Solvent medium effects and excess polarizabilities

The above expressions were derived for the polarizabilities of molecules in free space or in a dilute gas (mostly air). However, we often encounter molecules interacting in a liquid solvent medium, which reduces the interaction pair potential by around e, or more the extent of this reduction depends on several factors. First of all, the intrinsic polarizability and dipole moment of an isolated gas molecule may be different when it is itself in the liquid state, or alternatively when dissolved in a solvent medium. This is because of the difference in interaction strength and also the separation distance between molecules. Thus, the polarizability values are best determined by experiment. Second, a dissolved molecule can only move by displacing an equal volume of solvent from its path. If the molecule has the same polarizability as the solvent molecules, that is if no electric held is reflected by the molecule, it is invisible in the solvent medium and does not experience any induction force. Thus, the polarizability of the molecule, a, must represent the excess or effective polarizability of a molecule over that of the solvent. Landau and Lifshitz applied a continuum approach and modeled a molecule, i, as a dielectric sphere of radius, ah having 

On the other hand, Equation (49) can be used in the derivation of the classical Clausius-Mossotti equation (Equation (9)) so that, for an isolated gas molecule in free space, Equation (49) can be written as 

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