3 research outputs found
A Numerical Test of a High-Penetrability Approximation for the One-Dimensional Penetrable-Square-Well Model
The one-dimensional penetrable-square-well fluid is studied using both
analytical tools and specialized Monte Carlo simulations. The model consists of
a penetrable core characterized by a finite repulsive energy combined with a
short-range attractive well. This is a many-body one-dimensional problem,
lacking an exact analytical solution, for which the usual van Hove theorem on
the absence of phase transition does not apply. We determine a
high-penetrability approximation complementing a similar low-penetrability
approximation presented in previous work. This is shown to be equivalent to the
usual Debye-H\"{u}ckel theory for simple charged fluids for which the virial
and energy routes are identical. The internal thermodynamic consistency with
the compressibility route and the validity of the approximation in describing
the radial distribution function is assessed by a comparison against numerical
simulations. The Fisher-Widom line separating the oscillatory and monotonic
large-distance behavior of the radial distribution function is computed within
the high-penetrability approximation and compared with the opposite regime,
thus providing a strong indication of the location of the line in all possible
regimes. The high-penetrability approximation predicts the existence of a
critical point and a spinodal line, but this occurs outside the applicability
domain of the theory. We investigate the possibility of a fluid-fluid
transition by Gibbs ensemble Monte Carlo techniques, not finding any evidence
of such a transition. Additional analytical arguments are given to support this
claim. Finally, we find a clustering transition when Ruelle's stability
criterion is not fulfilled. The consequences of these findings on the
three-dimensional phase diagrams are also discussed.Comment: 17 pages, 12 figures; to be published in JC
Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids
An overview of some analytical approaches to the computation of the structural and thermodynamic properties of single component and multicomponent hard-sphere fluids is provided. For the structural properties, they yield a thermodynamically consistent formulation, thus improving and extending the known analytical results of the Percus–Yevick theory. Approximate expressions for the contact values of the radial distribution functions and the corresponding analytical equations of state are also discussed. Extensions of this methodology to related systems, such as sticky hard spheres and squarewell fluids, as well as its use in connection with the perturbation theory of fluids are briefly addressed.