Ternary critical point

Ternary Critical Point. The point where, upon adding a mutual solvent to two partially miscible liquids (as adding alcohol to ether and water), the two solutions become consolute and one phase results. 

Figure 2. Quantitave pressure-temperature diagram for carbon dioxide-water-1-propanol O, exp. ternary critical points, this work O four-phase equilibria, this work x four-phase equilibria, Fleck et al. [5]...

Pressure-temperature diagrams offer a useful way to depict the phase behaviour of multicomponent systems in a very condensed form. Here, they will be used to classify the phase behaviour of systems carbon dioxide-water-polar solvent, when the solvent is completely miscible with water. Unfortunately, pressure-temperature data on ternary critical points of these systems are scarcely published. Efremova and Shvarts [6,7] reported on results for such systems with methanol and ethanol as polar solvent, Wendland et al. [2,3] investigated such systems with acetone and isopropanol and Adrian et al. [4] measured critical points and phase equilibria of carbon dioxide-water-propionic acid. In addition, this work reports on the system with 1-propanol. The results can be classified into two groups. In systems behaving as described by pattern I, no four-phase equilibria are observed, whereas systems showing four-phase equilibria are designated by pattern II (cf. Figure 3). 

Binary critical points Ternary critical points... 

The composition of the nonsolvent-solvent mixture representing the critical composition of the ternary system with polymer of infinite molecular weight (see Fig. 123,a) possesses unique significance. Scott and Tompa have shown that the composition at the critical point in the limit of infinite molecular weight is specified by... 

Ternary equilibrium curves calculated by Scott,who developed the theory given here, are shown in Fig. 124 for x = 1000 and several values of X23. Tie lines are parallel to the 2,3-axis. The solute in each phase consists of a preponderance of one polymer component and a small proportion of the other. Critical points, which are easily derived from the analogy to a binary system, occur at... 

Figure 3.3 Illustration of the calculation of the phase diagram of a mixed biopolymer solution from the experimentally determined osmotic second virial coefficients. The phase diagram of the ternary system glycinin + pectinate + water (pH = 8.0, 0.3 mol/dm3 NaCl, 0.01 mol/dm3 mercaptoethanol, 25 °C) —, experimental binodal curve —, calculated spinodal curve O, experimental critical point A, calculated critical point O—O, binodal tielines AD, rectilinear diameter,, the threshold of phase separation (defined as the point on the binodal curve corresponding to minimal total concentration of biopolymer components). Reproduced from Semenova et al. (1990) with permission.

During the 1940s, a large amount of solubility data was obtained by Francis (6, 7), who carried out measurements on hundreds of binary and ternary systems with liquid carbon dioxide just below its critical point. Francis (6, 7) found that liquid carbon dioxide is also an excellent solvent for organic materials and that many of the compounds studied were completely miscible. In 1955, Todd and Elgin (8) reported on phase equilibrium studies with supercritical ethylene and a number of... 

The critical point of a specific mixture of methane and propane occurs at 1040 psia at this temperature, dot 5. The dew-point and bubble-point lines of the ternary intersect the methane-propane side of the diagram at the composition of this critical point. 

Above this pressure, dot 6, all mixtures of methane and propane are single phase. Thus only the methane-n-pentane binaries have two-phase behavior, and only the methane-n-pentane side of the ternary diagram can show a bubble point and a dew point. The bubble-point and dewpoint lines of the saturation envelope do not intercept another side of the diagram, rather the two lines join at a critical point, i.e., the composition of the three-component mixture that has a critical pressure of 1500 psia at 160°F. 

In a blend of immiscible homopolymers, macrophase separation is favoured on decreasing the temperature in a blend with an upper critical solution temperature (UCST) or on increasing the temperature in a blend with a lower critical solution temperature (LCST). Addition of a block copolymer leads to competition between this macrophase separation and microphase separation of the copolymer. From a practical viewpoint, addition of a block copolymer can be used to suppress phase separation or to compatibilize the homopolymers. Indeed, this is one of the main applications of block copolymers. The compatibilization results from the reduction of interfacial tension that accompanies the segregation of block copolymers to the interface. From a more fundamental viewpoint, the competing effects of macrophase and microphase separation lead to a rich critical phenomenology. In addition to the ordinary critical points of macrophase separation, tricritical points exist where critical lines for the ternary system meet. A Lifshitz point is defined along the line of critical transitions, at the crossover between regimes of macrophase separation and microphase separation. This critical behaviour is discussed in more depth in Chapter 6. 

A line of ordinary critical points for macrophase separation is shown as the line CA B in Fig. 6.42 for a ternary blend of two homopolymers with equal degrees of polymerization and a diblock copolymer at high temperature. Four regimes have been identified by Broseta and Fredrickson (1990) and are indicated in... 

We note that even short-range interactions may, however, allow a mean-field scenario, if the system has a tricritical point, where three phases are in equilibrium. A well-known example is the 3He-4He system, where a line of critical points of the fluid-superfluid transition meets the coexistence curve of the 3He-4He liquid-liquid transition at its critical point [33]. In D = 3, tricriticality implies that mean-field theory is exact [11], independently from the range of interactions. Such a mechanism is quite natural in ternary systems. For one or two components it would require a further line of hidden phase transitions that meets the coexistence curve at or near its critical point. 

There is a large body of experimental work on ternary systems of the type salt + water + organic cosolvent. In many cases the binary water + organic solvent subsystems show reentrant phase transitions, which means that there is more than one critical point. Well-known examples are closed miscibility loops that possess both a LCST and a UCST. Addition of salts may lead to an expansion or shrinking of these loops, or may even generate a loop in a completely miscible binary mixture. By judicious choice of the salt concentration, one can then achieve very special critical states, where two or even more critical points coincide [90, 160,161]. This leads to very peculiar critical behavior—for example, a doubling of the critical exponent y. We shall not discuss these aspects here in detail, but refer to a comprehensive review of reentrant phase transitions [90], We note, however, that for reentrant phase transitions one has to redefine the reduced temperature T, because near a given critical point the system s behavior is also affected by the existence of the second critical point. An improper treatment of these issues will obscure results on criticality. 

From a global assessment of these results, it seems inescapable to conclude that mean-field behavior does not remain valid asymptotically close to the critical point. Rather, ionic systems seem to show Ising-to-mean-field crossover. Such a crossover has been a recurring result observed near liquid-liquid consolute points in Coulombic electrolyte solutions, in ternary aqueous electrolyte solutions containing an organic cosolvent, and in binary aqueous solutions of NaCl near the liquid-vapor critical line. 

The solubility of carbon in iron is reduced by the addition of phosphorus, but the temperature of formation of the eutectoid pearlite is not influenced by the presence of the phosphide. P. Goerens and W. Dobbelstein gave for the composition of the ternary eutectic E, Fig. 27, at 953°, l-96 per cent, of carbon, 6-89 per cent, of phosphorus, and 9145 per cent, of iron and J. E. Stead, respectively 1 92, 6 89, and 9149. In Fig. 26, A represents the iron-phosphorus eutectic, and B, the iron-carbon eutectic. They showed that when sat. solid soln. of iron phosphide in iron are heated or cooled they show no critical point at Ars, and the structure is not broken up even... 

Figure 8.6 Ternary phase diagram for a typical chain polymerization (Crit. = critical point).

Phase equilibria and pressure-temperature coordinates of critical points in ternary systems were taken with a high-pressure apparatus based on a thermostated view cell equipped with two liquid flow loops which has been described in detail elsewhere [3]. The loops feed a sample valve which takes small amounts of probes for gas-chromatographic analysis. In addition to temperature, pressure and composition data, the densities of the coexisting liquid phases are measured with a vibrating tube densimeter. Critical points were determined by visual oberservation of the critical opalescence. 

An interesting investigation of the ternary mixture H2S + C02+CH4 was performed by Ng et al. (1985). Although much of this study was at temperatures below those of interest in acid gas injection, it provides data useful for testing phase-behavior prediction models. The multiphase equilibrium that Ng et al. observed for this mixture, including multiple critical points for a mixture of fixed composition, should be of interest to all engineers working with such mixtures. It demonstrates that the equilibria can be complex, even for relatively simple systems. 

The thermodynamic definition of the spinodal, binodal and critical point were given earlier by Eqs. (9), (7) and (8) respectively. The variation of AG with temperature and composition and the resulting phase diagram for a UCST behaviour were illustrated in Fig. 1. It is well known that the classical Flory-Huggins theory is incapable of predicting an LCST phase boundary. If has, however, been used by several authors to deal with ternary phase diagrams Other workers have extensively used a modified version of the classical model to explain binary UCST or ternary phase boundaries The more advanced equation-of-state theories, such as the theory... 

All calculations were carried out at T = 313.15 K. The vapor-liquid equilibrium (VLB) data for the ternary mixture and the corresponding binaries were taken from [32]. The excess volume data for the ternary mixture A,A-dimethylformamide-methanol-water and binary mixtures A, A-dimethylformamide-methanol and methanol-water were taken from [33], and the excess volume data for the binary mixture A,A-dimethylformamide-water from [34]. There are no isothermal compressibility data for the ternary mixture, but the contribution of compressibility to the binary KBls is almost negligible far from the critical point [6]. For this reason, the compressibilities in binary and ternary mixtures were taken to be equal to the ideal compressibilities, and were calculated from the isothermal compressibilities of the pure components as follows ... 

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