Differences between discontinuous and continuous soft-core attractive potentials: The appearance of density anomaly

Soft-core attractive potentials can give rise to a phase diagram with three fluid phases at different densities (gas, low-density liquid and high-density liquid), separated by first order phase transition lines ending in critical points. Experiments show a phase diagram with these features for phosphorous and triphenyl phosphite. Liquid-liquid phase transition could be relevant for water, silica, liquid metals, colloids and protein solutions, among others. Here we compare two potentials with short-range soft-core repulsion and narrow attraction. One of them is a squared potential that is known to have liquid-liquid phase transition, ending in a critical point, and no anomaly in density. The normal, monotonic, behavior of density for isobaric cooling is surprising if compared with molecular liquids, such as water, where a hypothetical critical point is proposed as rationale for the anomalous behavior of density. The second potential is a continuous version of the first. We show that the phase diagram associated to this new potential has, not only the liquid-liquid phase transition, but also the density anomaly.