A liquid-state theory that remains successful in the critical region

Abstract

A thermodynamically self-consistent Ornstein-Zernike approximation (SCOZA) is applied to a fluid of spherical particles with a pair potential given by a hard-core repulsion and a Yukawa attractive tail w(r) = − exp[−z(r − 1)]/r. This potential allows one to take advantage of the known analytical properties of the solution to the Ornstein-Zernike equation for the case in which the direct correlation function outside the repulsive core is given by a linear combination of two Yukawa tails and the radial distribution function g(r) satisfies the exact core condition g(r) = 0 for r < 1. The predictions for the thermodynamics, the critical point, and the coexistence curve are compared here to other theories and to simulation results. In order to unambiguously assess the ability of the SCOZA to locate the critical point and the phase boundary of the system, a new set of simulations has also been performed. The method adopted combines Monte Carlo and finite-size scaling techniques and is especially adapted to deal with critical fluctuations and phase separation. It is found that the version of the SCOZA considered here provides very good overall thermodynamics and a remarkably accurate critical point and coexistence curve. For the interaction range considered here, given by z = 1.8, the critical density and temperature predicted by the theory agree with the simulation results to about 0.6%.

Liquid-Vapor Transition from a Microscopic Theory: Beyond the Maxwell Construction

“…A closer inspection of the t evolution of ÿ1 at coexistence reveals that the approach toward zero proceeds differently deep inside the binodal, where ÿ1 remains negative throughout the evolution, and close to the phase boundary, where long-wavelength fluctuations first drive the system towards stability ( ÿ1 > 0) and then push the inverse compressibility to zero. It is [17] and z 1:8 (lower panel) [12]. The HRT spinodals are also shown (full circles).…”

Which Shape Characteristics of the Intermolecular Interaction of Liquid Water Determine Its Compressibility?

“…We obtain the thermodynamic properties of the models by using the SCOZA [33][34][35][36][37][38][39][40]. We express the physical quantities by the same symbols, and the numerical computations are performed as described in Yasutomi [39,40].…”

“…The SCOZA is known to describe the overall thermodynamics of liquids very well and provides a remarkably accurate critical point and coexistence curve. This scheme is entirely self-contained, which means that no supplementary thermodynamic or other input is necessary [33][34][35][36][37][38][39][40].…”

Thermodynamic mechanism of the density anomaly of liquid water

“…We express the physical quantities by the same symbols used in Yasutomi [41], and the numerical computations are performed by using the same method described in Pini et al [35,41]. Tables 3, 4 show the density grid ρ, the temperature grid β, the density ρ 0 at which we made use of the so-called high-temperature approximation [43], and β f ; numerical computations are performed in the range of 0 < β < β f .…”

“…This scheme is entirely self-contained, that is,no supplementary thermodynamic or other input is necessary. Up to now, the SCOZA has been applied to the Yukawa, Sogami-Ise, square-well, triangle-well, and screened-power series potentials, and many fruitful results have been obtained (see [35][36][37][38][39][40] and references quoted therein). Because any smooth potential tail can be approximated with sufficient accuracy by Yukawa terms, the SCOZA with Yukawa terms is applicable to a variety of liquids.…”