Variational Approach to the Dielectric Constant of a Polarizable Medium

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Abstract
The Kirkwood theory of the dielectric constant for a nonpolar fluid is shown to imply a negative electrostatic self‐energy for certain configurations of point dipoles. It is shown that this unphysical behavior can be eliminated by introducing a hard core of radius larger than or equal to the cube root of the molecular polarizability. The introduction of such a core also permits the derivation of variational upper and lower bounds on the dielectric constant. In particular, the Clausius–Mossotti formula can be shown to give too low a value for the dielectric constant of a polarizable sphere fluid. The relationship of these bounds to those developed elsewhere for the bulk properties of random two‐phase media is discussed, as is the effect of dipole fluctuations.

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