Waterlike anomalies for core-softened models of fluids: Two-dimensional systems

Abstract

We use a one-dimensional (1d) core-softened potential to develop a physical picture for some of the anomalies present in liquid water. The coresoftened potential mimics the effect of hydrogen bonding. The interest in the 1d system stems from the facts that closed-form results are possible and that the qualitative behavior in 1d is reproduced in the liquid phase for higher dimensions. We discuss the relation between the shape of the potential and the density anomaly, and we study the entropy anomaly resulting from the density anomaly. We find that certain forms of the two-step square well potential lead to the existence at T = 0 of a low-density phase favored at low pressures and of a high-density phase favored at high pressures, and to the appearance of a point C ′ at a positive pressure, which is the analog of the T = 0 "critical point" in the 1d Ising model. The existence of point C ′ leads to anomalous behavior of the isothermal compressibility K T and the isobaric specific heat C P .

Two-dimensional core-softened model with water like properties: Monte Carlo and integral equation study

“…In the liquid range the model has density maxima which disappear at high pressures. The same behavior was also observed by molecular dynamics by Scala et al 22 Next, we explored other thermodynamic properties, such as isothermal compressibility (Figure 4), thermal expansion coefficient ( Figure 5) and heat capacity ( Figure 6). Isothermal compressibility has minimum in temperature dependence like water has.…”

“…In this work, we use the smooth version of the coresoftened potential proposed by Scala et al 22 The interaction potential U(r) is calculated by adding a Gaussian well to the Lennard-Jones (LJ) part of the potential…”

“…For the sake of comparison with the previous studies, we adopt the units and values of model parameters as used before by Scala et al 22 We use ε = 1.0, σ = 1.0, λ = 1.7, a = 25.0, r 0 = 1.5σ . Figure 1 shows the shape of this smooth version of the core-softened potential.…”

“…On the other hand, 2D MD calculation produced only density anomaly but no liquid-liquid phase transition. 20,21 Scala et al 22 carried out MD simulations of 2D discrete and smoothed version of the potential to study liquid anomalies. These studies were continued by Buldyrev et al 17 to explore the liquid-liquid phase transition for 2D and 3D version of potentials, and by Almudallal et al 18 They both produced phase diagrams for the discrete version of potential with liquid anomalies, and no liquid-liquid critical point in stable liquid region was obtained.…”

The puzzling unsolved mysteries of liquid water: Some recent progress

“…The possibility is that liquid water could at low temperatures condense not into a single phase-as we anticipate when a gas with a simple interaction like a Lennard-Jones potential condenses into a fluid-but into two different phases. This possibility was first raised by Takahashi 60 years ago and various elaborations of this model have been made by a number of people since then, including seminal work of Per Hemmer and George Stell in 1971 [7][8][9]. The implications of this is the possibility of two different liquid phases contributing to an increase in these fluctuations in specific volume and a negative contribution to the cross-fluctuations, negative because the deeper well has a larger volume and a lower entropy.…”