Three and More Components

So far we restricted our deliberations to 2-component systems. It is possible to increase this number to 3 and still comprehend the action in a 3-dimensional space. We can even project the 3-dimensional space onto the plane of the paper or computer screen and see what is going on. 

As usual, we demonstrate the procedures based on a chemical process. Instead of another kinetics example, we use a spectrophotometric titration. The experiment follows the deprotonation of a two-protic acid by measuring the absorption spectra of the solution as a function of pH. 

The concentrations of the differently protonated species, as a function of pH, are calculated with the explicit function we developed in Special Case Explicit Calculation for Polyprotic Acids, (p.64). A data matrix Y is constructed as before. Data eqAH2a. m generates the data, it is called by Main eqAH2a. m. 

the rank of Y is 3 - there are 3 significant eigenvectors in V and U. The row vectors ofV form a set of three basis vectors in the spectral space. The coordinates of each vector y, , in this new system of axes, are given by the i-th row of the matrix US, see equations (5.17) and (5.18) or in a different notation  

At pH 7 there is a maximum in the concentration of AH and the measured spectrum is close to that of pure AH. With further increase in pH the spectrum veers towards the spectrum of fully deprotonated A which is represented at the end of the series. 

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The principle of LC LC separation with a narrow zone of an adsorb injected before sample solution called liquid chromatography under limiting conditions of desorption (LC LCD) is evident from Figure 16.12. It is also possible to apply multiple barriers in order to separate three and more components, such as statistical copolymers of different compositions or parent homopolymers from diblock copolymers [232]. The basic features of the LC LC methods are the following ... 

Free-radical-mediated reactions have clearly been shown to be a powerful means of connecting three and more components into one molecule. The diversity of examples presented in this chapter provides ample proof for the utility of radical-... 

Alfrey. T., and G. Goldfinger Copolymerisation of systems of three and more components. J. Chem. Phys. 12, 322 (1944). 

Beminger et al. [92] discussed various strategies for splitting three-component and N-component mixtures and applied SWD to mixtures with three and more components. They tried to identify the optimal splitting sequence in a tandem SMB process for the recovery of a component or a group of components with intermediate affinities. 

The study of three and more component systems would take us... 

Therefore, extractive distillation at three and more components in the top product is feasible in principle, but requires a search for an allowed composition of the pseudoproduct. If it is necessary to design a sharp extractive distillation column at ntr = 3, then it is not allowed to set the rate of the entrainer arbitrarily, but it is necessary to determine it from the conditions of joining of trajectories of the top and intermediate sections. The parameter E/D ensures an additional degree of freedom, which allows to increase by one the number of product components in the top product ntr. 

Prediction of the type of morphology in polymer blends containing three and more components is a more difficult task than for binary blends. Generally, properties of the components, interfacial tensions between them, and mixing conditions should be considered. A quite successful predictive scheme was proposed for blends with matrix component 2 and two minor dispersed components 1 and 3. It was proposed (70,83) that component 3 encapsulates the component 1 if the spreading coefficient X31 is positive. X31 is defined as... 

In contrast to conventional reaction setups, multicomponent approaches require a significantly higher level of chemoselectivity. Therefore, applications of enantioselective non-covalent organocatalysis in reactions of three and more components still remain limited in number. The potential of catalysts with a non-covalent mode of action to overcome the inherent difficulties of multicomponent reactions to be performed stereoselectively, however, makes these transformations particularly worthy of investigation. This section focuses on recent successes in this direction. 

The grouping of three or more components of a given compound into only two categories is in itself an oversimplification, and a more natural classification operates with one class for each kind of atom that can be chemically and structurally distinguished. As a consequence, the asymmetric treatments of valence and number of valence electrons per atom disappear. Within this framework, the generalized (8-N) rule formalism gives rise to a set of equations, one for each kind of atom. 

Diffusion in a system with three or more components is called multicomponent diffusion. One example is diffusion of Ca, Fe, Mn, and Mg in a zoned garnet (Ganguly et al., 1998a). Another example is diffusion between an andesitic melt... 

A necessary preface to a description of the procedure is that the solvent and the precipitant must be purified to exhaustion by contact with successive specimens of the acid to be purified. The acid A is dissolved in the minimum amount of solvent S. The precipitant P is then added under isothermal conditions to the solution until roughly one half to three quarters of A has been precipitated. At this stage there is a three-phase system present (vapour and two liquids) with three (or more) components (A, S, and Imp where Imp denotes an impurity), and the impurities are partitioned between A and the mixture of S and P. This mixture is separated from A by decantation or syphoning, A is redissolved in S and reprecipitated by the addition of P. At all stages of this process the mixtures must be stirred efficiently but so gently that an emulsion is not formed. It happens quite often that an acid A with a melting point near or above ambient temperature will start to crystallise after the first or second extraction. 

This chapter contains a survey of free-radical-mediated multicomponent reactions (MCRs), which permit the coupling of three or more components. Even though they are not technically classified as MCRs, remarkable intramolecular radical cascade processes have been developed. Some examples, such as those shown in Scheme 6.3, use an isonitrile or acrylonitrile as the intermolecular component for each reaction [6]. These examples demonstrate the tremendous power of the combination of inter- and intramolecular radical cascade processes in organic synthesis. Readers are advised to be aware of remarkable intramolecular aspects of modem radical chemistry through excellent review articles published elsewhere [1, 7]. It should also be noted that there has also been remarkable progress in the area of living radical polymerizations, but this will not be covered here. 

In practice most composites for use in transfer applications have consisted of three or more components. The most widely-used composites usually contain PTFE as well as molybdenum disulphide, and these must also include a reinforcing material... 

CoSii, and VaSi, and some have been known for more than 100 years (59). Other more complex types containing three or more components, such as MnsSiaC, are also known. They all form three-dimensional giant lattices, often of an unusual and complicated kind, and can best be considered as intermediate in nature between alloy systems and macromolecular covalent compounds. The study of silicides has considerably intensified in the past decade, since it has been found that some show promise as electronic materials, while at the same time they are strong and highly resistant to chemical attack. A number of books and general reviews may be noted (18, 257, 318, 340, 360, 423). 

If multi-compound mixtures are present, it is necessary to introduce the bottom product into a further continuous unit. Mixtures with n components require n-1 separation columns. This technology is used for processes on a large industrial scale. In the flavour industry, mixtures with three or more components are first separated into two to three fractions and then subjected to a discontinuous separation process. The after-run may be separated from its high-boiling constituents by thin-film evaporators. 

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