It is seen that the Molar Polarizability is proportional to , the molar volume; consequently dispersive forces (and thus "hydrophobic" or "lyophobic forces") will be related to the 'molar volume' of the interacting substances. A diagrammatic representation of dispersive interactions is shown in figure 4.

Figure 6. Dispersive Interactions

Dispersive interactions are not the result of a localized charge on any part of the molecule, but from 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.

Polar Forces

Polar interactions arise from electrical forces between localized charges resulting from permanent or induced dipoles. They cannot occur in isolation, but must be accompanied by dispersive interactions and under some circumstances may also be combined with ionic interactions. Polar interactions can be very strong and result in molecular associations that approach, in energy, that of a weak chemical bond. Examples of such instances are 'hydrogen bonding' and in particular the association of water with itself.

Dipole-Dipole Interactions

The interaction energy (UP) between two dipolar molecules is given, to a first approximation, by

where (a) is the polarizability of the molecule,

(m) is the dipole moment of the molecule,

and (r) is the distance between the molecules.

The energy is seen to depend on the square of the dipole moment, the magnitude of which can vary widely. Unfortunately, values of the dipole moment, taken from bulk measurements over a range of temperatures, does not always give a correct indication of the strength of any polar interactions that it might have with other molecules. For example, dioxane, an extremely polar solvent that is completely miscible with water has a dipole moment of only 2.2 debyes. In contrast, the dipole moment of diethyl ether a moderately polar solvent that is only soluble in water to the extent of about 5% v/v has a dipole moment as large as 4.3 debyes. Unusually low values of dipole moments for strongly polar substances is often due to internal electric field compensation when more than one dipole is present in the molecule. Another cause of the possible poor relationship between dipole moment and polar interactivity is caused by molecular association. Methanol and water associate strongly with themselves and each other. Examples of possible associates of water and methanol are shown in figure 5.

Figure 7. Two Possible Self Associates of Water and Methanol

Thus, with such associates (should they exist) the electric field from each dipole would oppose that from the other, resulting in a reduction in the net field as measured externally. It follows that bulk properties may not reflect the true value for the dipole moment of the individual dipoles. A molecule, however, approaching a water or methanol molecule would experience the uncompensated field of the single dipole and interact accordingly.