Rational-function approximation for fluids interacting via piece-wise constant potentials

Abstract

The structural properties of fluids whose molecules interact via potentials with a hard-core plus n piece-wise constant sections of different widths and heights are derived using a (semi-analytical) rational-function approximation method. The results are illustrated for the cases of a square-shoulder plus square-well potential and a shifted square-well potential and compared both with simulation data and with those that follow from the (numerical) solutions of the Percus-Yevick integral equation.

Structural properties of fluids interacting via piece-wise constant potentials with a hard core

“…It follows that, as already pointed out in Ref. 24, the RFA approach certainly outperforms the PY approximation in all the cases. This is noteworthy because, while the RFA reduces to the PY solution for hard spheres, 24 it is much simpler than the PY integral equation theory for two-step potentials.…”

“…24, the RFA approach certainly outperforms the PY approximation in all the cases. This is noteworthy because, while the RFA reduces to the PY solution for hard spheres, 24 it is much simpler than the PY integral equation theory for two-step potentials. As for the HNC integral equation theory, it presents the best agreement in the region 1 < r/σ < λ 1 in the cases A-C, i.e., when ǫ 1 ≥ 0 and ǫ 2 > 0.…”

“…As a final point, we want to stress that the results of this paper, together with the earlier ones, 24 encourage us to consider the problem in which the number of steps in the potential is much greater, leading in the limit n → ∞ to the very interesting case of the structure in a fluid whose molecules interact via, for instance, a Jagla potential. We plan to undertake such a task in the future.…”

“…In a previous paper, 24 following a semi-analytic methodology referred to generically as the rationalfunction approximation (RFA) that, although approximate, has proven successful for many other systems, 27 we derived the general formulae for the structural properties of fluids whose molecules interact via discrete potentials with a hard core plus an arbitrary number of piece-wise constant sections of different widths and heights. The theoretical scheme was illustrated by comparing it with available computer simulations results.…”

Structural properties of the Jagla fluid

“…While there has been a lot of work in the literature concerning the thermodynamic properties of the Jagla fluid, as far as we know no work other than the paper by Gibson and Wilding [60] has been devoted to the structural properties of a fluid whose molecules interact through such a potential. Therefore, the major aim of this paper is to present a semi-analytical approach based on the rationalfunction approximation (RFA) [78][79][80] to obtain the radial distribution function g(r) of the Jagla fluid, including its asymptotic behavior for large r. The application of the RFA to the Jagla fluid is made by assuming that a representation of the potential consisting in a hard core plus an appropriate piecewise constant function leads to essentially the same cavity function as the original Jagla potential. The outcome of the RFA approach will be assessed by testing its validity against integral equation results [both the Percus-Yevick (PY) and hypernettedchain (HNC) approximations will be considered] and our own Monte Carlo (MC) simulation data.…”