Abstract
The author's lecture notes concerning the correlation functions and the thermodynamics of a simple polar fluid are summarized. The emphasis is on the dipolar hard sphere fluid and the mean spherical approximation and on the relation of these results to the Clausius-Mossotti and Onsager formulae for the dielectric constant. Previous excerpts from these lecture notes, Condens. Matter Phys., 2009, 12, 127; ibid., 2010, 13, 13002, have contained results that were not widely known. It is hoped that this third, and likely final, excerpt will prove equally helpful by gathering several results together and making these more widely available and recording a few new results.
Highlights
This paper is dedicated to Yura Kalyuzhnyi on the occasion of his sixtieth birthday; it is the result of the beautiful work of Michael Wertheim on hard spheres and dipolar hard spheres that has inspired the author and many others, including Yura and his colleagues in Lviv
There is little in this paper, drawn from the author’s lecture notes, that is not well-known to Michael but, perhaps, lesser mortals will benefit from this collection of results and those in two previous papers [1, 2] taken from the author’s lecture notes
The well known definition for the h-particle correlation function for a simple atomistic fluid of N molecules in a volume V is generalized for a molecular fluid, g(1 · · · h)
Summary
This paper is dedicated to Yura Kalyuzhnyi on the occasion of his sixtieth birthday; it is the result of the beautiful work of Michael Wertheim on hard spheres and dipolar hard spheres that has inspired the author and many others, including Yura and his colleagues in Lviv. There is little in this paper, drawn from the author’s lecture notes, that is not well-known to Michael but, perhaps, lesser mortals will benefit from this collection of results and those in two previous papers [1, 2] taken from the author’s lecture notes. Dipolar hard spheres are a simple representative molecular fluid and polar fluid. The well known definition for the h-particle correlation function for a simple atomistic fluid of N molecules in a volume V is generalized for a molecular fluid, g(1 · · · h). Rij = |ri − rj| is the distance between the centers of a pair of molecules, i and j, whose centers are located at ri and rj. The function u(Rij, Ωi, Ωj), that can be written as u(ij) for brevity, is the intermolecular potential between a pair of molecules
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