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

TL;DR

This study compares two soft-core attractive potentials, revealing that the continuous potential exhibits both liquid-liquid phase transition and density anomaly, unlike the squared potential which only shows phase transition.

Contribution

It demonstrates that the presence of density anomaly depends on the potential's derivative, highlighting the importance of potential continuity in phase behavior.

Findings

Continuous potential shows density anomaly and phase transition.

Squared potential exhibits only phase transition without density anomaly.

Density behavior is strongly influenced by the potential's derivative.

Abstract

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. Our result, therefore, shows that the behavior in density is strongly dependent on the derivative of the potential.