Multi-component systems

The calculation of vapor and liquid fugacities in multi-component systems has been implemented by a set of computer programs in the form of FORTRAN IV subroutines. These are applicable to systems of up to twenty components, and operate on a thermodynamic data base including parameters for 92 compounds. The set includes subroutines for evaluation of vapor-phase fugacity... 

Crystallization-based separation of multi-component mixtures has widespread application. The technique consists of sequences of heating, cooling, evaporation, dilution, diluent addition and solid-liquid separation. Berry and Ng (1996, 1997), Cisternas and Rudd (1993), Dye and Ng (1995), Ng (1991) and Oyander etal. (1997) proposed various schemes based on the phase diagram. Cisternas (1999) presented an alternate network flow model for synthesizing crystallization-based separations for multi-component systems. The construction... 

In this review article we have tried to show that an analytical approach to the thermodynamics and the kinetics of adsorbates is not restricted to simple systems but can deal with rather complicated situations in a systematic approach, such as multi-site and multi-component systems with or without precursor-mediated adsorption and surface reconstruction, including multi-layers/subsurface species. This approach automatically ensures that such fundamental principles as detailed balance are implemented properly. 

B.H. Sage, Phase Behavior in Binary and Multi-component Systems at Elevated Pressures n-Pentane and Methane-m-Pentane , NSRDS-NBS 32 (1970) 20)A.S. Mal tseva et al,... 

A serious limitation of the STM technique so far is its lack of chemical sensitivity. Generally, STM is not specific for the elemental species in multi-component systems, though there are special cases where the direction of charge flow is well known as shown for the GaAs(llO) surface. The surface area which one is looking at by STM is typically quite small. The problem of how representative the obtained tunnel vision is, is at least partly solved by considerably increasing the total scan range of STM/SPM instruments. 

For the distillation of a multi-component system in a batch column, the established practice leads to sequential removal of products from lower to higher boiling points. A strategy has been suggested, with a proper analysis, which involves the removal of all the products except the heavies, with subsequent fractionation of the mixture. 

For multi-component systems, it is necessary to write the dynamic equation for each phase and for each solute, in turn. Thus for phase volume Vl, the balances for solute A and for solute B are... 

Here va and va are the stoichiometric coefficients for the reaction. The formulation is easily extended to treat a set of coupled chemical reactions. Reactive MPC dynamics again consists of free streaming and collisions, which take place at discrete times x. We partition the system into cells in order to carry out the reactive multiparticle collisions. The partition of the multicomponent system into collision cells is shown schematically in Fig. 7. In each cell, independently of the other cells, reactive and nonreactive collisions occur at times x. The nonreactive collisions can be carried out as described earlier for multi-component systems. The reactive collisions occur by birth-death stochastic rules. Such rules can be constructed to conserve mass, momentum, and energy. This is especially useful for coupling reactions to fluid flow. The reactive collision model can also be applied to far-from-equilibrium situations, where certain species are held fixed by constraints. In this case conservation laws... 

Not all samples consist of binary mixtures, and difficulties exist with the extension of the matrix factor approach to multi-component systems. 

Standard thin films of known composition may not always be available, and in multi-component systems many k factors should be determined, which is a time-consuming process. A new quantitative procedure for thin specimens has been developed to overcome these limitations ... 

Therefore, Ca, Cb and pt can be determined simultaneously by measuring X-ray intensities (if the specimen density and thickness are known). Only f factors are required and k factors are not used. This approach can be extended to any multi-component system if one assumes J]Ci=l. The factors are measured from standard thin films with known composition and thickness, the advantage being that pure element thin films can be applied as standards. 

The multi-component systems developed quite recently have allowed the efficient metal-catalyzed stereoselective reactions with synthetic potential [75-77]. Multi-components including a catalyst, a co-reductant, and additives cooperate with each other to construct the catalytic systems for efficient reduction. It is essential that the active catalyst is effectively regenerated by redox interaction with the co-reductant. The selection of the co-reductant is important. The oxidized form of the co-reductant should not interfere with, but assist the reduction reaction or at least, be tolerant under the conditions. Additives, which are considered to contribute to the redox cycle directly, possibly facilitate the electron transfer and liberate the catalyst from the reaction adduct. Co-reductants like Al, Zn, and Mg are used in the catalytic reactions, but from the viewpoint of green chemistry, an electron source should be environmentally harmonious, such as H2. 

The past two decades have produced a revival of interest in the synthesis of polyanhydrides for biomedical applications. These materials offer a unique combination of properties that includes hydrolytically labile backbone, hydrophobic bulk, and very flexible chemistry that can be combined with other functional groups to develop polymers with novel physical and chemical properties. This combination of properties leads to erosion kinetics that is primarily surface eroding and offers the potential to stabilize macromolecular drugs and extend release profiles from days to years. The microstructural characteristics and inhomogeneities of multi-component systems offer an additional dimension of drug release kinetics that can be exploited to tailor drug release profiles. 

In a binary solution AB-AC, the ionic fractions of B and C are identical to the mole fractions of AB and AC. It may therefore seem unnecessary to use the ionic fractions. However, in the case of multi-component systems the advantage of ionic fractions is evident, as will be shown in Chapter 9. 

The formalism shown above is in general easily extended to multi-component systems. All thermodynamic mixing properties may be derived from the integral Gibbs energy of mixing, which in general is expressed as... 

In general, the chemical potential of species i for a multi-component system is given as... 

Multi-component systems Ternary phase diagrams... 

Finally, it should be noted that the model can be extended to multi-component systems [6], Furthermore, the Gibbs energy of the pair exchange reaction may depend on the relative proportions of the different pairs. In this case tab is a polynomial function of the pair fractions XAA and XBB [4],... 

Although valence band spectra probe those electrons that are involved in chemical bond formation, they are rarely used in studying catalysts. One reason is that all elements have valence electrons, which makes valence band spectra of multi-component systems difficult to sort out. A second reason is that the mean free path of photoelectrons from the valence band is at its maximum, implying that the chemical effects of for example chemisorption, which are limited to the outer surface layer, can hardly be distinguished from the dominating substrate signal. In this respect UPS, discussed later in this chapter, is much more surface sensitive and therefore better suited for adsorption studies. 

First, the criteria for phase equilibria are discussed in terms of single-component systems. Then, when the ground rules are in place, multi-component systems are discussed in terms of partition, distillation and mixing. 

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