Free-energy functional of the Debye-Hückel model of simple fluids

Variational atomic model of plasma accounting for ion radial correlations and electronic structure of ions

We propose a model of ion-electron plasma (or nucleus-electron plasma) that accounts for the electronic structure around nuclei (i.e., ion structure) as well as for ion-ion correlations. The model equations are obtained through the minimization of an approximate free-energy functional, and it is shown that the model fulfills the virial theorem. The main hypotheses of this model are (1) nuclei are treated as classical indistinguishable particles, (2) electronic density is seen as a superposition of a uniform background and spherically symmetric distributions around each nucleus (system of ions in a plasma), (3) free energy is approached using a cluster expansion (nonoverlapping ions), and (4) resulting ion fluid is modeled through an approximate integral equation. In the present paper, the model is described only in its average-atom version.

Simpler free-energy functional of the Debye-Hückel model of fluids and the nonuniqueness of free-energy functionals in the theory of fluids

In previous publications [Piron and Blenski, Phys. Rev. E 94, 062128 (2016)2470-004510.1103/PhysRevE.94.062128; Blenski and Piron, High Energy Density Phys. 24, 28 (2017)1574-181810.1016/j.hedp.2017.05.005], the authors have proposed Debye-Hückel-approximate free-energy functionals of the pair distribution functions for one-component fluids and two-component plasmas. These functionals yield the corresponding Debye-Hückel integral equations when they are minimized with respect to the pair distribution functions, lead to correct thermodynamic relations, and fulfill the virial theorem. In the present paper, we update our results by providing simpler functionals that have the same properties. We relate these functionals to the approaches of Lado [Phys. Rev. A 8, 2548 (1973)0556-279110.1103/PhysRevA.8.2548] and of Olivares and McQuarrie [J. Chem. Phys. 65, 3604 (1976)JCPSA60021-960610.1063/1.433545]. We also discuss briefly the nonuniqueness issue that is raised by these results.