Liquid spinodal

Fig. 40 Schematic phase diagram of the disordered phases for particles interacting with isotropic potentials (upper panel) and limited valence potentials (lower panel). In the first, standard case, the glass line hits the gas-liquid spinodal at large densities. In the limited valence case, the shrunk gas-liquid coexistence region leaves a new region in which a stable network with saturated bonding can develop. Reproduced with permission from [167]...

The question of whether there is a tme glassy nature of amorphous ices is of interest when speculating about possible liquid-liquid transitions in (deeply) supercooled water. For true glasses, the amorphous-amorphous transitions described here can be viewed as the low-temperature extension of liquid-liquid transitions among LDL, HDL, and possibly VHDL. That is, the first-order like LDA <-> HDA transition may map into a first-order LDL HDL transition, and the continuous HDA <-> VHDA transition may map into a smeared HDL VHDL transition. Many possible scenarios are used how to explain water s anomalies [40], which share the feature of a liquid-liquid transition [202, 207-212]. They differ, however, in the details of the nature of the liquid-liquid transition Is it continuous or discontinuous Does it end in a liquid-liquid critical point or at the reentrant gas-liquid spinodal ... 

Figure 4 Cartoon for hidden liquid-liquid spinodal in a polymer melt, calculated for a Flory Rotational Isomeric State chain with a simple coupling between density and conformational order A is the trans-gauche energy gap and a dimensionless density. Shown is the path of an isochoric quence into the unstable regime. r, is the spinodal temperature, T the melting temperature, T the liquid-liquid critical point, and Tp the temperature at which the harrier between dense liquid and crystal is of order ksT ...

Fig. 16. Calculated phase diagram of the soft-sphere plus mean-field model, showing the vapor-liquid (VLB), solid-liquid (SI.E ), and solid-vapor (SVE) coexistence loci, the superheated liquid spinodal (s), and the Kauzmann locus (K) in the pressure-temperature plane (P = Pa /e-,T =k T/ ). The Kauzmann locus gives the pressure-dependent temperature at which the entropies of the supercooled lit]uid and the stable crystal are equal. Note the convergence of the Kauzmann and spinodal loci at T = 0. See Debenedetti et al. (1999) for details of this calculation.

Figure 1. Pressure-temperature diagram illustrating the different perturbation processes of liquid water, and their relations with the stable, metastable and unstable fields of Hf). Solid line the saturation curve (LG). Dotted lines the mechanical liquid spinodal curve Sp(L) and the mechanical gas spinodal curve Sp(G).

Nevertheless, thermodynamics provides us with a simple concept which can help us to analyze the possible evolution, explosive or not, of a boiling or gas exsolution process. However, while the liquid spinodal curve of water is presumably well known, at least in its high-temperature part, the topology of spinodal curves of aqueous solutions is poorly known. The purpose of the next two sections is to fill in this gap for CO2 and NaCl aqueous solutions. 

Figure 5 depicts the liquid spinodal curves Sp(L) in a pressure-temperature diagram for fixed CO2 compositions. The region of negative pressures, which is of interest for describing the capillary properties of CO2 aqueous solutions, has been also included. Interestingly, it can be noted that spinodal Sp(L) isopleths present a pressure-temperature trend, which looks similar to the liquid spinodal curve of pure water.At low temperatures, the Sp(L) isopleths are decreasing steeply before to reach a pressure minimum. Then at subcritical temperatures, isopleths are less spaced and sloped, and they finish to meet the H2O-CO2 critical curve. The temperature appears as a determining parameter in the explosivity control of CO2 aqueous solutions. Like for water, the easiest way to generate an explosive vaporization is a sudden depressurization in the superspinodal domain, where spinodal curves have a gentle slope in a P-T diagram (Fig. 5). This superspinodal field can be estimated theoretically irom the PRSV equation of...

Figure 5. The liquid spinodal curves in a pressure-temperature diagram for the H2O-CO2 system, as calculated by the PRSV equation of state. Numbers refer to the mole fraction XCO2 of dissolved CO2 in the aqueous. solution.

Figures. Stability fields, calculated by the Anderko andPitzer equation of state of the HzO-NaCl system in a pressure-temperature diagram. Solid lines the saturation curve (LG) of pure water and the spinodal isopleths of p[fD-NaCl fluids (numbers refer to the mole fractions of NaCl). Dotted lines the liquid spinodal curve Sp(L, Hfd) and gas. spinodal curve Sp(G, HfJ) of pure water.

Figure 9. a) A P-T diagram showing the boiling curves of adsorbed water in porous media (numbers refer to the radius of the pore). The dotted curve is the liquid spinodal curve Sp(L). b) The peperitic (fyke in the lava flow of Pardines (the boundaries are outlined by the thick curve). The horizontal dashed lines indicate the po,sitions of the successive growth pulses of the dyke. 

Figure 10. a) Conceptual sketch of hydrothermal systems, b) P-T diagram illustrating potentially explosive processes for the HfD-NaCl in an hydrothermal environment (see text). Thick solid lines the saturation curve for pure water (Sat) and the three-phase halite-liquid-vapour curve (HLG). Dotted line the critical curve (CC). Thin solid lines the spinodal curves forxj uCl 0.01 (3.2 wt% NaCl), 0.05 (14.6 wt % NaCl) and O.l (26.5 wt % NaCl) with their corresponding critical points (filled circles). The gray zones along liquid spinodal curves Sp(L) indicate the onset of the instability field of superheated NaCl... 

Here, line ABDFG represents the pressure-volume relationship for a temperature lower than the critical temperature. The liquid phase can exist in a metastable state along line BC and the vapor phase can similarly exist along line FE. The dotted line CDE represents an unstable region. Points C and E, representing the limits of the metastable region, are usually referred to as spinodal points, and these points have loci (for different isotherms) along the lines labeled Liquid Spinodal and Vapor Spinodal in Fig. 15.2. 

The Thermodynamic Limit. In the preceding text (see Fig. 15.2), the limit of the region in which the liquid phase can exist in a metastable state (the liquid spinodal) was introduced this is represented by point C in Fig. 15.2. One view of homogeneous nucleation is that it will occur at the spinodal limit that corresponds (see Fig. 15.2) to the condition (expressed in term of reduced quantities)... 

From the relationship between reduced properties given by Eq. 15.5, Carey [4] derived the following relationship for the liquid spinodal temperature (Tr)s ... 

Fig. 3. Phase diagram of n-pentane 1) saturation line. C) critical point. 2) liquid spinodal. 3) line J(T p )...

Figure 2. Equation of state features of (a) ST2 water and (b) WAC silica, projected into the P T plane. Density maxima (dashed lines) and liquid spinodal boundaries (dot-dashed lines) are shown. Isochores of P as a function of T are shown as symbols joined by thin solid lines. Equally spaced isochores are shown from bottom to top in (a) from p = 0.8 to 1.1 g/cm, and in (b) from p = 1.8 to 2.4 g/cm. ...

Figure 3. Schematic phase diagrams in the pressure-temperature (P, Ij plane illustrating three scenarios for liquids displaying anomalous thermodynamic behaviour, (a) The spinodal retracing scenario. (b) The liquid-liquid critical point scenario, (c) The singularity free scenario. The dashed line represent the liquid-gas coexistence line, the dotted line is the liquid liquid coexistence line, the thick solid line is the liquid spinodal, the long dashed lines is the locus of compressibility extrema and the dot dashed line is the locus of density extrema. The liquid-gas critical point is represented by filled circle and the liquid-liquid critical point by filled square.

We recognize that there are always two solutions x = 1 5x with the same T. The two solutions coincide if x = Xc = 1 corresponding to T = T = 1/16. The conclusion is that the RPM possesses a gas-liquid spinodal curve, here worked out in the vicinity of the critical point at... 

---