Dielectric constant of non-polar fluids

The theory of the static dielectric constant of non-polar fluids is re-examined using graph-theoretical techniques. A sample of arbitrary shape in an applied static electric field E ₀ is considered. The non-local tensor which transforms from E ₀ to the electrostatic polarization P is expressed as a sum of graphs. The relation appears simpler in terms of the inverse tensor, which is also obtained as a sum of graphs. Agreement with classical electrostatics is then manifest, and the shape-independence of the dielectric constant follows. An approximation suitable for numerical work is formulated, and a simplified version is solved analytically. The results are similar to those for fluids of rigid polar molecules in the Mean Spherical Model approximation. Reasons for both the similarities and the differences are given.