Theory of polar liquids

TLDR

Recent statistical theories of polar fluids, notably SRN perturbation theory and MSA, are compared for dipolar hard spheres. The authors numerically evaluate excess free energy, phase boundaries, and vapor pressures of dipolar hard spheres using the Carnahan–Starling equation of state across several reduced temperatures. MSA’s low‑density replacement of correlation functions is unsatisfactory, but its Padé‑approximant form captures some physics, and the two theories yield markedly different phase diagrams and vapor pressures.

Abstract

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.