Theory of polar liquids

Two recent contributions to the statistical theory of polar fluids, namely the perturbation theory of Stell, Rasaiah and Narang (SRN) and the meanspherical-approximation (MSA) results of Wertheim, and of Nienhuis and Deutch, are compared and contrasted for the conceptually simple model of hard spheres, diameter R, with central point dipoles, of strength μ (dipolar hard spheres). It is shown that the MSA approach replaces correlation functions which enter correctly into the SRN theory by their low-density limits : to this extent it is unsatisfactory. On the other hand the MSA work does suggest reasons why the naive Padé approximant featuring in SRN theory may be expected to do reasonable justice to the physics of the problem. Numerical comparisons of the excess free-energy (as compared with non-polar hard spheres) as a function of reduced density, ρ* = ρR ³, are given at two temperatures, T* = 2 and T* = 0·25, where T* = kTR ³/μ². Similar curves, for T* = 1 and T* = 0·5, are available from the authors. The gas-liquid (T*, ρ*)-phase boundary is located, near the critical point, on both theories, as are the vapour pressure curves. These are calculated using the Carnahan-Starling equation of state for hard spheres ; and critical comment is made in justification of employing this in the context of MSA results for the excess quantities. The two theories are found to have appreciably different numerical consequences.