Location of the Fisher-Widom line for systems interacting through short-ranged potentials.

Abstract

For finite-ranged potentials the behavior of the total correlation function h(r) at large distances can be of two different types. In three-dimensional systems at low densities the function r h(r) presents exponential decay whereas at high densities it presents exponentially damped oscillatory decay. The locus of points on the phase diagram where a transition from exponential to oscillatory decay occurs is denoted as the Fisher-Widom line after the work of these authors [M. E. Fisher and B. Widom, J. Chem. Phys. 50, 3756 (1969)]. These authors exactly computed the Fisher-Widom line for several one-dimensional systems and conjectured that the same behavior could occur in three dimensions. In this work the Fisher-Widom line is computed for a three-dimensional finite-range potential by using the structural information obtained from the reference hypernetted chain theory which is probably the most successful theory of liquid structure available now. By combining these results with computer simulations of the vapor-liquid equilibria of the considered model the Fisher-Widom line is located within the phase diagram of the model. For the considered model the Fisher-Widom line cuts the liquid branch of the vapor liquid equilibria at a reduced temperature of T/${\mathit{T}}_{\mathit{c}}$=0.88 and a reduced density of \ensuremath{\rho}/${\mathrm{\ensuremath{\rho}}}_{\mathit{c}}$=2.07. The effect of the range of the potential on the location of the Fisher-Widom line is also considered. Increasing the range of the potential reduces the region of the phase diagram where oscillatory behavior of the function r h(r) occurs. The long-range decay of a Lennard Jones fluid is also considered. Decay of h(r) to zero at large distances is different for a Lennard-Jones potential and for a finite-ranged potential. Although the Lennard Jones potential does not present a true Fisher-Widom line when the ultimate decay of h(r) is considered it is shown that it exhibits a Fisher-Widom--like transition when an intermediate range of distances is considered.