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%.