Waterlike anomalies in a two-dimensional core-softened potential

We investigate the structural, thermodynamic, and dynamic behavior of a two-dimensional (2D) core-corona system using Langevin dynamics simulations. The particles are modeled by employing a core-softened potential which exhibits waterlike anomalies in three dimensions. In previous studies in a quasi-2D system a new region in the pressure versus temperature phase diagram of structural anomalies was observed. Here we show that for the two-dimensional case two regions in the pressure versus temperature phase diagram with structural, density, and diffusion anomalies are observed. Our findings indicate that, while the anomalous region at lower densities is due the competition between the two length scales in the potential at higher densities, the anomalous region is related to the reentrance of the melting line.

Figure 1

Core-softened interaction potential $U$ between two core-corona particles. Inset: schematic depiction of the particles, with the core (first length scale at $r_{ij}\equiv r_1\approx 1.2\sigma$) and the soft corona (second length scale at $r_{ij}\equiv r_1\approx 2.0\sigma$).

Figure 2

(a) Diffusion constant $D$ and (b) translational order parameter $\tau$ as function of the system density. In both figures the maxima and minima that characterize the anomalies are represented by a dashed red line. For the diffusion anomaly, the anomalous region at lower densities ranges from the isotherm $T=0.07$ to $T=0.24$, while the second anomalous region goes from $T=0.07$ to $T=0.15$. In the case of the structural anomaly, the first anomalous regions goes from the isotherm $T=0.07$ to $T=0.40$, and the anomalous region at higher densities is located between the temperatures $T=0.07$ and $T=0.24$. The errors bars in $D$ and $\tau$ are smaller than the data point.

Figure 3

$p\times T$ phase diagram of the colloidal system. The gray lines are the isochores. The dashed blue line delimits the structural anomaly regions, with the maximum and minimum values of $\tau$. The dotted-dashed red line delimits the diffusion anomalous regions, with the minimum and maximum values of $D$. The green line defines the density anomaly region and corresponds to the temperature of maximum density (TMD) line. The black stars are located over the isotherm $T=$ 0.12 and correspond to the densities $\rho =0.15$, $\rho =0.225$, $\rho =0.325$, $\rho =0.35$, $\rho =0.425,$ and $\rho =0.525$. The dotted black line delimits the fluid and amorphous solid regions. The errors obtained for the mean value of $p$ and $T$ were smaller than ${10}^{-4}$ for all cases, and the errors bars were omitted for simplicity.

Figure 4

Analysis of the isotherm $T=$ 0.12 for the colloidal system. (a) Radial distribution function (RDF) $g\left(r_{ij}\right)$ for densities inside the first anomalous region indicates that these anomalies originate by the competition between the two length scales. Curves for densities $0.15\le \rho <0.225$ are represented by black lines, for $0.225\le \rho <0.325$ by red lines, and for $\rho =0.325$ by the green line. The arrows shows how the peaks in $g\left(r_{ij}\right)$ move. The black arrow shows the grow of the second peak for densities below $\rho =0.225$, the red arrow the decrease in the second peak, and the green arrow the increase in the first peak for densities between $\rho =0.225$ and $\rho =0.325$. (b) Radial distribution function (RDF) $g\left(r_{ij}\right)$ for densities inside the second anomalous region indicates that there is not a competition between the scales. Curves for densities $0.35\le \rho <0.425$ are represented by black lines, for $0.425\le \rho <0.525$ by red lines, and for $\rho =0.525$ by the green line. Both peaks increase from $\rho =0.35$ to $\rho =0.425$, while the valley between them decreases. This is indicated by the red arrows. The green arrows show that from $\rho =0.425$ to $\rho =0.525$ the peaks decrease and the valley increases. Therefore, the system becomes more structured and then more disordered, which explains the second structural anomaly. Related to this transition from disordered to ordered to disordered structure, the slope of the MSD curve decreases and then increases, as shown in (c). The snapshots in (d) show the disks' conformation, including a kagome lattice at $\rho =0.60$.