Binary systems description

An adequate prediction of multicomponent vapor-liquid equilibria requires an accurate description of the phase equilibria for the binary systems. We have reduced a large body of binary data including a variety of systems containing, for example, alcohols, ethers, ketones, organic acids, water, and hydrocarbons with the UNIQUAC equation. Experience has shown it to do as well as any of the other common models. V7hen all types of mixtures are considered, including partially miscible systems, the... 

The situation in the solid state is generally more complex. Several examples of binary systems were seen in which, in the solid state, a number of phases (intermediate and terminal) are formed. See for instance Figs 2.18-2.21. Both stoichiometric phases (compounds) and variable composition phases (solid solutions) may be considered and, as for their structures, both fully ordered or more or less completely disordered phases. This variety of types is characteristic for the solid alloys. After a few comments on liquid alloys, particular attention will therefore be dedicated in the following paragraphs to the description and classification of solid intermetallic phases. 

The LLE for ILs and common solvents such as alcohols is very important for developing ILs for liquid-liquid extraction processes. Previous studies in many laboratories have shown this potential. Most of the measured mixtures were of IL + short chain alcohol) binary systems. It is well known that an increase in the alkyl chain length of the alcohol resulted in an increase in the UCST. Nevertheless, the solubilities of many ILs were measured in 1-octanol (important value for the description of bioaccumulation) [14,50-54, 79,98-100,112,127,133]. The other short chain alcohols were pointed out earlier. 

In comparison with the qualitative description of diffusion in a binary system as embodied by Eqs. (11), (12) or (14), the thermodynamic factors are now represented by the quantities a, b, c, and d and the dynamic factors by the phenomenological coefficients which are complex functions of the binary frictional coefficients. Experimental measurements of Dy in a ternary system, made on the basis of the knowledge of the concentration gradients of each component and by use of Eqs. (21) and (22), have been reviewed 35). Another method, which has been used recently36), requires the evaluation of py from thermodynamic measurements such as osmotic pressure and evaluation of all fy from diffusion measurements and substitution of these terms into Eqs. (23)—(26). 

Binary and ternary spectra. We will be concerned mainly with absorption of electromagnetic radiation by binary complexes of inert atoms and/or simple molecules. For such systems, high-quality measurements of collision-induced spectra exist, which will be reviewed in Chapter 3. Furthermore, a rigorous, theoretical description of binary systems and spectra is possible which lends itself readily to numerical calculations, Chapters 5 and 6. Measurements of binary spectra may be directly compared with the fundamental theory. Interesting experimental and theoretical studies of various aspects of ternary spectra are also possible. These are aimed, for example, at a distinction of the fairly well understood pairwise-additive dipole components and the less well understood irreducible three-body induced components. Induced spectra of bigger complexes, and of reactive systems, are also of interest and will be considered to some limited extent below. 

Semi-empirical equations of state are used to fit binary systems, and thermodynamic data for the solute and the solvent have to be known. For systems with more than two components, the mathematical solution is very difficult. A useful equation of state for the description of simple binary systems is the Peng-Robinson equation [5], applicable for large pressure and temperature ranges. 

Finally, intraparticle diffusion appears to be an important factor in adsorption kinetics for many types of systems. In the past it has been customary to define such mass transfer quantitatively in terms of an effective diffusivity. However, even in gas-solid systems more than one process can be involved for porous particles. Thus, two-dimensional migration on the pore surface, surface diffusion, is a potential contribution. Liquid systems appear to be more complex, and, with electrolytes, it has been shown that the electric potential induced by counter-diffusing ions should be taken into account. A realistic description of intraparticle mass transfer in such cases requires more than a single rate coefficient for a binary system. 

The vacancy flux and the corresponding lattice shift vanish if bA = bB. In agreement with the irreversible thermodynamics of binary systems i.e., if local equilibrium prevails), there is only one single independent kinetic coefficient, D, necessary for a unique description of the chemical interdiffusion process. Information about individual mobilities and diffusivities can be obtained only from additional knowledge about vL, which must include concepts of the crystal lattice and point defects. 

The description of diffusion may be complex in mixtures with more than two components. Diffusion coefficients in multicomponent mixtures are usually unknown, although sufficient experimental and theoretical information on binary systems is available. The Maxwell-Stefan diffusivities can be estimated for dilute monatomic gases from D k Dkl when the Fick diffusivities are available. The Maxwell diflfusivity is independent of the concentration for ideal gases, and almost independent of the concentration for ideal liquid mixtures. The Maxwell-Stefan diffusivities can be calculated from... 

It is possible in many cases to predict highly accurate phase equihbria in multi-component systems by extrapolation. Experience has shown extrapolation of assessed (n — 1) data into an nth order system works well for n < 4, at least with metallurgical systems. Thus, the assessment of unary and binary systems is especially critical in the CALPHAD method. A thermodynamic assessment involves the optimization of aU the parameters in the thermodynamic description of a system, so that it reproduces the most accurate experimental phase diagram available. Even with experimental determinations of phase diagrams, one has to sample compositions at sufficiently small intervals to ensure accurate reflection of the phase boundaries. 

For a pure supercritical fluid, the relationships between pressure, temperature and density are easily estimated (except very near the critical point) with reasonable precision from equations of state and conform quite closely to that given in Figure 1. The phase behavior of binary fluid systems is highly varied and much more complex than in single-component systems and has been well-described for selected binary systems (see, for example, reference 13 and references therein). A detailed discussion of the different types of binary fluid mixtures and the phase behavior of these systems can be found elsewhere (X2). Cubic ecjuations of state have been used successfully to describe the properties and phase behavior of multicomponent systems, particularly fot hydrocarbon mixtures (14.) The use of conventional ecjuations of state to describe properties of surfactant-supercritical fluid mixtures is not appropriate since they do not account for the formation of aggregates (the micellar pseudophase) or their solubilization in a supercritical fluid phase. A complete thermodynamic description of micelle and microemulsion formation in liquids remains a challenging problem, and no attempts have been made to extend these models to supercritical fluid phases. 

As has become clear adsorption phenomena play an important, if not, decisive role in this behaviour, and good data and modelling of adsorption are mandatory, too, to serve as the input parameters for the permeation description. This should not be l ted to the T.angmnir model, but other theories like the IAS (ideal adsorbed solution) and NIAS (non-ideal) should be considered, since they sometines work well for binary systems where the Langmuir model fails. 

Thermodynamic Description of a Binary System With Limited Miscibility. 

Kinetic Description of a Binary System With Limited Miscibility. The kinetic interpretation of a system with limited miscibility can be expressed in terms of the diffusion coefficient D of the system. At constant pressure and temperature, again three different states can be distinguished (4) ... 

Platzer, B. and Maurer, G. (1993). Application of a generalized Bender equation of state to the description of vapour-liquid equihbria in binary systems. Fluid Phase Equilibria, 84, 79—110. 

This very simple description applies to those stars which evolve as single stars or as members of a wide binary system which do not interact. It is increasingly clear that a large fraction of stars are born in binary or multiple systems in which two stars exchange material at some point during their evolution. The possibilities of what can happen thereafter are too numerous to be able to cover here, but some of the more bizarre possibilities will be considered later. 

Recent years there have been a considerable interest in studying of binary catalytic systems based on stabilized nanocomposites and amorphous alloys of copper with other metals. The reason is that the catalytic activity of such systems in many cases is sufficiently higher than that of individual metals. The most convenient model for theoretical description of binary systems characterized by the absence of far order is a cluster model. However, quantum-chemical study of binary clusters comprises the significantly more c omplicated problem than that o f individual metals, b ecause a correct theoretical description of metal-another metal cluster systems requires that the used method should be in a position to provide good results of calculations of geometrical, electron stmctures and energetic characteristics of both of individual metals. 

In most practical situations the isomers will be dissolved in at least one solvent, meaning that analysis of a ternary system is required. The concepts are similar to those discussed above for binary systems. Jacques et al. (1994) provides an excellent description of ternary cases, and review much of the published literature on chiral separations. 

Descriptions will be given below of the methods available for determining the defect structure in nonstoichiometric compositions of nuclear ceramic fuels, but the discussions on the defect structure will be limited mainly to binary system. 

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