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 behaviors 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 the 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.

Structural properties of hard disks in a narrow tube

“…The pair correlation function was determined in various systems interacting with shortrange pair potentials [16,17,18], the link between the short-ranged pair potential and the pair correlation functions was examined in a charged-stabilized colloidal system trapped to one dimension [19] and the long-range interaction induced freezing transition of hard rods was studied by [20]. Even our knowledge of the ordering properties of onedimensional hard rod fluid (Tonks gas) has been widened by the exact determination of the percolation size [21] and by the study of the residual multiparticle entropy at the onset of solidlike behaviour [22].…”

The penetrable square-well model: extensive versus non-extensive phases

“…The PSW fluid combines features belonging to both limiting cases within a very subtle interplay between the repulsive and attractive energy scale that affects its thermodynamic stability [8][9][10]. Figure 1.…”

Phase diagram of the penetrable-square-well model

“…While the novel features appearing even in the one-dimensional case have been studied in some details [6][7][8][9], no analysis regarding the influence of penetrability and attractiveness on the phase behavior of PSW fluids have been reported, so far, in three dimensions. The present paper aims to fill this vacancy.…”

“…In Ref. [8] we proved that in the one-dimensional case the PSW model is Ruelle stable if ǫ a /ǫ r < 1/2(ℓ + 1), where ℓ is the integer part of ∆/σ. This result can be extended to any dimensionality d by the following arguments.…”

“…Instead, different minimal models accounting for the boundness of the potential have to be considered, the Gaussian core model [2] and the penetrable-sphere (PS) model [3][4][5] being well studied examples. More recently, the penetrable square-well (PSW) fluid has been added to this category [6][7][8][9] with the aim of including the existence of attractive effective potentials. The PSW model is obtained from the SW potential by reducing to a finite value the infinite repulsion at short range, φ PSW (r) =    ǫ r , r ≤ σ , −ǫ a , σ < r ≤ σ + ∆ , 0 , r > σ + ∆ ,…”