Statistical mechanics of polar systems: Dielectric constant for dipolar fluids

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Abstract
The Hemmer‐Lebowitz‐Stell‐Baer formalism is used to derive an exact expression for the dielectric constant ε of a polar (nonpolarizable) system. The Kac inverse‐range parameter γ is then introduced into the dipole‐dipole potential, and it is shown that in a ``mean‐field'' limit γ→0, the Clausius‐Mosotti expression is recovered in the same way that a van der Waals‐like theory has been previously recovered for simple fluids, a Debye‐Hückel‐like theory has been obtained for ionic fluids and the Weiss and Bragg‐Williams theories have been recovered for lattice systems. In this limit the zero‐field free energy reduces to the free energy of the same system at zero dipole moment. The relation this work bears to other formalisms and developments is discussed. In particular we show that our general expression and quite different‐looking earlier expressions give the same ε. We have avoided the approximations made in earlier treatments by Nienhuis and Deutch and by Ramshaw, and our work helps to clarify the status of those treatments.