Physics of the Liquid-Liquid Critical Point

Within the inherent structure thermodynamic formalism introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys. Rev. A 25, 978 (1982)], we address the basic question of the physics of the liquid-liquid transition and of density maxima observed in some complex liquids such as water by identifying, for the first time, the statistical properties of the potential energy landscape responsible for these anomalies. We also provide evidence of the connection between density anomalies and the liquid-liquid critical point. Within the simple (and physically transparent) model discussed, density anomalies do imply the existence of a liquid-liquid transition.

Figure 1

Schematic explanation of the connection between a minimum in ${\sigma }^2(V)$ and a liquid-liquid critical point. Square, circle, and diamond indicate, respectively, a $V$ smaller than, equal to, and larger than $V_{{\sigma }_{\min }^2}$. The central panel shows the corresponding isochores. Note that, as shown in Eq. (3), $P$ increases (decreases) on cooling when $d{\sigma }^2/dV>0$ ($<0$). The bottom panels report the corresponding high and low $T$ isotherms. At low $T$ an unstable van der Waals loop appears.

Figure 2

Volume dependence of the PEL parameters for the SPC/E potential. Dashed lines indicate the trends expected for simple liquids [27].

Figure 3

Harmonic Gaussian landscape phase diagram for the SPC/E potential, including the TMD line, the liquid-liquid critical point with the associated spinodal lines, and the Kauzmann locus. Lines below the Kauzmann locus have no physical meaning, since they correspond to states with negative $S_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{f}}$. They are drawn here to visualize the termination of the TMD line and the relative position of the critical point respect to the Kauzmann locus. Squares indicate the TMD as evaluated directly from the MD calculations. As discussed in the text, adding the anharmonic contributions in the theoretical calculation would move the liquid-liquid critical point into the physically meaningful $S_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{f}}>0$ region.