On the theory of the dielectric constant of dilute solutions of polar molecules in non-polar solvents

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Abstract
The dielectric constant of even a very dilute solution of polar molecules in non-polar solvents depends upon the geometry of how the non-polar molecules are arranged and how the polar molecules are placed relative to them. These are topological effects which the usual semi-macroscopic theories employing continuum approximations are inherently incapable of revealing. Their existence is demonstrated by making a microscopic calculation with classical mechanics in which for simplicity the non-polar molecules are treated as forming a cubic lattice, and in which isotropic harmonic oscillators are used to describe the polarizability. When the dipolar interaction between molecules is included in the second order, different formulas are obtained depending on whether the lattice is simple, body-centred or face-centred cubic, and whether the polar molecule goes in interstitially or at a regular lattice point. In the latter case, the formulas of Onsager and Buckingham are recovered if a lattice sum is arbitrarily replaced by a continuum integral which actually is about twice as large.

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