  Water is an unique material with a long list of thermodynamic, dynamic and
structural anomalies, which are usually attributed to the competition between
two characteristic length scales in the intermolecular interaction. It has been
argued that a potential liquid-liquid phase transition (LLPT) ending at a
liquid-liquid critical point (LLCP) lies at the core of the anomalous behavior
of water. This transition which has been evidenced in multiple simulation
studies seems to be preempted experimentally by spontaneous crystallization.
Here, in order to expose the connection between the spontaneous crystallization
observed in the supercooled regime in the vicinity of the LLPT, and the density
anomaly, we perform extensive Molecular Dynamics simulations of a model mixture
of core-softened water and methanol. The pure water-like fluid exhibits a LLPT
and a density anomaly. In contrast, our pure methanol-like model does have a
LLPT but lacks the density anomaly. Our results illustrate the relation between
the vanishing of the density anomaly and an increase in the temperature of the
spontaneous crystallization: once this temperature surpasses the LLCP critical
temperature, no density anomaly is observed. This peculiar feature illustrates
how fine tuning the competitive interactions determine the anomalous behavior
of water/alcohol mixtures.
