= 4
σ .
(3.7)
For more details see [1].
against any intuition, this does not lead to a hydrostatic pressure in the material,
rather to a stress in the surface plane. Consequently, the surface stress deforming
the surface results in the surface stretching. In a spherical particle of limited size,
the situation is different. Caused by the curvature, in connection with the surface
stress, a hydrostatic pressure, comparable with one stemming from a gas or a
liquid at the outside, in the particle comes into action. This allows modeling of
the surfaces of particles as a skin made of elastic material. Consequently, the
rubber skin model of the surface was developed.