Liquid-vapor critical temperature

The temperature of two-liquid phase appearance with rising temperature. The liquid-vapor critical temperature of very dilute phase. 

So, a stable macroscopic vapor layer between a liquid and a solid or its formation via a surface phase transition (drying transition) was never observed experimentally for water and for any other fluid. This well agrees with the theoretical expectations [117, 118, 124] that a drying transition is suppressed by the long-range fluid-surface interaction up to the bulk liquid-vapor critical temperature Tc. Even for the extremely weak fluid-surface interface (liquid neon on cesium), formation of a... 

Figure 35 Surface phase diagram of water. Solid lines indicate drying and wetting transitions. Horizontal dashed lines indicate liquid-vapor critical temperature Tc and freezing temperature respectively. Insets show arrangement of molecules in the coexisting phases of water in cylindrical pores (i p = 25 A, r = 300K) to the left (C/o =-3.08 kcal/mol) and to the right Uo = -0.77 kcal/mol) from the inclined line of the wetting transitions.

It is very difficult to measure the coexistence curves of confined fluid experimentally, as this requires estimation of the densities of the coexisting phases at various temperatures. Therefore, only a few experimental liquid-vapor coexistence curves of fluids in pores were constructed [279, 284,292,294-297]. In some experimental studies, the shift of the liquid-vapor critical temperature was estimated without reconstruction of the coexistence curve [281-283, 289]. The measurement of adsorption in pores is usually accompanied by a pronounced adsorption-desorption hysteresis. The hysteresis loop shrinks with increasing temperature and disappears at the so-called hysteresis critical temperature Teh. Hysteresis indicates nonequilibrium phase behavior due to the occurrence of metastable states, which should disappear in equilibrium state, but the time of equilibration may be very long. The microscopic origin of this phenomenon and its relation to the pore structure is still an area of discussion. In disordered porous systems, hysteresis may be observed even without phase transition up to hysteresis critical temperature Teh > 7c, if the latter exists [299]. In single uniform pores, Teh is expected to be equal to [300] or below [281-283] the critical temperature. Although a number of experimentally determined values of Teh and a few the so-called hysteresis coexistence curves are available in the literature, hysteresis... 

The coexistence curves and properties of confined fluid were extensively studied by computer simulations. Shift of the parameters of the liquid-vapor critical point of fluids in pores was seen in many simulation studies. The most accurate results were obtained by simulations of LJ fluid in the Gibbs ensemble [10, 28-30, 32, 127, 141, 186, 187, 205, 249,250,262,274,325,326], but this method is restricted to the pores of simple geometry only. In the narrow slit pore with weakly attractive walls and widths of 6,7.5, and 10 a, the liquid-vapor critical point of LJ fluid decreases to 0.8897] , 0.9197] , and 0.9577] , respectively [325, 326]. For comparable fluid-wall interaction, the liquid-vapor critical temperature is about 0.9647] and 0.9817] in the pores with a width Hp= 12 a and 77p = 40(7, respectively [29]. The dependence of the pore critical temperature on the pore width is shown in Fig. 53. This dependence may be satisfactorily described by equation (15) (solid line) when we take into account that centers of molecules do not enter an interval of about 0.5 <7 near each wall. The critical temperatures of U fluid in the pores with strongly attractive walls are noticeably lower than in pores with weakly attractive walls (compare circles and squares in Fig. 53) [325,326]. This should be attributed to the effective decrease in the pore width due to the appearance of adsorbed film on the pore walls, which is almost identical in both phases. In this case, dependence of Tc p on Hp may be satisfactorily described by equation (15) (dashed line) if we take into account that... 

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. 

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. 

Selected Physical Property Data (molecular weights, specific gravities of solids and liquids, melting and boiling points, heats of fusion and vaporization, critical temperature and pressure, standard heats of formation and combustion)... 

This presents difficulties when we want to examine the solubility of gases, such as oxygen which has a critical temperature of Tc = 154.59 K and nitrogen which has a critical temperature of Tc = 126.21 K, in liquids. The critical temperature of these gases are well below ambient temperatures. For these systems, another approach is required to determine the conditions for vapor-liquid equilibrium. 

Let s consider a binary mixture of carbon dioxide and hexane at a temperature of 393.15 K. The critical temperature of hexane is 507.5 K, which is higher than the system temperature, so pure liquid hexane can exist as a liquid. The critical temperature of carbon dioxide is 304.2 K, which is lower than the system temperature. Consequently, pure carbon dioxide does not possess a vapor-liquid transition at this temperature, and its vapor pressure is undefined. Raoult s law cannot be applied to this system. 

However, in nature, engineering and private life we deal with solutions. Addition of the second component considerably complicates the problem. In this connection, attention may be paid, firstly, to the transfer of the liquid-vapor critical curve and, hence, the binodals Ts p,c = const, c - the concentration in liquid phase) to the region of elevated pressures, see Fig. 1, and secondly to changes in the thermodynamic compatibility of components with temperature and pressure. These factors lead to considerable extent of the two-phase equilibrium region with respect to that of pure liquid and, consequently, to the principal increase in the requirements on the experimental methods and devices used to study this region. 

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.)...

Category VI phase behavior, shown in Fig. 10.3-3/, occurs with components that are so dissimilar that component 2 has a melting or triple point (Mj) that is well above the critical temperature of component 1. In this case there are two regions of solid-liquid-vapor equilibrium (SLVE). One starts at the triple point of pure component 2 (M ) and intersects the liquid-vapor critical line at the upper critical end point U. The second solid-liquid-vapor critical line starts below the melting point Mt and intersects the vapor-liquid critical line starting at component 1 at the lower critical end point L. Between the lower and upper critical points only solid-vapor (or solid-fluid) equilibrium exists. 

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

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 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... 

Temperature dependences of the fraction of water molecules with tetrahedral arrangement of the nearest four neighbors in liquid water calculated at the liquid-vapor coexistence curve for two water models are shown in Fig. 5. There are less than 10% of such water molecules at the liquid-vapor critical point. Upon cooling, more water molecules gain tetrahedral ordering and their fraction achieves 50% at ambient conditions. At some temperatures below the freezing temperature, fraction of tetrahedrally ordered water molecules in supercooled liquid water shows a rapid or even a stepwise increase. 

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