Free-energy functional of the Debye-H\"uckel model of simple fluids

TL;DR

This paper formulates a free-energy functional for the Debye-Hückel model of simple fluids, enabling derivation of integral equations and thermodynamic properties consistent with established theories.

Contribution

It introduces a variational free-energy functional for the Debye-Hückel approximation, aligning it with hyper-netted chain frameworks and ensuring thermodynamic consistency.

Findings

Functional reproduces Debye-Hückel integral equation

Correctly yields internal energy form

Satisfies the virial theorem

Abstract

The Debye-H\"uckel approximation to the free-energy of a simple fluid is written as a functional of the pair correlation function. This functional can be seen as the Debye-H\"uckel equivalent to the functional derived in the hyper-netted chain framework by Morita and Hiroike, as well as by Lado. It allows one to obtain the Debye-H\"uckel integral equation through a minimization with respect to the pair correlation function, leads to the correct form of the internal energy, and fulfills the virial theorem.