Multicomponent system composition

When all the SE s of a solid with non-hydrostatic (deviatoric) stresses are immobile, no chemical potential of the solid exists, although transport between differently stressed surfaces takes place provided external transport paths are available. Attention should be given to crystals with immobile SE s which contain an (equilibrium) network of mobile dislocations. In these crystals, no bulk diffusion takes place although there may be gradients of the chemical free energy density and, in multicomponent systems, composition gradients (e.g., Cottrell atmospheres [A.H. Cottrell (1953)]). 

As more sophisticated metal hydrides are developed (nanocrystalline, multicomponent systems, composites and nanocomposites, graphite/metals or similar hybrid systems, clusters, etc.), it is important to be a vare that, for practical applications, a large volume of material should be processed in a fast, inexpensive and reliable vay, for example casting. Techniques such as cold vapor deposition may be impossible to scale up but this does not mean they should be discarded as a means of studying new metal hydrides. On the contrary, laboratory techniques allow much better control of the end product and permit the elaboration of new compounds. Once an attractive compound is found then another challenge w ill have to be faced scaling up the synthesis. In this respect, it is important for the community of metal hydrides researchers to also study large-scale production techniques in order to make the transition from laboratory to industrial scale easier. 

For a multicomponent system, it is possible to simulate at constant pressure rather than constant volume, as separation into phases of different compositions is still allowed. The method allows one to study straightforwardly phase equilibria in confined systems such as pores [166]. Configuration-biased MC methods can be used in combination with the Gibbs ensemble. An impressive demonstration of this has been the detennination by Siepmaim et al [167] and Smit et al [168] of liquid-vapour coexistence curves for n-alkane chain molecules as long as 48 atoms. 

Synthetic polymers have become extremely important as materials over the past 50 years and have replaced other materials because they possess high strength-to-weight ratios, easy processabiUty, and other desirable features. Used in appHcations previously dominated by metals, ceramics, and natural fibers, polymers make up much of the sales in the automotive, durables, and clothing markets. In these appHcations, polymers possess desired attributes, often at a much lower cost than the materials they replace. The emphasis in research has shifted from developing new synthetic macromolecules toward preparation of cost-effective multicomponent systems (ie, copolymers, polymer blends, and composites) rather than preparation of new and frequendy more expensive homopolymers. These multicomponent systems can be "tuned" to achieve the desired properties (within limits, of course) much easier than through the total synthesis of new macromolecules. 

Conducting Polymer Blends, Composites, and Colloids. Incorporation of conducting polymers into multicomponent systems allows the preparation of materials that are electroactive and also possess specific properties contributed by the other components. Dispersion of a conducting polymer into an insulating matrix can be accompHshed as either a miscible or phase-separated blend, a heterogeneous composite, or a coUoidaHy dispersed latex. When the conductor is present in sufftcientiy high composition, electron transport is possible. 

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. 

The local-composition models have hmited flexibility in the fitting of data, but they are adequate for most engineering purposes. Moreover, they are implicitly generalizable to multicomponent systems without the introduction of any parameters beyond those required to describe the constituent binaiy systems. For example, the Wilson equation for multicomponent systems is written ... 

It is basically a fractionation process that depends not only on molecular size, but also on chemical composition, stereo-configuration, branching, and crosslinking. For multicomponent systems, fractionation with different ion polymolecularity, chemical heterogeneity and sequence length distribution, solubility or elution fractionation is of primary importance. Therefore, gel permeation chromatography or size exclusion chromatography is used as an important tool for the characterization of PBAs. 

The material in this section is divided into three parts. The first subsection deals with the general characteristics of chemical substances. The second subsection is concerned with the chemistry of petroleum it contains a brief review of the nature, composition, and chemical constituents of crude oil and natural gases. The final subsection touches upon selected topics in physical chemistry, including ideal gas behavior, the phase rule and its applications, physical properties of pure substances, ideal solution behavior in binary and multicomponent systems, standard heats of reaction, and combustion of fuels. Examples are provided to illustrate fundamental ideas and principles. Nevertheless, the reader is urged to refer to the recommended bibliography [47-52] or other standard textbooks to obtain a clearer understanding of the subject material. Topics not covered here owing to limitations of space may be readily found in appropriate technical literature. 

The relative amounts of the individual components (or species) making up a mixture or solution can be expressed in a variety of ways, depending upon the system at hand. A volumetric, mass, or molar basis may be employed to represent the compositions of multicomponent systems. 

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

Another very important technique for fundamental consideration of multicomponent systems is low energy ion scattering (LEIS) [Taglauer and Heiland, 1980 Brongersma et al., 2007]. This is a unique tool in surface analysis, since it provides the ability to define the atomic composition of the topmost surface layer under UHV conditions. The signal does not interfere with the subsurface atomic layers, and therefore the results of LEIS analysis represent exclusively the response from the outer surface. In LEIS, a surface is used as a target that scatters a noble gas ion beam (He, Ne, ... 

Figure 8.5 shows the LEIS spectra of ZnAl204 and ZnO as a characteristic example of a multicomponent system analyzed by this technique [Brongersma and Jacobs, 1994]. Since only the surface peaks of A1 and O were detected for ZnAl204, the Zn atoms must be located in the subsurface layers. The onset of the tail agrees between the spectra, indicating that Zn is present in the second and deeper layers. This example illustrates the strength of the LEIS technique, in that characteristic peaks from different elements can be used to selectively analyze the atomic composition of the topmost surface. In addition, the shape of the tails could provide information on the in-depth distribution of the elements. 

Temperature is often used as an indication of composition. The temperature sensor should be located at the position in the column where the rate of change of temperature with change in composition of the key component is a maximum see Parkins (1959). Near the top and bottom of the column the change is usually small. With multicomponent systems, temperature is not a unique function of composition. 

A significant advantage of the Wilson equation is that it can be used to calculate the equilibrium compositions for multicomponent systems using only the Wilson coefficients obtained for the binary pairs that comprise the multicomponent mixture. The Wilson coefficients for several hundred binary systems are given in the DECHEMA vapour-liquid data collection, DECHEMA (1977), and by Hirata (1975). Hirata gives methods for calculating the Wilson coefficients from vapour liquid equilibrium experimental data. 

The distillation of binary mixtures is covered thoroughly in Volume 2, Chapter 11, and the discussion in this section is limited to a brief review of the most useful design methods. Though binary systems are usually considered separately, the design methods developed for multicomponent systems (Section 11.6) can obviously also be used for binary systems. With binary mixtures fixing the composition of one component fixes the composition of the other, and iterative procedures are not usually needed to determine the stage and reflux requirements simple graphical methods are normally used. 

Figure 9.15 Pinch location (zones of constant composition) for binary and multicomponent systems. Brackets indicate key components remaining in a product stream due to incomplete recovery.

For multicomponent systems, Equations 10.13 and 10.14 can be used to determine the number of stages for the limiting component (i.e. the component with the lowest Kj). Equation 10.15 can then be applied to determine the compositions of the other components. 

Hanak, J.J. (1970) The multiple-sample concept in materials research synthesis, compositional analysis and testing of entire multicomponent systems. J. Mater. Sci., 5, 964. 

For thermoplastic composites, results of flammability tests are generally reported on the basis of oxygen index values and/or UL-94 ratings (e.g. (11-12). The general problems associated with composites and multicomponent systems have not been addressed in depth and published data pertain primarily to specific glass-filled resins offered by manufacturers, or to composite systems designed to meet the specifications of a particular end use. 

A microemulsion droplet is a multicomponent system containing oil, surfactant, cosurfactant, and probably water therefore there may be considerable variation in size and shape depending upon the overall composition. The packing constraints which dictate size and shape of normal micelles (Section 1) should be relaxed in microemulsions because of the presence of cosurfactant and oil. However, it is possible to draw analogies between the behavior of micelles and microemulsion droplets, at least in the more aqueous media. 

The Underwood and Fenske equations may be used to find the minimum number of plates and the minimum reflux ratio for a binary system. For a multicomponent system nm may be found by using the two key components in place of the binary system and the relative volatility between those components in equation 11.56 enables the minimum reflux ratio Rm to be found. Using the feed and top compositions of component A ... 

For multicomponent systems, components A and B refer to the light and heavy keys respectively. In this problem, o-cresol is the light key and m-cresol is the heavy key. A mass balance may be carried out in order to determine the bottom composition. Taking as a basis, 100 kmol of feed, then ... 

Covalently bonded substructures having compositions distinguishable from their surroundings are formed in multicomponent systems they are called chemical clusters. The adjective chemical defines covalency of bonds between units in the cluster. To be a part of a cluster, the units must have a common property. For example, hard clusters are composed of units yielding Tg domains. Hard chemical clusters are formed in three-component polyurethane systems composed of a macromolecular diol (soft component), a low-molecular-weight triol (hard component) and diisocyanate (hard component). Hard clusters consist of two hard... 

As will be seen later (Section V.l), meaningful molecular weights in multicomponent systems can be determined, if the specific refractive index increment appertains to conditions of constant chemical potential of low molecular weight solvents (instead of at constant composition). Practically, this can be realised by dialysing the solution against the mixed solvent and then measuring the specific refractive index increment of the dialysed solution. The theory and practice have been reviewed4-14-1S> 72>. 

Most copolymers are heterogeneous in both molecular weight and composition. The latter of these arises from the mechanism of the copolymerisation (particularly at high conversion) and individual copolymer molecules differ slightly in their value of WA. Solutions of heterogeneous copolymers constitute multicomponent systems... 

It is quite evident that in a multicomponent system wherein more than one component exhibits weight variations and that too at different temperature regions, the composition of the original compound may be estimated as depicted in Figure 11.2. 

The typical system for which the equilibrium composition is desired however does not contain a single salt in solution but more usually the equivalent of several salts in solution. In addition, the activities required in equilibrium expressions arising from the law of mass action are single ion activities or in general, single ion activity coefficients. And, we are interested in the ionic activity coefficeint of each species in a multicomponent system. 

For many systems K is constant over an appreciable temperature range and Equation 11.11 may be used to determine the vapour composition at any stage. The method is particularly suited to multicomponent systems, discussed further in Section 11.7.1. 

Fi and Fi are separate feed streams to the column. Sidestreams are most often removed with multicomponent systems, although they may be used with binary mixtures. A binary system is now considered, with one sidestream, as shown in Figure 11.22. S represents the rate of removal of the sidestream and xs> its composition. 

Thus, the composition of the vapour is conveniently found from that of the liquid by use of the relative volatilities of the components. Examples 11.14-11.17 which follow illustrate typical calculations using multicomponent systems. Such solutions are now computerised, as discussed further in Volume 6. 

---