Thermodynamic, dynamic, and structural anomalies for shoulderlike potentials

Using molecular dynamic simulations we study a family of continuous core-softened potentials consisting of a hard core, a shoulder at closest distances, and an attractive well at further distance. The repulsive shoulder and the well distances represent two length scales. We show that if the first scale, the shoulder, is repulsive or has a small well, the potential has a region in the pressure-temperature phase diagram with density, diffusion, and structural anomalies. However, if the closest scale becomes a deep well, the regions in the pressure-temperature phase diagram where the three anomalies are present shrink and disappear. This result helps in defining two length scales potentials that exhibit anomalies.