As a first approximation, the interaction energy, (U_D), involved with dispersive forces has been calculated to be (15).

where (a) is the polarizability of the molecule,

(n_o) is a characteristic frequency of the molecule,

(h) is Plank's constant,

and (r) is the distance between the molecules.

The dominant factor that controls the dispersive force is the polarizability (a) of the molecule (not to be confused with the same symbol used for the separation ratio in chromatography), which, for substances that have no dipoles is given by

where (e) is the dielectric constant of the material,

(n) is the number of molecules per unit volume.

If (r) and (M) are the density and the molecular weight of the medium, then the number of molecules per unit volume is where (N) is Avogadro's number,

Thus,

where (P) is called the Molar Polarizability.

It is seen that the Molar Polarizability is proportional to , the molar volume; consequently dispersive forces should be proportional to the 'molar volume' of the interacting substances.

A diagrammatic representation of dispersive interactions is shown in figure 29.

Figure 29. Dispersive Interactions

Dispersive interactions occur where there is no localized charge on any part of the molecule, just a host of fluctuating, closely associated charges that, at any instant, can interact with instantaneous charges of an opposite kind situated on a neighboring molecule.

Dispersive interactions are the only interactions that can occur between two molecules to the exclusion of all others.