Definition multicomponent

Biological systems are, by definition, multicomponent systems. One should keep in mind the difficulties of constructing molecular level pictures that satisfactorily describe systems such as a protein in a reverse micelle or a protein in a concentrated aqueous salt solution, which are certainly much simpler than anhydrobiotic organisms, for example. It is not clear to what extent the water of the hydration shell can be replaced by a third component (e.g., lipid) or what effect such replacement has on protein or enzyme properties. 

Just as it is not necessary for polymer chains to be linear, it is also not necessary for all repeat units to be the same. We have already mentioned molecules like proteins where a wide variety of different repeat units are present. Among synthetic polymers, those in which a single kind of repeat unit are involved are called homopolymers, and those containing more than one kind of repeat unit are copolymers. Note that these definitions are based on the repeat unit, not the monomer. An ordinary polyester is not a copolymer, even though two different monomers, acids and alcohols, are its monomers. By contrast, copolymers result when different monomers bond together in the same way to produce a chain in which each kind of monomer retains its respective substituents in the polymer molecule. The unmodified term copolymer is generally used to designate the case where two different repeat units are involved. Where three kinds of repeat units are present, the system is called a terpolymer where there are more than three, the system is called a multicomponent copolymer. The copolymers we discuss in this book will be primarily two-component molecules. We shall discuss copolymers in Chap. 7, so the present remarks are simply for purposes of orientation. 

Most distillation systems ia commercial columns have Murphree plate efficiencies of 70% or higher. Lower efficiencies are found under system conditions of a high slope of the equiHbrium curve (Fig. lb), of high Hquid viscosity, and of large molecules having characteristically low diffusion coefficients. FiaaHy, most experimental efficiencies have been for biaary systems where by definition the efficiency of one component is equal to that of the other component. For multicomponent systems it is possible for each component to have a different efficiency. Practice has been to use a pseudo-biaary approach involving the two key components. However, a theory for multicomponent efficiency prediction has been developed (66,67) and is amenable to computational analysis. 

From the definition of a partial molar quantity and some thermodynamic substitutions involving exact differentials, it is possible to derive the simple, yet powerful, Duhem data testing relation (2,3,18). Stated in words, the Duhem equation is a mole-fraction-weighted summation of the partial derivatives of a set of partial molar quantities, with respect to the composition of one of the components (2,3). For example, in an / -component system, there are n partial molar quantities, Af, representing any extensive molar property. At a specified temperature and pressure, only n — 1) of these properties are independent. Many experiments, however, measure quantities for every chemical in a multicomponent system. It is this redundance in reported data that makes thermodynamic consistency tests possible. 

Problem Solving Methods Most, if not aU, problems or applications that involve mass transfer can be approached by a systematic-course of action. In the simplest cases, the unknown quantities are obvious. In more complex (e.g., iTmlticomponent, multiphase, multidimensional, nonisothermal, and/or transient) systems, it is more subtle to resolve the known and unknown quantities. For example, in multicomponent systems, one must know the fluxes of the components before predicting their effective diffusivities and vice versa. More will be said about that dilemma later. Once the known and unknown quantities are resolved, however, a combination of conservation equations, definitions, empirical relations, and properties are apphed to arrive at an answer. Figure 5-24 is a flowchart that illustrates the primary types of information and their relationships, and it apphes to many mass-transfer problems. 

The following is a summary of definitions for the mass and molar compositions of a multicomponent system and the interrelationships between the various quantities. 

Unfortunately, relatively little work has been done on the solution thermodynamics of concentrated polymer solutions with "gathering". The definitive work on the subject Is the article of Yamamoto and White (17). The corresponding-states theory of Flory (11) does not account for gathering. We therefore restrict our consideration here to multicomponent solutions where the solvents and polymer are nonpolar. For such solutions, gathering Is unlikely to occur. 

In principle, any type of sample can be analysed by SEC provided that it can be solubilised and that there are no enthalpic interactions between sample and packing material. By definition then, this technique cannot be carried out on vulcanisates and even unvulcanised fully compounded rubber samples can present problems due to filler-rubber interactions. The primary use of SEC is to determine the whole MWD of polymers and the various averages (number, viscosity, weight, z-average) based on a calibration curve and to allow qualitative comparisons of different samples. Many commercial polymers have a broad MWD leading to strong peak overlap in the chromatography of complex multicomponent systems. 

In the list of contents, main terms separated by / are alternative names, and terms in parentheses give those which are defined in the context of main terms, usually as notes to the definitions of main terms, with their names printed in bold type in the main text. Multicomponent quantities (vectors, tensors, matrices) are printed in bold type. Names... 

Note 5 Although the definition holds strictly for binary mixtures, it is often erroneously applied to multicomponent mixtures. 

The above is not intended to be a definitive list but rather to indicate some of the more commonly used models at the present time. Other, more historical, models have been used extensively, for example the polymerisation models of Toop and Samis (1962) and Masson (1965), the models of Flood (1954), Richardson (1956) and Yokakawa and Niwa (1969). More recently the central atom model by Satsri and Lahiri (1985, 1986) and the complex model of Hoch and Arpshofen (1984) have been proposed. Each has been used with some success in lower-order systems, but the extension to multicomponent systems is not always straightforward. 

Table 3. Definitions of the parameters appearing in Eqs. (26)—(28) for multicomponent solutions...

Several remarks need to be made concerning the definition of the diffusion coefficients in Eqs. (32) to (36) above. The multicomponent diffusion coefficients Dij used here differ from those used in references (Hll) and (Bll). The latter must be multiplied by cRT/p to get the diffusion coefficients defined here. For perfect gases, of course, this difference in definition is unimportant since cRT/p is unity. For liquid, the definition used here is to be preferred, inasmuch as it is more in conformity with the customary definition used by experimentalists. The D ,- used here are defined in such a way that Da D, and Du = 0. 

Because of the definition of the ji, only v — 1 of these mass fluxes are independent (since 2ji = 0). It has been shown by Curtiss and Hirschfelder (C12) in their development of the kinetic theory of multicomponent gas mixtures that the foregoing relations may be put into an alternate form 12... 

Working with multicomponent mixtures requires quantifying the amounts of various chemical constituents that comprise the mixture. In the conservation equations a mass fraction will be the most appropriate measure, since mass is a conserved quantity. By definition, the mass fraction is... 

With these definitions the diffusive flux in the multicomponent form is exactly as before (Eqs. 12.165 and 12.166)... 

We will first consider phase diagrams. Then we will define the critical point for a two-component mixture. This will be the correct definition for multicomponent mixtures. Also, we will look at an important concept called retrograde condensation. Then the pressure-volume diagram will be discussed, and differences between pure substances and two-component mixtures in the two-phase region will be illustrated. Finally, the effects of temperature and pressure on the compositions of the coexisting liquid and gas will be illustrated. 

The maximum boiling point is that temperature corresponding to a definite composition of a Iwo-coinponenl or multicomponent system al which the boiling point of the system is a maximum. At this temperature the liquid and vapor have the same composition and the solution distills completely without change in temperature. Binary liquid systems that show negative deviations from Raoult s law have maximum boiling points. See Raoult s I xiw and Van t Hoff I,aw. 

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