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.

We use molecular dynamics simulations to study how the confinement affects the dynamic, thermodynamic, and structural properties of a confined anomalous fluid. The fluid is modeled using an effective pair potential derived from the ST4 atomistic model for water. This system exhibits density, structural, and dynamical anomalies, and the vapor-liquid and liquid-liquid critical points similar to the quantities observed in bulk water. The confinement is modeled both by smooth and structured walls. The temperatures of extreme density and diffusion for the confined fluid show a shift to lower values while the pressures move to higher amounts for both smooth and structured confinements. In the case of smooth walls, the critical points and the limit between fluid and amorphous phases show a non-monotonic change in the temperatures and pressures when the nanopore size is increase. In the case of structured walls, the pressures and temperatures of the critical points varies monotonically with the pore size. Our results are explained on basis of the competition between the different length scales of the fluid and the wall-fluid interaction.

Molecular dynamics simulations are used to examine the relationship between water-like anomalies and the liquid-liquid critical point in a family of model fluids with multi-Gaussian, core-softened pair interactions. The core-softened pair interactions have two length scales, such that the longer length scale associated with a shallow, attractive well is kept constant while the shorter length scale associated with the repulsive shoulder is varied from an inflection point to a minimum of progressively increasing depth. The maximum depth of the shoulder well is chosen so that the resulting potential reproduces the oxygen-oxygen radial distribution function of the ST4 model of water. As the shoulder well depth increases, the pressure required to form the high density liquid decreases and the temperature up to which the high-density liquid is stable increases, resulting in the shift of the liquid-liquid critical point to much lower pressures and higher temperatures. To understand the entropic effects associated with the changes in the interaction potential, the pair correlation entropy is computed to show that the excess entropy anomaly diminishes when the shoulder well depth increases. Excess entropy scaling of diffusivity in this class of fluids is demonstrated, showing that decreasing strength of the excess entropy anomaly with increasing shoulder depth results in the progressive loss of water-like thermodynamic, structural and transport anomalies. Instantaneous normal mode analysis was used to index the overall curvature distribution of the fluid and the fraction of imaginary frequency modes was shown to correlate well with the anomalous behavior of the diffusivity and the pair correlation entropy. The results suggest in the case of core-softened potentials, in addition to the presence of two length scales, energetic, and entropic effects associated with local minima and curvatures of the pair interaction play an important role in determining the presence of water-like anomalies and the liquid-liquid phase transition.

Using molecular dynamic simulations we study three families of continuous core-softened potentials consisting of two length scales: a shoulder scale and an attractive scale. All the families have the same slope between the two length scales but exhibit different potential energy gap between them. For each family three shoulder depths are analyzed. We show that all these systems exhibit a liquid-liquid phase transition between a high density liquid phase and a low density liquid phase ending at a critical point. The critical temperature is the same for all cases suggesting that the critical temperature is only dependent on the slope between the two scales. The critical pressure decreases with the decrease of the potential energy gap between the two scales suggesting that the pressure is responsible for forming the high density liquid. We also show, using the radial distribution function and the excess entropy analysis, that the density, the diffusion and the structural anomalies are present if particles move from the attractive scale to the shoulder scale with the increase of the temperature indicating that the anomalous behavior depends only in what happens up to the second coordination shell.

Three core-softened families of potentials are checked for the presence of density and diffusion anomalies. These potentials exhibit a repulsive core with a softening region and at larger distances an attractive well. We found that the region in the pressure-temperature phase diagram in which the anomalies are present increases if the slope between the core-softened scale and the attractive part of the potential decreases. The anomalous region also increases if the range of the coresoftened or of the attractive part of the potential decreases. We also show that the presence of the density anomaly is consistent with the non monotonic changes of the radial distribution function at each one of the two scales when temperature and density are varied. Then, using this anomalous behavior of the structure we show that the pressures and the temperatures in which the radial distribution functions of the two length scales are equal are identified with the Widom line.