Fig. 1.
Schematic phase diagram for the systems discussed in this article. (a) The critical region associated with a liquid–gas critical point. Shown are the two features displaying mathematical singularities: the critical point (filled circles) and the liquid–gas coexistence line (bold dashed curve). (b) Same as in a with the addition of the gas–liquid spinodal and the Widom line. Along the Widom line, thermodynamic response functions have extrema in their T dependence. Path α denotes a path along which the Widom line is crossed, whereas path β denotes a path crossing the coexistence line. (c) A hypothetical phase diagram for water of possible relevance to the recent neutron scattering experiments by Chen and colleagues (25, 26) on confined water. The negatively sloped liquid–liquid coexistence line generates a Widom line that extends beyond the critical point, suggesting that water may exhibit a fragile-to-strong transition for P < Pc (path α), whereas no dynamic changes will occur above the critical point (path β). (d) A sketch of the P–T phase diagram for the two-scale Jagla model. Upon cooling at constant pressure above the critical point (path α), the liquid changes, as the path crosses the Widom line, from a low-density state (characterized by a non-glassy Arrhenius dynamics) to a high-density state (characterized by non-Arrhenius dynamics) as the path crosses the Widom line. Upon cooling at constant pressure below the critical point (path β), the liquid remains in the LDL phase as long as path β does not cross the LDL spinodal line. Thus, one does not expect any dramatic change in the dynamic behavior along the path β.