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.

We report the results of Monte Carlo investigations of the structure and the interfacial tension of the liquid-liquid interface of the Widom-Rowlinson mixture. The results are compared with a mean-field theory.

The second-order integral-equation formalism of [Attard J. Chem. Phys. 91, 3072 (1989); 95, 4471 (1991)], applied previously to one-component hard spheres and Lennard-Jones fluids, as well as to their mixtures, is used to binary Widom-Rowlinson mixtures. Comparison with Monte Carlo simulations of the pair correlation functions and of the demixing phase diagram shows that this method is also quite accurate in the case of highly nonadditive mixtures. Moreover, the results of the second-order theory are compared with previous theoretical predictions. Our interest is also in the calculation of the bridge functions, i.e., parts of the radial distribution functions either not included or simply approximated in the usual theories.