Mixturelike Behavior Near a Liquid-Liquid Phase Transition in Simulations of Supercooled Water

In simulations of a waterlike model (ST2) that exhibits a liquid-liquid phase transition, we test for the occurrence of a thermodynamic region in which the liquid can be modeled as a two-component mixture. We assign each molecule to one of two species based on the distance to its fifth-nearest neighbor, and evaluate the concentration of each species over a wide range of temperature and density. Our concentration data compare well with mixture-model predictions in a region between the liquid-liquid critical temperature and the temperature of maximum density. Fits of the model to the data in this region yield accurate estimates for the location of the critical point. We also show that the liquid outside the region of density anomalies is poorly modeled as a simple mixture.

Figure 1

(a) $T\mathrm{\text{−}}P$ and (b) $\rho \mathrm{\text{−}}T$ projections of the properties of ST2 water. From Ref. 18 we show the line of density maxima (thick black line); density minima (thin black line); $K_T$ maxima (thick blue line); $K_T$ minima (thin blue line); the liquid spinodal (diamonds); the HDL spinodal (down triangles); and the LDL spinodal (up triangles). We also show the locus along which $x=0.5$ (open red squares); the location of the critical point (open black circle); and the state points falling inside the region $\mathcal{R}$ defined in the text (crosses). The green line in (a) is a line of slope $m$, and in (b) is the coexistence curve predicted by the MRS model.

Figure 2

(a) $g_5(r)$ at $T=245\mathrm{K}$, for $\rho =0.88$ to $1.06\mathrm{g}/{\mathrm{cm}}^3$ in steps of $0.02\mathrm{g}/{\mathrm{cm}}^3$. (b) $g_5(r)$ at $\rho =0.96\mathrm{g}/{\mathrm{cm}}^3$, for $T=220$ to 270 K in steps of 10 K. For clarity, curves for $T>220\mathrm{K}$ are successively shifted upward by 0.05. (c) A snapshot of a system of $N=13824$ ST2 molecules at $T=245\mathrm{K}$ and $\rho =0.96\mathrm{g}/{\mathrm{cm}}^3$; at this state we find $P=191\mathrm{MPa}$. Blue molecules have $r_5>0.35\mathrm{nm}$; red molecules have $r_5<0.35\mathrm{nm}$.

Figure 3

(a) Isotherms of $x$ as a function of $P$. (b) Isobars of $x$ as a function of $T$. Solid curves are the corresponding predictions of Eq. (1).

Figure 4

Isotherms near $T_c$ of $V$ as a function of $x$. The lines are linear fits to the data for $0.4>x>0.6$. For clarity, the data for $T=245\mathrm{K}$ have been shifted downward by $0.5{\mathrm{cm}}^3/\mathrm{mol}$. Inset: Isotherms of $P$ versus $V$ straddling $T_c$.