Liquid-vapor phase transition critical point

Let us first consider the liquid/vapor phase transition of NaCl. PVT data have been recorded up to about 2000 K, which is still far below the critical point. Extrapolations guided by simulations and theory predict Tc = 3300 K and the critical mass density dc = 0.18 g cm-3 [33], With a = 0.276 nm and e = 1, this maps onto Tc = 0.05 and p = 0.08. 

Although the liquid-vapor phase transition of bulk water is well studied experimentally, this is not the case for the phase transitions of interfacial and confined water, which we consider in the next sections. Therefore, studies of the phase transitions of confined water by computer simulation gain a special importance. For meaningful computer simulations, it is necessary to have water model, which is able to describe satisfactorily the liquid-vapor and other phase transitions of bulk water. The coexistence curves of some empirical water models, which represent a water molecule as a set of three to five interacting sites, are shown in Fig. 1. Some model adequately reproduces the location of the liquid-vapor critical point and. 

The experimental determination of the critical temperature Tcp of fluids in pores is a difficult problem. Usually, adsorption measurements are the main way to locate the liquid-vapor phase transition. When approaching the pore critical point, the jump in the adsorption decreases and should disappear. But due to the nonuniform distribution of pore sizes in real porous materials, this jump is smeared out and it is difficult to determine accurately its disappearance. The most accurate results were obtained for fluids in silica aerogels, where the shifts of the critical temperature ATc from 0.002Tc to 0.0077] was observed [294—296]. In porous glasses with mean pore radius /Jp = 157, 121, and 39 A,... 

Helium-4 Normal-Superfluid Transition Liquid helium has some unique and interesting properties, including a transition into a phase described as a superfluid. Unlike most materials where the isotopic nature of the atoms has little influence on the phase behavior, 4He and 3He have a very different phase behavior at low temperatures, and so we will consider them separately Figure 13.11 shows the phase diagram for 4He at low temperatures. The normal liquid phase of 4He is called liquid I. Line ab is the vapor pressure line along which (gas + liquid I) equilibrium is maintained, and the (liquid + gas) phase transition is first order. Point a is the critical point of 4He at T= 5.20 K and p — 0.229 MPa. At this point, the (liquid + gas) transition has become continuous. Line be represents the transition between normal liquid (liquid I) and a superfluid phase referred to as liquid II. Along this line the transition... 

This paper deals with the degradation of substances like PVC, Tetrabromobisphenol A, y-HCH and HCB in supercritical water. This process is called "Supercritical Water Oxidation", a process which gained a lot of interest in the past. The difference between subcritical and supercritical processes is easy to recognize in the phase diagram of water. The vapor pressure curve of water terminating at the critical point, i.e. at 374 °C and 221 bar. The relevant critical density is 0.32 g/cm3. This corresponds to approx. 1/3 of the density of normal liquid water. Above the critical point, a compression of water without condensation, i.e. without phase transition is possible. It is within this range that supercritical hydrolysis and oxidation are carried out. The vapor pressure curve is of special importance in subcritical hydrolysis as well as in wet oxidation. 

Figure 4.2 Variation of the vapor pressure, Pv, of a substance with the temperature, 7, showing the phase transition between solid, liquid and vapor phases. Two phases can coexist in equilibrium only at pressures and temperatures defined by the phase boundary lines in the phase diagram, such as liquid-vapor, solid-liquid and solid-vapor lines. The liquid-vapor phase boundary terminates at the critical point, 7C. All three phases can coexist in equilibrium only at the triple point, 73, which is the intersection of the three two-phase boundaries.

In P-r space, we see only two remarkable features the vapor pressure curve, indicating the conditions under which the vapor and liquid coexist, and the critical point, at which the distinction between vapor and liquid disappears. We indicate in this figure the critical isotherm 7 = Tc and the critical isobar P = Pc. If the liquid is heated at a constant pressure exceeding the critical pressure, it expands and reaches a vapor-like state without undergoing a phase transition. Andrews and Van der Waals called this phenomenon the continuity of states. 

Data such as those shown in Fig. 2.3 vividly illustrate the physical consequences of state-dependent electronic structure. These plots depict the isothermal variation of the density (Fig. 2.3a) and DC electrical conductivity (Fig. 2.3b) of fluid cesium as a function of pressure (Hensel et al., 1985, 1991). Near the critical point the conductivity drops sharply showing the strong influence of the phase transition on the electronic structure. Nevertheless, there is no indication of an actual discontinuity in the electronic character within the limits of experimental resolution. Except along the liquid-vapor phase boundary, the MNM transition is continuous. 

How does confinement affect the phase diagram that is, what is the influence of confinement on the vapor-Uquid and liquid-liquid phase transitions, critical properties, interfacial properties, and critical mixing point of a solute in a solvent ... 

Look back at the large phase diagram (Figure 7-1) and notice the intersection of the three lines at 0.01° and 6 X 10 atm. Only at this triple point can the solid, liquid, and vapor states of FljO all coexist. Now find the point at 374° C and 218 atm where the liquid/gas boundary terminates. This critical point is the highest temperature and highest pressure at which there is a difference between liquid and gas states. At either a temperature or a pressure over the critical point, only a single fluid state exists, and there is a smooth transition from a dense, liquid-like fluid to a tenuous, gas-like fluid. 

The order of a transition can be illustrated for a fixed-stoichiometry system with the familiar P-T diagram for solid, liquid, and vapor phases in Fig. 17.2. The curves in Fig. 17.2 are sets of P and T at which the molar volume, V, has two distinct equilibrium values—the discontinuous change in molar volume as the system s equilibrium environment crosses a curve indicates that the phase transition is first order. Critical points where the change in the order parameter goes to zero (e.g., at the end of the vapor-liquid coexistence curve) are second-order transitions. 

In 1958, Pitzer (141), in a remarkable contribution that appears to have been the first theoretical consideration of this phenomenon, likened the liquid-liquid phase separation in metal-ammonia solutions to the vapor-liquid condensation that accompanies the cooling of a nonideal alkali metal vapor in the gas phase. Thus, in sodium-ammonia solutions below 231 K we would have a phase separation into an insulating vapor (corresponding to matrix-bound, localized excess electrons) and a metallic (matrix-bound) liquid metal. This suggestion of a "matrix-bound analog of the critical liquid-vapor separation in pure metals preceeded almost all of the experimental investigations (41, 77, 91,92) into dense, metallic vapors formed by an expansion of the metallic liquid up to supercritical conditions. It was also in advance of the possible fundamental connection between this type of critical phenomenon and the NM-M transition, as pointed out by Mott (125) and Krumhansl (112) in the early 1960s. 

Because of the existence of the critical point, a path can be drawn from the liquid region to the gas region that does not cross a phase boundary e.g., the path from A to B in Fig. 3.1. This path represents a gradual transition from the liquid to the gas region. On the other hand, a path crossing phase boundary 2-C includes a vaporization step, where an abrupt change of properties occurs. 

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