Statistical mechanics of polar systems. II

Abstract

The results of Part I of this work [J. Chem. Phys. 61, 562 (1974)] are extended. A new formally exact expression for the dielectric constant ε of a polar nonpolarizable fluid is derived. It involves a ’’core parameter’’ Θ that depends upon the way one decomposes the pair potential into a reference and perturbing term, reducing to our earlier expression given in Part I for Θ=0 and to the expression proposed by Nienhuis and Deutch for Θ=1. It is shown how the Clausius–Mosotti, Onsager, and Wertheim expressions for ε can all three be regarded as mean‐field approximations, each associated with a different value of Θ. Each expression becomes exact for a somewhat different model of a continuum fluid. A mean‐field theory is given for phase transitions that involve dipolar ordering; the theory becomes exact (as do the other mean‐field results of the paper) for a model in which the Kac inverse‐range parameter γ goes to zero.