90
4 Interfacial Gaseous States
Of particular importance is that every molecule and every material has an intrinsic
frequency called the plasma frequency above which the molecule or the material
becomes transparent to light [13]. Simply put, the oscillation of the electric field of
light is too fast for an electron to respond or “keep up” above this frequency, and
ceases to interact with photons that have a greater frequency. We call a material
“transparent” when light goes through it without interacting with the light.
When a molecule is polarized by light, a dipole, quadrupole, and weaker higher
order ‘poles’ are induced that can only be described in the form of tensors [14].
Since the dipole is generally by far the strongest, the higher order poles can usually
be neglected for a first approximation. In an ensemble of multiple molecules, such
induced dipoles generate electromagnetic forces in that the like charges repel and
unlike charges attract with each other. This is the source of the Van der Waals forces.
The Van der Waals forces are thus ubiquitous in that they can arise in every material
and in every molecule that has an electron.
The Van der Waals forces between two molecules are short-range forces whose
potential energy rapidly diminishes with the inverse of the sixth power of the distance
[10]. The pre-factor (proportionality constant) in the Van der Waals force law is a
complex function of the polarizability and the dielectric function of the molecules
in question.
W (r ) = −C/r
6
(4.1.10)
We are more interested in the Van der Waals forces between condensed matters.
Since both the interacting objects and the medium in between consist of atoms or
molecules, the pairwise summation of the Van der Waals forces between all the
constituting atoms and molecules leads to various forms of Van der Waals force laws
that depend on the shape of the interacting objects [10]. For two parallel flat surfaces
of two semi-infinite media interacting across a thin film, the Van der Waals potential
energy per unit area diminishes with the inverse of the second power of the distance
between the two surfaces (thickness of the film), h. The Van der Waals forces between
macroscopic objects are thus much longer ranged than those between two molecules.
The pre-factor (proportionality constant) of such a Van der Waals force law is called
a Hamaker constant and customarily denoted by A instead of C [15, 16].
W (h) = −A/12π h
2
(4.1.11)
From the origin of the Van der Waals forces described above, one would expect
that the Van der Waals forces, and the Hamaker constants, would be intimately related
to the dielectric properties of a molecule or a material of interest. This is indeed the
case and the relevant property is the refractive index. Of our particular interest in
relation to the disjoining pressure is the Van der Waals force across a thin film that
is sandwiched between two semi-infinite media, like the one shown in (Fig. 4.4).
Useful methods of calculating a Hamaker constant from experimentally measurable dielectric functions have been developed [11, 17]. However, one is often as much
interested in the sign of a Hamaker constant as its numerical size that determines
4 Interfacial Gaseous States
Of particular importance is that every molecule and every material has an intrinsic
frequency called the plasma frequency above which the molecule or the material
becomes transparent to light [13]. Simply put, the oscillation of the electric field of
light is too fast for an electron to respond or “keep up” above this frequency, and
ceases to interact with photons that have a greater frequency. We call a material
“transparent” when light goes through it without interacting with the light.
When a molecule is polarized by light, a dipole, quadrupole, and weaker higher
order ‘poles’ are induced that can only be described in the form of tensors [14].
Since the dipole is generally by far the strongest, the higher order poles can usually
be neglected for a first approximation. In an ensemble of multiple molecules, such
induced dipoles generate electromagnetic forces in that the like charges repel and
unlike charges attract with each other. This is the source of the Van der Waals forces.
The Van der Waals forces are thus ubiquitous in that they can arise in every material
and in every molecule that has an electron.
The Van der Waals forces between two molecules are short-range forces whose
potential energy rapidly diminishes with the inverse of the sixth power of the distance
[10]. The pre-factor (proportionality constant) in the Van der Waals force law is a
complex function of the polarizability and the dielectric function of the molecules
in question.
W (r ) = −C/r
6
(4.1.10)
We are more interested in the Van der Waals forces between condensed matters.
Since both the interacting objects and the medium in between consist of atoms or
molecules, the pairwise summation of the Van der Waals forces between all the
constituting atoms and molecules leads to various forms of Van der Waals force laws
that depend on the shape of the interacting objects [10]. For two parallel flat surfaces
of two semi-infinite media interacting across a thin film, the Van der Waals potential
energy per unit area diminishes with the inverse of the second power of the distance
between the two surfaces (thickness of the film), h. The Van der Waals forces between
macroscopic objects are thus much longer ranged than those between two molecules.
The pre-factor (proportionality constant) of such a Van der Waals force law is called
a Hamaker constant and customarily denoted by A instead of C [15, 16].
W (h) = −A/12π h
2
(4.1.11)
From the origin of the Van der Waals forces described above, one would expect
that the Van der Waals forces, and the Hamaker constants, would be intimately related
to the dielectric properties of a molecule or a material of interest. This is indeed the
case and the relevant property is the refractive index. Of our particular interest in
relation to the disjoining pressure is the Van der Waals force across a thin film that
is sandwiched between two semi-infinite media, like the one shown in (Fig. 4.4).
Useful methods of calculating a Hamaker constant from experimentally measurable dielectric functions have been developed [11, 17]. However, one is often as much
interested in the sign of a Hamaker constant as its numerical size that determines