W. Richard Bowen and Nidal Hilal 4

TABLE 2.1 Energy and force expressions for different geometries.
Two spheres
R 1
D
Identical spheres
R
D
Sphere – Plane
R
D
Paraboloid – Plane
R 2
R
2.3 INTERACTION FORCES 39
V
V
V
V
A
A
A
A
AH
=
R R
D R R
−
1 2
6 +
A R H
=
D
−
12
A R H
=
D
−
6
A
=
l
D l
−
12
1 2
A R R
H
F =
D R R
−
6 +
2
1 2
A R H
F =
D
−
12 2
A R H
F =
D
−
6 2
1 2
where � 1 and � 2 are the number of atoms per unit volume in the two
interacting materials.
There are some general properties of van der Waals interactions
between macroscopic bodies, which are worthy of note. First, interactions
between two bodies across vacuum are always attractive, as are all interactions
between two bodies of identical composition across a medium.
However, for two bodies of dissimilar materials, the net interaction may
be either attractive or repulsive, depending upon the particular setup.
Whilst all van der Waals interactions per se are attractive, if one of
the bodies has a greater attraction for the intervening medium than for
the opposing body, then this will result in a net repulsion between the
two bodies [12]. Whether such an interaction is likely to be attractive or
repulsive can be assessed by comparison of the dielectric constants of the
materials involved. If the dielectric constant of the intervening medium
is between that of the materials of the two bodies, then the net forces
between the two bodies will be repulsive. If it matches the dielectric constant
of either of the interacting bodies, then the van der Waals force will
effectively vanish [13].
H xy
2
2
z
2
xy
2
z
A j
H
F =
D l
−
12 2