On the dielectric constant for a non-polar fluid, a comparison

Sullivan and Deutch recently showed how the Wertheim formula for the dielectric constant of a non-polar fluid can be obtained as the lowest order result in a systematic expansion. We compare the results of this procedure with the results obtained with the more usual analysis of deviations from Clausius-Mossotti. On the basis of some rigorous theoretical arguments and some numerical results we conclude that Wertheim's formula predicts deviations from Clausius-Mossotti accurately to second order in the density. For higher densities we find that higher order corrections in the systematic expansion are necessary to find agreement. It is concluded that Wertheim's formula is therefore only a valid improvement over Clausius-Mossotti for low and intermediate densities. Sullivan and Deutch derive an expression for the local field factor, which appears in light scattering, valid to lowest order. They compare this factor with experimental results and find that it agrees much better than the factor which follows from Clausius-Mossotti for liquid densities. We give a general expression and show that higher order corrections to Wertheim's theory change the local field factor by a few percent. On the basis of this we conclude that the better than one percent agreement found by Sullivan and Deutch is to some extent fortuitous.