Binary systems, phase behavior

Systems Containing More Than Two Components. As in binary systems, the behavior of systems containing more than two components can be understood on the basis of intermolecular forces and solubility parameters. Water and tetrachloromethane have widely differing solubility and hydrogen bond parameters, and are therefore immiscible. Added acetone dissolves partly in the aqueous phase due to hydrogen bond formation, and partly in the tetrachloromethane phase due to dispersion and induction forces. Twice as much acetone dissolves in the aqueous phase as in tetrachloromethane. On increasing the acetone concentration a homogeneous solution is obtained. The added solvent thus acts as a solubilizer for the two immiscible solvents. 

Similarly to the phase diagrams for binary systems, the main types for fluid phase diagrams of ternary mixtures should not have an intersection of critical curves and inunis-cibUity regions with a crystallization surface in them. Combination of four main types of binary fluid phase behavior la, lb, Ic and Id (Figure 1.2) for constituting binary subsystems gives six major classes of ternary fluid mixtures with one volatile component, two binary subsystems (with volatile component) complicated by the immiscibility phenomena and the third binary subsystem (consisted from two nonvolatile components) of type la with a continuous solid solutions. These six classes of ternary fluid mixtures can be referred as ternary class I (with binary subsystems Ib-lb-la), ternary class II (with binary subsystems Ic-lc-la), ternary class III (with binary subsystems Id-ld-la), or ternary class IV (with binary subsystems Ib-ld-la), ternary class V (with binary subsystems Ib-lc-la) and ternary class VI (with binary subsystems Ic-ld-la). 

Figure 20.1.6 Binary solid - supercritical system. Phase behavior of dissimilar binary systems...

To illustrate, predictions were first made for a ternary system of type II, using binary data only. Figure 14 compares calculated and experimental phase behavior for the system 2,2,4-trimethylpentane-furfural-cyclohexane. UNIQUAC parameters are given in Table 4. As expected for a type II system, agreement is good. 

Physical Equilibria and Solvent Selection. In order for two separate Hquid phases to exist in equiHbrium, there must be a considerable degree of thermodynamically nonideal behavior. If the Gibbs free energy, G, of a mixture of two solutions exceeds the energies of the initial solutions, mixing does not occur and the system remains in two phases. Eor the binary system containing only components A and B, the condition (22) for the formation of two phases is... 

The Class I binary diagram is the simplest case (see Fig. 6a). The P—T diagram consists of a vapor—pressure curve (soHd line) for each pure component, ending at the pure component critical point. The loci of critical points for the binary mixtures (shown by the dashed curve) are continuous from the critical point of component one, C , to the critical point of component two,Cp . Additional binary mixtures that exhibit Class I behavior are CO2—/ -hexane and CO2—benzene. More compHcated behavior exists for other classes, including the appearance of upper critical solution temperature (UCST) lines, two-phase (Hquid—Hquid) immiscihility lines, and even three-phase (Hquid—Hquid—gas) immiscihility lines. More complete discussions are available (1,4,22). Additional simple binary system examples for Class III include CO2—hexadecane and CO2—H2O Class IV, CO2—nitrobenzene Class V, ethane—/ -propanol and Class VI, H2O—/ -butanol. 

Fig. 6. Qualitative piessuie—tempeiatuie diagiams depicting ctitical curves for the six types of phase behaviors for binary systems, where C or Cp corresponds to pure component critical point G, vapor 1, Hquid U, upper critical end point and U, lower critical end point. Dashed curves are critical lines or phase boundaries (5). (a) Class I, the Ar—Kr system (b) Class 11, the CO2—CgH g system (c) Class 111, where the dashed lines A, B, C, and D correspond to the H2—CO, CH —H2S, He—H2, and He—CH system, respectively (d) Class IV, the CH —C H system (e) Class V, the C2H -C2H OH...

Because of the interest in its use in elevated-temperature molten salt electrolyte batteries, one of the first binary alloy systems studied in detail was the lithium-aluminium system. As shown in Fig. 1, the potential-composition behavior shows a long plateau between the lithium-saturated terminal solid solution and the intermediate P phase "LiAl", and a shorter one between the composition limits of the P and y phases, as well as composition-dependent values in the single-phase regions [35], This is as expected for a binary system with complete equilibrium. The potential of the first plateau varies linearly with temperature, as shown in Fig. 2. 

B.H. Sage, Phase Behavior in Binary and Multi-component Systems at Elevated Pressures n-Pentane and Methane-m-Pentane , NSRDS-NBS 32 (1970) 20)A.S. Mal tseva et al,... 

The dilated van Laar model is readily generalized to the multicomponent case, as discussed in detail elsewhere (C3, C4). The important technical advantage of the generalization is that it permits good estimates to be made of multicomponent phase behavior using only experimental data obtained for binary systems. For example, Fig. 14 presents a comparison of calculated and observed -factors for the methane-propane-n-pentane system at conditions close to the critical.7... 

A brief discussion of sohd-liquid phase equihbrium is presented prior to discussing specific crystalhzation methods. Figures 20-1 and 20-2 illustrate the phase diagrams for binary sohd-solution and eutectic systems, respectively. In the case of binary solid-solution systems, illustrated in Fig. 20-1, the liquid and solid phases contain equilibrium quantities of both components in a manner similar to vapor-hquid phase behavior. This type of behavior causes separation difficulties since multiple stages are required. In principle, however, high purity... 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binary and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predictive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilibria that is useful for estimating nonideal binary or multicomponent solid-liquid phase behavior has been reported by Muir (Pap. 71f, 73d ann. meet., AIChE, Chicago, 1980). 

The interaction parameters for binary systems containing water with methane, ethane, propane, n-butane, n-pentane, n-hexane, n-octane, and benzene have been determined using data from the literature. The phase behavior of the paraffin - water systems can be represented very well using the modified procedure. However, the aromatic - water system can not be correlated satisfactorily. Possibly a differetn type of mixing rule will be required for the aromatic - water systems, although this has not as yet been explored. 

Propane - Water System. The interaction parameters for the propane - water system were obtained over a temperature range from 42°F to 310°F using exclusively the data of Kobayashi and Katz (24). This is because among the available literature on the phase behavior of this binary system, their data appear to give the most extensive information. A constant interaction parameter was obtained for the propane-rich phases at all temperatures. The magnitude of the temperature - dependent interaction parameter for this binary was less than that for the ethane - water binary at the same temperature. Azarnoosh and McKetta (25) also presented experimental data for the solubility of propane in water over about the same temperature range as that of Kobayashi and Katz but at pressures up to 500 psia only. However, a different set of temperature - dependent parameters... 

Shariati, A. and Peters, C. J., High-pressure phase behavior of systems with ionic liquids Measurements and modeling of the binary system fluoroform + l-ethyl-3-methylimidazolium hexafluorophosphate, /. Supercrit. Fluids, 25, 109, 2003. 

Much of what we need to know abont the thermodynamics of composites has been described in the previous sections. For example, if the composite matrix is composed of a metal, ceramic, or polymer, its phase stability behavior will be dictated by the free energy considerations of the preceding sections. Unary, binary, ternary, and even higher-order phase diagrams can be employed as appropriate to describe the phase behavior of both the reinforcement or matrix component of the composite system. At this level of discussion on composites, there is really only one topic that needs some further elaboration a thermodynamic description of the interphase. As we did back in Chapter 1, we will reserve the term interphase for a phase consisting of three-dimensional structure (e.g., with a characteristic thickness) and will use the term interface for a two-dimensional surface. Once this topic has been addressed, we will briefly describe how composite phase diagrams differ from those of the metal, ceramic, and polymer constituents that we have studied so far. 

An accurate representation of the phase equilibrium behavior is required to design or simulate any separation process. Equilibrium data for salt-free systems are usually correlated by one of a number of possible equations, such as those of Wilson, Van Laar, Margules, Redlich-Kister, etc. These correlations can then be used in the appropriate process model. It has become common to utilize parameters from such correlations to obtain insight into the fundamentals underlying the behavior of solutions and to predict the behavior of other solutions. This has been particularly true of the Wilson equation, which is shown below for a binary system. 

Eutectic diagrams (from Greek svtt]ktoo- easily melted ) represent the T-x melting behavior for binary systems with completely immiscible solid phases a, /3. The solid a, /3 phases often correspond to (virtually) pure components A, B, respectively, so we may treat phase and component labels (rather loosely) as interchangeable in this limit. 

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