Liquid solution behavior, ternary

Liquid Solution Behavior. The component activity coefficients in the liquid phase can be addressed separately from those in the solid solution by direct experimental determination or by analysis of the binary limits, since y p = 1. Because of the large amount of experimental effort required to study a ternary composition field and the high vapor pressures encountered in the arsenide and phosphide melts, a direct experimental determination of ternary activity coefficients has been reported only for the Ga-In-Sb system (26). Typically, the available binary liquidus data have been used to fix the adjustable parameters in a solution model with 0,p determined by Equation 7. The solution model expression for the activity coefficient has been used not only to represent the component activities along the liquidus curve, but also the stoichiometric liquid activities needed in Equation 7. The ternary melt solution behavior is then obtained by extending the binary models to describe a ternary mixture without additional adjustable parameters. In general, interactions between atoms in different groups exhibit negative deviations from ideal behavior... 

The determination of was examined by first considering the liquid solution behavior and then the solid mixture properties. The liquid phase properties are typically determined by using a solution model to interpolate between the binary limits. In general, the use of only the binary phase diagrams in the data base for model parameter estimation does not give good values for the ternary liquid mixture properties. The solid solution behavior is normally determined from an analysis of the pseudo-binary phase diagram. Extrapolation of the solid solution behavior determined in this manner to lower values of temperature should be undertaken with caution. 

While the early work on molten NH4CI gave only some qualitative hints that the effective critical behavior of ionic fluids may be different from that of nonionic fluids, the possibility of apparent mean-field behavior has been substantiated in precise studies of two- and multicomponent ionic fluids. Crossover to mean-field criticality far away from Tc seems now well-established for several systems. Examples are liquid-liquid demixings in binary systems such as Bu4NPic + alcohols and Na + NH3, liquid-liquid demixings in ternary systems of the type salt + water + organic solvent, and liquid-vapor transitions in aqueous solutions of NaCl. On the other hand, Pitzer s conjecture that the asymptotic behavior itself might be mean-field-like has not been confirmed. 

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 thermodynamic quantity 0y is a reduced standard-state chemical potential difference and is a function only of T, P, and the choice of standard state. The principal temperature dependence of the liquidus and solidus surfaces is contained in 0 j. The term is the ratio of the deviation from ideal-solution behavior in the liquid phase to that in the solid phase. This term is consistent with the notion that only the difference between the values of the Gibbs energy for the solid and liquid phases determines which equilibrium phases are present. Expressions for the limits of the quaternary phase diagram are easily obtained (e.g., for a ternary AJB C system, y = 1 and xD = 0 for a pseudobinary section, y = 1, xD = 0, and xc = 1/2 and for a binary AC system, x = y = xAC = 1 and xB = xD = 0). 

When two species i = 1,2 diffuse through a membrane, we have a ternary system of i = l,2,m, where m represents the membrane material. We will now obtain a Fick s first law type of expression for IV, to represent the diffusion of 1 and 2 through a membrane mechanically restrained and therefore having a zero velocity (Lightfoot, 1974) using Maxwell-Stefan formulation. Assume no external forces, no pressure gradients, no temperature gradients and ideal solution behavior. The two phases on two sides are liquids. The subscript m for the membrane phase has not been used with species subscripts. 

With binary and ternary supercritical mixtures as chromatographic mobile phases, solute retention mechanisms are unclear. Polar modifiers produce a nonlinear relationship between the log of solute partition ratios (k ) and the percentage of modifier in the mobile phase. The only form of liquid chromatography (LC) that produces non-linear retention is liquid-solid adsorption chromatography (LSC) where the retention of solutes follows the adsorption isotherm of the polar modifier (6). Recent measurements confirm that extensive adsorption of both carbon dioxide (7,8) and methanol (8,9) occurs from supercritical methanol/carbon dioxide mixtures. Although extensive adsorption of mobile phase components clearly occurs, a classic adsorption mechanism does not appear to describe chromatographic behavior of polar solutes in packed column SFC. 

To illustrate the system behavior, the ternary mixture 1 = iso-propanol, 2 = water, and 3 = air is considered here. In order to obtain an algebraic solution, both the dif-fusivities of iso-propanol in air and iso-propanol in water vapor were assumed to be approximately the same, which is not far from reality. The liquid phase mass transfer resistance was negligibly small, as will be shown below. The phase equilibrium constants K/,c and Kjrs were calculated with activity coefficients from van Laar s equation. Water vapor diffuses 2.7-fold faster in the inert gas air than iso-propanol. The ratio of the respective mass transfer coefficients kj3 equals the ratio of the respective diffusivities to the power of 2/3rd according to standard convective mass transfer equations Sh =J Re, Sc). 

The non-random, two-liquid (NRTL) equation proposed by Renon and Prausnitz (8) seems to predict successfully multicomponent (ternary) mixtures of alcohols and water. The alcohols studied in this work ethanol, 1-propanol, 2-methyl-l-propanol, and 3-methyl-l-butanol, which occur from the fermentation of sugar solutions, show highly non-ideal behavior in aqueous solutions and present a severe test of the effectiveness of any prediction method. 

In the studies described here, we examine in more detail the properties of these surfactant aggregates solubilized in supercritical ethane and propane. We present the results of solubility measurements of AOT in pure ethane and propane and of conductance and density measurements of supercritical fluid reverse micelle solutions. The effect of temperature and pressure on phase behavior of ternary mixtures consisting of AOT/water/supercritical ethane or propane are also examined. We report that the phase behavior of these systems is dependent on fluid pressure in contrast to liquid systems where similar changes in pressure have little or no effect. We have focused our attention on the reverse micelle region where mixtures containing 80 to 100% by weight alkane were examined. The new evidence supports and extends our initial findings related to reverse micelle structures in supercritical fluids. We report properties of these systems which may be important in the field of enhanced oil recovery. 

Besides these thermodynamic criteria, the most common approach used in the literature is based on the operation at pressures above the binary (liquid - SC-CO2) mixture critical point, completely neglecting the influence of solute on VLEs of the system. But, the solubility behavior of a binary supercritical COj-containing system is frequently changed by the addition of a low volatile third component as the solute to be precipitated. In particular, the so-called cosolvency effect can occur when a mixture of two components solvent+solute is better soluble in a supercritical solvent than each of the pure components alone. In contrast to this behavior, a ternary system can show poorer solubility compared with the binary systems antisolvent+solvent and antisol-vent+solute a system with these characteristics is called a non-cosolvency (antisolvent) system. hi particular, in the case of the SAS process, they hypothesize that the solute does not induce cosolvency effects, because the scope of this process lies in the use of COj as an antisolvent for the solute, inducing its precipitation. 

Figure 4.6 illustrates the use of the IAS model to account for the competitive isotherm data of a ternary mixture of benzyl alcohol (BA), 2-phenylethanol (PE) and 2-methyl benzyl alcohol (MBA) in reversed phase liquid chromatography. The RAS model accounts for the nonideal behaviors in the mobile and the stationary phases through the variation of the activity coefficients with the concentrations. Figures 4.6d and 4.6e illustrate the variations of the activity coefficients in the stationary and the mobile phases, respectively. The solutes exhibit positive deviations from ideal behavior in the adsorbed phase and negative deviations from ideal behavior in the mobile phase. 

In most cases, it appears possible to interpret the critical behavior of microemulsion mixtures as a liquid/gas-like critical point [113-116]. Several light- and neutron-scattering studies on oil-rich ternary and quaternary microemulsions have clearly demonstrated that the structure of these media can be described as a solution of interacting water-in-oil droplets. As first shown by Calje et al. [117], the droplets may behave essentially as hard spheres. However, in many systems an attractive contribution to the interactions exists. It has been established that the strength of attractions between W/0 micelles is strongly dependent on the micellar size and on the chain lengths of both the alcohol and oil molecules. In particular, attractions have been found to increase when the micellar radius increases or the alcohol chain length decreases and the molecular volume of the oil increases [114, 115, 118-120]. 

When a soluble third component is added to two partially miscible liquids, we obtain a ternary system in which the third component (solute) is partitioned between the two liquid phases (solvents). The phase behavior of such systems is important in liquid-liquid extraction, a process that takes advantage of the differences in solubility to transfer a solute from one solvent into another. Since two mole fractions are required to represent composition in ternary systems, it is not possible to present temperature-composition or pressure-composition graphs in a two-dimensional plot. Instead, we map out the composition of the phases at constant pressure and temperature. This is done in triangular diagrams such... 

The classical thermodynamic approach has been applied to liquid phase adsorption by Larionov and Myers and by Minka and Myers. It was shown that for sorption of carbon tetrachloride-isooctane and benzene-carbon tetrachloride on aerosil the adsorbed solutions show approximately ideal behavior whereas adsorbed mixtures of benzene, ethyl acetate, and cyclohexane on activated carbon showed appreciable deviations from ideality. However, it is shown that the activity coefficients and hence the adsorption equilibrium data for the ternary systems may be successfully predicted, by classical methods, from data for the constituent binaries. 

---