A Numerical Test of a High-Penetrability Approximation for the One-Dimensional Penetrable-Square-Well Model

Abstract

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-Hückel 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.

17 pages, 12 figures; to be published in JCP

References in corpus (8)

• Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density functional theory
• Phase transitions and configuration space topology
• Penetrable Square-Well fluids: Exact results in one dimension
• Structure of penetrable-rod fluids: Exact properties and comparison between Monte Carlo simulations and two analytic theories
• Low-temperature and high-temperature approximations for penetrable-sphere fluids. Comparison with Monte Carlo simulations and integral equation theories
• Penetrable-Square-Well fluids: Analytical study and Monte Carlo simulations
• Non existence of a phase transition for the Penetrable Square Wells in one dimension
• Thermodynamic consistency between the energy and virial routes in the mean spherical approximation for soft potentials

Cited by in corpus (3)

• Phase diagram of the penetrable square well-model
• Molecular dynamics simulation study of self-diffusion for penetrable-sphere model fluids
• Non existence of a phase transition for the Penetrable Square Wells in one dimension