Liquid coexistence boundary

In these phase diagrams, the liquidus line represents the temperature at which one of the components crystallizes, while, below the solidus line, the whole system solidifies. Between the solidus and liquidus lines are the regions where solid and liquid coexist. Since there is no solid phase above the liquidus lines and the liquid is thermodynamically stable. Ding et al. suggested that the liquidus temperatures should be adopted as the lower boundary of the liquid phase, instead of the solidus temperatures. The patterns of these phase diagrams are... 

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. 

In accordance with the Clapeyron equation and Le Chatelier s principle, the more highly ordered (low-entropy) phases tend to lie further to the left (at lower 7), whereas the higher-density phases tend to lie further upward (at higher 7). The mnemonic (7.32) allows us to anticipate the relative densities of adjacent phases. From the slope, for example, of the ice II-ice III coexistence line (which tilts forward to cover ice III), we can expect that ice II is denser than ice III (pn > pm). Similarly, from the forward slopes of the liquid coexistence lines with the high-pressure ices II, V, and VI, we can expect that cubes of ice II, ice V, and ice VI would all sink in a glass of water, whereas ice I floats (in accord with the backward tilt of its phase boundary). Many such inferences can be drawn from the slopes of the various phase boundaries in Fig. 7.3, all consistent with the measured phase densities Pphase (in gL 1), namely,... 

In contrast, a heterogeneous solution of noncritical composition (e.g., v < xc, as shown by the arrow and dashed line in Fig. 7.11) shows a qualitatively different behavior as it is rises through the coexistence boundary and into the homogeneous region near and above Tc. For each increase in temperature along the dashed line in Fig. 7.11, a horizontal tie-line yields both the compositions of the A-rich and B-rich liquids (from the two ends of the tie-line), as well as the relative amounts of each phase (from the lever rule). Clearly, the critical composition xc remains near the middle of the tie-line as T increases toward Tc, whereas a noncritical composition x xc moves toward one or other terminus of the tie-line as the temperature is raised. 

In the phase diagram, panel (a). solid C02 (Dry Ice) is in equilibrium with gaseous C02 at a temperature of —78.7°C and a pressure of 1.00 bar." The solid sublimes without turning into liquid. At any temperature above the triple point at —56.6°C, there is a pressure at which liquid and vapor coexist as separate phases. For example, at 0°C, liquid is in equilibrium with gas at 34.9 bar. Moving up the liquid-gas boundary, we see that two phases always exist until the critical point is reached at 31.3 C... 

The solid-liquid boundary, the almost vertical line in the illustration, shows the pressures and temperatures at which solid and liquid coexist in equilibrium. In other words, it shows how the melting point varies with pressure. To show the slopes more clearly, the plots are not to scale, but despite this, the steepness of the lines show that even large changes in pressure result in quite small variations in melting point. 

The following data for the system methyl isobutyl ketone (MIK)-acetone-water are an example of such data. These data form the boundary of the dome-shaped liquid-liquid coexistence region that was plotted in the triangular diagram of Fig. 11.2-8. 

An isochoric equation has been developed for computing thermodynamic functions of pure fluids. It has its origin on a given liquid-vapor coexistence boundary, and it is structured to be consistent with the known behavior of specific heats, especially about the critical point. The number of adjustable, least-squares coefficients has been minimized to avoid irregularities in the calculated P(p,T) surface by using selected, temperature-dependent functions which are qualitatively consistent with isochores and specific heats over the entire surface. Several nonlinear parameters appear in these functions. Approximately fourteen additional constants appear in auxiliary equations, namely the vapor-pressure and orthobaric-densities equations, which provide the boundary for the P(p,T) equation-of-state surface. 

With the above objectives in mind, we constrain the equation to the liquid-vapor coexistence boundary. For any density, the coexistence temperature, Ta(p), is obtained by iteration from equations for the ortho-baric densities. Thus the vapor pressure, P[Pg.351]

Figure 3. Vapor-liquid coexistence line for the Lennard-Jones model. Solid line is presently the best determination of the phase boundary [50] triangles [86] and circles [59] are Gibbs ensemble data. Dashed line is obtained from Gibbs-Duhem integration beginning with the low-temperature (rightmost) Gibbs ensemble datum. Error bars on the true line are the stability analysis prediction of how the error in the initial datum propagates through the integration series.

According to some researchers, the two states are in fact two distinct phases, with real coexistence boundaries. If this claim can ever be verified, then it follows that there should exist a second critical point for water, akin to the critical point at 374°C, where the liquid and gas phases coalesce. It may, however, be impossible to confirm the existence of such a point by experiment, because it would lie well below Thom where freezing cannot be avoided. 

Figure 9.1 shows a typical phase diagram for a pure (one-component) substance. The three phase boundary lines (liquid-solid, liquid-gas, and solid-gas) meet at the triple point (the one temperature and pressure where all three phases coexist). The liquid-gas boundary line terminates at the critical point. These phase boundaries indicate how the coexistence pressure between two phases changes as the temperature changes. In this section, we will examine how we can use thermodynamics to predict the shape of phase coexistence curves for pure substances. For mixtures, more complicated phase diagrams can be constructed that indicate the dependence of the coexistence pressure and temperature upon the composition of the various phases. Phase diagrams for mixtures are discussed in Sections 9.2 and 9.3. 

We compare gas-liquid coexistence curves from GFVT in the good solvent limit with Monte Carlo simulation results of Bolhuis et al. [52] in Fig. 4.11 for q = 0.67 and 1.05. It is clear GFVT is capable of predicting the location of flie phase boundaries reasonably well. 

Far away from the critical temperature, the mean of the vapour and liquid densities is represented in first approximation by a rectilinear diameter. However, close to the eritical point, the critical fluctuations modify not only the shape of the coexistence boundary, which becomes... 

The lines separating the regions in a phase diagram are called phase boundaries. At any point on a boundary between two regions, the two neighboring phases coexist in dynamic equilibrium. If one of the phases is a vapor, the pressure corresponding to this equilibrium is just the vapor pressure of the substance. Therefore, the liquid-vapor phase boundary shows how the vapor pressure of the liquid varies with temperature. For example, the point at 80.°C and 0.47 atm in the phase diagram for water lies on the phase boundary between liquid and vapor (Fig. 8.10), and so we know that the vapor pressure of water at 80.°C is 0.47 atm. Similarly, the solid-vapor phase boundary shows how the vapor pressure of the solid varies with temperature (see Fig. 8.6). 

A triple point is a point where three phase boundaries meet on a phase diagram. For water, the triple point for the solid, liquid, and vapor phases lies at 4.6 Torr and 0.01°C (see Fig. 8.6). At this triple point, all three phases (ice, liquid, and vapor) coexist in mutual dynamic equilibrium solid is in equilibrium with liquid, liquid with vapor, and vapor with solid. The location of a triple point of a substance is a fixed property of that substance and cannot be changed by changing the conditions. The triple point of water is used to define the size of the kelvin by definition, there are exactly 273.16 kelvins between absolute zero and the triple point of water. Because the normal freezing point of water is found to lie 0.01 K below the triple point, 0°C corresponds to 273.15 K. 

It has been shown by FM that the phase state of the lipid exerted a marked influence on S-layer protein crystallization [138]. When the l,2-dimyristoyl-OT-glycero-3-phospho-ethanolamine (DMPE) surface monolayer was in the phase-separated state between hquid-expanded and ordered, liquid-condensed phase, the S-layer protein of B. coagulans E38/vl was preferentially adsorbed at the boundary line between the two coexisting phases. The adsorption was dominated by hydrophobic and van der Waals interactions. The two-dimensional crystallization proceeded predominately underneath the liquid-condensed phase. Crystal growth was much slower under the liquid-expanded monolayer, and the entire interface was overgrown only after prolonged protein incubation. 

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