Four-component systems

A one-phase, four-component or quaternary system has five degrees of freedom. Therefore the phase equilibria in these systems may be affected by the five 

A point on an edge of the tetrahedron represents a binary system, a point within it a quaternary. On the faces ABS, BCS and ACS the solubility curves meet at points L, M and A, respectively, which represent the solvent saturated with two solutes. They are the starting points for the three curves LO, MO and NO, which denote solutions of three solutes in the solvent point O represents the solution which, at the given temperature, is saturated with respect to all three solutes. All these curves form three curved surfaces within the space model. The section between these surfaces and the apex of the tetrahedron indicates unsaturated solution, that between the surfaces and the triangular base complex mixtures of liquid and solid. 

The second, and more important, type of quaternary system that will be considered is one consisting of two solutes and a liquid solvent where the two solutes inter-react and undergo double decomposition (metathesis). This behaviour is frequently encountered in aqueous solutions of two salts that do not have a common ion. Typical examples of double decomposition reactions of commercial importance are 

KCl -F NaNOs NaCl + KNO3 NaN03 +i(NH4)2S04 NH4NO3 +iNa2S04 

NaCl + i(NH4)2S04 NH4CI + iNa2S04 NaN03 -FiK2S04 KNO3 +iNa2S04 

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Changing the distance between the critical points requires a new variable (in addition to the three independent fractional concentrations of the four-component system). As illustrated by Figure 5, the addition of a fourth thermodynamic dimension makes it possible for the two critical end points to approach each other, until they occur at the same point. As the distance between the critical end points decreases and the height of the stack of tietriangles becomes smaller and smaller, the tietriangles also shrink. The distance between the critical end points (see Fig. 5) and the size of the tietriangles depend on the distance from the tricritical point. These dependencies also are described scaling theory equations, as are physical properties such as iuterfacial... 

For mixtures containing more than two species, an additional degree of freedom is available for each additional component. Thus, for a four-component system, the equihbrium vapor and liquid compositions are only fixed if the pressure, temperature, and mole fractious of two components are set. Representation of multicomponent vapor-hquid equihbrium data in tabular or graphical form of the type shown earlier for biuaiy systems is either difficult or impossible. Instead, such data, as well as biuaiy-system data, are commonly represented in terms of ivapor-liquid equilibrium ratios), which are defined by... 

Small FJ, SA Ensign (1997) Alkene monooxygenase from Xanthobacter strain Py2. Purification and characterization of a four-component system central to the bacterial metabolism of aliphatic alkenes. J Biol Chem 272 24913-24920. 

In 1959, J. H. Schulman introduced the term microemulsion for transparent-solutions of a model four-component system [126]. Basically, microemulsions consist of water, an oily component, surfactant, and co-surfactant. A three phase diagram illustrating the area of existence of microemulsions is presented in Fig. 6 [24]. The phase equilibria, structures, applications, and chemical reactions of microemulsion have been reviewed by Sjoblom et al. [127]. In contrast to macroemulsions, microemulsions are optically transparent, isotropic, and thermodynamically stable [128, 129]. Microemulsions have been subject of various... 

The complete four-component system is necessary when the diagnostic requirement is rapid, low unit-cost analysis for both the strain-level characterization of pathogenic agents and identification of hoax bio-terror materials. Using the complete system, we are proposing to validate MS-based microbial taxonomy and to transfer the technology from an analytical research to a clinical or public health production-diagnosis environment. 

Desulfurization of two LGO streams was studied using R. erythropolis rKA2-5-l [71] to determine the rate of desulfurization and develop a predictive model for desulfurization of diesel oil. The sulfur removal from various substituted DBTs was modeled using a competitive inhibition and lumping model and the desulfurization of the LGO streams was successfully assessed. The model consisted of a four component system based on... 

The extent to which the vehicle can affect the entire diffusion process can be shown by an example. In a four-component system of 40% oil, 40% water, and 20% of an emulsifying agent and coemulsifier, alteration of only the proportion of emulsifier to coemulsifier leads to systems of completely different colloidal-chemical structures, which can be labeled as either creams, gels, or microemulsions. 

DIPA) and methyldiethanolamine (MDEA) have also been employed. Earlier, Atwood et al. (J 5) proposed a thermodynamic model for the equilibria in I S+alkanol-amine+H20 systems. The central feature of this model is the use of mean ionic activity coefficient. The activity coefficients of all ionic species are assumed to be equal and to be a function only of ionic strengths. Klyamer and Kolesnikova ( 1j[) utilized this model for correlation of equilibria in C02+alkanol-amine+H O systems and Klyamer et al. (J 7) extended it to the H2S+C02+alkanolamine+H20 system. The model is restricted to low pressures as the fugacity coefficients are assumed unity and it has been found that the predictions are inaccurate in the four-component system since the activity coefficients are not equal when a number of different cations and anions are present. 

In this case data for mixtures of H2S+CO2+DIPA+H2O were used together with the data for H2S+DIPA+H2O and CO2+DIPA+H2O to obtain the interaction parameters and equilibrium constants. The results are shown in Figures 1 and 2 to be in good agreement with the experimental data ( 3). In this case, however, in contrast to the case of MEA, the predictions use parameters evaluated from data for the four component system. 

We consider an incompressible (m-l-1) multicomponent mixture of polymers consisting of m different types of polymer chains within a matrix referred to as 0 . Components may be either homopolymers of a given chemical species or, e.g. homopolymer sections in block copolymers. Hydrogenated and deuterated species of the same homopolymer are considered as different components. In this context a diblock copolymer is a two-component polymer system. A mixture of partially protonated diblock chains hA-dB with deuterated diblock chains is consequently regarded as a four-component system. 

These arguments may be extended to an -compositional space the straight paths will be replaced by planes in a three-component system, by hyperplanes in a four-component system, and so on. Moreover, in an -component system at fixed P and T, no more than n phases may be stable at the same P-T-Xcondition, and their compositions are uniquely determined at any combination of P, T, and X. 

Table 5.28 Macroscopic interaction parameters for garnets in the three four-component systems (Mg, Mn, Ca, Fe)3Al2Sl30i2, (Mg, Mn, Ca, Fe)3Cr2Sl30i2, and (Mg, Mn, Ca,Fe)3Fc2Si30i2 (Wohl s 1946 formulation). Terms in parentheses are Berman s (1990) thernary interaction parameters (from Ottonello et al., in prep.). Xcation (1) = Mg (2) = Mn (3) = Ca (4) = Fe. ...

FIGURE 9.4 Four-component system Oil (O)-Water (W)-Emulsifier (E)-Cosurfactant (S) (ratio of 0 S versus S W). 

Scheme 3.3-1. [LJ-control maps for a three- and a four-component system (product distribution in mol%)...

In Scheme 3.3-1 the [L]-control maps for the three-component system nickel/ triphenylphoq>hine/butadiene and the four-component system nickel/triphenyl-phosphine/butadiene/propene are compared. The amount of the produced... 

Kim H. (1969) Combined use of various experimental techniques for the determination of nine diffusion coefficients in four-component systems. /. Phys. Chem. 73, 1716-1722. 

Candau, F. Ballet, F. "Formation and Structure of Four -Component Systems Containing Polymeric Surfactants" in "Microemulsions Robb I. D. Plenum Press New York, 1982 p. 59. 

Since the major chemical reactions take place through the agency of an aqueous fluid, the system can be considered to be saturated with respect to water. H O is always the major component of an omnipresent fluid phase during the attainment of equilibrium and it is therefore considered a component in excess. We are left with a four component system, Na-K-Al-Si where, for unspecified P-T conditions over a short range, there will be a maximum of four phases coexisting. 

A totally different way of looking at microemulsions —and one that connects this topic with previous sections of the chapter —is to view them as complicated examples of micellar solubilization. From this perspective, there is no problem with spontaneous formation or stability with respect to separation. Furthermore, ordinary and reverse micelles provide the basis for both O/W and W/O microemulsions. From the micellar point of view, it is the phase diagram for the four-component system rather than y that holds the key to understanding microemulsions. 

Solutions of four cases of three- and four-component systems are presented by Tsuboka and Katayama (1976) the number of outer loop iterations ranged from 7 to 41. The four component case worked out by Henley and Seader (1981) is summarized in Example 14.9 they solved two cases with different water contents of the solvent, dimethylformamide. 

A model depicting composition paths in the simplex tetrahedron of a four-component system is shown in Figure 3. For systems with more than four components, one runs out of dimensions for graphical or spatial... 

Figure 3. Model showing sets of composition paths in mobile-phase composition simplex of four-component system with separation factors a12 = 2, aim = 4, and au = 8...

Figure 7. Mutarotation of a-v-galactopyranose, calculated for the four-component system and compared with observed values...

Photoinduced Hydrogen Evolution in Homogeneous Four-component Systems... 

Scheme 18.1 Photoinduced hydrogen evolution using a four-component system. D Electron donor, P Photosensitizer, C Electron carrier.

An efficient and convenient methodology for the aerobic oxidation of alcohols catalysed by sol-gel trapped perruthenate and promoted by an encapsulated ionic liquid in supercritical carbon dioxide solution has been reported. The reaction is highly selective and useful for substrates otherwise difficult to oxidize.263 A four-component system consisting of acetamido-TEMPO-Cu(C104)2-TMDP-DABCO has been developed for aerobic alcohol oxidation at room temperature. The catalytic system shows excellent selectivity towards the oxidation of benzylic and allylic alcohols and is not deactivated by heteroatom-containing (S, N) compounds. The use of DMSO as the reaction medium allows the catalysts to be recycled and reused for three runs with no significant loss of catalytic activity.264... 

Although this statistical model can qualitatively explain the observed results, it is by no means the only viable explanation. With crystals that melt at 45°C and a reaction carried out at room temperature (20°C), there should be some concern that the sample goes through liquid phases below the eutectic of the four-component system. 

Each term of the series applies to a single component and there are -terms for w-components. Eq (6-18) holds only when the voids of each component are the same. Now, if each term of the series is divided by > and multiplied by 100, we obtain the percentage volume of each component in a mixture to produce the minimum voids when the voids in each component are d. Furnas (1931) computed possible minimum voids in packings of two- to four-component systems when the initial voids of... 

Using the expression (5.22) together with Tables 5.5 and 5.6 on the base of the general principles reported in Sect. 5.2 one can carry out an exhaustive classification of the four-component systems as it has been already done for terpolymerization in Sect. 5.3. However, when the forth monomer is added, the number of the system types increases from 7 (see Fig. 6) to 41 (see Fig. 9) and that is a reason why the results of the complete theoretical analysis cannot be represented in the framework of this review. Without appealing to the classification and using only the algorithm described in Sect. 5.2 one may present a phase portrait of any concrete four-component system and hence predict the qualitative character of its dynamic behavior before the computer calculations of trajectories x(p) are performed. 

Fig. 9. Complete set of types of four-component systems. Number in circle denotes the number of binary azeotropes in such a system...

It is necessary to emphasize one principal peculiarity of the copolymerization dynamics which arises under the transition from the three-component to the four-component systems. While the attractors of the former systems are only SPs and limit cycles (see Fig. 5), for the latter ones we can also expect the realization of other more complex attractors [202]. Two-dimensional surfaces of torus on which the system accomplishes the complex oscillations (which are superpositions of the two simple oscillations with different periods) ate regarded to be trivial examples of such attractors. Other similar attractors are fitted by the superpositions of few simple oscillations, the number of which is arbitrary. And, finally, the most complicated type of dynamic behavior of the system when m 4 is fitted by chaotic oscillations [16], for which a so-called strange attractor is believed to be a mathematical image [206]. 

Ceglie, A., Das, K. P, and Lindman, B. (1987), Microemulsion structure in four component systems for different surfactants, Coll. Surf, 28,29 40. 

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