Phase Behavior of Liquids

The Vapor Pressure of Liquids. Vapor pressure is defined as the pressure exerted by a vapor in equilibrium with its liquid. Consider a closed, evacuated container which has been partially filled with a liquid. The molecules of the liquid are in constant motion but not all the molecules move with the same velocity and there will be some which possess a relatively high kinetic energy. If one of these fast moving molecules reaches the liquid surface, it may possess sufficient energy to overcome the attractive forces in the liquid and pass into tiie vapor space above. As the number of molecules in the vapor phase increases the rate of return to the liquid phase also increases and eventually a condition of dynamic equilibrium is attained when the number of molecules leaving the liquid is equal to the number returning. The molecules in the vapor phase obviously exert a pressure on the containing vessel and this pressure is known as the vapor pressure. 

Logaritibm vapor pressure versus reciprocal of the absolute temperature. 

Measurement of Vapor Pressure. A number of experimental methods for the measurement of vapor pressure are available. Two of these methods will be briefly described since they illustrate the physical meaning of vapor pressure. 

A second method for the determination of vapor pressure which is based on the general gas law is known as the Gas Saturation method. A weighed quantity of a liquid of known molecular wei t is placed 

Equation 3 is not exact since V in this equation should be the volume of air and vapor that comes out of the trap and not the volume of air passed in. The higher the vapor pressure of the liquid, the 

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A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

The distinct properties of liquid-crystalline polymer solutions arise mainly from extended conformations of the polymers. Thus it is reasonable to start theoretical considerations of liquid-crystalline polymers from those of straight rods. Long ago, Onsager [2] and Flory [3] worked out statistical thermodynamic theories for rodlike polymer solutions, which aimed at explaining the isotropic-liquid crystal phase behavior of liquid-crystalline polymer solutions. Dynamical properties of these systems have often been discussed by using the tube model theory for rodlike polymer solutions due originally to Doi and Edwards [4], This theory, the counterpart of Doi and Edward s tube model theory for flexible polymers, can intuitively explain the dynamic difference between rodlike and flexible polymers in concentrated systems [4]. 

On a ternary equilibrium diagram like that of Figure 14.1, the limits of mutual solubilities are marked by the binodal curve and the compositions of phases in equilibrium by tielines. The region within the dome is two-phase and that outside is one-phase. The most common systems are those with one pair (Type I, Fig. 14.1) and two pairs (Type II. Fig. 14.4) of partially miscible substances. For instance, of the approximately 1000 sets of data collected and analyzed by Sorensen and Arlt (1979), 75% are Type I and 20% are Type II. The remaining small percentage of systems exhibit a considerable variety of behaviors, a few of which appear in Figure 14.4. As some of these examples show, the effect of temperature on phase behavior of liquids often is very pronounced. 

As the pressure of the system decreases, the boiling temperature decreases, in general. Therefore, we expect the vapor-liquid coexistence envelope to drop to lower temperatures as the pressures decrease. Changes in pressure, however, do not have a strong influence on the phase behavior of liquids. As a result, we do not expect the liquid-liquid phase envelope to change much with pressure. Consequently, we expect that at a low enough pressure, the vapor-liquid coexistence curve will intersect the liquid-liquid coexistence curve. When this occurs, we can have vapor-liquid-liquid equilibria, which is shown in Figure 3.9. 

Despite extensive investigation of phase behavior of liquid crystals in computer simulation studies [97-99], the literature on computational studies of their dynamics is somewhat limited. The focal point of the latter studies has often been the single-particle and collective orientational correlation functions. The Zth rank single-particle orientational time correlation function (OTCF) is defined by... 

A Predictive Method for PVT and Phase Behavior of Liquids Containing Supercritical Components... 

Global Fluid Phase Behavior of Liquids and Cases... 

For an understanding of the phase behavior of liquid-crystalline systems in general knowledge of the dynamics is necessary. Moreover, in these materials molecular, dynamics is contemporary and important for their application in memory devices because the storage of information is directly connected with a reorientation of molecules or parts of it. Dielectric relaxation spectroscopy has proven to be a very suitable tool to study the molecular motion in these compounds for several reasons. Firstly, mesogens are usually polar. If different molecular reorientations involve... 

Mathias, P. M. and J. P. O Connell. 1979. A predictive method for PVT and phase behavior of liquids containing supercritical components. In Equations of State in Engineering and Research. Washington, DC American Chemical Society. 

Different experimental techniques have been used to characterize structural and phase behavior of liquid crystalline materials. Polarizing optical microscopy is one of the essential tools for the characterization of newly synthesized mesogenic materials, together with differential scanning calorimetry (DSC) and x-ray investigations, while DSC provides information on phase transition temperatures and order of transitions. X-ray investigations for actual structural evaluation, i. e. determination of phase type, have to be performed on macroscopically well oriented samples, which is often time consuming and sometimes hard to realize. Therefore... 

Fig. 1). Liquid crystalline phases can disappear with increasing pressure and appear again at still higher pressures. Thus there exists a valuable tool for influencing the phase behavior of liquid crystals. 

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