Self-consistent theory of freezing of the classical one-component plasma

Abstract

A new formulation of the modified weighted density approximation of inhomogeneous classical fluids is presented which is exact to third order in the functional expansion of the excess free energy but includes, approximately, correlations to all orders. It requires as input the pair and triplet structure of the uniform liquid, and when applied to the one-component plasma yields results which are in good agreement with simulation data. PACS numbers: 64.70.Dv, 05.70.-a, 64.60.-i It has been shown [l] that for systems interacting by means of purely repulsive power-law potentials, ~r~m, the change in specific volume Ai? on melting approaches zero as m -• d, where d is the dimensionality of the system. When m < d, the thermodynamic functions are undefined, unless the system is provided with a "uniform neutralizing background," in which case Av at melting again vanishes [1]. The dense one-component plasma (OCP; m = l; ion charge Ze) [2] is a case in point: it freezes under constant density, and not under the usual condition of constant pressure [3]. Here we examine the application of density-functional theory (DFT) to this problem of isochoric freezing, and propose a new approximation to deal with it.The excess thermodynamic properties of the OCP depend on a single dimensionless variable, the plasma parameter T defined by r=p(Ze) 2 /a (p = \/k B T)

Density functional theory of freezing for soft interactions in two dimensions

“…Rosenfeld's fundamental measure theory [15]), the freezing of soft inverse-power law-fluids turns out to be much harder [16]. For the extreme case of the one-component plasma, featuring a 1/r interaction, it has been shown by Likos and Ashcroft [17] that an extended modified weighted density approximation (EMA) which contains correct triplet correlation of the fluid yields reliable freezing data. In this letter, we overcome the first problem in a similar way and generalize the EMA to two dimensions and apply it to the 1/r 3 interaction.…”

“…These conditions uniquely determine the weight functions and lead to simple algebraic equations for v and w that can be found in reference [17].…”

“…The EMA, on the other hand, is exact up to third order and, similarly, includes approximate contributions from all higher-order terms. The normalized weight functions have to fulfill the requirements [17] lim ρ(r)→ρ…”

On the triplet structure of binary liquids

“…The increased interest in the triplet structure is, however, not only of purely academic origin: density-functional based approaches that describe freezing phenomena have indeed brought along an improvement of the results if the ͑approximate͒ functional that describes the property of the solid is expanded up to third order, i.e., including three-particle correlation functions. 3,4 Among the frameworks proposed during the past two decades to calculate the triplet structure of a liquid, we quote in particular some of those that have been implemented and tested against computer simulation results: they are due to Ashcroft and co-workers, 5,4 Attard, 6 Barrat, Hansen, and Pastore, 7,8 and Leidl and Wagner. 9 However, up to now-and to the best of our knowledge-only the theory by Rosenfeld 10 has been extended to the study of the hard-sphere mixture fluid, including the calculation of the triplet structure.…”

“…One of the simplest approximations of the threeparticle distribution function g (3) is the Kirkwood superposition approximation ͑KSA͒ 1 g ͑ 3 ͒ ͑ r,s,t ͒ϭg͑ r ͒g͑ s ͒g͑ t ͒, ͑1͒…”