Vaporization critical point

Point c is a critical point known as the upper critical end point (UCEP).y The temperature, Tc, where this occurs is known as the upper critical solution temperature (UCST) and the composition as the critical solution mole fraction, JC2,C- The phenomenon that occurs at the UCEP is in many ways similar to that which happens at the (liquid + vapor) critical point of a pure substance. For example, at a temperature just above Tc. critical opalescence occurs, and at point c, the coefficient of expansion, compressibility, and heat capacity become infinite. 

A number of Ya.B. s papers were devoted to the properties of states close to the fluid-vapor critical point, to periodic crystallization, and to the limiting chemical kinetic laws of bimolecular and chain reactions. We will not, however, attempt to take the place of the bibliography at the end of the book which provides a complete list of Ya.B. s papers on the subjects of this volume. 

The transition to the continuum fluid may be mimicked by a discretization of the model choosing > 1. To this end, Panagiotopoulos and Kumar [292] performed simulations for several integer ratios 1 < < 5. For — 2 the tricritical point is shifted to very high density and was not exactly located. The absence of a liquid-vapor transition for = 1 and 2 appears to follow from solidification, before a liquid is formed. For > 3, ordinary liquid-vapor critical points were observed which were consistent with Ising-like behavior. Obviously, for finely discretisized lattice models the behavior approaches that of the continuum RPM. Already at = 4 the critical parameters of the lattice and continuum RPM agree closely. From the computational point of view, the exploitation of these discretization effects may open many possibilities for methodological improvements of simulations [292], From the fundamental point of view these discretization effects need to be explored in detail. 

F liquid + vapor G liquid + vapor (critical point) H vapor the first dashed line (at the lower temperature) is the normal melting point, and the second dashed line is the normal boiling point. The solid phase is denser because of the positive slope of the solid/liquid equilibrium line. 

Figure 8. Phase diagram of the Gay-Berne model with the original and the most-studied parameterization (k = 3, k = 5, fi = 2, v = 1) in the density-temperature plane as obtained from computer simulations. Filled diamonds mark simulation results the phase boundaries away from these points are drawn as a guide only. The domains of the thermodynamic stability of the isotropic (/), nematic (N), and smectic (SB) phases are shown. The liquid-vapor critical point is denoted by C. Two-phase regions are shaded. (Reproduced from Ref. 104.)...

Recent experiments have demonstrated that the 0 condition may be also induced in polymer solutions in supercritical fluids (SCFs) by varying the temperature and/or pressure [4]. A SCF is a substance at a pressure and temperature above e liquid-vapor critical point where the coexisting liquid and vapor phases become indistinguishable. The physical properties of SCFs are similar to those of dense gases, although when highly... 

Figure 8. Left panel phase diagram of ice T> T (P)) and transition lines corresponding to the ice Ih-to-HDA, LDA-to-HDA, and HDA-to-LDA transformations T

IJ. The Liquid-Vapor Critical Point Data of Fluid Metals and Semiconductors... 

The problem of temperature and pressure control, temperature stability, and temperature homogeneity becomes particularly important in studies close to the liquid-vapor critical point. The difficulties are directly related to the strong critical divergences of the isothermal compressibility, xt = = —V dVldp)j and the isobaric expan-... 

Fig. 2.7. Pressure-temperature phase diagram of selenium showing solid, liquid, and vapor phases together with regions of semiconducting (SC), metallic (M), and insulator (I) behavior. The line of semiconductor-metal transitions observed in the liquid at high pressure (Brazhkin et al., 1989) is extrapolated to contour of constant DC electrical conductivity (

Experimental data for the DC conductivity pressure dependences of the conductivity at constant temperature near the liquid-vapor critical point. Comparison with the equation-of-state data displayed in Fig. 2.3(a) clearly shows a qualitative relationship between rapid variation in the conductivity and density. Conductivity data obtained along the liquid-vapor coexistence curve, shown in Fig. 3.20, demonstrate, furthermore that the electronic structures of the liquid and vapor are fundamentally different. The liquid structure of cesium just above the melting point is characterized by a high degree of correlation in the atomic positions (see Section 3.4) and, as we have noted previously, cesium is a normal liquid metal with physical properties very similar to those of the corresponding solid. The electrical conductivity, in particular, is ical for a material with metallic electron concentration, that is, an electron density comparable with the atomic density. 

Mercury has the lowest known critical temperature (1478 °C) of any fluid metal. It is therefore particularly attractive to experimentalists. Mercury is also considerably less corrosive than many metals, especially the alkali metals discussed in the preceding chapter. These relatively favorable circumstances permit precise measurement of the electrical, optical, magnetic, and thermophysical properties of fluid mercury. With care, one can control temperatures accurately enough to determine the asymptotic behavior of physical properties as the liquid-vapor critical point is approached. Such truly critical data are especially valuable for exploring the relationship between the liquid-vapor and MNM transitions. Of the expanded metals exhibiting MNM transitions, mercury is therefore the most extensively investigated. It is the only expanded divalent metal whose critical region has proven to be experimentally accessible. 

Fluid-fluid phase separations have been observed in many binary mixtures at high pressures, including a large number of systems in which helium is one of the components (Rowlinson and Swinton, 1982). Fluid-fluid phase separation may actually be the rule rather than the exception in mixtures of unlike molecules at high pressures. Fig. 6.4 shows the three-dimensional phase behavior of a binary mixture in schematic form. This diagram includes the vapor pressure curves and liquid-vapor critical points of the less volatile component (1) and the more volatile component (2) in their respective constant-x planes. The critical lines are interrupted one branch remains open up to very high temperatures and pressures. Systems that can be represented by a diagram such as Fig. 6.4, those for which the critical lines always have positive slope in the p — T projection, have been called fluid-fluid mixtures of the first kind. A second class of system, in which the critical line first drops to temperatures below T (l) and then increases, exhibit fluid-fluid equilibrium of the second kind. There is, however, no fundamental distinction between these two classes of fluid mixtures. 

The fonnation of wetting layers in mercury vapor is one example of heterogeneous behavior that is strongly influenced by the liquid-vapor critical point and the MNM transition. Another is the formation of dense liquid droplets in supersaturated metal vapor. The gradual size-dependent transition to metallic properties of isolated metal clusters (described in Sec. 4.7 for mercury clusters) should play an important role in the kinetics of the vapor-liquid phase transition of metals. As droplets grow during homogeneous nucleation in a supersaturated metal vapor, the MNM transition must affect the interparticle interactions. 

The liquid-vapor transition of fluid metals forces one to search for the unity in physical science. The existence of the liquid-vapor critical point makes possible a continuous transition from a dilute atomic vapor to a dense metallic liquid. Thus a single set of experiments on a single pure... 

The synthesis of low-density (long-chain branched) polyethylene (LDPE), which proceeds along a free radical mechanism, is performed in bulk ethylene at temperatures and pressures far above those of the liquid-vapor critical point of the monomer ethylene. The production of LDPE takes place in autoclaves at pressures between 1400 and 3500 bar and temperatures up to 600 K. About 10 35% of the ethylene is converted into LDPE. The separation of LDPE from the... 

Figure 5.14 The Molar Volume Near a Liquid-Vapor Critical Point.

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. 

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