Ternary solute-solution system

An alternative approach to multisolute adsorption is by application of the Polanyi potential theory. Its use for binary solute systems was outlined in reference 3 (pp. 111-114) Rosene and Manes have now extended consideration to ternary solute systems. The same principles apply as in the binary solute case the driving force for adsorption per unit volume is... 

As the feed composition approaches a plait point, the rate of convergence of the calculation procedure is markedly reduced. Typically, 10 to 20 iterations are required, as shown in Cases 2 and 6 for ternary type-I systems. Very near a plait point, convergence can be extremely slow, requiring 50 iterations or more. ELIPS checks for these situations, terminates without a solution, and returns an error flag (ERR=7) to avoid unwarranted computational effort. This is not a significant disadvantage since liquid-liquid separations are not intentionally conducted near plait points. 

If the partially labelled star/solvent system is considered as an incompressible ternary solution, the double differential cross section 02ct/0 20E can be written as... 

About the same time Beutier and Renon (11) also proposed a similar model for the representation of the equilibria in aqueous solutions of weak electrolytes. The vapor was assumed to be an ideal gas and < >a was set equal to unity. Pitzer s method was used for the estimation of the activity coefficients, but, in contrast to Edwards et al. (j)), two ternary parameters in the activity coefficient expression were employed. These were obtained from data on the two-solute systems It was found that the equilibria in the systems NH3+ H2S+H20, NH3+C02+H20 and NH3+S02+H20 could be represented very well up to high concentrations of the ionic species. However, the model was unreliable at high concentrations of undissociated ammonia. Edwards et al. (1 2) have recently proposed a new expression for the representation of the activity coefficients in the NH3+H20 system, over the complete concentration range from pure water to pure NH3. it appears that this area will assume increasing importance and that one must be able to represent activity coefficients in the region of high concentrations of molecular species as well as in dilute solutions. Cruz and Renon (13) have proposed an expression which combines the equations for electrolytes with the non-random two-liquid (NRTL) model for non-electrolytes in order to represent the complete composition range. In a later publication, Cruz and Renon (J4J, this model was applied to the acetic acid-water system. 

The parameters Dca m are binary parameters representing the interactions between salt ca and molecular solute m in an aqueous single salt, single molecular solute system. Binary parameters gc. m and aa1 m represent the differences between the interactions of a specific molecular solute with two unlike salts sharing one common anion or cation. Ternary molecule-ion virial coefficients are neglected in this study to simplify the extension. 

The work of Vera and co-workers nasHed to a semi-empirical expression for the excess Gibbs energy which is consistent with our choice of the saturated solution as the standard state for the electrolyte. Vera has, however, shown that pure water is a more convenient standard state for hLO in place of the saturated solution used by Vega and Funk (19). This is particularly convenient for ternary and higher systems since it avoids the complication of having a composition-dependent standard state. 

Introductory remarks. Phases related to the 1 3 stoichiometry and their derivative structures, either as point compounds or as solid solution ranges, are frequently found in binary and ternary intermetallic alloy systems. 

Many different types of phase behaviour are encountered in ternary systems that consist of water and two solid solutes. For example, the system KNO3—NaNC>3— H20 which does not form hydrates or combine chemically at 323 K is shown in Figure 15.6, which is taken from Mullin 3 . Point A represents the solubility of KNO3 in water at 323 K (46.2 kg/100 kg solution), C the solubility of NaN(>3 (53.2 kg/100 kg solution), AB is the composition of saturated ternary solutions in equilibrium with solid KNO3 and BC... 

Given a nonionic solute that has a relatively low solubility in each of the two liquids, and given equations that permit estimates of its solubility in each liquid to be made, the distribution ratio would be approximately the ratio of these solubilities. The approximation arises from several sources. One is that, in the ternary (solvent extraction) system, the two liquid phases are not the pure liquid solvents where the solubilities have been measured or estimated, but rather, their mutually saturated solutions. The lower the mutual solubility of the two solvents, the better can the approximation be made. Even at low concentrations, however, the solute may not obey Henry s law in one or both of the solvents (i.e., not form a dilute ideal solution with it). It may, for instance, dimerize or form a regular solution with an appreciable value of b(J) (see section 2.2). Such complications become negligible at very low concentrations, but not necessarily in the saturated solutions. 

A ternary system consisting of two polymer species of the same kind having different molecular weights and a solvent is the simplest case of polydisperse polymer solutions. Therefore, it is a prototype for investigating polydispersity effects on polymer solution properties. In 1978, Abe and Flory [74] studied theoretically the phase behavior in ternary solutions of rodlike polymers using the Flory lattice theory [3], Subsequently, ternary phase diagrams have been measured for several stiff-chain polymer solution systems, and work [6,17] has been done to improve the Abe-Flory theory. 

The solid curves in the figure represent the molecular weight dependence of r)0 for quasi-binary system consisting of a fractionated xanthan sample and 0.1 mol/1 aqueous NaCl. The circles for quasi-ternary solutions almost follow them at the same c, except at small 2. Thus, to a first approximation, r)o of stiff polymer solutions is independent of molecular weight distribution, and may be treated as a function of Mw or Mv and c. 

Knowledge of the expressions for the chemical potentials of each of the components allows theoretical prediction of the critical concentration boundaries of the phase diagram for ternary solutions of biopolymeri + biopolymer2 + solvent. According to Prigogine and Defay (1954), a sufficient condition for material stability of this multicomponent system in relation to phase separation at constant temperature and pressure is the following set of inequalities for all the components of the system ... 

In Section 4.3.3, it was explained how to construct the reaction (diffusion) path for ternary and higher solid solution systems. In practice, one plots, for example, in a ternary system, the composition variables (measured along the pertinent space coordinate of the reacting solid) into a Gibbs phase triangle, noting that the spatial information is thereby lost. For certain boundary conditions, such a reaction path is independent of reaction time and therefore characterizes the diffusion process. For a one dimensional ternary system with stable interfaces, these boundary conditions are c,-( = oo,f) = c°( oo) q( <0,0) = c (-oo) c,(f>0,0) = c (+oo). 

Generally, a set of coupled diffusion equations arises for multiple-component diffusion when N > 3. The least complicated case is for ternary (N = 3) systems that have two independent concentrations (or fluxes) and a 2 x 2 matrix of interdiffusivities. A matrix and vector notation simplifies the general case. Below, the equations are developed for the ternary case along with a parallel development using compact notation for the more extended general case. Many characteristic features of general multicomponent diffusion can be illustrated through specific solutions of the ternary case. 

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). 

Qualitatively, the same effect has been observed in ternary solutions of p- PODZ, PA-6 and sulfuric acid [104]. At room temperature the quiescent system displays phase separation above 14% of total polymer concentration. Above the critical concentration shearing of initially biphasic solutions led to transparent one-phase systems. After cessation of the shear stress the biphasic morphologies recovered. 

As a third liquid is added to the partially miscible binary liquid system, the ternary (three-component) system is dependent on the relative solubility of the third liquid in the two liquids. If the third substance is soluble only in one liquid of the original binary mixture or if the solubility of the third in the two liquids is considerably different, the solubility of one liquid in the others will be lowered. The upper consolute temperature should be raised or the lower consolute temperature should be lowered in order to obtain a homogeneous solution. On the other hand, if the third substance is soluble to the same extent in both liquids of the binary system, the complementary solubility of the two liquids is increased. This results in the lowering of an upper consolute temperature or the elevation of a lower consolute temperature. 

The extension of the CNT to homogeneous nucleation in atmospheric, essentially multicomponent, systems have faced significant problems due to difficulties in determining the activity coefficients, surface tension and density of binary and ternary solutions. The BHN and THN theories have been experiences a number of modifications and updates. At the present time, the updated quasi-steady state BHN model [16] and kinetic quasi-imary nucleation theory [24,66], and classical THN theory [25,33] and kinetic THN model constrained by the experimental data... 

The solubilities of carbon dioxide in aqueous solutions of seven binary and three ternary mixed salts chosen from eight kinds of electrolytes were measured at 25°C and 1 atm partial pressure of carbon dioxide by the saturation method. The experimental results were not correlated easily by the modified Setschenow equation, but they were correlated very well by the empirical two-parameter equation. The parameters in the equation for the binary and ternary solutions could be estimated by assuming an additive rule for the parameters of the component salt systems. This method, therefore, is useful for predicting the solubility of carbon dioxide in aqueous mixed-salt solutions. 

Ternary solutions of cellulose, or CTA, and PET were prefixed by mixing appropriate volumes of stock solutions and mechanically mixed with a magnetic stirrer at 28°C for 5 h and then stored for one week. Some of the ternary systems separated into an isotropic and anisotropic phase. Similar results were ot rved for mixtures of cellulose triacetare and PMMA. The volume of these phases were measured and the isotropic phase decanted. Each phase was analyzed for cellulose triacetate by extraction with CH2CI2 or 1,1,1-trichloroethane. 

C02-solute systems in terms of a number of phase diagrams. E. L. Quinn and C. L. Jonesf °b(42] produced a number of papers in the 1920 s and 1930 s expanding this CO2 data, but an extensive study of CO2 was not made until much later in 1954, when A. W. Francisf produced a comprehensive report citing the solubility of 261 compounds and 464 ternary systems in liquid CO2 at 25 C. Since the 1970 s, the study of CO2 as a solvent has increased dramatically. In 1983, M. E. Paulaitis, V. J. Krukonis, R. T. Kumik and R. C. Reid produced a review called Supercritical Fluid Extractiod which detailed references on the solubility of a number of compounds in liquid and supercritical CO2. More recently Bartle et al. have compiled, from various references, binary phase diagrams for over 120 compounds mainly in supercritical CO2. 

The remainder of the data on ternary solutions is on systems too diverse to allow comparisons. 

The objective of this paper is to propose a predictive method for the estimation of the change in the solubility of a solid in a supercritical solvent when another solute (entrainer) or a cosolvent is added to the system. To achieve this goal, the solubility equations were coupled with the Kirkwood-Buff (KB) theory of dilute ternary solutions. In this manner, the solubility of a solid in a supercritical fluid (SCF) in the presence of an entrainer or a cosolvent could be expressed in terms of only binary data. The obtained predictive method was applied to six ternary SCF-solute-cosolute and two SCF-solute-cosolvent systems. In the former case, the agreement with experiment was very good, whereas in the latter, the agreement was only satisfactory, because the data were not for the very dilute systems for which the present approach is valid. 2001 Elsevier Science B.V. All rights reserved. 

High-performance liquid chromatography is performed using a Hewlett-Packard 1090 chromatograph equipped with a ternary-solvent delivery system, an autoinjector with a 0 -20- u.L injection loop, an oven compartment, and a diode-array UV detector. An ELS detector (Alltech Associates, Deerfield, IL) is connected in series to the UV detector. Hexane, 2-propanol, and water were used for the analysis of nonionic surfactants. Water and tetrahydrofuran (THF) are used for the analysis of anionic surfactants. No preliminary sample preparation is used other than dilution. The nonionic surfactants are diluted 1 40 (v/v) with hexane. The anionic surfactants (alkyl ether sulfates and synthetic and petroleum sulfonates) are diluted 1 20 (v/v) with water-THF (50 50). The calcium sulfonate surfactants were diluted 1 20 (v/v) with a THF-38% hydrochloric acid solution of pH 1. Hydrochloric add is required to prevent salt precipitation by converting any excess water-insoluble caldum carbonate into water-soluble calcium chloride. All diluted samples are... 

The usefulness of inverse gas chromatography for determining polymer-small molecule interactions is well established (1,2). This method provides a fast and convenient way of obtaining thermodynamic data for concentrated polymer systems. However, this technique can also be used to measure polymer-polymer interaction parameters via a ternary solution approach Q). Measurements of specific retention volumes of two binary (volatile probe-polymer) and one ternary (volatile probe-polymer blend) system are sufficient to calculate xp3 > the Flory-Huggins interaction parameter, which is a measure of the thermodynamic... 

The simplest case of adsorption from multicomponent solutions is the adsorption from ternary solutions. The isotherms of components adsorption in such systems are expressed... 

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