Quaternary system method

The low interfacial tensions between two liquids have been measured for different systems by using the pendant drop method. In the case of the quaternary system Ci2ll25S 3 tNa+H20+n-Butanol+Toluene, the interfacial data as measured by pendant drop method are compared with reported literature data, using other methods (with varying NaCl concentration). In order to understand the role of co-surfactant, ternary systems were also investigated. The pendant drop method was also used for measuring the interfacial tension between surfactant-H20/n-alcohol (with number of carbon atoms in alcohol varying from 4-10). The interfacial tension variation was dependent on both the surfactant and alcohol. 

These studies, carried out by measuring interfacial tensions, Yq , between aqueous and oil phases, by using the pendant drop method, show that this method is very useful for ternary and quaternary systems. In one system (A), NaDDS + H2O + n-butanol + Toluene... 

Theory for blends of two homopolymers with block copolymers was developed by Noolandi and Hong (1982) using the SCF method. They considered a quaternary system with a diblock in a good solvent for two incompatible homopolymers. Calculation of density profiles revealed that the block copolymer tends to be selectively located at the interface, and that the homopolymer tends to be excluded from the interphase. This is illustrated by the representative density profiles in Fig. 6.37. The exclusion of homopolymer from the interphase was found to be enhanced by increasing the molecular weight of the block... 

A general formulation of the problem of solid-liquid phase equilibrium in quaternary systems was presented and required the evaluation of two thermodynamic quantities, By and Ty. Four methods for calculating Gy from experimental data were suggested. With these methods, reliable values of Gy for most compound semiconductors could be determined. The term Ty involves the deviation of the liquid solution from ideal behavior relative to that in the solid. This term is less important than the individual activity coefficients because of a partial cancellation of the composition and temperature dependence of the individual activity coefficients. The thermodynamic data base available for liquid mixtures is far more extensive than that for solid solutions. Future work aimed at measurement of solid-mixture properties would be helpful in identifying miscibility limits and their relation to LPE as a problem of constrained equilibrium. 

The methods of Darken and Gokcen discussed here can be applied to quaternary systems. New composition variables are defined in order to convert the quaternary system into pseudobinary systems. The paths of integration can be illustrated by the use of an equilateral tetrahedron. 

The methods discussed in this section can be extended to systems that have more than three components. The problem is to convert each system to a pseudobinary system. For a quaternary system, the properties of an equilateral tetrahedron may be used to depict the composition of the system. The composition axes would be four lines drawn from the four apexes perpendicular to the opposite faces. Planes cutting the tetrahedron parallel to the bases would represent pseudoternary systems for which one composition variable would be constant. Pseudobinary systems would be depicted by the intersections of two of the pseudoternary planes. Indeed, the experimental measurements and calculations would be extensive. 

These additions to the conjugated system are catalyzed by bases such as sodium hydroxide, sodium methoxide, tertiary amines, piperidine, and quaternary ammonium hydroxides. Cupric acetate catalyst is used in the conversion of acrolein to /S-methylmercaptopropionaldehyde, CHjSCHjCHjCHO (84%). The addition of mercaptans is analogous to the addition of alcohols to these systems (method 121). However, the thiol group is more active than the hydroxyl group, as is shown by... 

The purpose of this paper was twofold (i) to investigate how to visualize all four perturbation peaks on a quaternary concentration plateau and to (ii) validate the accuracy of the PP method for determination of isotherm parameters directly from quaternary mixtures of l/l/l/l compositions. For this purpose the technique developed and validated for the binary case in papers IV and V (the Lindholm-technique ) was extended to the multi-component case. The approach is to inject the same excess as deficiency for every second solute. Thus, in a quaternary system the excess of components 1 and 3 is the same as the deficiency of components 2 and 4, or the converse. The concentrations of the components in the sample can be calculated according to Csample i = Chateau i - (-1 ) n, for some number n chosen so that the injected concentrations always are equal to or greater than zero. This technique made all perturbation peaks clearly detectable, although the area were not the same for all of them, see Figure 22. 

The crystallization behaviour of the glasses containing MgO is more difficult to describe. Unlike ternary systems, four component phase diagrams are properly represented by a regular tetrahedron with each apex representing 100% of each component. The crystallization path is therefore in three dimensions which is sometimes difficult to visualize. The method of representation chosen to describe the observed behaviour is as planes of constant MgO content in the regions of interest to this study. Figures 2, 3, and 4 are planes of the quaternary system at 5, 10 and 15 wt% levels respectively and have been compiled from various sources... 

Although a three-dimensional method of representation is necessary in order to give a complete picture of the isothermal conditions in a quaternary system, it is very convenient, for practical purposes, to make use of a plane diagram. Such a diagram can be obtained by projecting the curves in Fig. 143 perpendicularly on the base of the tetrahedron. The vertex of the tetrahedron (D) then comes to lie at the centre D of the triangle ABC (Fig. 144), and the edges AD, BD, and CD find their projections in the three medians AD, BD, and CD. 

The example of Li2MogSeg illustrates one synthetic method towards low dimensional mineral compounds, commonly referred to as the shake and bake method. It usually implies the mixing of the starting materials followed by a high temperature treatment. Then, in order to obtain a liquid crystal, one needs to bring these charged low-dimensional mineral anions into solution. Thus, how can one control, within a given ternary or quaternary system, the dimensionality of the synthesized polymeric compounds This problem has been addressed in the literature and an answer, based upon the 8-N electron rule, can be found... 

In principle, it would be desirable to have information on vapor-liquid equilibria of all binary systems in the temperature range in which the RD is carried out, which is about 100-150 °C in the case studied here. Furthermore, it would be desirable to have at least some data points for ternary systems (all of which are reactive) and for the quaternary system to be able to check the predictive power of the phase equilibrium model. That ideal situation is almost never encountered in reality. In many cases, even reliable experimental data on the binary systems is missing. In the present study, no data was available for the binary systems acetic acid + hexyl acetate and 1-hexanol - - hexyl acetate. Estimations of missing data using group contribution methods such as UNIFAC are possible, but their quality is often hard to assess. 

Quaternary systems, such as surfactant-alcohol-oil-water (SAOW), are analyzed in a quaternary diagram made in a regular tetrahedron as indicated in Fig. 16. The brute force method that consists of selecting hundred.s of composition points in the diagram (located at some grid pattern) and in analyzing the phase behavior in all the.se points is of course too tedious to be carried out. 

Extensive regions of homogeneous solid solutions close to indium arsenide were established by physicochemical methods of analysis in the following quaternary systems InAs-CdS, InAs-CdSe, InAs-CdTe, InAs-ZnS, InAs-ZnSe, InAs-ZnTe. All the melts crystallize in the sphalerite structure and exhibit a linear relationship between the lattice constant and composition. The results ate presented of studies of the electrical conductivity, the Hall effect, and the thermoelectric power, and of electron-microscope studies of the cleaved surfaces of the alloys. 

Azeotropic behavior is not limited to binary systems only. Also ternary and quaternary azeotropic points are observed. For the determination of the azeotropic points in ternary and quaternary systems, thermodynamic models (g -models, equations of state, group contribution methods) can again be applied [40]. Azeotropic points in homogeneous systems can be found with the help of nonlinear regression methods. At the azeotropic point all separation factors aij show a value of 1 in the case of homogeneous systems. This means that the following condition has to be fulfilled ... 

For the stable equilibrium study, the isothermal dissolution method was used in this study. The series of complexes of the quaternary system were loaded into clean polyethylene bottles and capped tightly. The bottles were placed in the thermostatic rotary shaker, whose temperature was controlled to (298.15 + 0.1) K, and rotated at 120 rpm to accelerate the equilibrium of those complexes. A 5.0 cm sample of the clarified solution was taken from the liquid phase of each polyethylene bottle with a pipet at regular intervals and diluted to 50.0 cm3 final volumes in a volumetric flask filled with DDW. If the compositions of the liquid phase in the bottle became constant, then equilibrium was achieved. Generally, it takes about 50 days to come to equilibrium. 

According to the equilibria constants and the Pitzer ion-interaction parameters, the solubilities of the quaternary system at 298.15 K have been calculated though the Newton s Iteration Method to solve the non-linearity simultaneous equations system, and shown in Table 9. 

Artificial neural network Group method of data handling Least-squares technique Liquid-liquid equilibrium Mass fractions Neural network structure Quaternary system... 

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